diff --git "a/data/connectivity/QA/Vision_Text_test.json" "b/data/connectivity/QA/Vision_Text_test.json" new file mode 100644--- /dev/null +++ "b/data/connectivity/QA/Vision_Text_test.json" @@ -0,0 +1,68938 @@ +[ + { + "id": "connectivity-easy-graph53-8_1", + "image": "data/connectivity/graph_visual/easy/graph53.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,4) (1,2) (1,8) (1,4) (1,3) (3,8) (3,4) (4,8) (5,7) (5,6) (6,7)\nIs there a path between node 8 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph28-3_5", + "image": "data/connectivity/graph_visual/easy/graph28.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,4) (0,2) (0,5) (1,6) (2,4) (2,5) (3,6)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph35-5_4", + "image": "data/connectivity/graph_visual/easy/graph35.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,2) (0,5) (0,6) (0,3) (0,4) (0,1) (1,2) (1,5) (1,6) (1,3) (1,4) (2,5) (2,6) (2,3) (2,4) (3,5) (3,6) (3,4) (4,5) (4,6) (5,6)\nIs there a path between node 5 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph5-1_0", + "image": "data/connectivity/graph_visual/easy/graph5.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,2) (1,2) (2,3)\nIs there a path between node 1 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph57-8_7", + "image": "data/connectivity/graph_visual/easy/graph57.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,7) (0,3) (1,6) (1,5) (1,4) (1,8) (2,7) (2,3) (3,7) (4,6) (4,5) (4,8) (5,6) (5,8) (6,8)\nIs there a path between node 8 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph31-0_1", + "image": "data/connectivity/graph_visual/easy/graph31.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,2) (0,5) (1,3) (1,6) (1,4) (2,5) (3,6) (3,4) (4,6)\nIs there a path between node 0 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph34-7_6", + "image": "data/connectivity/graph_visual/easy/graph34.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,3) (0,2) (0,1) (0,4) (1,3) (1,2) (1,4) (1,6) (2,3) (2,4) (2,5) (3,4) (3,6) (4,6) (5,6)\nIs there a path between node 7 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph14-1_4", + "image": "data/connectivity/graph_visual/easy/graph14.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,3) (1,3) (2,5)\nIs there a path between node 1 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph28-6_1", + "image": "data/connectivity/graph_visual/easy/graph28.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,4) (0,2) (0,5) (1,6) (2,4) (2,5) (3,6)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph69-6_1", + "image": "data/connectivity/graph_visual/easy/graph69.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (0,1) (0,9) (1,8) (1,4) (3,8) (3,5) (3,4) (3,9) (4,9) (5,8) (5,6) (6,9) (8,9)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph36-4_6", + "image": "data/connectivity/graph_visual/easy/graph36.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,1) (3,7) (4,6) (5,6)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph40-3_6", + "image": "data/connectivity/graph_visual/easy/graph40.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,5) (2,3) (3,5) (3,4) (3,6) (4,7) (4,5) (4,6) (5,7) (5,6)\nIs there a path between node 3 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph66-3_8", + "image": "data/connectivity/graph_visual/easy/graph66.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,4) (1,9) (1,3) (2,4) (2,5) (4,9)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph18-5_1", + "image": "data/connectivity/graph_visual/easy/graph18.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,4) (0,2) (0,3) (1,5) (2,4) (2,3) (3,4)\nIs there a path between node 5 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph8-0_4", + "image": "data/connectivity/graph_visual/easy/graph8.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,3) (0,2) (0,1) (1,3) (1,2) (2,3)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph37-4_0", + "image": "data/connectivity/graph_visual/easy/graph37.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,3) (1,3) (1,7) (2,6) (2,5) (2,4) (4,5)\nIs there a path between node 4 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph53-2_5", + "image": "data/connectivity/graph_visual/easy/graph53.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,4) (1,2) (1,8) (1,4) (1,3) (3,8) (3,4) (4,8) (5,7) (5,6) (6,7)\nIs there a path between node 2 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph27-6_3", + "image": "data/connectivity/graph_visual/easy/graph27.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,4) (1,3) (1,2) (1,6) (2,5) (2,6) (3,5) (5,6)\nIs there a path between node 6 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph13-2_4", + "image": "data/connectivity/graph_visual/easy/graph13.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,2) (0,4)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph19-0_1", + "image": "data/connectivity/graph_visual/easy/graph19.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,4) (0,2) (0,1) (0,3) (1,4) (1,2) (1,3) (2,4) (2,3) (3,4)\nIs there a path between node 0 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph30-0_5", + "image": "data/connectivity/graph_visual/easy/graph30.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,6) (0,3) (0,2) (0,1) (1,6) (1,3) (1,2) (2,6) (2,3) (3,6) (4,5)\nIs there a path between node 0 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph0-0_4", + "image": "data/connectivity/graph_visual/easy/graph0.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,4) (1,4) (2,4)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph30-2_4", + "image": "data/connectivity/graph_visual/easy/graph30.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,6) (0,3) (0,2) (0,1) (1,6) (1,3) (1,2) (2,6) (2,3) (3,6) (4,5)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph24-2_1", + "image": "data/connectivity/graph_visual/easy/graph24.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (1,2)\nIs there a path between node 2 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph0-4_2", + "image": "data/connectivity/graph_visual/easy/graph0.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,4) (1,4) (2,4)\nIs there a path between node 4 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph60-9_2", + "image": "data/connectivity/graph_visual/easy/graph60.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (0,1) (2,3) (4,6) (5,6) (5,7)\nIs there a path between node 9 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph67-5_3", + "image": "data/connectivity/graph_visual/easy/graph67.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,9) (0,1) (0,2) (0,7) (0,6) (1,2) (1,8) (1,7) (1,4) (1,6) (2,7) (2,4) (2,6) (3,5) (4,9) (4,8) (4,7) (6,9) (6,7) (7,8)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph2-1_2", + "image": "data/connectivity/graph_visual/easy/graph2.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,1) (0,3) (0,4) (1,3) (1,4) (3,4)\nIs there a path between node 1 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph52-1_7", + "image": "data/connectivity/graph_visual/easy/graph52.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (2,8) (2,4) (2,3) (3,8) (5,7) (6,7)\nIs there a path between node 1 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph19-5_2", + "image": "data/connectivity/graph_visual/easy/graph19.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,4) (0,2) (0,1) (0,3) (1,4) (1,2) (1,3) (2,4) (2,3) (3,4)\nIs there a path between node 5 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph59-3_0", + "image": "data/connectivity/graph_visual/easy/graph59.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,5) (0,4) (0,1) (0,7) (0,6) (1,2) (1,5) (1,4) (1,7) (1,6) (2,5) (2,4) (2,7) (2,6) (3,8) (4,5) (4,7) (4,6) (5,7) (5,6) (6,7)\nIs there a path between node 3 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph2-3_1", + "image": "data/connectivity/graph_visual/easy/graph2.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,1) (0,3) (0,4) (1,3) (1,4) (3,4)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph36-5_7", + "image": "data/connectivity/graph_visual/easy/graph36.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,1) (3,7) (4,6) (5,6)\nIs there a path between node 5 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph51-8_5", + "image": "data/connectivity/graph_visual/easy/graph51.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (1,5) (2,4) (3,5) (5,6)\nIs there a path between node 8 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph45-7_4", + "image": "data/connectivity/graph_visual/easy/graph45.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,8) (0,6) (2,7) (2,6) (2,4) (5,7) (6,8)\nIs there a path between node 7 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph27-3_4", + "image": "data/connectivity/graph_visual/easy/graph27.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,4) (1,3) (1,2) (1,6) (2,5) (2,6) (3,5) (5,6)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph54-8_1", + "image": "data/connectivity/graph_visual/easy/graph54.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,6) (0,5) (0,7) (0,3) (2,6) (2,5) (2,7) (2,3) (3,6) (3,5) (3,4) (3,8) (4,5) (4,7) (4,8) (5,6) (5,7) (5,8) (6,7) (6,8) (7,8)\nIs there a path between node 8 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph35-6_7", + "image": "data/connectivity/graph_visual/easy/graph35.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,2) (0,5) (0,6) (0,3) (0,4) (0,1) (1,2) (1,5) (1,6) (1,3) (1,4) (2,5) (2,6) (2,3) (2,4) (3,5) (3,6) (3,4) (4,5) (4,6) (5,6)\nIs there a path between node 6 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph59-0_1", + "image": "data/connectivity/graph_visual/easy/graph59.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,5) (0,4) (0,1) (0,7) (0,6) (1,2) (1,5) (1,4) (1,7) (1,6) (2,5) (2,4) (2,7) (2,6) (3,8) (4,5) (4,7) (4,6) (5,7) (5,6) (6,7)\nIs there a path between node 0 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph41-0_7", + "image": "data/connectivity/graph_visual/easy/graph41.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,5) (0,7) (0,2) (0,6) (1,3) (2,5) (2,7) (5,7) (5,6)\nIs there a path between node 0 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph7-2_0", + "image": "data/connectivity/graph_visual/easy/graph7.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,3) (0,4) (1,2) (3,4)\nIs there a path between node 2 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph68-7_1", + "image": "data/connectivity/graph_visual/easy/graph68.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (0,2) (0,1) (0,9) (0,3) (1,5) (1,2) (1,7) (1,9) (1,8) (2,5) (2,3) (2,8) (3,5) (3,7) (3,9) (3,8) (5,9) (5,8) (7,9) (7,8) (8,9)\nIs there a path between node 7 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph57-0_3", + "image": "data/connectivity/graph_visual/easy/graph57.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,7) (0,3) (1,6) (1,5) (1,4) (1,8) (2,7) (2,3) (3,7) (4,6) (4,5) (4,8) (5,6) (5,8) (6,8)\nIs there a path between node 0 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph13-1_2", + "image": "data/connectivity/graph_visual/easy/graph13.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,2) (0,4)\nIs there a path between node 1 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph71-9_2", + "image": "data/connectivity/graph_visual/easy/graph71.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (0,2) (0,8) (0,4) (0,7) (0,3) (0,1) (1,5) (1,2) (1,8) (1,4) (1,7) (1,3) (2,5) (2,8) (2,4) (2,7) (2,3) (3,5) (3,8) (3,4) (3,7) (4,5) (4,8) (4,7) (5,8) (5,7) (6,9) (7,8)\nIs there a path between node 9 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph26-4_1", + "image": "data/connectivity/graph_visual/easy/graph26.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (4,5)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph40-6_4", + "image": "data/connectivity/graph_visual/easy/graph40.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,5) (2,3) (3,5) (3,4) (3,6) (4,7) (4,5) (4,6) (5,7) (5,6)\nIs there a path between node 6 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph66-5_3", + "image": "data/connectivity/graph_visual/easy/graph66.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,4) (1,9) (1,3) (2,4) (2,5) (4,9)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph66-9_1", + "image": "data/connectivity/graph_visual/easy/graph66.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,4) (1,9) (1,3) (2,4) (2,5) (4,9)\nIs there a path between node 9 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph22-3_2", + "image": "data/connectivity/graph_visual/easy/graph22.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,5) (2,3) (2,5) (3,5) (4,6)\nIs there a path between node 3 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph0-1_0", + "image": "data/connectivity/graph_visual/easy/graph0.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,4) (1,4) (2,4)\nIs there a path between node 1 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph61-8_2", + "image": "data/connectivity/graph_visual/easy/graph61.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,8) (0,6) (0,4) (1,3) (1,7) (1,2) (2,3) (3,9) (4,6) (5,9) (6,8) (7,9)\nIs there a path between node 8 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph65-2_4", + "image": "data/connectivity/graph_visual/easy/graph65.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,2) (1,5) (2,8) (2,5) (3,5) (3,7) (4,9) (5,6) (5,8) (5,7) (6,7)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph68-4_9", + "image": "data/connectivity/graph_visual/easy/graph68.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (0,2) (0,1) (0,9) (0,3) (1,5) (1,2) (1,7) (1,9) (1,8) (2,5) (2,3) (2,8) (3,5) (3,7) (3,9) (3,8) (5,9) (5,8) (7,9) (7,8) (8,9)\nIs there a path between node 4 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph53-6_3", + "image": "data/connectivity/graph_visual/easy/graph53.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,4) (1,2) (1,8) (1,4) (1,3) (3,8) (3,4) (4,8) (5,7) (5,6) (6,7)\nIs there a path between node 6 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph15-3_4", + "image": "data/connectivity/graph_visual/easy/graph15.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,5) (0,4) (0,1) (1,2) (1,5) (1,4) (2,5) (2,4) (4,5)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph53-4_6", + "image": "data/connectivity/graph_visual/easy/graph53.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,4) (1,2) (1,8) (1,4) (1,3) (3,8) (3,4) (4,8) (5,7) (5,6) (6,7)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph72-3_7", + "image": "data/connectivity/graph_visual/easy/graph72.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,8) (0,1) (0,4) (0,5) (0,9) (0,6) (0,7) (0,2) (1,8) (1,4) (1,5) (1,9) (1,6) (1,7) (1,2) (2,8) (2,4) (2,5) (2,9) (2,6) (2,7) (4,8) (4,5) (4,9) (4,6) (4,7) (5,8) (5,9) (5,6) (5,7) (6,8) (6,9) (6,7) (7,8) (7,9) (8,9)\nIs there a path between node 3 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph12-2_1", + "image": "data/connectivity/graph_visual/easy/graph12.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,2) (1,2) (3,5)\nIs there a path between node 2 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph4-2_4", + "image": "data/connectivity/graph_visual/easy/graph4.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (2,4)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph62-0_6", + "image": "data/connectivity/graph_visual/easy/graph62.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,3) (1,8) (1,4) (1,5) (1,7) (1,2) (1,9) (1,6) (2,8) (2,4) (2,5) (2,7) (2,9) (2,6) (4,8) (4,5) (4,7) (4,9) (4,6) (5,8) (5,7) (5,9) (5,6) (6,8) (6,7) (6,9) (7,8) (7,9) (8,9)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph61-3_4", + "image": "data/connectivity/graph_visual/easy/graph61.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,8) (0,6) (0,4) (1,3) (1,7) (1,2) (2,3) (3,9) (4,6) (5,9) (6,8) (7,9)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph9-3_1", + "image": "data/connectivity/graph_visual/easy/graph9.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (1,5) (3,5)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph60-2_3", + "image": "data/connectivity/graph_visual/easy/graph60.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (0,1) (2,3) (4,6) (5,6) (5,7)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph22-2_0", + "image": "data/connectivity/graph_visual/easy/graph22.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,5) (2,3) (2,5) (3,5) (4,6)\nIs there a path between node 2 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph8-2_1", + "image": "data/connectivity/graph_visual/easy/graph8.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,3) (0,2) (0,1) (1,3) (1,2) (2,3)\nIs there a path between node 2 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph58-3_2", + "image": "data/connectivity/graph_visual/easy/graph58.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (0,2) (0,8) (0,4) (0,7) (0,6) (1,2) (1,8) (1,4) (1,7) (1,6) (2,8) (2,4) (2,7) (2,6) (3,5) (4,8) (4,7) (4,6) (6,8) (6,7) (7,8)\nIs there a path between node 3 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph44-6_1", + "image": "data/connectivity/graph_visual/easy/graph44.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,3) (1,7) (1,4) (1,6) (1,2) (1,5) (2,3) (2,7) (2,4) (2,6) (2,5) (3,7) (3,4) (3,6) (3,5) (4,7) (4,6) (4,5) (5,7) (5,6) (6,7)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph50-0_4", + "image": "data/connectivity/graph_visual/easy/graph50.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,3) (2,6) (2,7) (3,8) (3,7) (6,7)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph67-6_5", + "image": "data/connectivity/graph_visual/easy/graph67.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,9) (0,1) (0,2) (0,7) (0,6) (1,2) (1,8) (1,7) (1,4) (1,6) (2,7) (2,4) (2,6) (3,5) (4,9) (4,8) (4,7) (6,9) (6,7) (7,8)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph73-3_2", + "image": "data/connectivity/graph_visual/easy/graph73.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (0,9) (0,2) (0,8) (0,3) (0,1) (1,5) (1,9) (1,2) (1,8) (1,3) (2,5) (2,9) (2,8) (2,3) (3,5) (3,9) (3,8) (4,6) (4,7) (5,9) (5,8) (6,7) (8,9)\nIs there a path between node 3 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph16-3_1", + "image": "data/connectivity/graph_visual/easy/graph16.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,5) (0,2) (0,1) (1,5) (1,2) (2,5)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph47-0_8", + "image": "data/connectivity/graph_visual/easy/graph47.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,7) (0,6) (0,8) (0,4) (0,1) (1,2) (1,7) (1,6) (1,8) (1,4) (2,7) (2,6) (2,8) (2,4) (3,5) (4,7) (4,6) (4,8) (6,7) (6,8) (7,8)\nIs there a path between node 0 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph33-6_5", + "image": "data/connectivity/graph_visual/easy/graph33.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,1) (0,6) (1,2) (3,7) (3,5)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph6-4_1", + "image": "data/connectivity/graph_visual/easy/graph6.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (1,3) (1,4) (1,2) (2,3) (2,4) (3,4)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph33-6_0", + "image": "data/connectivity/graph_visual/easy/graph33.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,1) (0,6) (1,2) (3,7) (3,5)\nIs there a path between node 6 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph71-5_8", + "image": "data/connectivity/graph_visual/easy/graph71.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (0,2) (0,8) (0,4) (0,7) (0,3) (0,1) (1,5) (1,2) (1,8) (1,4) (1,7) (1,3) (2,5) (2,8) (2,4) (2,7) (2,3) (3,5) (3,8) (3,4) (3,7) (4,5) (4,8) (4,7) (5,8) (5,7) (6,9) (7,8)\nIs there a path between node 5 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph60-5_4", + "image": "data/connectivity/graph_visual/easy/graph60.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (0,1) (2,3) (4,6) (5,6) (5,7)\nIs there a path between node 5 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph23-0_6", + "image": "data/connectivity/graph_visual/easy/graph23.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph58-7_8", + "image": "data/connectivity/graph_visual/easy/graph58.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (0,2) (0,8) (0,4) (0,7) (0,6) (1,2) (1,8) (1,4) (1,7) (1,6) (2,8) (2,4) (2,7) (2,6) (3,5) (4,8) (4,7) (4,6) (6,8) (6,7) (7,8)\nIs there a path between node 7 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph54-7_8", + "image": "data/connectivity/graph_visual/easy/graph54.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,6) (0,5) (0,7) (0,3) (2,6) (2,5) (2,7) (2,3) (3,6) (3,5) (3,4) (3,8) (4,5) (4,7) (4,8) (5,6) (5,7) (5,8) (6,7) (6,8) (7,8)\nIs there a path between node 7 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph68-9_6", + "image": "data/connectivity/graph_visual/easy/graph68.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (0,2) (0,1) (0,9) (0,3) (1,5) (1,2) (1,7) (1,9) (1,8) (2,5) (2,3) (2,8) (3,5) (3,7) (3,9) (3,8) (5,9) (5,8) (7,9) (7,8) (8,9)\nIs there a path between node 9 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph21-6_5", + "image": "data/connectivity/graph_visual/easy/graph21.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (0,4) (1,5)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph46-0_3", + "image": "data/connectivity/graph_visual/easy/graph46.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nIs there a path between node 0 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph21-6_1", + "image": "data/connectivity/graph_visual/easy/graph21.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (0,4) (1,5)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph31-3_1", + "image": "data/connectivity/graph_visual/easy/graph31.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,2) (0,5) (1,3) (1,6) (1,4) (2,5) (3,6) (3,4) (4,6)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph47-1_5", + "image": "data/connectivity/graph_visual/easy/graph47.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,7) (0,6) (0,8) (0,4) (0,1) (1,2) (1,7) (1,6) (1,8) (1,4) (2,7) (2,6) (2,8) (2,4) (3,5) (4,7) (4,6) (4,8) (6,7) (6,8) (7,8)\nIs there a path between node 1 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph62-1_8", + "image": "data/connectivity/graph_visual/easy/graph62.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,3) (1,8) (1,4) (1,5) (1,7) (1,2) (1,9) (1,6) (2,8) (2,4) (2,5) (2,7) (2,9) (2,6) (4,8) (4,5) (4,7) (4,9) (4,6) (5,8) (5,7) (5,9) (5,6) (6,8) (6,7) (6,9) (7,8) (7,9) (8,9)\nIs there a path between node 1 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph32-2_1", + "image": "data/connectivity/graph_visual/easy/graph32.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (0,5) (0,2) (0,6) (0,1) (1,3) (1,5) (1,2) (1,6) (2,3) (2,5) (2,6) (3,5) (3,6) (5,6)\nIs there a path between node 2 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph36-2_6", + "image": "data/connectivity/graph_visual/easy/graph36.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,1) (3,7) (4,6) (5,6)\nIs there a path between node 2 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph13-1_0", + "image": "data/connectivity/graph_visual/easy/graph13.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,2) (0,4)\nIs there a path between node 1 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph49-0_4", + "image": "data/connectivity/graph_visual/easy/graph49.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,2) (3,8) (3,4) (4,8) (5,6)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph29-0_5", + "image": "data/connectivity/graph_visual/easy/graph29.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,5) (0,4) (0,2) (1,6) (2,5) (2,3) (3,5) (3,4) (4,5)\nIs there a path between node 0 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph29-4_1", + "image": "data/connectivity/graph_visual/easy/graph29.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,5) (0,4) (0,2) (1,6) (2,5) (2,3) (3,5) (3,4) (4,5)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph24-3_2", + "image": "data/connectivity/graph_visual/easy/graph24.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (1,2)\nIs there a path between node 3 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph46-4_0", + "image": "data/connectivity/graph_visual/easy/graph46.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nIs there a path between node 4 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph46-4_5", + "image": "data/connectivity/graph_visual/easy/graph46.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nIs there a path between node 4 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph55-0_5", + "image": "data/connectivity/graph_visual/easy/graph55.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,8) (0,1) (2,5) (2,6) (2,4) (2,7) (3,6) (3,4) (4,6) (4,7) (5,6) (6,7)\nIs there a path between node 0 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph47-2_8", + "image": "data/connectivity/graph_visual/easy/graph47.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,7) (0,6) (0,8) (0,4) (0,1) (1,2) (1,7) (1,6) (1,8) (1,4) (2,7) (2,6) (2,8) (2,4) (3,5) (4,7) (4,6) (4,8) (6,7) (6,8) (7,8)\nIs there a path between node 2 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph48-3_4", + "image": "data/connectivity/graph_visual/easy/graph48.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,8) (1,2) (1,5) (5,6)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph34-7_5", + "image": "data/connectivity/graph_visual/easy/graph34.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,3) (0,2) (0,1) (0,4) (1,3) (1,2) (1,4) (1,6) (2,3) (2,4) (2,5) (3,4) (3,6) (4,6) (5,6)\nIs there a path between node 7 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph70-1_6", + "image": "data/connectivity/graph_visual/easy/graph70.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,8) (0,2) (0,4) (0,7) (0,9) (1,6) (1,5) (2,8) (2,4) (2,7) (4,8) (4,9) (7,8) (7,9)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph33-3_0", + "image": "data/connectivity/graph_visual/easy/graph33.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,1) (0,6) (1,2) (3,7) (3,5)\nIs there a path between node 3 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph63-0_6", + "image": "data/connectivity/graph_visual/easy/graph63.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,3) (0,7) (0,2) (0,8) (1,6) (2,3) (3,6) (3,7) (4,6) (4,5) (5,8) (7,8)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph20-5_0", + "image": "data/connectivity/graph_visual/easy/graph20.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,2) (0,3) (0,5) (0,1) (1,2) (1,3) (1,5) (2,3) (2,5) (3,5)\nIs there a path between node 5 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph68-0_3", + "image": "data/connectivity/graph_visual/easy/graph68.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (0,2) (0,1) (0,9) (0,3) (1,5) (1,2) (1,7) (1,9) (1,8) (2,5) (2,3) (2,8) (3,5) (3,7) (3,9) (3,8) (5,9) (5,8) (7,9) (7,8) (8,9)\nIs there a path between node 0 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph25-1_4", + "image": "data/connectivity/graph_visual/easy/graph25.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (1,4)\nIs there a path between node 1 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph3-3_2", + "image": "data/connectivity/graph_visual/easy/graph3.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (2,3)\nIs there a path between node 3 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph57-3_8", + "image": "data/connectivity/graph_visual/easy/graph57.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,7) (0,3) (1,6) (1,5) (1,4) (1,8) (2,7) (2,3) (3,7) (4,6) (4,5) (4,8) (5,6) (5,8) (6,8)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph3-4_3", + "image": "data/connectivity/graph_visual/easy/graph3.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (2,3)\nIs there a path between node 4 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph38-1_6", + "image": "data/connectivity/graph_visual/easy/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,7) (1,6) (3,6)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph22-1_6", + "image": "data/connectivity/graph_visual/easy/graph22.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,5) (2,3) (2,5) (3,5) (4,6)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph67-3_9", + "image": "data/connectivity/graph_visual/easy/graph67.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,9) (0,1) (0,2) (0,7) (0,6) (1,2) (1,8) (1,7) (1,4) (1,6) (2,7) (2,4) (2,6) (3,5) (4,9) (4,8) (4,7) (6,9) (6,7) (7,8)\nIs there a path between node 3 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph36-3_7", + "image": "data/connectivity/graph_visual/easy/graph36.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,1) (3,7) (4,6) (5,6)\nIs there a path between node 3 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph21-0_3", + "image": "data/connectivity/graph_visual/easy/graph21.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (0,4) (1,5)\nIs there a path between node 0 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph38-6_1", + "image": "data/connectivity/graph_visual/easy/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,7) (1,6) (3,6)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph63-9_1", + "image": "data/connectivity/graph_visual/easy/graph63.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,3) (0,7) (0,2) (0,8) (1,6) (2,3) (3,6) (3,7) (4,6) (4,5) (5,8) (7,8)\nIs there a path between node 9 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph45-3_2", + "image": "data/connectivity/graph_visual/easy/graph45.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,8) (0,6) (2,7) (2,6) (2,4) (5,7) (6,8)\nIs there a path between node 3 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph64-2_4", + "image": "data/connectivity/graph_visual/easy/graph64.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (0,3) (0,1) (1,6) (1,9) (1,7) (1,3) (2,8) (3,9) (3,5) (3,7) (6,9) (7,9)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph70-1_7", + "image": "data/connectivity/graph_visual/easy/graph70.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,8) (0,2) (0,4) (0,7) (0,9) (1,6) (1,5) (2,8) (2,4) (2,7) (4,8) (4,9) (7,8) (7,9)\nIs there a path between node 1 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph74-6_4", + "image": "data/connectivity/graph_visual/easy/graph74.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,9) (0,5) (0,8) (0,2) (0,7) (0,3) (0,4) (1,6) (2,9) (2,5) (2,8) (2,7) (2,3) (2,4) (3,9) (3,5) (3,8) (3,7) (3,4) (4,9) (4,5) (4,8) (4,7) (5,9) (5,8) (5,7) (7,9) (7,8) (8,9)\nIs there a path between node 6 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph41-0_6", + "image": "data/connectivity/graph_visual/easy/graph41.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,5) (0,7) (0,2) (0,6) (1,3) (2,5) (2,7) (5,7) (5,6)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph35-7_4", + "image": "data/connectivity/graph_visual/easy/graph35.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,2) (0,5) (0,6) (0,3) (0,4) (0,1) (1,2) (1,5) (1,6) (1,3) (1,4) (2,5) (2,6) (2,3) (2,4) (3,5) (3,6) (3,4) (4,5) (4,6) (5,6)\nIs there a path between node 7 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph74-6_5", + "image": "data/connectivity/graph_visual/easy/graph74.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,9) (0,5) (0,8) (0,2) (0,7) (0,3) (0,4) (1,6) (2,9) (2,5) (2,8) (2,7) (2,3) (2,4) (3,9) (3,5) (3,8) (3,7) (3,4) (4,9) (4,5) (4,8) (4,7) (5,9) (5,8) (5,7) (7,9) (7,8) (8,9)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph24-3_5", + "image": "data/connectivity/graph_visual/easy/graph24.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (1,2)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph38-0_6", + "image": "data/connectivity/graph_visual/easy/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,7) (1,6) (3,6)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph25-1_3", + "image": "data/connectivity/graph_visual/easy/graph25.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (1,4)\nIs there a path between node 1 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph41-0_1", + "image": "data/connectivity/graph_visual/easy/graph41.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,5) (0,7) (0,2) (0,6) (1,3) (2,5) (2,7) (5,7) (5,6)\nIs there a path between node 0 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph59-4_8", + "image": "data/connectivity/graph_visual/easy/graph59.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,5) (0,4) (0,1) (0,7) (0,6) (1,2) (1,5) (1,4) (1,7) (1,6) (2,5) (2,4) (2,7) (2,6) (3,8) (4,5) (4,7) (4,6) (5,7) (5,6) (6,7)\nIs there a path between node 4 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph2-2_4", + "image": "data/connectivity/graph_visual/easy/graph2.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,1) (0,3) (0,4) (1,3) (1,4) (3,4)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph15-3_5", + "image": "data/connectivity/graph_visual/easy/graph15.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,5) (0,4) (0,1) (1,2) (1,5) (1,4) (2,5) (2,4) (4,5)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph9-3_5", + "image": "data/connectivity/graph_visual/easy/graph9.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (1,5) (3,5)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph18-5_2", + "image": "data/connectivity/graph_visual/easy/graph18.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,4) (0,2) (0,3) (1,5) (2,4) (2,3) (3,4)\nIs there a path between node 5 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph32-4_1", + "image": "data/connectivity/graph_visual/easy/graph32.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (0,5) (0,2) (0,6) (0,1) (1,3) (1,5) (1,2) (1,6) (2,3) (2,5) (2,6) (3,5) (3,6) (5,6)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph38-0_3", + "image": "data/connectivity/graph_visual/easy/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,7) (1,6) (3,6)\nIs there a path between node 0 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph29-2_5", + "image": "data/connectivity/graph_visual/easy/graph29.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,5) (0,4) (0,2) (1,6) (2,5) (2,3) (3,5) (3,4) (4,5)\nIs there a path between node 2 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph49-2_1", + "image": "data/connectivity/graph_visual/easy/graph49.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,2) (3,8) (3,4) (4,8) (5,6)\nIs there a path between node 2 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph58-5_2", + "image": "data/connectivity/graph_visual/easy/graph58.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (0,2) (0,8) (0,4) (0,7) (0,6) (1,2) (1,8) (1,4) (1,7) (1,6) (2,8) (2,4) (2,7) (2,6) (3,5) (4,8) (4,7) (4,6) (6,8) (6,7) (7,8)\nIs there a path between node 5 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph21-6_0", + "image": "data/connectivity/graph_visual/easy/graph21.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (0,4) (1,5)\nIs there a path between node 6 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph22-3_5", + "image": "data/connectivity/graph_visual/easy/graph22.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,5) (2,3) (2,5) (3,5) (4,6)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph26-4_0", + "image": "data/connectivity/graph_visual/easy/graph26.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (4,5)\nIs there a path between node 4 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph23-4_1", + "image": "data/connectivity/graph_visual/easy/graph23.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph71-0_8", + "image": "data/connectivity/graph_visual/easy/graph71.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (0,2) (0,8) (0,4) (0,7) (0,3) (0,1) (1,5) (1,2) (1,8) (1,4) (1,7) (1,3) (2,5) (2,8) (2,4) (2,7) (2,3) (3,5) (3,8) (3,4) (3,7) (4,5) (4,8) (4,7) (5,8) (5,7) (6,9) (7,8)\nIs there a path between node 0 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph0-1_3", + "image": "data/connectivity/graph_visual/easy/graph0.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,4) (1,4) (2,4)\nIs there a path between node 1 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph38-1_2", + "image": "data/connectivity/graph_visual/easy/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,7) (1,6) (3,6)\nIs there a path between node 1 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph74-1_0", + "image": "data/connectivity/graph_visual/easy/graph74.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,9) (0,5) (0,8) (0,2) (0,7) (0,3) (0,4) (1,6) (2,9) (2,5) (2,8) (2,7) (2,3) (2,4) (3,9) (3,5) (3,8) (3,7) (3,4) (4,9) (4,5) (4,8) (4,7) (5,9) (5,8) (5,7) (7,9) (7,8) (8,9)\nIs there a path between node 1 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph5-0_4", + "image": "data/connectivity/graph_visual/easy/graph5.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,2) (1,2) (2,3)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph44-1_2", + "image": "data/connectivity/graph_visual/easy/graph44.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,3) (1,7) (1,4) (1,6) (1,2) (1,5) (2,3) (2,7) (2,4) (2,6) (2,5) (3,7) (3,4) (3,6) (3,5) (4,7) (4,6) (4,5) (5,7) (5,6) (6,7)\nIs there a path between node 1 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph58-8_5", + "image": "data/connectivity/graph_visual/easy/graph58.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (0,2) (0,8) (0,4) (0,7) (0,6) (1,2) (1,8) (1,4) (1,7) (1,6) (2,8) (2,4) (2,7) (2,6) (3,5) (4,8) (4,7) (4,6) (6,8) (6,7) (7,8)\nIs there a path between node 8 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph12-3_4", + "image": "data/connectivity/graph_visual/easy/graph12.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,2) (1,2) (3,5)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph56-1_6", + "image": "data/connectivity/graph_visual/easy/graph56.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,8) (0,1) (0,6) (0,2) (0,3) (0,7) (0,5) (1,8) (1,6) (1,2) (1,3) (1,7) (1,5) (2,8) (2,6) (2,3) (2,7) (2,5) (3,8) (3,6) (3,7) (3,5) (5,8) (5,6) (5,7) (6,8) (6,7) (7,8)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph45-4_7", + "image": "data/connectivity/graph_visual/easy/graph45.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,8) (0,6) (2,7) (2,6) (2,4) (5,7) (6,8)\nIs there a path between node 4 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph46-2_4", + "image": "data/connectivity/graph_visual/easy/graph46.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph31-5_6", + "image": "data/connectivity/graph_visual/easy/graph31.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,2) (0,5) (1,3) (1,6) (1,4) (2,5) (3,6) (3,4) (4,6)\nIs there a path between node 5 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph17-5_4", + "image": "data/connectivity/graph_visual/easy/graph17.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nIs there a path between node 5 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph59-2_4", + "image": "data/connectivity/graph_visual/easy/graph59.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,5) (0,4) (0,1) (0,7) (0,6) (1,2) (1,5) (1,4) (1,7) (1,6) (2,5) (2,4) (2,7) (2,6) (3,8) (4,5) (4,7) (4,6) (5,7) (5,6) (6,7)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph65-7_3", + "image": "data/connectivity/graph_visual/easy/graph65.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,2) (1,5) (2,8) (2,5) (3,5) (3,7) (4,9) (5,6) (5,8) (5,7) (6,7)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph43-1_6", + "image": "data/connectivity/graph_visual/easy/graph43.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,2) (0,5) (0,7) (0,6) (0,4) (1,3) (2,5) (2,7) (2,6) (2,4) (4,5) (4,7) (4,6) (5,7) (5,6) (6,7)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph2-2_3", + "image": "data/connectivity/graph_visual/easy/graph2.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,1) (0,3) (0,4) (1,3) (1,4) (3,4)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph48-3_1", + "image": "data/connectivity/graph_visual/easy/graph48.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,8) (1,2) (1,5) (5,6)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph0-1_4", + "image": "data/connectivity/graph_visual/easy/graph0.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,4) (1,4) (2,4)\nIs there a path between node 1 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph14-5_1", + "image": "data/connectivity/graph_visual/easy/graph14.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,3) (1,3) (2,5)\nIs there a path between node 5 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph73-9_4", + "image": "data/connectivity/graph_visual/easy/graph73.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (0,9) (0,2) (0,8) (0,3) (0,1) (1,5) (1,9) (1,2) (1,8) (1,3) (2,5) (2,9) (2,8) (2,3) (3,5) (3,9) (3,8) (4,6) (4,7) (5,9) (5,8) (6,7) (8,9)\nIs there a path between node 9 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph12-1_0", + "image": "data/connectivity/graph_visual/easy/graph12.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,2) (1,2) (3,5)\nIs there a path between node 1 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph30-0_2", + "image": "data/connectivity/graph_visual/easy/graph30.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,6) (0,3) (0,2) (0,1) (1,6) (1,3) (1,2) (2,6) (2,3) (3,6) (4,5)\nIs there a path between node 0 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph20-3_1", + "image": "data/connectivity/graph_visual/easy/graph20.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,2) (0,3) (0,5) (0,1) (1,2) (1,3) (1,5) (2,3) (2,5) (3,5)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph16-5_1", + "image": "data/connectivity/graph_visual/easy/graph16.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,5) (0,2) (0,1) (1,5) (1,2) (2,5)\nIs there a path between node 5 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph32-2_6", + "image": "data/connectivity/graph_visual/easy/graph32.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (0,5) (0,2) (0,6) (0,1) (1,3) (1,5) (1,2) (1,6) (2,3) (2,5) (2,6) (3,5) (3,6) (5,6)\nIs there a path between node 2 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph65-8_1", + "image": "data/connectivity/graph_visual/easy/graph65.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,2) (1,5) (2,8) (2,5) (3,5) (3,7) (4,9) (5,6) (5,8) (5,7) (6,7)\nIs there a path between node 8 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph44-0_1", + "image": "data/connectivity/graph_visual/easy/graph44.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,3) (1,7) (1,4) (1,6) (1,2) (1,5) (2,3) (2,7) (2,4) (2,6) (2,5) (3,7) (3,4) (3,6) (3,5) (4,7) (4,6) (4,5) (5,7) (5,6) (6,7)\nIs there a path between node 0 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph51-3_8", + "image": "data/connectivity/graph_visual/easy/graph51.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (1,5) (2,4) (3,5) (5,6)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph22-3_6", + "image": "data/connectivity/graph_visual/easy/graph22.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,5) (2,3) (2,5) (3,5) (4,6)\nIs there a path between node 3 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph45-3_8", + "image": "data/connectivity/graph_visual/easy/graph45.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,8) (0,6) (2,7) (2,6) (2,4) (5,7) (6,8)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph48-1_2", + "image": "data/connectivity/graph_visual/easy/graph48.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,8) (1,2) (1,5) (5,6)\nIs there a path between node 1 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph38-7_3", + "image": "data/connectivity/graph_visual/easy/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,7) (1,6) (3,6)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph69-2_0", + "image": "data/connectivity/graph_visual/easy/graph69.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (0,1) (0,9) (1,8) (1,4) (3,8) (3,5) (3,4) (3,9) (4,9) (5,8) (5,6) (6,9) (8,9)\nIs there a path between node 2 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph39-5_6", + "image": "data/connectivity/graph_visual/easy/graph39.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,5) (0,2) (0,1) (1,5) (1,6) (2,6) (3,7) (4,7) (5,6)\nIs there a path between node 5 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph5-4_3", + "image": "data/connectivity/graph_visual/easy/graph5.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,2) (1,2) (2,3)\nIs there a path between node 4 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph17-2_3", + "image": "data/connectivity/graph_visual/easy/graph17.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph29-4_2", + "image": "data/connectivity/graph_visual/easy/graph29.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,5) (0,4) (0,2) (1,6) (2,5) (2,3) (3,5) (3,4) (4,5)\nIs there a path between node 4 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph34-6_7", + "image": "data/connectivity/graph_visual/easy/graph34.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,3) (0,2) (0,1) (0,4) (1,3) (1,2) (1,4) (1,6) (2,3) (2,4) (2,5) (3,4) (3,6) (4,6) (5,6)\nIs there a path between node 6 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph21-3_4", + "image": "data/connectivity/graph_visual/easy/graph21.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (0,4) (1,5)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph19-5_3", + "image": "data/connectivity/graph_visual/easy/graph19.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,4) (0,2) (0,1) (0,3) (1,4) (1,2) (1,3) (2,4) (2,3) (3,4)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph18-2_3", + "image": "data/connectivity/graph_visual/easy/graph18.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,4) (0,2) (0,3) (1,5) (2,4) (2,3) (3,4)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph58-8_1", + "image": "data/connectivity/graph_visual/easy/graph58.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (0,2) (0,8) (0,4) (0,7) (0,6) (1,2) (1,8) (1,4) (1,7) (1,6) (2,8) (2,4) (2,7) (2,6) (3,5) (4,8) (4,7) (4,6) (6,8) (6,7) (7,8)\nIs there a path between node 8 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph67-0_4", + "image": "data/connectivity/graph_visual/easy/graph67.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,9) (0,1) (0,2) (0,7) (0,6) (1,2) (1,8) (1,7) (1,4) (1,6) (2,7) (2,4) (2,6) (3,5) (4,9) (4,8) (4,7) (6,9) (6,7) (7,8)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph39-4_3", + "image": "data/connectivity/graph_visual/easy/graph39.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,5) (0,2) (0,1) (1,5) (1,6) (2,6) (3,7) (4,7) (5,6)\nIs there a path between node 4 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph59-2_3", + "image": "data/connectivity/graph_visual/easy/graph59.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,5) (0,4) (0,1) (0,7) (0,6) (1,2) (1,5) (1,4) (1,7) (1,6) (2,5) (2,4) (2,7) (2,6) (3,8) (4,5) (4,7) (4,6) (5,7) (5,6) (6,7)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph58-2_5", + "image": "data/connectivity/graph_visual/easy/graph58.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (0,2) (0,8) (0,4) (0,7) (0,6) (1,2) (1,8) (1,4) (1,7) (1,6) (2,8) (2,4) (2,7) (2,6) (3,5) (4,8) (4,7) (4,6) (6,8) (6,7) (7,8)\nIs there a path between node 2 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph60-7_0", + "image": "data/connectivity/graph_visual/easy/graph60.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (0,1) (2,3) (4,6) (5,6) (5,7)\nIs there a path between node 7 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph37-2_3", + "image": "data/connectivity/graph_visual/easy/graph37.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,3) (1,3) (1,7) (2,6) (2,5) (2,4) (4,5)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph50-8_2", + "image": "data/connectivity/graph_visual/easy/graph50.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,3) (2,6) (2,7) (3,8) (3,7) (6,7)\nIs there a path between node 8 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph10-4_5", + "image": "data/connectivity/graph_visual/easy/graph10.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,5) (0,3) (0,2) (1,5) (1,3) (2,5) (2,3) (3,5)\nIs there a path between node 4 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph18-1_2", + "image": "data/connectivity/graph_visual/easy/graph18.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,4) (0,2) (0,3) (1,5) (2,4) (2,3) (3,4)\nIs there a path between node 1 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph42-6_2", + "image": "data/connectivity/graph_visual/easy/graph42.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,5) (0,6) (0,1) (0,7) (0,4) (1,5) (1,6) (1,7) (1,4) (2,3) (4,5) (4,6) (4,7) (5,6) (5,7) (6,7)\nIs there a path between node 6 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph21-4_0", + "image": "data/connectivity/graph_visual/easy/graph21.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (0,4) (1,5)\nIs there a path between node 4 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph23-2_4", + "image": "data/connectivity/graph_visual/easy/graph23.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph7-1_3", + "image": "data/connectivity/graph_visual/easy/graph7.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,3) (0,4) (1,2) (3,4)\nIs there a path between node 1 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph35-2_6", + "image": "data/connectivity/graph_visual/easy/graph35.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,2) (0,5) (0,6) (0,3) (0,4) (0,1) (1,2) (1,5) (1,6) (1,3) (1,4) (2,5) (2,6) (2,3) (2,4) (3,5) (3,6) (3,4) (4,5) (4,6) (5,6)\nIs there a path between node 2 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph52-4_1", + "image": "data/connectivity/graph_visual/easy/graph52.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (2,8) (2,4) (2,3) (3,8) (5,7) (6,7)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph69-7_1", + "image": "data/connectivity/graph_visual/easy/graph69.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (0,1) (0,9) (1,8) (1,4) (3,8) (3,5) (3,4) (3,9) (4,9) (5,8) (5,6) (6,9) (8,9)\nIs there a path between node 7 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph33-2_3", + "image": "data/connectivity/graph_visual/easy/graph33.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,1) (0,6) (1,2) (3,7) (3,5)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph53-2_8", + "image": "data/connectivity/graph_visual/easy/graph53.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,4) (1,2) (1,8) (1,4) (1,3) (3,8) (3,4) (4,8) (5,7) (5,6) (6,7)\nIs there a path between node 2 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph18-5_3", + "image": "data/connectivity/graph_visual/easy/graph18.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,4) (0,2) (0,3) (1,5) (2,4) (2,3) (3,4)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph34-1_7", + "image": "data/connectivity/graph_visual/easy/graph34.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,3) (0,2) (0,1) (0,4) (1,3) (1,2) (1,4) (1,6) (2,3) (2,4) (2,5) (3,4) (3,6) (4,6) (5,6)\nIs there a path between node 1 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph11-1_5", + "image": "data/connectivity/graph_visual/easy/graph11.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,5) (0,1) (0,3) (1,5) (1,3) (2,4) (3,5)\nIs there a path between node 1 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph11-5_3", + "image": "data/connectivity/graph_visual/easy/graph11.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,5) (0,1) (0,3) (1,5) (1,3) (2,4) (3,5)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph57-0_2", + "image": "data/connectivity/graph_visual/easy/graph57.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,7) (0,3) (1,6) (1,5) (1,4) (1,8) (2,7) (2,3) (3,7) (4,6) (4,5) (4,8) (5,6) (5,8) (6,8)\nIs there a path between node 0 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph50-1_8", + "image": "data/connectivity/graph_visual/easy/graph50.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,3) (2,6) (2,7) (3,8) (3,7) (6,7)\nIs there a path between node 1 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph34-2_6", + "image": "data/connectivity/graph_visual/easy/graph34.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,3) (0,2) (0,1) (0,4) (1,3) (1,2) (1,4) (1,6) (2,3) (2,4) (2,5) (3,4) (3,6) (4,6) (5,6)\nIs there a path between node 2 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph8-4_2", + "image": "data/connectivity/graph_visual/easy/graph8.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,3) (0,2) (0,1) (1,3) (1,2) (2,3)\nIs there a path between node 4 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph46-5_1", + "image": "data/connectivity/graph_visual/easy/graph46.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nIs there a path between node 5 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph17-0_4", + "image": "data/connectivity/graph_visual/easy/graph17.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph63-3_1", + "image": "data/connectivity/graph_visual/easy/graph63.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,3) (0,7) (0,2) (0,8) (1,6) (2,3) (3,6) (3,7) (4,6) (4,5) (5,8) (7,8)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph2-3_4", + "image": "data/connectivity/graph_visual/easy/graph2.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,1) (0,3) (0,4) (1,3) (1,4) (3,4)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph36-7_3", + "image": "data/connectivity/graph_visual/easy/graph36.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,1) (3,7) (4,6) (5,6)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph37-7_0", + "image": "data/connectivity/graph_visual/easy/graph37.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,3) (1,3) (1,7) (2,6) (2,5) (2,4) (4,5)\nIs there a path between node 7 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-easy-graph52-7_3", + "image": "data/connectivity/graph_visual/easy/graph52.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (2,8) (2,4) (2,3) (3,8) (5,7) (6,7)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph47-5_4", + "image": "data/connectivity/graph_visual/easy/graph47.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (0,7) (0,6) (0,8) (0,4) (0,1) (1,2) (1,7) (1,6) (1,8) (1,4) (2,7) (2,6) (2,8) (2,4) (3,5) (4,7) (4,6) (4,8) (6,7) (6,8) (7,8)\nIs there a path between node 5 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-easy-graph56-6_0", + "image": "data/connectivity/graph_visual/easy/graph56.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,8) (0,1) (0,6) (0,2) (0,3) (0,7) (0,5) (1,8) (1,6) (1,2) (1,3) (1,7) (1,5) (2,8) (2,6) (2,3) (2,7) (2,5) (3,8) (3,6) (3,7) (3,5) (5,8) (5,6) (5,7) (6,8) (6,7) (7,8)\nIs there a path between node 6 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph788-17_23", + "image": "data/connectivity/graph_visual/medium/graph788.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,2) (0,20) (0,18) (0,19) (0,7) (0,1) (0,9) (0,24) (1,15) (1,10) (1,2) (1,5) (1,7) (1,12) (1,3) (1,9) (1,22) (1,17) (1,11) (2,6) (2,18) (2,16) (2,3) (2,11) (3,15) (3,20) (3,18) (3,5) (3,22) (3,11) (5,18) (5,9) (5,11) (6,15) (6,23) (6,18) (6,8) (6,12) (6,22) (7,10) (7,20) (7,18) (7,16) (7,9) (8,15) (8,20) (8,24) (9,15) (9,17) (9,11) (10,23) (10,18) (10,13) (10,24) (10,11) (11,23) (11,13) (11,12) (11,17) (12,15) (12,23) (12,19) (12,16) (12,17) (13,23) (13,17) (14,21) (15,23) (15,20) (15,19) (15,22) (16,24) (18,23) (18,20) (19,23) (19,20) (20,22) (20,24)\nIs there a path between node 17 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph273-13_15", + "image": "data/connectivity/graph_visual/medium/graph273.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,18) (0,5) (0,19) (0,11) (0,8) (0,6) (0,14) (0,10) (1,7) (1,2) (2,7) (2,17) (3,9) (3,18) (3,13) (3,19) (3,11) (3,16) (3,8) (3,6) (3,14) (3,10) (4,9) (4,13) (4,5) (4,15) (4,19) (4,11) (4,16) (4,8) (4,6) (4,10) (5,9) (5,18) (5,13) (5,15) (5,19) (5,11) (5,8) (5,14) (5,10) (6,13) (6,12) (6,15) (6,19) (6,11) (6,16) (6,8) (6,10) (7,17) (8,9) (8,13) (8,12) (8,15) (8,14) (8,10) (9,18) (9,12) (9,19) (9,16) (9,14) (9,10) (10,18) (10,13) (10,12) (10,15) (10,19) (10,16) (10,14) (11,15) (11,19) (11,16) (12,13) (12,19) (13,15) (13,19) (13,16) (14,18) (14,16) (15,18) (15,16) (16,18) (16,19)\nIs there a path between node 13 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph101-12_8", + "image": "data/connectivity/graph_visual/medium/graph101.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,15) (0,8) (0,6) (0,10) (0,13) (0,2) (0,11) (0,4) (0,14) (0,5) (1,8) (1,10) (1,13) (1,2) (1,9) (1,4) (1,14) (1,5) (2,8) (2,6) (2,10) (2,13) (2,11) (2,7) (2,4) (2,14) (2,5) (3,12) (4,8) (4,6) (4,10) (4,13) (4,7) (5,8) (5,6) (5,10) (5,11) (5,7) (5,14) (6,8) (6,14) (7,15) (7,8) (7,10) (7,9) (7,14) (8,13) (8,11) (8,14) (9,15) (9,10) (9,11) (9,14) (10,13) (10,11) (10,14) (11,15) (11,13) (11,14) (13,15) (14,15)\nIs there a path between node 12 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph32-11_6", + "image": "data/connectivity/graph_visual/medium/graph32.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (0,5) (0,4) (1,10) (1,8) (1,11) (1,9) (1,7) (1,6) (1,2) (2,10) (2,8) (2,11) (2,9) (2,7) (2,6) (3,5) (3,4) (4,5) (6,10) (6,8) (6,11) (6,9) (6,7) (7,10) (7,8) (7,11) (7,9) (8,10) (8,11) (8,9) (9,10) (9,11) (10,11)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph547-5_0", + "image": "data/connectivity/graph_visual/medium/graph547.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,8) (1,15) (1,14) (1,20) (1,23) (2,5) (2,12) (2,10) (2,19) (2,7) (3,16) (4,12) (4,7) (5,7) (6,15) (6,18) (6,22) (6,20) (6,23) (7,12) (8,16) (8,14) (8,18) (8,13) (9,12) (9,10) (12,19) (13,18) (13,20) (14,23) (15,16) (16,22) (16,23) (20,22)\nIs there a path between node 5 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph746-11_17", + "image": "data/connectivity/graph_visual/medium/graph746.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,21) (0,14) (0,1) (0,22) (0,16) (0,19) (0,5) (0,10) (0,20) (0,11) (0,24) (0,13) (1,21) (1,9) (1,3) (1,14) (1,22) (1,10) (1,20) (1,12) (1,11) (1,24) (1,13) (1,23) (2,8) (2,4) (2,18) (2,15) (3,9) (3,14) (3,16) (3,19) (3,7) (3,6) (3,5) (3,10) (3,11) (4,8) (4,17) (4,18) (4,15) (5,9) (5,14) (5,22) (5,7) (5,6) (5,10) (5,20) (5,12) (5,11) (5,13) (5,23) (6,21) (6,9) (6,22) (6,19) (6,7) (6,20) (6,12) (6,11) (6,13) (6,23) (7,21) (7,9) (7,14) (7,16) (7,19) (7,10) (7,20) (7,12) (7,11) (7,24) (7,13) (7,23) (8,17) (8,18) (8,15) (9,21) (9,16) (9,10) (9,20) (9,12) (9,11) (9,24) (9,13) (9,23) (10,22) (10,19) (10,12) (10,11) (10,13) (10,23) (11,21) (11,22) (11,19) (11,20) (11,12) (11,24) (11,13) (11,23) (12,21) (12,14) (12,22) (12,20) (12,24) (12,13) (12,23) (13,21) (13,14) (13,22) (13,16) (13,20) (13,23) (14,21) (14,16) (14,20) (14,24) (14,23) (15,18) (16,21) (16,22) (16,19) (16,20) (16,24) (16,23) (17,18) (19,21) (19,20) (19,24) (19,23) (20,21) (20,24) (20,23) (21,24) (21,23) (22,23) (23,24)\nIs there a path between node 11 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph167-0_15", + "image": "data/connectivity/graph_visual/medium/graph167.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,17) (0,8) (0,6) (0,12) (0,16) (0,3) (1,17) (1,2) (1,8) (1,9) (1,4) (1,12) (1,3) (2,17) (2,11) (2,9) (2,16) (2,14) (2,5) (3,13) (3,9) (3,14) (4,17) (4,7) (4,13) (4,16) (4,5) (5,7) (5,13) (5,9) (5,14) (6,8) (6,11) (6,9) (6,12) (6,16) (6,14) (7,8) (7,13) (8,13) (9,13) (9,12) (11,13) (11,12) (11,14) (13,14)\nIs there a path between node 0 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph336-6_8", + "image": "data/connectivity/graph_visual/medium/graph336.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,10) (0,3) (0,13) (0,7) (0,1) (0,9) (0,17) (0,15) (0,14) (0,18) (0,6) (0,12) (1,10) (1,7) (1,20) (1,11) (1,9) (1,15) (1,14) (1,18) (1,4) (1,12) (2,19) (3,16) (3,13) (3,7) (3,11) (3,17) (3,15) (3,18) (3,6) (4,16) (4,10) (4,13) (4,7) (4,20) (4,11) (4,9) (4,17) (4,14) (4,18) (4,6) (4,12) (5,8) (5,19) (6,16) (6,10) (6,13) (6,20) (6,9) (6,18) (6,12) (7,16) (7,10) (7,13) (7,20) (7,11) (7,9) (7,17) (7,15) (7,14) (7,18) (7,12) (8,19) (9,10) (9,13) (9,11) (9,17) (9,15) (9,14) (10,20) (10,17) (10,14) (11,16) (11,20) (11,17) (11,18) (12,15) (12,14) (13,16) (13,17) (13,14) (13,18) (14,16) (14,20) (14,17) (14,15) (14,18) (15,16) (15,20) (15,18) (16,20) (16,17) (16,18) (17,20) (17,18) (18,20)\nIs there a path between node 6 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph782-7_16", + "image": "data/connectivity/graph_visual/medium/graph782.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,11) (0,5) (1,9) (1,17) (2,6) (2,22) (2,15) (2,11) (2,18) (2,7) (3,12) (3,11) (4,12) (4,14) (4,15) (4,13) (5,10) (5,14) (5,22) (5,11) (5,7) (6,8) (6,15) (7,8) (7,10) (7,22) (7,13) (7,16) (8,20) (8,14) (8,19) (8,15) (8,11) (9,24) (9,23) (9,17) (10,14) (10,11) (10,18) (11,20) (12,15) (12,13) (13,22) (13,15) (13,18) (13,16) (14,20) (14,22) (14,18) (15,20) (15,19) (15,18) (17,23) (20,21) (21,22) (23,24)\nIs there a path between node 7 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph514-2_15", + "image": "data/connectivity/graph_visual/medium/graph514.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,14) (0,19) (0,12) (0,1) (1,10) (1,19) (1,12) (1,3) (1,21) (2,9) (2,15) (2,4) (2,11) (2,22) (2,17) (2,7) (2,5) (2,18) (3,10) (3,19) (3,12) (3,21) (4,6) (4,16) (4,9) (4,8) (4,15) (4,11) (4,22) (4,7) (4,13) (4,5) (4,18) (5,6) (5,9) (5,8) (5,11) (5,22) (5,17) (5,7) (5,18) (6,16) (6,9) (6,11) (6,22) (6,17) (6,7) (6,13) (7,9) (7,11) (7,22) (7,17) (7,13) (7,18) (8,16) (8,11) (8,22) (8,13) (8,18) (9,16) (9,15) (9,11) (9,22) (9,17) (9,13) (9,18) (10,14) (10,19) (10,12) (10,21) (11,15) (11,17) (11,13) (12,14) (12,19) (12,21) (13,15) (13,22) (13,18) (14,21) (15,16) (15,22) (15,17) (16,22) (16,17) (16,18) (17,22) (17,18) (18,22) (19,21)\nIs there a path between node 2 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph855-4_12", + "image": "data/connectivity/graph_visual/medium/graph855.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,13) (0,18) (0,21) (0,5) (0,12) (0,10) (0,7) (0,20) (0,17) (0,8) (0,24) (0,3) (0,9) (0,22) (0,16) (0,6) (0,19) (0,15) (1,4) (1,11) (1,23) (1,14) (2,13) (2,18) (2,21) (2,5) (2,12) (2,10) (2,7) (2,20) (2,17) (2,8) (2,24) (2,3) (2,9) (2,22) (2,16) (2,6) (2,19) (2,15) (3,13) (3,18) (3,21) (3,5) (3,12) (3,10) (3,7) (3,20) (3,17) (3,8) (3,24) (3,9) (3,22) (3,16) (3,6) (3,19) (3,15) (4,11) (4,23) (4,14) (5,13) (5,18) (5,21) (5,12) (5,10) (5,7) (5,20) (5,17) (5,8) (5,24) (5,9) (5,22) (5,16) (5,6) (5,19) (5,15) (6,13) (6,18) (6,21) (6,12) (6,10) (6,7) (6,20) (6,17) (6,8) (6,24) (6,9) (6,22) (6,16) (6,19) (6,15) (7,13) (7,18) (7,21) (7,12) (7,10) (7,20) (7,17) (7,8) (7,24) (7,9) (7,22) (7,16) (7,19) (7,15) (8,13) (8,18) (8,21) (8,12) (8,10) (8,20) (8,17) (8,24) (8,9) (8,22) (8,16) (8,19) (8,15) (9,13) (9,18) (9,21) (9,12) (9,10) (9,20) (9,17) (9,24) (9,22) (9,16) (9,19) (9,15) (10,13) (10,18) (10,21) (10,12) (10,20) (10,17) (10,24) (10,22) (10,16) (10,19) (10,15) (11,23) (11,14) (12,13) (12,18) (12,21) (12,20) (12,17) (12,24) (12,22) (12,16) (12,19) (12,15) (13,18) (13,21) (13,20) (13,17) (13,24) (13,22) (13,16) (13,19) (13,15) (14,23) (15,18) (15,21) (15,20) (15,17) (15,24) (15,22) (15,16) (15,19) (16,18) (16,21) (16,20) (16,17) (16,24) (16,22) (16,19) (17,18) (17,21) (17,20) (17,24) (17,22) (17,19) (18,21) (18,20) (18,24) (18,22) (18,19) (19,21) (19,20) (19,24) (19,22) (20,21) (20,24) (20,22) (21,24) (21,22) (22,24)\nIs there a path between node 4 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph253-18_9", + "image": "data/connectivity/graph_visual/medium/graph253.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,7) (0,14) (0,13) (0,12) (0,17) (0,16) (0,18) (0,9) (1,5) (1,4) (1,3) (1,8) (1,11) (1,6) (2,10) (2,15) (3,5) (3,4) (3,8) (3,11) (3,6) (4,5) (4,8) (4,11) (4,6) (5,8) (5,11) (5,6) (6,8) (6,11) (7,14) (7,13) (7,12) (7,17) (7,16) (7,18) (7,9) (8,11) (9,14) (9,13) (9,12) (9,17) (9,16) (9,18) (10,15) (12,14) (12,13) (12,17) (12,16) (12,18) (13,14) (13,17) (13,16) (13,18) (14,17) (14,16) (14,18) (16,17) (16,18) (17,18)\nIs there a path between node 18 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph171-8_3", + "image": "data/connectivity/graph_visual/medium/graph171.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,10) (0,7) (0,15) (0,17) (0,6) (1,12) (1,3) (1,4) (1,14) (1,16) (2,8) (2,5) (2,4) (2,9) (2,14) (2,16) (3,12) (3,11) (3,8) (3,4) (3,9) (3,14) (3,16) (4,12) (4,11) (4,8) (4,5) (4,14) (4,16) (5,12) (5,8) (5,9) (5,14) (5,16) (6,10) (6,13) (6,7) (6,15) (6,17) (7,10) (7,13) (7,15) (7,17) (8,11) (8,9) (9,14) (9,16) (10,15) (10,17) (11,12) (11,14) (12,14) (12,16) (13,15) (13,17) (15,17)\nIs there a path between node 8 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph380-7_10", + "image": "data/connectivity/graph_visual/medium/graph380.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,11) (0,16) (0,3) (0,20) (0,12) (0,5) (0,17) (0,8) (0,14) (0,18) (0,2) (0,1) (0,6) (1,11) (1,16) (1,3) (1,20) (1,12) (1,5) (1,4) (1,17) (1,14) (1,2) (1,13) (1,6) (2,11) (2,16) (2,3) (2,20) (2,5) (2,8) (2,14) (2,18) (2,13) (2,6) (2,19) (2,9) (3,11) (3,16) (3,20) (3,5) (3,4) (3,17) (3,14) (3,13) (3,6) (3,19) (3,9) (4,11) (4,16) (4,20) (4,12) (4,8) (4,18) (4,13) (4,6) (4,19) (4,9) (5,11) (5,16) (5,20) (5,12) (5,17) (5,8) (5,14) (5,6) (5,19) (5,9) (6,11) (6,16) (6,20) (6,12) (6,17) (6,14) (6,19) (6,9) (8,11) (8,16) (8,20) (8,14) (8,18) (8,19) (8,9) (9,11) (9,12) (9,18) (9,19) (11,20) (11,12) (11,17) (11,14) (11,13) (11,19) (12,16) (12,20) (12,14) (12,18) (12,13) (12,19) (13,16) (13,14) (14,20) (14,18) (14,19) (16,20) (16,18) (17,20) (17,18) (18,20) (19,20)\nIs there a path between node 7 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph199-18_5", + "image": "data/connectivity/graph_visual/medium/graph199.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,14) (1,15) (1,6) (2,5) (2,10) (2,9) (3,12) (3,16) (3,18) (4,13) (5,7) (5,10) (6,17) (6,7) (6,14) (6,11) (6,9) (7,10) (8,12) (8,13) (9,15) (9,14) (10,15) (10,11) (12,13) (13,16) (13,18) (14,17)\nIs there a path between node 18 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph193-5_17", + "image": "data/connectivity/graph_visual/medium/graph193.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,5) (0,7) (0,14) (0,2) (0,16) (0,13) (0,3) (0,12) (0,4) (1,9) (1,15) (1,6) (1,10) (1,17) (2,5) (2,7) (2,14) (2,16) (2,13) (2,3) (2,12) (2,4) (3,5) (3,7) (3,14) (3,16) (3,13) (3,12) (3,4) (4,5) (4,7) (4,14) (4,16) (4,13) (4,12) (5,7) (5,14) (5,16) (5,13) (5,12) (6,9) (6,15) (6,10) (6,17) (7,14) (7,16) (7,13) (7,12) (8,11) (9,15) (9,10) (9,17) (10,15) (10,17) (12,14) (12,16) (12,13) (13,14) (13,16) (14,16) (15,17)\nIs there a path between node 5 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph33-9_4", + "image": "data/connectivity/graph_visual/medium/graph33.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,3) (0,8) (1,5) (1,10) (1,8) (2,6) (2,7) (3,9) (3,10) (4,11) (4,8) (6,7) (8,9) (8,10) (11,12)\nIs there a path between node 9 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph644-7_3", + "image": "data/connectivity/graph_visual/medium/graph644.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,9) (1,4) (2,16) (4,18) (4,11) (5,14) (6,8) (7,15) (7,21) (9,15) (9,19) (13,15) (13,16) (15,20) (16,20) (19,21) (19,20)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph636-0_18", + "image": "data/connectivity/graph_visual/medium/graph636.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (0,8) (0,22) (0,15) (0,18) (1,12) (1,16) (1,8) (1,9) (1,22) (1,15) (1,18) (2,6) (2,21) (3,21) (3,11) (3,10) (4,23) (5,20) (5,17) (6,20) (7,11) (8,16) (8,14) (8,13) (8,15) (9,16) (9,15) (9,19) (10,20) (10,21) (10,17) (13,16) (13,14) (14,19) (15,22) (15,18) (17,20) (17,23) (18,22) (21,23)\nIs there a path between node 0 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph401-5_1", + "image": "data/connectivity/graph_visual/medium/graph401.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,11) (0,1) (1,11) (2,4) (2,14) (3,21) (3,18) (3,6) (3,12) (3,13) (5,6) (6,21) (6,20) (6,8) (6,12) (6,13) (7,16) (7,12) (8,20) (9,20) (9,13) (10,11) (12,17) (12,16) (13,20) (13,17) (13,19) (15,21) (15,16) (15,19) (16,21) (16,19) (17,19) (18,19) (19,20) (20,21)\nIs there a path between node 5 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph34-2_5", + "image": "data/connectivity/graph_visual/medium/graph34.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,4) (0,3) (0,11) (0,8) (0,2) (0,12) (0,9) (0,1) (1,4) (1,3) (1,6) (1,11) (1,8) (1,7) (1,10) (1,2) (1,12) (2,3) (2,6) (2,11) (2,8) (2,9) (3,6) (3,11) (3,8) (3,7) (3,10) (3,9) (4,6) (4,11) (4,8) (4,7) (4,10) (4,12) (4,9) (6,8) (6,10) (7,10) (7,12) (7,9) (8,11) (8,10) (8,12) (9,10) (10,12)\nIs there a path between node 2 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph656-11_14", + "image": "data/connectivity/graph_visual/medium/graph656.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,19) (0,4) (0,17) (0,16) (0,22) (0,20) (0,18) (0,10) (0,21) (0,7) (0,8) (0,9) (0,15) (0,14) (1,3) (1,13) (1,6) (1,4) (1,16) (1,22) (1,20) (1,10) (1,21) (1,5) (1,7) (1,9) (1,15) (1,14) (2,11) (3,13) (3,6) (3,19) (3,4) (3,17) (3,16) (3,22) (3,20) (3,18) (3,10) (3,5) (3,7) (3,23) (3,8) (3,14) (4,13) (4,19) (4,17) (4,20) (4,18) (4,10) (4,5) (4,7) (4,23) (4,8) (4,15) (4,14) (5,13) (5,6) (5,19) (5,17) (5,16) (5,22) (5,20) (5,10) (5,23) (5,9) (5,14) (6,13) (6,17) (6,22) (6,18) (6,10) (6,21) (6,7) (6,23) (6,15) (6,14) (7,13) (7,19) (7,17) (7,16) (7,22) (7,20) (7,18) (7,10) (7,21) (7,9) (7,14) (8,19) (8,20) (8,18) (8,10) (8,21) (8,9) (8,15) (9,13) (9,19) (9,17) (9,16) (9,22) (9,21) (9,14) (10,13) (10,17) (10,22) (10,20) (10,18) (10,23) (10,15) (10,14) (13,17) (13,16) (13,22) (13,20) (13,18) (13,21) (13,23) (13,15) (13,14) (14,17) (14,16) (14,20) (14,18) (14,23) (15,19) (15,17) (15,16) (15,22) (15,20) (15,21) (15,23) (16,18) (16,21) (17,19) (17,22) (17,20) (17,23) (18,19) (18,22) (18,20) (18,21) (18,23) (19,22) (19,20) (19,21) (20,22) (21,22) (21,23) (22,23)\nIs there a path between node 11 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph487-0_10", + "image": "data/connectivity/graph_visual/medium/graph487.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,14) (0,6) (0,11) (0,19) (0,20) (0,1) (0,15) (0,12) (0,7) (0,22) (0,5) (0,21) (0,3) (0,4) (0,18) (0,17) (1,14) (1,6) (1,11) (1,19) (1,20) (1,15) (1,12) (1,7) (1,22) (1,5) (1,21) (1,3) (1,4) (1,18) (1,17) (2,13) (2,10) (2,8) (2,16) (2,9) (3,14) (3,6) (3,11) (3,19) (3,20) (3,15) (3,12) (3,7) (3,22) (3,5) (3,21) (3,4) (3,18) (3,17) (4,14) (4,6) (4,11) (4,19) (4,20) (4,15) (4,12) (4,7) (4,22) (4,5) (4,21) (4,18) (4,17) (5,14) (5,6) (5,11) (5,19) (5,20) (5,15) (5,12) (5,7) (5,22) (5,21) (5,18) (5,17) (6,14) (6,11) (6,19) (6,20) (6,15) (6,12) (6,7) (6,22) (6,21) (6,18) (6,17) (7,14) (7,11) (7,19) (7,20) (7,15) (7,12) (7,22) (7,21) (7,18) (7,17) (8,13) (8,10) (8,16) (8,9) (9,13) (9,10) (9,16) (10,13) (10,16) (11,14) (11,19) (11,20) (11,15) (11,12) (11,22) (11,21) (11,18) (11,17) (12,14) (12,19) (12,20) (12,15) (12,22) (12,21) (12,18) (12,17) (13,16) (14,19) (14,20) (14,15) (14,22) (14,21) (14,18) (14,17) (15,19) (15,20) (15,22) (15,21) (15,18) (15,17) (17,19) (17,20) (17,22) (17,21) (17,18) (18,19) (18,20) (18,22) (18,21) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22)\nIs there a path between node 0 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph5-4_6", + "image": "data/connectivity/graph_visual/medium/graph5.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,10) (1,8) (1,9) (2,10) (2,3) (3,7) (5,10) (6,8) (7,8) (7,9)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph214-0_5", + "image": "data/connectivity/graph_visual/medium/graph214.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,1) (0,6) (0,17) (0,10) (0,16) (0,13) (1,11) (1,6) (1,17) (1,10) (1,16) (1,13) (2,12) (2,8) (2,15) (2,14) (2,3) (2,9) (2,7) (2,4) (2,18) (2,5) (3,12) (3,8) (3,15) (3,14) (3,9) (3,7) (3,4) (3,18) (3,5) (4,12) (4,8) (4,15) (4,14) (4,9) (4,7) (4,18) (4,5) (5,12) (5,8) (5,15) (5,14) (5,9) (5,7) (5,18) (6,11) (6,17) (6,10) (6,16) (6,13) (7,12) (7,8) (7,15) (7,14) (7,9) (7,18) (8,12) (8,15) (8,14) (8,9) (8,18) (9,12) (9,15) (9,14) (9,18) (10,11) (10,17) (10,16) (10,13) (11,17) (11,16) (11,13) (12,15) (12,14) (12,18) (13,17) (13,16) (14,15) (14,18) (15,18) (16,17)\nIs there a path between node 0 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph343-8_15", + "image": "data/connectivity/graph_visual/medium/graph343.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (0,1) (0,14) (0,18) (1,17) (1,14) (1,18) (2,19) (2,7) (2,10) (2,3) (2,12) (2,16) (2,11) (2,5) (2,9) (2,15) (2,6) (2,20) (2,8) (2,4) (2,13) (3,19) (3,7) (3,10) (3,12) (3,16) (3,11) (3,5) (3,9) (3,15) (3,6) (3,20) (3,8) (3,4) (3,13) (4,19) (4,7) (4,10) (4,12) (4,16) (4,11) (4,5) (4,9) (4,15) (4,6) (4,20) (4,8) (4,13) (5,19) (5,7) (5,10) (5,12) (5,16) (5,11) (5,9) (5,15) (5,6) (5,20) (5,8) (5,13) (6,19) (6,7) (6,10) (6,12) (6,16) (6,11) (6,9) (6,15) (6,20) (6,8) (6,13) (7,19) (7,10) (7,12) (7,16) (7,11) (7,9) (7,15) (7,20) (7,8) (7,13) (8,19) (8,10) (8,12) (8,16) (8,11) (8,9) (8,15) (8,20) (8,13) (9,19) (9,10) (9,12) (9,16) (9,11) (9,15) (9,20) (9,13) (10,19) (10,12) (10,16) (10,11) (10,15) (10,20) (10,13) (11,19) (11,12) (11,16) (11,15) (11,20) (11,13) (12,19) (12,16) (12,15) (12,20) (12,13) (13,19) (13,16) (13,15) (13,20) (14,17) (14,18) (15,19) (15,16) (15,20) (16,19) (16,20) (17,18) (19,20)\nIs there a path between node 8 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph352-10_18", + "image": "data/connectivity/graph_visual/medium/graph352.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,3) (2,11) (2,19) (2,5) (2,17) (2,10) (3,4) (3,6) (3,18) (3,7) (4,6) (4,19) (5,13) (5,19) (5,10) (6,7) (6,10) (7,13) (7,17) (7,10) (8,9) (10,18) (10,19) (10,17) (11,13)\nIs there a path between node 10 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph192-8_7", + "image": "data/connectivity/graph_visual/medium/graph192.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,11) (0,14) (0,5) (0,7) (0,9) (0,1) (0,12) (1,11) (1,14) (1,5) (1,7) (1,9) (1,12) (2,6) (2,10) (2,15) (2,8) (2,17) (2,13) (2,16) (2,3) (2,4) (3,6) (3,10) (3,15) (3,8) (3,17) (3,13) (3,16) (3,4) (4,6) (4,10) (4,15) (4,8) (4,17) (4,13) (4,16) (5,11) (5,14) (5,7) (5,9) (5,12) (6,10) (6,15) (6,8) (6,17) (6,13) (6,16) (7,11) (7,14) (7,9) (7,12) (8,10) (8,15) (8,17) (8,13) (8,16) (9,11) (9,14) (9,12) (10,15) (10,17) (10,13) (10,16) (11,14) (11,12) (12,14) (13,15) (13,17) (13,16) (15,17) (15,16) (16,17)\nIs there a path between node 8 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph620-7_11", + "image": "data/connectivity/graph_visual/medium/graph620.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,14) (0,2) (0,15) (0,4) (0,11) (0,23) (0,12) (0,10) (0,20) (0,9) (0,7) (0,1) (0,16) (0,22) (0,3) (0,13) (0,19) (1,14) (1,2) (1,15) (1,4) (1,11) (1,23) (1,12) (1,10) (1,20) (1,9) (1,7) (1,16) (1,22) (1,3) (1,13) (1,19) (2,14) (2,15) (2,4) (2,11) (2,23) (2,12) (2,10) (2,20) (2,9) (2,7) (2,16) (2,22) (2,3) (2,13) (2,19) (3,14) (3,15) (3,4) (3,11) (3,23) (3,12) (3,10) (3,20) (3,9) (3,7) (3,16) (3,22) (3,13) (3,19) (4,14) (4,15) (4,11) (4,23) (4,12) (4,10) (4,20) (4,9) (4,7) (4,16) (4,22) (4,13) (4,19) (5,8) (5,6) (5,18) (5,21) (6,8) (6,18) (6,21) (7,14) (7,15) (7,11) (7,23) (7,12) (7,10) (7,20) (7,9) (7,16) (7,22) (7,13) (7,19) (8,18) (8,21) (9,14) (9,15) (9,11) (9,23) (9,12) (9,10) (9,20) (9,16) (9,22) (9,13) (9,19) (10,14) (10,15) (10,11) (10,23) (10,12) (10,20) (10,16) (10,22) (10,13) (10,19) (11,14) (11,15) (11,23) (11,12) (11,20) (11,16) (11,22) (11,13) (11,19) (12,14) (12,15) (12,23) (12,20) (12,16) (12,22) (12,13) (12,19) (13,14) (13,15) (13,23) (13,20) (13,16) (13,22) (13,19) (14,15) (14,23) (14,20) (14,16) (14,22) (14,19) (15,23) (15,20) (15,16) (15,22) (15,19) (16,23) (16,20) (16,22) (16,19) (18,21) (19,23) (19,20) (19,22) (20,23) (20,22) (22,23)\nIs there a path between node 7 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph608-11_2", + "image": "data/connectivity/graph_visual/medium/graph608.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,10) (0,6) (0,9) (0,5) (0,3) (0,17) (0,18) (0,15) (0,21) (1,16) (1,23) (1,12) (1,14) (1,22) (1,4) (1,13) (1,19) (1,2) (1,20) (1,11) (1,7) (2,16) (2,23) (2,12) (2,14) (2,22) (2,4) (2,13) (2,19) (2,20) (2,11) (2,7) (3,8) (3,10) (3,6) (3,9) (3,5) (3,17) (3,18) (3,15) (3,21) (4,16) (4,23) (4,12) (4,14) (4,22) (4,13) (4,19) (4,20) (4,11) (4,7) (5,8) (5,10) (5,6) (5,9) (5,17) (5,18) (5,15) (5,21) (6,8) (6,10) (6,9) (6,17) (6,18) (6,15) (6,21) (7,16) (7,23) (7,12) (7,14) (7,22) (7,13) (7,19) (7,20) (7,11) (8,10) (8,9) (8,17) (8,18) (8,15) (8,21) (9,10) (9,17) (9,18) (9,15) (9,21) (10,17) (10,18) (10,15) (10,21) (11,16) (11,23) (11,12) (11,14) (11,22) (11,13) (11,19) (11,20) (12,16) (12,23) (12,14) (12,22) (12,13) (12,19) (12,20) (13,16) (13,23) (13,14) (13,22) (13,19) (13,20) (14,16) (14,23) (14,22) (14,19) (14,20) (15,17) (15,18) (15,21) (16,23) (16,22) (16,19) (16,20) (17,18) (17,21) (18,21) (19,23) (19,22) (19,20) (20,23) (20,22) (22,23)\nIs there a path between node 11 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph795-11_10", + "image": "data/connectivity/graph_visual/medium/graph795.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,7) (2,18) (2,8) (2,9) (3,5) (3,8) (3,6) (3,20) (4,11) (5,24) (5,19) (5,23) (5,20) (5,15) (6,11) (6,24) (6,8) (6,9) (6,19) (7,22) (8,14) (8,11) (8,23) (8,13) (9,17) (9,21) (9,24) (9,19) (10,12) (11,21) (11,24) (11,19) (11,23) (13,17) (13,19) (13,20) (14,20) (15,24) (15,19) (15,23) (17,18) (17,19) (17,23) (18,24) (19,24) (20,21) (21,23)\nIs there a path between node 11 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph120-10_11", + "image": "data/connectivity/graph_visual/medium/graph120.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,12) (0,7) (0,8) (0,9) (0,13) (0,14) (0,15) (0,5) (1,2) (1,12) (1,16) (1,11) (1,3) (1,6) (1,14) (1,4) (2,12) (2,7) (2,9) (2,13) (2,14) (3,16) (3,11) (3,7) (3,8) (3,14) (3,15) (3,5) (3,4) (4,12) (4,11) (4,8) (4,9) (4,13) (4,14) (4,5) (5,12) (5,16) (5,11) (5,7) (5,8) (5,13) (5,14) (5,15) (6,12) (6,16) (6,11) (6,7) (6,14) (6,15) (7,12) (7,16) (7,11) (7,8) (7,9) (7,13) (8,12) (8,16) (8,11) (8,9) (8,13) (8,14) (9,12) (9,16) (9,11) (9,14) (9,15) (11,12) (11,16) (11,14) (12,13) (12,15) (13,16) (13,15) (14,16)\nIs there a path between node 10 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph458-6_15", + "image": "data/connectivity/graph_visual/medium/graph458.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,7) (0,5) (0,11) (0,3) (0,10) (0,6) (0,18) (0,15) (0,2) (0,13) (0,16) (0,8) (0,20) (1,12) (1,14) (1,21) (1,9) (1,4) (1,17) (2,19) (2,7) (2,5) (2,11) (2,3) (2,10) (2,6) (2,18) (2,15) (2,13) (2,16) (2,8) (2,20) (3,19) (3,7) (3,5) (3,11) (3,10) (3,6) (3,18) (3,15) (3,13) (3,16) (3,8) (3,20) (4,12) (4,14) (4,21) (4,9) (4,17) (5,19) (5,7) (5,11) (5,10) (5,6) (5,18) (5,15) (5,13) (5,16) (5,8) (5,20) (6,19) (6,7) (6,11) (6,10) (6,18) (6,15) (6,13) (6,16) (6,8) (6,20) (7,19) (7,11) (7,10) (7,18) (7,15) (7,13) (7,16) (7,8) (7,20) (8,19) (8,11) (8,10) (8,18) (8,15) (8,13) (8,16) (8,20) (9,12) (9,14) (9,21) (9,17) (10,19) (10,11) (10,18) (10,15) (10,13) (10,16) (10,20) (11,19) (11,18) (11,15) (11,13) (11,16) (11,20) (12,14) (12,21) (12,17) (13,19) (13,18) (13,15) (13,16) (13,20) (14,21) (14,17) (15,19) (15,18) (15,16) (15,20) (16,19) (16,18) (16,20) (17,21) (18,19) (18,20) (19,20)\nIs there a path between node 6 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph64-12_4", + "image": "data/connectivity/graph_visual/medium/graph64.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,8) (0,5) (0,2) (0,3) (0,10) (0,6) (0,1) (0,4) (0,9) (0,7) (0,12) (1,8) (1,5) (1,2) (1,3) (1,10) (1,6) (1,4) (1,9) (1,7) (1,12) (2,8) (2,5) (2,3) (2,10) (2,6) (2,4) (2,9) (2,7) (2,12) (3,8) (3,5) (3,10) (3,6) (3,4) (3,9) (3,7) (3,12) (4,8) (4,5) (4,10) (4,6) (4,9) (4,7) (4,12) (5,8) (5,10) (5,6) (5,9) (5,7) (5,12) (6,8) (6,10) (6,9) (6,7) (6,12) (7,8) (7,10) (7,9) (7,12) (8,10) (8,9) (8,12) (9,10) (9,12) (10,12) (11,13)\nIs there a path between node 12 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph643-8_11", + "image": "data/connectivity/graph_visual/medium/graph643.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,18) (0,5) (2,3) (2,7) (2,15) (2,18) (3,16) (3,7) (3,15) (3,21) (4,8) (5,7) (6,16) (6,22) (6,18) (8,23) (9,11) (10,23) (11,20) (12,13) (15,22) (15,21) (16,22) (17,22) (17,21) (19,23) (20,23)\nIs there a path between node 8 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph839-15_18", + "image": "data/connectivity/graph_visual/medium/graph839.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,8) (0,24) (0,14) (0,4) (0,21) (0,1) (0,15) (0,19) (1,23) (1,8) (1,24) (1,14) (1,4) (1,21) (1,15) (1,19) (2,18) (2,22) (2,16) (2,17) (2,5) (2,10) (2,11) (3,12) (3,13) (3,9) (3,6) (3,20) (3,7) (4,23) (4,8) (4,24) (4,14) (4,21) (4,15) (4,19) (5,18) (5,22) (5,16) (5,17) (5,10) (5,11) (6,12) (6,13) (6,9) (6,20) (6,7) (7,12) (7,13) (7,9) (7,20) (8,23) (8,24) (8,14) (8,21) (8,15) (8,19) (9,12) (9,13) (9,20) (10,18) (10,22) (10,16) (10,17) (10,11) (11,18) (11,22) (11,16) (11,17) (12,13) (12,20) (13,20) (14,23) (14,24) (14,21) (14,15) (14,19) (15,23) (15,24) (15,21) (15,19) (16,18) (16,22) (16,17) (17,18) (17,22) (18,22) (19,23) (19,24) (19,21) (21,23) (21,24) (23,24)\nIs there a path between node 15 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph623-14_1", + "image": "data/connectivity/graph_visual/medium/graph623.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,17) (0,18) (0,4) (0,10) (0,21) (0,8) (0,22) (0,9) (0,19) (0,23) (0,5) (0,1) (0,14) (0,6) (0,15) (0,16) (1,20) (1,17) (1,18) (1,4) (1,10) (1,21) (1,8) (1,22) (1,9) (1,19) (1,23) (1,5) (1,14) (1,6) (1,15) (1,16) (2,12) (2,13) (2,11) (2,7) (2,3) (3,12) (3,13) (3,11) (3,7) (4,20) (4,17) (4,18) (4,10) (4,21) (4,8) (4,22) (4,9) (4,19) (4,23) (4,5) (4,14) (4,6) (4,15) (4,16) (5,20) (5,17) (5,18) (5,10) (5,21) (5,8) (5,22) (5,9) (5,19) (5,23) (5,14) (5,6) (5,15) (5,16) (6,20) (6,17) (6,18) (6,10) (6,21) (6,8) (6,22) (6,9) (6,19) (6,23) (6,14) (6,15) (6,16) (7,12) (7,13) (7,11) (8,20) (8,17) (8,18) (8,10) (8,21) (8,22) (8,9) (8,19) (8,23) (8,14) (8,15) (8,16) (9,20) (9,17) (9,18) (9,10) (9,21) (9,22) (9,19) (9,23) (9,14) (9,15) (9,16) (10,20) (10,17) (10,18) (10,21) (10,22) (10,19) (10,23) (10,14) (10,15) (10,16) (11,12) (11,13) (12,13) (14,20) (14,17) (14,18) (14,21) (14,22) (14,19) (14,23) (14,15) (14,16) (15,20) (15,17) (15,18) (15,21) (15,22) (15,19) (15,23) (15,16) (16,20) (16,17) (16,18) (16,21) (16,22) (16,19) (16,23) (17,20) (17,18) (17,21) (17,22) (17,19) (17,23) (18,20) (18,21) (18,22) (18,19) (18,23) (19,20) (19,21) (19,22) (19,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 14 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph685-19_14", + "image": "data/connectivity/graph_visual/medium/graph685.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,21) (0,7) (0,18) (0,8) (0,11) (0,4) (0,6) (0,13) (0,17) (0,9) (0,22) (0,14) (0,2) (1,21) (1,7) (1,18) (1,8) (1,11) (1,4) (1,6) (1,13) (1,17) (1,9) (1,22) (1,14) (1,2) (2,21) (2,7) (2,18) (2,8) (2,11) (2,4) (2,6) (2,13) (2,17) (2,9) (2,22) (2,14) (3,5) (3,10) (3,15) (3,12) (3,16) (3,20) (4,21) (4,7) (4,18) (4,8) (4,11) (4,6) (4,13) (4,17) (4,9) (4,22) (4,14) (5,10) (5,15) (5,12) (5,16) (5,20) (6,21) (6,7) (6,18) (6,8) (6,11) (6,13) (6,17) (6,9) (6,22) (6,14) (7,21) (7,18) (7,8) (7,11) (7,13) (7,17) (7,9) (7,22) (7,14) (8,21) (8,18) (8,11) (8,13) (8,17) (8,9) (8,22) (8,14) (9,21) (9,18) (9,11) (9,13) (9,17) (9,22) (9,14) (10,15) (10,12) (10,16) (10,20) (11,21) (11,18) (11,13) (11,17) (11,22) (11,14) (12,15) (12,16) (12,20) (13,21) (13,18) (13,17) (13,22) (13,14) (14,21) (14,18) (14,17) (14,22) (15,16) (15,20) (16,20) (17,21) (17,18) (17,22) (18,21) (18,22) (19,23) (21,22)\nIs there a path between node 19 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph196-2_7", + "image": "data/connectivity/graph_visual/medium/graph196.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,2) (0,14) (0,7) (0,13) (1,17) (1,3) (1,10) (1,6) (2,11) (2,12) (2,14) (2,13) (3,17) (3,10) (3,6) (4,9) (4,5) (5,9) (5,16) (6,17) (6,8) (6,10) (7,11) (7,12) (7,14) (7,13) (8,17) (8,15) (9,18) (9,16) (10,17) (12,14) (12,13) (13,14) (15,17)\nIs there a path between node 2 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph430-21_6", + "image": "data/connectivity/graph_visual/medium/graph430.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,16) (1,11) (1,2) (1,14) (2,3) (2,10) (2,6) (3,21) (3,9) (3,11) (3,10) (3,6) (4,12) (5,8) (5,13) (6,9) (6,14) (6,10) (6,7) (7,21) (7,9) (7,16) (7,11) (7,18) (7,14) (7,17) (8,12) (8,13) (9,16) (9,11) (11,16) (11,17) (12,13) (15,20) (16,18) (16,17) (17,18) (18,21)\nIs there a path between node 21 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph5-0_6", + "image": "data/connectivity/graph_visual/medium/graph5.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,10) (1,8) (1,9) (2,10) (2,3) (3,7) (5,10) (6,8) (7,8) (7,9)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph628-15_20", + "image": "data/connectivity/graph_visual/medium/graph628.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,12) (1,13) (1,2) (1,17) (2,10) (2,23) (3,14) (3,9) (3,4) (3,19) (4,5) (4,9) (4,21) (5,14) (6,11) (7,20) (7,8) (9,14) (9,21) (10,13) (10,17) (10,12) (11,18) (11,20) (12,22) (12,23) (12,15) (12,17) (13,15) (14,21) (16,18) (17,23)\nIs there a path between node 15 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph99-2_12", + "image": "data/connectivity/graph_visual/medium/graph99.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,14) (0,2) (0,4) (0,5) (0,15) (0,7) (1,9) (1,13) (1,12) (1,3) (2,14) (2,10) (2,4) (2,8) (2,15) (2,7) (3,9) (3,13) (3,12) (3,11) (4,14) (4,6) (4,10) (4,8) (4,15) (5,6) (5,8) (5,7) (6,14) (6,8) (6,15) (7,14) (7,10) (7,8) (7,15) (8,14) (8,10) (8,15) (9,13) (9,12) (9,11) (10,14) (10,15) (11,13) (11,12) (12,13) (14,15)\nIs there a path between node 2 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph425-13_3", + "image": "data/connectivity/graph_visual/medium/graph425.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,16) (0,8) (0,11) (0,20) (1,14) (1,19) (2,7) (2,16) (2,4) (2,10) (2,11) (2,3) (3,4) (3,10) (4,12) (4,8) (4,17) (5,8) (5,6) (5,10) (5,11) (5,13) (6,7) (6,15) (6,18) (7,13) (8,16) (8,18) (8,20) (10,12) (10,17) (10,20) (11,15) (11,13) (12,16) (12,18) (15,16) (16,20) (19,21)\nIs there a path between node 13 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph633-16_21", + "image": "data/connectivity/graph_visual/medium/graph633.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,10) (1,9) (3,17) (3,8) (3,23) (4,17) (4,15) (4,22) (4,8) (4,23) (4,16) (6,11) (6,10) (7,21) (8,17) (8,23) (8,16) (10,18) (10,19) (11,18) (11,14) (15,23) (16,17) (16,23) (19,20) (21,22) (21,23)\nIs there a path between node 16 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph596-13_23", + "image": "data/connectivity/graph_visual/medium/graph596.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (0,16) (0,19) (0,21) (0,18) (0,6) (0,2) (0,3) (0,15) (0,4) (0,14) (1,8) (1,9) (1,11) (1,20) (1,7) (2,13) (2,16) (2,19) (2,18) (2,6) (3,13) (3,16) (3,12) (3,19) (3,5) (3,21) (3,15) (4,10) (4,16) (4,12) (4,19) (4,5) (4,21) (4,18) (4,15) (4,14) (5,16) (5,19) (5,18) (5,6) (5,15) (5,14) (6,10) (6,16) (6,19) (6,21) (6,18) (6,15) (6,14) (7,17) (7,9) (7,23) (7,11) (7,22) (8,9) (8,23) (8,22) (9,23) (9,11) (9,20) (10,13) (10,12) (10,19) (10,21) (10,14) (11,17) (11,23) (11,20) (11,22) (12,13) (12,16) (12,19) (12,21) (12,18) (12,15) (13,16) (13,19) (13,21) (13,18) (13,14) (14,16) (14,19) (14,21) (14,18) (14,15) (15,16) (15,21) (15,18) (16,19) (17,20) (17,22) (18,19) (18,21) (19,21) (20,23)\nIs there a path between node 13 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph99-4_15", + "image": "data/connectivity/graph_visual/medium/graph99.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,14) (0,2) (0,4) (0,5) (0,15) (0,7) (1,9) (1,13) (1,12) (1,3) (2,14) (2,10) (2,4) (2,8) (2,15) (2,7) (3,9) (3,13) (3,12) (3,11) (4,14) (4,6) (4,10) (4,8) (4,15) (5,6) (5,8) (5,7) (6,14) (6,8) (6,15) (7,14) (7,10) (7,8) (7,15) (8,14) (8,10) (8,15) (9,13) (9,12) (9,11) (10,14) (10,15) (11,13) (11,12) (12,13) (14,15)\nIs there a path between node 4 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph213-4_8", + "image": "data/connectivity/graph_visual/medium/graph213.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (0,6) (0,7) (0,1) (1,4) (1,6) (1,7) (2,18) (2,12) (2,5) (2,17) (2,10) (2,8) (2,16) (2,3) (2,14) (2,11) (2,13) (3,18) (3,12) (3,5) (3,17) (3,10) (3,8) (3,16) (3,14) (3,11) (3,13) (4,6) (4,7) (5,18) (5,12) (5,17) (5,10) (5,8) (5,16) (5,14) (5,11) (5,13) (6,7) (8,18) (8,12) (8,17) (8,10) (8,16) (8,14) (8,11) (8,13) (9,15) (10,18) (10,12) (10,17) (10,16) (10,14) (10,11) (10,13) (11,18) (11,12) (11,17) (11,16) (11,14) (11,13) (12,18) (12,17) (12,16) (12,14) (12,13) (13,18) (13,17) (13,16) (13,14) (14,18) (14,17) (14,16) (16,18) (16,17) (17,18)\nIs there a path between node 4 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph77-4_13", + "image": "data/connectivity/graph_visual/medium/graph77.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,11) (0,10) (1,8) (1,9) (2,13) (2,7) (2,12) (3,11) (4,14) (4,5) (6,14) (7,11) (7,12) (8,14)\nIs there a path between node 4 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph255-4_16", + "image": "data/connectivity/graph_visual/medium/graph255.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,10) (0,15) (0,5) (0,1) (0,6) (0,9) (0,2) (0,8) (1,10) (1,15) (1,5) (1,6) (1,9) (1,2) (1,8) (2,10) (2,15) (2,5) (2,6) (2,9) (2,8) (3,17) (3,16) (3,12) (3,4) (3,18) (3,11) (3,13) (4,17) (4,16) (4,12) (4,18) (4,11) (4,13) (5,10) (5,15) (5,6) (5,9) (5,8) (6,10) (6,15) (6,9) (6,8) (7,14) (8,10) (8,15) (8,9) (9,10) (9,15) (10,15) (11,17) (11,16) (11,12) (11,18) (11,13) (12,17) (12,16) (12,18) (12,13) (13,17) (13,16) (13,18) (16,17) (16,18) (17,18)\nIs there a path between node 4 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph607-0_5", + "image": "data/connectivity/graph_visual/medium/graph607.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,11) (0,8) (0,17) (0,13) (0,6) (0,3) (0,15) (0,7) (1,14) (1,19) (1,9) (1,21) (1,12) (1,22) (1,4) (1,18) (1,5) (1,10) (1,20) (2,16) (3,23) (3,11) (3,8) (3,17) (3,13) (3,6) (3,15) (3,7) (4,14) (4,19) (4,9) (4,21) (4,12) (4,22) (4,18) (4,5) (4,10) (4,20) (5,14) (5,19) (5,9) (5,21) (5,12) (5,22) (5,18) (5,10) (5,20) (6,23) (6,11) (6,8) (6,17) (6,13) (6,15) (6,7) (7,23) (7,11) (7,8) (7,17) (7,13) (7,15) (8,23) (8,11) (8,17) (8,13) (8,15) (9,14) (9,19) (9,21) (9,12) (9,22) (9,18) (9,10) (9,20) (10,14) (10,19) (10,21) (10,12) (10,22) (10,18) (10,20) (11,23) (11,17) (11,13) (11,15) (12,14) (12,19) (12,21) (12,22) (12,18) (12,20) (13,23) (13,17) (13,15) (14,19) (14,21) (14,22) (14,18) (14,20) (15,23) (15,17) (17,23) (18,19) (18,21) (18,22) (18,20) (19,21) (19,22) (19,20) (20,21) (20,22) (21,22)\nIs there a path between node 0 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph820-13_15", + "image": "data/connectivity/graph_visual/medium/graph820.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,6) (1,2) (1,4) (1,12) (1,19) (1,3) (1,18) (1,21) (1,16) (1,22) (1,23) (1,24) (1,20) (1,8) (1,13) (1,9) (2,6) (2,4) (2,14) (2,17) (2,15) (2,19) (2,3) (2,18) (2,21) (2,16) (2,22) (2,23) (2,24) (2,20) (2,11) (2,8) (2,13) (2,9) (3,7) (3,6) (3,4) (3,14) (3,15) (3,12) (3,18) (3,16) (3,22) (3,23) (3,24) (3,20) (3,11) (3,8) (4,6) (4,14) (4,17) (4,15) (4,12) (4,19) (4,21) (4,22) (4,23) (4,11) (4,13) (4,9) (5,10) (6,14) (6,15) (6,19) (6,18) (6,21) (6,22) (6,23) (6,20) (6,11) (6,8) (6,13) (6,9) (7,14) (7,18) (7,16) (7,22) (7,23) (7,20) (7,11) (7,9) (8,14) (8,15) (8,19) (8,21) (8,16) (8,22) (8,23) (8,20) (8,11) (8,13) (8,9) (9,14) (9,15) (9,12) (9,19) (9,18) (9,21) (9,16) (9,22) (9,23) (9,20) (9,13) (11,14) (11,17) (11,15) (11,12) (11,21) (11,22) (11,24) (11,20) (12,17) (12,15) (12,19) (12,18) (12,21) (12,16) (12,23) (12,13) (13,17) (13,15) (13,19) (13,18) (13,21) (13,22) (13,23) (13,24) (14,17) (14,15) (14,19) (14,18) (14,16) (14,20) (15,17) (15,19) (15,16) (15,22) (15,24) (15,20) (16,17) (16,19) (16,18) (16,22) (16,23) (16,24) (16,20) (17,19) (17,21) (17,22) (18,19) (18,21) (18,22) (18,23) (18,24) (19,23) (19,20) (20,21) (20,24) (21,22) (21,24) (22,24)\nIs there a path between node 13 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph588-4_16", + "image": "data/connectivity/graph_visual/medium/graph588.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (1,5) (1,12) (1,3) (1,17) (1,15) (1,16) (2,21) (2,9) (2,11) (2,13) (2,4) (2,14) (3,23) (3,13) (3,15) (3,19) (3,14) (4,5) (4,12) (4,9) (4,17) (4,11) (5,8) (5,12) (5,22) (5,16) (5,14) (6,10) (7,18) (7,10) (8,12) (8,17) (8,23) (8,11) (8,16) (9,22) (9,13) (11,21) (11,15) (12,17) (12,23) (12,16) (12,14) (13,22) (13,23) (13,19) (13,16) (14,20) (14,22) (14,17) (15,20) (15,19) (16,22) (16,17) (16,23) (16,19) (19,23) (20,22) (22,23)\nIs there a path between node 4 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph276-19_8", + "image": "data/connectivity/graph_visual/medium/graph276.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,10) (1,9) (1,16) (1,4) (1,12) (2,8) (2,19) (2,7) (2,14) (2,17) (2,5) (2,18) (2,6) (2,11) (2,3) (2,13) (2,15) (3,8) (3,19) (3,7) (3,14) (3,17) (3,5) (3,18) (3,6) (3,11) (3,13) (3,15) (4,10) (4,9) (4,16) (4,12) (5,8) (5,19) (5,7) (5,14) (5,17) (5,18) (5,6) (5,11) (5,13) (5,15) (6,8) (6,19) (6,7) (6,14) (6,17) (6,18) (6,11) (6,13) (6,15) (7,8) (7,19) (7,14) (7,17) (7,18) (7,11) (7,13) (7,15) (8,19) (8,14) (8,17) (8,18) (8,11) (8,13) (8,15) (9,10) (9,16) (9,12) (10,16) (10,12) (11,19) (11,14) (11,17) (11,18) (11,13) (11,15) (12,16) (13,19) (13,14) (13,17) (13,18) (13,15) (14,19) (14,17) (14,18) (14,15) (15,19) (15,17) (15,18) (17,19) (17,18) (18,19)\nIs there a path between node 19 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph55-2_13", + "image": "data/connectivity/graph_visual/medium/graph55.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (0,13) (1,10) (1,4) (1,12) (3,11) (3,10) (3,7) (3,12) (4,6) (4,9) (4,10) (5,6) (5,12) (6,11) (6,9) (9,10) (10,12)\nIs there a path between node 2 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph62-3_5", + "image": "data/connectivity/graph_visual/medium/graph62.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,12) (0,11) (0,13) (0,5) (1,12) (1,11) (1,7) (1,13) (1,5) (2,6) (2,8) (2,9) (2,10) (3,4) (3,8) (3,9) (3,10) (4,6) (4,8) (4,9) (5,11) (5,7) (6,8) (6,9) (6,10) (7,12) (7,11) (8,10) (9,10) (12,13)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph310-2_3", + "image": "data/connectivity/graph_visual/medium/graph310.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,10) (0,19) (0,16) (0,7) (0,8) (0,4) (0,3) (0,11) (0,1) (0,18) (0,9) (0,5) (0,2) (0,13) (1,17) (1,10) (1,19) (1,16) (1,7) (1,8) (1,4) (1,3) (1,11) (1,18) (1,9) (1,5) (1,2) (1,13) (2,17) (2,10) (2,19) (2,16) (2,7) (2,8) (2,4) (2,3) (2,11) (2,18) (2,9) (2,5) (2,13) (3,17) (3,10) (3,19) (3,16) (3,7) (3,8) (3,4) (3,11) (3,18) (3,9) (3,5) (3,13) (4,17) (4,10) (4,19) (4,16) (4,7) (4,8) (4,11) (4,18) (4,9) (4,5) (4,13) (5,17) (5,10) (5,19) (5,16) (5,7) (5,8) (5,11) (5,18) (5,9) (5,13) (6,15) (7,17) (7,10) (7,19) (7,16) (7,8) (7,11) (7,18) (7,9) (7,13) (8,17) (8,10) (8,19) (8,16) (8,11) (8,18) (8,9) (8,13) (9,17) (9,10) (9,19) (9,16) (9,11) (9,18) (9,13) (10,17) (10,19) (10,16) (10,11) (10,18) (10,13) (11,17) (11,19) (11,16) (11,18) (11,13) (12,14) (13,17) (13,19) (13,16) (13,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph34-6_3", + "image": "data/connectivity/graph_visual/medium/graph34.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,4) (0,3) (0,11) (0,8) (0,2) (0,12) (0,9) (0,1) (1,4) (1,3) (1,6) (1,11) (1,8) (1,7) (1,10) (1,2) (1,12) (2,3) (2,6) (2,11) (2,8) (2,9) (3,6) (3,11) (3,8) (3,7) (3,10) (3,9) (4,6) (4,11) (4,8) (4,7) (4,10) (4,12) (4,9) (6,8) (6,10) (7,10) (7,12) (7,9) (8,11) (8,10) (8,12) (9,10) (10,12)\nIs there a path between node 6 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph769-9_6", + "image": "data/connectivity/graph_visual/medium/graph769.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,10) (0,7) (0,11) (0,9) (0,21) (0,12) (0,19) (0,17) (0,24) (0,23) (0,1) (0,4) (0,8) (0,6) (0,16) (0,14) (0,22) (0,20) (0,13) (1,2) (1,10) (1,7) (1,11) (1,9) (1,21) (1,12) (1,19) (1,17) (1,24) (1,23) (1,4) (1,8) (1,6) (1,16) (1,14) (1,22) (1,20) (1,13) (2,10) (2,7) (2,11) (2,9) (2,21) (2,12) (2,19) (2,17) (2,24) (2,23) (2,4) (2,8) (2,6) (2,16) (2,14) (2,22) (2,20) (2,13) (3,5) (3,15) (3,18) (4,10) (4,7) (4,11) (4,9) (4,21) (4,12) (4,19) (4,17) (4,24) (4,23) (4,8) (4,6) (4,16) (4,14) (4,22) (4,20) (4,13) (5,15) (5,18) (6,10) (6,7) (6,11) (6,9) (6,21) (6,12) (6,19) (6,17) (6,24) (6,23) (6,8) (6,16) (6,14) (6,22) (6,20) (6,13) (7,10) (7,11) (7,9) (7,21) (7,12) (7,19) (7,17) (7,24) (7,23) (7,8) (7,16) (7,14) (7,22) (7,20) (7,13) (8,10) (8,11) (8,9) (8,21) (8,12) (8,19) (8,17) (8,24) (8,23) (8,16) (8,14) (8,22) (8,20) (8,13) (9,10) (9,11) (9,21) (9,12) (9,19) (9,17) (9,24) (9,23) (9,16) (9,14) (9,22) (9,20) (9,13) (10,11) (10,21) (10,12) (10,19) (10,17) (10,24) (10,23) (10,16) (10,14) (10,22) (10,20) (10,13) (11,21) (11,12) (11,19) (11,17) (11,24) (11,23) (11,16) (11,14) (11,22) (11,20) (11,13) (12,21) (12,19) (12,17) (12,24) (12,23) (12,16) (12,14) (12,22) (12,20) (12,13) (13,21) (13,19) (13,17) (13,24) (13,23) (13,16) (13,14) (13,22) (13,20) (14,21) (14,19) (14,17) (14,24) (14,23) (14,16) (14,22) (14,20) (15,18) (16,21) (16,19) (16,17) (16,24) (16,23) (16,22) (16,20) (17,21) (17,19) (17,24) (17,23) (17,22) (17,20) (19,21) (19,24) (19,23) (19,22) (19,20) (20,21) (20,24) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nIs there a path between node 9 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph243-18_8", + "image": "data/connectivity/graph_visual/medium/graph243.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,3) (0,4) (0,8) (0,13) (0,7) (0,2) (0,14) (0,18) (0,1) (0,10) (0,5) (1,15) (1,4) (1,9) (1,8) (1,7) (1,17) (1,2) (1,10) (1,12) (1,5) (2,15) (2,4) (2,8) (2,17) (2,14) (2,18) (2,10) (2,5) (3,15) (3,4) (3,9) (3,13) (3,7) (3,14) (3,18) (3,10) (4,9) (4,8) (4,7) (4,17) (4,14) (4,18) (4,12) (4,5) (5,15) (5,8) (5,13) (5,11) (5,14) (5,18) (6,16) (7,15) (7,8) (7,13) (7,18) (7,10) (8,15) (8,9) (8,13) (8,11) (8,14) (8,18) (8,10) (8,12) (9,15) (9,13) (9,17) (9,11) (9,14) (9,18) (9,10) (9,12) (10,15) (10,18) (11,15) (11,13) (11,18) (11,12) (12,15) (12,17) (12,18) (13,15) (13,17) (13,18) (14,15) (14,18) (15,17) (17,18)\nIs there a path between node 18 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph466-20_6", + "image": "data/connectivity/graph_visual/medium/graph466.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,10) (0,14) (0,1) (0,11) (0,17) (0,13) (1,2) (1,10) (1,14) (1,11) (1,17) (1,13) (2,10) (2,14) (2,11) (2,17) (2,13) (3,19) (3,9) (3,12) (3,16) (3,5) (3,7) (3,18) (3,21) (4,15) (4,20) (4,6) (4,8) (5,19) (5,9) (5,12) (5,16) (5,7) (5,18) (5,21) (6,15) (6,20) (6,8) (7,19) (7,9) (7,12) (7,16) (7,18) (7,21) (8,15) (8,20) (9,19) (9,12) (9,16) (9,18) (9,21) (10,14) (10,11) (10,17) (10,13) (11,14) (11,17) (11,13) (12,19) (12,16) (12,18) (12,21) (13,14) (13,17) (14,17) (15,20) (16,19) (16,18) (16,21) (18,19) (18,21) (19,21)\nIs there a path between node 20 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph629-20_5", + "image": "data/connectivity/graph_visual/medium/graph629.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,14) (2,17) (2,7) (4,16) (4,11) (4,20) (4,12) (5,15) (6,15) (7,10) (7,12) (9,22) (9,18) (10,16) (11,21) (11,16) (12,21) (12,17) (14,23) (14,19) (16,20) (17,21) (20,21)\nIs there a path between node 20 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph13-10_2", + "image": "data/connectivity/graph_visual/medium/graph13.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (0,7) (0,10) (0,2) (1,8) (1,4) (1,9) (1,3) (1,5) (2,6) (2,7) (2,10) (3,8) (3,4) (3,9) (3,5) (4,8) (4,9) (4,5) (5,8) (5,9) (6,7) (6,10) (7,10) (8,9)\nIs there a path between node 10 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph805-9_21", + "image": "data/connectivity/graph_visual/medium/graph805.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,1) (1,12) (1,15) (2,11) (2,19) (2,16) (2,10) (3,17) (3,11) (3,19) (3,7) (3,23) (3,10) (6,18) (7,11) (7,19) (7,23) (8,12) (8,15) (9,17) (9,11) (9,21) (9,22) (9,10) (10,24) (10,14) (11,17) (11,24) (11,14) (11,21) (11,22) (12,15) (14,23) (14,16) (16,24) (16,21) (17,24) (17,19) (19,24) (19,22) (21,24) (23,24)\nIs there a path between node 9 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph726-16_15", + "image": "data/connectivity/graph_visual/medium/graph726.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (0,22) (0,16) (0,23) (0,12) (0,14) (0,1) (0,4) (0,21) (0,10) (0,6) (0,20) (0,3) (0,8) (0,9) (0,2) (0,24) (0,19) (0,13) (0,7) (0,17) (1,18) (1,22) (1,16) (1,23) (1,12) (1,14) (1,4) (1,21) (1,10) (1,6) (1,20) (1,3) (1,8) (1,9) (1,2) (1,24) (1,19) (1,13) (1,7) (1,17) (2,18) (2,22) (2,16) (2,23) (2,12) (2,14) (2,4) (2,21) (2,10) (2,6) (2,20) (2,3) (2,8) (2,9) (2,24) (2,19) (2,13) (2,7) (2,17) (3,18) (3,22) (3,16) (3,23) (3,12) (3,14) (3,4) (3,21) (3,10) (3,6) (3,20) (3,8) (3,9) (3,24) (3,19) (3,13) (3,7) (3,17) (4,18) (4,22) (4,16) (4,23) (4,12) (4,14) (4,21) (4,10) (4,6) (4,20) (4,8) (4,9) (4,24) (4,19) (4,13) (4,7) (4,17) (5,11) (5,15) (6,18) (6,22) (6,16) (6,23) (6,12) (6,14) (6,21) (6,10) (6,20) (6,8) (6,9) (6,24) (6,19) (6,13) (6,7) (6,17) (7,18) (7,22) (7,16) (7,23) (7,12) (7,14) (7,21) (7,10) (7,20) (7,8) (7,9) (7,24) (7,19) (7,13) (7,17) (8,18) (8,22) (8,16) (8,23) (8,12) (8,14) (8,21) (8,10) (8,20) (8,9) (8,24) (8,19) (8,13) (8,17) (9,18) (9,22) (9,16) (9,23) (9,12) (9,14) (9,21) (9,10) (9,20) (9,24) (9,19) (9,13) (9,17) (10,18) (10,22) (10,16) (10,23) (10,12) (10,14) (10,21) (10,20) (10,24) (10,19) (10,13) (10,17) (11,15) (12,18) (12,22) (12,16) (12,23) (12,14) (12,21) (12,20) (12,24) (12,19) (12,13) (12,17) (13,18) (13,22) (13,16) (13,23) (13,14) (13,21) (13,20) (13,24) (13,19) (13,17) (14,18) (14,22) (14,16) (14,23) (14,21) (14,20) (14,24) (14,19) (14,17) (16,18) (16,22) (16,23) (16,21) (16,20) (16,24) (16,19) (16,17) (17,18) (17,22) (17,23) (17,21) (17,20) (17,24) (17,19) (18,22) (18,23) (18,21) (18,20) (18,24) (18,19) (19,22) (19,23) (19,21) (19,20) (19,24) (20,22) (20,23) (20,21) (20,24) (21,22) (21,23) (21,24) (22,23) (22,24) (23,24)\nIs there a path between node 16 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph255-8_10", + "image": "data/connectivity/graph_visual/medium/graph255.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,10) (0,15) (0,5) (0,1) (0,6) (0,9) (0,2) (0,8) (1,10) (1,15) (1,5) (1,6) (1,9) (1,2) (1,8) (2,10) (2,15) (2,5) (2,6) (2,9) (2,8) (3,17) (3,16) (3,12) (3,4) (3,18) (3,11) (3,13) (4,17) (4,16) (4,12) (4,18) (4,11) (4,13) (5,10) (5,15) (5,6) (5,9) (5,8) (6,10) (6,15) (6,9) (6,8) (7,14) (8,10) (8,15) (8,9) (9,10) (9,15) (10,15) (11,17) (11,16) (11,12) (11,18) (11,13) (12,17) (12,16) (12,18) (12,13) (13,17) (13,16) (13,18) (16,17) (16,18) (17,18)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph71-14_6", + "image": "data/connectivity/graph_visual/medium/graph71.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,2) (0,5) (0,12) (0,11) (0,8) (0,1) (0,13) (0,10) (0,3) (1,2) (1,5) (1,12) (1,11) (1,8) (1,13) (1,10) (1,3) (2,5) (2,12) (2,11) (2,8) (2,13) (2,10) (2,3) (3,5) (3,12) (3,11) (3,8) (3,13) (3,10) (4,9) (4,6) (4,7) (4,14) (5,12) (5,11) (5,8) (5,13) (5,10) (6,9) (6,7) (6,14) (7,9) (7,14) (8,12) (8,11) (8,13) (8,10) (9,14) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nIs there a path between node 14 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph550-8_21", + "image": "data/connectivity/graph_visual/medium/graph550.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,10) (0,19) (0,13) (0,20) (1,15) (1,23) (3,5) (3,7) (3,14) (3,22) (4,18) (4,19) (4,20) (5,7) (5,14) (5,15) (5,12) (6,10) (7,11) (7,14) (7,22) (7,8) (8,14) (8,22) (8,21) (10,18) (10,19) (10,13) (10,20) (11,17) (11,14) (11,23) (11,16) (12,23) (13,18) (13,20) (14,22) (14,21) (15,21) (15,16) (17,21) (18,19) (19,20) (21,22)\nIs there a path between node 8 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph383-12_16", + "image": "data/connectivity/graph_visual/medium/graph383.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,6) (0,14) (0,17) (0,16) (0,7) (0,5) (0,18) (0,12) (0,13) (0,2) (0,19) (2,6) (2,14) (2,17) (2,16) (2,7) (2,5) (2,18) (2,12) (2,13) (2,19) (3,9) (3,4) (3,11) (3,8) (3,10) (3,15) (3,20) (4,9) (4,11) (4,8) (4,10) (4,15) (4,20) (5,6) (5,14) (5,17) (5,16) (5,7) (5,18) (5,12) (5,13) (5,19) (6,14) (6,17) (6,16) (6,7) (6,18) (6,12) (6,13) (6,19) (7,14) (7,17) (7,16) (7,18) (7,12) (7,13) (7,19) (8,9) (8,11) (8,10) (8,15) (8,20) (9,11) (9,10) (9,15) (9,20) (10,11) (10,15) (10,20) (11,15) (11,20) (12,14) (12,17) (12,16) (12,18) (12,13) (12,19) (13,14) (13,17) (13,16) (13,18) (13,19) (14,17) (14,16) (14,18) (14,19) (15,20) (16,17) (16,18) (16,19) (17,18) (17,19) (18,19)\nIs there a path between node 12 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph356-19_1", + "image": "data/connectivity/graph_visual/medium/graph356.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,11) (1,16) (1,10) (1,12) (2,16) (2,11) (3,8) (3,13) (4,20) (4,8) (4,17) (5,14) (6,15) (7,13) (7,9) (7,18) (7,17) (8,9) (9,15) (10,19) (11,14) (11,12) (12,14) (17,18) (18,20)\nIs there a path between node 19 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph644-10_8", + "image": "data/connectivity/graph_visual/medium/graph644.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,9) (1,4) (2,16) (4,18) (4,11) (5,14) (6,8) (7,15) (7,21) (9,15) (9,19) (13,15) (13,16) (15,20) (16,20) (19,21) (19,20)\nIs there a path between node 10 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph310-6_9", + "image": "data/connectivity/graph_visual/medium/graph310.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,10) (0,19) (0,16) (0,7) (0,8) (0,4) (0,3) (0,11) (0,1) (0,18) (0,9) (0,5) (0,2) (0,13) (1,17) (1,10) (1,19) (1,16) (1,7) (1,8) (1,4) (1,3) (1,11) (1,18) (1,9) (1,5) (1,2) (1,13) (2,17) (2,10) (2,19) (2,16) (2,7) (2,8) (2,4) (2,3) (2,11) (2,18) (2,9) (2,5) (2,13) (3,17) (3,10) (3,19) (3,16) (3,7) (3,8) (3,4) (3,11) (3,18) (3,9) (3,5) (3,13) (4,17) (4,10) (4,19) (4,16) (4,7) (4,8) (4,11) (4,18) (4,9) (4,5) (4,13) (5,17) (5,10) (5,19) (5,16) (5,7) (5,8) (5,11) (5,18) (5,9) (5,13) (6,15) (7,17) (7,10) (7,19) (7,16) (7,8) (7,11) (7,18) (7,9) (7,13) (8,17) (8,10) (8,19) (8,16) (8,11) (8,18) (8,9) (8,13) (9,17) (9,10) (9,19) (9,16) (9,11) (9,18) (9,13) (10,17) (10,19) (10,16) (10,11) (10,18) (10,13) (11,17) (11,19) (11,16) (11,18) (11,13) (12,14) (13,17) (13,19) (13,16) (13,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nIs there a path between node 6 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph335-3_13", + "image": "data/connectivity/graph_visual/medium/graph335.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,6) (0,19) (0,17) (0,3) (0,10) (0,14) (1,7) (1,8) (1,15) (1,13) (2,9) (2,12) (2,18) (2,4) (3,6) (3,19) (3,17) (3,16) (3,10) (3,14) (4,12) (4,18) (5,9) (5,18) (6,19) (6,17) (6,16) (6,14) (6,20) (7,8) (7,15) (7,13) (9,12) (9,18) (10,16) (10,14) (10,20) (11,15) (12,18) (13,15) (14,19) (14,17) (14,20) (16,19) (16,17) (17,20) (19,20)\nIs there a path between node 3 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph780-23_15", + "image": "data/connectivity/graph_visual/medium/graph780.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,18) (0,15) (0,12) (0,5) (1,24) (2,21) (2,23) (2,9) (2,15) (2,19) (3,23) (3,15) (3,8) (3,16) (5,21) (5,22) (5,6) (5,19) (5,8) (5,10) (5,16) (6,14) (6,22) (6,9) (6,12) (6,17) (9,23) (9,22) (9,20) (9,10) (10,22) (10,18) (10,19) (11,24) (12,14) (13,14) (13,21) (13,23) (13,18) (13,15) (14,21) (14,18) (14,15) (14,16) (15,20) (15,17) (17,23) (17,22) (17,18) (17,20) (17,19) (18,19) (19,20) (21,23)\nIs there a path between node 23 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph757-1_10", + "image": "data/connectivity/graph_visual/medium/graph757.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,5) (0,22) (0,20) (0,1) (0,7) (0,9) (0,23) (0,4) (0,8) (0,17) (0,6) (0,21) (0,12) (0,3) (0,16) (0,18) (1,5) (1,20) (1,13) (1,7) (1,9) (1,23) (1,14) (1,4) (1,8) (1,6) (1,21) (1,12) (1,3) (1,24) (1,16) (1,2) (1,11) (2,5) (2,20) (2,13) (2,9) (2,23) (2,14) (2,8) (2,21) (2,12) (2,3) (2,11) (2,18) (3,5) (3,22) (3,20) (3,13) (3,9) (3,14) (3,4) (3,8) (3,6) (3,24) (3,16) (3,11) (3,18) (4,5) (4,22) (4,20) (4,7) (4,9) (4,23) (4,14) (4,17) (4,21) (4,12) (4,24) (5,22) (5,20) (5,7) (5,23) (5,14) (5,8) (5,17) (5,12) (5,16) (5,11) (5,18) (6,20) (6,13) (6,7) (6,23) (6,14) (6,17) (6,24) (6,16) (6,11) (6,18) (7,22) (7,13) (7,23) (7,14) (7,8) (7,17) (7,12) (7,24) (7,16) (7,11) (7,18) (8,14) (8,12) (8,24) (8,16) (8,11) (8,18) (9,22) (9,20) (9,13) (9,23) (9,14) (9,17) (9,21) (9,12) (9,16) (9,11) (9,18) (10,15) (10,19) (11,22) (11,13) (11,23) (11,17) (11,12) (11,16) (12,22) (12,20) (12,14) (12,17) (12,21) (12,24) (12,16) (12,18) (13,22) (13,23) (13,14) (13,17) (13,21) (13,24) (13,16) (13,18) (14,20) (14,23) (14,24) (14,18) (15,19) (16,22) (16,20) (16,23) (16,24) (16,18) (17,22) (17,20) (17,23) (17,21) (17,24) (18,22) (18,20) (18,23) (18,21) (18,24) (20,22) (20,23) (20,24) (21,22) (21,23) (21,24)\nIs there a path between node 1 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph131-3_4", + "image": "data/connectivity/graph_visual/medium/graph131.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,5) (0,12) (0,10) (0,9) (0,6) (0,7) (0,15) (0,4) (0,2) (0,13) (0,8) (0,16) (1,14) (1,11) (1,3) (2,5) (2,12) (2,10) (2,9) (2,6) (2,7) (2,15) (2,4) (2,13) (2,8) (2,16) (3,14) (3,11) (4,5) (4,12) (4,10) (4,9) (4,6) (4,7) (4,15) (4,13) (4,8) (4,16) (5,12) (5,10) (5,9) (5,6) (5,7) (5,15) (5,13) (5,8) (5,16) (6,12) (6,10) (6,9) (6,7) (6,15) (6,13) (6,8) (6,16) (7,12) (7,10) (7,9) (7,15) (7,13) (7,8) (7,16) (8,12) (8,10) (8,9) (8,15) (8,13) (8,16) (9,12) (9,10) (9,15) (9,13) (9,16) (10,12) (10,15) (10,13) (10,16) (11,14) (12,15) (12,13) (12,16) (13,15) (13,16) (15,16)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph181-15_10", + "image": "data/connectivity/graph_visual/medium/graph181.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,17) (0,16) (0,5) (0,12) (0,13) (0,14) (0,7) (0,1) (1,5) (1,12) (1,9) (3,11) (3,6) (3,15) (5,17) (5,16) (5,12) (5,14) (5,7) (6,8) (7,16) (7,12) (7,14) (7,10) (7,9) (9,17) (9,16) (9,12) (9,14) (10,17) (10,16) (10,12) (10,13) (10,14) (11,15) (12,17) (12,16) (13,16) (13,14) (14,17) (14,16) (16,17)\nIs there a path between node 15 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph637-1_9", + "image": "data/connectivity/graph_visual/medium/graph637.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,12) (0,2) (1,13) (1,20) (1,6) (1,8) (1,3) (2,22) (3,10) (3,13) (3,20) (3,15) (3,6) (3,12) (3,14) (4,5) (4,23) (5,16) (5,23) (5,11) (6,12) (6,14) (6,21) (7,22) (7,8) (8,18) (8,22) (8,14) (9,16) (9,23) (9,19) (10,18) (10,15) (10,12) (10,22) (11,16) (12,18) (13,18) (13,14) (14,21) (15,21) (16,19) (17,20) (17,18) (20,22) (21,22)\nIs there a path between node 1 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph46-7_12", + "image": "data/connectivity/graph_visual/medium/graph46.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,4) (0,9) (0,2) (0,5) (0,10) (0,1) (1,4) (1,9) (1,2) (1,5) (1,10) (2,4) (2,9) (2,5) (2,10) (3,11) (3,8) (3,12) (3,7) (3,6) (4,9) (4,5) (4,10) (5,9) (5,10) (6,11) (6,8) (6,12) (6,7) (7,11) (7,8) (7,12) (8,11) (8,12) (9,10) (11,12)\nIs there a path between node 7 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph717-6_23", + "image": "data/connectivity/graph_visual/medium/graph717.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,13) (0,6) (0,16) (0,20) (1,21) (1,18) (1,2) (1,23) (1,7) (1,5) (1,11) (1,9) (1,3) (1,19) (1,14) (1,24) (2,4) (2,22) (2,18) (2,23) (2,5) (2,11) (2,19) (3,18) (3,5) (3,11) (3,19) (3,24) (4,21) (4,22) (4,8) (4,18) (4,23) (4,7) (4,5) (4,9) (4,14) (5,8) (5,7) (5,11) (5,9) (5,19) (6,10) (6,13) (6,16) (6,20) (6,12) (6,15) (7,21) (7,8) (7,23) (7,11) (7,9) (7,19) (8,18) (8,11) (8,14) (8,24) (9,21) (9,22) (9,18) (9,19) (9,14) (9,24) (10,13) (10,20) (10,15) (11,21) (11,22) (11,18) (11,23) (11,14) (12,13) (12,16) (12,20) (13,16) (13,15) (14,22) (14,18) (14,19) (14,24) (15,16) (15,20) (16,20) (18,22) (18,23) (18,19) (18,24) (19,22) (19,23) (19,24) (21,22) (22,23) (22,24) (23,24)\nIs there a path between node 6 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph564-18_2", + "image": "data/connectivity/graph_visual/medium/graph564.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,12) (0,1) (0,7) (0,16) (0,13) (0,9) (0,2) (0,10) (0,21) (0,19) (0,3) (0,20) (0,8) (0,23) (0,5) (0,4) (0,6) (0,22) (1,15) (1,12) (1,7) (1,16) (1,13) (1,9) (1,2) (1,10) (1,21) (1,19) (1,3) (1,20) (1,8) (1,23) (1,5) (1,4) (1,6) (1,22) (2,15) (2,12) (2,7) (2,16) (2,13) (2,9) (2,10) (2,21) (2,19) (2,3) (2,20) (2,8) (2,23) (2,5) (2,4) (2,6) (2,22) (3,15) (3,12) (3,7) (3,16) (3,13) (3,9) (3,10) (3,21) (3,19) (3,20) (3,8) (3,23) (3,5) (3,4) (3,6) (3,22) (4,15) (4,12) (4,7) (4,16) (4,13) (4,9) (4,10) (4,21) (4,19) (4,20) (4,8) (4,23) (4,5) (4,6) (4,22) (5,15) (5,12) (5,7) (5,16) (5,13) (5,9) (5,10) (5,21) (5,19) (5,20) (5,8) (5,23) (5,6) (5,22) (6,15) (6,12) (6,7) (6,16) (6,13) (6,9) (6,10) (6,21) (6,19) (6,20) (6,8) (6,23) (6,22) (7,15) (7,12) (7,16) (7,13) (7,9) (7,10) (7,21) (7,19) (7,20) (7,8) (7,23) (7,22) (8,15) (8,12) (8,16) (8,13) (8,9) (8,10) (8,21) (8,19) (8,20) (8,23) (8,22) (9,15) (9,12) (9,16) (9,13) (9,10) (9,21) (9,19) (9,20) (9,23) (9,22) (10,15) (10,12) (10,16) (10,13) (10,21) (10,19) (10,20) (10,23) (10,22) (11,17) (11,14) (11,18) (12,15) (12,16) (12,13) (12,21) (12,19) (12,20) (12,23) (12,22) (13,15) (13,16) (13,21) (13,19) (13,20) (13,23) (13,22) (14,17) (14,18) (15,16) (15,21) (15,19) (15,20) (15,23) (15,22) (16,21) (16,19) (16,20) (16,23) (16,22) (17,18) (19,21) (19,20) (19,23) (19,22) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 18 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph140-8_2", + "image": "data/connectivity/graph_visual/medium/graph140.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,14) (1,9) (2,14) (2,6) (2,5) (3,16) (4,7) (4,9) (4,15) (5,9) (5,15) (6,14) (6,9) (6,12) (7,14) (7,15) (7,12) (8,17) (10,13) (12,14)\nIs there a path between node 8 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph675-22_16", + "image": "data/connectivity/graph_visual/medium/graph675.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,22) (0,21) (0,14) (0,19) (0,13) (0,18) (0,12) (0,15) (0,6) (0,7) (0,10) (0,20) (0,2) (0,4) (0,8) (0,17) (0,23) (1,3) (1,16) (1,11) (1,9) (2,5) (2,22) (2,21) (2,14) (2,19) (2,13) (2,18) (2,12) (2,15) (2,6) (2,7) (2,10) (2,20) (2,4) (2,8) (2,17) (2,23) (3,16) (3,11) (3,9) (4,5) (4,22) (4,21) (4,14) (4,19) (4,13) (4,18) (4,12) (4,15) (4,6) (4,7) (4,10) (4,20) (4,8) (4,17) (4,23) (5,22) (5,21) (5,14) (5,19) (5,13) (5,18) (5,12) (5,15) (5,6) (5,7) (5,10) (5,20) (5,8) (5,17) (5,23) (6,22) (6,21) (6,14) (6,19) (6,13) (6,18) (6,12) (6,15) (6,7) (6,10) (6,20) (6,8) (6,17) (6,23) (7,22) (7,21) (7,14) (7,19) (7,13) (7,18) (7,12) (7,15) (7,10) (7,20) (7,8) (7,17) (7,23) (8,22) (8,21) (8,14) (8,19) (8,13) (8,18) (8,12) (8,15) (8,10) (8,20) (8,17) (8,23) (9,16) (9,11) (10,22) (10,21) (10,14) (10,19) (10,13) (10,18) (10,12) (10,15) (10,20) (10,17) (10,23) (11,16) (12,22) (12,21) (12,14) (12,19) (12,13) (12,18) (12,15) (12,20) (12,17) (12,23) (13,22) (13,21) (13,14) (13,19) (13,18) (13,15) (13,20) (13,17) (13,23) (14,22) (14,21) (14,19) (14,18) (14,15) (14,20) (14,17) (14,23) (15,22) (15,21) (15,19) (15,18) (15,20) (15,17) (15,23) (17,22) (17,21) (17,19) (17,18) (17,20) (17,23) (18,22) (18,21) (18,19) (18,20) (18,23) (19,22) (19,21) (19,20) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 22 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph313-12_0", + "image": "data/connectivity/graph_visual/medium/graph313.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,6) (0,5) (1,7) (1,8) (1,19) (1,2) (1,14) (1,11) (1,10) (1,18) (1,13) (1,16) (1,4) (1,12) (1,15) (1,9) (1,17) (1,3) (2,7) (2,8) (2,19) (2,14) (2,11) (2,10) (2,18) (2,13) (2,16) (2,4) (2,12) (2,15) (2,9) (2,17) (2,3) (3,7) (3,8) (3,19) (3,14) (3,11) (3,10) (3,18) (3,13) (3,16) (3,4) (3,12) (3,15) (3,9) (3,17) (4,7) (4,8) (4,19) (4,14) (4,11) (4,10) (4,18) (4,13) (4,16) (4,12) (4,15) (4,9) (4,17) (5,6) (7,8) (7,19) (7,14) (7,11) (7,10) (7,18) (7,13) (7,16) (7,12) (7,15) (7,9) (7,17) (8,19) (8,14) (8,11) (8,10) (8,18) (8,13) (8,16) (8,12) (8,15) (8,9) (8,17) (9,19) (9,14) (9,11) (9,10) (9,18) (9,13) (9,16) (9,12) (9,15) (9,17) (10,19) (10,14) (10,11) (10,18) (10,13) (10,16) (10,12) (10,15) (10,17) (11,19) (11,14) (11,18) (11,13) (11,16) (11,12) (11,15) (11,17) (12,19) (12,14) (12,18) (12,13) (12,16) (12,15) (12,17) (13,19) (13,14) (13,18) (13,16) (13,15) (13,17) (14,19) (14,18) (14,16) (14,15) (14,17) (15,19) (15,18) (15,16) (15,17) (16,19) (16,18) (16,17) (17,19) (17,18) (18,19)\nIs there a path between node 12 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph824-19_14", + "image": "data/connectivity/graph_visual/medium/graph824.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,8) (0,12) (0,5) (0,14) (0,15) (0,17) (0,11) (0,16) (0,1) (1,9) (1,8) (1,12) (1,5) (1,14) (1,15) (1,11) (1,16) (1,22) (2,9) (2,8) (2,15) (2,17) (2,11) (2,16) (2,6) (3,20) (3,24) (3,4) (3,13) (3,18) (3,19) (4,24) (4,21) (4,10) (4,18) (4,7) (5,9) (5,12) (5,15) (5,6) (5,22) (6,9) (6,8) (6,12) (6,14) (6,15) (6,17) (6,11) (7,20) (7,24) (7,23) (7,13) (7,21) (7,18) (7,19) (8,12) (8,14) (8,15) (8,11) (8,16) (8,22) (9,12) (9,17) (9,16) (9,22) (10,20) (10,23) (10,13) (10,19) (11,12) (11,14) (11,15) (11,17) (11,16) (12,15) (12,16) (12,22) (13,20) (13,24) (13,21) (13,18) (14,15) (14,17) (14,22) (15,17) (15,22) (16,17) (16,22) (18,20) (18,24) (18,23) (18,21) (18,19) (19,24) (20,24) (20,23) (20,21) (21,24) (21,23) (23,24)\nIs there a path between node 19 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph835-9_16", + "image": "data/connectivity/graph_visual/medium/graph835.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (0,3) (1,24) (1,12) (1,17) (1,9) (1,15) (1,16) (1,2) (1,10) (1,13) (1,4) (1,19) (1,7) (1,14) (2,24) (2,12) (2,17) (2,9) (2,15) (2,16) (2,10) (2,13) (2,4) (2,19) (2,7) (2,14) (3,18) (4,24) (4,12) (4,17) (4,9) (4,15) (4,16) (4,10) (4,13) (4,19) (4,7) (4,14) (5,11) (5,23) (5,20) (5,8) (6,22) (6,21) (7,24) (7,12) (7,17) (7,9) (7,15) (7,16) (7,10) (7,13) (7,19) (7,14) (8,11) (8,23) (8,20) (9,24) (9,12) (9,17) (9,15) (9,16) (9,10) (9,13) (9,19) (9,14) (10,24) (10,12) (10,17) (10,15) (10,16) (10,13) (10,19) (10,14) (11,23) (11,20) (12,24) (12,17) (12,15) (12,16) (12,13) (12,19) (12,14) (13,24) (13,17) (13,15) (13,16) (13,19) (13,14) (14,24) (14,17) (14,15) (14,16) (14,19) (15,24) (15,17) (15,16) (15,19) (16,24) (16,17) (16,19) (17,24) (17,19) (19,24) (20,23) (21,22)\nIs there a path between node 9 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph624-12_20", + "image": "data/connectivity/graph_visual/medium/graph624.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (0,11) (0,13) (0,3) (0,15) (0,4) (0,2) (1,7) (1,8) (2,14) (2,23) (2,21) (2,6) (2,10) (3,9) (3,17) (3,13) (3,5) (3,19) (3,4) (3,16) (3,10) (4,9) (4,22) (4,6) (5,11) (5,18) (5,23) (6,9) (6,14) (6,17) (6,20) (6,15) (6,21) (7,8) (9,17) (9,15) (9,21) (10,18) (10,12) (10,16) (11,17) (11,15) (11,22) (11,16) (12,15) (12,22) (13,23) (13,16) (14,17) (14,18) (14,20) (14,21) (14,22) (14,16) (15,20) (17,20) (17,19) (17,23) (18,19) (18,23) (19,20) (19,23) (21,23) (21,22)\nIs there a path between node 12 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph538-8_21", + "image": "data/connectivity/graph_visual/medium/graph538.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,4) (0,11) (0,17) (0,18) (0,6) (0,10) (0,7) (0,12) (0,5) (0,21) (0,8) (0,13) (0,9) (0,3) (0,15) (0,14) (0,20) (0,2) (1,19) (1,16) (2,22) (2,4) (2,11) (2,17) (2,18) (2,6) (2,10) (2,7) (2,12) (2,5) (2,21) (2,8) (2,13) (2,9) (2,3) (2,15) (2,14) (2,20) (3,22) (3,4) (3,11) (3,17) (3,18) (3,6) (3,10) (3,7) (3,12) (3,5) (3,21) (3,8) (3,13) (3,9) (3,15) (3,14) (3,20) (4,22) (4,11) (4,17) (4,18) (4,6) (4,10) (4,7) (4,12) (4,5) (4,21) (4,8) (4,13) (4,9) (4,15) (4,14) (4,20) (5,22) (5,11) (5,17) (5,18) (5,6) (5,10) (5,7) (5,12) (5,21) (5,8) (5,13) (5,9) (5,15) (5,14) (5,20) (6,22) (6,11) (6,17) (6,18) (6,10) (6,7) (6,12) (6,21) (6,8) (6,13) (6,9) (6,15) (6,14) (6,20) (7,22) (7,11) (7,17) (7,18) (7,10) (7,12) (7,21) (7,8) (7,13) (7,9) (7,15) (7,14) (7,20) (8,22) (8,11) (8,17) (8,18) (8,10) (8,12) (8,21) (8,13) (8,9) (8,15) (8,14) (8,20) (9,22) (9,11) (9,17) (9,18) (9,10) (9,12) (9,21) (9,13) (9,15) (9,14) (9,20) (10,22) (10,11) (10,17) (10,18) (10,12) (10,21) (10,13) (10,15) (10,14) (10,20) (11,22) (11,17) (11,18) (11,12) (11,21) (11,13) (11,15) (11,14) (11,20) (12,22) (12,17) (12,18) (12,21) (12,13) (12,15) (12,14) (12,20) (13,22) (13,17) (13,18) (13,21) (13,15) (13,14) (13,20) (14,22) (14,17) (14,18) (14,21) (14,15) (14,20) (15,22) (15,17) (15,18) (15,21) (15,20) (16,19) (17,22) (17,18) (17,21) (17,20) (18,22) (18,21) (18,20) (20,22) (20,21) (21,22)\nIs there a path between node 8 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph62-4_1", + "image": "data/connectivity/graph_visual/medium/graph62.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,12) (0,11) (0,13) (0,5) (1,12) (1,11) (1,7) (1,13) (1,5) (2,6) (2,8) (2,9) (2,10) (3,4) (3,8) (3,9) (3,10) (4,6) (4,8) (4,9) (5,11) (5,7) (6,8) (6,9) (6,10) (7,12) (7,11) (8,10) (9,10) (12,13)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph552-16_19", + "image": "data/connectivity/graph_visual/medium/graph552.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,12) (2,13) (2,22) (3,4) (3,18) (3,10) (3,7) (3,20) (4,21) (4,5) (5,18) (5,23) (5,10) (5,7) (5,20) (5,16) (6,11) (6,10) (6,7) (6,14) (6,16) (6,15) (7,18) (7,9) (7,11) (7,8) (7,16) (8,18) (8,9) (8,10) (8,20) (8,14) (8,16) (8,15) (9,21) (9,23) (10,21) (10,11) (10,15) (11,18) (11,17) (11,16) (12,13) (13,22) (14,18) (14,23) (14,17) (14,16) (14,15) (15,21) (16,18) (16,20) (18,20) (19,22) (20,23)\nIs there a path between node 16 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph152-7_16", + "image": "data/connectivity/graph_visual/medium/graph152.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,11) (1,13) (1,16) (1,8) (1,5) (1,4) (1,9) (1,3) (1,15) (1,17) (1,7) (1,6) (1,14) (1,2) (2,13) (2,16) (2,8) (2,5) (2,4) (2,9) (2,3) (2,15) (2,17) (2,7) (2,6) (2,14) (3,13) (3,16) (3,8) (3,5) (3,4) (3,9) (3,15) (3,17) (3,7) (3,6) (3,14) (4,13) (4,16) (4,8) (4,5) (4,9) (4,15) (4,17) (4,7) (4,6) (4,14) (5,13) (5,16) (5,8) (5,9) (5,15) (5,17) (5,7) (5,6) (5,14) (6,13) (6,16) (6,8) (6,9) (6,15) (6,17) (6,7) (6,14) (7,13) (7,16) (7,8) (7,9) (7,15) (7,17) (7,14) (8,13) (8,16) (8,9) (8,15) (8,17) (8,14) (9,13) (9,16) (9,15) (9,17) (9,14) (11,12) (13,16) (13,15) (13,17) (13,14) (14,16) (14,15) (14,17) (15,16) (15,17) (16,17)\nIs there a path between node 7 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph420-14_11", + "image": "data/connectivity/graph_visual/medium/graph420.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,20) (0,15) (0,1) (0,17) (0,16) (0,19) (0,2) (0,7) (0,5) (0,8) (0,14) (0,6) (0,18) (0,9) (0,3) (0,12) (1,4) (1,20) (1,15) (1,17) (1,16) (1,19) (1,2) (1,7) (1,5) (1,8) (1,14) (1,6) (1,18) (1,9) (1,3) (1,12) (2,4) (2,20) (2,15) (2,17) (2,16) (2,19) (2,7) (2,5) (2,8) (2,14) (2,6) (2,18) (2,9) (2,3) (2,12) (3,4) (3,20) (3,15) (3,17) (3,16) (3,19) (3,7) (3,5) (3,8) (3,14) (3,6) (3,18) (3,9) (3,12) (4,20) (4,15) (4,17) (4,16) (4,19) (4,7) (4,5) (4,8) (4,14) (4,6) (4,18) (4,9) (4,12) (5,20) (5,15) (5,17) (5,16) (5,19) (5,7) (5,8) (5,14) (5,6) (5,18) (5,9) (5,12) (6,20) (6,15) (6,17) (6,16) (6,19) (6,7) (6,8) (6,14) (6,18) (6,9) (6,12) (7,20) (7,15) (7,17) (7,16) (7,19) (7,8) (7,14) (7,18) (7,9) (7,12) (8,20) (8,15) (8,17) (8,16) (8,19) (8,14) (8,18) (8,9) (8,12) (9,20) (9,15) (9,17) (9,16) (9,19) (9,14) (9,18) (9,12) (10,13) (10,11) (11,13) (12,20) (12,15) (12,17) (12,16) (12,19) (12,14) (12,18) (14,20) (14,15) (14,17) (14,16) (14,19) (14,18) (15,20) (15,17) (15,16) (15,19) (15,18) (16,20) (16,17) (16,19) (16,18) (17,20) (17,19) (17,18) (18,20) (18,19) (19,20)\nIs there a path between node 14 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph244-16_11", + "image": "data/connectivity/graph_visual/medium/graph244.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,12) (0,11) (0,6) (0,17) (0,5) (0,18) (1,9) (1,16) (1,10) (1,4) (2,12) (2,6) (2,14) (2,5) (2,18) (2,7) (4,15) (4,9) (4,16) (5,11) (5,14) (5,18) (6,11) (6,18) (7,12) (7,17) (9,13) (10,15) (10,16) (11,12) (11,17) (11,14) (11,18) (12,14) (12,18) (13,15) (14,17) (15,16)\nIs there a path between node 16 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph764-15_0", + "image": "data/connectivity/graph_visual/medium/graph764.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,4) (0,24) (1,22) (1,13) (1,2) (1,18) (1,5) (1,3) (1,19) (1,7) (1,9) (1,21) (1,8) (1,10) (1,23) (1,6) (1,20) (1,14) (1,11) (1,16) (1,17) (1,15) (2,22) (2,13) (2,18) (2,5) (2,3) (2,19) (2,7) (2,9) (2,21) (2,8) (2,10) (2,23) (2,6) (2,20) (2,14) (2,11) (2,16) (2,17) (2,15) (3,22) (3,13) (3,18) (3,5) (3,19) (3,7) (3,9) (3,21) (3,8) (3,10) (3,23) (3,6) (3,20) (3,14) (3,11) (3,16) (3,17) (3,15) (4,12) (4,24) (5,22) (5,13) (5,18) (5,19) (5,7) (5,9) (5,21) (5,8) (5,10) (5,23) (5,6) (5,20) (5,14) (5,11) (5,16) (5,17) (5,15) (6,22) (6,13) (6,18) (6,19) (6,7) (6,9) (6,21) (6,8) (6,10) (6,23) (6,20) (6,14) (6,11) (6,16) (6,17) (6,15) (7,22) (7,13) (7,18) (7,19) (7,9) (7,21) (7,8) (7,10) (7,23) (7,20) (7,14) (7,11) (7,16) (7,17) (7,15) (8,22) (8,13) (8,18) (8,19) (8,9) (8,21) (8,10) (8,23) (8,20) (8,14) (8,11) (8,16) (8,17) (8,15) (9,22) (9,13) (9,18) (9,19) (9,21) (9,10) (9,23) (9,20) (9,14) (9,11) (9,16) (9,17) (9,15) (10,22) (10,13) (10,18) (10,19) (10,21) (10,23) (10,20) (10,14) (10,11) (10,16) (10,17) (10,15) (11,22) (11,13) (11,18) (11,19) (11,21) (11,23) (11,20) (11,14) (11,16) (11,17) (11,15) (12,24) (13,22) (13,18) (13,19) (13,21) (13,23) (13,20) (13,14) (13,16) (13,17) (13,15) (14,22) (14,18) (14,19) (14,21) (14,23) (14,20) (14,16) (14,17) (14,15) (15,22) (15,18) (15,19) (15,21) (15,23) (15,20) (15,16) (15,17) (16,22) (16,18) (16,19) (16,21) (16,23) (16,20) (16,17) (17,22) (17,18) (17,19) (17,21) (17,23) (17,20) (18,22) (18,19) (18,21) (18,23) (18,20) (19,22) (19,21) (19,23) (19,20) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 15 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph827-17_2", + "image": "data/connectivity/graph_visual/medium/graph827.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,23) (0,22) (1,9) (1,24) (1,11) (1,13) (1,8) (1,20) (1,5) (1,4) (1,21) (1,16) (1,3) (1,19) (1,10) (1,18) (1,2) (2,9) (2,24) (2,11) (2,14) (2,8) (2,20) (2,5) (2,21) (2,6) (2,16) (2,3) (2,19) (2,12) (2,10) (2,18) (3,9) (3,11) (3,14) (3,8) (3,5) (3,21) (3,6) (3,16) (3,19) (3,12) (3,10) (3,18) (4,9) (4,11) (4,13) (4,14) (4,20) (4,5) (4,21) (4,16) (4,19) (4,12) (4,18) (5,9) (5,11) (5,13) (5,8) (5,20) (5,21) (5,6) (5,16) (5,12) (5,10) (5,18) (6,9) (6,24) (6,11) (6,13) (6,14) (6,20) (6,16) (6,19) (6,10) (6,18) (7,23) (7,15) (8,9) (8,24) (8,11) (8,13) (8,14) (8,20) (8,21) (8,16) (8,10) (8,18) (9,24) (9,11) (9,14) (9,20) (9,21) (9,16) (9,19) (9,10) (9,18) (10,24) (10,11) (10,14) (10,20) (10,16) (10,19) (10,12) (10,18) (11,13) (11,14) (11,20) (11,21) (11,16) (11,12) (11,18) (12,24) (12,13) (12,14) (12,20) (12,21) (12,16) (12,19) (12,18) (13,24) (13,14) (13,21) (13,16) (13,18) (14,24) (14,21) (14,19) (14,18) (15,22) (15,17) (16,24) (16,19) (16,18) (17,23) (17,22) (18,24) (18,19) (19,24) (19,21) (20,24) (20,21) (21,24)\nIs there a path between node 17 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph598-18_0", + "image": "data/connectivity/graph_visual/medium/graph598.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,22) (0,12) (0,10) (0,7) (0,5) (0,14) (0,9) (1,13) (1,6) (1,21) (1,18) (1,20) (1,3) (2,23) (2,22) (2,12) (2,10) (2,17) (2,15) (2,5) (2,14) (2,9) (3,13) (3,21) (3,18) (3,20) (3,4) (4,6) (4,21) (4,18) (4,20) (5,16) (5,22) (5,12) (5,17) (5,8) (5,19) (5,7) (5,15) (6,13) (6,21) (6,18) (7,23) (7,22) (7,12) (7,14) (7,9) (8,23) (8,16) (8,22) (8,12) (8,10) (8,17) (8,19) (8,15) (8,14) (9,16) (9,12) (9,10) (9,17) (9,19) (9,15) (9,14) (10,23) (10,16) (10,22) (10,12) (10,19) (10,14) (12,16) (12,22) (12,17) (12,19) (12,14) (13,21) (13,18) (13,20) (14,23) (14,16) (14,19) (14,15) (15,23) (15,16) (15,22) (15,17) (15,19) (16,23) (16,22) (16,19) (17,23) (17,19) (18,21) (18,20) (19,22) (22,23)\nIs there a path between node 18 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph529-9_12", + "image": "data/connectivity/graph_visual/medium/graph529.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,20) (0,19) (0,14) (0,2) (0,9) (0,13) (0,21) (0,12) (0,18) (0,16) (0,7) (1,17) (1,5) (1,4) (1,22) (1,11) (1,3) (1,8) (1,15) (1,10) (1,6) (2,20) (2,19) (2,14) (2,9) (2,13) (2,21) (2,12) (2,18) (2,16) (2,7) (3,17) (3,5) (3,4) (3,22) (3,11) (3,8) (3,15) (3,10) (3,6) (4,17) (4,5) (4,22) (4,11) (4,8) (4,15) (4,10) (4,6) (5,17) (5,22) (5,11) (5,8) (5,15) (5,10) (5,6) (6,17) (6,22) (6,11) (6,8) (6,15) (6,10) (7,20) (7,19) (7,14) (7,9) (7,13) (7,21) (7,12) (7,18) (7,16) (8,17) (8,22) (8,11) (8,15) (8,10) (9,20) (9,19) (9,14) (9,13) (9,21) (9,12) (9,18) (9,16) (10,17) (10,22) (10,11) (10,15) (11,17) (11,22) (11,15) (12,20) (12,19) (12,14) (12,13) (12,21) (12,18) (12,16) (13,20) (13,19) (13,14) (13,21) (13,18) (13,16) (14,20) (14,19) (14,21) (14,18) (14,16) (15,17) (15,22) (16,20) (16,19) (16,21) (16,18) (17,22) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 9 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph706-5_1", + "image": "data/connectivity/graph_visual/medium/graph706.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (0,2) (0,23) (0,1) (1,16) (1,17) (1,5) (1,15) (1,19) (1,13) (1,4) (2,3) (2,13) (2,4) (2,10) (3,17) (3,15) (3,14) (3,9) (3,20) (3,6) (4,12) (4,18) (5,13) (5,14) (5,9) (6,19) (6,13) (6,23) (6,14) (6,20) (7,21) (9,16) (9,13) (9,23) (9,11) (9,18) (10,16) (10,13) (11,15) (11,23) (12,16) (12,17) (12,23) (13,17) (13,23) (14,16) (14,17) (14,19) (14,18) (15,16) (15,19) (15,23) (15,18) (15,20) (16,17) (17,18) (18,20)\nIs there a path between node 5 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph551-3_6", + "image": "data/connectivity/graph_visual/medium/graph551.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,11) (2,20) (3,22) (3,6) (3,14) (3,12) (3,13) (3,4) (4,23) (4,12) (5,23) (5,22) (5,12) (5,10) (5,13) (5,15) (6,10) (6,13) (6,18) (8,11) (9,20) (10,12) (11,17) (11,16) (12,14) (12,15) (12,21) (13,19) (13,18) (14,23) (14,15) (14,18) (15,23) (18,23)\nIs there a path between node 3 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph19-5_7", + "image": "data/connectivity/graph_visual/medium/graph19.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,8) (0,4) (0,11) (1,3) (3,9) (3,7) (4,8) (5,11) (6,10) (6,9) (6,7) (8,11)\nIs there a path between node 5 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph87-2_7", + "image": "data/connectivity/graph_visual/medium/graph87.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (0,13) (0,7) (0,3) (0,14) (0,6) (0,10) (0,1) (0,12) (1,9) (1,13) (1,7) (1,3) (1,14) (1,6) (1,10) (1,12) (2,5) (2,11) (2,8) (2,4) (3,9) (3,13) (3,7) (3,14) (3,6) (3,10) (3,12) (4,5) (4,11) (4,8) (5,11) (5,8) (6,9) (6,13) (6,7) (6,14) (6,10) (6,12) (7,9) (7,13) (7,14) (7,10) (7,12) (8,11) (9,13) (9,14) (9,10) (9,12) (10,13) (10,14) (10,12) (12,13) (12,14) (13,14)\nIs there a path between node 2 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph416-18_20", + "image": "data/connectivity/graph_visual/medium/graph416.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,4) (0,21) (0,7) (0,11) (0,1) (0,12) (0,10) (0,6) (0,9) (0,17) (0,20) (0,15) (0,13) (1,2) (1,4) (1,21) (1,7) (1,11) (1,12) (1,10) (1,6) (1,9) (1,17) (1,20) (1,15) (1,13) (2,4) (2,21) (2,7) (2,11) (2,12) (2,10) (2,6) (2,9) (2,17) (2,20) (2,15) (2,13) (3,8) (3,16) (3,14) (3,18) (3,5) (3,19) (4,21) (4,7) (4,11) (4,12) (4,10) (4,6) (4,9) (4,17) (4,20) (4,15) (4,13) (5,8) (5,16) (5,14) (5,18) (5,19) (6,21) (6,7) (6,11) (6,12) (6,10) (6,9) (6,17) (6,20) (6,15) (6,13) (7,21) (7,11) (7,12) (7,10) (7,9) (7,17) (7,20) (7,15) (7,13) (8,16) (8,14) (8,18) (8,19) (9,21) (9,11) (9,12) (9,10) (9,17) (9,20) (9,15) (9,13) (10,21) (10,11) (10,12) (10,17) (10,20) (10,15) (10,13) (11,21) (11,12) (11,17) (11,20) (11,15) (11,13) (12,21) (12,17) (12,20) (12,15) (12,13) (13,21) (13,17) (13,20) (13,15) (14,16) (14,18) (14,19) (15,21) (15,17) (15,20) (16,18) (16,19) (17,21) (17,20) (18,19) (20,21)\nIs there a path between node 18 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph60-13_12", + "image": "data/connectivity/graph_visual/medium/graph60.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (0,7) (0,4) (0,5) (1,10) (2,11) (2,6) (2,13) (2,7) (2,12) (2,4) (3,9) (3,8) (3,10) (4,11) (4,7) (4,12) (4,5) (5,11) (5,6) (5,7) (5,12) (6,11) (6,13) (6,7) (6,12) (7,11) (7,13) (7,12) (8,9) (8,10) (9,10)\nIs there a path between node 13 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph833-20_3", + "image": "data/connectivity/graph_visual/medium/graph833.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,22) (0,18) (0,8) (0,21) (0,5) (0,11) (0,1) (0,24) (0,19) (0,9) (0,15) (0,14) (0,10) (0,4) (0,23) (0,6) (0,17) (0,13) (1,20) (1,22) (1,18) (1,8) (1,21) (1,5) (1,11) (1,24) (1,19) (1,9) (1,15) (1,14) (1,10) (1,4) (1,23) (1,6) (1,17) (1,13) (2,3) (2,7) (2,12) (2,16) (3,7) (3,12) (3,16) (4,20) (4,22) (4,18) (4,8) (4,21) (4,5) (4,11) (4,24) (4,19) (4,9) (4,15) (4,14) (4,10) (4,23) (4,6) (4,17) (4,13) (5,20) (5,22) (5,18) (5,8) (5,21) (5,11) (5,24) (5,19) (5,9) (5,15) (5,14) (5,10) (5,23) (5,6) (5,17) (5,13) (6,20) (6,22) (6,18) (6,8) (6,21) (6,11) (6,24) (6,19) (6,9) (6,15) (6,14) (6,10) (6,23) (6,17) (6,13) (7,12) (7,16) (8,20) (8,22) (8,18) (8,21) (8,11) (8,24) (8,19) (8,9) (8,15) (8,14) (8,10) (8,23) (8,17) (8,13) (9,20) (9,22) (9,18) (9,21) (9,11) (9,24) (9,19) (9,15) (9,14) (9,10) (9,23) (9,17) (9,13) (10,20) (10,22) (10,18) (10,21) (10,11) (10,24) (10,19) (10,15) (10,14) (10,23) (10,17) (10,13) (11,20) (11,22) (11,18) (11,21) (11,24) (11,19) (11,15) (11,14) (11,23) (11,17) (11,13) (12,16) (13,20) (13,22) (13,18) (13,21) (13,24) (13,19) (13,15) (13,14) (13,23) (13,17) (14,20) (14,22) (14,18) (14,21) (14,24) (14,19) (14,15) (14,23) (14,17) (15,20) (15,22) (15,18) (15,21) (15,24) (15,19) (15,23) (15,17) (17,20) (17,22) (17,18) (17,21) (17,24) (17,19) (17,23) (18,20) (18,22) (18,21) (18,24) (18,19) (18,23) (19,20) (19,22) (19,21) (19,24) (19,23) (20,22) (20,21) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 20 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph677-14_0", + "image": "data/connectivity/graph_visual/medium/graph677.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,4) (0,9) (0,19) (0,14) (0,17) (0,7) (0,6) (0,5) (0,16) (0,13) (0,22) (0,12) (0,15) (0,23) (1,3) (1,2) (1,21) (1,8) (1,20) (2,3) (2,21) (2,8) (2,20) (3,21) (3,8) (3,20) (4,11) (4,9) (4,19) (4,14) (4,17) (4,7) (4,6) (4,5) (4,16) (4,13) (4,22) (4,12) (4,15) (4,23) (5,11) (5,9) (5,19) (5,14) (5,17) (5,7) (5,6) (5,16) (5,13) (5,22) (5,12) (5,15) (5,23) (6,11) (6,9) (6,19) (6,14) (6,17) (6,7) (6,16) (6,13) (6,22) (6,12) (6,15) (6,23) (7,11) (7,9) (7,19) (7,14) (7,17) (7,16) (7,13) (7,22) (7,12) (7,15) (7,23) (8,21) (8,20) (9,11) (9,19) (9,14) (9,17) (9,16) (9,13) (9,22) (9,12) (9,15) (9,23) (11,19) (11,14) (11,17) (11,16) (11,13) (11,22) (11,12) (11,15) (11,23) (12,19) (12,14) (12,17) (12,16) (12,13) (12,22) (12,15) (12,23) (13,19) (13,14) (13,17) (13,16) (13,22) (13,15) (13,23) (14,19) (14,17) (14,16) (14,22) (14,15) (14,23) (15,19) (15,17) (15,16) (15,22) (15,23) (16,19) (16,17) (16,22) (16,23) (17,19) (17,22) (17,23) (19,22) (19,23) (20,21) (22,23)\nIs there a path between node 14 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph228-11_8", + "image": "data/connectivity/graph_visual/medium/graph228.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,9) (0,15) (1,14) (1,17) (2,12) (3,14) (3,16) (4,18) (7,13) (8,16) (8,11) (8,10) (9,12) (11,14) (15,18)\nIs there a path between node 11 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph587-13_12", + "image": "data/connectivity/graph_visual/medium/graph587.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,5) (0,14) (0,23) (0,10) (1,5) (1,14) (1,15) (2,21) (2,9) (2,3) (2,15) (3,21) (3,11) (3,15) (3,18) (4,7) (4,22) (5,21) (5,9) (5,17) (5,10) (5,18) (6,17) (6,18) (7,19) (8,12) (9,21) (9,11) (9,15) (9,18) (10,15) (13,22) (16,19) (17,21) (18,21) (18,23)\nIs there a path between node 13 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph232-18_2", + "image": "data/connectivity/graph_visual/medium/graph232.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,1) (0,13) (0,15) (0,16) (0,9) (0,14) (0,3) (0,12) (0,17) (0,2) (0,18) (1,11) (1,13) (1,15) (1,16) (1,9) (1,8) (1,14) (1,3) (1,4) (1,17) (1,18) (2,11) (2,13) (2,15) (2,9) (2,8) (2,14) (2,3) (2,12) (2,17) (2,18) (3,11) (3,13) (3,15) (3,16) (3,9) (3,8) (3,14) (3,12) (3,17) (3,18) (4,13) (4,15) (4,16) (4,8) (4,14) (4,12) (4,18) (5,6) (5,7) (5,10) (6,7) (6,10) (7,10) (8,11) (8,15) (8,16) (8,18) (9,11) (9,13) (9,15) (9,16) (9,14) (9,12) (9,17) (9,18) (11,13) (11,16) (11,17) (11,18) (12,15) (12,16) (12,17) (12,18) (13,15) (13,18) (14,15) (14,17) (15,16) (16,17) (16,18) (17,18)\nIs there a path between node 18 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph76-0_12", + "image": "data/connectivity/graph_visual/medium/graph76.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,6) (0,12) (0,8) (1,4) (1,6) (1,12) (1,8) (1,7) (2,4) (2,5) (2,13) (2,10) (4,5) (4,9) (4,8) (4,10) (5,12) (5,10) (5,14) (6,11) (7,9) (7,12) (8,11) (8,13) (8,14) (9,10) (11,12) (11,14) (13,14)\nIs there a path between node 0 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph471-1_8", + "image": "data/connectivity/graph_visual/medium/graph471.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,19) (1,12) (1,19) (2,13) (3,20) (3,11) (4,7) (4,16) (4,18) (5,17) (5,7) (6,15) (6,20) (6,11) (7,20) (7,11) (8,12) (8,13) (8,19) (11,17) (11,15) (12,19) (16,17) (16,20) (17,20) (18,20)\nIs there a path between node 1 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph589-9_8", + "image": "data/connectivity/graph_visual/medium/graph589.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,6) (0,23) (0,19) (1,8) (1,4) (2,20) (2,17) (2,19) (2,15) (3,13) (3,15) (5,23) (5,12) (5,15) (5,18) (7,9) (9,14) (10,11) (12,23) (12,22) (12,15) (13,21) (13,15) (16,23) (16,17) (16,22) (16,18) (17,22) (18,21) (18,20) (18,22) (19,23) (20,23)\nIs there a path between node 9 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph606-20_4", + "image": "data/connectivity/graph_visual/medium/graph606.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,23) (1,16) (2,10) (2,11) (2,20) (2,21) (2,3) (3,15) (3,20) (3,21) (4,22) (4,7) (4,9) (4,12) (4,8) (4,14) (4,19) (5,22) (5,7) (5,9) (5,12) (5,8) (5,14) (5,19) (7,13) (7,22) (7,9) (7,12) (7,18) (7,19) (8,13) (8,9) (8,12) (8,18) (8,14) (8,19) (9,13) (9,12) (9,14) (10,15) (10,11) (11,15) (11,20) (11,21) (12,13) (12,22) (12,18) (12,14) (13,22) (13,18) (13,19) (14,22) (14,18) (14,19) (15,21) (16,17) (18,19) (19,22)\nIs there a path between node 20 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph228-11_16", + "image": "data/connectivity/graph_visual/medium/graph228.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,9) (0,15) (1,14) (1,17) (2,12) (3,14) (3,16) (4,18) (7,13) (8,16) (8,11) (8,10) (9,12) (11,14) (15,18)\nIs there a path between node 11 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph510-17_10", + "image": "data/connectivity/graph_visual/medium/graph510.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,16) (0,13) (0,7) (0,18) (0,8) (0,20) (0,15) (1,22) (1,21) (1,8) (1,20) (1,15) (2,11) (2,20) (3,17) (4,16) (4,11) (4,7) (4,9) (4,8) (4,20) (5,22) (5,7) (5,18) (5,9) (7,22) (7,20) (8,9) (8,20) (9,16) (9,19) (9,20) (10,17) (11,16) (11,13) (11,18) (12,17) (13,16) (13,22) (13,14) (13,21) (14,22) (14,19) (15,16) (16,19) (16,18) (16,21)\nIs there a path between node 17 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph35-10_5", + "image": "data/connectivity/graph_visual/medium/graph35.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,5) (0,7) (0,8) (0,10) (0,3) (1,4) (1,11) (1,9) (1,6) (1,12) (1,2) (2,4) (2,11) (2,9) (2,6) (2,12) (3,5) (3,7) (3,8) (3,10) (4,11) (4,9) (4,6) (4,12) (5,7) (5,8) (5,10) (6,11) (6,9) (6,12) (7,8) (7,10) (8,10) (9,11) (9,12) (11,12)\nIs there a path between node 10 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph87-2_12", + "image": "data/connectivity/graph_visual/medium/graph87.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (0,13) (0,7) (0,3) (0,14) (0,6) (0,10) (0,1) (0,12) (1,9) (1,13) (1,7) (1,3) (1,14) (1,6) (1,10) (1,12) (2,5) (2,11) (2,8) (2,4) (3,9) (3,13) (3,7) (3,14) (3,6) (3,10) (3,12) (4,5) (4,11) (4,8) (5,11) (5,8) (6,9) (6,13) (6,7) (6,14) (6,10) (6,12) (7,9) (7,13) (7,14) (7,10) (7,12) (8,11) (9,13) (9,14) (9,10) (9,12) (10,13) (10,14) (10,12) (12,13) (12,14) (13,14)\nIs there a path between node 2 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph413-3_9", + "image": "data/connectivity/graph_visual/medium/graph413.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,13) (0,19) (0,21) (0,4) (0,2) (0,16) (0,6) (0,7) (0,8) (0,3) (0,20) (0,14) (1,9) (1,10) (2,13) (2,19) (2,21) (2,12) (2,16) (2,5) (2,8) (2,20) (2,14) (3,13) (3,21) (3,4) (3,12) (3,16) (3,7) (3,8) (3,20) (3,14) (4,21) (4,12) (4,16) (4,6) (4,5) (4,8) (5,13) (5,19) (5,21) (5,12) (5,6) (5,7) (5,8) (5,14) (6,13) (6,19) (6,12) (6,16) (6,7) (6,8) (6,20) (6,14) (7,13) (7,21) (7,12) (7,16) (7,20) (7,14) (8,19) (8,12) (8,20) (8,14) (9,11) (9,10) (9,15) (9,18) (9,17) (10,11) (10,15) (10,17) (11,15) (11,18) (11,17) (12,21) (12,16) (12,20) (13,19) (13,16) (13,20) (13,14) (14,19) (14,21) (14,16) (14,20) (15,18) (15,17) (16,19) (16,21) (17,18) (19,21) (19,20) (20,21)\nIs there a path between node 3 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph501-19_16", + "image": "data/connectivity/graph_visual/medium/graph501.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,19) (0,7) (0,10) (0,3) (0,15) (0,11) (0,1) (1,6) (1,9) (1,10) (1,15) (1,12) (2,7) (2,3) (2,12) (2,14) (2,13) (3,8) (3,19) (3,7) (3,21) (3,11) (3,12) (3,18) (4,16) (5,9) (5,8) (6,7) (6,17) (6,10) (6,15) (6,21) (6,20) (7,17) (7,15) (7,12) (7,14) (7,22) (7,20) (7,13) (8,9) (8,19) (8,17) (8,15) (8,20) (9,17) (9,11) (9,20) (10,19) (10,15) (11,21) (11,12) (11,14) (11,18) (12,19) (12,17) (12,14) (12,13) (13,20) (14,17) (14,22) (14,20) (14,18) (15,20) (15,18) (17,18) (20,21) (20,22)\nIs there a path between node 19 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph240-0_2", + "image": "data/connectivity/graph_visual/medium/graph240.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,16) (0,6) (0,8) (0,13) (0,7) (0,12) (1,14) (1,15) (1,11) (2,14) (2,11) (3,16) (3,18) (3,13) (4,14) (4,15) (4,11) (5,17) (5,9) (6,16) (6,7) (6,12) (7,18) (7,8) (7,13) (7,12) (8,18) (8,13) (8,12) (9,17) (10,16) (10,18) (10,13) (11,14) (11,15) (12,16) (12,18) (13,18) (14,15) (16,18)\nIs there a path between node 0 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph727-23_3", + "image": "data/connectivity/graph_visual/medium/graph727.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,2) (1,12) (1,21) (1,18) (1,15) (1,10) (1,13) (1,19) (1,16) (1,22) (1,7) (1,24) (1,14) (1,9) (1,6) (1,17) (1,3) (1,11) (1,20) (1,5) (1,8) (2,12) (2,21) (2,18) (2,15) (2,10) (2,13) (2,19) (2,16) (2,22) (2,7) (2,24) (2,14) (2,9) (2,6) (2,17) (2,3) (2,11) (2,20) (2,5) (2,8) (3,12) (3,21) (3,18) (3,15) (3,10) (3,13) (3,19) (3,16) (3,22) (3,7) (3,24) (3,14) (3,9) (3,6) (3,17) (3,11) (3,20) (3,5) (3,8) (4,23) (5,12) (5,21) (5,18) (5,15) (5,10) (5,13) (5,19) (5,16) (5,22) (5,7) (5,24) (5,14) (5,9) (5,6) (5,17) (5,11) (5,20) (5,8) (6,12) (6,21) (6,18) (6,15) (6,10) (6,13) (6,19) (6,16) (6,22) (6,7) (6,24) (6,14) (6,9) (6,17) (6,11) (6,20) (6,8) (7,12) (7,21) (7,18) (7,15) (7,10) (7,13) (7,19) (7,16) (7,22) (7,24) (7,14) (7,9) (7,17) (7,11) (7,20) (7,8) (8,12) (8,21) (8,18) (8,15) (8,10) (8,13) (8,19) (8,16) (8,22) (8,24) (8,14) (8,9) (8,17) (8,11) (8,20) (9,12) (9,21) (9,18) (9,15) (9,10) (9,13) (9,19) (9,16) (9,22) (9,24) (9,14) (9,17) (9,11) (9,20) (10,12) (10,21) (10,18) (10,15) (10,13) (10,19) (10,16) (10,22) (10,24) (10,14) (10,17) (10,11) (10,20) (11,12) (11,21) (11,18) (11,15) (11,13) (11,19) (11,16) (11,22) (11,24) (11,14) (11,17) (11,20) (12,21) (12,18) (12,15) (12,13) (12,19) (12,16) (12,22) (12,24) (12,14) (12,17) (12,20) (13,21) (13,18) (13,15) (13,19) (13,16) (13,22) (13,24) (13,14) (13,17) (13,20) (14,21) (14,18) (14,15) (14,19) (14,16) (14,22) (14,24) (14,17) (14,20) (15,21) (15,18) (15,19) (15,16) (15,22) (15,24) (15,17) (15,20) (16,21) (16,18) (16,19) (16,22) (16,24) (16,17) (16,20) (17,21) (17,18) (17,19) (17,22) (17,24) (17,20) (18,21) (18,19) (18,22) (18,24) (18,20) (19,21) (19,22) (19,24) (19,20) (20,21) (20,22) (20,24) (21,22) (21,24) (22,24)\nIs there a path between node 23 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph242-1_11", + "image": "data/connectivity/graph_visual/medium/graph242.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,2) (0,10) (0,14) (0,1) (0,18) (0,11) (0,9) (0,6) (0,15) (1,10) (1,11) (1,9) (1,17) (1,6) (1,15) (2,18) (2,11) (2,9) (2,17) (2,15) (3,5) (3,7) (3,12) (3,16) (4,5) (4,7) (4,8) (5,7) (5,13) (5,16) (6,10) (6,14) (6,18) (6,11) (6,15) (7,8) (7,12) (7,16) (8,13) (8,12) (8,16) (9,10) (9,14) (9,18) (9,11) (10,14) (10,18) (10,11) (10,17) (10,15) (11,14) (11,17) (11,15) (12,13) (13,16) (14,18) (14,17) (14,15) (15,17) (17,18)\nIs there a path between node 1 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph553-15_9", + "image": "data/connectivity/graph_visual/medium/graph553.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,10) (0,9) (0,3) (1,10) (1,4) (1,2) (1,12) (1,14) (1,6) (1,15) (2,7) (2,10) (2,9) (2,17) (2,15) (3,20) (3,14) (3,18) (3,6) (3,15) (4,7) (4,16) (4,13) (4,9) (4,14) (4,21) (4,22) (4,17) (5,23) (5,11) (6,10) (6,16) (6,20) (6,22) (7,16) (7,20) (8,23) (8,19) (9,22) (12,14) (12,17) (13,16) (13,14) (13,17) (14,21) (15,21) (15,18) (16,18) (17,18) (19,23) (20,21)\nIs there a path between node 15 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph82-9_14", + "image": "data/connectivity/graph_visual/medium/graph82.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,12) (0,1) (0,8) (0,5) (0,9) (0,13) (0,11) (0,10) (0,6) (1,4) (1,8) (1,2) (1,11) (1,6) (2,12) (2,9) (2,13) (2,7) (2,11) (2,3) (2,10) (2,6) (3,4) (3,12) (3,8) (3,5) (3,13) (3,7) (3,11) (3,10) (3,6) (4,12) (4,5) (4,9) (4,7) (4,11) (5,8) (5,7) (5,11) (5,10) (6,8) (6,9) (6,7) (6,11) (6,10) (7,8) (7,9) (7,13) (7,10) (8,9) (8,13) (8,10) (9,12) (9,13) (9,11) (10,11) (11,13)\nIs there a path between node 9 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph557-6_17", + "image": "data/connectivity/graph_visual/medium/graph557.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,2) (0,18) (0,23) (0,21) (0,13) (0,16) (0,15) (0,22) (0,6) (0,14) (1,17) (1,11) (1,10) (1,4) (1,19) (1,9) (2,8) (2,18) (2,23) (2,21) (2,22) (2,14) (2,20) (3,17) (3,11) (3,10) (3,4) (3,19) (3,9) (4,7) (4,10) (4,9) (5,8) (5,21) (5,13) (5,16) (5,15) (5,22) (5,6) (5,14) (5,20) (6,8) (6,18) (6,13) (6,15) (6,14) (6,20) (7,17) (7,10) (7,19) (7,9) (8,18) (8,23) (8,21) (8,13) (8,16) (8,14) (8,20) (9,17) (9,10) (9,19) (10,17) (10,19) (11,19) (13,18) (13,23) (13,21) (13,16) (13,22) (13,14) (13,20) (14,18) (14,23) (14,21) (14,16) (14,22) (14,20) (15,18) (15,21) (15,22) (16,23) (16,21) (17,19) (18,22) (20,23) (20,21) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 6 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph555-13_11", + "image": "data/connectivity/graph_visual/medium/graph555.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,14) (0,5) (0,9) (0,8) (0,6) (0,21) (1,4) (1,15) (1,18) (1,11) (1,10) (1,12) (2,20) (2,14) (2,5) (2,9) (2,22) (2,6) (2,16) (3,9) (3,23) (3,22) (3,6) (3,21) (4,15) (4,11) (4,19) (4,13) (5,20) (5,14) (5,9) (5,8) (5,6) (5,21) (6,20) (6,14) (6,9) (6,23) (6,8) (6,16) (7,18) (7,11) (7,10) (7,12) (7,19) (7,13) (8,20) (8,14) (8,23) (8,21) (9,20) (9,23) (9,22) (9,21) (10,15) (10,18) (10,11) (10,12) (10,19) (10,13) (11,15) (11,13) (12,18) (12,19) (13,18) (13,19) (14,23) (14,22) (14,21) (15,19) (16,23) (16,22) (20,21) (22,23)\nIs there a path between node 13 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph720-11_22", + "image": "data/connectivity/graph_visual/medium/graph720.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,21) (0,11) (0,15) (0,4) (0,22) (0,5) (0,3) (0,6) (0,20) (0,13) (0,18) (0,9) (0,1) (0,12) (0,24) (0,16) (0,8) (0,23) (0,2) (1,21) (1,11) (1,15) (1,4) (1,22) (1,5) (1,3) (1,6) (1,20) (1,13) (1,18) (1,9) (1,12) (1,24) (1,16) (1,8) (1,23) (1,2) (2,21) (2,11) (2,15) (2,4) (2,22) (2,5) (2,3) (2,6) (2,20) (2,13) (2,18) (2,9) (2,12) (2,24) (2,16) (2,8) (2,23) (3,21) (3,11) (3,15) (3,4) (3,22) (3,5) (3,6) (3,20) (3,13) (3,18) (3,9) (3,12) (3,24) (3,16) (3,8) (3,23) (4,21) (4,11) (4,15) (4,22) (4,5) (4,6) (4,20) (4,13) (4,18) (4,9) (4,12) (4,24) (4,16) (4,8) (4,23) (5,21) (5,11) (5,15) (5,22) (5,6) (5,20) (5,13) (5,18) (5,9) (5,12) (5,24) (5,16) (5,8) (5,23) (6,21) (6,11) (6,15) (6,22) (6,20) (6,13) (6,18) (6,9) (6,12) (6,24) (6,16) (6,8) (6,23) (7,10) (7,14) (7,17) (7,19) (8,21) (8,11) (8,15) (8,22) (8,20) (8,13) (8,18) (8,9) (8,12) (8,24) (8,16) (8,23) (9,21) (9,11) (9,15) (9,22) (9,20) (9,13) (9,18) (9,12) (9,24) (9,16) (9,23) (10,14) (10,17) (10,19) (11,21) (11,15) (11,22) (11,20) (11,13) (11,18) (11,12) (11,24) (11,16) (11,23) (12,21) (12,15) (12,22) (12,20) (12,13) (12,18) (12,24) (12,16) (12,23) (13,21) (13,15) (13,22) (13,20) (13,18) (13,24) (13,16) (13,23) (14,17) (14,19) (15,21) (15,22) (15,20) (15,18) (15,24) (15,16) (15,23) (16,21) (16,22) (16,20) (16,18) (16,24) (16,23) (17,19) (18,21) (18,22) (18,20) (18,24) (18,23) (20,21) (20,22) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 11 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph822-20_10", + "image": "data/connectivity/graph_visual/medium/graph822.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (0,19) (0,5) (0,22) (0,2) (0,16) (0,10) (0,24) (0,20) (0,8) (0,15) (1,18) (1,19) (1,4) (1,23) (1,2) (1,10) (1,24) (1,21) (1,20) (1,15) (2,18) (2,6) (2,19) (2,23) (2,7) (2,22) (2,12) (2,16) (2,24) (2,21) (2,20) (2,15) (3,17) (3,13) (3,11) (4,18) (4,9) (4,19) (4,23) (4,7) (4,22) (4,16) (4,10) (4,24) (4,21) (4,20) (4,15) (5,18) (5,23) (5,7) (5,22) (5,12) (5,16) (5,10) (5,24) (5,8) (5,15) (6,18) (6,19) (6,7) (6,22) (6,12) (6,16) (6,10) (6,24) (6,21) (6,20) (6,15) (7,9) (7,19) (7,23) (7,12) (7,10) (7,21) (7,20) (7,15) (8,18) (8,9) (8,19) (8,23) (8,22) (8,12) (8,16) (8,10) (8,20) (8,15) (9,18) (9,19) (9,23) (9,12) (9,10) (9,24) (9,21) (9,20) (9,15) (10,18) (10,19) (10,23) (10,22) (10,12) (10,24) (10,21) (10,20) (10,15) (11,17) (12,18) (12,23) (12,22) (12,16) (12,24) (12,20) (13,17) (15,18) (15,19) (15,22) (15,24) (15,20) (16,18) (16,19) (16,23) (16,22) (16,24) (16,20) (18,23) (18,22) (18,21) (19,23) (19,22) (19,24) (19,20) (20,24) (20,21) (21,23) (21,22) (21,24) (22,24) (23,24)\nIs there a path between node 20 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph31-3_8", + "image": "data/connectivity/graph_visual/medium/graph31.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,6) (0,9) (0,11) (1,7) (1,3) (1,4) (1,5) (1,8) (1,2) (1,10) (2,7) (2,3) (2,4) (2,5) (2,8) (2,10) (3,7) (3,4) (3,5) (3,8) (3,10) (4,7) (4,5) (4,8) (4,10) (5,7) (5,8) (5,10) (6,9) (6,11) (7,8) (7,10) (8,10) (9,11)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph793-8_16", + "image": "data/connectivity/graph_visual/medium/graph793.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,3) (1,17) (2,12) (2,4) (2,20) (2,9) (2,11) (2,5) (3,13) (3,20) (3,21) (3,10) (4,13) (4,10) (5,21) (6,12) (6,19) (6,9) (6,11) (7,15) (8,17) (9,20) (9,21) (10,13) (10,21) (10,19) (11,13) (11,20) (12,21) (13,21) (14,17) (17,24) (17,22) (20,21)\nIs there a path between node 8 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph698-17_20", + "image": "data/connectivity/graph_visual/medium/graph698.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,2) (1,22) (1,7) (1,20) (1,13) (1,10) (1,16) (2,11) (3,6) (3,21) (3,18) (3,4) (3,12) (3,9) (3,5) (3,8) (3,19) (3,15) (3,23) (3,17) (3,14) (4,6) (4,21) (4,18) (4,12) (4,9) (4,5) (4,8) (4,19) (4,15) (4,23) (4,17) (4,14) (5,6) (5,21) (5,18) (5,12) (5,9) (5,8) (5,19) (5,15) (5,23) (5,17) (5,14) (6,21) (6,18) (6,12) (6,9) (6,8) (6,19) (6,15) (6,23) (6,17) (6,14) (7,22) (7,20) (7,13) (7,10) (7,16) (8,21) (8,18) (8,12) (8,9) (8,19) (8,15) (8,23) (8,17) (8,14) (9,21) (9,18) (9,12) (9,19) (9,15) (9,23) (9,17) (9,14) (10,22) (10,20) (10,13) (10,16) (12,21) (12,18) (12,19) (12,15) (12,23) (12,17) (12,14) (13,22) (13,20) (13,16) (14,21) (14,18) (14,19) (14,15) (14,23) (14,17) (15,21) (15,18) (15,19) (15,23) (15,17) (16,22) (16,20) (17,21) (17,18) (17,19) (17,23) (18,21) (18,19) (18,23) (19,21) (19,23) (20,22) (21,23)\nIs there a path between node 17 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph591-17_5", + "image": "data/connectivity/graph_visual/medium/graph591.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,2) (0,1) (0,16) (0,17) (1,12) (1,2) (1,16) (1,21) (1,5) (1,17) (2,12) (2,8) (2,21) (2,17) (3,6) (3,23) (3,18) (3,14) (4,10) (4,7) (4,22) (4,19) (4,11) (4,15) (4,20) (5,12) (5,8) (5,16) (6,23) (6,18) (7,13) (7,22) (7,19) (7,11) (8,16) (8,17) (10,22) (10,19) (10,11) (10,15) (10,20) (11,13) (11,22) (11,15) (11,20) (12,21) (13,19) (13,15) (13,20) (14,23) (14,18) (15,22) (15,19) (16,21) (16,17) (18,23) (19,22) (20,22)\nIs there a path between node 17 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph454-21_16", + "image": "data/connectivity/graph_visual/medium/graph454.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,21) (0,11) (0,7) (0,1) (0,20) (0,14) (0,16) (0,17) (0,12) (0,9) (0,6) (0,19) (0,2) (0,8) (0,15) (0,10) (1,18) (1,21) (1,11) (1,7) (1,20) (1,14) (1,16) (1,17) (1,12) (1,9) (1,6) (1,19) (1,2) (1,8) (1,15) (1,10) (2,18) (2,21) (2,11) (2,7) (2,20) (2,14) (2,16) (2,17) (2,12) (2,9) (2,6) (2,19) (2,8) (2,15) (2,10) (3,13) (3,4) (3,5) (4,13) (4,5) (5,13) (6,18) (6,21) (6,11) (6,7) (6,20) (6,14) (6,16) (6,17) (6,12) (6,9) (6,19) (6,8) (6,15) (6,10) (7,18) (7,21) (7,11) (7,20) (7,14) (7,16) (7,17) (7,12) (7,9) (7,19) (7,8) (7,15) (7,10) (8,18) (8,21) (8,11) (8,20) (8,14) (8,16) (8,17) (8,12) (8,9) (8,19) (8,15) (8,10) (9,18) (9,21) (9,11) (9,20) (9,14) (9,16) (9,17) (9,12) (9,19) (9,15) (9,10) (10,18) (10,21) (10,11) (10,20) (10,14) (10,16) (10,17) (10,12) (10,19) (10,15) (11,18) (11,21) (11,20) (11,14) (11,16) (11,17) (11,12) (11,19) (11,15) (12,18) (12,21) (12,20) (12,14) (12,16) (12,17) (12,19) (12,15) (14,18) (14,21) (14,20) (14,16) (14,17) (14,19) (14,15) (15,18) (15,21) (15,20) (15,16) (15,17) (15,19) (16,18) (16,21) (16,20) (16,17) (16,19) (17,18) (17,21) (17,20) (17,19) (18,21) (18,20) (18,19) (19,21) (19,20) (20,21)\nIs there a path between node 21 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph588-8_5", + "image": "data/connectivity/graph_visual/medium/graph588.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (1,5) (1,12) (1,3) (1,17) (1,15) (1,16) (2,21) (2,9) (2,11) (2,13) (2,4) (2,14) (3,23) (3,13) (3,15) (3,19) (3,14) (4,5) (4,12) (4,9) (4,17) (4,11) (5,8) (5,12) (5,22) (5,16) (5,14) (6,10) (7,18) (7,10) (8,12) (8,17) (8,23) (8,11) (8,16) (9,22) (9,13) (11,21) (11,15) (12,17) (12,23) (12,16) (12,14) (13,22) (13,23) (13,19) (13,16) (14,20) (14,22) (14,17) (15,20) (15,19) (16,22) (16,17) (16,23) (16,19) (19,23) (20,22) (22,23)\nIs there a path between node 8 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph772-5_2", + "image": "data/connectivity/graph_visual/medium/graph772.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,18) (0,22) (0,4) (0,12) (0,21) (0,24) (0,16) (1,3) (1,11) (1,10) (1,5) (1,8) (1,19) (1,9) (1,17) (1,7) (1,2) (1,20) (2,3) (2,11) (2,10) (2,5) (2,8) (2,19) (2,9) (2,17) (2,7) (2,20) (3,11) (3,10) (3,5) (3,8) (3,19) (3,9) (3,17) (3,7) (3,20) (4,15) (4,18) (4,22) (4,12) (4,21) (4,24) (4,16) (5,11) (5,10) (5,8) (5,19) (5,9) (5,17) (5,7) (5,20) (6,23) (6,14) (6,13) (7,11) (7,10) (7,8) (7,19) (7,9) (7,17) (7,20) (8,11) (8,10) (8,19) (8,9) (8,17) (8,20) (9,11) (9,10) (9,19) (9,17) (9,20) (10,11) (10,19) (10,17) (10,20) (11,19) (11,17) (11,20) (12,15) (12,18) (12,22) (12,21) (12,24) (12,16) (13,23) (13,14) (14,23) (15,18) (15,22) (15,21) (15,24) (15,16) (16,18) (16,22) (16,21) (16,24) (17,19) (17,20) (18,22) (18,21) (18,24) (19,20) (21,22) (21,24) (22,24)\nIs there a path between node 5 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph270-4_1", + "image": "data/connectivity/graph_visual/medium/graph270.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,16) (0,3) (0,5) (1,6) (1,7) (1,2) (1,8) (1,14) (1,13) (1,9) (1,4) (1,12) (1,19) (2,6) (2,11) (2,8) (2,14) (2,13) (2,9) (2,12) (2,19) (3,17) (3,16) (3,15) (3,5) (3,18) (4,7) (4,8) (4,14) (4,9) (4,12) (5,17) (5,16) (5,10) (5,15) (6,7) (6,11) (6,8) (6,14) (6,12) (6,19) (7,11) (7,19) (8,11) (8,13) (8,9) (8,19) (9,11) (9,14) (9,13) (9,12) (9,19) (10,17) (10,16) (10,15) (11,14) (11,13) (11,12) (12,13) (12,19) (13,14) (13,19) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph90-1_9", + "image": "data/connectivity/graph_visual/medium/graph90.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,10) (1,11) (1,9) (1,14) (2,5) (2,6) (3,11) (3,13) (4,11) (4,13) (4,15) (5,7) (5,6) (7,10) (8,11) (8,9) (9,14) (9,12) (11,13) (13,14) (13,15)\nIs there a path between node 1 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph40-12_1", + "image": "data/connectivity/graph_visual/medium/graph40.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,1) (0,4) (1,11) (2,3) (2,12) (4,6) (4,7) (5,9) (6,7) (7,9) (7,11) (8,10) (8,12) (9,11)\nIs there a path between node 12 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph719-7_6", + "image": "data/connectivity/graph_visual/medium/graph719.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,22) (0,21) (0,7) (0,16) (0,14) (1,22) (1,10) (1,16) (2,6) (2,13) (2,24) (2,19) (2,3) (2,9) (2,23) (2,4) (2,15) (2,17) (2,11) (2,5) (3,6) (3,24) (3,19) (3,9) (3,23) (3,4) (3,12) (3,15) (3,17) (3,11) (3,5) (3,8) (4,6) (4,24) (4,9) (4,23) (4,15) (4,17) (4,18) (4,11) (4,5) (5,6) (5,13) (5,24) (5,19) (5,9) (5,23) (5,15) (5,18) (5,8) (6,24) (6,15) (6,17) (6,18) (6,8) (7,20) (7,22) (7,16) (8,24) (8,9) (8,12) (8,15) (8,17) (8,18) (9,13) (9,24) (9,23) (9,12) (9,17) (9,11) (10,20) (10,21) (10,16) (10,14) (11,24) (11,15) (11,17) (11,18) (12,13) (12,19) (12,17) (12,18) (13,24) (13,23) (13,17) (13,18) (14,20) (14,21) (14,16) (15,24) (15,19) (15,23) (15,18) (16,20) (16,21) (17,24) (17,23) (18,19) (19,24) (20,22) (20,21) (21,22)\nIs there a path between node 7 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph153-0_7", + "image": "data/connectivity/graph_visual/medium/graph153.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,15) (0,4) (0,13) (0,14) (0,8) (0,16) (0,7) (0,1) (0,2) (0,5) (1,3) (1,15) (1,4) (1,13) (1,14) (1,8) (1,16) (1,7) (1,2) (1,5) (2,3) (2,15) (2,4) (2,13) (2,14) (2,8) (2,16) (2,7) (2,5) (3,15) (3,4) (3,13) (3,14) (3,8) (3,16) (3,7) (3,5) (4,15) (4,13) (4,14) (4,8) (4,16) (4,7) (4,5) (5,15) (5,13) (5,14) (5,8) (5,16) (5,7) (6,11) (6,9) (6,10) (6,12) (7,15) (7,13) (7,14) (7,8) (7,16) (8,15) (8,13) (8,14) (8,16) (9,11) (9,10) (9,12) (10,11) (10,12) (11,12) (13,15) (13,14) (13,16) (14,15) (14,16) (15,16)\nIs there a path between node 0 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph398-1_0", + "image": "data/connectivity/graph_visual/medium/graph398.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,12) (0,3) (0,11) (0,18) (0,7) (0,8) (0,9) (0,1) (0,10) (0,15) (0,17) (0,13) (0,16) (0,19) (0,2) (0,6) (0,5) (0,14) (1,12) (1,3) (1,11) (1,18) (1,7) (1,8) (1,9) (1,10) (1,15) (1,17) (1,13) (1,16) (1,19) (1,2) (1,6) (1,5) (1,14) (2,12) (2,3) (2,11) (2,18) (2,7) (2,8) (2,9) (2,10) (2,15) (2,17) (2,13) (2,16) (2,19) (2,6) (2,5) (2,14) (3,12) (3,11) (3,18) (3,7) (3,8) (3,9) (3,10) (3,15) (3,17) (3,13) (3,16) (3,19) (3,6) (3,5) (3,14) (4,20) (4,21) (5,12) (5,11) (5,18) (5,7) (5,8) (5,9) (5,10) (5,15) (5,17) (5,13) (5,16) (5,19) (5,6) (5,14) (6,12) (6,11) (6,18) (6,7) (6,8) (6,9) (6,10) (6,15) (6,17) (6,13) (6,16) (6,19) (6,14) (7,12) (7,11) (7,18) (7,8) (7,9) (7,10) (7,15) (7,17) (7,13) (7,16) (7,19) (7,14) (8,12) (8,11) (8,18) (8,9) (8,10) (8,15) (8,17) (8,13) (8,16) (8,19) (8,14) (9,12) (9,11) (9,18) (9,10) (9,15) (9,17) (9,13) (9,16) (9,19) (9,14) (10,12) (10,11) (10,18) (10,15) (10,17) (10,13) (10,16) (10,19) (10,14) (11,12) (11,18) (11,15) (11,17) (11,13) (11,16) (11,19) (11,14) (12,18) (12,15) (12,17) (12,13) (12,16) (12,19) (12,14) (13,18) (13,15) (13,17) (13,16) (13,19) (13,14) (14,18) (14,15) (14,17) (14,16) (14,19) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19) (20,21)\nIs there a path between node 1 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph713-0_12", + "image": "data/connectivity/graph_visual/medium/graph713.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (1,6) (1,4) (1,20) (1,18) (1,10) (1,14) (1,21) (1,24) (1,23) (1,15) (1,11) (2,17) (2,19) (2,22) (2,13) (2,9) (4,6) (4,12) (4,10) (4,14) (4,21) (4,23) (4,15) (4,11) (5,17) (5,8) (5,22) (5,13) (5,16) (5,9) (6,20) (6,18) (6,14) (6,21) (6,24) (6,23) (6,15) (8,19) (8,22) (8,13) (8,16) (8,9) (9,17) (9,19) (9,13) (9,16) (10,12) (10,20) (10,21) (10,24) (10,23) (11,12) (11,20) (11,18) (11,14) (11,21) (11,24) (11,23) (12,18) (12,14) (12,21) (12,24) (12,23) (12,15) (13,19) (13,22) (14,18) (14,21) (14,23) (15,20) (15,18) (15,24) (16,17) (16,19) (16,22) (18,20) (18,21) (20,24) (20,23) (21,24) (21,23)\nIs there a path between node 0 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph29-0_2", + "image": "data/connectivity/graph_visual/medium/graph29.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,9) (0,11) (1,6) (1,3) (1,4) (1,7) (1,8) (1,10) (1,2) (1,5) (2,6) (2,3) (2,4) (2,7) (2,8) (2,10) (2,5) (3,6) (3,4) (3,7) (3,8) (3,10) (3,5) (4,6) (4,7) (4,8) (4,10) (4,5) (5,6) (5,7) (5,8) (5,10) (6,7) (6,8) (6,10) (7,8) (7,10) (8,10) (9,11)\nIs there a path between node 0 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph520-11_2", + "image": "data/connectivity/graph_visual/medium/graph520.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,18) (0,19) (0,3) (0,17) (0,2) (0,21) (0,13) (0,22) (1,19) (1,3) (1,2) (1,13) (2,18) (2,19) (2,5) (2,3) (2,17) (2,13) (2,22) (3,18) (3,5) (3,17) (4,8) (4,9) (4,7) (4,20) (4,12) (5,19) (5,21) (5,13) (6,8) (6,9) (6,20) (6,14) (6,10) (6,15) (6,12) (6,16) (7,9) (7,10) (7,15) (7,12) (7,16) (8,14) (8,16) (9,14) (9,11) (9,15) (9,12) (9,16) (10,20) (10,14) (10,11) (10,16) (11,20) (11,14) (11,12) (11,16) (12,15) (13,18) (13,17) (13,21) (14,20) (14,15) (14,16) (15,20) (15,16) (17,18) (17,21) (17,22) (18,19) (18,22)\nIs there a path between node 11 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph163-13_7", + "image": "data/connectivity/graph_visual/medium/graph163.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,6) (1,13) (1,5) (2,17) (3,5) (3,15) (3,7) (4,8) (5,6) (5,16) (5,11) (5,15) (7,11) (10,16) (10,12) (10,13) (12,13)\nIs there a path between node 13 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph546-4_17", + "image": "data/connectivity/graph_visual/medium/graph546.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,19) (0,17) (0,7) (0,16) (0,21) (1,22) (1,19) (1,20) (1,21) (2,23) (2,6) (3,13) (3,18) (3,4) (3,10) (3,21) (4,19) (4,10) (4,16) (5,14) (5,12) (5,9) (5,11) (6,14) (6,23) (7,15) (7,22) (7,18) (7,8) (7,17) (7,20) (8,13) (8,21) (9,12) (9,11) (10,17) (13,19) (13,17) (13,21) (15,20) (16,18) (16,20) (19,20) (19,21)\nIs there a path between node 4 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph680-3_2", + "image": "data/connectivity/graph_visual/medium/graph680.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,1) (0,4) (0,13) (0,9) (0,5) (0,21) (0,8) (0,17) (0,3) (0,12) (0,14) (0,19) (0,20) (0,16) (1,2) (1,4) (1,13) (1,9) (1,5) (1,21) (1,8) (1,17) (1,3) (1,12) (1,14) (1,19) (1,20) (1,16) (2,4) (2,13) (2,9) (2,5) (2,21) (2,8) (2,17) (2,3) (2,12) (2,14) (2,19) (2,20) (2,16) (3,4) (3,13) (3,9) (3,5) (3,21) (3,8) (3,17) (3,12) (3,14) (3,19) (3,20) (3,16) (4,13) (4,9) (4,5) (4,21) (4,8) (4,17) (4,12) (4,14) (4,19) (4,20) (4,16) (5,13) (5,9) (5,21) (5,8) (5,17) (5,12) (5,14) (5,19) (5,20) (5,16) (6,23) (6,11) (6,18) (6,7) (6,22) (6,10) (6,15) (7,23) (7,11) (7,18) (7,22) (7,10) (7,15) (8,13) (8,9) (8,21) (8,17) (8,12) (8,14) (8,19) (8,20) (8,16) (9,13) (9,21) (9,17) (9,12) (9,14) (9,19) (9,20) (9,16) (10,23) (10,11) (10,18) (10,22) (10,15) (11,23) (11,18) (11,22) (11,15) (12,13) (12,21) (12,17) (12,14) (12,19) (12,20) (12,16) (13,21) (13,17) (13,14) (13,19) (13,20) (13,16) (14,21) (14,17) (14,19) (14,20) (14,16) (15,23) (15,18) (15,22) (16,21) (16,17) (16,19) (16,20) (17,21) (17,19) (17,20) (18,23) (18,22) (19,21) (19,20) (20,21) (22,23)\nIs there a path between node 3 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph80-2_0", + "image": "data/connectivity/graph_visual/medium/graph80.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,2) (0,1) (0,13) (0,12) (0,6) (0,14) (0,11) (0,9) (1,2) (1,3) (1,8) (1,4) (1,6) (1,11) (1,5) (2,7) (2,3) (2,13) (2,12) (2,6) (2,14) (2,11) (2,5) (3,7) (3,12) (3,4) (3,6) (3,14) (3,5) (3,9) (4,7) (4,13) (4,12) (4,8) (4,14) (4,11) (5,7) (5,12) (5,8) (5,6) (5,14) (5,11) (5,9) (6,7) (6,13) (6,12) (6,14) (6,9) (7,12) (7,8) (7,14) (7,11) (8,13) (8,14) (8,11) (9,13) (9,12) (9,14) (9,11) (11,12) (12,13) (12,14) (13,14)\nIs there a path between node 2 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph619-5_0", + "image": "data/connectivity/graph_visual/medium/graph619.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,18) (0,8) (0,2) (0,12) (0,22) (0,19) (0,10) (0,21) (0,3) (0,14) (0,20) (0,6) (0,15) (0,23) (0,16) (0,4) (0,17) (0,1) (1,18) (1,8) (1,2) (1,12) (1,22) (1,19) (1,10) (1,21) (1,3) (1,14) (1,20) (1,6) (1,15) (1,23) (1,16) (1,4) (1,17) (2,18) (2,8) (2,12) (2,22) (2,19) (2,10) (2,21) (2,3) (2,14) (2,20) (2,6) (2,15) (2,23) (2,16) (2,4) (2,17) (3,18) (3,8) (3,12) (3,22) (3,19) (3,10) (3,21) (3,14) (3,20) (3,6) (3,15) (3,23) (3,16) (3,4) (3,17) (4,18) (4,8) (4,12) (4,22) (4,19) (4,10) (4,21) (4,14) (4,20) (4,6) (4,15) (4,23) (4,16) (4,17) (5,9) (5,11) (5,7) (5,13) (6,18) (6,8) (6,12) (6,22) (6,19) (6,10) (6,21) (6,14) (6,20) (6,15) (6,23) (6,16) (6,17) (7,9) (7,11) (7,13) (8,18) (8,12) (8,22) (8,19) (8,10) (8,21) (8,14) (8,20) (8,15) (8,23) (8,16) (8,17) (9,11) (9,13) (10,18) (10,12) (10,22) (10,19) (10,21) (10,14) (10,20) (10,15) (10,23) (10,16) (10,17) (11,13) (12,18) (12,22) (12,19) (12,21) (12,14) (12,20) (12,15) (12,23) (12,16) (12,17) (14,18) (14,22) (14,19) (14,21) (14,20) (14,15) (14,23) (14,16) (14,17) (15,18) (15,22) (15,19) (15,21) (15,20) (15,23) (15,16) (15,17) (16,18) (16,22) (16,19) (16,21) (16,20) (16,23) (16,17) (17,18) (17,22) (17,19) (17,21) (17,20) (17,23) (18,22) (18,19) (18,21) (18,20) (18,23) (19,22) (19,21) (19,20) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 5 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph74-8_2", + "image": "data/connectivity/graph_visual/medium/graph74.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,11) (1,9) (2,14) (3,11) (4,13) (4,7) (5,11) (5,9) (6,9) (7,10) (7,12) (10,13) (10,12) (12,13)\nIs there a path between node 8 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph631-4_13", + "image": "data/connectivity/graph_visual/medium/graph631.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,8) (0,10) (0,12) (0,13) (1,21) (1,15) (1,9) (1,18) (2,4) (2,17) (3,11) (3,4) (4,20) (4,22) (5,21) (5,19) (5,8) (5,18) (5,13) (6,15) (6,14) (8,12) (9,21) (9,19) (9,15) (10,16) (10,15) (10,12) (12,19) (12,14) (13,16) (14,16) (14,19) (14,18) (16,19) (20,22)\nIs there a path between node 4 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph567-6_14", + "image": "data/connectivity/graph_visual/medium/graph567.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,14) (0,6) (0,18) (0,11) (0,5) (0,21) (0,10) (1,22) (1,16) (1,2) (1,9) (1,7) (1,13) (1,20) (1,19) (1,15) (1,23) (1,4) (1,3) (1,12) (1,8) (1,17) (2,22) (2,16) (2,9) (2,7) (2,13) (2,20) (2,19) (2,15) (2,23) (2,4) (2,3) (2,12) (2,8) (2,17) (3,22) (3,16) (3,9) (3,7) (3,13) (3,20) (3,19) (3,15) (3,23) (3,4) (3,12) (3,8) (3,17) (4,22) (4,16) (4,9) (4,7) (4,13) (4,20) (4,19) (4,15) (4,23) (4,12) (4,8) (4,17) (5,14) (5,6) (5,18) (5,11) (5,21) (5,10) (6,14) (6,18) (6,11) (6,21) (6,10) (7,22) (7,16) (7,9) (7,13) (7,20) (7,19) (7,15) (7,23) (7,12) (7,8) (7,17) (8,22) (8,16) (8,9) (8,13) (8,20) (8,19) (8,15) (8,23) (8,12) (8,17) (9,22) (9,16) (9,13) (9,20) (9,19) (9,15) (9,23) (9,12) (9,17) (10,14) (10,18) (10,11) (10,21) (11,14) (11,18) (11,21) (12,22) (12,16) (12,13) (12,20) (12,19) (12,15) (12,23) (12,17) (13,22) (13,16) (13,20) (13,19) (13,15) (13,23) (13,17) (14,18) (14,21) (15,22) (15,16) (15,20) (15,19) (15,23) (15,17) (16,22) (16,20) (16,19) (16,23) (16,17) (17,22) (17,20) (17,19) (17,23) (18,21) (19,22) (19,20) (19,23) (20,22) (20,23) (22,23)\nIs there a path between node 6 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph680-15_12", + "image": "data/connectivity/graph_visual/medium/graph680.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,1) (0,4) (0,13) (0,9) (0,5) (0,21) (0,8) (0,17) (0,3) (0,12) (0,14) (0,19) (0,20) (0,16) (1,2) (1,4) (1,13) (1,9) (1,5) (1,21) (1,8) (1,17) (1,3) (1,12) (1,14) (1,19) (1,20) (1,16) (2,4) (2,13) (2,9) (2,5) (2,21) (2,8) (2,17) (2,3) (2,12) (2,14) (2,19) (2,20) (2,16) (3,4) (3,13) (3,9) (3,5) (3,21) (3,8) (3,17) (3,12) (3,14) (3,19) (3,20) (3,16) (4,13) (4,9) (4,5) (4,21) (4,8) (4,17) (4,12) (4,14) (4,19) (4,20) (4,16) (5,13) (5,9) (5,21) (5,8) (5,17) (5,12) (5,14) (5,19) (5,20) (5,16) (6,23) (6,11) (6,18) (6,7) (6,22) (6,10) (6,15) (7,23) (7,11) (7,18) (7,22) (7,10) (7,15) (8,13) (8,9) (8,21) (8,17) (8,12) (8,14) (8,19) (8,20) (8,16) (9,13) (9,21) (9,17) (9,12) (9,14) (9,19) (9,20) (9,16) (10,23) (10,11) (10,18) (10,22) (10,15) (11,23) (11,18) (11,22) (11,15) (12,13) (12,21) (12,17) (12,14) (12,19) (12,20) (12,16) (13,21) (13,17) (13,14) (13,19) (13,20) (13,16) (14,21) (14,17) (14,19) (14,20) (14,16) (15,23) (15,18) (15,22) (16,21) (16,17) (16,19) (16,20) (17,21) (17,19) (17,20) (18,23) (18,22) (19,21) (19,20) (20,21) (22,23)\nIs there a path between node 15 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph663-22_19", + "image": "data/connectivity/graph_visual/medium/graph663.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,8) (0,23) (0,19) (0,9) (0,21) (1,14) (2,7) (2,11) (2,4) (3,5) (3,7) (3,16) (3,17) (3,18) (3,11) (3,4) (4,5) (4,7) (4,10) (4,16) (4,18) (5,7) (5,10) (5,11) (6,22) (6,8) (6,12) (6,19) (7,10) (7,16) (7,17) (7,13) (7,18) (7,11) (8,22) (8,23) (8,15) (8,21) (9,22) (9,23) (9,19) (9,15) (10,18) (11,16) (11,17) (11,13) (12,22) (12,23) (12,15) (12,21) (13,16) (13,17) (13,18) (14,20) (15,23) (15,19) (15,21) (16,18) (17,18) (19,22) (19,21) (21,22) (21,23)\nIs there a path between node 22 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph587-11_9", + "image": "data/connectivity/graph_visual/medium/graph587.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,5) (0,14) (0,23) (0,10) (1,5) (1,14) (1,15) (2,21) (2,9) (2,3) (2,15) (3,21) (3,11) (3,15) (3,18) (4,7) (4,22) (5,21) (5,9) (5,17) (5,10) (5,18) (6,17) (6,18) (7,19) (8,12) (9,21) (9,11) (9,15) (9,18) (10,15) (13,22) (16,19) (17,21) (18,21) (18,23)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph512-9_21", + "image": "data/connectivity/graph_visual/medium/graph512.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,19) (0,3) (0,15) (0,6) (1,17) (1,2) (1,11) (1,12) (1,9) (2,11) (2,12) (2,7) (2,10) (2,9) (2,4) (3,19) (3,22) (3,15) (4,11) (4,5) (4,12) (4,7) (4,10) (4,9) (5,17) (5,11) (5,12) (5,10) (5,9) (6,21) (6,19) (6,22) (6,15) (7,11) (7,10) (7,9) (8,13) (8,20) (8,18) (9,17) (9,11) (9,10) (10,11) (10,12) (11,17) (11,12) (12,17) (13,20) (14,20) (15,21) (15,19) (15,22) (15,16) (16,21) (16,19) (18,20) (19,21) (19,22)\nIs there a path between node 9 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph301-7_0", + "image": "data/connectivity/graph_visual/medium/graph301.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,5) (0,14) (0,8) (0,1) (0,17) (0,2) (0,4) (0,10) (0,12) (0,6) (0,7) (0,3) (0,11) (1,5) (1,14) (1,8) (1,17) (1,12) (1,13) (1,3) (2,5) (2,4) (2,10) (2,12) (2,6) (2,7) (2,13) (2,11) (3,14) (3,8) (3,10) (3,12) (3,6) (3,7) (4,14) (4,8) (4,17) (4,10) (4,12) (4,7) (4,11) (5,8) (5,17) (5,12) (5,6) (5,7) (5,13) (5,11) (6,14) (6,10) (6,12) (6,13) (6,11) (7,14) (7,8) (7,17) (7,10) (7,12) (7,13) (7,11) (8,14) (8,17) (8,10) (8,12) (8,11) (9,15) (10,13) (11,14) (11,12) (11,13) (12,17) (12,13) (15,19) (15,18) (15,16) (16,19) (16,18) (18,19)\nIs there a path between node 7 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph717-8_5", + "image": "data/connectivity/graph_visual/medium/graph717.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,13) (0,6) (0,16) (0,20) (1,21) (1,18) (1,2) (1,23) (1,7) (1,5) (1,11) (1,9) (1,3) (1,19) (1,14) (1,24) (2,4) (2,22) (2,18) (2,23) (2,5) (2,11) (2,19) (3,18) (3,5) (3,11) (3,19) (3,24) (4,21) (4,22) (4,8) (4,18) (4,23) (4,7) (4,5) (4,9) (4,14) (5,8) (5,7) (5,11) (5,9) (5,19) (6,10) (6,13) (6,16) (6,20) (6,12) (6,15) (7,21) (7,8) (7,23) (7,11) (7,9) (7,19) (8,18) (8,11) (8,14) (8,24) (9,21) (9,22) (9,18) (9,19) (9,14) (9,24) (10,13) (10,20) (10,15) (11,21) (11,22) (11,18) (11,23) (11,14) (12,13) (12,16) (12,20) (13,16) (13,15) (14,22) (14,18) (14,19) (14,24) (15,16) (15,20) (16,20) (18,22) (18,23) (18,19) (18,24) (19,22) (19,23) (19,24) (21,22) (22,23) (22,24) (23,24)\nIs there a path between node 8 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph642-20_1", + "image": "data/connectivity/graph_visual/medium/graph642.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,23) (0,10) (1,8) (1,2) (1,3) (1,6) (1,16) (2,5) (2,21) (2,6) (2,19) (2,10) (3,8) (3,5) (3,4) (4,17) (4,5) (4,9) (4,14) (5,17) (5,22) (5,11) (5,19) (5,13) (5,10) (6,9) (6,11) (6,21) (6,13) (7,12) (7,18) (7,20) (8,15) (8,13) (8,16) (9,17) (10,16) (11,17) (11,14) (11,13) (12,18) (13,17) (13,22) (13,14) (13,21) (14,22) (14,23) (14,19) (14,16) (16,22) (16,23) (17,23)\nIs there a path between node 20 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph402-3_2", + "image": "data/connectivity/graph_visual/medium/graph402.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,16) (0,1) (0,8) (2,6) (2,17) (2,20) (3,7) (3,13) (5,20) (5,13) (6,17) (6,10) (6,13) (7,10) (7,11) (7,9) (8,19) (8,14) (9,10) (12,17) (12,20) (12,13) (14,21)\nIs there a path between node 3 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph12-0_4", + "image": "data/connectivity/graph_visual/medium/graph12.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,3) (0,10) (0,7) (0,2) (0,9) (0,1) (0,8) (0,5) (1,3) (1,10) (1,7) (1,2) (1,9) (1,8) (1,5) (2,3) (2,10) (2,7) (2,9) (2,8) (2,5) (3,10) (3,7) (3,9) (3,8) (3,5) (4,6) (5,10) (5,7) (5,9) (5,8) (7,10) (7,9) (7,8) (8,10) (8,9) (9,10)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph469-15_10", + "image": "data/connectivity/graph_visual/medium/graph469.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,3) (0,21) (0,8) (0,11) (0,16) (0,13) (0,10) (0,20) (0,6) (0,4) (1,14) (1,17) (1,18) (1,5) (1,19) (1,2) (2,22) (2,14) (2,5) (3,8) (3,11) (3,10) (3,12) (3,6) (4,11) (4,13) (4,20) (4,12) (5,22) (5,14) (5,17) (5,18) (5,9) (5,19) (6,8) (6,11) (6,16) (6,13) (6,10) (6,20) (6,12) (7,15) (8,11) (8,13) (8,10) (8,20) (8,12) (9,22) (9,14) (9,17) (9,18) (9,19) (10,21) (10,13) (11,16) (11,13) (11,20) (11,12) (12,21) (12,16) (12,13) (12,20) (13,21) (13,16) (13,20) (14,22) (14,18) (16,21) (16,20) (17,22) (17,18) (17,19) (18,19) (20,21)\nIs there a path between node 15 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph390-4_11", + "image": "data/connectivity/graph_visual/medium/graph390.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,20) (0,11) (0,2) (0,10) (0,8) (0,17) (0,6) (0,7) (0,9) (0,5) (1,13) (1,19) (1,14) (1,18) (1,12) (1,3) (1,4) (1,16) (1,15) (2,20) (2,11) (2,10) (2,8) (2,17) (2,6) (2,7) (2,9) (2,5) (3,13) (3,19) (3,14) (3,18) (3,12) (3,4) (3,16) (3,15) (4,13) (4,19) (4,14) (4,18) (4,12) (4,16) (4,15) (5,20) (5,11) (5,10) (5,8) (5,17) (5,6) (5,7) (5,9) (6,20) (6,11) (6,10) (6,8) (6,17) (6,7) (6,9) (7,20) (7,11) (7,10) (7,8) (7,17) (7,9) (8,20) (8,11) (8,10) (8,17) (8,9) (9,20) (9,11) (9,10) (9,17) (10,20) (10,11) (10,17) (11,20) (11,17) (12,13) (12,19) (12,14) (12,18) (12,16) (12,15) (13,19) (13,14) (13,18) (13,16) (13,15) (14,19) (14,18) (14,16) (14,15) (15,19) (15,18) (15,16) (16,19) (16,18) (17,20) (18,19)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph414-18_13", + "image": "data/connectivity/graph_visual/medium/graph414.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,1) (0,18) (1,18) (1,14) (1,11) (2,4) (2,21) (2,15) (2,9) (2,12) (2,8) (2,3) (2,10) (3,4) (3,9) (3,12) (3,5) (3,20) (3,8) (3,17) (3,10) (3,19) (4,21) (4,15) (4,12) (4,6) (4,5) (4,17) (4,19) (5,21) (5,9) (5,6) (5,20) (5,8) (5,10) (6,15) (6,9) (6,12) (6,8) (6,10) (6,19) (7,13) (8,21) (8,15) (8,9) (8,12) (8,17) (8,10) (8,19) (9,21) (9,20) (9,19) (10,21) (10,20) (10,17) (11,14) (12,21) (12,15) (12,20) (12,19) (14,16) (15,20) (15,17) (17,21) (17,20) (17,19) (19,21)\nIs there a path between node 18 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph303-5_17", + "image": "data/connectivity/graph_visual/medium/graph303.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,11) (0,15) (0,17) (1,11) (1,17) (2,10) (2,3) (2,18) (2,14) (2,8) (2,13) (2,4) (2,6) (2,19) (2,9) (3,10) (3,5) (3,7) (3,14) (3,13) (3,12) (3,4) (3,6) (3,19) (3,9) (4,5) (4,18) (4,14) (4,8) (4,13) (4,12) (4,6) (4,19) (4,9) (5,14) (5,8) (5,13) (5,12) (5,19) (6,10) (6,7) (6,18) (6,14) (6,8) (6,13) (6,12) (6,19) (6,9) (7,10) (7,8) (7,19) (8,10) (8,18) (8,14) (8,12) (8,19) (8,9) (9,10) (9,18) (9,14) (9,13) (9,19) (10,18) (10,14) (10,13) (10,19) (11,16) (12,19) (13,18) (14,19) (16,17) (18,19)\nIs there a path between node 5 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph471-14_19", + "image": "data/connectivity/graph_visual/medium/graph471.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,19) (1,12) (1,19) (2,13) (3,20) (3,11) (4,7) (4,16) (4,18) (5,17) (5,7) (6,15) (6,20) (6,11) (7,20) (7,11) (8,12) (8,13) (8,19) (11,17) (11,15) (12,19) (16,17) (16,20) (17,20) (18,20)\nIs there a path between node 14 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph667-3_16", + "image": "data/connectivity/graph_visual/medium/graph667.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,14) (0,6) (0,21) (0,7) (0,12) (0,5) (0,16) (0,15) (0,3) (0,17) (0,22) (1,4) (1,2) (1,11) (2,4) (2,18) (2,11) (3,14) (3,21) (3,7) (3,12) (3,5) (3,19) (3,23) (3,15) (3,22) (3,20) (4,18) (4,11) (5,6) (5,21) (5,12) (5,16) (5,19) (5,15) (5,17) (5,22) (5,20) (6,21) (6,12) (6,16) (6,19) (6,23) (6,15) (6,17) (6,22) (6,20) (7,12) (7,19) (7,23) (7,17) (7,22) (7,20) (8,13) (9,10) (9,13) (10,13) (12,14) (12,21) (12,19) (12,23) (12,15) (12,17) (12,22) (14,21) (14,16) (14,19) (14,23) (14,17) (14,22) (14,20) (15,16) (15,19) (15,23) (15,17) (15,22) (16,21) (16,17) (16,22) (16,20) (17,21) (17,19) (17,22) (17,20) (19,21) (19,23) (19,22) (19,20) (20,23) (20,22) (21,22) (22,23)\nIs there a path between node 3 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph166-9_2", + "image": "data/connectivity/graph_visual/medium/graph166.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,7) (1,11) (1,16) (1,2) (1,9) (1,4) (2,10) (2,7) (2,11) (2,5) (3,12) (3,5) (3,16) (3,8) (4,16) (4,17) (5,13) (5,15) (5,11) (5,16) (5,6) (5,17) (6,9) (7,10) (7,11) (8,11) (8,9) (9,15) (9,11) (9,17) (10,11) (10,12) (11,15) (12,16) (13,15) (13,16) (15,17) (16,17)\nIs there a path between node 9 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph806-4_1", + "image": "data/connectivity/graph_visual/medium/graph806.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,21) (1,17) (1,15) (1,2) (1,4) (1,18) (2,8) (2,13) (2,17) (2,15) (2,23) (2,22) (2,4) (2,18) (2,12) (4,21) (4,8) (4,13) (4,15) (4,23) (4,22) (4,18) (4,12) (5,21) (5,8) (5,13) (5,17) (5,15) (5,22) (5,18) (7,14) (7,16) (7,10) (7,11) (7,19) (8,21) (8,17) (8,23) (8,18) (9,14) (9,24) (10,14) (10,24) (10,19) (11,14) (11,16) (11,24) (12,21) (12,13) (12,17) (12,15) (12,23) (12,22) (12,18) (13,21) (13,17) (13,15) (13,23) (13,22) (14,24) (15,21) (15,17) (15,23) (15,22) (15,18) (16,19) (17,21) (17,18) (18,21) (18,23) (21,22) (22,23)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph531-12_19", + "image": "data/connectivity/graph_visual/medium/graph531.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,13) (0,7) (0,4) (0,9) (0,21) (0,16) (0,1) (0,18) (0,11) (0,8) (0,6) (0,15) (0,14) (0,12) (0,20) (0,2) (0,22) (1,10) (1,13) (1,7) (1,4) (1,9) (1,21) (1,16) (1,18) (1,11) (1,8) (1,6) (1,15) (1,14) (1,12) (1,20) (1,2) (1,22) (2,10) (2,13) (2,7) (2,4) (2,9) (2,21) (2,16) (2,18) (2,11) (2,8) (2,6) (2,15) (2,14) (2,12) (2,20) (2,22) (3,17) (3,19) (3,5) (4,10) (4,13) (4,7) (4,9) (4,21) (4,16) (4,18) (4,11) (4,8) (4,6) (4,15) (4,14) (4,12) (4,20) (4,22) (5,17) (5,19) (6,10) (6,13) (6,7) (6,9) (6,21) (6,16) (6,18) (6,11) (6,8) (6,15) (6,14) (6,12) (6,20) (6,22) (7,10) (7,13) (7,9) (7,21) (7,16) (7,18) (7,11) (7,8) (7,15) (7,14) (7,12) (7,20) (7,22) (8,10) (8,13) (8,9) (8,21) (8,16) (8,18) (8,11) (8,15) (8,14) (8,12) (8,20) (8,22) (9,10) (9,13) (9,21) (9,16) (9,18) (9,11) (9,15) (9,14) (9,12) (9,20) (9,22) (10,13) (10,21) (10,16) (10,18) (10,11) (10,15) (10,14) (10,12) (10,20) (10,22) (11,13) (11,21) (11,16) (11,18) (11,15) (11,14) (11,12) (11,20) (11,22) (12,13) (12,21) (12,16) (12,18) (12,15) (12,14) (12,20) (12,22) (13,21) (13,16) (13,18) (13,15) (13,14) (13,20) (13,22) (14,21) (14,16) (14,18) (14,15) (14,20) (14,22) (15,21) (15,16) (15,18) (15,20) (15,22) (16,21) (16,18) (16,20) (16,22) (17,19) (18,21) (18,20) (18,22) (20,21) (20,22) (21,22)\nIs there a path between node 12 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph535-7_8", + "image": "data/connectivity/graph_visual/medium/graph535.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,3) (0,7) (0,4) (0,18) (0,13) (0,2) (0,12) (0,10) (0,11) (0,9) (0,5) (0,20) (0,22) (0,19) (0,6) (0,8) (0,14) (1,17) (1,15) (1,16) (2,21) (2,3) (2,7) (2,4) (2,18) (2,13) (2,12) (2,10) (2,11) (2,9) (2,5) (2,20) (2,22) (2,19) (2,6) (2,8) (2,14) (3,21) (3,7) (3,4) (3,18) (3,13) (3,12) (3,10) (3,11) (3,9) (3,5) (3,20) (3,22) (3,19) (3,6) (3,8) (3,14) (4,21) (4,7) (4,18) (4,13) (4,12) (4,10) (4,11) (4,9) (4,5) (4,20) (4,22) (4,19) (4,6) (4,8) (4,14) (5,21) (5,7) (5,18) (5,13) (5,12) (5,10) (5,11) (5,9) (5,20) (5,22) (5,19) (5,6) (5,8) (5,14) (6,21) (6,7) (6,18) (6,13) (6,12) (6,10) (6,11) (6,9) (6,20) (6,22) (6,19) (6,8) (6,14) (7,21) (7,18) (7,13) (7,12) (7,10) (7,11) (7,9) (7,20) (7,22) (7,19) (7,8) (7,14) (8,21) (8,18) (8,13) (8,12) (8,10) (8,11) (8,9) (8,20) (8,22) (8,19) (8,14) (9,21) (9,18) (9,13) (9,12) (9,10) (9,11) (9,20) (9,22) (9,19) (9,14) (10,21) (10,18) (10,13) (10,12) (10,11) (10,20) (10,22) (10,19) (10,14) (11,21) (11,18) (11,13) (11,12) (11,20) (11,22) (11,19) (11,14) (12,21) (12,18) (12,13) (12,20) (12,22) (12,19) (12,14) (13,21) (13,18) (13,20) (13,22) (13,19) (13,14) (14,21) (14,18) (14,20) (14,22) (14,19) (15,17) (15,16) (16,17) (18,21) (18,20) (18,22) (18,19) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 7 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph466-16_14", + "image": "data/connectivity/graph_visual/medium/graph466.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,10) (0,14) (0,1) (0,11) (0,17) (0,13) (1,2) (1,10) (1,14) (1,11) (1,17) (1,13) (2,10) (2,14) (2,11) (2,17) (2,13) (3,19) (3,9) (3,12) (3,16) (3,5) (3,7) (3,18) (3,21) (4,15) (4,20) (4,6) (4,8) (5,19) (5,9) (5,12) (5,16) (5,7) (5,18) (5,21) (6,15) (6,20) (6,8) (7,19) (7,9) (7,12) (7,16) (7,18) (7,21) (8,15) (8,20) (9,19) (9,12) (9,16) (9,18) (9,21) (10,14) (10,11) (10,17) (10,13) (11,14) (11,17) (11,13) (12,19) (12,16) (12,18) (12,21) (13,14) (13,17) (14,17) (15,20) (16,19) (16,18) (16,21) (18,19) (18,21) (19,21)\nIs there a path between node 16 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph811-17_6", + "image": "data/connectivity/graph_visual/medium/graph811.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,16) (0,23) (0,6) (0,5) (0,4) (0,11) (0,20) (0,7) (0,21) (0,8) (2,3) (2,12) (2,16) (2,23) (2,5) (2,4) (2,11) (2,20) (2,21) (2,8) (3,19) (3,12) (3,16) (3,23) (3,17) (3,4) (3,11) (3,7) (3,21) (4,19) (4,12) (4,16) (4,6) (4,17) (4,11) (4,20) (4,7) (5,12) (5,16) (5,23) (5,17) (5,11) (5,20) (5,7) (5,21) (6,12) (6,16) (6,11) (6,20) (7,19) (7,12) (7,16) (7,23) (7,17) (7,11) (7,20) (7,21) (7,8) (8,19) (8,10) (8,12) (8,16) (8,23) (8,17) (8,20) (9,22) (9,24) (9,15) (9,13) (10,23) (10,17) (10,11) (10,20) (10,21) (11,19) (11,16) (11,23) (11,20) (11,21) (12,19) (12,23) (12,17) (12,21) (13,14) (13,24) (13,15) (15,22) (15,24) (16,19) (16,23) (16,17) (16,20) (16,21) (17,19) (17,23) (17,20) (19,23) (19,21) (20,23) (20,21) (22,24)\nIs there a path between node 17 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph512-5_2", + "image": "data/connectivity/graph_visual/medium/graph512.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,19) (0,3) (0,15) (0,6) (1,17) (1,2) (1,11) (1,12) (1,9) (2,11) (2,12) (2,7) (2,10) (2,9) (2,4) (3,19) (3,22) (3,15) (4,11) (4,5) (4,12) (4,7) (4,10) (4,9) (5,17) (5,11) (5,12) (5,10) (5,9) (6,21) (6,19) (6,22) (6,15) (7,11) (7,10) (7,9) (8,13) (8,20) (8,18) (9,17) (9,11) (9,10) (10,11) (10,12) (11,17) (11,12) (12,17) (13,20) (14,20) (15,21) (15,19) (15,22) (15,16) (16,21) (16,19) (18,20) (19,21) (19,22)\nIs there a path between node 5 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph677-10_18", + "image": "data/connectivity/graph_visual/medium/graph677.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,4) (0,9) (0,19) (0,14) (0,17) (0,7) (0,6) (0,5) (0,16) (0,13) (0,22) (0,12) (0,15) (0,23) (1,3) (1,2) (1,21) (1,8) (1,20) (2,3) (2,21) (2,8) (2,20) (3,21) (3,8) (3,20) (4,11) (4,9) (4,19) (4,14) (4,17) (4,7) (4,6) (4,5) (4,16) (4,13) (4,22) (4,12) (4,15) (4,23) (5,11) (5,9) (5,19) (5,14) (5,17) (5,7) (5,6) (5,16) (5,13) (5,22) (5,12) (5,15) (5,23) (6,11) (6,9) (6,19) (6,14) (6,17) (6,7) (6,16) (6,13) (6,22) (6,12) (6,15) (6,23) (7,11) (7,9) (7,19) (7,14) (7,17) (7,16) (7,13) (7,22) (7,12) (7,15) (7,23) (8,21) (8,20) (9,11) (9,19) (9,14) (9,17) (9,16) (9,13) (9,22) (9,12) (9,15) (9,23) (11,19) (11,14) (11,17) (11,16) (11,13) (11,22) (11,12) (11,15) (11,23) (12,19) (12,14) (12,17) (12,16) (12,13) (12,22) (12,15) (12,23) (13,19) (13,14) (13,17) (13,16) (13,22) (13,15) (13,23) (14,19) (14,17) (14,16) (14,22) (14,15) (14,23) (15,19) (15,17) (15,16) (15,22) (15,23) (16,19) (16,17) (16,22) (16,23) (17,19) (17,22) (17,23) (19,22) (19,23) (20,21) (22,23)\nIs there a path between node 10 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph126-2_14", + "image": "data/connectivity/graph_visual/medium/graph126.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,11) (0,3) (0,7) (0,10) (0,13) (0,12) (0,16) (1,14) (1,2) (1,5) (1,9) (1,8) (1,15) (1,4) (1,6) (2,14) (2,5) (2,9) (2,8) (2,15) (2,4) (2,6) (3,11) (3,7) (3,10) (3,13) (3,12) (3,16) (4,14) (4,5) (4,9) (4,8) (4,15) (4,6) (5,14) (5,9) (5,8) (5,15) (5,6) (6,14) (6,9) (6,8) (6,15) (7,11) (7,10) (7,13) (7,12) (7,16) (8,14) (8,9) (8,15) (9,14) (9,15) (10,11) (10,13) (10,12) (10,16) (11,13) (11,12) (11,16) (12,13) (12,16) (13,16) (14,15)\nIs there a path between node 2 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph151-11_16", + "image": "data/connectivity/graph_visual/medium/graph151.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,13) (0,14) (0,7) (0,8) (0,17) (0,4) (1,5) (1,3) (1,15) (1,16) (1,11) (1,12) (1,10) (1,9) (1,6) (1,2) (2,5) (2,3) (2,15) (2,16) (2,11) (2,12) (2,10) (2,9) (2,6) (3,5) (3,15) (3,16) (3,11) (3,12) (3,10) (3,9) (3,6) (4,13) (4,14) (4,7) (4,8) (4,17) (5,15) (5,16) (5,11) (5,12) (5,10) (5,9) (5,6) (6,15) (6,16) (6,11) (6,12) (6,10) (6,9) (7,13) (7,14) (7,8) (7,17) (8,13) (8,14) (8,17) (9,15) (9,16) (9,11) (9,12) (9,10) (10,15) (10,16) (10,11) (10,12) (11,15) (11,16) (11,12) (12,15) (12,16) (13,14) (13,17) (14,17) (15,16)\nIs there a path between node 11 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph610-12_9", + "image": "data/connectivity/graph_visual/medium/graph610.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,21) (0,7) (0,14) (0,2) (0,19) (0,1) (0,18) (0,10) (0,13) (0,16) (1,23) (1,21) (1,7) (1,14) (1,2) (1,19) (1,18) (1,10) (1,13) (1,16) (2,23) (2,21) (2,7) (2,14) (2,19) (2,18) (2,10) (2,13) (2,16) (3,9) (3,12) (3,6) (3,15) (3,20) (3,5) (3,17) (3,22) (3,4) (3,8) (3,11) (4,9) (4,12) (4,6) (4,15) (4,20) (4,5) (4,17) (4,22) (4,8) (4,11) (5,9) (5,12) (5,6) (5,15) (5,20) (5,17) (5,22) (5,8) (5,11) (6,9) (6,12) (6,15) (6,20) (6,17) (6,22) (6,8) (6,11) (7,23) (7,21) (7,14) (7,19) (7,18) (7,10) (7,13) (7,16) (8,9) (8,12) (8,15) (8,20) (8,17) (8,22) (8,11) (9,12) (9,15) (9,20) (9,17) (9,22) (9,11) (10,23) (10,21) (10,14) (10,19) (10,18) (10,13) (10,16) (11,12) (11,15) (11,20) (11,17) (11,22) (12,15) (12,20) (12,17) (12,22) (13,23) (13,21) (13,14) (13,19) (13,18) (13,16) (14,23) (14,21) (14,19) (14,18) (14,16) (15,20) (15,17) (15,22) (16,23) (16,21) (16,19) (16,18) (17,20) (17,22) (18,23) (18,21) (18,19) (19,23) (19,21) (20,22) (21,23)\nIs there a path between node 12 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph721-9_8", + "image": "data/connectivity/graph_visual/medium/graph721.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,3) (0,9) (0,20) (0,15) (1,21) (1,11) (1,13) (1,23) (1,19) (1,17) (1,5) (1,4) (1,22) (1,2) (1,16) (1,24) (1,7) (1,18) (1,6) (1,12) (1,8) (1,10) (2,21) (2,11) (2,13) (2,23) (2,19) (2,17) (2,5) (2,4) (2,22) (2,16) (2,24) (2,7) (2,18) (2,6) (2,12) (2,8) (2,10) (3,14) (3,9) (3,20) (3,15) (4,21) (4,11) (4,13) (4,23) (4,19) (4,17) (4,5) (4,22) (4,16) (4,24) (4,7) (4,18) (4,6) (4,12) (4,8) (4,10) (5,21) (5,11) (5,13) (5,23) (5,19) (5,17) (5,22) (5,16) (5,24) (5,7) (5,18) (5,6) (5,12) (5,8) (5,10) (6,21) (6,11) (6,13) (6,23) (6,19) (6,17) (6,22) (6,16) (6,24) (6,7) (6,18) (6,12) (6,8) (6,10) (7,21) (7,11) (7,13) (7,23) (7,19) (7,17) (7,22) (7,16) (7,24) (7,18) (7,12) (7,8) (7,10) (8,21) (8,11) (8,13) (8,23) (8,19) (8,17) (8,22) (8,16) (8,24) (8,18) (8,12) (8,10) (9,14) (9,20) (9,15) (10,21) (10,11) (10,13) (10,23) (10,19) (10,17) (10,22) (10,16) (10,24) (10,18) (10,12) (11,21) (11,13) (11,23) (11,19) (11,17) (11,22) (11,16) (11,24) (11,18) (11,12) (12,21) (12,13) (12,23) (12,19) (12,17) (12,22) (12,16) (12,24) (12,18) (13,21) (13,23) (13,19) (13,17) (13,22) (13,16) (13,24) (13,18) (14,20) (14,15) (15,20) (16,21) (16,23) (16,19) (16,17) (16,22) (16,24) (16,18) (17,21) (17,23) (17,19) (17,22) (17,24) (17,18) (18,21) (18,23) (18,19) (18,22) (18,24) (19,21) (19,23) (19,22) (19,24) (21,23) (21,22) (21,24) (22,23) (22,24) (23,24)\nIs there a path between node 9 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph248-3_11", + "image": "data/connectivity/graph_visual/medium/graph248.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,9) (0,4) (0,3) (0,6) (0,10) (0,17) (0,11) (1,13) (1,5) (1,18) (1,2) (1,8) (1,7) (1,12) (1,14) (2,13) (2,5) (2,18) (2,8) (2,7) (2,12) (2,14) (3,9) (3,4) (3,6) (3,10) (3,17) (3,11) (4,9) (4,6) (4,10) (4,17) (4,11) (5,13) (5,18) (5,8) (5,7) (5,12) (5,14) (6,9) (6,10) (6,17) (6,11) (7,13) (7,18) (7,8) (7,12) (7,14) (8,13) (8,18) (8,12) (8,14) (9,10) (9,17) (9,11) (10,17) (10,11) (11,17) (12,13) (12,18) (12,14) (13,18) (13,14) (14,18) (15,16)\nIs there a path between node 3 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph212-8_1", + "image": "data/connectivity/graph_visual/medium/graph212.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,5) (0,9) (0,14) (0,18) (0,3) (0,1) (0,17) (0,4) (0,8) (0,7) (0,15) (0,11) (0,10) (0,13) (1,5) (1,9) (1,14) (1,18) (1,3) (1,17) (1,4) (1,8) (1,7) (1,15) (1,11) (1,10) (1,13) (3,5) (3,9) (3,14) (3,18) (3,17) (3,4) (3,8) (3,7) (3,15) (3,11) (3,10) (3,13) (4,5) (4,9) (4,14) (4,18) (4,17) (4,8) (4,7) (4,15) (4,11) (4,10) (4,13) (5,9) (5,14) (5,18) (5,17) (5,8) (5,7) (5,15) (5,11) (5,10) (5,13) (6,12) (6,16) (7,9) (7,14) (7,18) (7,17) (7,8) (7,15) (7,11) (7,10) (7,13) (8,9) (8,14) (8,18) (8,17) (8,15) (8,11) (8,10) (8,13) (9,14) (9,18) (9,17) (9,15) (9,11) (9,10) (9,13) (10,14) (10,18) (10,17) (10,15) (10,11) (10,13) (11,14) (11,18) (11,17) (11,15) (11,13) (12,16) (13,14) (13,18) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (15,17) (17,18)\nIs there a path between node 8 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph378-10_7", + "image": "data/connectivity/graph_visual/medium/graph378.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (0,1) (0,19) (0,11) (0,17) (0,16) (0,6) (1,9) (1,5) (1,4) (1,18) (1,20) (1,11) (1,16) (1,6) (1,12) (2,15) (2,7) (2,13) (3,9) (3,5) (3,4) (3,20) (3,8) (3,11) (3,17) (3,6) (3,12) (4,5) (4,18) (4,19) (4,20) (4,17) (4,16) (4,12) (5,9) (5,18) (5,20) (5,8) (5,11) (6,9) (6,18) (6,19) (6,11) (6,12) (7,15) (7,13) (8,9) (8,18) (8,19) (8,20) (8,17) (8,16) (9,18) (9,19) (9,20) (9,11) (9,16) (9,12) (11,18) (11,17) (11,16) (12,18) (12,20) (12,17) (13,15) (16,18) (16,19) (16,17) (17,19) (17,20) (18,19) (19,20)\nIs there a path between node 10 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph419-8_13", + "image": "data/connectivity/graph_visual/medium/graph419.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,13) (0,1) (0,18) (0,4) (0,2) (0,9) (0,3) (1,13) (1,18) (1,4) (1,2) (1,9) (1,3) (2,13) (2,18) (2,4) (2,9) (2,3) (3,13) (3,18) (3,4) (3,9) (4,13) (4,18) (4,9) (5,10) (5,12) (5,14) (5,21) (5,20) (5,19) (5,17) (5,8) (5,16) (5,7) (5,15) (5,6) (5,11) (6,10) (6,12) (6,14) (6,21) (6,20) (6,19) (6,17) (6,8) (6,16) (6,7) (6,15) (6,11) (7,10) (7,12) (7,14) (7,21) (7,20) (7,19) (7,17) (7,8) (7,16) (7,15) (7,11) (8,10) (8,12) (8,14) (8,21) (8,20) (8,19) (8,17) (8,16) (8,15) (8,11) (9,13) (9,18) (10,12) (10,14) (10,21) (10,20) (10,19) (10,17) (10,16) (10,15) (10,11) (11,12) (11,14) (11,21) (11,20) (11,19) (11,17) (11,16) (11,15) (12,14) (12,21) (12,20) (12,19) (12,17) (12,16) (12,15) (13,18) (14,21) (14,20) (14,19) (14,17) (14,16) (14,15) (15,21) (15,20) (15,19) (15,17) (15,16) (16,21) (16,20) (16,19) (16,17) (17,21) (17,20) (17,19) (19,21) (19,20) (20,21)\nIs there a path between node 8 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph765-17_9", + "image": "data/connectivity/graph_visual/medium/graph765.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,4) (0,7) (0,6) (0,8) (0,2) (0,22) (0,11) (0,21) (0,10) (1,5) (1,19) (1,14) (1,23) (2,3) (2,4) (2,7) (2,6) (2,8) (2,22) (2,11) (2,21) (2,10) (3,4) (3,7) (3,6) (3,8) (3,22) (3,11) (3,21) (3,10) (4,7) (4,6) (4,8) (4,22) (4,11) (4,21) (4,10) (5,19) (5,14) (5,23) (6,7) (6,8) (6,22) (6,11) (6,21) (6,10) (7,8) (7,22) (7,11) (7,21) (7,10) (8,22) (8,11) (8,21) (8,10) (9,24) (9,15) (9,16) (9,20) (9,17) (10,22) (10,11) (10,21) (11,22) (11,21) (12,13) (12,18) (13,18) (14,19) (14,23) (15,24) (15,16) (15,20) (15,17) (16,24) (16,20) (16,17) (17,24) (17,20) (19,23) (20,24) (21,22)\nIs there a path between node 17 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph46-5_4", + "image": "data/connectivity/graph_visual/medium/graph46.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,4) (0,9) (0,2) (0,5) (0,10) (0,1) (1,4) (1,9) (1,2) (1,5) (1,10) (2,4) (2,9) (2,5) (2,10) (3,11) (3,8) (3,12) (3,7) (3,6) (4,9) (4,5) (4,10) (5,9) (5,10) (6,11) (6,8) (6,12) (6,7) (7,11) (7,8) (7,12) (8,11) (8,12) (9,10) (11,12)\nIs there a path between node 5 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph781-17_13", + "image": "data/connectivity/graph_visual/medium/graph781.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,14) (1,7) (1,20) (1,12) (1,10) (2,15) (2,21) (4,13) (4,19) (4,22) (5,14) (5,7) (5,9) (6,23) (6,18) (6,21) (7,11) (7,20) (8,14) (8,12) (9,11) (9,10) (10,17) (10,12) (11,17) (13,19) (15,21) (18,24) (23,24)\nIs there a path between node 17 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph457-11_14", + "image": "data/connectivity/graph_visual/medium/graph457.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,5) (0,4) (0,12) (0,8) (0,14) (1,16) (1,9) (1,11) (1,2) (1,10) (1,21) (1,7) (1,6) (1,15) (1,13) (1,19) (1,3) (1,17) (1,20) (2,16) (2,9) (2,11) (2,10) (2,21) (2,7) (2,6) (2,15) (2,13) (2,19) (2,3) (2,17) (2,20) (3,16) (3,9) (3,11) (3,10) (3,21) (3,7) (3,6) (3,15) (3,13) (3,19) (3,17) (3,20) (4,18) (4,5) (4,12) (4,8) (4,14) (5,18) (5,12) (5,8) (5,14) (6,16) (6,9) (6,11) (6,10) (6,21) (6,7) (6,15) (6,13) (6,19) (6,17) (6,20) (7,16) (7,9) (7,11) (7,10) (7,21) (7,15) (7,13) (7,19) (7,17) (7,20) (8,18) (8,12) (8,14) (9,16) (9,11) (9,10) (9,21) (9,15) (9,13) (9,19) (9,17) (9,20) (10,16) (10,11) (10,21) (10,15) (10,13) (10,19) (10,17) (10,20) (11,16) (11,21) (11,15) (11,13) (11,19) (11,17) (11,20) (12,18) (12,14) (13,16) (13,21) (13,15) (13,19) (13,17) (13,20) (14,18) (15,16) (15,21) (15,19) (15,17) (15,20) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (19,21) (19,20) (20,21)\nIs there a path between node 11 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph350-0_4", + "image": "data/connectivity/graph_visual/medium/graph350.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,20) (0,4) (0,9) (0,18) (0,12) (0,5) (0,1) (0,17) (0,13) (0,2) (0,10) (0,7) (0,19) (0,15) (0,11) (0,8) (1,16) (1,20) (1,4) (1,9) (1,18) (1,12) (1,5) (1,17) (1,13) (1,2) (1,10) (1,7) (1,19) (1,15) (1,11) (1,8) (2,16) (2,20) (2,4) (2,9) (2,18) (2,12) (2,5) (2,17) (2,13) (2,10) (2,7) (2,19) (2,15) (2,11) (2,8) (3,14) (3,6) (4,16) (4,20) (4,9) (4,18) (4,12) (4,5) (4,17) (4,13) (4,10) (4,7) (4,19) (4,15) (4,11) (4,8) (5,16) (5,20) (5,9) (5,18) (5,12) (5,17) (5,13) (5,10) (5,7) (5,19) (5,15) (5,11) (5,8) (6,14) (7,16) (7,20) (7,9) (7,18) (7,12) (7,17) (7,13) (7,10) (7,19) (7,15) (7,11) (7,8) (8,16) (8,20) (8,9) (8,18) (8,12) (8,17) (8,13) (8,10) (8,19) (8,15) (8,11) (9,16) (9,20) (9,18) (9,12) (9,17) (9,13) (9,10) (9,19) (9,15) (9,11) (10,16) (10,20) (10,18) (10,12) (10,17) (10,13) (10,19) (10,15) (10,11) (11,16) (11,20) (11,18) (11,12) (11,17) (11,13) (11,19) (11,15) (12,16) (12,20) (12,18) (12,17) (12,13) (12,19) (12,15) (13,16) (13,20) (13,18) (13,17) (13,19) (13,15) (15,16) (15,20) (15,18) (15,17) (15,19) (16,20) (16,18) (16,17) (16,19) (17,20) (17,18) (17,19) (18,20) (18,19) (19,20)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph721-11_23", + "image": "data/connectivity/graph_visual/medium/graph721.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,3) (0,9) (0,20) (0,15) (1,21) (1,11) (1,13) (1,23) (1,19) (1,17) (1,5) (1,4) (1,22) (1,2) (1,16) (1,24) (1,7) (1,18) (1,6) (1,12) (1,8) (1,10) (2,21) (2,11) (2,13) (2,23) (2,19) (2,17) (2,5) (2,4) (2,22) (2,16) (2,24) (2,7) (2,18) (2,6) (2,12) (2,8) (2,10) (3,14) (3,9) (3,20) (3,15) (4,21) (4,11) (4,13) (4,23) (4,19) (4,17) (4,5) (4,22) (4,16) (4,24) (4,7) (4,18) (4,6) (4,12) (4,8) (4,10) (5,21) (5,11) (5,13) (5,23) (5,19) (5,17) (5,22) (5,16) (5,24) (5,7) (5,18) (5,6) (5,12) (5,8) (5,10) (6,21) (6,11) (6,13) (6,23) (6,19) (6,17) (6,22) (6,16) (6,24) (6,7) (6,18) (6,12) (6,8) (6,10) (7,21) (7,11) (7,13) (7,23) (7,19) (7,17) (7,22) (7,16) (7,24) (7,18) (7,12) (7,8) (7,10) (8,21) (8,11) (8,13) (8,23) (8,19) (8,17) (8,22) (8,16) (8,24) (8,18) (8,12) (8,10) (9,14) (9,20) (9,15) (10,21) (10,11) (10,13) (10,23) (10,19) (10,17) (10,22) (10,16) (10,24) (10,18) (10,12) (11,21) (11,13) (11,23) (11,19) (11,17) (11,22) (11,16) (11,24) (11,18) (11,12) (12,21) (12,13) (12,23) (12,19) (12,17) (12,22) (12,16) (12,24) (12,18) (13,21) (13,23) (13,19) (13,17) (13,22) (13,16) (13,24) (13,18) (14,20) (14,15) (15,20) (16,21) (16,23) (16,19) (16,17) (16,22) (16,24) (16,18) (17,21) (17,23) (17,19) (17,22) (17,24) (17,18) (18,21) (18,23) (18,19) (18,22) (18,24) (19,21) (19,23) (19,22) (19,24) (21,23) (21,22) (21,24) (22,23) (22,24) (23,24)\nIs there a path between node 11 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph229-1_4", + "image": "data/connectivity/graph_visual/medium/graph229.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,7) (0,4) (1,18) (1,6) (1,13) (2,16) (2,12) (2,6) (3,5) (3,10) (3,17) (3,13) (4,7) (5,18) (5,6) (5,15) (5,10) (5,17) (10,15) (10,14) (11,17) (12,13) (12,14) (14,18) (14,15) (15,17) (16,18)\nIs there a path between node 1 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph81-4_5", + "image": "data/connectivity/graph_visual/medium/graph81.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,11) (0,14) (0,9) (0,4) (0,1) (0,10) (0,7) (0,3) (0,8) (1,11) (1,4) (1,7) (1,3) (1,2) (1,8) (2,11) (2,14) (2,4) (2,7) (2,3) (2,8) (3,11) (3,14) (3,9) (3,10) (3,7) (4,14) (4,9) (4,7) (5,6) (5,12) (5,13) (6,12) (6,13) (7,11) (7,14) (7,9) (7,8) (8,14) (8,9) (8,10) (9,11) (9,14) (9,10) (10,11) (10,14) (12,13)\nIs there a path between node 4 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph546-2_3", + "image": "data/connectivity/graph_visual/medium/graph546.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,19) (0,17) (0,7) (0,16) (0,21) (1,22) (1,19) (1,20) (1,21) (2,23) (2,6) (3,13) (3,18) (3,4) (3,10) (3,21) (4,19) (4,10) (4,16) (5,14) (5,12) (5,9) (5,11) (6,14) (6,23) (7,15) (7,22) (7,18) (7,8) (7,17) (7,20) (8,13) (8,21) (9,12) (9,11) (10,17) (13,19) (13,17) (13,21) (15,20) (16,18) (16,20) (19,20) (19,21)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph3-1_6", + "image": "data/connectivity/graph_visual/medium/graph3.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph291-9_1", + "image": "data/connectivity/graph_visual/medium/graph291.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,12) (1,2) (1,15) (1,17) (1,8) (1,10) (1,18) (2,3) (2,15) (2,18) (3,16) (3,5) (3,8) (3,10) (4,11) (5,16) (5,7) (5,14) (5,10) (5,18) (7,14) (7,8) (8,10) (8,18) (9,16) (10,14) (14,16) (15,17) (16,17)\nIs there a path between node 9 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph731-11_4", + "image": "data/connectivity/graph_visual/medium/graph731.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,6) (0,8) (1,2) (1,9) (1,24) (1,22) (1,20) (1,3) (1,17) (2,12) (2,19) (2,24) (2,13) (2,10) (3,12) (3,9) (3,24) (3,22) (3,10) (3,18) (4,5) (4,10) (4,17) (5,23) (5,11) (5,16) (5,14) (5,18) (6,7) (7,15) (7,8) (8,15) (9,11) (9,13) (10,21) (10,13) (10,16) (10,17) (11,13) (11,22) (12,21) (12,24) (12,22) (12,16) (12,14) (13,14) (13,17) (14,19) (14,21) (14,16) (16,24) (16,18) (17,19) (17,21) (17,24) (17,22) (17,20) (18,23) (18,19) (18,24) (18,22) (20,23) (20,21) (20,24) (21,22)\nIs there a path between node 11 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph762-13_1", + "image": "data/connectivity/graph_visual/medium/graph762.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,24) (0,4) (0,17) (0,22) (0,7) (0,23) (0,9) (0,8) (0,3) (0,1) (0,10) (0,19) (0,6) (1,12) (1,24) (1,4) (1,17) (1,5) (1,22) (1,16) (1,23) (1,9) (1,14) (1,3) (1,13) (1,21) (1,10) (1,19) (1,6) (2,15) (2,18) (2,11) (3,12) (3,24) (3,4) (3,17) (3,22) (3,7) (3,16) (3,20) (3,13) (3,21) (4,12) (4,24) (4,5) (4,16) (4,20) (4,23) (4,13) (4,21) (4,10) (4,19) (4,6) (5,12) (5,24) (5,17) (5,22) (5,16) (5,20) (5,23) (5,9) (5,8) (5,13) (5,10) (5,6) (6,12) (6,24) (6,17) (6,22) (6,7) (6,20) (6,23) (6,8) (6,14) (6,13) (6,21) (7,12) (7,24) (7,17) (7,16) (7,23) (7,14) (7,13) (7,21) (7,10) (7,19) (8,12) (8,24) (8,17) (8,22) (8,16) (8,20) (8,23) (8,14) (8,13) (8,21) (8,10) (9,12) (9,24) (9,17) (9,22) (9,20) (9,14) (9,13) (9,21) (9,10) (9,19) (10,17) (10,16) (10,23) (10,14) (10,13) (11,18) (12,17) (12,22) (12,16) (12,23) (12,13) (12,19) (13,24) (13,16) (13,20) (13,21) (13,19) (14,24) (14,17) (14,22) (14,16) (14,21) (16,24) (16,20) (16,23) (16,19) (17,24) (17,22) (17,20) (17,23) (17,21) (17,19) (19,24) (19,22) (19,21) (20,24) (20,22) (20,23) (20,21) (21,24) (21,23) (22,24)\nIs there a path between node 13 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph693-15_1", + "image": "data/connectivity/graph_visual/medium/graph693.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,18) (0,15) (0,19) (0,13) (0,10) (0,6) (0,1) (0,17) (0,22) (1,4) (1,18) (1,15) (1,19) (1,13) (1,10) (1,6) (1,17) (1,22) (2,7) (2,8) (2,5) (2,12) (2,21) (2,3) (2,23) (2,9) (2,11) (2,14) (2,20) (2,16) (3,7) (3,8) (3,5) (3,12) (3,21) (3,23) (3,9) (3,11) (3,14) (3,20) (3,16) (4,18) (4,15) (4,19) (4,13) (4,10) (4,6) (4,17) (4,22) (5,7) (5,8) (5,12) (5,21) (5,23) (5,9) (5,11) (5,14) (5,20) (5,16) (6,18) (6,15) (6,19) (6,13) (6,10) (6,17) (6,22) (7,8) (7,12) (7,21) (7,23) (7,9) (7,11) (7,14) (7,20) (7,16) (8,12) (8,21) (8,23) (8,9) (8,11) (8,14) (8,20) (8,16) (9,12) (9,21) (9,23) (9,11) (9,14) (9,20) (9,16) (10,18) (10,15) (10,19) (10,13) (10,17) (10,22) (11,12) (11,21) (11,23) (11,14) (11,20) (11,16) (12,21) (12,23) (12,14) (12,20) (12,16) (13,18) (13,15) (13,19) (13,17) (13,22) (14,21) (14,23) (14,20) (14,16) (15,18) (15,19) (15,17) (15,22) (16,21) (16,23) (16,20) (17,18) (17,19) (17,22) (18,19) (18,22) (19,22) (20,21) (20,23) (21,23)\nIs there a path between node 15 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph127-16_11", + "image": "data/connectivity/graph_visual/medium/graph127.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,4) (0,2) (0,14) (0,5) (0,1) (0,7) (0,8) (0,15) (0,3) (0,10) (0,13) (0,9) (0,16) (0,12) (1,4) (1,2) (1,14) (1,5) (1,7) (1,8) (1,15) (1,3) (1,10) (1,13) (1,9) (1,16) (1,12) (2,4) (2,14) (2,5) (2,7) (2,8) (2,15) (2,3) (2,10) (2,13) (2,9) (2,16) (2,12) (3,4) (3,14) (3,5) (3,7) (3,8) (3,15) (3,10) (3,13) (3,9) (3,16) (3,12) (4,14) (4,5) (4,7) (4,8) (4,15) (4,10) (4,13) (4,9) (4,16) (4,12) (5,14) (5,7) (5,8) (5,15) (5,10) (5,13) (5,9) (5,16) (5,12) (6,11) (7,14) (7,8) (7,15) (7,10) (7,13) (7,9) (7,16) (7,12) (8,14) (8,15) (8,10) (8,13) (8,9) (8,16) (8,12) (9,14) (9,15) (9,10) (9,13) (9,16) (9,12) (10,14) (10,15) (10,13) (10,16) (10,12) (12,14) (12,15) (12,13) (12,16) (13,14) (13,15) (13,16) (14,15) (14,16) (15,16)\nIs there a path between node 16 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph93-3_9", + "image": "data/connectivity/graph_visual/medium/graph93.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,2) (0,4) (0,9) (0,5) (0,13) (1,14) (1,15) (1,12) (1,5) (1,7) (2,4) (2,6) (2,9) (2,12) (2,13) (4,11) (4,6) (4,15) (4,7) (4,8) (4,13) (5,11) (5,10) (5,14) (5,6) (5,9) (5,15) (5,12) (5,7) (5,13) (6,14) (7,14) (7,8) (9,13) (10,14) (12,15)\nIs there a path between node 3 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph58-6_7", + "image": "data/connectivity/graph_visual/medium/graph58.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (0,1) (1,3) (1,11) (1,2) (1,4) (2,9) (2,12) (3,8) (4,12) (5,11) (5,8) (5,7) (6,13) (10,12)\nIs there a path between node 6 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph610-8_17", + "image": "data/connectivity/graph_visual/medium/graph610.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,21) (0,7) (0,14) (0,2) (0,19) (0,1) (0,18) (0,10) (0,13) (0,16) (1,23) (1,21) (1,7) (1,14) (1,2) (1,19) (1,18) (1,10) (1,13) (1,16) (2,23) (2,21) (2,7) (2,14) (2,19) (2,18) (2,10) (2,13) (2,16) (3,9) (3,12) (3,6) (3,15) (3,20) (3,5) (3,17) (3,22) (3,4) (3,8) (3,11) (4,9) (4,12) (4,6) (4,15) (4,20) (4,5) (4,17) (4,22) (4,8) (4,11) (5,9) (5,12) (5,6) (5,15) (5,20) (5,17) (5,22) (5,8) (5,11) (6,9) (6,12) (6,15) (6,20) (6,17) (6,22) (6,8) (6,11) (7,23) (7,21) (7,14) (7,19) (7,18) (7,10) (7,13) (7,16) (8,9) (8,12) (8,15) (8,20) (8,17) (8,22) (8,11) (9,12) (9,15) (9,20) (9,17) (9,22) (9,11) (10,23) (10,21) (10,14) (10,19) (10,18) (10,13) (10,16) (11,12) (11,15) (11,20) (11,17) (11,22) (12,15) (12,20) (12,17) (12,22) (13,23) (13,21) (13,14) (13,19) (13,18) (13,16) (14,23) (14,21) (14,19) (14,18) (14,16) (15,20) (15,17) (15,22) (16,23) (16,21) (16,19) (16,18) (17,20) (17,22) (18,23) (18,21) (18,19) (19,23) (19,21) (20,22) (21,23)\nIs there a path between node 8 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph29-7_2", + "image": "data/connectivity/graph_visual/medium/graph29.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,9) (0,11) (1,6) (1,3) (1,4) (1,7) (1,8) (1,10) (1,2) (1,5) (2,6) (2,3) (2,4) (2,7) (2,8) (2,10) (2,5) (3,6) (3,4) (3,7) (3,8) (3,10) (3,5) (4,6) (4,7) (4,8) (4,10) (4,5) (5,6) (5,7) (5,8) (5,10) (6,7) (6,8) (6,10) (7,8) (7,10) (8,10) (9,11)\nIs there a path between node 7 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph693-3_7", + "image": "data/connectivity/graph_visual/medium/graph693.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,18) (0,15) (0,19) (0,13) (0,10) (0,6) (0,1) (0,17) (0,22) (1,4) (1,18) (1,15) (1,19) (1,13) (1,10) (1,6) (1,17) (1,22) (2,7) (2,8) (2,5) (2,12) (2,21) (2,3) (2,23) (2,9) (2,11) (2,14) (2,20) (2,16) (3,7) (3,8) (3,5) (3,12) (3,21) (3,23) (3,9) (3,11) (3,14) (3,20) (3,16) (4,18) (4,15) (4,19) (4,13) (4,10) (4,6) (4,17) (4,22) (5,7) (5,8) (5,12) (5,21) (5,23) (5,9) (5,11) (5,14) (5,20) (5,16) (6,18) (6,15) (6,19) (6,13) (6,10) (6,17) (6,22) (7,8) (7,12) (7,21) (7,23) (7,9) (7,11) (7,14) (7,20) (7,16) (8,12) (8,21) (8,23) (8,9) (8,11) (8,14) (8,20) (8,16) (9,12) (9,21) (9,23) (9,11) (9,14) (9,20) (9,16) (10,18) (10,15) (10,19) (10,13) (10,17) (10,22) (11,12) (11,21) (11,23) (11,14) (11,20) (11,16) (12,21) (12,23) (12,14) (12,20) (12,16) (13,18) (13,15) (13,19) (13,17) (13,22) (14,21) (14,23) (14,20) (14,16) (15,18) (15,19) (15,17) (15,22) (16,21) (16,23) (16,20) (17,18) (17,19) (17,22) (18,19) (18,22) (19,22) (20,21) (20,23) (21,23)\nIs there a path between node 3 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph176-16_1", + "image": "data/connectivity/graph_visual/medium/graph176.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,7) (0,13) (0,10) (0,9) (1,16) (1,12) (1,17) (1,8) (2,3) (2,14) (2,15) (2,5) (2,11) (3,14) (3,5) (4,7) (4,10) (4,9) (5,15) (5,11) (6,7) (6,10) (7,13) (7,10) (7,9) (8,12) (9,13) (10,13) (11,14) (11,15) (12,16) (12,17) (14,15) (16,17)\nIs there a path between node 16 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph289-3_16", + "image": "data/connectivity/graph_visual/medium/graph289.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,13) (0,17) (0,4) (1,14) (2,8) (3,15) (4,11) (4,18) (4,17) (5,19) (7,13) (7,12) (7,10) (8,16) (8,14) (9,12) (9,10) (10,18) (11,18) (11,12) (12,13) (13,18) (13,17) (14,16) (17,18)\nIs there a path between node 3 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph528-7_16", + "image": "data/connectivity/graph_visual/medium/graph528.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,14) (0,6) (0,20) (0,2) (0,21) (0,17) (0,1) (0,9) (0,22) (1,10) (1,14) (1,6) (1,20) (1,2) (1,21) (1,17) (1,9) (1,22) (2,10) (2,14) (2,6) (2,20) (2,21) (2,17) (2,9) (2,22) (3,7) (3,5) (3,8) (3,16) (3,19) (3,18) (3,13) (3,4) (3,12) (3,15) (3,11) (4,7) (4,5) (4,8) (4,16) (4,19) (4,18) (4,13) (4,12) (4,15) (4,11) (5,7) (5,8) (5,16) (5,19) (5,18) (5,13) (5,12) (5,15) (5,11) (6,10) (6,14) (6,20) (6,21) (6,17) (6,9) (6,22) (7,8) (7,16) (7,19) (7,18) (7,13) (7,12) (7,15) (7,11) (8,16) (8,19) (8,18) (8,13) (8,12) (8,15) (8,11) (9,10) (9,14) (9,20) (9,21) (9,17) (9,22) (10,14) (10,20) (10,21) (10,17) (10,22) (11,16) (11,19) (11,18) (11,13) (11,12) (11,15) (12,16) (12,19) (12,18) (12,13) (12,15) (13,16) (13,19) (13,18) (13,15) (14,20) (14,21) (14,17) (14,22) (15,16) (15,19) (15,18) (16,19) (16,18) (17,20) (17,21) (17,22) (18,19) (20,21) (20,22) (21,22)\nIs there a path between node 7 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph524-6_17", + "image": "data/connectivity/graph_visual/medium/graph524.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,16) (0,20) (0,21) (0,2) (0,14) (0,18) (0,10) (0,8) (1,16) (1,20) (1,12) (1,14) (1,18) (1,10) (2,16) (2,12) (2,21) (2,14) (2,18) (2,10) (2,8) (3,17) (3,11) (3,9) (3,22) (3,19) (3,5) (3,6) (3,4) (4,17) (4,9) (4,22) (4,5) (4,6) (4,7) (5,17) (5,13) (5,11) (6,11) (6,9) (6,7) (7,17) (7,13) (7,11) (7,9) (8,16) (8,12) (8,14) (8,18) (8,15) (8,10) (9,17) (9,13) (9,11) (9,19) (10,16) (10,20) (10,12) (10,14) (10,18) (11,17) (11,13) (11,22) (11,19) (12,16) (12,20) (12,21) (12,14) (13,17) (13,22) (14,16) (14,21) (14,18) (14,15) (15,16) (15,20) (15,21) (15,18) (16,20) (16,21) (16,18) (17,22) (17,19) (18,20) (18,21) (19,22)\nIs there a path between node 6 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph807-6_3", + "image": "data/connectivity/graph_visual/medium/graph807.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,12) (0,18) (0,10) (0,14) (0,7) (0,23) (0,1) (1,20) (1,12) (1,11) (1,13) (1,10) (1,5) (1,16) (1,14) (1,7) (2,15) (2,22) (2,4) (2,8) (2,21) (3,17) (3,19) (3,9) (4,6) (4,15) (4,22) (4,8) (4,21) (4,24) (5,12) (5,11) (5,18) (5,13) (5,10) (5,16) (5,14) (5,23) (6,22) (6,21) (6,24) (7,12) (7,11) (7,18) (8,15) (8,22) (8,24) (10,20) (10,11) (10,18) (10,13) (10,23) (11,20) (11,12) (11,18) (11,16) (11,14) (11,23) (12,20) (12,18) (12,13) (12,23) (13,20) (13,14) (13,23) (14,16) (14,23) (15,22) (15,21) (15,24) (16,20) (16,18) (17,19) (18,20) (18,23) (21,22) (21,24) (22,24)\nIs there a path between node 6 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph438-17_21", + "image": "data/connectivity/graph_visual/medium/graph438.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,10) (0,5) (0,20) (0,7) (0,19) (0,1) (0,14) (0,12) (0,15) (0,18) (0,4) (1,10) (1,5) (1,7) (1,2) (1,14) (1,12) (1,3) (1,15) (1,16) (1,4) (2,10) (2,5) (2,20) (2,7) (2,19) (2,14) (2,12) (2,15) (2,16) (2,17) (2,18) (2,4) (3,5) (3,20) (3,7) (3,19) (3,14) (3,16) (3,17) (3,18) (4,10) (4,5) (4,20) (4,7) (4,19) (4,14) (4,12) (4,15) (4,16) (4,17) (5,20) (5,7) (5,19) (5,14) (5,12) (5,16) (5,17) (5,18) (6,11) (6,8) (7,10) (7,19) (7,14) (7,12) (7,15) (7,16) (7,17) (7,18) (8,11) (9,21) (9,13) (10,19) (10,14) (10,12) (10,16) (10,18) (12,20) (12,19) (12,14) (12,15) (12,16) (12,17) (14,20) (14,19) (14,15) (14,16) (14,17) (15,20) (15,19) (15,16) (15,17) (15,18) (16,20) (16,19) (16,17) (16,18) (17,20) (17,19) (17,18) (18,19) (19,20)\nIs there a path between node 17 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph738-5_0", + "image": "data/connectivity/graph_visual/medium/graph738.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (1,24) (2,18) (2,9) (3,10) (3,5) (4,8) (4,9) (5,18) (5,11) (5,13) (6,10) (6,8) (6,13) (7,14) (8,9) (8,20) (9,11) (9,13) (9,20) (10,17) (10,13) (11,18) (11,17) (13,18) (13,17) (14,19) (16,23) (16,21) (18,20) (21,23)\nIs there a path between node 5 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph835-8_23", + "image": "data/connectivity/graph_visual/medium/graph835.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (0,3) (1,24) (1,12) (1,17) (1,9) (1,15) (1,16) (1,2) (1,10) (1,13) (1,4) (1,19) (1,7) (1,14) (2,24) (2,12) (2,17) (2,9) (2,15) (2,16) (2,10) (2,13) (2,4) (2,19) (2,7) (2,14) (3,18) (4,24) (4,12) (4,17) (4,9) (4,15) (4,16) (4,10) (4,13) (4,19) (4,7) (4,14) (5,11) (5,23) (5,20) (5,8) (6,22) (6,21) (7,24) (7,12) (7,17) (7,9) (7,15) (7,16) (7,10) (7,13) (7,19) (7,14) (8,11) (8,23) (8,20) (9,24) (9,12) (9,17) (9,15) (9,16) (9,10) (9,13) (9,19) (9,14) (10,24) (10,12) (10,17) (10,15) (10,16) (10,13) (10,19) (10,14) (11,23) (11,20) (12,24) (12,17) (12,15) (12,16) (12,13) (12,19) (12,14) (13,24) (13,17) (13,15) (13,16) (13,19) (13,14) (14,24) (14,17) (14,15) (14,16) (14,19) (15,24) (15,17) (15,16) (15,19) (16,24) (16,17) (16,19) (17,24) (17,19) (19,24) (20,23) (21,22)\nIs there a path between node 8 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph429-16_14", + "image": "data/connectivity/graph_visual/medium/graph429.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,10) (0,2) (0,8) (0,13) (1,11) (1,21) (1,7) (2,20) (2,6) (2,10) (2,3) (2,4) (2,12) (2,18) (3,17) (3,6) (3,4) (3,19) (3,18) (4,17) (4,19) (4,13) (6,17) (6,10) (6,19) (7,14) (8,15) (8,20) (9,20) (9,16) (9,18) (10,20) (10,16) (10,19) (12,19) (12,13) (13,17) (13,15) (13,16) (15,17) (15,19) (16,17) (17,20) (18,19) (19,20)\nIs there a path between node 16 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph292-15_12", + "image": "data/connectivity/graph_visual/medium/graph292.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,14) (0,8) (0,12) (1,5) (1,16) (1,6) (1,7) (2,11) (3,16) (3,9) (4,5) (4,9) (5,19) (5,16) (5,6) (5,7) (5,18) (6,16) (6,7) (7,16) (7,18) (8,14) (8,10) (12,15) (13,19) (13,16) (14,15)\nIs there a path between node 15 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph552-19_8", + "image": "data/connectivity/graph_visual/medium/graph552.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,12) (2,13) (2,22) (3,4) (3,18) (3,10) (3,7) (3,20) (4,21) (4,5) (5,18) (5,23) (5,10) (5,7) (5,20) (5,16) (6,11) (6,10) (6,7) (6,14) (6,16) (6,15) (7,18) (7,9) (7,11) (7,8) (7,16) (8,18) (8,9) (8,10) (8,20) (8,14) (8,16) (8,15) (9,21) (9,23) (10,21) (10,11) (10,15) (11,18) (11,17) (11,16) (12,13) (13,22) (14,18) (14,23) (14,17) (14,16) (14,15) (15,21) (16,18) (16,20) (18,20) (19,22) (20,23)\nIs there a path between node 19 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph378-15_17", + "image": "data/connectivity/graph_visual/medium/graph378.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (0,1) (0,19) (0,11) (0,17) (0,16) (0,6) (1,9) (1,5) (1,4) (1,18) (1,20) (1,11) (1,16) (1,6) (1,12) (2,15) (2,7) (2,13) (3,9) (3,5) (3,4) (3,20) (3,8) (3,11) (3,17) (3,6) (3,12) (4,5) (4,18) (4,19) (4,20) (4,17) (4,16) (4,12) (5,9) (5,18) (5,20) (5,8) (5,11) (6,9) (6,18) (6,19) (6,11) (6,12) (7,15) (7,13) (8,9) (8,18) (8,19) (8,20) (8,17) (8,16) (9,18) (9,19) (9,20) (9,11) (9,16) (9,12) (11,18) (11,17) (11,16) (12,18) (12,20) (12,17) (13,15) (16,18) (16,19) (16,17) (17,19) (17,20) (18,19) (19,20)\nIs there a path between node 15 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph350-7_14", + "image": "data/connectivity/graph_visual/medium/graph350.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,20) (0,4) (0,9) (0,18) (0,12) (0,5) (0,1) (0,17) (0,13) (0,2) (0,10) (0,7) (0,19) (0,15) (0,11) (0,8) (1,16) (1,20) (1,4) (1,9) (1,18) (1,12) (1,5) (1,17) (1,13) (1,2) (1,10) (1,7) (1,19) (1,15) (1,11) (1,8) (2,16) (2,20) (2,4) (2,9) (2,18) (2,12) (2,5) (2,17) (2,13) (2,10) (2,7) (2,19) (2,15) (2,11) (2,8) (3,14) (3,6) (4,16) (4,20) (4,9) (4,18) (4,12) (4,5) (4,17) (4,13) (4,10) (4,7) (4,19) (4,15) (4,11) (4,8) (5,16) (5,20) (5,9) (5,18) (5,12) (5,17) (5,13) (5,10) (5,7) (5,19) (5,15) (5,11) (5,8) (6,14) (7,16) (7,20) (7,9) (7,18) (7,12) (7,17) (7,13) (7,10) (7,19) (7,15) (7,11) (7,8) (8,16) (8,20) (8,9) (8,18) (8,12) (8,17) (8,13) (8,10) (8,19) (8,15) (8,11) (9,16) (9,20) (9,18) (9,12) (9,17) (9,13) (9,10) (9,19) (9,15) (9,11) (10,16) (10,20) (10,18) (10,12) (10,17) (10,13) (10,19) (10,15) (10,11) (11,16) (11,20) (11,18) (11,12) (11,17) (11,13) (11,19) (11,15) (12,16) (12,20) (12,18) (12,17) (12,13) (12,19) (12,15) (13,16) (13,20) (13,18) (13,17) (13,19) (13,15) (15,16) (15,20) (15,18) (15,17) (15,19) (16,20) (16,18) (16,17) (16,19) (17,20) (17,18) (17,19) (18,20) (18,19) (19,20)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph407-10_6", + "image": "data/connectivity/graph_visual/medium/graph407.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,8) (0,11) (0,17) (0,1) (0,2) (0,12) (0,6) (0,18) (0,7) (0,15) (1,19) (1,8) (1,9) (1,11) (1,2) (1,12) (1,6) (1,7) (1,15) (2,19) (2,4) (2,9) (2,11) (2,17) (2,12) (2,6) (2,18) (2,15) (3,5) (3,13) (3,10) (4,19) (4,8) (4,9) (4,11) (4,17) (4,12) (4,6) (4,7) (4,15) (5,13) (5,10) (6,9) (6,11) (6,12) (6,18) (7,19) (7,8) (7,9) (7,11) (7,17) (7,15) (8,19) (8,11) (8,17) (8,12) (9,17) (9,12) (9,18) (10,13) (11,17) (11,15) (12,19) (12,17) (12,18) (12,15) (14,20) (14,21) (15,17) (15,18) (17,19) (17,18) (18,19) (20,21)\nIs there a path between node 10 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph700-24_9", + "image": "data/connectivity/graph_visual/medium/graph700.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,22) (0,6) (0,11) (0,10) (0,4) (0,5) (0,9) (0,1) (0,13) (0,21) (0,20) (0,12) (1,22) (1,11) (1,10) (1,5) (1,16) (1,9) (1,13) (1,21) (1,20) (2,8) (2,19) (2,3) (2,18) (2,24) (3,19) (3,17) (3,24) (3,23) (4,22) (4,6) (4,16) (4,9) (4,21) (4,20) (5,22) (5,6) (5,14) (5,11) (5,16) (5,15) (5,9) (5,13) (5,21) (5,20) (6,22) (6,11) (6,10) (6,16) (6,13) (6,21) (6,12) (7,8) (7,17) (7,18) (7,24) (7,23) (8,17) (8,24) (9,14) (9,11) (9,10) (9,16) (9,15) (9,21) (9,20) (9,12) (10,22) (10,14) (10,11) (10,16) (10,15) (10,21) (10,20) (11,22) (11,16) (11,15) (11,20) (12,22) (12,14) (12,15) (12,13) (12,21) (12,20) (13,14) (13,16) (13,15) (13,21) (13,20) (14,22) (14,16) (14,15) (14,21) (15,16) (15,21) (16,22) (16,21) (16,20) (17,19) (17,18) (17,24) (17,23) (18,23) (19,24) (23,24)\nIs there a path between node 24 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph691-3_16", + "image": "data/connectivity/graph_visual/medium/graph691.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,23) (0,3) (0,7) (0,9) (0,21) (0,13) (0,16) (0,6) (0,8) (0,12) (1,5) (1,22) (1,15) (1,14) (1,18) (1,17) (1,20) (1,11) (1,2) (2,5) (2,22) (2,15) (2,14) (2,18) (2,17) (2,20) (2,11) (3,10) (3,19) (3,23) (3,7) (3,9) (3,21) (3,13) (3,16) (3,6) (3,8) (3,12) (5,22) (5,15) (5,14) (5,18) (5,17) (5,20) (5,11) (6,10) (6,19) (6,23) (6,7) (6,9) (6,21) (6,13) (6,16) (6,8) (6,12) (7,10) (7,19) (7,23) (7,9) (7,21) (7,13) (7,16) (7,8) (7,12) (8,10) (8,19) (8,23) (8,9) (8,21) (8,13) (8,16) (8,12) (9,10) (9,19) (9,23) (9,21) (9,13) (9,16) (9,12) (10,19) (10,23) (10,21) (10,13) (10,16) (10,12) (11,22) (11,15) (11,14) (11,18) (11,17) (11,20) (12,19) (12,23) (12,21) (12,13) (12,16) (13,19) (13,23) (13,21) (13,16) (14,22) (14,15) (14,18) (14,17) (14,20) (15,22) (15,18) (15,17) (15,20) (16,19) (16,23) (16,21) (17,22) (17,18) (17,20) (18,22) (18,20) (19,23) (19,21) (20,22) (21,23)\nIs there a path between node 3 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph322-15_14", + "image": "data/connectivity/graph_visual/medium/graph322.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,3) (0,1) (0,11) (0,4) (0,16) (0,5) (0,19) (0,6) (0,10) (0,17) (0,12) (1,3) (1,11) (1,4) (1,16) (1,5) (1,19) (1,6) (1,10) (1,17) (1,12) (2,15) (2,14) (2,9) (2,18) (2,7) (3,11) (3,4) (3,16) (3,5) (3,19) (3,6) (3,10) (3,17) (3,12) (4,11) (4,16) (4,5) (4,19) (4,6) (4,10) (4,17) (4,12) (5,11) (5,16) (5,19) (5,6) (5,10) (5,17) (5,12) (6,11) (6,16) (6,19) (6,10) (6,17) (6,12) (7,15) (7,14) (7,9) (7,18) (8,13) (9,15) (9,14) (9,18) (10,11) (10,16) (10,19) (10,17) (10,12) (11,16) (11,19) (11,17) (11,12) (12,16) (12,19) (12,17) (14,15) (14,18) (15,18) (16,19) (16,17) (17,19)\nIs there a path between node 15 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph725-9_2", + "image": "data/connectivity/graph_visual/medium/graph725.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,7) (0,2) (0,5) (0,18) (0,9) (0,16) (0,21) (0,13) (0,11) (0,14) (0,22) (0,15) (0,6) (2,20) (2,7) (2,5) (2,18) (2,9) (2,16) (2,21) (2,13) (2,11) (2,14) (2,22) (2,15) (2,6) (3,4) (3,10) (3,8) (3,17) (3,19) (3,23) (3,24) (4,10) (4,8) (4,17) (4,19) (4,23) (4,24) (5,20) (5,7) (5,18) (5,9) (5,16) (5,21) (5,13) (5,11) (5,14) (5,22) (5,15) (5,6) (6,20) (6,7) (6,18) (6,9) (6,16) (6,21) (6,13) (6,11) (6,14) (6,22) (6,15) (7,20) (7,18) (7,9) (7,16) (7,21) (7,13) (7,11) (7,14) (7,22) (7,15) (8,10) (8,17) (8,19) (8,23) (8,24) (9,20) (9,18) (9,16) (9,21) (9,13) (9,11) (9,14) (9,22) (9,15) (10,17) (10,19) (10,23) (10,24) (11,20) (11,18) (11,16) (11,21) (11,13) (11,14) (11,22) (11,15) (13,20) (13,18) (13,16) (13,21) (13,14) (13,22) (13,15) (14,20) (14,18) (14,16) (14,21) (14,22) (14,15) (15,20) (15,18) (15,16) (15,21) (15,22) (16,20) (16,18) (16,21) (16,22) (17,19) (17,23) (17,24) (18,20) (18,21) (18,22) (19,23) (19,24) (20,21) (20,22) (21,22) (23,24)\nIs there a path between node 9 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph352-0_4", + "image": "data/connectivity/graph_visual/medium/graph352.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,3) (2,11) (2,19) (2,5) (2,17) (2,10) (3,4) (3,6) (3,18) (3,7) (4,6) (4,19) (5,13) (5,19) (5,10) (6,7) (6,10) (7,13) (7,17) (7,10) (8,9) (10,18) (10,19) (10,17) (11,13)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph846-23_12", + "image": "data/connectivity/graph_visual/medium/graph846.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,17) (0,7) (0,21) (0,19) (0,6) (0,11) (0,5) (1,15) (1,20) (1,2) (1,4) (1,14) (1,16) (1,3) (1,22) (1,12) (1,24) (1,18) (1,9) (1,13) (1,23) (1,8) (2,15) (2,20) (2,4) (2,14) (2,16) (2,3) (2,22) (2,12) (2,24) (2,18) (2,9) (2,13) (2,23) (2,8) (3,15) (3,20) (3,4) (3,14) (3,16) (3,22) (3,12) (3,24) (3,18) (3,9) (3,13) (3,23) (3,8) (4,15) (4,20) (4,14) (4,16) (4,22) (4,12) (4,24) (4,18) (4,9) (4,13) (4,23) (4,8) (5,10) (5,17) (5,7) (5,21) (5,19) (5,6) (5,11) (6,10) (6,17) (6,7) (6,21) (6,19) (6,11) (7,10) (7,17) (7,21) (7,19) (7,11) (8,15) (8,20) (8,14) (8,16) (8,22) (8,12) (8,24) (8,18) (8,9) (8,13) (8,23) (9,15) (9,20) (9,14) (9,16) (9,22) (9,12) (9,24) (9,18) (9,13) (9,23) (10,17) (10,21) (10,19) (10,11) (11,17) (11,21) (11,19) (12,15) (12,20) (12,14) (12,16) (12,22) (12,24) (12,18) (12,13) (12,23) (13,15) (13,20) (13,14) (13,16) (13,22) (13,24) (13,18) (13,23) (14,15) (14,20) (14,16) (14,22) (14,24) (14,18) (14,23) (15,20) (15,16) (15,22) (15,24) (15,18) (15,23) (16,20) (16,22) (16,24) (16,18) (16,23) (17,21) (17,19) (18,20) (18,22) (18,24) (18,23) (19,21) (20,22) (20,24) (20,23) (22,24) (22,23) (23,24)\nIs there a path between node 23 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph489-1_16", + "image": "data/connectivity/graph_visual/medium/graph489.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,12) (0,13) (0,1) (0,5) (0,3) (1,12) (1,13) (1,5) (1,3) (2,19) (2,10) (2,22) (2,9) (2,4) (2,21) (2,16) (2,17) (2,6) (2,20) (2,8) (2,11) (2,15) (2,18) (2,7) (2,14) (3,12) (3,13) (3,5) (4,19) (4,10) (4,22) (4,9) (4,21) (4,16) (4,17) (4,6) (4,20) (4,8) (4,11) (4,15) (4,18) (4,7) (4,14) (5,12) (5,13) (6,19) (6,10) (6,22) (6,9) (6,21) (6,16) (6,17) (6,20) (6,8) (6,11) (6,15) (6,18) (6,7) (6,14) (7,19) (7,10) (7,22) (7,9) (7,21) (7,16) (7,17) (7,20) (7,8) (7,11) (7,15) (7,18) (7,14) (8,19) (8,10) (8,22) (8,9) (8,21) (8,16) (8,17) (8,20) (8,11) (8,15) (8,18) (8,14) (9,19) (9,10) (9,22) (9,21) (9,16) (9,17) (9,20) (9,11) (9,15) (9,18) (9,14) (10,19) (10,22) (10,21) (10,16) (10,17) (10,20) (10,11) (10,15) (10,18) (10,14) (11,19) (11,22) (11,21) (11,16) (11,17) (11,20) (11,15) (11,18) (11,14) (12,13) (14,19) (14,22) (14,21) (14,16) (14,17) (14,20) (14,15) (14,18) (15,19) (15,22) (15,21) (15,16) (15,17) (15,20) (15,18) (16,19) (16,22) (16,21) (16,17) (16,20) (16,18) (17,19) (17,22) (17,21) (17,20) (17,18) (18,19) (18,22) (18,21) (18,20) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 1 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph519-17_9", + "image": "data/connectivity/graph_visual/medium/graph519.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,9) (0,3) (0,10) (0,14) (0,1) (1,9) (1,3) (1,10) (1,14) (1,20) (2,5) (2,13) (2,7) (2,16) (2,19) (2,21) (2,8) (2,4) (2,12) (2,18) (2,11) (2,17) (3,9) (3,10) (3,14) (3,20) (4,6) (4,5) (4,13) (4,16) (4,18) (4,11) (4,17) (5,6) (5,13) (5,7) (5,16) (5,22) (5,8) (5,12) (6,19) (6,12) (6,11) (6,17) (7,15) (7,16) (7,19) (7,22) (7,21) (7,8) (7,12) (7,11) (7,17) (8,13) (8,16) (8,22) (8,21) (9,14) (10,20) (11,15) (11,13) (11,16) (11,22) (11,21) (11,12) (11,18) (11,17) (12,15) (12,13) (12,16) (12,22) (12,21) (12,17) (13,16) (13,19) (13,22) (13,21) (13,18) (13,17) (14,20) (15,16) (15,17) (16,19) (16,22) (16,21) (16,18) (18,21) (19,21) (21,22)\nIs there a path between node 17 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph190-7_5", + "image": "data/connectivity/graph_visual/medium/graph190.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,10) (0,11) (0,5) (0,8) (0,12) (0,17) (0,13) (0,16) (0,6) (0,2) (0,9) (1,10) (1,11) (1,5) (1,8) (1,12) (1,17) (1,13) (1,16) (1,6) (1,2) (1,9) (2,10) (2,11) (2,5) (2,8) (2,12) (2,17) (2,13) (2,16) (2,6) (2,9) (3,15) (3,4) (3,7) (3,14) (4,15) (4,7) (4,14) (5,10) (5,11) (5,8) (5,12) (5,17) (5,13) (5,16) (5,6) (5,9) (6,10) (6,11) (6,8) (6,12) (6,17) (6,13) (6,16) (6,9) (7,15) (7,14) (8,10) (8,11) (8,12) (8,17) (8,13) (8,16) (8,9) (9,10) (9,11) (9,12) (9,17) (9,13) (9,16) (10,11) (10,12) (10,17) (10,13) (10,16) (11,12) (11,17) (11,13) (11,16) (12,17) (12,13) (12,16) (13,17) (13,16) (14,15) (16,17)\nIs there a path between node 7 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph178-4_8", + "image": "data/connectivity/graph_visual/medium/graph178.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,1) (0,7) (0,14) (0,8) (0,5) (0,11) (0,16) (1,7) (1,17) (1,14) (1,8) (1,6) (1,5) (1,9) (1,16) (1,3) (2,12) (2,4) (2,7) (2,8) (2,5) (2,9) (2,11) (2,16) (2,3) (2,13) (3,12) (3,14) (3,8) (3,5) (3,11) (3,16) (3,13) (4,17) (4,8) (4,6) (4,16) (4,13) (5,12) (5,7) (5,17) (5,14) (5,8) (5,11) (5,16) (6,12) (6,17) (6,9) (6,16) (7,17) (7,14) (7,9) (7,11) (7,16) (8,17) (8,14) (9,17) (9,14) (9,11) (9,16) (11,12) (11,17) (11,14) (11,13) (12,14) (13,17) (13,14) (13,16) (14,17) (16,17)\nIs there a path between node 4 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph534-13_15", + "image": "data/connectivity/graph_visual/medium/graph534.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,19) (0,20) (0,13) (0,2) (0,3) (0,16) (0,15) (0,4) (0,11) (0,22) (0,5) (0,6) (0,7) (0,1) (0,10) (1,21) (1,19) (1,20) (1,13) (1,2) (1,3) (1,16) (1,15) (1,4) (1,11) (1,22) (1,5) (1,6) (1,7) (1,10) (2,21) (2,19) (2,20) (2,13) (2,3) (2,16) (2,15) (2,4) (2,11) (2,22) (2,5) (2,6) (2,7) (2,10) (3,21) (3,19) (3,20) (3,13) (3,16) (3,15) (3,4) (3,11) (3,22) (3,5) (3,6) (3,7) (3,10) (4,21) (4,19) (4,20) (4,13) (4,16) (4,15) (4,11) (4,22) (4,5) (4,6) (4,7) (4,10) (5,21) (5,19) (5,20) (5,13) (5,16) (5,15) (5,11) (5,22) (5,6) (5,7) (5,10) (6,21) (6,19) (6,20) (6,13) (6,16) (6,15) (6,11) (6,22) (6,7) (6,10) (7,21) (7,19) (7,20) (7,13) (7,16) (7,15) (7,11) (7,22) (7,10) (8,12) (8,14) (8,9) (8,18) (9,12) (9,14) (9,18) (10,21) (10,19) (10,20) (10,13) (10,16) (10,15) (10,11) (10,22) (11,21) (11,19) (11,20) (11,13) (11,16) (11,15) (11,22) (12,14) (12,18) (13,21) (13,19) (13,20) (13,16) (13,15) (13,22) (14,18) (15,21) (15,19) (15,20) (15,16) (15,22) (16,21) (16,19) (16,20) (16,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 13 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph623-8_0", + "image": "data/connectivity/graph_visual/medium/graph623.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,17) (0,18) (0,4) (0,10) (0,21) (0,8) (0,22) (0,9) (0,19) (0,23) (0,5) (0,1) (0,14) (0,6) (0,15) (0,16) (1,20) (1,17) (1,18) (1,4) (1,10) (1,21) (1,8) (1,22) (1,9) (1,19) (1,23) (1,5) (1,14) (1,6) (1,15) (1,16) (2,12) (2,13) (2,11) (2,7) (2,3) (3,12) (3,13) (3,11) (3,7) (4,20) (4,17) (4,18) (4,10) (4,21) (4,8) (4,22) (4,9) (4,19) (4,23) (4,5) (4,14) (4,6) (4,15) (4,16) (5,20) (5,17) (5,18) (5,10) (5,21) (5,8) (5,22) (5,9) (5,19) (5,23) (5,14) (5,6) (5,15) (5,16) (6,20) (6,17) (6,18) (6,10) (6,21) (6,8) (6,22) (6,9) (6,19) (6,23) (6,14) (6,15) (6,16) (7,12) (7,13) (7,11) (8,20) (8,17) (8,18) (8,10) (8,21) (8,22) (8,9) (8,19) (8,23) (8,14) (8,15) (8,16) (9,20) (9,17) (9,18) (9,10) (9,21) (9,22) (9,19) (9,23) (9,14) (9,15) (9,16) (10,20) (10,17) (10,18) (10,21) (10,22) (10,19) (10,23) (10,14) (10,15) (10,16) (11,12) (11,13) (12,13) (14,20) (14,17) (14,18) (14,21) (14,22) (14,19) (14,23) (14,15) (14,16) (15,20) (15,17) (15,18) (15,21) (15,22) (15,19) (15,23) (15,16) (16,20) (16,17) (16,18) (16,21) (16,22) (16,19) (16,23) (17,20) (17,18) (17,21) (17,22) (17,19) (17,23) (18,20) (18,21) (18,22) (18,19) (18,23) (19,20) (19,21) (19,22) (19,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 8 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph69-8_4", + "image": "data/connectivity/graph_visual/medium/graph69.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,5) (0,9) (1,8) (1,4) (2,8) (2,4) (2,3) (3,7) (3,6) (3,10) (3,12) (3,11) (4,10) (4,12) (6,14) (6,8) (6,10) (7,14) (7,11) (8,14) (8,12) (10,14) (11,14) (12,14)\nIs there a path between node 8 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph545-11_2", + "image": "data/connectivity/graph_visual/medium/graph545.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,17) (0,23) (0,22) (0,1) (0,9) (0,11) (0,14) (0,19) (0,12) (0,18) (0,8) (0,4) (0,16) (0,15) (0,10) (0,6) (1,20) (1,17) (1,23) (1,22) (1,9) (1,11) (1,14) (1,19) (1,12) (1,18) (1,8) (1,4) (1,16) (1,15) (1,10) (1,6) (2,13) (2,5) (2,3) (2,21) (2,7) (3,13) (3,5) (3,21) (3,7) (4,20) (4,17) (4,23) (4,22) (4,9) (4,11) (4,14) (4,19) (4,12) (4,18) (4,8) (4,16) (4,15) (4,10) (4,6) (5,13) (5,21) (5,7) (6,20) (6,17) (6,23) (6,22) (6,9) (6,11) (6,14) (6,19) (6,12) (6,18) (6,8) (6,16) (6,15) (6,10) (7,13) (7,21) (8,20) (8,17) (8,23) (8,22) (8,9) (8,11) (8,14) (8,19) (8,12) (8,18) (8,16) (8,15) (8,10) (9,20) (9,17) (9,23) (9,22) (9,11) (9,14) (9,19) (9,12) (9,18) (9,16) (9,15) (9,10) (10,20) (10,17) (10,23) (10,22) (10,11) (10,14) (10,19) (10,12) (10,18) (10,16) (10,15) (11,20) (11,17) (11,23) (11,22) (11,14) (11,19) (11,12) (11,18) (11,16) (11,15) (12,20) (12,17) (12,23) (12,22) (12,14) (12,19) (12,18) (12,16) (12,15) (13,21) (14,20) (14,17) (14,23) (14,22) (14,19) (14,18) (14,16) (14,15) (15,20) (15,17) (15,23) (15,22) (15,19) (15,18) (15,16) (16,20) (16,17) (16,23) (16,22) (16,19) (16,18) (17,20) (17,23) (17,22) (17,19) (17,18) (18,20) (18,23) (18,22) (18,19) (19,20) (19,23) (19,22) (20,23) (20,22) (22,23)\nIs there a path between node 11 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph161-0_8", + "image": "data/connectivity/graph_visual/medium/graph161.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,5) (0,2) (0,7) (0,16) (0,6) (1,7) (1,10) (1,4) (2,15) (2,10) (4,5) (4,6) (6,7) (8,11) (8,13) (8,12) (8,14) (11,14) (13,17) (14,17)\nIs there a path between node 0 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph753-21_12", + "image": "data/connectivity/graph_visual/medium/graph753.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,3) (0,23) (0,18) (0,9) (0,5) (0,2) (0,4) (0,8) (0,24) (1,6) (1,3) (1,23) (1,16) (1,10) (1,12) (1,18) (1,9) (1,5) (1,2) (1,4) (1,22) (1,24) (2,6) (2,3) (2,13) (2,23) (2,16) (2,10) (2,12) (2,18) (2,15) (2,19) (2,9) (2,5) (2,11) (2,7) (2,22) (2,8) (2,24) (3,6) (3,13) (3,23) (3,10) (3,12) (3,18) (3,15) (3,9) (3,11) (3,7) (3,4) (3,22) (4,6) (4,13) (4,16) (4,12) (4,15) (4,19) (4,9) (4,5) (4,11) (4,7) (4,22) (4,8) (4,24) (5,6) (5,13) (5,23) (5,16) (5,10) (5,15) (5,19) (5,9) (5,11) (5,22) (6,23) (6,16) (6,10) (6,12) (6,18) (6,19) (6,9) (6,11) (6,7) (6,24) (7,13) (7,23) (7,16) (7,10) (7,12) (7,18) (7,15) (7,19) (7,11) (7,22) (7,24) (8,13) (8,23) (8,10) (8,12) (8,18) (8,15) (8,19) (8,9) (8,11) (8,24) (9,23) (9,16) (9,10) (9,12) (9,18) (9,15) (9,19) (9,22) (10,13) (10,23) (10,16) (10,12) (10,18) (10,15) (10,11) (10,22) (11,13) (11,23) (11,12) (11,18) (11,15) (11,19) (11,22) (11,24) (12,13) (12,23) (12,16) (12,18) (12,19) (13,23) (13,16) (13,18) (13,22) (15,23) (15,16) (15,18) (15,19) (15,24) (16,23) (16,18) (16,19) (16,22) (16,24) (18,23) (18,19) (18,22) (18,24) (19,23) (19,22) (19,24) (22,23) (22,24)\nIs there a path between node 21 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph80-7_10", + "image": "data/connectivity/graph_visual/medium/graph80.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,2) (0,1) (0,13) (0,12) (0,6) (0,14) (0,11) (0,9) (1,2) (1,3) (1,8) (1,4) (1,6) (1,11) (1,5) (2,7) (2,3) (2,13) (2,12) (2,6) (2,14) (2,11) (2,5) (3,7) (3,12) (3,4) (3,6) (3,14) (3,5) (3,9) (4,7) (4,13) (4,12) (4,8) (4,14) (4,11) (5,7) (5,12) (5,8) (5,6) (5,14) (5,11) (5,9) (6,7) (6,13) (6,12) (6,14) (6,9) (7,12) (7,8) (7,14) (7,11) (8,13) (8,14) (8,11) (9,13) (9,12) (9,14) (9,11) (11,12) (12,13) (12,14) (13,14)\nIs there a path between node 7 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph601-13_21", + "image": "data/connectivity/graph_visual/medium/graph601.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,17) (0,8) (0,9) (0,2) (0,13) (0,11) (1,6) (1,12) (1,10) (2,15) (2,17) (2,9) (2,14) (2,7) (2,5) (2,11) (3,4) (3,6) (3,12) (3,10) (4,23) (4,6) (4,10) (5,22) (5,9) (5,13) (5,11) (6,23) (6,10) (7,17) (7,22) (7,16) (7,13) (8,15) (8,17) (8,22) (8,13) (9,15) (9,17) (9,22) (9,16) (9,13) (9,11) (10,23) (11,14) (11,13) (12,23) (13,17) (13,16) (14,15) (14,17) (14,22) (14,16) (15,17) (15,22) (16,17) (16,22) (17,22) (19,21) (20,21)\nIs there a path between node 13 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph534-8_14", + "image": "data/connectivity/graph_visual/medium/graph534.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,19) (0,20) (0,13) (0,2) (0,3) (0,16) (0,15) (0,4) (0,11) (0,22) (0,5) (0,6) (0,7) (0,1) (0,10) (1,21) (1,19) (1,20) (1,13) (1,2) (1,3) (1,16) (1,15) (1,4) (1,11) (1,22) (1,5) (1,6) (1,7) (1,10) (2,21) (2,19) (2,20) (2,13) (2,3) (2,16) (2,15) (2,4) (2,11) (2,22) (2,5) (2,6) (2,7) (2,10) (3,21) (3,19) (3,20) (3,13) (3,16) (3,15) (3,4) (3,11) (3,22) (3,5) (3,6) (3,7) (3,10) (4,21) (4,19) (4,20) (4,13) (4,16) (4,15) (4,11) (4,22) (4,5) (4,6) (4,7) (4,10) (5,21) (5,19) (5,20) (5,13) (5,16) (5,15) (5,11) (5,22) (5,6) (5,7) (5,10) (6,21) (6,19) (6,20) (6,13) (6,16) (6,15) (6,11) (6,22) (6,7) (6,10) (7,21) (7,19) (7,20) (7,13) (7,16) (7,15) (7,11) (7,22) (7,10) (8,12) (8,14) (8,9) (8,18) (9,12) (9,14) (9,18) (10,21) (10,19) (10,20) (10,13) (10,16) (10,15) (10,11) (10,22) (11,21) (11,19) (11,20) (11,13) (11,16) (11,15) (11,22) (12,14) (12,18) (13,21) (13,19) (13,20) (13,16) (13,15) (13,22) (14,18) (15,21) (15,19) (15,20) (15,16) (15,22) (16,21) (16,19) (16,20) (16,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 8 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph770-9_10", + "image": "data/connectivity/graph_visual/medium/graph770.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,24) (0,6) (0,5) (0,7) (0,17) (0,21) (0,10) (0,18) (0,14) (1,13) (1,19) (1,3) (1,12) (1,4) (1,11) (2,9) (2,8) (2,15) (3,13) (3,19) (3,12) (3,4) (3,11) (4,13) (4,19) (4,12) (4,11) (5,20) (5,24) (5,6) (5,7) (5,17) (5,21) (5,10) (5,18) (5,14) (6,20) (6,24) (6,7) (6,17) (6,21) (6,10) (6,18) (6,14) (7,20) (7,24) (7,17) (7,21) (7,10) (7,18) (7,14) (8,9) (8,15) (9,15) (10,20) (10,24) (10,17) (10,21) (10,18) (10,14) (11,13) (11,19) (11,12) (12,13) (12,19) (13,19) (14,20) (14,24) (14,17) (14,21) (14,18) (16,22) (16,23) (17,20) (17,24) (17,21) (17,18) (18,20) (18,24) (18,21) (20,24) (20,21) (21,24) (22,23)\nIs there a path between node 9 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph496-5_17", + "image": "data/connectivity/graph_visual/medium/graph496.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,20) (0,2) (0,16) (0,1) (1,14) (1,7) (1,21) (1,19) (2,14) (2,20) (2,16) (3,5) (4,13) (4,5) (5,6) (6,9) (7,17) (7,20) (7,22) (8,21) (8,22) (9,13) (9,12) (10,12) (11,14) (11,15) (11,22) (12,13) (15,22) (16,18) (16,21) (16,17) (17,19) (18,19) (18,20) (19,21) (19,22) (20,22) (21,22)\nIs there a path between node 5 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph353-19_1", + "image": "data/connectivity/graph_visual/medium/graph353.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,14) (0,17) (0,8) (0,5) (0,3) (0,18) (0,10) (1,4) (2,5) (2,3) (2,9) (2,15) (2,19) (3,8) (3,9) (4,7) (5,14) (5,12) (5,11) (5,18) (6,20) (6,15) (8,13) (8,18) (9,20) (9,13) (9,18) (9,19) (10,16) (10,20) (10,14) (10,19) (11,20) (11,17) (11,15) (13,14) (13,19) (15,16) (15,17) (16,19) (17,20) (17,18) (19,20)\nIs there a path between node 19 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph474-16_6", + "image": "data/connectivity/graph_visual/medium/graph474.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,12) (0,21) (0,17) (0,16) (0,20) (1,15) (1,14) (1,20) (1,19) (1,9) (1,2) (1,6) (1,3) (2,18) (2,20) (2,19) (2,10) (3,16) (3,13) (4,5) (6,14) (6,18) (6,11) (6,22) (6,7) (6,13) (7,21) (7,15) (7,14) (7,18) (7,19) (7,11) (7,8) (8,12) (8,21) (8,15) (8,14) (8,20) (8,11) (8,9) (8,10) (9,15) (9,11) (9,10) (9,13) (10,18) (10,20) (10,19) (10,11) (10,22) (11,15) (11,16) (11,22) (12,21) (12,17) (12,18) (13,21) (13,17) (13,20) (13,19) (14,20) (15,21) (15,17) (15,18) (16,18) (16,20) (16,19) (17,20) (17,19) (17,22) (18,22)\nIs there a path between node 16 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph554-1_4", + "image": "data/connectivity/graph_visual/medium/graph554.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,8) (0,4) (0,10) (2,13) (3,17) (4,12) (4,14) (4,19) (6,22) (7,18) (7,23) (7,16) (7,17) (7,13) (8,12) (8,20) (9,21) (9,19) (10,14) (11,21) (11,15) (12,20) (13,18) (13,23) (14,15) (16,18) (17,23) (19,20)\nIs there a path between node 1 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph574-10_5", + "image": "data/connectivity/graph_visual/medium/graph574.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,11) (0,20) (0,12) (0,23) (0,9) (1,3) (2,13) (2,6) (2,8) (2,5) (2,17) (3,18) (3,22) (4,21) (5,6) (5,16) (5,10) (5,17) (6,15) (6,11) (6,12) (6,17) (8,16) (8,9) (9,20) (9,12) (9,10) (9,23) (10,15) (11,15) (11,12) (11,16) (12,13) (13,20) (15,20) (16,20) (16,23) (16,17) (18,19) (18,21) (21,22)\nIs there a path between node 10 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph611-0_9", + "image": "data/connectivity/graph_visual/medium/graph611.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (0,19) (0,1) (0,14) (0,16) (0,4) (1,17) (1,19) (1,14) (1,16) (1,4) (2,11) (2,15) (3,18) (3,7) (3,9) (3,22) (3,23) (3,21) (3,10) (4,17) (4,19) (4,14) (4,16) (5,6) (5,20) (5,13) (5,8) (5,12) (6,20) (6,13) (6,8) (6,12) (7,18) (7,9) (7,22) (7,23) (7,21) (7,10) (8,20) (8,13) (8,12) (9,18) (9,22) (9,23) (9,21) (9,10) (10,18) (10,22) (10,23) (10,21) (11,15) (12,20) (12,13) (13,20) (14,17) (14,19) (14,16) (16,17) (16,19) (17,19) (18,22) (18,23) (18,21) (21,22) (21,23) (22,23)\nIs there a path between node 0 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph569-2_23", + "image": "data/connectivity/graph_visual/medium/graph569.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,19) (0,20) (0,9) (1,13) (1,7) (1,12) (1,5) (1,2) (1,21) (1,18) (1,15) (1,22) (1,17) (2,13) (2,7) (2,12) (2,5) (2,21) (2,18) (2,15) (2,22) (2,17) (3,19) (3,20) (3,9) (4,8) (4,16) (4,6) (4,11) (5,13) (5,7) (5,12) (5,21) (5,18) (5,15) (5,22) (5,17) (6,8) (6,16) (6,11) (7,13) (7,12) (7,21) (7,18) (7,15) (7,22) (7,17) (8,16) (8,11) (9,19) (9,20) (10,14) (10,23) (11,16) (12,13) (12,21) (12,18) (12,15) (12,22) (12,17) (13,21) (13,18) (13,15) (13,22) (13,17) (14,23) (15,21) (15,18) (15,22) (15,17) (17,21) (17,18) (17,22) (18,21) (18,22) (19,20) (21,22)\nIs there a path between node 2 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph66-2_10", + "image": "data/connectivity/graph_visual/medium/graph66.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (0,1) (0,13) (0,7) (0,4) (0,10) (0,12) (0,5) (0,11) (0,6) (0,9) (0,8) (1,3) (1,13) (1,7) (1,4) (1,10) (1,12) (1,5) (1,11) (1,6) (1,9) (1,8) (3,13) (3,7) (3,4) (3,10) (3,12) (3,5) (3,11) (3,6) (3,9) (3,8) (4,13) (4,7) (4,10) (4,12) (4,5) (4,11) (4,6) (4,9) (4,8) (5,13) (5,7) (5,10) (5,12) (5,11) (5,6) (5,9) (5,8) (6,13) (6,7) (6,10) (6,12) (6,11) (6,9) (6,8) (7,13) (7,10) (7,12) (7,11) (7,9) (7,8) (8,13) (8,10) (8,12) (8,11) (8,9) (9,13) (9,10) (9,12) (9,11) (10,13) (10,12) (10,11) (11,13) (11,12) (12,13)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph678-0_15", + "image": "data/connectivity/graph_visual/medium/graph678.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,16) (0,15) (0,3) (0,1) (0,8) (1,23) (1,16) (1,15) (1,3) (1,8) (2,7) (2,4) (2,20) (2,14) (3,23) (3,16) (3,15) (3,8) (4,7) (4,20) (4,14) (5,12) (5,10) (5,18) (5,9) (5,22) (5,13) (5,17) (6,19) (6,11) (6,21) (7,20) (7,14) (8,23) (8,16) (8,15) (9,12) (9,10) (9,18) (9,22) (9,13) (9,17) (10,12) (10,18) (10,22) (10,13) (10,17) (11,19) (11,21) (12,18) (12,22) (12,13) (12,17) (13,18) (13,22) (13,17) (14,20) (15,23) (15,16) (16,23) (17,18) (17,22) (18,22) (19,21)\nIs there a path between node 0 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph670-15_19", + "image": "data/connectivity/graph_visual/medium/graph670.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,21) (0,18) (0,20) (0,16) (1,14) (1,23) (1,7) (1,3) (2,23) (2,7) (2,3) (3,14) (3,23) (3,7) (3,22) (4,11) (5,6) (5,21) (5,20) (5,16) (5,15) (6,21) (6,20) (6,16) (6,15) (7,23) (7,22) (8,12) (8,19) (8,17) (9,13) (9,12) (9,19) (9,10) (10,13) (10,12) (10,19) (10,17) (12,13) (12,19) (12,17) (13,17) (14,23) (15,21) (15,18) (15,16) (16,21) (16,18) (16,20) (17,19) (18,21) (18,20)\nIs there a path between node 15 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph611-14_19", + "image": "data/connectivity/graph_visual/medium/graph611.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (0,19) (0,1) (0,14) (0,16) (0,4) (1,17) (1,19) (1,14) (1,16) (1,4) (2,11) (2,15) (3,18) (3,7) (3,9) (3,22) (3,23) (3,21) (3,10) (4,17) (4,19) (4,14) (4,16) (5,6) (5,20) (5,13) (5,8) (5,12) (6,20) (6,13) (6,8) (6,12) (7,18) (7,9) (7,22) (7,23) (7,21) (7,10) (8,20) (8,13) (8,12) (9,18) (9,22) (9,23) (9,21) (9,10) (10,18) (10,22) (10,23) (10,21) (11,15) (12,20) (12,13) (13,20) (14,17) (14,19) (14,16) (16,17) (16,19) (17,19) (18,22) (18,23) (18,21) (21,22) (21,23) (22,23)\nIs there a path between node 14 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph687-3_5", + "image": "data/connectivity/graph_visual/medium/graph687.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,2) (0,4) (0,11) (0,8) (0,3) (0,20) (0,15) (0,13) (0,6) (0,7) (0,12) (0,14) (0,18) (0,23) (0,16) (0,9) (1,2) (1,4) (1,11) (1,8) (1,3) (1,20) (1,15) (1,13) (1,6) (1,7) (1,12) (1,14) (1,18) (1,23) (1,16) (1,9) (2,4) (2,11) (2,8) (2,3) (2,20) (2,15) (2,13) (2,6) (2,7) (2,12) (2,14) (2,18) (2,23) (2,16) (2,9) (3,4) (3,11) (3,8) (3,20) (3,15) (3,13) (3,6) (3,7) (3,12) (3,14) (3,18) (3,23) (3,16) (3,9) (4,11) (4,8) (4,20) (4,15) (4,13) (4,6) (4,7) (4,12) (4,14) (4,18) (4,23) (4,16) (4,9) (5,21) (5,19) (5,17) (5,22) (6,11) (6,8) (6,20) (6,15) (6,13) (6,7) (6,12) (6,14) (6,18) (6,23) (6,16) (6,9) (7,11) (7,8) (7,20) (7,15) (7,13) (7,12) (7,14) (7,18) (7,23) (7,16) (7,9) (8,11) (8,20) (8,15) (8,13) (8,12) (8,14) (8,18) (8,23) (8,16) (8,9) (9,11) (9,20) (9,15) (9,13) (9,12) (9,14) (9,18) (9,23) (9,16) (11,20) (11,15) (11,13) (11,12) (11,14) (11,18) (11,23) (11,16) (12,20) (12,15) (12,13) (12,14) (12,18) (12,23) (12,16) (13,20) (13,15) (13,14) (13,18) (13,23) (13,16) (14,20) (14,15) (14,18) (14,23) (14,16) (15,20) (15,18) (15,23) (15,16) (16,20) (16,18) (16,23) (17,21) (17,19) (17,22) (18,20) (18,23) (19,21) (19,22) (20,23) (21,22)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph470-22_9", + "image": "data/connectivity/graph_visual/medium/graph470.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,15) (0,22) (0,18) (1,5) (1,14) (1,21) (1,16) (1,19) (1,3) (1,17) (1,13) (1,11) (1,2) (1,20) (1,8) (1,6) (1,12) (1,9) (1,7) (2,5) (2,14) (2,21) (2,16) (2,19) (2,3) (2,17) (2,13) (2,11) (2,20) (2,8) (2,6) (2,12) (2,9) (2,7) (3,5) (3,14) (3,21) (3,16) (3,19) (3,17) (3,13) (3,11) (3,20) (3,8) (3,6) (3,12) (3,9) (3,7) (5,14) (5,21) (5,16) (5,19) (5,17) (5,13) (5,11) (5,20) (5,8) (5,6) (5,12) (5,9) (5,7) (6,14) (6,21) (6,16) (6,19) (6,17) (6,13) (6,11) (6,20) (6,8) (6,12) (6,9) (6,7) (7,14) (7,21) (7,16) (7,19) (7,17) (7,13) (7,11) (7,20) (7,8) (7,12) (7,9) (8,14) (8,21) (8,16) (8,19) (8,17) (8,13) (8,11) (8,20) (8,12) (8,9) (9,14) (9,21) (9,16) (9,19) (9,17) (9,13) (9,11) (9,20) (9,12) (10,15) (10,22) (10,18) (11,14) (11,21) (11,16) (11,19) (11,17) (11,13) (11,20) (11,12) (12,14) (12,21) (12,16) (12,19) (12,17) (12,13) (12,20) (13,14) (13,21) (13,16) (13,19) (13,17) (13,20) (14,21) (14,16) (14,19) (14,17) (14,20) (15,22) (15,18) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (18,22) (19,21) (19,20) (20,21)\nIs there a path between node 22 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph465-11_13", + "image": "data/connectivity/graph_visual/medium/graph465.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,14) (0,3) (0,12) (1,21) (1,18) (1,2) (1,17) (1,9) (1,20) (2,21) (2,18) (2,17) (2,9) (2,20) (3,14) (3,12) (4,16) (4,6) (4,5) (4,10) (4,19) (4,7) (4,13) (4,15) (4,11) (4,8) (5,16) (5,6) (5,10) (5,19) (5,7) (5,13) (5,15) (5,11) (5,8) (6,16) (6,10) (6,19) (6,7) (6,13) (6,15) (6,11) (6,8) (7,16) (7,10) (7,19) (7,13) (7,15) (7,11) (7,8) (8,16) (8,10) (8,19) (8,13) (8,15) (8,11) (9,21) (9,18) (9,17) (9,20) (10,16) (10,19) (10,13) (10,15) (10,11) (11,16) (11,19) (11,13) (11,15) (12,14) (13,16) (13,19) (13,15) (15,16) (15,19) (16,19) (17,21) (17,18) (17,20) (18,21) (18,20) (20,21)\nIs there a path between node 11 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph831-24_23", + "image": "data/connectivity/graph_visual/medium/graph831.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (1,14) (1,20) (2,3) (2,17) (2,18) (2,9) (2,23) (2,6) (2,21) (2,11) (3,24) (3,13) (3,18) (3,9) (3,23) (3,21) (3,16) (3,10) (3,8) (4,12) (4,7) (4,22) (4,20) (4,5) (5,14) (5,12) (5,7) (5,22) (5,20) (6,13) (6,17) (6,15) (6,21) (6,11) (6,10) (6,8) (7,14) (7,12) (7,22) (8,24) (8,13) (8,15) (8,18) (8,23) (8,11) (8,16) (8,10) (9,24) (9,15) (9,23) (9,11) (9,16) (9,10) (10,24) (10,13) (10,17) (10,15) (10,18) (10,23) (10,11) (10,16) (11,24) (11,13) (11,18) (11,23) (11,21) (12,22) (12,20) (13,24) (13,17) (13,18) (13,23) (13,21) (13,16) (14,20) (15,24) (15,17) (15,18) (15,21) (16,24) (16,17) (16,23) (17,24) (17,18) (17,23) (18,24) (20,22) (21,24) (21,23) (23,24)\nIs there a path between node 24 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph292-4_19", + "image": "data/connectivity/graph_visual/medium/graph292.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,14) (0,8) (0,12) (1,5) (1,16) (1,6) (1,7) (2,11) (3,16) (3,9) (4,5) (4,9) (5,19) (5,16) (5,6) (5,7) (5,18) (6,16) (6,7) (7,16) (7,18) (8,14) (8,10) (12,15) (13,19) (13,16) (14,15)\nIs there a path between node 4 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph117-11_6", + "image": "data/connectivity/graph_visual/medium/graph117.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,8) (0,15) (1,6) (1,8) (1,5) (1,14) (1,10) (4,15) (4,11) (4,7) (5,12) (5,11) (6,9) (6,10) (6,7) (7,8) (7,9) (7,11) (8,13) (8,12) (8,14) (8,10) (9,13) (9,11) (9,10) (10,12) (11,15) (12,15) (12,16) (12,14) (13,15) (13,16) (14,15) (15,16)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph361-14_8", + "image": "data/connectivity/graph_visual/medium/graph361.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,8) (0,14) (0,2) (0,16) (1,5) (1,7) (1,18) (1,15) (1,2) (1,10) (2,19) (2,12) (3,5) (3,15) (3,4) (3,6) (4,13) (4,15) (4,8) (4,14) (4,12) (4,10) (5,13) (5,18) (5,14) (5,16) (5,10) (6,13) (6,18) (6,10) (7,15) (7,10) (8,14) (8,12) (10,19) (10,16) (12,16) (13,18) (15,19) (15,16)\nIs there a path between node 14 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph665-11_15", + "image": "data/connectivity/graph_visual/medium/graph665.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,10) (0,14) (0,2) (0,8) (1,18) (1,23) (1,5) (1,4) (1,11) (1,9) (1,20) (1,17) (1,7) (2,10) (2,14) (2,16) (2,3) (2,8) (2,22) (3,12) (3,10) (3,14) (3,16) (3,8) (4,18) (4,15) (4,20) (4,17) (4,7) (5,23) (5,15) (5,21) (5,11) (5,9) (5,19) (5,17) (5,7) (7,23) (7,21) (7,11) (7,9) (7,20) (7,17) (8,12) (8,10) (8,14) (8,22) (9,18) (9,23) (9,15) (9,21) (9,11) (9,20) (9,19) (10,16) (10,22) (11,18) (11,15) (11,21) (11,20) (11,19) (11,17) (12,14) (12,16) (14,22) (15,18) (15,20) (17,20) (18,23) (18,19) (19,23) (19,21) (21,23)\nIs there a path between node 11 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph824-7_15", + "image": "data/connectivity/graph_visual/medium/graph824.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,8) (0,12) (0,5) (0,14) (0,15) (0,17) (0,11) (0,16) (0,1) (1,9) (1,8) (1,12) (1,5) (1,14) (1,15) (1,11) (1,16) (1,22) (2,9) (2,8) (2,15) (2,17) (2,11) (2,16) (2,6) (3,20) (3,24) (3,4) (3,13) (3,18) (3,19) (4,24) (4,21) (4,10) (4,18) (4,7) (5,9) (5,12) (5,15) (5,6) (5,22) (6,9) (6,8) (6,12) (6,14) (6,15) (6,17) (6,11) (7,20) (7,24) (7,23) (7,13) (7,21) (7,18) (7,19) (8,12) (8,14) (8,15) (8,11) (8,16) (8,22) (9,12) (9,17) (9,16) (9,22) (10,20) (10,23) (10,13) (10,19) (11,12) (11,14) (11,15) (11,17) (11,16) (12,15) (12,16) (12,22) (13,20) (13,24) (13,21) (13,18) (14,15) (14,17) (14,22) (15,17) (15,22) (16,17) (16,22) (18,20) (18,24) (18,23) (18,21) (18,19) (19,24) (20,24) (20,23) (20,21) (21,24) (21,23) (23,24)\nIs there a path between node 7 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph834-20_22", + "image": "data/connectivity/graph_visual/medium/graph834.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,5) (0,17) (0,4) (0,7) (0,21) (0,8) (0,22) (0,3) (0,16) (0,23) (0,13) (1,24) (1,15) (1,11) (1,20) (1,10) (1,18) (1,12) (1,14) (1,9) (1,19) (1,6) (2,5) (2,17) (2,4) (2,7) (2,21) (2,8) (2,22) (2,3) (2,16) (2,23) (2,13) (3,5) (3,17) (3,4) (3,7) (3,21) (3,8) (3,22) (3,16) (3,23) (3,13) (4,5) (4,17) (4,7) (4,21) (4,8) (4,22) (4,16) (4,23) (4,13) (5,17) (5,7) (5,21) (5,8) (5,22) (5,16) (5,23) (5,13) (6,24) (6,15) (6,11) (6,20) (6,10) (6,18) (6,12) (6,14) (6,9) (6,19) (7,17) (7,21) (7,8) (7,22) (7,16) (7,23) (7,13) (8,17) (8,21) (8,22) (8,16) (8,23) (8,13) (9,24) (9,15) (9,11) (9,20) (9,10) (9,18) (9,12) (9,14) (9,19) (10,24) (10,15) (10,11) (10,20) (10,18) (10,12) (10,14) (10,19) (11,24) (11,15) (11,20) (11,18) (11,12) (11,14) (11,19) (12,24) (12,15) (12,20) (12,18) (12,14) (12,19) (13,17) (13,21) (13,22) (13,16) (13,23) (14,24) (14,15) (14,20) (14,18) (14,19) (15,24) (15,20) (15,18) (15,19) (16,17) (16,21) (16,22) (16,23) (17,21) (17,22) (17,23) (18,24) (18,20) (18,19) (19,24) (19,20) (20,24) (21,22) (21,23) (22,23)\nIs there a path between node 20 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph139-13_5", + "image": "data/connectivity/graph_visual/medium/graph139.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,10) (0,17) (1,13) (1,14) (2,11) (3,11) (5,6) (5,13) (6,12) (6,14) (7,16) (8,17) (10,17) (12,13) (12,15) (12,14) (13,15)\nIs there a path between node 13 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph421-16_10", + "image": "data/connectivity/graph_visual/medium/graph421.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,18) (0,10) (0,17) (0,14) (0,16) (0,3) (0,7) (0,15) (0,9) (0,11) (0,20) (0,1) (0,12) (0,4) (0,21) (0,8) (1,19) (1,18) (1,10) (1,17) (1,14) (1,16) (1,3) (1,7) (1,15) (1,9) (1,11) (1,20) (1,12) (1,4) (1,21) (1,8) (2,6) (2,5) (2,13) (3,19) (3,18) (3,10) (3,17) (3,14) (3,16) (3,7) (3,15) (3,9) (3,11) (3,20) (3,12) (3,4) (3,21) (3,8) (4,19) (4,18) (4,10) (4,17) (4,14) (4,16) (4,7) (4,15) (4,9) (4,11) (4,20) (4,12) (4,21) (4,8) (5,6) (5,13) (6,13) (7,19) (7,18) (7,10) (7,17) (7,14) (7,16) (7,15) (7,9) (7,11) (7,20) (7,12) (7,21) (7,8) (8,19) (8,18) (8,10) (8,17) (8,14) (8,16) (8,15) (8,9) (8,11) (8,20) (8,12) (8,21) (9,19) (9,18) (9,10) (9,17) (9,14) (9,16) (9,15) (9,11) (9,20) (9,12) (9,21) (10,19) (10,18) (10,17) (10,14) (10,16) (10,15) (10,11) (10,20) (10,12) (10,21) (11,19) (11,18) (11,17) (11,14) (11,16) (11,15) (11,20) (11,12) (11,21) (12,19) (12,18) (12,17) (12,14) (12,16) (12,15) (12,20) (12,21) (14,19) (14,18) (14,17) (14,16) (14,15) (14,20) (14,21) (15,19) (15,18) (15,17) (15,16) (15,20) (15,21) (16,19) (16,18) (16,17) (16,20) (16,21) (17,19) (17,18) (17,20) (17,21) (18,19) (18,20) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 16 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph155-11_5", + "image": "data/connectivity/graph_visual/medium/graph155.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,9) (0,1) (0,6) (0,10) (0,3) (0,13) (0,8) (0,14) (0,15) (0,2) (0,7) (0,11) (1,9) (1,6) (1,10) (1,3) (1,13) (1,8) (1,14) (1,15) (1,2) (1,7) (1,11) (2,9) (2,6) (2,10) (2,3) (2,13) (2,8) (2,14) (2,15) (2,7) (2,11) (3,9) (3,6) (3,10) (3,13) (3,8) (3,14) (3,15) (3,7) (3,11) (4,12) (4,5) (4,16) (5,12) (5,16) (6,9) (6,10) (6,13) (6,8) (6,14) (6,15) (6,7) (6,11) (7,9) (7,10) (7,13) (7,8) (7,14) (7,15) (7,11) (8,9) (8,10) (8,13) (8,14) (8,15) (8,11) (9,10) (9,13) (9,14) (9,15) (9,11) (10,13) (10,14) (10,15) (10,11) (11,13) (11,14) (11,15) (12,16) (13,14) (13,15) (14,15)\nIs there a path between node 11 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph114-10_8", + "image": "data/connectivity/graph_visual/medium/graph114.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,15) (0,8) (0,10) (0,12) (0,13) (1,10) (2,5) (2,16) (3,13) (4,16) (5,7) (5,14) (6,7) (7,16) (7,14) (9,13) (10,15) (11,12) (12,15)\nIs there a path between node 10 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph519-14_20", + "image": "data/connectivity/graph_visual/medium/graph519.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,9) (0,3) (0,10) (0,14) (0,1) (1,9) (1,3) (1,10) (1,14) (1,20) (2,5) (2,13) (2,7) (2,16) (2,19) (2,21) (2,8) (2,4) (2,12) (2,18) (2,11) (2,17) (3,9) (3,10) (3,14) (3,20) (4,6) (4,5) (4,13) (4,16) (4,18) (4,11) (4,17) (5,6) (5,13) (5,7) (5,16) (5,22) (5,8) (5,12) (6,19) (6,12) (6,11) (6,17) (7,15) (7,16) (7,19) (7,22) (7,21) (7,8) (7,12) (7,11) (7,17) (8,13) (8,16) (8,22) (8,21) (9,14) (10,20) (11,15) (11,13) (11,16) (11,22) (11,21) (11,12) (11,18) (11,17) (12,15) (12,13) (12,16) (12,22) (12,21) (12,17) (13,16) (13,19) (13,22) (13,21) (13,18) (13,17) (14,20) (15,16) (15,17) (16,19) (16,22) (16,21) (16,18) (18,21) (19,21) (21,22)\nIs there a path between node 14 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph66-13_3", + "image": "data/connectivity/graph_visual/medium/graph66.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (0,1) (0,13) (0,7) (0,4) (0,10) (0,12) (0,5) (0,11) (0,6) (0,9) (0,8) (1,3) (1,13) (1,7) (1,4) (1,10) (1,12) (1,5) (1,11) (1,6) (1,9) (1,8) (3,13) (3,7) (3,4) (3,10) (3,12) (3,5) (3,11) (3,6) (3,9) (3,8) (4,13) (4,7) (4,10) (4,12) (4,5) (4,11) (4,6) (4,9) (4,8) (5,13) (5,7) (5,10) (5,12) (5,11) (5,6) (5,9) (5,8) (6,13) (6,7) (6,10) (6,12) (6,11) (6,9) (6,8) (7,13) (7,10) (7,12) (7,11) (7,9) (7,8) (8,13) (8,10) (8,12) (8,11) (8,9) (9,13) (9,10) (9,12) (9,11) (10,13) (10,12) (10,11) (11,13) (11,12) (12,13)\nIs there a path between node 13 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph507-18_11", + "image": "data/connectivity/graph_visual/medium/graph507.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,13) (0,17) (1,19) (1,22) (1,13) (1,17) (1,10) (1,14) (2,6) (2,16) (2,7) (4,11) (4,21) (4,16) (4,7) (5,15) (5,8) (5,7) (6,11) (6,21) (7,8) (8,15) (8,16) (9,22) (9,14) (10,19) (10,13) (10,18) (12,14) (12,20) (13,17) (13,18) (13,14) (14,18) (14,20) (15,16) (17,22) (18,20) (19,20) (20,22)\nIs there a path between node 18 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph526-4_9", + "image": "data/connectivity/graph_visual/medium/graph526.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,16) (0,9) (0,20) (0,8) (0,18) (0,4) (0,3) (0,1) (0,12) (0,15) (0,10) (0,14) (1,11) (1,17) (1,5) (1,22) (1,21) (1,9) (1,20) (1,8) (1,18) (1,3) (1,2) (1,10) (2,17) (2,5) (2,22) (2,16) (2,21) (2,20) (2,8) (2,18) (2,3) (2,12) (2,15) (3,11) (3,17) (3,5) (3,22) (3,16) (3,21) (3,9) (3,8) (3,18) (3,4) (3,15) (3,10) (4,17) (4,5) (4,22) (4,16) (4,9) (4,20) (4,8) (4,12) (4,10) (4,14) (5,16) (5,9) (5,20) (5,18) (5,10) (5,14) (7,13) (8,11) (8,17) (8,22) (8,16) (8,21) (8,9) (8,18) (8,12) (8,15) (8,10) (8,14) (9,11) (9,17) (9,16) (9,21) (9,20) (9,18) (9,10) (9,14) (10,11) (10,17) (10,22) (10,16) (10,21) (10,20) (10,18) (10,12) (10,15) (10,14) (11,22) (11,16) (11,21) (11,18) (11,15) (11,14) (12,22) (12,18) (12,14) (14,17) (14,20) (14,18) (14,15) (15,17) (15,22) (15,21) (15,20) (15,18) (16,17) (16,21) (16,20) (16,18) (17,22) (17,20) (17,18) (18,22) (18,21) (20,22) (21,22)\nIs there a path between node 4 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph440-3_16", + "image": "data/connectivity/graph_visual/medium/graph440.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,5) (0,4) (0,14) (0,8) (0,20) (0,3) (0,12) (0,10) (0,2) (0,9) (1,16) (1,7) (1,21) (1,17) (2,5) (2,11) (2,18) (2,4) (2,8) (2,20) (2,12) (2,9) (3,5) (3,11) (3,18) (3,4) (3,20) (3,13) (3,12) (3,15) (3,9) (4,5) (4,18) (4,14) (4,8) (4,20) (4,13) (4,12) (4,10) (4,15) (4,9) (5,11) (5,18) (5,14) (5,8) (5,12) (5,10) (5,15) (6,11) (6,18) (6,8) (6,20) (6,13) (6,10) (6,15) (7,16) (7,21) (7,19) (7,17) (8,11) (8,18) (8,14) (8,20) (8,12) (8,10) (8,15) (8,9) (9,11) (9,14) (9,20) (9,13) (9,15) (10,11) (10,18) (10,14) (10,20) (10,13) (10,12) (10,15) (11,14) (11,20) (11,13) (11,12) (11,15) (12,18) (12,14) (12,20) (12,13) (13,14) (13,20) (13,15) (14,18) (14,15) (15,20) (16,21) (16,19) (17,21) (17,19) (18,20)\nIs there a path between node 3 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph675-10_3", + "image": "data/connectivity/graph_visual/medium/graph675.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,22) (0,21) (0,14) (0,19) (0,13) (0,18) (0,12) (0,15) (0,6) (0,7) (0,10) (0,20) (0,2) (0,4) (0,8) (0,17) (0,23) (1,3) (1,16) (1,11) (1,9) (2,5) (2,22) (2,21) (2,14) (2,19) (2,13) (2,18) (2,12) (2,15) (2,6) (2,7) (2,10) (2,20) (2,4) (2,8) (2,17) (2,23) (3,16) (3,11) (3,9) (4,5) (4,22) (4,21) (4,14) (4,19) (4,13) (4,18) (4,12) (4,15) (4,6) (4,7) (4,10) (4,20) (4,8) (4,17) (4,23) (5,22) (5,21) (5,14) (5,19) (5,13) (5,18) (5,12) (5,15) (5,6) (5,7) (5,10) (5,20) (5,8) (5,17) (5,23) (6,22) (6,21) (6,14) (6,19) (6,13) (6,18) (6,12) (6,15) (6,7) (6,10) (6,20) (6,8) (6,17) (6,23) (7,22) (7,21) (7,14) (7,19) (7,13) (7,18) (7,12) (7,15) (7,10) (7,20) (7,8) (7,17) (7,23) (8,22) (8,21) (8,14) (8,19) (8,13) (8,18) (8,12) (8,15) (8,10) (8,20) (8,17) (8,23) (9,16) (9,11) (10,22) (10,21) (10,14) (10,19) (10,13) (10,18) (10,12) (10,15) (10,20) (10,17) (10,23) (11,16) (12,22) (12,21) (12,14) (12,19) (12,13) (12,18) (12,15) (12,20) (12,17) (12,23) (13,22) (13,21) (13,14) (13,19) (13,18) (13,15) (13,20) (13,17) (13,23) (14,22) (14,21) (14,19) (14,18) (14,15) (14,20) (14,17) (14,23) (15,22) (15,21) (15,19) (15,18) (15,20) (15,17) (15,23) (17,22) (17,21) (17,19) (17,18) (17,20) (17,23) (18,22) (18,21) (18,19) (18,20) (18,23) (19,22) (19,21) (19,20) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 10 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph621-6_0", + "image": "data/connectivity/graph_visual/medium/graph621.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,17) (0,21) (0,2) (0,19) (0,5) (0,7) (0,10) (0,13) (0,1) (0,9) (0,20) (1,22) (1,17) (1,21) (1,2) (1,19) (1,5) (1,7) (1,10) (1,13) (1,9) (1,20) (2,22) (2,17) (2,21) (2,19) (2,5) (2,7) (2,10) (2,13) (2,9) (2,20) (3,18) (3,12) (3,11) (3,16) (3,23) (3,6) (3,4) (3,8) (3,14) (3,15) (4,18) (4,12) (4,11) (4,16) (4,23) (4,6) (4,8) (4,14) (4,15) (5,22) (5,17) (5,21) (5,19) (5,7) (5,10) (5,13) (5,9) (5,20) (6,18) (6,12) (6,11) (6,16) (6,23) (6,8) (6,14) (6,15) (7,22) (7,17) (7,21) (7,19) (7,10) (7,13) (7,9) (7,20) (8,18) (8,12) (8,11) (8,16) (8,23) (8,14) (8,15) (9,22) (9,17) (9,21) (9,19) (9,10) (9,13) (9,20) (10,22) (10,17) (10,21) (10,19) (10,13) (10,20) (11,18) (11,12) (11,16) (11,23) (11,14) (11,15) (12,18) (12,16) (12,23) (12,14) (12,15) (13,22) (13,17) (13,21) (13,19) (13,20) (14,18) (14,16) (14,23) (14,15) (15,18) (15,16) (15,23) (16,18) (16,23) (17,22) (17,21) (17,19) (17,20) (18,23) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 6 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph576-4_2", + "image": "data/connectivity/graph_visual/medium/graph576.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,18) (0,11) (0,23) (0,17) (0,7) (0,16) (0,1) (1,18) (1,6) (1,11) (1,21) (1,22) (1,2) (2,8) (2,16) (3,9) (3,13) (5,18) (5,6) (5,21) (5,17) (6,8) (6,11) (6,17) (6,19) (7,20) (7,8) (7,15) (7,19) (8,18) (8,22) (8,15) (11,14) (11,20) (11,22) (11,17) (11,16) (12,13) (14,18) (14,21) (14,23) (14,19) (15,21) (15,23) (16,21) (16,23) (18,20) (18,21) (18,23) (21,22)\nIs there a path between node 4 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph455-0_20", + "image": "data/connectivity/graph_visual/medium/graph455.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,14) (1,19) (1,12) (1,18) (1,5) (1,13) (1,2) (1,17) (1,7) (1,15) (1,3) (1,16) (1,11) (1,9) (1,10) (1,20) (1,21) (1,4) (2,19) (2,12) (2,18) (2,5) (2,13) (2,17) (2,7) (2,15) (2,3) (2,16) (2,11) (2,9) (2,10) (2,20) (2,21) (2,4) (3,19) (3,12) (3,18) (3,5) (3,13) (3,17) (3,7) (3,15) (3,16) (3,11) (3,9) (3,10) (3,20) (3,21) (3,4) (4,19) (4,12) (4,18) (4,5) (4,13) (4,17) (4,7) (4,15) (4,16) (4,11) (4,9) (4,10) (4,20) (4,21) (5,19) (5,12) (5,18) (5,13) (5,17) (5,7) (5,15) (5,16) (5,11) (5,9) (5,10) (5,20) (5,21) (6,8) (7,19) (7,12) (7,18) (7,13) (7,17) (7,15) (7,16) (7,11) (7,9) (7,10) (7,20) (7,21) (9,19) (9,12) (9,18) (9,13) (9,17) (9,15) (9,16) (9,11) (9,10) (9,20) (9,21) (10,19) (10,12) (10,18) (10,13) (10,17) (10,15) (10,16) (10,11) (10,20) (10,21) (11,19) (11,12) (11,18) (11,13) (11,17) (11,15) (11,16) (11,20) (11,21) (12,19) (12,18) (12,13) (12,17) (12,15) (12,16) (12,20) (12,21) (13,19) (13,18) (13,17) (13,15) (13,16) (13,20) (13,21) (15,19) (15,18) (15,17) (15,16) (15,20) (15,21) (16,19) (16,18) (16,17) (16,20) (16,21) (17,19) (17,18) (17,20) (17,21) (18,19) (18,20) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 0 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph162-8_14", + "image": "data/connectivity/graph_visual/medium/graph162.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,5) (0,11) (1,7) (1,14) (2,8) (2,4) (2,5) (2,7) (3,6) (4,11) (5,14) (5,11) (6,12) (7,8) (7,16) (8,14) (8,17) (9,17) (12,13) (13,15) (14,17)\nIs there a path between node 8 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph330-15_1", + "image": "data/connectivity/graph_visual/medium/graph330.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,5) (1,17) (2,16) (3,18) (3,14) (4,20) (5,17) (6,16) (6,12) (6,8) (8,15) (8,17) (10,13) (10,11) (11,20) (12,15) (12,17) (14,18) (14,19) (16,17)\nIs there a path between node 15 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph260-14_13", + "image": "data/connectivity/graph_visual/medium/graph260.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,18) (0,1) (0,8) (0,10) (0,11) (0,7) (0,4) (0,2) (0,6) (0,17) (0,14) (1,19) (1,18) (1,8) (1,10) (1,11) (1,7) (1,4) (1,2) (1,6) (1,17) (1,14) (2,19) (2,18) (2,8) (2,10) (2,11) (2,7) (2,4) (2,6) (2,17) (2,14) (3,13) (3,9) (3,15) (4,19) (4,18) (4,8) (4,10) (4,11) (4,7) (4,6) (4,17) (4,14) (5,12) (5,16) (6,19) (6,18) (6,8) (6,10) (6,11) (6,7) (6,17) (6,14) (7,19) (7,18) (7,8) (7,10) (7,11) (7,17) (7,14) (8,19) (8,18) (8,10) (8,11) (8,17) (8,14) (9,13) (9,15) (10,19) (10,18) (10,11) (10,17) (10,14) (11,19) (11,18) (11,17) (11,14) (12,16) (13,15) (14,19) (14,18) (14,17) (17,19) (17,18) (18,19)\nIs there a path between node 14 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph594-9_14", + "image": "data/connectivity/graph_visual/medium/graph594.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,13) (0,4) (0,19) (0,9) (0,18) (0,17) (0,21) (0,10) (0,16) (0,2) (0,1) (0,23) (0,14) (0,7) (1,11) (1,13) (1,4) (1,9) (1,6) (1,17) (1,21) (1,10) (1,23) (1,14) (1,7) (2,11) (2,13) (2,19) (2,18) (2,17) (2,21) (2,10) (2,16) (2,23) (2,14) (3,8) (3,12) (3,5) (3,20) (3,22) (4,13) (4,19) (4,9) (4,18) (4,17) (4,21) (4,10) (4,14) (4,7) (5,8) (5,15) (5,20) (5,22) (6,13) (6,19) (6,18) (6,21) (6,10) (6,7) (7,13) (7,9) (7,18) (7,17) (7,10) (7,14) (8,15) (8,12) (8,22) (9,11) (9,19) (9,18) (9,17) (9,21) (9,10) (9,16) (9,23) (9,14) (10,11) (10,13) (10,19) (10,18) (10,17) (10,16) (10,23) (10,14) (11,13) (11,19) (11,17) (11,21) (11,16) (11,23) (11,14) (12,20) (12,22) (13,19) (13,18) (13,17) (13,16) (13,23) (13,14) (14,19) (14,18) (14,17) (14,16) (14,23) (15,22) (16,19) (16,17) (16,21) (16,23) (17,18) (18,23) (19,23) (20,22)\nIs there a path between node 9 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph315-3_12", + "image": "data/connectivity/graph_visual/medium/graph315.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,16) (0,8) (0,12) (0,9) (0,4) (0,6) (0,11) (1,19) (1,15) (2,7) (2,10) (2,13) (2,3) (2,5) (2,18) (2,17) (2,14) (3,7) (3,10) (3,13) (3,5) (3,18) (3,17) (3,14) (4,16) (4,8) (4,12) (4,9) (4,6) (4,11) (5,7) (5,10) (5,13) (5,18) (5,17) (5,14) (6,16) (6,8) (6,12) (6,9) (6,11) (7,10) (7,13) (7,18) (7,17) (7,14) (8,16) (8,12) (8,9) (8,11) (9,16) (9,12) (9,11) (10,13) (10,18) (10,17) (10,14) (11,16) (11,12) (12,16) (13,18) (13,17) (13,14) (14,18) (14,17) (15,19) (17,18)\nIs there a path between node 3 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph675-4_18", + "image": "data/connectivity/graph_visual/medium/graph675.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,22) (0,21) (0,14) (0,19) (0,13) (0,18) (0,12) (0,15) (0,6) (0,7) (0,10) (0,20) (0,2) (0,4) (0,8) (0,17) (0,23) (1,3) (1,16) (1,11) (1,9) (2,5) (2,22) (2,21) (2,14) (2,19) (2,13) (2,18) (2,12) (2,15) (2,6) (2,7) (2,10) (2,20) (2,4) (2,8) (2,17) (2,23) (3,16) (3,11) (3,9) (4,5) (4,22) (4,21) (4,14) (4,19) (4,13) (4,18) (4,12) (4,15) (4,6) (4,7) (4,10) (4,20) (4,8) (4,17) (4,23) (5,22) (5,21) (5,14) (5,19) (5,13) (5,18) (5,12) (5,15) (5,6) (5,7) (5,10) (5,20) (5,8) (5,17) (5,23) (6,22) (6,21) (6,14) (6,19) (6,13) (6,18) (6,12) (6,15) (6,7) (6,10) (6,20) (6,8) (6,17) (6,23) (7,22) (7,21) (7,14) (7,19) (7,13) (7,18) (7,12) (7,15) (7,10) (7,20) (7,8) (7,17) (7,23) (8,22) (8,21) (8,14) (8,19) (8,13) (8,18) (8,12) (8,15) (8,10) (8,20) (8,17) (8,23) (9,16) (9,11) (10,22) (10,21) (10,14) (10,19) (10,13) (10,18) (10,12) (10,15) (10,20) (10,17) (10,23) (11,16) (12,22) (12,21) (12,14) (12,19) (12,13) (12,18) (12,15) (12,20) (12,17) (12,23) (13,22) (13,21) (13,14) (13,19) (13,18) (13,15) (13,20) (13,17) (13,23) (14,22) (14,21) (14,19) (14,18) (14,15) (14,20) (14,17) (14,23) (15,22) (15,21) (15,19) (15,18) (15,20) (15,17) (15,23) (17,22) (17,21) (17,19) (17,18) (17,20) (17,23) (18,22) (18,21) (18,19) (18,20) (18,23) (19,22) (19,21) (19,20) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 4 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph186-13_17", + "image": "data/connectivity/graph_visual/medium/graph186.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,8) (0,7) (0,14) (0,17) (0,4) (0,1) (0,15) (0,2) (0,6) (0,16) (0,9) (0,12) (0,11) (0,3) (0,10) (1,8) (1,7) (1,14) (1,17) (1,4) (1,15) (1,2) (1,6) (1,16) (1,9) (1,12) (1,11) (1,3) (1,10) (2,8) (2,7) (2,14) (2,17) (2,4) (2,15) (2,6) (2,16) (2,9) (2,12) (2,11) (2,3) (2,10) (3,8) (3,7) (3,14) (3,17) (3,4) (3,15) (3,6) (3,16) (3,9) (3,12) (3,11) (3,10) (4,8) (4,7) (4,14) (4,17) (4,15) (4,6) (4,16) (4,9) (4,12) (4,11) (4,10) (5,13) (6,8) (6,7) (6,14) (6,17) (6,15) (6,16) (6,9) (6,12) (6,11) (6,10) (7,8) (7,14) (7,17) (7,15) (7,16) (7,9) (7,12) (7,11) (7,10) (8,14) (8,17) (8,15) (8,16) (8,9) (8,12) (8,11) (8,10) (9,14) (9,17) (9,15) (9,16) (9,12) (9,11) (9,10) (10,14) (10,17) (10,15) (10,16) (10,12) (10,11) (11,14) (11,17) (11,15) (11,16) (11,12) (12,14) (12,17) (12,15) (12,16) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 13 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph28-10_0", + "image": "data/connectivity/graph_visual/medium/graph28.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,1) (0,4) (0,3) (0,6) (0,2) (0,8) (0,5) (0,11) (1,4) (1,3) (1,6) (1,2) (1,8) (1,5) (1,11) (2,4) (2,3) (2,6) (2,8) (2,5) (2,11) (3,4) (3,6) (3,8) (3,5) (3,11) (4,6) (4,8) (4,5) (4,11) (5,6) (5,8) (5,11) (6,8) (6,11) (7,9) (7,10) (8,11) (9,10)\nIs there a path between node 10 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph273-2_16", + "image": "data/connectivity/graph_visual/medium/graph273.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,18) (0,5) (0,19) (0,11) (0,8) (0,6) (0,14) (0,10) (1,7) (1,2) (2,7) (2,17) (3,9) (3,18) (3,13) (3,19) (3,11) (3,16) (3,8) (3,6) (3,14) (3,10) (4,9) (4,13) (4,5) (4,15) (4,19) (4,11) (4,16) (4,8) (4,6) (4,10) (5,9) (5,18) (5,13) (5,15) (5,19) (5,11) (5,8) (5,14) (5,10) (6,13) (6,12) (6,15) (6,19) (6,11) (6,16) (6,8) (6,10) (7,17) (8,9) (8,13) (8,12) (8,15) (8,14) (8,10) (9,18) (9,12) (9,19) (9,16) (9,14) (9,10) (10,18) (10,13) (10,12) (10,15) (10,19) (10,16) (10,14) (11,15) (11,19) (11,16) (12,13) (12,19) (13,15) (13,19) (13,16) (14,18) (14,16) (15,18) (15,16) (16,18) (16,19)\nIs there a path between node 2 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph665-10_23", + "image": "data/connectivity/graph_visual/medium/graph665.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,10) (0,14) (0,2) (0,8) (1,18) (1,23) (1,5) (1,4) (1,11) (1,9) (1,20) (1,17) (1,7) (2,10) (2,14) (2,16) (2,3) (2,8) (2,22) (3,12) (3,10) (3,14) (3,16) (3,8) (4,18) (4,15) (4,20) (4,17) (4,7) (5,23) (5,15) (5,21) (5,11) (5,9) (5,19) (5,17) (5,7) (7,23) (7,21) (7,11) (7,9) (7,20) (7,17) (8,12) (8,10) (8,14) (8,22) (9,18) (9,23) (9,15) (9,21) (9,11) (9,20) (9,19) (10,16) (10,22) (11,18) (11,15) (11,21) (11,20) (11,19) (11,17) (12,14) (12,16) (14,22) (15,18) (15,20) (17,20) (18,23) (18,19) (19,23) (19,21) (21,23)\nIs there a path between node 10 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph777-13_24", + "image": "data/connectivity/graph_visual/medium/graph777.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,3) (0,9) (0,12) (0,24) (0,2) (0,17) (0,20) (0,14) (0,13) (0,21) (0,7) (0,8) (0,15) (0,18) (0,5) (0,23) (0,16) (1,4) (1,19) (1,11) (1,22) (1,6) (2,10) (2,3) (2,9) (2,12) (2,24) (2,17) (2,20) (2,14) (2,13) (2,21) (2,7) (2,8) (2,15) (2,18) (2,5) (2,23) (2,16) (3,10) (3,9) (3,12) (3,24) (3,17) (3,20) (3,14) (3,13) (3,21) (3,7) (3,8) (3,15) (3,18) (3,5) (3,23) (3,16) (4,19) (4,11) (4,22) (4,6) (5,10) (5,9) (5,12) (5,24) (5,17) (5,20) (5,14) (5,13) (5,21) (5,7) (5,8) (5,15) (5,18) (5,23) (5,16) (6,19) (6,11) (6,22) (7,10) (7,9) (7,12) (7,24) (7,17) (7,20) (7,14) (7,13) (7,21) (7,8) (7,15) (7,18) (7,23) (7,16) (8,10) (8,9) (8,12) (8,24) (8,17) (8,20) (8,14) (8,13) (8,21) (8,15) (8,18) (8,23) (8,16) (9,10) (9,12) (9,24) (9,17) (9,20) (9,14) (9,13) (9,21) (9,15) (9,18) (9,23) (9,16) (10,12) (10,24) (10,17) (10,20) (10,14) (10,13) (10,21) (10,15) (10,18) (10,23) (10,16) (11,19) (11,22) (12,24) (12,17) (12,20) (12,14) (12,13) (12,21) (12,15) (12,18) (12,23) (12,16) (13,24) (13,17) (13,20) (13,14) (13,21) (13,15) (13,18) (13,23) (13,16) (14,24) (14,17) (14,20) (14,21) (14,15) (14,18) (14,23) (14,16) (15,24) (15,17) (15,20) (15,21) (15,18) (15,23) (15,16) (16,24) (16,17) (16,20) (16,21) (16,18) (16,23) (17,24) (17,20) (17,21) (17,18) (17,23) (18,24) (18,20) (18,21) (18,23) (19,22) (20,24) (20,21) (20,23) (21,24) (21,23) (23,24)\nIs there a path between node 13 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph343-8_16", + "image": "data/connectivity/graph_visual/medium/graph343.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (0,1) (0,14) (0,18) (1,17) (1,14) (1,18) (2,19) (2,7) (2,10) (2,3) (2,12) (2,16) (2,11) (2,5) (2,9) (2,15) (2,6) (2,20) (2,8) (2,4) (2,13) (3,19) (3,7) (3,10) (3,12) (3,16) (3,11) (3,5) (3,9) (3,15) (3,6) (3,20) (3,8) (3,4) (3,13) (4,19) (4,7) (4,10) (4,12) (4,16) (4,11) (4,5) (4,9) (4,15) (4,6) (4,20) (4,8) (4,13) (5,19) (5,7) (5,10) (5,12) (5,16) (5,11) (5,9) (5,15) (5,6) (5,20) (5,8) (5,13) (6,19) (6,7) (6,10) (6,12) (6,16) (6,11) (6,9) (6,15) (6,20) (6,8) (6,13) (7,19) (7,10) (7,12) (7,16) (7,11) (7,9) (7,15) (7,20) (7,8) (7,13) (8,19) (8,10) (8,12) (8,16) (8,11) (8,9) (8,15) (8,20) (8,13) (9,19) (9,10) (9,12) (9,16) (9,11) (9,15) (9,20) (9,13) (10,19) (10,12) (10,16) (10,11) (10,15) (10,20) (10,13) (11,19) (11,12) (11,16) (11,15) (11,20) (11,13) (12,19) (12,16) (12,15) (12,20) (12,13) (13,19) (13,16) (13,15) (13,20) (14,17) (14,18) (15,19) (15,16) (15,20) (16,19) (16,20) (17,18) (19,20)\nIs there a path between node 8 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph321-0_16", + "image": "data/connectivity/graph_visual/medium/graph321.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,15) (0,19) (0,18) (0,2) (0,17) (0,16) (0,4) (0,10) (0,14) (0,1) (0,5) (0,7) (0,9) (1,15) (1,19) (1,18) (1,2) (1,17) (1,16) (1,4) (1,10) (1,14) (1,5) (1,7) (1,9) (2,15) (2,19) (2,18) (2,17) (2,16) (2,4) (2,10) (2,14) (2,5) (2,7) (2,9) (3,8) (3,6) (3,13) (4,15) (4,19) (4,18) (4,17) (4,16) (4,10) (4,14) (4,5) (4,7) (4,9) (5,15) (5,19) (5,18) (5,17) (5,16) (5,10) (5,14) (5,7) (5,9) (6,8) (6,13) (7,15) (7,19) (7,18) (7,17) (7,16) (7,10) (7,14) (7,9) (8,13) (9,15) (9,19) (9,18) (9,17) (9,16) (9,10) (9,14) (10,15) (10,19) (10,18) (10,17) (10,16) (10,14) (11,12) (14,15) (14,19) (14,18) (14,17) (14,16) (15,19) (15,18) (15,17) (15,16) (16,19) (16,18) (16,17) (17,19) (17,18) (18,19)\nIs there a path between node 0 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph220-13_2", + "image": "data/connectivity/graph_visual/medium/graph220.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,5) (0,16) (0,3) (1,16) (1,2) (1,4) (1,3) (2,8) (4,5) (4,16) (5,16) (6,15) (7,14) (7,9) (7,12) (8,16) (9,15) (10,15) (12,13) (13,17) (14,15) (16,18)\nIs there a path between node 13 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph265-19_16", + "image": "data/connectivity/graph_visual/medium/graph265.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,12) (0,19) (0,11) (0,8) (0,10) (1,14) (1,13) (2,11) (2,6) (3,12) (3,19) (3,9) (4,7) (5,11) (5,10) (6,10) (7,16) (7,13) (8,19) (8,11) (9,12) (9,11) (9,18) (11,12) (11,19) (13,16) (13,17) (14,16) (14,17)\nIs there a path between node 19 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph447-5_14", + "image": "data/connectivity/graph_visual/medium/graph447.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,6) (0,3) (0,15) (0,12) (0,20) (0,18) (0,2) (0,13) (0,21) (0,9) (0,14) (0,4) (1,17) (2,16) (2,6) (2,7) (2,12) (2,13) (2,21) (2,5) (3,16) (3,12) (3,18) (3,13) (3,21) (3,9) (3,4) (4,15) (4,7) (4,12) (4,20) (4,13) (4,21) (4,5) (4,9) (5,16) (5,6) (5,15) (5,7) (5,12) (5,18) (5,13) (5,9) (5,14) (6,16) (6,7) (6,12) (6,20) (6,21) (6,14) (7,16) (7,15) (7,12) (7,20) (7,13) (7,9) (8,19) (9,15) (9,20) (9,21) (9,14) (10,19) (11,17) (12,16) (12,20) (12,18) (12,21) (13,20) (13,21) (14,16) (14,15) (14,20) (14,18) (14,21) (15,21) (16,20) (16,18) (18,20) (18,21) (20,21)\nIs there a path between node 5 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph643-14_18", + "image": "data/connectivity/graph_visual/medium/graph643.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,18) (0,5) (2,3) (2,7) (2,15) (2,18) (3,16) (3,7) (3,15) (3,21) (4,8) (5,7) (6,16) (6,22) (6,18) (8,23) (9,11) (10,23) (11,20) (12,13) (15,22) (15,21) (16,22) (17,22) (17,21) (19,23) (20,23)\nIs there a path between node 14 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph625-8_18", + "image": "data/connectivity/graph_visual/medium/graph625.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (1,11) (1,7) (1,13) (1,21) (1,19) (1,5) (2,17) (2,20) (2,5) (4,9) (4,22) (5,21) (5,19) (6,23) (7,11) (8,11) (8,13) (8,19) (8,18) (11,23) (11,13) (11,18) (13,20) (13,21) (13,19) (13,18) (14,16) (14,15) (18,20) (19,20) (19,21) (20,23)\nIs there a path between node 8 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph562-4_22", + "image": "data/connectivity/graph_visual/medium/graph562.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,5) (0,6) (0,13) (0,17) (0,23) (0,9) (0,10) (0,22) (0,2) (0,20) (0,21) (0,12) (1,14) (1,18) (1,3) (1,4) (1,11) (1,16) (1,7) (2,5) (2,13) (2,17) (2,23) (2,9) (2,10) (2,20) (2,21) (2,12) (3,18) (3,4) (3,11) (3,16) (3,7) (4,18) (4,11) (4,16) (4,8) (5,19) (5,13) (5,17) (5,23) (5,9) (5,10) (5,22) (5,15) (5,12) (6,19) (6,13) (6,23) (6,9) (6,22) (6,15) (6,20) (6,12) (7,14) (7,11) (7,16) (8,14) (8,11) (9,19) (9,13) (9,17) (9,23) (9,10) (9,15) (9,20) (9,21) (10,19) (10,13) (10,23) (10,15) (10,20) (11,18) (12,19) (12,23) (12,22) (12,15) (12,20) (12,21) (13,19) (13,23) (13,22) (13,20) (14,18) (15,19) (15,17) (15,22) (15,20) (17,23) (17,22) (17,21) (19,21) (20,23) (20,22) (21,23) (22,23)\nIs there a path between node 4 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph322-9_17", + "image": "data/connectivity/graph_visual/medium/graph322.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,3) (0,1) (0,11) (0,4) (0,16) (0,5) (0,19) (0,6) (0,10) (0,17) (0,12) (1,3) (1,11) (1,4) (1,16) (1,5) (1,19) (1,6) (1,10) (1,17) (1,12) (2,15) (2,14) (2,9) (2,18) (2,7) (3,11) (3,4) (3,16) (3,5) (3,19) (3,6) (3,10) (3,17) (3,12) (4,11) (4,16) (4,5) (4,19) (4,6) (4,10) (4,17) (4,12) (5,11) (5,16) (5,19) (5,6) (5,10) (5,17) (5,12) (6,11) (6,16) (6,19) (6,10) (6,17) (6,12) (7,15) (7,14) (7,9) (7,18) (8,13) (9,15) (9,14) (9,18) (10,11) (10,16) (10,19) (10,17) (10,12) (11,16) (11,19) (11,17) (11,12) (12,16) (12,19) (12,17) (14,15) (14,18) (15,18) (16,19) (16,17) (17,19)\nIs there a path between node 9 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph643-13_12", + "image": "data/connectivity/graph_visual/medium/graph643.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,18) (0,5) (2,3) (2,7) (2,15) (2,18) (3,16) (3,7) (3,15) (3,21) (4,8) (5,7) (6,16) (6,22) (6,18) (8,23) (9,11) (10,23) (11,20) (12,13) (15,22) (15,21) (16,22) (17,22) (17,21) (19,23) (20,23)\nIs there a path between node 13 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph263-14_16", + "image": "data/connectivity/graph_visual/medium/graph263.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,12) (0,3) (1,18) (2,11) (2,17) (2,9) (3,12) (4,10) (4,17) (4,6) (4,7) (6,14) (6,11) (6,17) (6,7) (7,15) (7,14) (7,19) (8,16) (9,10) (10,15) (10,11) (10,13) (11,13) (13,15) (13,14) (13,19)\nIs there a path between node 14 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph223-4_10", + "image": "data/connectivity/graph_visual/medium/graph223.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,1) (1,12) (2,18) (2,14) (3,17) (4,5) (4,11) (6,11) (6,13) (9,14) (13,17)\nIs there a path between node 4 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph764-1_8", + "image": "data/connectivity/graph_visual/medium/graph764.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,4) (0,24) (1,22) (1,13) (1,2) (1,18) (1,5) (1,3) (1,19) (1,7) (1,9) (1,21) (1,8) (1,10) (1,23) (1,6) (1,20) (1,14) (1,11) (1,16) (1,17) (1,15) (2,22) (2,13) (2,18) (2,5) (2,3) (2,19) (2,7) (2,9) (2,21) (2,8) (2,10) (2,23) (2,6) (2,20) (2,14) (2,11) (2,16) (2,17) (2,15) (3,22) (3,13) (3,18) (3,5) (3,19) (3,7) (3,9) (3,21) (3,8) (3,10) (3,23) (3,6) (3,20) (3,14) (3,11) (3,16) (3,17) (3,15) (4,12) (4,24) (5,22) (5,13) (5,18) (5,19) (5,7) (5,9) (5,21) (5,8) (5,10) (5,23) (5,6) (5,20) (5,14) (5,11) (5,16) (5,17) (5,15) (6,22) (6,13) (6,18) (6,19) (6,7) (6,9) (6,21) (6,8) (6,10) (6,23) (6,20) (6,14) (6,11) (6,16) (6,17) (6,15) (7,22) (7,13) (7,18) (7,19) (7,9) (7,21) (7,8) (7,10) (7,23) (7,20) (7,14) (7,11) (7,16) (7,17) (7,15) (8,22) (8,13) (8,18) (8,19) (8,9) (8,21) (8,10) (8,23) (8,20) (8,14) (8,11) (8,16) (8,17) (8,15) (9,22) (9,13) (9,18) (9,19) (9,21) (9,10) (9,23) (9,20) (9,14) (9,11) (9,16) (9,17) (9,15) (10,22) (10,13) (10,18) (10,19) (10,21) (10,23) (10,20) (10,14) (10,11) (10,16) (10,17) (10,15) (11,22) (11,13) (11,18) (11,19) (11,21) (11,23) (11,20) (11,14) (11,16) (11,17) (11,15) (12,24) (13,22) (13,18) (13,19) (13,21) (13,23) (13,20) (13,14) (13,16) (13,17) (13,15) (14,22) (14,18) (14,19) (14,21) (14,23) (14,20) (14,16) (14,17) (14,15) (15,22) (15,18) (15,19) (15,21) (15,23) (15,20) (15,16) (15,17) (16,22) (16,18) (16,19) (16,21) (16,23) (16,20) (16,17) (17,22) (17,18) (17,19) (17,21) (17,23) (17,20) (18,22) (18,19) (18,21) (18,23) (18,20) (19,22) (19,21) (19,23) (19,20) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 1 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph124-3_5", + "image": "data/connectivity/graph_visual/medium/graph124.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,12) (0,4) (0,7) (0,15) (0,2) (0,5) (0,11) (0,8) (0,14) (0,13) (0,10) (0,1) (1,4) (1,7) (1,15) (1,9) (1,2) (1,5) (1,11) (1,8) (1,14) (1,16) (1,10) (2,7) (2,15) (2,9) (2,6) (2,5) (2,11) (2,8) (2,14) (2,16) (2,13) (2,10) (4,12) (4,7) (4,9) (4,6) (4,5) (4,8) (4,16) (4,13) (4,10) (5,12) (5,7) (5,15) (5,9) (5,6) (5,16) (5,13) (5,10) (6,12) (6,15) (6,9) (6,14) (6,16) (7,12) (7,11) (7,8) (7,16) (7,10) (8,12) (8,9) (8,11) (8,14) (8,16) (8,10) (9,11) (10,12) (10,15) (10,14) (10,16) (10,13) (11,15) (11,14) (11,16) (11,13) (12,15) (12,14) (12,16) (12,13) (13,15) (14,15) (14,16) (15,16)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph154-3_5", + "image": "data/connectivity/graph_visual/medium/graph154.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,1) (0,6) (0,13) (0,4) (1,12) (1,6) (1,13) (1,4) (2,16) (2,15) (2,10) (2,11) (2,14) (2,3) (2,17) (2,5) (2,7) (2,8) (2,9) (3,16) (3,15) (3,10) (3,11) (3,14) (3,17) (3,5) (3,7) (3,8) (3,9) (4,12) (4,6) (4,13) (5,16) (5,15) (5,10) (5,11) (5,14) (5,17) (5,7) (5,8) (5,9) (6,12) (6,13) (7,16) (7,15) (7,10) (7,11) (7,14) (7,17) (7,8) (7,9) (8,16) (8,15) (8,10) (8,11) (8,14) (8,17) (8,9) (9,16) (9,15) (9,10) (9,11) (9,14) (9,17) (10,16) (10,15) (10,11) (10,14) (10,17) (11,16) (11,15) (11,14) (11,17) (12,13) (14,16) (14,15) (14,17) (15,16) (15,17) (16,17)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph684-11_0", + "image": "data/connectivity/graph_visual/medium/graph684.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,21) (0,12) (0,9) (0,2) (0,6) (0,4) (0,5) (0,14) (0,17) (0,8) (0,20) (0,13) (0,19) (0,22) (0,1) (0,15) (0,10) (0,18) (1,7) (1,21) (1,12) (1,9) (1,2) (1,6) (1,4) (1,5) (1,14) (1,17) (1,8) (1,20) (1,13) (1,19) (1,22) (1,15) (1,10) (1,18) (2,7) (2,21) (2,12) (2,9) (2,6) (2,4) (2,5) (2,14) (2,17) (2,8) (2,20) (2,13) (2,19) (2,22) (2,15) (2,10) (2,18) (3,11) (3,23) (4,7) (4,21) (4,12) (4,9) (4,6) (4,5) (4,14) (4,17) (4,8) (4,20) (4,13) (4,19) (4,22) (4,15) (4,10) (4,18) (5,7) (5,21) (5,12) (5,9) (5,6) (5,14) (5,17) (5,8) (5,20) (5,13) (5,19) (5,22) (5,15) (5,10) (5,18) (6,7) (6,21) (6,12) (6,9) (6,14) (6,17) (6,8) (6,20) (6,13) (6,19) (6,22) (6,15) (6,10) (6,18) (7,21) (7,12) (7,9) (7,14) (7,17) (7,8) (7,20) (7,13) (7,19) (7,22) (7,15) (7,10) (7,18) (8,21) (8,12) (8,9) (8,14) (8,17) (8,20) (8,13) (8,19) (8,22) (8,15) (8,10) (8,18) (9,21) (9,12) (9,14) (9,17) (9,20) (9,13) (9,19) (9,22) (9,15) (9,10) (9,18) (10,21) (10,12) (10,14) (10,17) (10,20) (10,13) (10,19) (10,22) (10,15) (10,18) (11,23) (12,21) (12,14) (12,17) (12,20) (12,13) (12,19) (12,22) (12,15) (12,18) (13,21) (13,14) (13,17) (13,20) (13,19) (13,22) (13,15) (13,18) (14,21) (14,17) (14,20) (14,19) (14,22) (14,15) (14,18) (15,21) (15,17) (15,20) (15,19) (15,22) (15,18) (17,21) (17,20) (17,19) (17,22) (17,18) (18,21) (18,20) (18,19) (18,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 11 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph664-19_18", + "image": "data/connectivity/graph_visual/medium/graph664.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,4) (0,14) (0,9) (0,19) (0,7) (0,20) (0,17) (0,16) (1,11) (1,12) (1,2) (1,15) (1,3) (1,23) (1,5) (1,21) (2,12) (2,15) (2,3) (2,23) (2,13) (2,10) (3,22) (3,12) (3,15) (3,23) (3,5) (3,21) (3,13) (4,14) (4,18) (4,9) (4,19) (4,16) (5,22) (5,11) (5,12) (5,23) (5,21) (5,10) (6,18) (6,9) (6,7) (6,20) (6,17) (6,16) (7,14) (7,9) (7,19) (7,20) (7,17) (7,8) (8,14) (8,18) (8,9) (8,19) (8,20) (8,17) (8,16) (9,14) (9,19) (10,11) (10,15) (10,23) (10,21) (10,13) (11,22) (11,12) (11,15) (11,13) (12,22) (12,15) (12,23) (12,21) (12,13) (13,15) (13,21) (14,18) (14,19) (14,20) (14,16) (15,22) (16,20) (16,17) (18,19) (18,20) (19,20) (21,22) (22,23)\nIs there a path between node 19 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph658-15_21", + "image": "data/connectivity/graph_visual/medium/graph658.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,5) (0,18) (0,14) (0,15) (0,22) (0,3) (0,2) (0,13) (0,8) (1,23) (1,6) (1,10) (2,5) (2,9) (2,18) (2,4) (2,12) (2,15) (2,22) (2,19) (2,3) (2,13) (3,7) (3,5) (3,12) (3,14) (3,20) (3,15) (3,22) (3,16) (3,8) (4,17) (4,7) (4,9) (4,18) (4,12) (4,20) (4,22) (4,19) (4,13) (4,8) (5,17) (5,7) (5,9) (5,18) (5,12) (5,14) (5,20) (5,22) (5,19) (5,16) (5,13) (6,11) (6,23) (6,21) (6,10) (7,17) (7,9) (7,18) (7,12) (7,14) (7,22) (7,13) (7,8) (8,17) (8,9) (8,18) (8,12) (8,14) (8,20) (8,15) (8,22) (8,19) (8,16) (8,13) (9,12) (9,14) (9,20) (9,15) (9,22) (9,16) (10,11) (10,23) (10,21) (11,23) (11,21) (12,18) (12,14) (12,20) (12,15) (12,22) (12,19) (12,16) (13,17) (13,18) (13,14) (13,20) (13,15) (13,19) (14,17) (14,18) (14,20) (14,15) (14,22) (14,19) (14,16) (15,17) (15,20) (15,22) (16,17) (16,18) (16,20) (16,22) (16,19) (17,18) (17,20) (17,22) (17,19) (18,20) (18,19) (19,20) (20,22) (21,23)\nIs there a path between node 15 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph186-15_14", + "image": "data/connectivity/graph_visual/medium/graph186.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,8) (0,7) (0,14) (0,17) (0,4) (0,1) (0,15) (0,2) (0,6) (0,16) (0,9) (0,12) (0,11) (0,3) (0,10) (1,8) (1,7) (1,14) (1,17) (1,4) (1,15) (1,2) (1,6) (1,16) (1,9) (1,12) (1,11) (1,3) (1,10) (2,8) (2,7) (2,14) (2,17) (2,4) (2,15) (2,6) (2,16) (2,9) (2,12) (2,11) (2,3) (2,10) (3,8) (3,7) (3,14) (3,17) (3,4) (3,15) (3,6) (3,16) (3,9) (3,12) (3,11) (3,10) (4,8) (4,7) (4,14) (4,17) (4,15) (4,6) (4,16) (4,9) (4,12) (4,11) (4,10) (5,13) (6,8) (6,7) (6,14) (6,17) (6,15) (6,16) (6,9) (6,12) (6,11) (6,10) (7,8) (7,14) (7,17) (7,15) (7,16) (7,9) (7,12) (7,11) (7,10) (8,14) (8,17) (8,15) (8,16) (8,9) (8,12) (8,11) (8,10) (9,14) (9,17) (9,15) (9,16) (9,12) (9,11) (9,10) (10,14) (10,17) (10,15) (10,16) (10,12) (10,11) (11,14) (11,17) (11,15) (11,16) (11,12) (12,14) (12,17) (12,15) (12,16) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 15 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph791-6_18", + "image": "data/connectivity/graph_visual/medium/graph791.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (1,16) (1,5) (1,10) (1,18) (2,7) (2,14) (2,11) (2,15) (3,16) (3,5) (3,12) (3,15) (3,10) (5,20) (5,24) (5,12) (5,7) (5,14) (7,20) (7,24) (7,18) (8,21) (8,23) (9,20) (9,16) (9,24) (10,20) (10,24) (10,15) (10,18) (11,16) (11,22) (12,24) (12,14) (12,15) (13,24) (13,14) (13,22) (15,18) (15,22) (16,24) (16,18) (17,19) (18,20) (19,21) (19,23) (21,23)\nIs there a path between node 6 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph557-4_13", + "image": "data/connectivity/graph_visual/medium/graph557.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,2) (0,18) (0,23) (0,21) (0,13) (0,16) (0,15) (0,22) (0,6) (0,14) (1,17) (1,11) (1,10) (1,4) (1,19) (1,9) (2,8) (2,18) (2,23) (2,21) (2,22) (2,14) (2,20) (3,17) (3,11) (3,10) (3,4) (3,19) (3,9) (4,7) (4,10) (4,9) (5,8) (5,21) (5,13) (5,16) (5,15) (5,22) (5,6) (5,14) (5,20) (6,8) (6,18) (6,13) (6,15) (6,14) (6,20) (7,17) (7,10) (7,19) (7,9) (8,18) (8,23) (8,21) (8,13) (8,16) (8,14) (8,20) (9,17) (9,10) (9,19) (10,17) (10,19) (11,19) (13,18) (13,23) (13,21) (13,16) (13,22) (13,14) (13,20) (14,18) (14,23) (14,21) (14,16) (14,22) (14,20) (15,18) (15,21) (15,22) (16,23) (16,21) (17,19) (18,22) (20,23) (20,21) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 4 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph189-1_17", + "image": "data/connectivity/graph_visual/medium/graph189.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,15) (0,9) (0,1) (0,17) (0,12) (0,11) (0,13) (0,7) (1,15) (1,9) (1,17) (1,12) (1,11) (1,13) (1,7) (2,3) (2,5) (2,10) (2,14) (2,6) (2,8) (2,4) (3,5) (3,10) (3,14) (3,6) (3,8) (3,4) (4,5) (4,10) (4,14) (4,6) (4,8) (5,10) (5,14) (5,6) (5,8) (6,10) (6,14) (6,8) (7,15) (7,9) (7,17) (7,12) (7,11) (7,13) (8,10) (8,14) (9,15) (9,17) (9,12) (9,11) (9,13) (10,14) (11,15) (11,17) (11,12) (11,13) (12,15) (12,17) (12,13) (13,15) (13,17) (15,17)\nIs there a path between node 1 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph403-17_4", + "image": "data/connectivity/graph_visual/medium/graph403.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,3) (0,10) (1,13) (1,4) (1,12) (1,9) (2,20) (2,3) (3,6) (4,12) (5,14) (6,10) (6,14) (7,15) (8,18) (8,15) (9,18) (10,20) (10,16) (10,11) (10,21) (11,14) (12,15) (13,18) (14,20) (17,19) (17,18) (18,19)\nIs there a path between node 17 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph530-14_9", + "image": "data/connectivity/graph_visual/medium/graph530.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,5) (0,1) (0,18) (0,20) (0,19) (0,4) (0,10) (0,16) (0,12) (0,8) (0,21) (0,3) (0,9) (0,6) (0,11) (0,13) (1,5) (1,18) (1,20) (1,19) (1,4) (1,10) (1,16) (1,12) (1,8) (1,21) (1,3) (1,9) (1,6) (1,11) (1,13) (2,15) (2,22) (3,5) (3,18) (3,20) (3,19) (3,4) (3,10) (3,16) (3,12) (3,8) (3,21) (3,9) (3,6) (3,11) (3,13) (4,5) (4,18) (4,20) (4,19) (4,10) (4,16) (4,12) (4,8) (4,21) (4,9) (4,6) (4,11) (4,13) (5,18) (5,20) (5,19) (5,10) (5,16) (5,12) (5,8) (5,21) (5,9) (5,6) (5,11) (5,13) (6,18) (6,20) (6,19) (6,10) (6,16) (6,12) (6,8) (6,21) (6,9) (6,11) (6,13) (7,14) (7,17) (8,18) (8,20) (8,19) (8,10) (8,16) (8,12) (8,21) (8,9) (8,11) (8,13) (9,18) (9,20) (9,19) (9,10) (9,16) (9,12) (9,21) (9,11) (9,13) (10,18) (10,20) (10,19) (10,16) (10,12) (10,21) (10,11) (10,13) (11,18) (11,20) (11,19) (11,16) (11,12) (11,21) (11,13) (12,18) (12,20) (12,19) (12,16) (12,21) (12,13) (13,18) (13,20) (13,19) (13,16) (13,21) (14,17) (15,22) (16,18) (16,20) (16,19) (16,21) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 14 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph314-12_5", + "image": "data/connectivity/graph_visual/medium/graph314.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,2) (0,18) (0,4) (0,12) (0,1) (0,19) (0,14) (0,16) (0,13) (0,15) (0,11) (0,8) (1,2) (1,18) (1,4) (1,12) (1,19) (1,14) (1,16) (1,13) (1,15) (1,11) (1,8) (2,18) (2,4) (2,12) (2,19) (2,14) (2,16) (2,13) (2,15) (2,11) (2,8) (3,6) (3,9) (3,10) (3,17) (4,18) (4,12) (4,19) (4,14) (4,16) (4,13) (4,15) (4,11) (4,8) (5,7) (6,9) (6,10) (6,17) (8,18) (8,12) (8,19) (8,14) (8,16) (8,13) (8,15) (8,11) (9,10) (9,17) (10,17) (11,18) (11,12) (11,19) (11,14) (11,16) (11,13) (11,15) (12,18) (12,19) (12,14) (12,16) (12,13) (12,15) (13,18) (13,19) (13,14) (13,16) (13,15) (14,18) (14,19) (14,16) (14,15) (15,18) (15,19) (15,16) (16,18) (16,19) (18,19)\nIs there a path between node 12 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph277-12_16", + "image": "data/connectivity/graph_visual/medium/graph277.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,12) (0,10) (0,16) (1,7) (1,18) (1,3) (1,14) (1,11) (1,5) (1,13) (1,19) (1,15) (1,6) (1,9) (1,8) (1,4) (3,7) (3,18) (3,14) (3,11) (3,5) (3,13) (3,19) (3,15) (3,6) (3,9) (3,8) (3,4) (4,7) (4,18) (4,14) (4,11) (4,5) (4,13) (4,19) (4,15) (4,6) (4,9) (4,8) (5,7) (5,18) (5,14) (5,11) (5,13) (5,19) (5,15) (5,6) (5,9) (5,8) (6,7) (6,18) (6,14) (6,11) (6,13) (6,19) (6,15) (6,9) (6,8) (7,18) (7,14) (7,11) (7,13) (7,19) (7,15) (7,9) (7,8) (8,18) (8,14) (8,11) (8,13) (8,19) (8,15) (8,9) (9,18) (9,14) (9,11) (9,13) (9,19) (9,15) (10,17) (10,12) (10,16) (11,18) (11,14) (11,13) (11,19) (11,15) (12,17) (12,16) (13,18) (13,14) (13,19) (13,15) (14,18) (14,19) (14,15) (15,18) (15,19) (16,17) (18,19)\nIs there a path between node 12 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph334-9_7", + "image": "data/connectivity/graph_visual/medium/graph334.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,7) (0,3) (0,20) (1,13) (2,9) (2,12) (2,13) (3,7) (3,20) (5,6) (5,10) (5,11) (5,15) (5,17) (5,12) (6,9) (6,10) (6,11) (8,16) (9,17) (9,13) (10,17) (11,16) (11,18) (12,16) (13,15) (13,17) (13,18) (14,19) (19,20)\nIs there a path between node 9 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph213-16_10", + "image": "data/connectivity/graph_visual/medium/graph213.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (0,6) (0,7) (0,1) (1,4) (1,6) (1,7) (2,18) (2,12) (2,5) (2,17) (2,10) (2,8) (2,16) (2,3) (2,14) (2,11) (2,13) (3,18) (3,12) (3,5) (3,17) (3,10) (3,8) (3,16) (3,14) (3,11) (3,13) (4,6) (4,7) (5,18) (5,12) (5,17) (5,10) (5,8) (5,16) (5,14) (5,11) (5,13) (6,7) (8,18) (8,12) (8,17) (8,10) (8,16) (8,14) (8,11) (8,13) (9,15) (10,18) (10,12) (10,17) (10,16) (10,14) (10,11) (10,13) (11,18) (11,12) (11,17) (11,16) (11,14) (11,13) (12,18) (12,17) (12,16) (12,14) (12,13) (13,18) (13,17) (13,16) (13,14) (14,18) (14,17) (14,16) (16,18) (16,17) (17,18)\nIs there a path between node 16 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph716-11_12", + "image": "data/connectivity/graph_visual/medium/graph716.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,22) (0,23) (0,15) (0,21) (0,8) (0,12) (0,2) (0,1) (1,24) (1,14) (1,11) (1,22) (1,19) (1,15) (1,8) (1,12) (1,2) (1,17) (2,24) (2,11) (2,19) (2,15) (2,8) (2,7) (2,17) (3,16) (3,6) (3,13) (3,4) (4,16) (4,6) (4,10) (4,13) (4,9) (4,18) (5,16) (5,10) (5,13) (5,9) (5,18) (6,10) (6,9) (6,18) (7,24) (7,14) (7,22) (7,19) (7,21) (7,12) (7,20) (7,17) (8,24) (8,14) (8,23) (8,21) (8,20) (9,16) (9,10) (9,13) (9,18) (10,13) (10,18) (11,24) (11,14) (11,22) (11,19) (11,15) (11,21) (11,17) (12,24) (12,14) (12,19) (12,23) (12,21) (12,20) (12,17) (13,16) (13,18) (14,24) (14,22) (14,19) (14,23) (14,15) (14,21) (14,20) (14,17) (15,24) (15,22) (15,19) (15,20) (15,17) (16,18) (17,24) (17,22) (17,19) (17,21) (17,20) (19,24) (19,22) (19,21) (19,20) (20,24) (20,22) (21,24) (21,22) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 11 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph147-14_16", + "image": "data/connectivity/graph_visual/medium/graph147.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,9) (0,7) (0,10) (0,6) (0,14) (0,8) (0,16) (0,13) (1,3) (1,6) (1,17) (1,8) (1,12) (1,16) (1,15) (2,5) (2,4) (3,10) (3,6) (3,14) (3,12) (3,16) (3,15) (4,5) (4,11) (5,11) (6,9) (6,7) (6,10) (6,17) (6,8) (6,12) (6,16) (6,13) (6,15) (7,10) (7,17) (7,14) (7,12) (7,16) (7,13) (7,15) (8,10) (8,17) (8,14) (8,12) (8,16) (8,13) (9,10) (9,17) (9,13) (9,15) (10,17) (10,14) (10,12) (10,13) (10,15) (12,17) (12,13) (12,15) (13,14) (13,15) (14,16) (15,16)\nIs there a path between node 14 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph290-14_17", + "image": "data/connectivity/graph_visual/medium/graph290.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,5) (0,4) (1,6) (1,14) (1,2) (3,18) (3,4) (4,5) (4,15) (6,11) (6,16) (6,14) (6,10) (6,19) (6,12) (6,9) (7,8) (9,13) (9,10) (9,17) (9,19) (10,13) (10,12) (11,16) (11,14) (11,13) (12,17) (12,19) (13,16) (13,14) (14,19) (16,17)\nIs there a path between node 14 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph390-2_3", + "image": "data/connectivity/graph_visual/medium/graph390.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,20) (0,11) (0,2) (0,10) (0,8) (0,17) (0,6) (0,7) (0,9) (0,5) (1,13) (1,19) (1,14) (1,18) (1,12) (1,3) (1,4) (1,16) (1,15) (2,20) (2,11) (2,10) (2,8) (2,17) (2,6) (2,7) (2,9) (2,5) (3,13) (3,19) (3,14) (3,18) (3,12) (3,4) (3,16) (3,15) (4,13) (4,19) (4,14) (4,18) (4,12) (4,16) (4,15) (5,20) (5,11) (5,10) (5,8) (5,17) (5,6) (5,7) (5,9) (6,20) (6,11) (6,10) (6,8) (6,17) (6,7) (6,9) (7,20) (7,11) (7,10) (7,8) (7,17) (7,9) (8,20) (8,11) (8,10) (8,17) (8,9) (9,20) (9,11) (9,10) (9,17) (10,20) (10,11) (10,17) (11,20) (11,17) (12,13) (12,19) (12,14) (12,18) (12,16) (12,15) (13,19) (13,14) (13,18) (13,16) (13,15) (14,19) (14,18) (14,16) (14,15) (15,19) (15,18) (15,16) (16,19) (16,18) (17,20) (18,19)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph42-12_9", + "image": "data/connectivity/graph_visual/medium/graph42.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,6) (0,7) (0,10) (0,8) (0,11) (0,12) (1,3) (1,4) (1,9) (2,6) (2,7) (2,10) (2,8) (2,11) (2,12) (3,4) (3,5) (3,9) (4,5) (4,9) (5,9) (6,7) (6,10) (6,12) (7,10) (7,12) (8,10) (8,11) (8,12) (10,11) (11,12)\nIs there a path between node 12 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph412-18_2", + "image": "data/connectivity/graph_visual/medium/graph412.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,14) (0,15) (0,1) (0,7) (0,4) (0,8) (0,13) (0,12) (0,2) (0,16) (0,20) (0,18) (0,11) (0,21) (1,19) (1,14) (1,15) (1,7) (1,8) (1,6) (1,13) (1,12) (1,2) (1,16) (1,20) (1,18) (1,11) (1,21) (1,17) (2,19) (2,14) (2,15) (2,7) (2,4) (2,13) (2,12) (2,18) (2,21) (2,17) (2,5) (3,9) (3,10) (4,19) (4,15) (4,7) (4,8) (4,6) (4,12) (4,16) (4,11) (4,21) (4,17) (4,5) (5,14) (5,15) (5,7) (5,8) (5,13) (5,12) (5,20) (5,11) (5,21) (6,19) (6,14) (6,15) (6,13) (6,16) (6,20) (6,18) (6,11) (6,21) (6,17) (7,19) (7,14) (7,15) (7,8) (7,12) (7,16) (7,20) (7,18) (7,11) (7,21) (8,19) (8,14) (8,15) (8,13) (8,20) (8,11) (8,21) (9,10) (11,19) (11,14) (11,15) (11,13) (11,12) (11,16) (11,20) (11,18) (11,21) (12,14) (12,20) (12,21) (13,19) (13,14) (13,15) (13,16) (13,18) (13,21) (13,17) (14,19) (14,15) (14,21) (15,19) (15,20) (15,18) (16,19) (16,18) (16,21) (16,17) (17,19) (17,20) (17,18) (18,19) (19,20) (19,21)\nIs there a path between node 18 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph555-21_11", + "image": "data/connectivity/graph_visual/medium/graph555.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,14) (0,5) (0,9) (0,8) (0,6) (0,21) (1,4) (1,15) (1,18) (1,11) (1,10) (1,12) (2,20) (2,14) (2,5) (2,9) (2,22) (2,6) (2,16) (3,9) (3,23) (3,22) (3,6) (3,21) (4,15) (4,11) (4,19) (4,13) (5,20) (5,14) (5,9) (5,8) (5,6) (5,21) (6,20) (6,14) (6,9) (6,23) (6,8) (6,16) (7,18) (7,11) (7,10) (7,12) (7,19) (7,13) (8,20) (8,14) (8,23) (8,21) (9,20) (9,23) (9,22) (9,21) (10,15) (10,18) (10,11) (10,12) (10,19) (10,13) (11,15) (11,13) (12,18) (12,19) (13,18) (13,19) (14,23) (14,22) (14,21) (15,19) (16,23) (16,22) (20,21) (22,23)\nIs there a path between node 21 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph703-21_15", + "image": "data/connectivity/graph_visual/medium/graph703.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,13) (0,17) (0,11) (0,16) (0,14) (0,8) (1,3) (1,20) (2,3) (2,20) (2,21) (3,23) (3,20) (3,18) (6,13) (6,22) (6,14) (6,9) (7,17) (7,22) (7,14) (7,24) (7,9) (8,13) (8,17) (8,22) (8,16) (8,14) (8,24) (9,15) (9,17) (9,11) (9,19) (9,10) (9,24) (9,12) (10,15) (10,17) (10,11) (11,15) (11,22) (12,22) (12,24) (13,15) (13,22) (13,16) (13,24) (14,15) (14,19) (15,24) (16,22) (16,24) (18,20) (18,21) (21,23) (22,24)\nIs there a path between node 21 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph85-1_4", + "image": "data/connectivity/graph_visual/medium/graph85.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,3) (0,8) (0,6) (0,10) (0,14) (0,2) (0,1) (1,3) (1,8) (1,6) (1,10) (1,14) (1,2) (2,3) (2,8) (2,6) (2,10) (2,14) (3,8) (3,6) (3,10) (3,14) (4,11) (4,5) (4,13) (4,7) (4,9) (4,12) (5,11) (5,13) (5,7) (5,9) (5,12) (6,8) (6,10) (6,14) (7,11) (7,13) (7,9) (7,12) (8,10) (8,14) (9,11) (9,13) (9,12) (10,14) (11,13) (11,12) (12,13)\nIs there a path between node 1 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph792-13_5", + "image": "data/connectivity/graph_visual/medium/graph792.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,23) (1,6) (1,7) (1,3) (2,4) (2,22) (3,10) (3,12) (3,9) (4,13) (4,19) (4,5) (4,22) (5,22) (5,11) (6,16) (6,10) (7,24) (9,23) (9,10) (11,13) (11,18) (11,19) (11,22) (12,24) (13,18) (13,14) (16,23) (17,19) (18,20) (19,20)\nIs there a path between node 13 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph503-10_18", + "image": "data/connectivity/graph_visual/medium/graph503.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,7) (0,9) (0,16) (0,6) (0,13) (0,1) (1,2) (1,10) (1,16) (1,13) (2,16) (2,12) (4,21) (4,6) (4,13) (4,18) (5,22) (5,8) (5,15) (6,10) (6,13) (8,22) (8,15) (9,17) (9,10) (9,21) (9,13) (9,18) (10,19) (10,12) (10,13) (12,17) (12,19) (12,13) (12,18) (13,17) (13,18) (15,22) (15,20) (16,19) (17,19) (17,21) (18,21) (20,22)\nIs there a path between node 10 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph205-16_10", + "image": "data/connectivity/graph_visual/medium/graph205.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,16) (0,3) (0,12) (0,6) (0,11) (1,16) (1,3) (1,12) (1,6) (1,11) (1,14) (1,10) (2,15) (2,7) (2,13) (2,5) (2,9) (2,4) (2,18) (3,17) (3,12) (3,11) (3,14) (4,15) (4,7) (4,5) (4,9) (4,8) (5,15) (5,13) (5,9) (5,8) (5,18) (6,16) (6,17) (6,12) (6,14) (6,10) (7,15) (7,13) (7,9) (7,18) (8,15) (8,9) (8,18) (9,13) (9,18) (10,16) (10,17) (10,12) (10,11) (11,16) (11,17) (11,12) (12,16) (12,17) (12,14) (13,15) (13,18) (14,16) (14,17) (15,18) (16,17)\nIs there a path between node 16 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph571-22_18", + "image": "data/connectivity/graph_visual/medium/graph571.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,22) (0,3) (0,15) (0,6) (0,5) (0,7) (0,2) (0,19) (0,4) (0,11) (0,9) (0,14) (0,21) (1,16) (1,12) (1,18) (1,17) (1,20) (1,23) (1,13) (1,10) (2,8) (2,22) (2,3) (2,15) (2,6) (2,5) (2,7) (2,19) (2,4) (2,11) (2,9) (2,14) (2,21) (3,8) (3,22) (3,15) (3,6) (3,5) (3,7) (3,19) (3,4) (3,11) (3,9) (3,14) (3,21) (4,8) (4,22) (4,15) (4,6) (4,5) (4,7) (4,19) (4,11) (4,9) (4,14) (4,21) (5,8) (5,22) (5,15) (5,6) (5,7) (5,19) (5,11) (5,9) (5,14) (5,21) (6,8) (6,22) (6,15) (6,7) (6,19) (6,11) (6,9) (6,14) (6,21) (7,8) (7,22) (7,15) (7,19) (7,11) (7,9) (7,14) (7,21) (8,22) (8,15) (8,19) (8,11) (8,9) (8,14) (8,21) (9,22) (9,15) (9,19) (9,11) (9,14) (9,21) (10,16) (10,12) (10,18) (10,17) (10,20) (10,23) (10,13) (11,22) (11,15) (11,19) (11,14) (11,21) (12,16) (12,18) (12,17) (12,20) (12,23) (12,13) (13,16) (13,18) (13,17) (13,20) (13,23) (14,22) (14,15) (14,19) (14,21) (15,22) (15,19) (15,21) (16,18) (16,17) (16,20) (16,23) (17,18) (17,20) (17,23) (18,20) (18,23) (19,22) (19,21) (20,23) (21,22)\nIs there a path between node 22 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph64-2_7", + "image": "data/connectivity/graph_visual/medium/graph64.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,8) (0,5) (0,2) (0,3) (0,10) (0,6) (0,1) (0,4) (0,9) (0,7) (0,12) (1,8) (1,5) (1,2) (1,3) (1,10) (1,6) (1,4) (1,9) (1,7) (1,12) (2,8) (2,5) (2,3) (2,10) (2,6) (2,4) (2,9) (2,7) (2,12) (3,8) (3,5) (3,10) (3,6) (3,4) (3,9) (3,7) (3,12) (4,8) (4,5) (4,10) (4,6) (4,9) (4,7) (4,12) (5,8) (5,10) (5,6) (5,9) (5,7) (5,12) (6,8) (6,10) (6,9) (6,7) (6,12) (7,8) (7,10) (7,9) (7,12) (8,10) (8,9) (8,12) (9,10) (9,12) (10,12) (11,13)\nIs there a path between node 2 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph666-8_23", + "image": "data/connectivity/graph_visual/medium/graph666.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,5) (0,23) (0,3) (0,4) (0,16) (0,12) (0,1) (0,20) (1,21) (1,15) (1,5) (1,23) (1,22) (1,4) (1,11) (1,12) (1,14) (1,17) (1,20) (2,9) (2,6) (2,13) (3,5) (3,23) (3,18) (3,22) (3,4) (3,16) (3,19) (3,14) (3,20) (4,21) (4,15) (4,5) (4,23) (4,18) (4,22) (4,11) (4,19) (4,14) (4,20) (5,21) (5,15) (5,23) (5,18) (5,22) (5,11) (5,16) (5,10) (5,19) (5,14) (5,17) (6,13) (8,9) (8,13) (9,13) (10,15) (10,23) (10,22) (10,16) (10,12) (10,14) (10,17) (10,20) (11,21) (11,15) (11,23) (11,18) (11,22) (11,16) (11,19) (11,14) (11,17) (11,20) (12,23) (12,22) (12,16) (12,19) (12,14) (12,17) (12,20) (14,21) (14,23) (14,18) (14,16) (14,19) (14,17) (14,20) (15,18) (15,22) (15,16) (15,19) (15,17) (15,20) (16,18) (16,19) (17,21) (17,18) (17,22) (17,19) (17,20) (18,21) (18,20) (19,22) (19,20) (20,21) (20,22) (21,22)\nIs there a path between node 8 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph102-10_9", + "image": "data/connectivity/graph_visual/medium/graph102.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,13) (0,3) (0,15) (0,4) (0,12) (0,9) (0,14) (0,2) (0,11) (1,15) (1,4) (1,12) (1,9) (1,14) (1,2) (2,8) (2,13) (2,15) (2,12) (2,6) (2,11) (3,8) (3,13) (3,12) (3,6) (3,10) (3,14) (3,11) (4,8) (4,13) (4,15) (4,10) (4,9) (4,14) (4,11) (5,7) (6,8) (6,13) (6,15) (6,10) (6,9) (6,14) (6,11) (8,15) (8,12) (8,9) (8,14) (9,15) (9,12) (9,10) (9,14) (10,15) (10,12) (10,14) (11,13) (11,15) (11,12) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nIs there a path between node 10 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph312-8_6", + "image": "data/connectivity/graph_visual/medium/graph312.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (0,12) (0,6) (0,18) (0,16) (1,15) (1,17) (1,2) (1,19) (1,5) (1,14) (1,10) (1,13) (1,4) (1,7) (1,11) (1,9) (2,15) (2,17) (2,19) (2,5) (2,14) (2,10) (2,13) (2,4) (2,7) (2,11) (2,9) (4,15) (4,17) (4,19) (4,5) (4,14) (4,10) (4,13) (4,7) (4,11) (4,9) (5,15) (5,17) (5,19) (5,14) (5,10) (5,13) (5,7) (5,11) (5,9) (6,8) (6,12) (6,18) (6,16) (7,15) (7,17) (7,19) (7,14) (7,10) (7,13) (7,11) (7,9) (8,12) (8,18) (8,16) (9,15) (9,17) (9,19) (9,14) (9,10) (9,13) (9,11) (10,15) (10,17) (10,19) (10,14) (10,13) (10,11) (11,15) (11,17) (11,19) (11,14) (11,13) (12,18) (12,16) (13,15) (13,17) (13,19) (13,14) (14,15) (14,17) (14,19) (15,17) (15,19) (16,18) (17,19)\nIs there a path between node 8 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph115-2_5", + "image": "data/connectivity/graph_visual/medium/graph115.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,14) (0,10) (0,16) (0,12) (0,11) (2,7) (3,10) (3,16) (3,13) (3,9) (4,10) (4,16) (5,8) (5,16) (5,13) (5,12) (5,11) (5,9) (6,13) (6,11) (8,10) (8,16) (8,13) (8,15) (9,16) (10,12) (12,14) (13,16) (13,15) (14,15)\nIs there a path between node 2 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph587-11_7", + "image": "data/connectivity/graph_visual/medium/graph587.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,5) (0,14) (0,23) (0,10) (1,5) (1,14) (1,15) (2,21) (2,9) (2,3) (2,15) (3,21) (3,11) (3,15) (3,18) (4,7) (4,22) (5,21) (5,9) (5,17) (5,10) (5,18) (6,17) (6,18) (7,19) (8,12) (9,21) (9,11) (9,15) (9,18) (10,15) (13,22) (16,19) (17,21) (18,21) (18,23)\nIs there a path between node 11 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph435-9_0", + "image": "data/connectivity/graph_visual/medium/graph435.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,21) (0,10) (0,6) (0,17) (0,11) (1,6) (1,16) (1,4) (1,11) (1,8) (2,3) (4,21) (4,12) (4,17) (4,7) (4,11) (4,13) (5,21) (5,10) (5,16) (5,12) (5,19) (5,14) (5,9) (5,13) (5,8) (6,12) (6,19) (6,14) (6,13) (7,18) (7,12) (7,17) (7,19) (7,9) (8,12) (8,17) (8,19) (8,14) (8,11) (9,21) (9,10) (9,16) (9,17) (9,19) (9,11) (10,18) (10,21) (10,16) (11,18) (11,21) (11,19) (12,17) (13,17) (14,21) (14,19) (16,19)\nIs there a path between node 9 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph447-14_8", + "image": "data/connectivity/graph_visual/medium/graph447.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,6) (0,3) (0,15) (0,12) (0,20) (0,18) (0,2) (0,13) (0,21) (0,9) (0,14) (0,4) (1,17) (2,16) (2,6) (2,7) (2,12) (2,13) (2,21) (2,5) (3,16) (3,12) (3,18) (3,13) (3,21) (3,9) (3,4) (4,15) (4,7) (4,12) (4,20) (4,13) (4,21) (4,5) (4,9) (5,16) (5,6) (5,15) (5,7) (5,12) (5,18) (5,13) (5,9) (5,14) (6,16) (6,7) (6,12) (6,20) (6,21) (6,14) (7,16) (7,15) (7,12) (7,20) (7,13) (7,9) (8,19) (9,15) (9,20) (9,21) (9,14) (10,19) (11,17) (12,16) (12,20) (12,18) (12,21) (13,20) (13,21) (14,16) (14,15) (14,20) (14,18) (14,21) (15,21) (16,20) (16,18) (18,20) (18,21) (20,21)\nIs there a path between node 14 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph226-12_16", + "image": "data/connectivity/graph_visual/medium/graph226.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,14) (0,18) (0,6) (0,5) (0,10) (1,2) (5,9) (5,7) (5,16) (5,10) (6,7) (6,12) (7,9) (7,17) (7,16) (8,9) (8,11) (8,10) (9,17) (10,11) (10,16) (11,14) (12,17) (12,14) (14,17) (14,18) (14,16) (14,15) (15,17) (15,18) (16,18) (17,18)\nIs there a path between node 12 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph119-12_13", + "image": "data/connectivity/graph_visual/medium/graph119.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,6) (0,1) (0,3) (0,4) (0,15) (0,10) (1,5) (2,9) (2,8) (2,12) (2,7) (3,14) (3,9) (3,15) (3,5) (4,14) (4,9) (4,15) (4,5) (4,12) (5,14) (5,7) (6,15) (6,11) (6,12) (7,11) (7,12) (8,16) (9,11) (9,16) (11,12) (12,14)\nIs there a path between node 12 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph572-19_10", + "image": "data/connectivity/graph_visual/medium/graph572.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,19) (0,9) (0,7) (0,15) (0,18) (0,3) (0,2) (0,22) (0,5) (0,13) (0,4) (0,17) (0,20) (0,10) (0,1) (0,23) (0,21) (0,8) (1,12) (1,19) (1,9) (1,7) (1,15) (1,18) (1,3) (1,2) (1,22) (1,5) (1,13) (1,4) (1,17) (1,20) (1,10) (1,23) (1,21) (1,8) (2,12) (2,19) (2,9) (2,7) (2,15) (2,18) (2,3) (2,22) (2,5) (2,13) (2,4) (2,17) (2,20) (2,10) (2,23) (2,21) (2,8) (3,12) (3,19) (3,9) (3,7) (3,15) (3,18) (3,22) (3,5) (3,13) (3,4) (3,17) (3,20) (3,10) (3,23) (3,21) (3,8) (4,12) (4,19) (4,9) (4,7) (4,15) (4,18) (4,22) (4,5) (4,13) (4,17) (4,20) (4,10) (4,23) (4,21) (4,8) (5,12) (5,19) (5,9) (5,7) (5,15) (5,18) (5,22) (5,13) (5,17) (5,20) (5,10) (5,23) (5,21) (5,8) (7,12) (7,19) (7,9) (7,15) (7,18) (7,22) (7,13) (7,17) (7,20) (7,10) (7,23) (7,21) (7,8) (8,12) (8,19) (8,9) (8,15) (8,18) (8,22) (8,13) (8,17) (8,20) (8,10) (8,23) (8,21) (9,12) (9,19) (9,15) (9,18) (9,22) (9,13) (9,17) (9,20) (9,10) (9,23) (9,21) (10,12) (10,19) (10,15) (10,18) (10,22) (10,13) (10,17) (10,20) (10,23) (10,21) (11,16) (12,19) (12,15) (12,18) (12,22) (12,13) (12,17) (12,20) (12,23) (12,21) (13,19) (13,15) (13,18) (13,22) (13,17) (13,20) (13,23) (13,21) (15,19) (15,18) (15,22) (15,17) (15,20) (15,23) (15,21) (17,19) (17,18) (17,22) (17,20) (17,23) (17,21) (18,19) (18,22) (18,20) (18,23) (18,21) (19,22) (19,20) (19,23) (19,21) (20,22) (20,23) (20,21) (21,22) (21,23) (22,23)\nIs there a path between node 19 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph470-14_0", + "image": "data/connectivity/graph_visual/medium/graph470.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,15) (0,22) (0,18) (1,5) (1,14) (1,21) (1,16) (1,19) (1,3) (1,17) (1,13) (1,11) (1,2) (1,20) (1,8) (1,6) (1,12) (1,9) (1,7) (2,5) (2,14) (2,21) (2,16) (2,19) (2,3) (2,17) (2,13) (2,11) (2,20) (2,8) (2,6) (2,12) (2,9) (2,7) (3,5) (3,14) (3,21) (3,16) (3,19) (3,17) (3,13) (3,11) (3,20) (3,8) (3,6) (3,12) (3,9) (3,7) (5,14) (5,21) (5,16) (5,19) (5,17) (5,13) (5,11) (5,20) (5,8) (5,6) (5,12) (5,9) (5,7) (6,14) (6,21) (6,16) (6,19) (6,17) (6,13) (6,11) (6,20) (6,8) (6,12) (6,9) (6,7) (7,14) (7,21) (7,16) (7,19) (7,17) (7,13) (7,11) (7,20) (7,8) (7,12) (7,9) (8,14) (8,21) (8,16) (8,19) (8,17) (8,13) (8,11) (8,20) (8,12) (8,9) (9,14) (9,21) (9,16) (9,19) (9,17) (9,13) (9,11) (9,20) (9,12) (10,15) (10,22) (10,18) (11,14) (11,21) (11,16) (11,19) (11,17) (11,13) (11,20) (11,12) (12,14) (12,21) (12,16) (12,19) (12,17) (12,13) (12,20) (13,14) (13,21) (13,16) (13,19) (13,17) (13,20) (14,21) (14,16) (14,19) (14,17) (14,20) (15,22) (15,18) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (18,22) (19,21) (19,20) (20,21)\nIs there a path between node 14 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph209-15_8", + "image": "data/connectivity/graph_visual/medium/graph209.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,7) (0,6) (0,13) (0,12) (0,9) (0,18) (0,15) (0,17) (1,16) (1,2) (1,3) (2,3) (4,11) (4,8) (4,7) (4,9) (4,18) (4,14) (4,15) (5,8) (5,12) (5,10) (5,15) (6,11) (6,8) (6,7) (6,12) (6,18) (6,10) (6,14) (6,15) (6,17) (7,11) (7,8) (7,13) (7,12) (7,9) (7,10) (7,14) (7,15) (8,13) (8,12) (8,9) (8,18) (8,14) (8,17) (9,11) (9,12) (9,18) (9,10) (9,14) (9,15) (9,17) (10,11) (10,13) (10,18) (10,14) (10,17) (11,13) (11,18) (11,14) (12,18) (12,15) (12,17) (13,18) (13,14) (13,15) (14,18) (14,15) (14,17) (15,18) (15,17) (17,18)\nIs there a path between node 15 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph776-2_21", + "image": "data/connectivity/graph_visual/medium/graph776.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,22) (0,5) (0,12) (0,20) (0,6) (0,19) (0,21) (0,9) (0,17) (0,7) (0,14) (0,15) (1,2) (1,13) (1,3) (1,10) (1,4) (1,18) (1,24) (1,11) (1,16) (1,8) (2,13) (2,3) (2,10) (2,4) (2,18) (2,24) (2,11) (2,16) (2,8) (3,13) (3,10) (3,4) (3,18) (3,24) (3,11) (3,16) (3,8) (4,13) (4,10) (4,18) (4,24) (4,11) (4,16) (4,8) (5,23) (5,22) (5,12) (5,20) (5,6) (5,19) (5,21) (5,9) (5,17) (5,7) (5,14) (5,15) (6,23) (6,22) (6,12) (6,20) (6,19) (6,21) (6,9) (6,17) (6,7) (6,14) (6,15) (7,23) (7,22) (7,12) (7,20) (7,19) (7,21) (7,9) (7,17) (7,14) (7,15) (8,13) (8,10) (8,18) (8,24) (8,11) (8,16) (9,23) (9,22) (9,12) (9,20) (9,19) (9,21) (9,17) (9,14) (9,15) (10,13) (10,18) (10,24) (10,11) (10,16) (11,13) (11,18) (11,24) (11,16) (12,23) (12,22) (12,20) (12,19) (12,21) (12,17) (12,14) (12,15) (13,18) (13,24) (13,16) (14,23) (14,22) (14,20) (14,19) (14,21) (14,17) (14,15) (15,23) (15,22) (15,20) (15,19) (15,21) (15,17) (16,18) (16,24) (17,23) (17,22) (17,20) (17,19) (17,21) (18,24) (19,23) (19,22) (19,20) (19,21) (20,23) (20,22) (20,21) (21,23) (21,22) (22,23)\nIs there a path between node 2 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph237-18_0", + "image": "data/connectivity/graph_visual/medium/graph237.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,11) (0,17) (0,16) (1,2) (1,12) (1,7) (1,3) (2,15) (2,5) (2,7) (2,3) (3,15) (3,5) (3,12) (3,7) (4,8) (4,10) (4,18) (4,6) (4,11) (4,9) (4,17) (4,14) (4,16) (5,15) (5,7) (6,8) (6,10) (6,18) (6,11) (6,9) (6,17) (6,16) (7,15) (7,12) (8,11) (8,9) (8,17) (8,14) (9,18) (9,11) (10,18) (10,11) (10,14) (10,16) (11,18) (11,17) (11,16) (14,18) (14,16) (16,18) (16,17) (17,18)\nIs there a path between node 18 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph51-10_2", + "image": "data/connectivity/graph_visual/medium/graph51.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,6) (0,13) (1,6) (1,8) (1,3) (1,4) (2,5) (2,9) (3,12) (3,9) (3,13) (4,6) (4,10) (5,6) (5,9) (6,12) (6,8) (8,9) (9,10) (12,13)\nIs there a path between node 10 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph244-16_14", + "image": "data/connectivity/graph_visual/medium/graph244.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,12) (0,11) (0,6) (0,17) (0,5) (0,18) (1,9) (1,16) (1,10) (1,4) (2,12) (2,6) (2,14) (2,5) (2,18) (2,7) (4,15) (4,9) (4,16) (5,11) (5,14) (5,18) (6,11) (6,18) (7,12) (7,17) (9,13) (10,15) (10,16) (11,12) (11,17) (11,14) (11,18) (12,14) (12,18) (13,15) (14,17) (15,16)\nIs there a path between node 16 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph140-2_5", + "image": "data/connectivity/graph_visual/medium/graph140.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,14) (1,9) (2,14) (2,6) (2,5) (3,16) (4,7) (4,9) (4,15) (5,9) (5,15) (6,14) (6,9) (6,12) (7,14) (7,15) (7,12) (8,17) (10,13) (12,14)\nIs there a path between node 2 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph698-7_11", + "image": "data/connectivity/graph_visual/medium/graph698.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,2) (1,22) (1,7) (1,20) (1,13) (1,10) (1,16) (2,11) (3,6) (3,21) (3,18) (3,4) (3,12) (3,9) (3,5) (3,8) (3,19) (3,15) (3,23) (3,17) (3,14) (4,6) (4,21) (4,18) (4,12) (4,9) (4,5) (4,8) (4,19) (4,15) (4,23) (4,17) (4,14) (5,6) (5,21) (5,18) (5,12) (5,9) (5,8) (5,19) (5,15) (5,23) (5,17) (5,14) (6,21) (6,18) (6,12) (6,9) (6,8) (6,19) (6,15) (6,23) (6,17) (6,14) (7,22) (7,20) (7,13) (7,10) (7,16) (8,21) (8,18) (8,12) (8,9) (8,19) (8,15) (8,23) (8,17) (8,14) (9,21) (9,18) (9,12) (9,19) (9,15) (9,23) (9,17) (9,14) (10,22) (10,20) (10,13) (10,16) (12,21) (12,18) (12,19) (12,15) (12,23) (12,17) (12,14) (13,22) (13,20) (13,16) (14,21) (14,18) (14,19) (14,15) (14,23) (14,17) (15,21) (15,18) (15,19) (15,23) (15,17) (16,22) (16,20) (17,21) (17,18) (17,19) (17,23) (18,21) (18,19) (18,23) (19,21) (19,23) (20,22) (21,23)\nIs there a path between node 7 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph545-3_9", + "image": "data/connectivity/graph_visual/medium/graph545.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,17) (0,23) (0,22) (0,1) (0,9) (0,11) (0,14) (0,19) (0,12) (0,18) (0,8) (0,4) (0,16) (0,15) (0,10) (0,6) (1,20) (1,17) (1,23) (1,22) (1,9) (1,11) (1,14) (1,19) (1,12) (1,18) (1,8) (1,4) (1,16) (1,15) (1,10) (1,6) (2,13) (2,5) (2,3) (2,21) (2,7) (3,13) (3,5) (3,21) (3,7) (4,20) (4,17) (4,23) (4,22) (4,9) (4,11) (4,14) (4,19) (4,12) (4,18) (4,8) (4,16) (4,15) (4,10) (4,6) (5,13) (5,21) (5,7) (6,20) (6,17) (6,23) (6,22) (6,9) (6,11) (6,14) (6,19) (6,12) (6,18) (6,8) (6,16) (6,15) (6,10) (7,13) (7,21) (8,20) (8,17) (8,23) (8,22) (8,9) (8,11) (8,14) (8,19) (8,12) (8,18) (8,16) (8,15) (8,10) (9,20) (9,17) (9,23) (9,22) (9,11) (9,14) (9,19) (9,12) (9,18) (9,16) (9,15) (9,10) (10,20) (10,17) (10,23) (10,22) (10,11) (10,14) (10,19) (10,12) (10,18) (10,16) (10,15) (11,20) (11,17) (11,23) (11,22) (11,14) (11,19) (11,12) (11,18) (11,16) (11,15) (12,20) (12,17) (12,23) (12,22) (12,14) (12,19) (12,18) (12,16) (12,15) (13,21) (14,20) (14,17) (14,23) (14,22) (14,19) (14,18) (14,16) (14,15) (15,20) (15,17) (15,23) (15,22) (15,19) (15,18) (15,16) (16,20) (16,17) (16,23) (16,22) (16,19) (16,18) (17,20) (17,23) (17,22) (17,19) (17,18) (18,20) (18,23) (18,22) (18,19) (19,20) (19,23) (19,22) (20,23) (20,22) (22,23)\nIs there a path between node 3 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph671-1_2", + "image": "data/connectivity/graph_visual/medium/graph671.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,15) (0,13) (0,6) (0,20) (2,12) (2,18) (2,22) (2,19) (2,8) (2,4) (3,10) (3,11) (3,13) (3,6) (3,5) (3,21) (3,20) (4,17) (4,16) (4,18) (4,22) (4,23) (4,19) (4,8) (5,10) (5,15) (5,13) (5,21) (5,20) (6,11) (6,15) (6,13) (6,21) (6,20) (7,12) (7,17) (7,18) (7,22) (7,23) (7,8) (8,12) (8,16) (8,18) (8,19) (9,14) (10,11) (10,15) (10,13) (10,20) (11,13) (12,17) (12,16) (12,18) (12,23) (12,19) (13,15) (13,21) (15,21) (15,20) (16,17) (16,18) (16,22) (16,23) (16,19) (17,23) (17,19) (18,23) (18,19) (20,21) (22,23)\nIs there a path between node 1 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph7-7_4", + "image": "data/connectivity/graph_visual/medium/graph7.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,6) (1,4) (1,3) (1,2) (1,7) (2,10) (2,4) (2,8) (3,10) (3,6) (3,4) (3,8) (3,5) (4,6) (4,8) (4,5) (4,7) (5,10) (5,8) (6,10) (6,8) (7,10)\nIs there a path between node 7 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph305-3_18", + "image": "data/connectivity/graph_visual/medium/graph305.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,1) (0,18) (1,11) (1,18) (2,15) (2,14) (2,7) (2,5) (2,4) (2,3) (2,8) (2,6) (2,16) (3,15) (3,14) (3,5) (3,13) (3,4) (3,9) (3,6) (4,15) (4,7) (4,5) (4,12) (4,8) (4,9) (4,16) (5,14) (5,12) (5,17) (5,9) (5,6) (5,16) (6,15) (6,14) (6,7) (6,17) (6,16) (7,15) (7,14) (7,13) (7,12) (7,9) (7,16) (8,15) (8,14) (8,13) (8,12) (8,17) (8,16) (9,15) (9,14) (9,12) (11,19) (11,18) (12,15) (12,14) (12,13) (12,17) (13,15) (13,14) (14,15) (15,17) (15,16) (16,17) (18,19)\nIs there a path between node 3 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph446-19_10", + "image": "data/connectivity/graph_visual/medium/graph446.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,13) (0,2) (0,5) (0,4) (0,18) (0,9) (0,3) (0,12) (0,21) (0,8) (0,20) (1,16) (1,17) (1,14) (1,19) (2,11) (2,13) (2,5) (2,4) (2,3) (2,21) (2,10) (2,8) (3,11) (3,5) (3,18) (3,12) (3,21) (3,10) (3,8) (3,20) (4,11) (4,13) (4,5) (4,18) (4,9) (4,12) (4,21) (4,10) (4,8) (4,20) (5,11) (5,13) (5,18) (5,12) (5,21) (5,10) (5,8) (5,20) (6,15) (7,15) (8,13) (8,12) (8,10) (9,11) (9,18) (9,12) (9,21) (9,10) (10,11) (10,13) (10,18) (10,21) (10,20) (11,12) (11,20) (12,13) (12,21) (12,20) (13,21) (14,16) (14,17) (14,19) (16,17) (16,19) (18,21) (18,20) (20,21)\nIs there a path between node 19 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph809-24_13", + "image": "data/connectivity/graph_visual/medium/graph809.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (1,23) (1,15) (1,8) (1,17) (1,19) (1,9) (1,12) (1,20) (1,10) (1,5) (1,22) (1,14) (1,4) (1,18) (1,21) (2,13) (2,3) (2,16) (3,16) (4,23) (4,15) (4,7) (4,17) (4,9) (4,12) (4,20) (4,5) (4,22) (4,14) (4,21) (5,23) (5,15) (5,8) (5,7) (5,19) (5,9) (5,20) (5,22) (5,14) (5,21) (6,24) (6,11) (7,15) (7,8) (7,17) (7,12) (7,20) (7,10) (7,18) (7,21) (8,15) (8,17) (8,19) (8,9) (8,22) (8,14) (8,18) (9,23) (9,15) (9,17) (9,19) (9,20) (9,10) (9,18) (9,21) (10,23) (10,19) (10,22) (10,14) (10,21) (12,23) (12,15) (12,17) (12,19) (12,22) (12,18) (14,15) (14,19) (14,20) (14,22) (14,18) (14,21) (15,19) (15,20) (15,22) (15,18) (17,23) (17,19) (17,20) (17,18) (17,21) (18,23) (18,22) (19,23) (19,20) (19,21) (20,22) (20,21) (21,22)\nIs there a path between node 24 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph444-2_8", + "image": "data/connectivity/graph_visual/medium/graph444.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,3) (0,15) (0,21) (0,17) (0,7) (0,12) (0,5) (0,9) (0,2) (0,19) (0,14) (0,20) (1,3) (1,15) (1,16) (1,17) (1,11) (1,7) (1,12) (1,13) (1,8) (1,18) (1,9) (1,2) (1,19) (1,14) (1,20) (2,15) (2,21) (2,17) (2,11) (2,7) (2,12) (2,5) (2,8) (2,19) (2,14) (2,10) (2,20) (3,15) (3,21) (3,16) (3,17) (3,11) (3,13) (3,5) (3,8) (3,18) (3,14) (3,10) (3,20) (5,15) (5,21) (5,16) (5,17) (5,11) (5,7) (5,12) (5,13) (5,9) (5,19) (5,14) (5,10) (5,20) (7,21) (7,17) (7,11) (7,12) (7,8) (7,18) (7,19) (7,10) (7,20) (8,15) (8,21) (8,16) (8,17) (8,9) (8,19) (8,14) (8,10) (8,20) (9,15) (9,21) (9,16) (9,13) (9,18) (9,14) (10,15) (10,21) (10,16) (10,17) (10,11) (10,12) (10,13) (10,18) (10,19) (10,14) (10,20) (11,15) (11,21) (11,16) (11,17) (11,13) (11,18) (11,14) (11,20) (12,16) (12,17) (12,13) (12,18) (12,20) (13,15) (13,21) (13,16) (13,17) (13,18) (13,14) (13,20) (14,16) (14,17) (14,19) (14,20) (15,16) (15,17) (15,19) (16,17) (16,18) (16,19) (16,20) (17,21) (17,18) (18,19) (18,20) (19,21) (20,21)\nIs there a path between node 2 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph429-9_17", + "image": "data/connectivity/graph_visual/medium/graph429.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,10) (0,2) (0,8) (0,13) (1,11) (1,21) (1,7) (2,20) (2,6) (2,10) (2,3) (2,4) (2,12) (2,18) (3,17) (3,6) (3,4) (3,19) (3,18) (4,17) (4,19) (4,13) (6,17) (6,10) (6,19) (7,14) (8,15) (8,20) (9,20) (9,16) (9,18) (10,20) (10,16) (10,19) (12,19) (12,13) (13,17) (13,15) (13,16) (15,17) (15,19) (16,17) (17,20) (18,19) (19,20)\nIs there a path between node 9 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph161-15_4", + "image": "data/connectivity/graph_visual/medium/graph161.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,5) (0,2) (0,7) (0,16) (0,6) (1,7) (1,10) (1,4) (2,15) (2,10) (4,5) (4,6) (6,7) (8,11) (8,13) (8,12) (8,14) (11,14) (13,17) (14,17)\nIs there a path between node 15 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph691-1_16", + "image": "data/connectivity/graph_visual/medium/graph691.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,23) (0,3) (0,7) (0,9) (0,21) (0,13) (0,16) (0,6) (0,8) (0,12) (1,5) (1,22) (1,15) (1,14) (1,18) (1,17) (1,20) (1,11) (1,2) (2,5) (2,22) (2,15) (2,14) (2,18) (2,17) (2,20) (2,11) (3,10) (3,19) (3,23) (3,7) (3,9) (3,21) (3,13) (3,16) (3,6) (3,8) (3,12) (5,22) (5,15) (5,14) (5,18) (5,17) (5,20) (5,11) (6,10) (6,19) (6,23) (6,7) (6,9) (6,21) (6,13) (6,16) (6,8) (6,12) (7,10) (7,19) (7,23) (7,9) (7,21) (7,13) (7,16) (7,8) (7,12) (8,10) (8,19) (8,23) (8,9) (8,21) (8,13) (8,16) (8,12) (9,10) (9,19) (9,23) (9,21) (9,13) (9,16) (9,12) (10,19) (10,23) (10,21) (10,13) (10,16) (10,12) (11,22) (11,15) (11,14) (11,18) (11,17) (11,20) (12,19) (12,23) (12,21) (12,13) (12,16) (13,19) (13,23) (13,21) (13,16) (14,22) (14,15) (14,18) (14,17) (14,20) (15,22) (15,18) (15,17) (15,20) (16,19) (16,23) (16,21) (17,22) (17,18) (17,20) (18,22) (18,20) (19,23) (19,21) (20,22) (21,23)\nIs there a path between node 1 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph577-11_2", + "image": "data/connectivity/graph_visual/medium/graph577.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (0,12) (0,18) (1,3) (1,16) (1,17) (1,14) (1,9) (1,8) (2,18) (2,9) (2,13) (2,22) (3,17) (3,14) (4,5) (4,21) (5,11) (5,6) (5,10) (6,11) (6,21) (7,19) (8,16) (8,22) (9,20) (9,18) (9,23) (11,19) (11,21) (12,14) (12,23) (12,22) (13,16) (13,20) (13,17) (13,22) (14,16) (15,18) (15,23) (16,18) (17,20) (17,18) (17,23) (17,22) (19,21) (20,23)\nIs there a path between node 11 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph364-13_15", + "image": "data/connectivity/graph_visual/medium/graph364.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,2) (1,11) (1,7) (2,11) (2,15) (2,12) (2,3) (3,9) (3,7) (4,19) (4,7) (6,16) (6,13) (6,18) (8,17) (8,15) (8,12) (9,17) (9,19) (9,11) (10,19) (10,11) (11,20) (15,19) (17,20)\nIs there a path between node 13 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph633-14_20", + "image": "data/connectivity/graph_visual/medium/graph633.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,10) (1,9) (3,17) (3,8) (3,23) (4,17) (4,15) (4,22) (4,8) (4,23) (4,16) (6,11) (6,10) (7,21) (8,17) (8,23) (8,16) (10,18) (10,19) (11,18) (11,14) (15,23) (16,17) (16,23) (19,20) (21,22) (21,23)\nIs there a path between node 14 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph368-0_13", + "image": "data/connectivity/graph_visual/medium/graph368.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,11) (0,9) (0,14) (0,7) (0,8) (0,15) (0,16) (0,1) (0,5) (1,9) (1,2) (1,14) (1,7) (1,16) (1,10) (1,17) (1,3) (1,6) (2,11) (2,14) (2,7) (2,8) (2,15) (2,16) (2,3) (2,5) (2,6) (3,11) (3,7) (3,8) (3,16) (3,10) (3,17) (3,6) (4,12) (4,19) (5,14) (5,8) (5,15) (5,16) (5,10) (5,17) (6,9) (6,14) (6,7) (6,8) (6,15) (6,10) (6,17) (7,11) (7,9) (7,14) (7,8) (7,16) (7,10) (8,11) (8,14) (8,15) (8,16) (8,17) (9,11) (9,14) (9,15) (9,16) (9,10) (10,11) (10,14) (10,15) (11,15) (11,16) (11,17) (12,18) (13,18) (14,15) (14,17) (15,16) (15,17) (18,19)\nIs there a path between node 0 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph505-6_9", + "image": "data/connectivity/graph_visual/medium/graph505.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,13) (0,9) (0,10) (1,2) (1,15) (1,7) (1,11) (1,16) (2,3) (2,18) (2,7) (2,11) (2,14) (3,8) (3,4) (4,20) (4,15) (4,22) (4,7) (4,16) (4,14) (5,21) (5,9) (5,10) (7,17) (7,15) (8,20) (8,14) (9,12) (9,21) (9,13) (9,10) (10,12) (10,21) (11,20) (11,15) (11,22) (14,18) (15,16) (16,17) (16,22) (17,22) (18,20)\nIs there a path between node 6 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph360-10_6", + "image": "data/connectivity/graph_visual/medium/graph360.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,8) (1,2) (1,10) (1,7) (1,3) (1,12) (1,17) (2,11) (2,12) (2,20) (2,6) (2,17) (3,7) (3,9) (3,17) (4,12) (4,20) (4,6) (6,7) (6,12) (6,9) (10,11) (10,12) (10,20) (13,19) (14,16) (15,16) (16,18)\nIs there a path between node 10 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph320-6_16", + "image": "data/connectivity/graph_visual/medium/graph320.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,1) (0,18) (1,19) (1,18) (2,6) (2,10) (2,7) (2,5) (2,16) (2,11) (2,15) (2,4) (3,8) (3,9) (3,13) (3,12) (3,14) (3,17) (4,6) (4,10) (4,7) (4,5) (4,16) (4,11) (4,15) (5,6) (5,10) (5,7) (5,16) (5,11) (5,15) (6,10) (6,7) (6,16) (6,11) (6,15) (7,10) (7,16) (7,11) (7,15) (8,9) (8,13) (8,12) (8,14) (8,17) (9,13) (9,12) (9,14) (9,17) (10,16) (10,11) (10,15) (11,16) (11,15) (12,13) (12,14) (12,17) (13,14) (13,17) (14,17) (15,16) (18,19)\nIs there a path between node 6 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph548-11_3", + "image": "data/connectivity/graph_visual/medium/graph548.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,9) (0,17) (0,7) (1,18) (1,3) (1,23) (1,19) (2,21) (2,14) (2,9) (2,16) (2,11) (2,5) (3,23) (3,6) (4,9) (4,11) (4,8) (4,20) (5,21) (5,8) (5,13) (6,10) (7,21) (7,17) (7,22) (8,14) (9,11) (9,13) (9,20) (9,22) (10,23) (11,16) (11,12) (12,21) (12,14) (13,21) (13,17) (14,16) (16,20) (19,23)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph647-2_8", + "image": "data/connectivity/graph_visual/medium/graph647.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,18) (0,6) (0,1) (1,12) (1,6) (1,3) (2,8) (2,18) (2,20) (2,13) (2,11) (3,23) (3,18) (3,13) (4,16) (4,22) (5,7) (6,18) (6,11) (6,15) (7,9) (8,23) (8,14) (8,20) (8,11) (12,14) (13,18) (14,23) (14,18) (15,18) (16,17) (16,21) (18,23) (18,20)\nIs there a path between node 2 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph132-16_11", + "image": "data/connectivity/graph_visual/medium/graph132.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,4) (0,9) (0,1) (0,11) (0,2) (1,10) (1,6) (1,9) (1,15) (1,13) (2,12) (2,9) (2,17) (2,15) (3,4) (3,6) (3,11) (4,12) (4,9) (4,11) (6,10) (6,12) (6,9) (6,15) (6,13) (8,12) (8,9) (8,15) (8,13) (9,10) (9,11) (10,13) (10,11) (11,13) (12,13) (14,16)\nIs there a path between node 16 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph118-15_6", + "image": "data/connectivity/graph_visual/medium/graph118.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,4) (1,3) (1,7) (1,13) (1,6) (1,10) (2,12) (2,8) (3,8) (3,11) (3,6) (3,10) (5,12) (5,15) (5,9) (7,16) (7,13) (7,8) (8,15) (8,16) (8,9) (9,15) (9,13) (10,12) (11,14) (11,12) (11,13) (12,15) (13,14) (14,16)\nIs there a path between node 15 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph562-14_11", + "image": "data/connectivity/graph_visual/medium/graph562.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,5) (0,6) (0,13) (0,17) (0,23) (0,9) (0,10) (0,22) (0,2) (0,20) (0,21) (0,12) (1,14) (1,18) (1,3) (1,4) (1,11) (1,16) (1,7) (2,5) (2,13) (2,17) (2,23) (2,9) (2,10) (2,20) (2,21) (2,12) (3,18) (3,4) (3,11) (3,16) (3,7) (4,18) (4,11) (4,16) (4,8) (5,19) (5,13) (5,17) (5,23) (5,9) (5,10) (5,22) (5,15) (5,12) (6,19) (6,13) (6,23) (6,9) (6,22) (6,15) (6,20) (6,12) (7,14) (7,11) (7,16) (8,14) (8,11) (9,19) (9,13) (9,17) (9,23) (9,10) (9,15) (9,20) (9,21) (10,19) (10,13) (10,23) (10,15) (10,20) (11,18) (12,19) (12,23) (12,22) (12,15) (12,20) (12,21) (13,19) (13,23) (13,22) (13,20) (14,18) (15,19) (15,17) (15,22) (15,20) (17,23) (17,22) (17,21) (19,21) (20,23) (20,22) (21,23) (22,23)\nIs there a path between node 14 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph682-10_15", + "image": "data/connectivity/graph_visual/medium/graph682.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,21) (0,6) (0,16) (0,3) (0,10) (0,12) (0,22) (0,19) (0,13) (0,18) (0,17) (0,7) (0,2) (0,14) (0,5) (0,23) (1,20) (1,9) (2,8) (2,21) (2,6) (2,16) (2,3) (2,10) (2,12) (2,22) (2,19) (2,13) (2,18) (2,17) (2,7) (2,14) (2,5) (2,23) (3,8) (3,21) (3,6) (3,16) (3,10) (3,12) (3,22) (3,19) (3,13) (3,18) (3,17) (3,7) (3,14) (3,5) (3,23) (4,15) (4,11) (5,8) (5,21) (5,6) (5,16) (5,10) (5,12) (5,22) (5,19) (5,13) (5,18) (5,17) (5,7) (5,14) (5,23) (6,8) (6,21) (6,16) (6,10) (6,12) (6,22) (6,19) (6,13) (6,18) (6,17) (6,7) (6,14) (6,23) (7,8) (7,21) (7,16) (7,10) (7,12) (7,22) (7,19) (7,13) (7,18) (7,17) (7,14) (7,23) (8,21) (8,16) (8,10) (8,12) (8,22) (8,19) (8,13) (8,18) (8,17) (8,14) (8,23) (9,20) (10,21) (10,16) (10,12) (10,22) (10,19) (10,13) (10,18) (10,17) (10,14) (10,23) (11,15) (12,21) (12,16) (12,22) (12,19) (12,13) (12,18) (12,17) (12,14) (12,23) (13,21) (13,16) (13,22) (13,19) (13,18) (13,17) (13,14) (13,23) (14,21) (14,16) (14,22) (14,19) (14,18) (14,17) (14,23) (16,21) (16,22) (16,19) (16,18) (16,17) (16,23) (17,21) (17,22) (17,19) (17,18) (17,23) (18,21) (18,22) (18,19) (18,23) (19,21) (19,22) (19,23) (21,22) (21,23) (22,23)\nIs there a path between node 10 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph296-10_0", + "image": "data/connectivity/graph_visual/medium/graph296.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,1) (0,11) (0,17) (0,3) (0,19) (0,9) (0,16) (0,15) (0,7) (0,12) (0,2) (1,11) (1,10) (1,3) (1,4) (1,8) (1,19) (1,13) (1,9) (1,16) (1,15) (1,7) (1,12) (1,2) (2,17) (2,5) (2,16) (2,15) (3,17) (3,10) (3,5) (3,6) (3,8) (3,13) (3,9) (3,16) (3,15) (3,7) (3,12) (4,11) (4,5) (4,8) (4,19) (4,13) (4,9) (4,7) (4,12) (5,11) (5,10) (5,6) (5,8) (5,19) (5,13) (5,7) (6,11) (6,17) (6,10) (6,8) (6,19) (6,13) (6,16) (6,15) (6,7) (6,12) (7,11) (7,17) (7,10) (7,19) (7,9) (7,16) (7,15) (8,11) (8,17) (8,10) (8,19) (8,13) (8,15) (8,12) (9,11) (9,17) (9,10) (9,13) (9,16) (9,15) (10,11) (10,17) (10,19) (10,13) (10,15) (10,12) (11,19) (11,15) (11,12) (12,17) (12,19) (12,13) (13,19) (13,16) (13,15) (14,18) (15,19) (15,16) (16,17) (17,19)\nIs there a path between node 10 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph552-7_2", + "image": "data/connectivity/graph_visual/medium/graph552.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,12) (2,13) (2,22) (3,4) (3,18) (3,10) (3,7) (3,20) (4,21) (4,5) (5,18) (5,23) (5,10) (5,7) (5,20) (5,16) (6,11) (6,10) (6,7) (6,14) (6,16) (6,15) (7,18) (7,9) (7,11) (7,8) (7,16) (8,18) (8,9) (8,10) (8,20) (8,14) (8,16) (8,15) (9,21) (9,23) (10,21) (10,11) (10,15) (11,18) (11,17) (11,16) (12,13) (13,22) (14,18) (14,23) (14,17) (14,16) (14,15) (15,21) (16,18) (16,20) (18,20) (19,22) (20,23)\nIs there a path between node 7 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph156-13_10", + "image": "data/connectivity/graph_visual/medium/graph156.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,8) (0,1) (1,12) (1,15) (2,9) (2,6) (3,10) (3,17) (3,15) (5,7) (6,10) (6,9) (6,11) (7,13) (8,17) (8,16) (10,15) (11,12) (15,17)\nIs there a path between node 13 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph350-14_9", + "image": "data/connectivity/graph_visual/medium/graph350.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,20) (0,4) (0,9) (0,18) (0,12) (0,5) (0,1) (0,17) (0,13) (0,2) (0,10) (0,7) (0,19) (0,15) (0,11) (0,8) (1,16) (1,20) (1,4) (1,9) (1,18) (1,12) (1,5) (1,17) (1,13) (1,2) (1,10) (1,7) (1,19) (1,15) (1,11) (1,8) (2,16) (2,20) (2,4) (2,9) (2,18) (2,12) (2,5) (2,17) (2,13) (2,10) (2,7) (2,19) (2,15) (2,11) (2,8) (3,14) (3,6) (4,16) (4,20) (4,9) (4,18) (4,12) (4,5) (4,17) (4,13) (4,10) (4,7) (4,19) (4,15) (4,11) (4,8) (5,16) (5,20) (5,9) (5,18) (5,12) (5,17) (5,13) (5,10) (5,7) (5,19) (5,15) (5,11) (5,8) (6,14) (7,16) (7,20) (7,9) (7,18) (7,12) (7,17) (7,13) (7,10) (7,19) (7,15) (7,11) (7,8) (8,16) (8,20) (8,9) (8,18) (8,12) (8,17) (8,13) (8,10) (8,19) (8,15) (8,11) (9,16) (9,20) (9,18) (9,12) (9,17) (9,13) (9,10) (9,19) (9,15) (9,11) (10,16) (10,20) (10,18) (10,12) (10,17) (10,13) (10,19) (10,15) (10,11) (11,16) (11,20) (11,18) (11,12) (11,17) (11,13) (11,19) (11,15) (12,16) (12,20) (12,18) (12,17) (12,13) (12,19) (12,15) (13,16) (13,20) (13,18) (13,17) (13,19) (13,15) (15,16) (15,20) (15,18) (15,17) (15,19) (16,20) (16,18) (16,17) (16,19) (17,20) (17,18) (17,19) (18,20) (18,19) (19,20)\nIs there a path between node 14 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph688-16_8", + "image": "data/connectivity/graph_visual/medium/graph688.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,6) (0,11) (0,14) (0,2) (1,20) (1,8) (1,7) (1,16) (1,21) (1,9) (1,17) (1,5) (1,23) (1,12) (1,22) (2,4) (2,6) (2,11) (2,14) (3,15) (3,18) (3,13) (3,19) (3,10) (4,6) (4,11) (4,14) (5,20) (5,8) (5,7) (5,16) (5,21) (5,9) (5,17) (5,23) (5,12) (5,22) (6,11) (6,14) (7,20) (7,8) (7,16) (7,21) (7,9) (7,17) (7,23) (7,12) (7,22) (8,20) (8,16) (8,21) (8,9) (8,17) (8,23) (8,12) (8,22) (9,20) (9,16) (9,21) (9,17) (9,23) (9,12) (9,22) (10,15) (10,18) (10,13) (10,19) (11,14) (12,20) (12,16) (12,21) (12,17) (12,23) (12,22) (13,15) (13,18) (13,19) (15,18) (15,19) (16,20) (16,21) (16,17) (16,23) (16,22) (17,20) (17,21) (17,23) (17,22) (18,19) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 16 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph253-7_17", + "image": "data/connectivity/graph_visual/medium/graph253.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,7) (0,14) (0,13) (0,12) (0,17) (0,16) (0,18) (0,9) (1,5) (1,4) (1,3) (1,8) (1,11) (1,6) (2,10) (2,15) (3,5) (3,4) (3,8) (3,11) (3,6) (4,5) (4,8) (4,11) (4,6) (5,8) (5,11) (5,6) (6,8) (6,11) (7,14) (7,13) (7,12) (7,17) (7,16) (7,18) (7,9) (8,11) (9,14) (9,13) (9,12) (9,17) (9,16) (9,18) (10,15) (12,14) (12,13) (12,17) (12,16) (12,18) (13,14) (13,17) (13,16) (13,18) (14,17) (14,16) (14,18) (16,17) (16,18) (17,18)\nIs there a path between node 7 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph549-5_20", + "image": "data/connectivity/graph_visual/medium/graph549.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (1,10) (2,11) (2,9) (3,21) (4,10) (4,23) (5,7) (5,9) (7,11) (7,9) (8,18) (8,17) (10,22) (13,19) (14,16) (15,19) (16,17) (17,19)\nIs there a path between node 5 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph732-12_8", + "image": "data/connectivity/graph_visual/medium/graph732.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (0,1) (0,11) (0,22) (0,12) (1,18) (1,21) (1,11) (1,4) (1,20) (1,22) (1,12) (2,15) (2,21) (2,4) (2,6) (2,22) (3,19) (4,24) (4,14) (4,8) (4,21) (4,20) (4,7) (4,22) (4,12) (5,23) (5,15) (5,20) (5,9) (5,7) (6,14) (6,8) (6,21) (6,20) (6,10) (7,23) (7,8) (7,11) (7,22) (8,15) (8,21) (9,23) (9,21) (9,20) (9,12) (10,17) (10,14) (10,15) (10,21) (10,20) (10,22) (10,12) (10,16) (11,20) (11,12) (11,16) (12,24) (12,14) (12,23) (14,24) (14,17) (14,15) (14,21) (15,24) (16,24) (16,23) (17,24) (17,18) (17,20) (17,22) (18,24) (18,22) (22,24)\nIs there a path between node 12 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph230-7_12", + "image": "data/connectivity/graph_visual/medium/graph230.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,9) (1,14) (1,2) (1,17) (1,16) (1,8) (2,4) (2,17) (3,7) (4,12) (4,18) (4,17) (4,10) (5,14) (5,18) (5,17) (5,10) (5,8) (6,18) (6,17) (6,10) (8,12) (8,10) (8,16) (10,12) (10,14) (12,15) (12,17) (12,16) (14,15) (14,17) (15,17) (15,16) (16,18) (17,18)\nIs there a path between node 7 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph408-11_4", + "image": "data/connectivity/graph_visual/medium/graph408.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,17) (0,7) (0,18) (0,14) (0,8) (0,19) (0,15) (0,4) (0,21) (1,3) (1,6) (1,11) (2,7) (2,9) (2,14) (2,8) (2,19) (2,13) (2,15) (2,10) (3,5) (3,20) (3,6) (3,11) (4,17) (4,7) (4,18) (4,9) (4,21) (5,12) (5,6) (5,11) (6,12) (6,20) (7,17) (7,18) (7,9) (7,14) (7,8) (7,13) (7,15) (8,17) (8,18) (8,14) (8,13) (8,15) (8,21) (8,10) (9,17) (9,18) (9,14) (9,13) (9,21) (10,17) (10,18) (10,14) (10,13) (10,15) (11,12) (11,20) (12,20) (12,16) (13,18) (13,14) (13,19) (13,15) (13,21) (14,18) (14,15) (14,21) (15,17) (15,18) (15,19) (15,21) (17,18) (17,19) (18,19) (19,21)\nIs there a path between node 11 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph82-1_14", + "image": "data/connectivity/graph_visual/medium/graph82.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,12) (0,1) (0,8) (0,5) (0,9) (0,13) (0,11) (0,10) (0,6) (1,4) (1,8) (1,2) (1,11) (1,6) (2,12) (2,9) (2,13) (2,7) (2,11) (2,3) (2,10) (2,6) (3,4) (3,12) (3,8) (3,5) (3,13) (3,7) (3,11) (3,10) (3,6) (4,12) (4,5) (4,9) (4,7) (4,11) (5,8) (5,7) (5,11) (5,10) (6,8) (6,9) (6,7) (6,11) (6,10) (7,8) (7,9) (7,13) (7,10) (8,9) (8,13) (8,10) (9,12) (9,13) (9,11) (10,11) (11,13)\nIs there a path between node 1 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph775-14_11", + "image": "data/connectivity/graph_visual/medium/graph775.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,5) (0,11) (0,24) (0,6) (0,21) (0,14) (0,16) (0,2) (0,23) (0,1) (0,8) (0,19) (0,7) (0,15) (0,17) (0,20) (0,3) (0,22) (0,13) (0,10) (1,5) (1,11) (1,24) (1,6) (1,21) (1,14) (1,16) (1,2) (1,23) (1,8) (1,19) (1,7) (1,15) (1,17) (1,20) (1,3) (1,22) (1,13) (1,10) (2,5) (2,11) (2,24) (2,6) (2,21) (2,14) (2,16) (2,23) (2,8) (2,19) (2,7) (2,15) (2,17) (2,20) (2,3) (2,22) (2,13) (2,10) (3,5) (3,11) (3,24) (3,6) (3,21) (3,14) (3,16) (3,23) (3,8) (3,19) (3,7) (3,15) (3,17) (3,20) (3,22) (3,13) (3,10) (4,18) (4,12) (4,9) (5,11) (5,24) (5,6) (5,21) (5,14) (5,16) (5,23) (5,8) (5,19) (5,7) (5,15) (5,17) (5,20) (5,22) (5,13) (5,10) (6,11) (6,24) (6,21) (6,14) (6,16) (6,23) (6,8) (6,19) (6,7) (6,15) (6,17) (6,20) (6,22) (6,13) (6,10) (7,11) (7,24) (7,21) (7,14) (7,16) (7,23) (7,8) (7,19) (7,15) (7,17) (7,20) (7,22) (7,13) (7,10) (8,11) (8,24) (8,21) (8,14) (8,16) (8,23) (8,19) (8,15) (8,17) (8,20) (8,22) (8,13) (8,10) (9,18) (9,12) (10,11) (10,24) (10,21) (10,14) (10,16) (10,23) (10,19) (10,15) (10,17) (10,20) (10,22) (10,13) (11,24) (11,21) (11,14) (11,16) (11,23) (11,19) (11,15) (11,17) (11,20) (11,22) (11,13) (12,18) (13,24) (13,21) (13,14) (13,16) (13,23) (13,19) (13,15) (13,17) (13,20) (13,22) (14,24) (14,21) (14,16) (14,23) (14,19) (14,15) (14,17) (14,20) (14,22) (15,24) (15,21) (15,16) (15,23) (15,19) (15,17) (15,20) (15,22) (16,24) (16,21) (16,23) (16,19) (16,17) (16,20) (16,22) (17,24) (17,21) (17,23) (17,19) (17,20) (17,22) (19,24) (19,21) (19,23) (19,20) (19,22) (20,24) (20,21) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nIs there a path between node 14 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph90-8_9", + "image": "data/connectivity/graph_visual/medium/graph90.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,10) (1,11) (1,9) (1,14) (2,5) (2,6) (3,11) (3,13) (4,11) (4,13) (4,15) (5,7) (5,6) (7,10) (8,11) (8,9) (9,14) (9,12) (11,13) (13,14) (13,15)\nIs there a path between node 8 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph673-22_1", + "image": "data/connectivity/graph_visual/medium/graph673.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,10) (0,9) (0,11) (0,19) (0,23) (0,20) (0,17) (0,16) (1,2) (1,10) (1,21) (1,9) (1,11) (1,12) (1,16) (1,6) (2,15) (2,21) (2,19) (2,23) (2,20) (2,16) (2,6) (3,8) (4,7) (6,10) (6,21) (6,9) (6,11) (6,19) (6,23) (6,20) (6,17) (6,16) (8,22) (8,18) (9,10) (9,21) (9,11) (9,19) (9,23) (9,12) (9,20) (9,17) (9,16) (10,15) (10,21) (10,11) (10,12) (10,20) (10,16) (11,15) (11,19) (11,20) (11,17) (11,16) (12,15) (12,21) (12,19) (12,23) (12,20) (13,14) (15,21) (15,23) (15,20) (15,16) (16,21) (16,19) (16,17) (17,21) (17,19) (17,20) (19,21) (19,20) (20,21) (20,23) (21,23)\nIs there a path between node 22 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph187-12_13", + "image": "data/connectivity/graph_visual/medium/graph187.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,10) (0,17) (0,1) (0,15) (0,14) (0,4) (0,8) (0,16) (0,13) (0,9) (0,5) (0,11) (1,10) (1,17) (1,15) (1,14) (1,4) (1,8) (1,16) (1,13) (1,9) (1,5) (1,11) (2,3) (2,7) (2,12) (2,6) (3,7) (3,12) (3,6) (4,10) (4,17) (4,15) (4,14) (4,8) (4,16) (4,13) (4,9) (4,5) (4,11) (5,10) (5,17) (5,15) (5,14) (5,8) (5,16) (5,13) (5,9) (5,11) (6,7) (6,12) (7,12) (8,10) (8,17) (8,15) (8,14) (8,16) (8,13) (8,9) (8,11) (9,10) (9,17) (9,15) (9,14) (9,16) (9,13) (9,11) (10,17) (10,15) (10,14) (10,16) (10,13) (10,11) (11,17) (11,15) (11,14) (11,16) (11,13) (13,17) (13,15) (13,14) (13,16) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 12 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph696-12_5", + "image": "data/connectivity/graph_visual/medium/graph696.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,17) (0,12) (0,5) (0,7) (0,20) (0,13) (0,14) (0,8) (0,9) (0,19) (0,4) (0,21) (0,1) (1,15) (1,17) (1,12) (1,5) (1,7) (1,20) (1,13) (1,14) (1,8) (1,9) (1,19) (1,4) (1,21) (2,6) (2,18) (2,23) (2,3) (2,16) (2,11) (2,22) (2,10) (3,6) (3,18) (3,23) (3,16) (3,11) (3,22) (3,10) (4,15) (4,17) (4,12) (4,5) (4,7) (4,20) (4,13) (4,14) (4,8) (4,9) (4,19) (4,21) (5,15) (5,17) (5,12) (5,7) (5,20) (5,13) (5,14) (5,8) (5,9) (5,19) (5,21) (6,18) (6,23) (6,16) (6,11) (6,22) (6,10) (7,15) (7,17) (7,12) (7,20) (7,13) (7,14) (7,8) (7,9) (7,19) (7,21) (8,15) (8,17) (8,12) (8,20) (8,13) (8,14) (8,9) (8,19) (8,21) (9,15) (9,17) (9,12) (9,20) (9,13) (9,14) (9,19) (9,21) (10,18) (10,23) (10,16) (10,11) (10,22) (11,18) (11,23) (11,16) (11,22) (12,15) (12,17) (12,20) (12,13) (12,14) (12,19) (12,21) (13,15) (13,17) (13,20) (13,14) (13,19) (13,21) (14,15) (14,17) (14,20) (14,19) (14,21) (15,17) (15,20) (15,19) (15,21) (16,18) (16,23) (16,22) (17,20) (17,19) (17,21) (18,23) (18,22) (19,20) (19,21) (20,21) (22,23)\nIs there a path between node 12 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph169-12_0", + "image": "data/connectivity/graph_visual/medium/graph169.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,17) (0,13) (0,12) (0,4) (0,1) (1,3) (1,17) (1,16) (1,14) (1,4) (2,5) (2,7) (2,9) (2,11) (2,8) (3,15) (3,13) (3,16) (3,12) (3,14) (3,6) (4,15) (4,13) (4,16) (4,12) (4,6) (5,9) (5,11) (5,10) (6,17) (6,13) (6,12) (7,11) (7,10) (7,8) (8,9) (8,11) (9,10) (10,11) (12,15) (12,17) (12,16) (12,14) (13,17) (13,16) (14,15) (14,17) (15,17) (15,16) (16,17)\nIs there a path between node 12 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph542-0_21", + "image": "data/connectivity/graph_visual/medium/graph542.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,14) (0,9) (0,13) (0,4) (0,12) (0,5) (0,3) (0,15) (0,21) (0,2) (0,18) (0,17) (1,14) (1,9) (1,13) (1,4) (1,12) (1,5) (1,3) (1,15) (1,21) (1,2) (1,18) (1,17) (2,14) (2,9) (2,13) (2,4) (2,12) (2,5) (2,3) (2,15) (2,21) (2,18) (2,17) (3,14) (3,9) (3,13) (3,4) (3,12) (3,5) (3,15) (3,21) (3,18) (3,17) (4,14) (4,9) (4,13) (4,12) (4,5) (4,15) (4,21) (4,18) (4,17) (5,14) (5,9) (5,13) (5,12) (5,15) (5,21) (5,18) (5,17) (6,22) (6,8) (6,11) (6,10) (6,19) (6,20) (6,7) (7,22) (7,8) (7,11) (7,10) (7,19) (7,20) (8,22) (8,11) (8,10) (8,19) (8,20) (9,14) (9,13) (9,12) (9,15) (9,21) (9,18) (9,17) (10,22) (10,11) (10,19) (10,20) (11,22) (11,19) (11,20) (12,14) (12,13) (12,15) (12,21) (12,18) (12,17) (13,14) (13,15) (13,21) (13,18) (13,17) (14,15) (14,21) (14,18) (14,17) (15,21) (15,18) (15,17) (17,21) (17,18) (18,21) (19,22) (19,20) (20,22)\nIs there a path between node 0 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph446-19_13", + "image": "data/connectivity/graph_visual/medium/graph446.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,13) (0,2) (0,5) (0,4) (0,18) (0,9) (0,3) (0,12) (0,21) (0,8) (0,20) (1,16) (1,17) (1,14) (1,19) (2,11) (2,13) (2,5) (2,4) (2,3) (2,21) (2,10) (2,8) (3,11) (3,5) (3,18) (3,12) (3,21) (3,10) (3,8) (3,20) (4,11) (4,13) (4,5) (4,18) (4,9) (4,12) (4,21) (4,10) (4,8) (4,20) (5,11) (5,13) (5,18) (5,12) (5,21) (5,10) (5,8) (5,20) (6,15) (7,15) (8,13) (8,12) (8,10) (9,11) (9,18) (9,12) (9,21) (9,10) (10,11) (10,13) (10,18) (10,21) (10,20) (11,12) (11,20) (12,13) (12,21) (12,20) (13,21) (14,16) (14,17) (14,19) (16,17) (16,19) (18,21) (18,20) (20,21)\nIs there a path between node 19 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph521-13_16", + "image": "data/connectivity/graph_visual/medium/graph521.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,10) (0,12) (0,16) (0,9) (0,17) (0,11) (0,5) (0,13) (0,21) (0,4) (1,8) (1,18) (1,7) (3,6) (3,14) (3,10) (3,16) (3,9) (3,11) (3,5) (3,21) (3,4) (3,15) (4,6) (4,10) (4,12) (4,16) (4,9) (4,17) (4,11) (4,13) (4,21) (4,15) (5,6) (5,12) (5,9) (5,19) (5,17) (5,13) (5,21) (5,15) (6,14) (6,10) (6,12) (6,16) (6,19) (6,17) (6,13) (6,21) (6,15) (7,20) (7,8) (7,18) (8,20) (9,14) (9,10) (9,16) (9,19) (9,17) (9,11) (9,13) (9,21) (10,12) (10,19) (10,17) (10,11) (10,15) (11,14) (11,16) (11,19) (11,17) (11,21) (12,14) (12,17) (12,13) (12,21) (13,14) (13,16) (13,17) (13,21) (14,16) (14,21) (15,19) (15,17) (15,21) (16,17) (16,21) (17,19) (17,21) (18,20) (19,21)\nIs there a path between node 13 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph246-0_2", + "image": "data/connectivity/graph_visual/medium/graph246.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,7) (0,16) (0,1) (0,13) (0,9) (0,12) (0,4) (0,14) (0,10) (0,18) (0,15) (0,6) (1,8) (1,7) (1,16) (1,13) (1,9) (1,12) (1,4) (1,14) (1,10) (1,18) (1,15) (1,6) (2,5) (3,17) (3,11) (4,8) (4,7) (4,16) (4,13) (4,9) (4,12) (4,14) (4,10) (4,18) (4,15) (4,6) (6,8) (6,7) (6,16) (6,13) (6,9) (6,12) (6,14) (6,10) (6,18) (6,15) (7,8) (7,16) (7,13) (7,9) (7,12) (7,14) (7,10) (7,18) (7,15) (8,16) (8,13) (8,9) (8,12) (8,14) (8,10) (8,18) (8,15) (9,16) (9,13) (9,12) (9,14) (9,10) (9,18) (9,15) (10,16) (10,13) (10,12) (10,14) (10,18) (10,15) (11,17) (12,16) (12,13) (12,14) (12,18) (12,15) (13,16) (13,14) (13,18) (13,15) (14,16) (14,18) (14,15) (15,16) (15,18) (16,18)\nIs there a path between node 0 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph742-5_14", + "image": "data/connectivity/graph_visual/medium/graph742.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,4) (0,5) (0,10) (0,22) (0,8) (3,9) (3,24) (3,11) (4,21) (4,13) (5,13) (7,9) (8,21) (8,17) (8,18) (9,20) (10,21) (10,22) (13,14) (13,18) (14,18) (15,19) (15,16) (21,22)\nIs there a path between node 5 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph782-22_5", + "image": "data/connectivity/graph_visual/medium/graph782.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,11) (0,5) (1,9) (1,17) (2,6) (2,22) (2,15) (2,11) (2,18) (2,7) (3,12) (3,11) (4,12) (4,14) (4,15) (4,13) (5,10) (5,14) (5,22) (5,11) (5,7) (6,8) (6,15) (7,8) (7,10) (7,22) (7,13) (7,16) (8,20) (8,14) (8,19) (8,15) (8,11) (9,24) (9,23) (9,17) (10,14) (10,11) (10,18) (11,20) (12,15) (12,13) (13,22) (13,15) (13,18) (13,16) (14,20) (14,22) (14,18) (15,20) (15,19) (15,18) (17,23) (20,21) (21,22) (23,24)\nIs there a path between node 22 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph142-16_15", + "image": "data/connectivity/graph_visual/medium/graph142.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,11) (0,6) (1,5) (1,8) (1,10) (1,15) (1,17) (1,13) (1,16) (2,5) (2,4) (2,8) (2,10) (2,14) (2,17) (2,13) (2,16) (3,9) (3,6) (3,12) (4,8) (4,15) (4,14) (4,17) (4,13) (5,8) (5,15) (5,17) (6,7) (6,9) (7,11) (7,9) (8,15) (8,17) (8,13) (8,16) (9,11) (10,15) (10,14) (10,17) (11,12) (13,15) (13,14) (13,16) (14,15) (14,17) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 16 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph771-20_19", + "image": "data/connectivity/graph_visual/medium/graph771.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,21) (0,18) (0,10) (0,11) (0,4) (0,24) (0,1) (0,5) (0,12) (0,6) (0,23) (1,7) (1,21) (1,18) (1,10) (1,11) (1,4) (1,24) (1,5) (1,12) (1,6) (1,23) (2,22) (2,17) (2,19) (2,14) (2,3) (2,13) (2,15) (2,9) (2,8) (2,20) (2,16) (3,22) (3,17) (3,19) (3,14) (3,13) (3,15) (3,9) (3,8) (3,20) (3,16) (4,7) (4,21) (4,18) (4,10) (4,11) (4,24) (4,5) (4,12) (4,6) (4,23) (5,7) (5,21) (5,18) (5,10) (5,11) (5,24) (5,12) (5,6) (5,23) (6,7) (6,21) (6,18) (6,10) (6,11) (6,24) (6,12) (6,23) (7,21) (7,18) (7,10) (7,11) (7,24) (7,12) (7,23) (8,22) (8,17) (8,19) (8,14) (8,13) (8,15) (8,9) (8,20) (8,16) (9,22) (9,17) (9,19) (9,14) (9,13) (9,15) (9,20) (9,16) (10,21) (10,18) (10,11) (10,24) (10,12) (10,23) (11,21) (11,18) (11,24) (11,12) (11,23) (12,21) (12,18) (12,24) (12,23) (13,22) (13,17) (13,19) (13,14) (13,15) (13,20) (13,16) (14,22) (14,17) (14,19) (14,15) (14,20) (14,16) (15,22) (15,17) (15,19) (15,20) (15,16) (16,22) (16,17) (16,19) (16,20) (17,22) (17,19) (17,20) (18,21) (18,24) (18,23) (19,22) (19,20) (20,22) (21,24) (21,23) (23,24)\nIs there a path between node 20 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph200-3_8", + "image": "data/connectivity/graph_visual/medium/graph200.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,12) (0,18) (0,6) (0,5) (0,7) (0,16) (1,11) (1,14) (2,4) (3,15) (5,12) (5,17) (5,9) (6,17) (6,7) (7,12) (7,18) (7,17) (7,13) (8,11) (9,12) (9,18) (9,17) (10,15) (13,17) (14,15)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph815-2_19", + "image": "data/connectivity/graph_visual/medium/graph815.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,16) (0,22) (0,3) (0,20) (0,14) (0,6) (0,19) (0,15) (0,13) (1,18) (1,9) (1,24) (1,2) (1,21) (1,23) (2,9) (2,24) (2,12) (2,10) (2,23) (2,4) (3,11) (3,16) (3,20) (3,14) (3,6) (3,7) (3,8) (3,15) (3,13) (4,9) (4,24) (4,12) (4,10) (4,21) (4,17) (4,23) (5,9) (5,24) (5,12) (5,10) (5,21) (5,17) (6,16) (6,22) (6,20) (6,7) (6,19) (6,8) (6,15) (6,13) (7,11) (7,16) (7,22) (7,20) (7,19) (7,8) (7,13) (8,22) (8,20) (8,19) (8,15) (8,13) (9,18) (9,10) (9,21) (9,23) (10,18) (10,24) (10,12) (10,17) (10,23) (11,16) (11,22) (11,20) (11,14) (11,19) (12,24) (12,21) (12,17) (12,23) (13,16) (13,22) (13,20) (13,19) (13,15) (14,16) (14,22) (14,19) (14,15) (15,16) (15,22) (15,19) (16,22) (16,20) (16,19) (18,24) (18,21) (19,20) (20,22) (21,24)\nIs there a path between node 2 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph618-21_7", + "image": "data/connectivity/graph_visual/medium/graph618.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,20) (0,21) (0,22) (0,9) (0,17) (0,12) (0,15) (0,7) (0,16) (0,6) (0,3) (0,1) (0,4) (1,10) (1,19) (1,20) (1,21) (1,22) (1,9) (1,17) (1,12) (1,15) (1,7) (1,16) (1,6) (1,3) (1,4) (2,23) (2,8) (2,5) (2,18) (2,11) (2,13) (2,14) (3,10) (3,19) (3,20) (3,21) (3,22) (3,9) (3,17) (3,12) (3,15) (3,7) (3,16) (3,6) (3,4) (4,10) (4,19) (4,20) (4,21) (4,22) (4,9) (4,17) (4,12) (4,15) (4,7) (4,16) (4,6) (5,23) (5,8) (5,18) (5,11) (5,13) (5,14) (6,10) (6,19) (6,20) (6,21) (6,22) (6,9) (6,17) (6,12) (6,15) (6,7) (6,16) (7,10) (7,19) (7,20) (7,21) (7,22) (7,9) (7,17) (7,12) (7,15) (7,16) (8,23) (8,18) (8,11) (8,13) (8,14) (9,10) (9,19) (9,20) (9,21) (9,22) (9,17) (9,12) (9,15) (9,16) (10,19) (10,20) (10,21) (10,22) (10,17) (10,12) (10,15) (10,16) (11,23) (11,18) (11,13) (11,14) (12,19) (12,20) (12,21) (12,22) (12,17) (12,15) (12,16) (13,23) (13,18) (13,14) (14,23) (14,18) (15,19) (15,20) (15,21) (15,22) (15,17) (15,16) (16,19) (16,20) (16,21) (16,22) (16,17) (17,19) (17,20) (17,21) (17,22) (18,23) (19,20) (19,21) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 21 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph171-10_6", + "image": "data/connectivity/graph_visual/medium/graph171.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,10) (0,7) (0,15) (0,17) (0,6) (1,12) (1,3) (1,4) (1,14) (1,16) (2,8) (2,5) (2,4) (2,9) (2,14) (2,16) (3,12) (3,11) (3,8) (3,4) (3,9) (3,14) (3,16) (4,12) (4,11) (4,8) (4,5) (4,14) (4,16) (5,12) (5,8) (5,9) (5,14) (5,16) (6,10) (6,13) (6,7) (6,15) (6,17) (7,10) (7,13) (7,15) (7,17) (8,11) (8,9) (9,14) (9,16) (10,15) (10,17) (11,12) (11,14) (12,14) (12,16) (13,15) (13,17) (15,17)\nIs there a path between node 10 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph182-15_9", + "image": "data/connectivity/graph_visual/medium/graph182.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,15) (0,9) (0,4) (0,14) (0,6) (0,10) (0,12) (0,2) (1,13) (1,11) (1,3) (1,5) (1,7) (1,16) (1,8) (1,17) (2,15) (2,9) (2,4) (2,14) (2,6) (2,10) (2,12) (3,13) (3,11) (3,5) (3,7) (3,16) (3,8) (3,17) (4,15) (4,9) (4,14) (4,6) (4,10) (4,12) (5,13) (5,11) (5,7) (5,16) (5,8) (5,17) (6,15) (6,9) (6,14) (6,10) (6,12) (7,13) (7,11) (7,16) (7,8) (7,17) (8,13) (8,11) (8,16) (8,17) (9,15) (9,14) (9,10) (9,12) (10,15) (10,14) (10,12) (11,13) (11,16) (11,17) (12,15) (12,14) (13,16) (13,17) (14,15) (16,17)\nIs there a path between node 15 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph279-7_13", + "image": "data/connectivity/graph_visual/medium/graph279.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,2) (0,14) (0,16) (0,7) (0,10) (1,12) (1,11) (1,13) (1,8) (1,17) (1,4) (2,19) (2,14) (2,16) (2,7) (2,10) (3,5) (3,15) (3,18) (3,6) (3,9) (4,12) (4,11) (4,13) (4,8) (4,17) (5,15) (5,18) (5,6) (5,9) (6,15) (6,18) (6,9) (7,19) (7,14) (7,16) (7,10) (8,12) (8,11) (8,13) (8,17) (9,15) (9,18) (10,19) (10,14) (10,16) (11,12) (11,13) (11,17) (12,13) (12,17) (13,17) (14,19) (14,16) (15,18) (16,19)\nIs there a path between node 7 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph43-3_6", + "image": "data/connectivity/graph_visual/medium/graph43.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,11) (0,3) (0,10) (1,4) (1,9) (1,6) (2,10) (3,5) (3,10) (4,7) (4,9) (4,6) (4,12) (5,10) (6,7) (6,12) (7,9) (8,9) (8,12) (9,12) (10,11)\nIs there a path between node 3 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph61-4_3", + "image": "data/connectivity/graph_visual/medium/graph61.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,11) (0,9) (0,10) (0,6) (1,7) (2,11) (2,10) (3,5) (3,13) (3,7) (4,7) (5,13) (6,11) (6,9) (6,12) (7,8) (7,13) (8,13) (9,10) (9,12) (10,11) (10,12) (11,12)\nIs there a path between node 4 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph537-3_18", + "image": "data/connectivity/graph_visual/medium/graph537.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (0,16) (1,12) (1,10) (1,7) (1,6) (1,22) (1,13) (1,9) (1,2) (1,19) (1,14) (1,11) (1,21) (1,15) (1,5) (1,20) (1,4) (1,8) (1,17) (1,3) (2,12) (2,10) (2,7) (2,6) (2,22) (2,13) (2,9) (2,19) (2,14) (2,11) (2,21) (2,15) (2,5) (2,20) (2,4) (2,8) (2,17) (2,3) (3,12) (3,10) (3,7) (3,6) (3,22) (3,13) (3,9) (3,19) (3,14) (3,11) (3,21) (3,15) (3,5) (3,20) (3,4) (3,8) (3,17) (4,12) (4,10) (4,7) (4,6) (4,22) (4,13) (4,9) (4,19) (4,14) (4,11) (4,21) (4,15) (4,5) (4,20) (4,8) (4,17) (5,12) (5,10) (5,7) (5,6) (5,22) (5,13) (5,9) (5,19) (5,14) (5,11) (5,21) (5,15) (5,20) (5,8) (5,17) (6,12) (6,10) (6,7) (6,22) (6,13) (6,9) (6,19) (6,14) (6,11) (6,21) (6,15) (6,20) (6,8) (6,17) (7,12) (7,10) (7,22) (7,13) (7,9) (7,19) (7,14) (7,11) (7,21) (7,15) (7,20) (7,8) (7,17) (8,12) (8,10) (8,22) (8,13) (8,9) (8,19) (8,14) (8,11) (8,21) (8,15) (8,20) (8,17) (9,12) (9,10) (9,22) (9,13) (9,19) (9,14) (9,11) (9,21) (9,15) (9,20) (9,17) (10,12) (10,22) (10,13) (10,19) (10,14) (10,11) (10,21) (10,15) (10,20) (10,17) (11,12) (11,22) (11,13) (11,19) (11,14) (11,21) (11,15) (11,20) (11,17) (12,22) (12,13) (12,19) (12,14) (12,21) (12,15) (12,20) (12,17) (13,22) (13,19) (13,14) (13,21) (13,15) (13,20) (13,17) (14,22) (14,19) (14,21) (14,15) (14,20) (14,17) (15,22) (15,19) (15,21) (15,20) (15,17) (16,18) (17,22) (17,19) (17,21) (17,20) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 3 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph757-0_19", + "image": "data/connectivity/graph_visual/medium/graph757.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,5) (0,22) (0,20) (0,1) (0,7) (0,9) (0,23) (0,4) (0,8) (0,17) (0,6) (0,21) (0,12) (0,3) (0,16) (0,18) (1,5) (1,20) (1,13) (1,7) (1,9) (1,23) (1,14) (1,4) (1,8) (1,6) (1,21) (1,12) (1,3) (1,24) (1,16) (1,2) (1,11) (2,5) (2,20) (2,13) (2,9) (2,23) (2,14) (2,8) (2,21) (2,12) (2,3) (2,11) (2,18) (3,5) (3,22) (3,20) (3,13) (3,9) (3,14) (3,4) (3,8) (3,6) (3,24) (3,16) (3,11) (3,18) (4,5) (4,22) (4,20) (4,7) (4,9) (4,23) (4,14) (4,17) (4,21) (4,12) (4,24) (5,22) (5,20) (5,7) (5,23) (5,14) (5,8) (5,17) (5,12) (5,16) (5,11) (5,18) (6,20) (6,13) (6,7) (6,23) (6,14) (6,17) (6,24) (6,16) (6,11) (6,18) (7,22) (7,13) (7,23) (7,14) (7,8) (7,17) (7,12) (7,24) (7,16) (7,11) (7,18) (8,14) (8,12) (8,24) (8,16) (8,11) (8,18) (9,22) (9,20) (9,13) (9,23) (9,14) (9,17) (9,21) (9,12) (9,16) (9,11) (9,18) (10,15) (10,19) (11,22) (11,13) (11,23) (11,17) (11,12) (11,16) (12,22) (12,20) (12,14) (12,17) (12,21) (12,24) (12,16) (12,18) (13,22) (13,23) (13,14) (13,17) (13,21) (13,24) (13,16) (13,18) (14,20) (14,23) (14,24) (14,18) (15,19) (16,22) (16,20) (16,23) (16,24) (16,18) (17,22) (17,20) (17,23) (17,21) (17,24) (18,22) (18,20) (18,23) (18,21) (18,24) (20,22) (20,23) (20,24) (21,22) (21,23) (21,24)\nIs there a path between node 0 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph264-15_10", + "image": "data/connectivity/graph_visual/medium/graph264.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,7) (0,18) (0,16) (1,4) (1,2) (1,13) (1,11) (1,7) (2,19) (2,15) (2,3) (2,7) (2,18) (3,19) (3,17) (3,13) (3,14) (3,18) (3,16) (4,17) (4,11) (4,5) (5,17) (5,15) (5,13) (5,14) (5,11) (5,7) (5,18) (5,12) (5,16) (6,10) (7,19) (7,8) (7,14) (7,12) (8,17) (8,13) (8,14) (8,12) (11,18) (11,12) (12,13) (13,19) (13,15) (13,14) (13,18) (15,17) (16,19) (16,18) (17,19) (18,19)\nIs there a path between node 15 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph20-7_8", + "image": "data/connectivity/graph_visual/medium/graph20.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,4) (1,8) (1,2) (3,4) (4,7) (6,11) (7,10) (7,9) (8,10) (9,10)\nIs there a path between node 7 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph45-6_8", + "image": "data/connectivity/graph_visual/medium/graph45.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,6) (0,1) (0,8) (0,12) (0,9) (0,3) (1,8) (1,12) (1,9) (1,3) (1,11) (1,4) (2,7) (3,8) (3,12) (3,9) (4,6) (4,8) (4,11) (5,7) (5,10) (6,8) (6,12) (6,9) (6,11) (7,10) (8,11) (9,12) (9,11) (11,12)\nIs there a path between node 6 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph504-9_3", + "image": "data/connectivity/graph_visual/medium/graph504.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,3) (0,20) (0,18) (0,14) (0,10) (0,11) (1,16) (1,2) (1,18) (1,13) (1,4) (1,8) (2,11) (2,8) (2,12) (3,16) (3,14) (3,9) (3,10) (3,12) (4,20) (4,6) (4,8) (6,20) (6,14) (6,11) (6,12) (7,21) (7,13) (7,12) (8,21) (8,10) (8,11) (9,16) (9,20) (9,10) (10,15) (10,14) (10,17) (10,12) (11,16) (11,20) (11,21) (11,13) (12,14) (14,21) (14,17) (15,20) (15,17) (17,20) (18,21)\nIs there a path between node 9 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph344-0_13", + "image": "data/connectivity/graph_visual/medium/graph344.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,14) (0,8) (0,2) (0,1) (0,18) (0,4) (0,5) (0,16) (0,10) (0,19) (0,6) (0,7) (1,14) (1,8) (1,2) (1,18) (1,4) (1,5) (1,16) (1,10) (1,19) (1,6) (1,7) (2,14) (2,8) (2,18) (2,4) (2,5) (2,16) (2,10) (2,19) (2,6) (2,7) (3,17) (3,11) (3,9) (3,15) (3,20) (3,12) (3,13) (4,14) (4,8) (4,18) (4,5) (4,16) (4,10) (4,19) (4,6) (4,7) (5,14) (5,8) (5,18) (5,16) (5,10) (5,19) (5,6) (5,7) (6,14) (6,8) (6,18) (6,16) (6,10) (6,19) (6,7) (7,14) (7,8) (7,18) (7,16) (7,10) (7,19) (8,14) (8,18) (8,16) (8,10) (8,19) (9,17) (9,11) (9,15) (9,20) (9,12) (9,13) (10,14) (10,18) (10,16) (10,19) (11,17) (11,15) (11,20) (11,12) (11,13) (12,17) (12,15) (12,20) (12,13) (13,17) (13,15) (13,20) (14,18) (14,16) (14,19) (15,17) (15,20) (16,18) (16,19) (17,20) (18,19)\nIs there a path between node 0 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph461-6_4", + "image": "data/connectivity/graph_visual/medium/graph461.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,11) (0,17) (0,16) (0,3) (0,9) (0,15) (0,12) (0,1) (0,20) (0,19) (0,6) (0,21) (0,7) (0,8) (0,14) (0,5) (0,2) (1,18) (1,11) (1,17) (1,16) (1,3) (1,9) (1,15) (1,12) (1,20) (1,19) (1,6) (1,21) (1,7) (1,8) (1,14) (1,5) (1,2) (2,18) (2,11) (2,17) (2,16) (2,3) (2,9) (2,15) (2,12) (2,20) (2,19) (2,6) (2,21) (2,7) (2,8) (2,14) (2,5) (3,18) (3,11) (3,17) (3,16) (3,9) (3,15) (3,12) (3,20) (3,19) (3,6) (3,21) (3,7) (3,8) (3,14) (3,5) (5,18) (5,11) (5,17) (5,16) (5,9) (5,15) (5,12) (5,20) (5,19) (5,6) (5,21) (5,7) (5,8) (5,14) (6,18) (6,11) (6,17) (6,16) (6,9) (6,15) (6,12) (6,20) (6,19) (6,21) (6,7) (6,8) (6,14) (7,18) (7,11) (7,17) (7,16) (7,9) (7,15) (7,12) (7,20) (7,19) (7,21) (7,8) (7,14) (8,18) (8,11) (8,17) (8,16) (8,9) (8,15) (8,12) (8,20) (8,19) (8,21) (8,14) (9,18) (9,11) (9,17) (9,16) (9,15) (9,12) (9,20) (9,19) (9,21) (9,14) (10,13) (11,18) (11,17) (11,16) (11,15) (11,12) (11,20) (11,19) (11,21) (11,14) (12,18) (12,17) (12,16) (12,15) (12,20) (12,19) (12,21) (12,14) (14,18) (14,17) (14,16) (14,15) (14,20) (14,19) (14,21) (15,18) (15,17) (15,16) (15,20) (15,19) (15,21) (16,18) (16,17) (16,20) (16,19) (16,21) (17,18) (17,20) (17,19) (17,21) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 6 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph831-14_8", + "image": "data/connectivity/graph_visual/medium/graph831.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (1,14) (1,20) (2,3) (2,17) (2,18) (2,9) (2,23) (2,6) (2,21) (2,11) (3,24) (3,13) (3,18) (3,9) (3,23) (3,21) (3,16) (3,10) (3,8) (4,12) (4,7) (4,22) (4,20) (4,5) (5,14) (5,12) (5,7) (5,22) (5,20) (6,13) (6,17) (6,15) (6,21) (6,11) (6,10) (6,8) (7,14) (7,12) (7,22) (8,24) (8,13) (8,15) (8,18) (8,23) (8,11) (8,16) (8,10) (9,24) (9,15) (9,23) (9,11) (9,16) (9,10) (10,24) (10,13) (10,17) (10,15) (10,18) (10,23) (10,11) (10,16) (11,24) (11,13) (11,18) (11,23) (11,21) (12,22) (12,20) (13,24) (13,17) (13,18) (13,23) (13,21) (13,16) (14,20) (15,24) (15,17) (15,18) (15,21) (16,24) (16,17) (16,23) (17,24) (17,18) (17,23) (18,24) (20,22) (21,24) (21,23) (23,24)\nIs there a path between node 14 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph83-4_2", + "image": "data/connectivity/graph_visual/medium/graph83.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,6) (0,9) (0,10) (0,2) (0,11) (0,12) (1,13) (1,5) (2,6) (2,9) (2,8) (2,7) (2,10) (2,14) (2,12) (4,6) (4,9) (4,8) (4,7) (4,10) (4,14) (4,11) (4,12) (5,13) (6,8) (6,7) (6,10) (6,14) (6,11) (6,12) (7,9) (7,10) (7,14) (8,9) (8,10) (8,11) (8,12) (9,14) (9,11) (10,11) (11,14) (12,14)\nIs there a path between node 4 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph640-14_6", + "image": "data/connectivity/graph_visual/medium/graph640.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,22) (0,16) (0,23) (1,8) (1,4) (1,22) (1,16) (1,18) (1,3) (2,19) (2,9) (2,17) (2,20) (3,14) (3,13) (3,7) (4,8) (4,12) (4,16) (4,23) (4,18) (5,10) (5,9) (5,20) (6,14) (6,13) (6,22) (6,7) (7,22) (7,18) (8,22) (8,18) (9,19) (9,11) (9,20) (9,21) (10,20) (10,21) (11,20) (12,18) (13,22) (13,16) (13,23) (13,18) (15,19) (15,17) (15,21) (16,23) (16,18) (17,19) (18,22)\nIs there a path between node 14 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph682-9_7", + "image": "data/connectivity/graph_visual/medium/graph682.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,21) (0,6) (0,16) (0,3) (0,10) (0,12) (0,22) (0,19) (0,13) (0,18) (0,17) (0,7) (0,2) (0,14) (0,5) (0,23) (1,20) (1,9) (2,8) (2,21) (2,6) (2,16) (2,3) (2,10) (2,12) (2,22) (2,19) (2,13) (2,18) (2,17) (2,7) (2,14) (2,5) (2,23) (3,8) (3,21) (3,6) (3,16) (3,10) (3,12) (3,22) (3,19) (3,13) (3,18) (3,17) (3,7) (3,14) (3,5) (3,23) (4,15) (4,11) (5,8) (5,21) (5,6) (5,16) (5,10) (5,12) (5,22) (5,19) (5,13) (5,18) (5,17) (5,7) (5,14) (5,23) (6,8) (6,21) (6,16) (6,10) (6,12) (6,22) (6,19) (6,13) (6,18) (6,17) (6,7) (6,14) (6,23) (7,8) (7,21) (7,16) (7,10) (7,12) (7,22) (7,19) (7,13) (7,18) (7,17) (7,14) (7,23) (8,21) (8,16) (8,10) (8,12) (8,22) (8,19) (8,13) (8,18) (8,17) (8,14) (8,23) (9,20) (10,21) (10,16) (10,12) (10,22) (10,19) (10,13) (10,18) (10,17) (10,14) (10,23) (11,15) (12,21) (12,16) (12,22) (12,19) (12,13) (12,18) (12,17) (12,14) (12,23) (13,21) (13,16) (13,22) (13,19) (13,18) (13,17) (13,14) (13,23) (14,21) (14,16) (14,22) (14,19) (14,18) (14,17) (14,23) (16,21) (16,22) (16,19) (16,18) (16,17) (16,23) (17,21) (17,22) (17,19) (17,18) (17,23) (18,21) (18,22) (18,19) (18,23) (19,21) (19,22) (19,23) (21,22) (21,23) (22,23)\nIs there a path between node 9 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph131-1_0", + "image": "data/connectivity/graph_visual/medium/graph131.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,5) (0,12) (0,10) (0,9) (0,6) (0,7) (0,15) (0,4) (0,2) (0,13) (0,8) (0,16) (1,14) (1,11) (1,3) (2,5) (2,12) (2,10) (2,9) (2,6) (2,7) (2,15) (2,4) (2,13) (2,8) (2,16) (3,14) (3,11) (4,5) (4,12) (4,10) (4,9) (4,6) (4,7) (4,15) (4,13) (4,8) (4,16) (5,12) (5,10) (5,9) (5,6) (5,7) (5,15) (5,13) (5,8) (5,16) (6,12) (6,10) (6,9) (6,7) (6,15) (6,13) (6,8) (6,16) (7,12) (7,10) (7,9) (7,15) (7,13) (7,8) (7,16) (8,12) (8,10) (8,9) (8,15) (8,13) (8,16) (9,12) (9,10) (9,15) (9,13) (9,16) (10,12) (10,15) (10,13) (10,16) (11,14) (12,15) (12,13) (12,16) (13,15) (13,16) (15,16)\nIs there a path between node 1 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph166-4_13", + "image": "data/connectivity/graph_visual/medium/graph166.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,7) (1,11) (1,16) (1,2) (1,9) (1,4) (2,10) (2,7) (2,11) (2,5) (3,12) (3,5) (3,16) (3,8) (4,16) (4,17) (5,13) (5,15) (5,11) (5,16) (5,6) (5,17) (6,9) (7,10) (7,11) (8,11) (8,9) (9,15) (9,11) (9,17) (10,11) (10,12) (11,15) (12,16) (13,15) (13,16) (15,17) (16,17)\nIs there a path between node 4 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph736-8_24", + "image": "data/connectivity/graph_visual/medium/graph736.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,9) (2,24) (2,5) (2,21) (2,19) (2,23) (2,4) (3,17) (3,7) (4,14) (4,5) (4,21) (4,15) (4,23) (5,10) (5,24) (5,6) (5,15) (6,15) (6,23) (7,16) (8,11) (8,13) (10,14) (11,22) (11,12) (13,22) (13,18) (13,20) (14,15) (14,23) (15,24) (15,21) (16,17) (18,20)\nIs there a path between node 8 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph152-3_4", + "image": "data/connectivity/graph_visual/medium/graph152.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,11) (1,13) (1,16) (1,8) (1,5) (1,4) (1,9) (1,3) (1,15) (1,17) (1,7) (1,6) (1,14) (1,2) (2,13) (2,16) (2,8) (2,5) (2,4) (2,9) (2,3) (2,15) (2,17) (2,7) (2,6) (2,14) (3,13) (3,16) (3,8) (3,5) (3,4) (3,9) (3,15) (3,17) (3,7) (3,6) (3,14) (4,13) (4,16) (4,8) (4,5) (4,9) (4,15) (4,17) (4,7) (4,6) (4,14) (5,13) (5,16) (5,8) (5,9) (5,15) (5,17) (5,7) (5,6) (5,14) (6,13) (6,16) (6,8) (6,9) (6,15) (6,17) (6,7) (6,14) (7,13) (7,16) (7,8) (7,9) (7,15) (7,17) (7,14) (8,13) (8,16) (8,9) (8,15) (8,17) (8,14) (9,13) (9,16) (9,15) (9,17) (9,14) (11,12) (13,16) (13,15) (13,17) (13,14) (14,16) (14,15) (14,17) (15,16) (15,17) (16,17)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph491-2_19", + "image": "data/connectivity/graph_visual/medium/graph491.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,2) (0,22) (0,9) (0,7) (0,21) (0,15) (0,6) (0,18) (0,16) (0,1) (0,17) (0,19) (0,13) (0,4) (0,5) (0,14) (0,20) (1,10) (1,2) (1,22) (1,9) (1,7) (1,21) (1,15) (1,6) (1,18) (1,16) (1,17) (1,19) (1,13) (1,4) (1,5) (1,14) (1,20) (2,10) (2,22) (2,9) (2,7) (2,21) (2,15) (2,6) (2,18) (2,16) (2,17) (2,19) (2,13) (2,4) (2,5) (2,14) (2,20) (3,11) (3,8) (3,12) (4,10) (4,22) (4,9) (4,7) (4,21) (4,15) (4,6) (4,18) (4,16) (4,17) (4,19) (4,13) (4,5) (4,14) (4,20) (5,10) (5,22) (5,9) (5,7) (5,21) (5,15) (5,6) (5,18) (5,16) (5,17) (5,19) (5,13) (5,14) (5,20) (6,10) (6,22) (6,9) (6,7) (6,21) (6,15) (6,18) (6,16) (6,17) (6,19) (6,13) (6,14) (6,20) (7,10) (7,22) (7,9) (7,21) (7,15) (7,18) (7,16) (7,17) (7,19) (7,13) (7,14) (7,20) (8,11) (8,12) (9,10) (9,22) (9,21) (9,15) (9,18) (9,16) (9,17) (9,19) (9,13) (9,14) (9,20) (10,22) (10,21) (10,15) (10,18) (10,16) (10,17) (10,19) (10,13) (10,14) (10,20) (11,12) (13,22) (13,21) (13,15) (13,18) (13,16) (13,17) (13,19) (13,14) (13,20) (14,22) (14,21) (14,15) (14,18) (14,16) (14,17) (14,19) (14,20) (15,22) (15,21) (15,18) (15,16) (15,17) (15,19) (15,20) (16,22) (16,21) (16,18) (16,17) (16,19) (16,20) (17,22) (17,21) (17,18) (17,19) (17,20) (18,22) (18,21) (18,19) (18,20) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 2 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph845-11_15", + "image": "data/connectivity/graph_visual/medium/graph845.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,3) (0,7) (0,16) (0,8) (0,11) (0,12) (0,19) (0,10) (0,1) (0,5) (0,21) (0,2) (0,13) (0,17) (1,24) (1,3) (1,7) (1,16) (1,8) (1,11) (1,12) (1,19) (1,10) (1,5) (1,21) (1,2) (1,13) (1,17) (2,24) (2,3) (2,7) (2,16) (2,8) (2,11) (2,12) (2,19) (2,10) (2,5) (2,21) (2,13) (2,17) (3,24) (3,7) (3,16) (3,8) (3,11) (3,12) (3,19) (3,10) (3,5) (3,21) (3,13) (3,17) (4,22) (4,20) (4,6) (4,18) (4,15) (4,23) (5,24) (5,7) (5,16) (5,8) (5,11) (5,12) (5,19) (5,10) (5,21) (5,13) (5,17) (6,22) (6,20) (6,18) (6,15) (6,23) (7,24) (7,16) (7,8) (7,11) (7,12) (7,19) (7,10) (7,21) (7,13) (7,17) (8,24) (8,16) (8,11) (8,12) (8,19) (8,10) (8,21) (8,13) (8,17) (9,14) (10,24) (10,16) (10,11) (10,12) (10,19) (10,21) (10,13) (10,17) (11,24) (11,16) (11,12) (11,19) (11,21) (11,13) (11,17) (12,24) (12,16) (12,19) (12,21) (12,13) (12,17) (13,24) (13,16) (13,19) (13,21) (13,17) (15,22) (15,20) (15,18) (15,23) (16,24) (16,19) (16,21) (16,17) (17,24) (17,19) (17,21) (18,22) (18,20) (18,23) (19,24) (19,21) (20,22) (20,23) (21,24) (22,23)\nIs there a path between node 11 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph462-6_4", + "image": "data/connectivity/graph_visual/medium/graph462.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,20) (0,6) (0,10) (0,15) (0,5) (0,1) (0,19) (1,20) (1,6) (1,10) (1,15) (1,5) (1,19) (2,13) (2,8) (2,21) (2,18) (2,7) (3,14) (3,12) (3,4) (3,11) (3,9) (3,16) (3,17) (4,14) (4,12) (4,11) (4,9) (4,16) (4,17) (5,20) (5,6) (5,10) (5,15) (5,19) (6,20) (6,10) (6,15) (6,19) (7,13) (7,8) (7,21) (7,18) (8,13) (8,21) (8,18) (9,14) (9,12) (9,11) (9,16) (9,17) (10,20) (10,15) (10,19) (11,14) (11,12) (11,16) (11,17) (12,14) (12,16) (12,17) (13,21) (13,18) (14,16) (14,17) (15,20) (15,19) (16,17) (18,21) (19,20)\nIs there a path between node 6 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph157-14_2", + "image": "data/connectivity/graph_visual/medium/graph157.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,6) (0,16) (0,3) (1,9) (2,10) (2,12) (2,3) (3,10) (3,12) (5,6) (6,8) (7,8) (8,10) (9,15) (9,13) (13,14)\nIs there a path between node 14 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph197-11_3", + "image": "data/connectivity/graph_visual/medium/graph197.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,3) (0,18) (0,12) (0,2) (0,11) (0,8) (0,13) (1,4) (1,10) (1,17) (1,5) (1,14) (1,7) (1,6) (1,15) (2,3) (2,18) (2,12) (2,11) (2,8) (2,13) (3,18) (3,12) (3,11) (3,8) (3,13) (4,10) (4,17) (4,5) (4,14) (4,7) (4,6) (4,15) (5,10) (5,17) (5,14) (5,7) (5,6) (5,15) (6,10) (6,17) (6,14) (6,7) (6,15) (7,10) (7,17) (7,14) (7,15) (8,18) (8,12) (8,11) (8,13) (9,16) (10,17) (10,14) (10,15) (11,18) (11,12) (11,13) (12,18) (12,13) (13,18) (14,17) (14,15) (15,17)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph837-2_24", + "image": "data/connectivity/graph_visual/medium/graph837.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,24) (0,6) (1,2) (1,21) (1,9) (1,8) (1,17) (1,5) (1,3) (1,11) (1,4) (1,15) (2,21) (2,9) (2,8) (2,17) (2,5) (2,3) (2,11) (2,4) (2,15) (3,21) (3,9) (3,8) (3,17) (3,5) (3,11) (3,4) (3,15) (4,21) (4,9) (4,8) (4,17) (4,5) (4,11) (4,15) (5,21) (5,9) (5,8) (5,17) (5,11) (5,15) (6,10) (6,24) (7,12) (7,18) (7,16) (7,23) (7,13) (7,20) (7,22) (7,14) (7,19) (8,21) (8,9) (8,17) (8,11) (8,15) (9,21) (9,17) (9,11) (9,15) (10,24) (11,21) (11,17) (11,15) (12,18) (12,16) (12,23) (12,13) (12,20) (12,22) (12,14) (12,19) (13,18) (13,16) (13,23) (13,20) (13,22) (13,14) (13,19) (14,18) (14,16) (14,23) (14,20) (14,22) (14,19) (15,21) (15,17) (16,18) (16,23) (16,20) (16,22) (16,19) (17,21) (18,23) (18,20) (18,22) (18,19) (19,23) (19,20) (19,22) (20,23) (20,22) (22,23)\nIs there a path between node 2 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph749-14_18", + "image": "data/connectivity/graph_visual/medium/graph749.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,24) (0,22) (0,18) (0,2) (0,6) (0,23) (0,12) (0,15) (0,19) (0,16) (0,10) (0,8) (0,20) (1,5) (1,22) (1,23) (1,9) (1,12) (1,15) (1,16) (1,8) (1,20) (2,24) (2,5) (2,22) (2,18) (2,6) (2,23) (2,9) (2,3) (2,15) (2,19) (2,16) (2,10) (2,8) (2,20) (3,24) (3,5) (3,22) (3,18) (3,6) (3,9) (3,15) (3,10) (3,17) (3,20) (4,13) (4,7) (4,14) (5,11) (5,24) (5,23) (5,12) (5,15) (5,19) (5,10) (5,8) (5,17) (6,11) (6,24) (6,22) (6,18) (6,23) (6,9) (6,19) (6,10) (6,8) (6,17) (6,20) (7,13) (8,11) (8,24) (8,22) (8,18) (8,12) (8,15) (8,17) (8,20) (9,11) (9,24) (9,23) (9,15) (9,19) (9,10) (9,17) (9,20) (10,24) (10,22) (10,18) (10,23) (10,19) (10,16) (10,20) (11,24) (11,22) (11,18) (11,12) (11,19) (11,16) (11,17) (11,20) (12,18) (12,23) (12,19) (12,16) (12,20) (13,14) (15,22) (15,16) (15,17) (15,20) (16,24) (16,22) (16,18) (16,23) (16,19) (16,20) (17,24) (17,18) (17,23) (17,20) (18,22) (18,19) (18,20) (19,24) (19,23) (20,22) (20,23) (22,24) (23,24)\nIs there a path between node 14 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph246-16_5", + "image": "data/connectivity/graph_visual/medium/graph246.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,7) (0,16) (0,1) (0,13) (0,9) (0,12) (0,4) (0,14) (0,10) (0,18) (0,15) (0,6) (1,8) (1,7) (1,16) (1,13) (1,9) (1,12) (1,4) (1,14) (1,10) (1,18) (1,15) (1,6) (2,5) (3,17) (3,11) (4,8) (4,7) (4,16) (4,13) (4,9) (4,12) (4,14) (4,10) (4,18) (4,15) (4,6) (6,8) (6,7) (6,16) (6,13) (6,9) (6,12) (6,14) (6,10) (6,18) (6,15) (7,8) (7,16) (7,13) (7,9) (7,12) (7,14) (7,10) (7,18) (7,15) (8,16) (8,13) (8,9) (8,12) (8,14) (8,10) (8,18) (8,15) (9,16) (9,13) (9,12) (9,14) (9,10) (9,18) (9,15) (10,16) (10,13) (10,12) (10,14) (10,18) (10,15) (11,17) (12,16) (12,13) (12,14) (12,18) (12,15) (13,16) (13,14) (13,18) (13,15) (14,16) (14,18) (14,15) (15,16) (15,18) (16,18)\nIs there a path between node 16 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph91-8_9", + "image": "data/connectivity/graph_visual/medium/graph91.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,15) (1,14) (1,3) (1,9) (1,10) (1,4) (1,7) (1,6) (1,13) (1,12) (1,11) (2,15) (3,14) (3,8) (3,9) (3,10) (3,4) (3,12) (3,11) (4,8) (4,9) (4,10) (4,7) (4,5) (4,11) (5,9) (5,7) (5,13) (5,12) (5,11) (6,14) (6,8) (6,7) (6,13) (6,11) (7,8) (7,9) (7,10) (7,11) (8,14) (8,10) (8,12) (8,11) (9,14) (9,10) (9,13) (9,12) (10,14) (10,13) (10,12) (11,14) (11,13) (11,12) (12,14)\nIs there a path between node 8 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph450-13_1", + "image": "data/connectivity/graph_visual/medium/graph450.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,10) (0,20) (0,12) (0,2) (1,13) (1,19) (1,10) (1,9) (1,7) (1,2) (2,13) (2,19) (2,10) (2,20) (2,7) (3,21) (3,8) (3,4) (3,17) (4,21) (4,8) (4,17) (5,11) (5,14) (5,16) (5,15) (6,11) (6,14) (6,16) (6,18) (6,15) (7,13) (7,19) (7,20) (8,17) (9,13) (10,19) (11,18) (12,13) (12,20) (13,19) (13,20) (14,16) (14,18) (14,15) (15,16) (17,21) (19,20)\nIs there a path between node 13 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph761-23_8", + "image": "data/connectivity/graph_visual/medium/graph761.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,16) (0,17) (0,9) (1,18) (1,8) (1,22) (1,21) (1,19) (1,6) (1,24) (1,13) (1,3) (1,7) (1,2) (1,15) (1,10) (1,11) (1,23) (2,8) (2,22) (2,21) (2,19) (2,6) (2,24) (2,13) (2,15) (2,14) (2,4) (2,12) (2,23) (3,18) (3,21) (3,24) (3,15) (3,10) (3,11) (3,14) (3,12) (3,23) (4,20) (4,8) (4,21) (4,6) (4,24) (4,13) (4,7) (4,15) (4,10) (4,11) (4,14) (4,12) (4,23) (5,16) (5,9) (6,20) (6,18) (6,8) (6,21) (6,19) (6,24) (6,13) (6,7) (6,15) (6,11) (6,14) (6,12) (6,23) (7,20) (7,18) (7,22) (7,21) (7,24) (7,13) (7,15) (7,11) (7,12) (7,23) (8,20) (8,18) (8,22) (8,21) (8,19) (8,24) (8,13) (8,15) (8,10) (8,11) (8,14) (8,23) (9,16) (9,17) (10,20) (10,18) (10,22) (10,21) (10,19) (10,13) (10,15) (10,14) (10,12) (11,20) (11,18) (11,22) (11,21) (11,19) (11,24) (11,13) (11,14) (11,12) (11,23) (12,18) (12,22) (12,21) (12,19) (12,24) (12,14) (12,23) (13,22) (13,21) (13,24) (13,15) (13,14) (13,23) (14,20) (14,18) (14,22) (14,21) (14,19) (14,23) (15,21) (16,17) (18,20) (18,21) (18,19) (18,23) (19,20) (19,24) (19,23) (20,21) (20,24) (20,23) (21,24) (21,23) (22,24) (22,23)\nIs there a path between node 23 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph59-8_2", + "image": "data/connectivity/graph_visual/medium/graph59.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,6) (0,4) (0,1) (0,11) (0,9) (0,12) (1,2) (1,4) (1,11) (1,9) (1,13) (1,8) (1,12) (2,6) (2,3) (2,4) (2,11) (2,9) (2,13) (2,8) (3,6) (3,9) (3,13) (3,8) (3,12) (4,6) (4,11) (4,9) (4,13) (4,8) (4,12) (5,7) (5,10) (6,11) (6,9) (6,8) (6,12) (8,9) (8,12) (9,11) (9,12) (11,13) (12,13)\nIs there a path between node 8 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph524-4_2", + "image": "data/connectivity/graph_visual/medium/graph524.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,16) (0,20) (0,21) (0,2) (0,14) (0,18) (0,10) (0,8) (1,16) (1,20) (1,12) (1,14) (1,18) (1,10) (2,16) (2,12) (2,21) (2,14) (2,18) (2,10) (2,8) (3,17) (3,11) (3,9) (3,22) (3,19) (3,5) (3,6) (3,4) (4,17) (4,9) (4,22) (4,5) (4,6) (4,7) (5,17) (5,13) (5,11) (6,11) (6,9) (6,7) (7,17) (7,13) (7,11) (7,9) (8,16) (8,12) (8,14) (8,18) (8,15) (8,10) (9,17) (9,13) (9,11) (9,19) (10,16) (10,20) (10,12) (10,14) (10,18) (11,17) (11,13) (11,22) (11,19) (12,16) (12,20) (12,21) (12,14) (13,17) (13,22) (14,16) (14,21) (14,18) (14,15) (15,16) (15,20) (15,21) (15,18) (16,20) (16,21) (16,18) (17,22) (17,19) (18,20) (18,21) (19,22)\nIs there a path between node 4 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph273-2_15", + "image": "data/connectivity/graph_visual/medium/graph273.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,18) (0,5) (0,19) (0,11) (0,8) (0,6) (0,14) (0,10) (1,7) (1,2) (2,7) (2,17) (3,9) (3,18) (3,13) (3,19) (3,11) (3,16) (3,8) (3,6) (3,14) (3,10) (4,9) (4,13) (4,5) (4,15) (4,19) (4,11) (4,16) (4,8) (4,6) (4,10) (5,9) (5,18) (5,13) (5,15) (5,19) (5,11) (5,8) (5,14) (5,10) (6,13) (6,12) (6,15) (6,19) (6,11) (6,16) (6,8) (6,10) (7,17) (8,9) (8,13) (8,12) (8,15) (8,14) (8,10) (9,18) (9,12) (9,19) (9,16) (9,14) (9,10) (10,18) (10,13) (10,12) (10,15) (10,19) (10,16) (10,14) (11,15) (11,19) (11,16) (12,13) (12,19) (13,15) (13,19) (13,16) (14,18) (14,16) (15,18) (15,16) (16,18) (16,19)\nIs there a path between node 2 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph841-12_11", + "image": "data/connectivity/graph_visual/medium/graph841.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,2) (0,7) (0,8) (0,4) (0,13) (1,6) (1,12) (1,14) (1,17) (1,16) (1,10) (1,18) (1,21) (1,15) (1,24) (1,11) (1,22) (1,9) (1,23) (2,20) (2,7) (2,8) (2,4) (2,13) (3,19) (3,5) (4,20) (4,7) (4,8) (4,13) (5,19) (6,12) (6,14) (6,17) (6,16) (6,10) (6,18) (6,21) (6,15) (6,24) (6,11) (6,22) (6,9) (6,23) (7,20) (7,8) (7,13) (8,20) (8,13) (9,12) (9,14) (9,17) (9,16) (9,10) (9,18) (9,21) (9,15) (9,24) (9,11) (9,22) (9,23) (10,12) (10,14) (10,17) (10,16) (10,18) (10,21) (10,15) (10,24) (10,11) (10,22) (10,23) (11,12) (11,14) (11,17) (11,16) (11,18) (11,21) (11,15) (11,24) (11,22) (11,23) (12,14) (12,17) (12,16) (12,18) (12,21) (12,15) (12,24) (12,22) (12,23) (13,20) (14,17) (14,16) (14,18) (14,21) (14,15) (14,24) (14,22) (14,23) (15,17) (15,16) (15,18) (15,21) (15,24) (15,22) (15,23) (16,17) (16,18) (16,21) (16,24) (16,22) (16,23) (17,18) (17,21) (17,24) (17,22) (17,23) (18,21) (18,24) (18,22) (18,23) (21,24) (21,22) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 12 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph190-6_11", + "image": "data/connectivity/graph_visual/medium/graph190.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,10) (0,11) (0,5) (0,8) (0,12) (0,17) (0,13) (0,16) (0,6) (0,2) (0,9) (1,10) (1,11) (1,5) (1,8) (1,12) (1,17) (1,13) (1,16) (1,6) (1,2) (1,9) (2,10) (2,11) (2,5) (2,8) (2,12) (2,17) (2,13) (2,16) (2,6) (2,9) (3,15) (3,4) (3,7) (3,14) (4,15) (4,7) (4,14) (5,10) (5,11) (5,8) (5,12) (5,17) (5,13) (5,16) (5,6) (5,9) (6,10) (6,11) (6,8) (6,12) (6,17) (6,13) (6,16) (6,9) (7,15) (7,14) (8,10) (8,11) (8,12) (8,17) (8,13) (8,16) (8,9) (9,10) (9,11) (9,12) (9,17) (9,13) (9,16) (10,11) (10,12) (10,17) (10,13) (10,16) (11,12) (11,17) (11,13) (11,16) (12,17) (12,13) (12,16) (13,17) (13,16) (14,15) (16,17)\nIs there a path between node 6 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph392-7_18", + "image": "data/connectivity/graph_visual/medium/graph392.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,12) (0,2) (0,7) (0,17) (0,10) (0,16) (0,9) (0,3) (0,13) (0,4) (0,11) (0,20) (0,15) (0,14) (0,1) (1,5) (1,12) (1,2) (1,7) (1,17) (1,10) (1,16) (1,9) (1,3) (1,13) (1,4) (1,11) (1,20) (1,15) (1,14) (2,5) (2,12) (2,7) (2,17) (2,10) (2,16) (2,9) (2,3) (2,13) (2,4) (2,11) (2,20) (2,15) (2,14) (3,5) (3,12) (3,7) (3,17) (3,10) (3,16) (3,9) (3,13) (3,4) (3,11) (3,20) (3,15) (3,14) (4,5) (4,12) (4,7) (4,17) (4,10) (4,16) (4,9) (4,13) (4,11) (4,20) (4,15) (4,14) (5,12) (5,7) (5,17) (5,10) (5,16) (5,9) (5,13) (5,11) (5,20) (5,15) (5,14) (6,18) (6,8) (6,19) (7,12) (7,17) (7,10) (7,16) (7,9) (7,13) (7,11) (7,20) (7,15) (7,14) (8,18) (8,19) (9,12) (9,17) (9,10) (9,16) (9,13) (9,11) (9,20) (9,15) (9,14) (10,12) (10,17) (10,16) (10,13) (10,11) (10,20) (10,15) (10,14) (11,12) (11,17) (11,16) (11,13) (11,20) (11,15) (11,14) (12,17) (12,16) (12,13) (12,20) (12,15) (12,14) (13,17) (13,16) (13,20) (13,15) (13,14) (14,17) (14,16) (14,20) (14,15) (15,17) (15,16) (15,20) (16,17) (16,20) (17,20) (18,19)\nIs there a path between node 7 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph158-16_6", + "image": "data/connectivity/graph_visual/medium/graph158.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,9) (1,14) (1,8) (2,11) (2,16) (2,7) (2,6) (3,17) (3,11) (3,4) (3,13) (3,6) (4,10) (5,15) (5,10) (6,17) (6,15) (7,17) (7,16) (8,9) (10,17) (10,16) (11,17) (11,15) (11,16) (12,17) (12,16) (15,17) (15,16)\nIs there a path between node 16 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph361-17_7", + "image": "data/connectivity/graph_visual/medium/graph361.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,8) (0,14) (0,2) (0,16) (1,5) (1,7) (1,18) (1,15) (1,2) (1,10) (2,19) (2,12) (3,5) (3,15) (3,4) (3,6) (4,13) (4,15) (4,8) (4,14) (4,12) (4,10) (5,13) (5,18) (5,14) (5,16) (5,10) (6,13) (6,18) (6,10) (7,15) (7,10) (8,14) (8,12) (10,19) (10,16) (12,16) (13,18) (15,19) (15,16)\nIs there a path between node 17 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph615-9_5", + "image": "data/connectivity/graph_visual/medium/graph615.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,16) (0,3) (0,11) (0,19) (0,14) (0,7) (1,20) (1,2) (1,10) (1,21) (1,15) (1,23) (1,13) (1,18) (2,20) (2,10) (2,21) (2,15) (2,23) (2,13) (2,18) (3,22) (3,16) (3,11) (3,19) (3,14) (3,7) (4,17) (5,9) (5,6) (5,8) (5,12) (6,9) (6,8) (6,12) (7,22) (7,16) (7,11) (7,19) (7,14) (8,9) (8,12) (9,12) (10,20) (10,21) (10,15) (10,23) (10,13) (10,18) (11,22) (11,16) (11,19) (11,14) (13,20) (13,21) (13,15) (13,23) (13,18) (14,22) (14,16) (14,19) (15,20) (15,21) (15,23) (15,18) (16,22) (16,19) (18,20) (18,21) (18,23) (19,22) (20,21) (20,23) (21,23)\nIs there a path between node 9 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph59-4_1", + "image": "data/connectivity/graph_visual/medium/graph59.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,6) (0,4) (0,1) (0,11) (0,9) (0,12) (1,2) (1,4) (1,11) (1,9) (1,13) (1,8) (1,12) (2,6) (2,3) (2,4) (2,11) (2,9) (2,13) (2,8) (3,6) (3,9) (3,13) (3,8) (3,12) (4,6) (4,11) (4,9) (4,13) (4,8) (4,12) (5,7) (5,10) (6,11) (6,9) (6,8) (6,12) (8,9) (8,12) (9,11) (9,12) (11,13) (12,13)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph312-19_15", + "image": "data/connectivity/graph_visual/medium/graph312.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (0,12) (0,6) (0,18) (0,16) (1,15) (1,17) (1,2) (1,19) (1,5) (1,14) (1,10) (1,13) (1,4) (1,7) (1,11) (1,9) (2,15) (2,17) (2,19) (2,5) (2,14) (2,10) (2,13) (2,4) (2,7) (2,11) (2,9) (4,15) (4,17) (4,19) (4,5) (4,14) (4,10) (4,13) (4,7) (4,11) (4,9) (5,15) (5,17) (5,19) (5,14) (5,10) (5,13) (5,7) (5,11) (5,9) (6,8) (6,12) (6,18) (6,16) (7,15) (7,17) (7,19) (7,14) (7,10) (7,13) (7,11) (7,9) (8,12) (8,18) (8,16) (9,15) (9,17) (9,19) (9,14) (9,10) (9,13) (9,11) (10,15) (10,17) (10,19) (10,14) (10,13) (10,11) (11,15) (11,17) (11,19) (11,14) (11,13) (12,18) (12,16) (13,15) (13,17) (13,19) (13,14) (14,15) (14,17) (14,19) (15,17) (15,19) (16,18) (17,19)\nIs there a path between node 19 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph519-2_3", + "image": "data/connectivity/graph_visual/medium/graph519.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,9) (0,3) (0,10) (0,14) (0,1) (1,9) (1,3) (1,10) (1,14) (1,20) (2,5) (2,13) (2,7) (2,16) (2,19) (2,21) (2,8) (2,4) (2,12) (2,18) (2,11) (2,17) (3,9) (3,10) (3,14) (3,20) (4,6) (4,5) (4,13) (4,16) (4,18) (4,11) (4,17) (5,6) (5,13) (5,7) (5,16) (5,22) (5,8) (5,12) (6,19) (6,12) (6,11) (6,17) (7,15) (7,16) (7,19) (7,22) (7,21) (7,8) (7,12) (7,11) (7,17) (8,13) (8,16) (8,22) (8,21) (9,14) (10,20) (11,15) (11,13) (11,16) (11,22) (11,21) (11,12) (11,18) (11,17) (12,15) (12,13) (12,16) (12,22) (12,21) (12,17) (13,16) (13,19) (13,22) (13,21) (13,18) (13,17) (14,20) (15,16) (15,17) (16,19) (16,22) (16,21) (16,18) (18,21) (19,21) (21,22)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph242-16_9", + "image": "data/connectivity/graph_visual/medium/graph242.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,2) (0,10) (0,14) (0,1) (0,18) (0,11) (0,9) (0,6) (0,15) (1,10) (1,11) (1,9) (1,17) (1,6) (1,15) (2,18) (2,11) (2,9) (2,17) (2,15) (3,5) (3,7) (3,12) (3,16) (4,5) (4,7) (4,8) (5,7) (5,13) (5,16) (6,10) (6,14) (6,18) (6,11) (6,15) (7,8) (7,12) (7,16) (8,13) (8,12) (8,16) (9,10) (9,14) (9,18) (9,11) (10,14) (10,18) (10,11) (10,17) (10,15) (11,14) (11,17) (11,15) (12,13) (13,16) (14,18) (14,17) (14,15) (15,17) (17,18)\nIs there a path between node 16 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph644-5_21", + "image": "data/connectivity/graph_visual/medium/graph644.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,9) (1,4) (2,16) (4,18) (4,11) (5,14) (6,8) (7,15) (7,21) (9,15) (9,19) (13,15) (13,16) (15,20) (16,20) (19,21) (19,20)\nIs there a path between node 5 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph226-18_15", + "image": "data/connectivity/graph_visual/medium/graph226.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,14) (0,18) (0,6) (0,5) (0,10) (1,2) (5,9) (5,7) (5,16) (5,10) (6,7) (6,12) (7,9) (7,17) (7,16) (8,9) (8,11) (8,10) (9,17) (10,11) (10,16) (11,14) (12,17) (12,14) (14,17) (14,18) (14,16) (14,15) (15,17) (15,18) (16,18) (17,18)\nIs there a path between node 18 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph280-7_10", + "image": "data/connectivity/graph_visual/medium/graph280.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,7) (0,14) (0,13) (0,18) (0,6) (0,19) (1,8) (1,11) (1,10) (1,15) (1,2) (1,3) (1,12) (1,5) (2,8) (2,11) (2,10) (2,15) (2,3) (2,12) (2,5) (3,8) (3,11) (3,10) (3,15) (3,12) (3,5) (4,16) (4,9) (5,8) (5,11) (5,10) (5,15) (5,12) (6,17) (6,7) (6,14) (6,13) (6,18) (6,19) (7,17) (7,14) (7,13) (7,18) (7,19) (8,11) (8,10) (8,15) (8,12) (9,16) (10,11) (10,15) (10,12) (11,15) (11,12) (12,15) (13,17) (13,14) (13,18) (13,19) (14,17) (14,18) (14,19) (17,18) (17,19) (18,19)\nIs there a path between node 7 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph661-4_8", + "image": "data/connectivity/graph_visual/medium/graph661.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,4) (1,8) (1,17) (1,20) (1,13) (1,18) (1,19) (1,2) (1,23) (1,21) (1,16) (1,7) (2,10) (2,8) (2,6) (2,15) (2,9) (2,17) (2,20) (2,13) (2,18) (2,19) (2,12) (2,21) (2,16) (3,10) (3,8) (3,6) (3,15) (3,9) (3,20) (3,13) (3,18) (3,5) (3,19) (3,12) (3,16) (3,14) (4,11) (5,8) (5,6) (5,15) (5,9) (5,17) (5,20) (5,13) (5,18) (5,19) (5,21) (5,7) (6,10) (6,8) (6,15) (6,17) (6,20) (6,13) (6,18) (6,19) (6,12) (6,21) (6,16) (6,22) (7,15) (7,9) (7,13) (7,18) (7,12) (7,23) (7,14) (7,22) (8,10) (8,20) (8,13) (8,12) (8,21) (8,16) (8,14) (8,22) (9,10) (9,15) (9,20) (9,13) (9,12) (9,16) (9,14) (9,22) (10,15) (10,17) (10,13) (10,18) (10,12) (10,16) (10,14) (10,22) (12,15) (12,17) (12,13) (12,18) (12,23) (12,21) (12,16) (12,14) (12,22) (13,17) (13,20) (13,19) (13,21) (13,14) (13,22) (14,15) (14,17) (14,18) (14,16) (14,22) (15,17) (15,19) (15,16) (15,22) (16,17) (16,20) (16,19) (16,21) (17,19) (17,23) (17,21) (17,22) (18,23) (18,21) (18,22) (19,20) (19,23) (19,21) (19,22) (20,21) (20,22) (21,23) (22,23)\nIs there a path between node 4 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph42-4_5", + "image": "data/connectivity/graph_visual/medium/graph42.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,6) (0,7) (0,10) (0,8) (0,11) (0,12) (1,3) (1,4) (1,9) (2,6) (2,7) (2,10) (2,8) (2,11) (2,12) (3,4) (3,5) (3,9) (4,5) (4,9) (5,9) (6,7) (6,10) (6,12) (7,10) (7,12) (8,10) (8,11) (8,12) (10,11) (11,12)\nIs there a path between node 4 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph848-2_1", + "image": "data/connectivity/graph_visual/medium/graph848.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,20) (0,4) (0,14) (0,8) (0,1) (0,17) (0,15) (0,21) (0,10) (0,11) (0,18) (1,7) (1,20) (1,4) (1,14) (1,8) (1,17) (1,15) (1,21) (1,10) (1,11) (1,18) (2,3) (2,24) (2,5) (2,22) (2,6) (2,13) (2,16) (2,12) (2,23) (2,19) (2,9) (3,24) (3,5) (3,22) (3,6) (3,13) (3,16) (3,12) (3,23) (3,19) (3,9) (4,7) (4,20) (4,14) (4,8) (4,17) (4,15) (4,21) (4,10) (4,11) (4,18) (5,24) (5,22) (5,6) (5,13) (5,16) (5,12) (5,23) (5,19) (5,9) (6,24) (6,22) (6,13) (6,16) (6,12) (6,23) (6,19) (6,9) (7,20) (7,14) (7,8) (7,17) (7,15) (7,21) (7,10) (7,11) (7,18) (8,20) (8,14) (8,17) (8,15) (8,21) (8,10) (8,11) (8,18) (9,24) (9,22) (9,13) (9,16) (9,12) (9,23) (9,19) (10,20) (10,14) (10,17) (10,15) (10,21) (10,11) (10,18) (11,20) (11,14) (11,17) (11,15) (11,21) (11,18) (12,24) (12,22) (12,13) (12,16) (12,23) (12,19) (13,24) (13,22) (13,16) (13,23) (13,19) (14,20) (14,17) (14,15) (14,21) (14,18) (15,20) (15,17) (15,21) (15,18) (16,24) (16,22) (16,23) (16,19) (17,20) (17,21) (17,18) (18,20) (18,21) (19,24) (19,22) (19,23) (20,21) (22,24) (22,23) (23,24)\nIs there a path between node 2 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph258-9_10", + "image": "data/connectivity/graph_visual/medium/graph258.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,2) (1,18) (1,12) (1,15) (1,7) (2,17) (2,3) (3,17) (4,12) (5,17) (5,19) (6,18) (6,10) (6,9) (6,12) (6,16) (7,18) (7,9) (7,13) (7,8) (8,14) (9,18) (9,14) (9,12) (9,13) (10,12) (10,15) (11,17) (12,16) (14,18)\nIs there a path between node 9 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph442-0_9", + "image": "data/connectivity/graph_visual/medium/graph442.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (1,11) (1,21) (1,5) (1,7) (1,17) (1,8) (2,18) (2,12) (2,19) (2,13) (2,11) (2,21) (2,9) (2,14) (2,17) (2,8) (3,10) (3,6) (5,18) (5,15) (5,12) (5,11) (5,7) (5,9) (5,14) (5,8) (6,20) (6,16) (7,18) (7,15) (7,19) (7,13) (7,9) (7,14) (7,17) (7,8) (8,15) (8,12) (8,19) (8,11) (8,21) (8,9) (8,14) (9,18) (9,15) (9,12) (9,19) (9,11) (9,14) (9,17) (10,16) (11,18) (11,15) (11,12) (11,19) (11,21) (12,18) (12,15) (12,13) (12,21) (12,17) (13,15) (13,19) (13,14) (14,18) (14,19) (14,21) (14,17) (15,18) (15,21) (15,17) (16,20) (17,18) (17,21) (18,19) (18,21) (19,21)\nIs there a path between node 0 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph689-4_6", + "image": "data/connectivity/graph_visual/medium/graph689.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,8) (0,9) (0,2) (0,10) (0,16) (0,11) (0,17) (0,1) (0,19) (0,13) (0,6) (1,3) (1,8) (1,9) (1,2) (1,10) (1,16) (1,11) (1,17) (1,19) (1,13) (1,6) (2,3) (2,8) (2,9) (2,10) (2,16) (2,11) (2,17) (2,19) (2,13) (2,6) (3,8) (3,9) (3,10) (3,16) (3,11) (3,17) (3,19) (3,13) (3,6) (4,5) (4,21) (4,22) (4,20) (4,18) (4,15) (4,12) (4,23) (4,14) (4,7) (5,21) (5,22) (5,20) (5,18) (5,15) (5,12) (5,23) (5,14) (5,7) (6,8) (6,9) (6,10) (6,16) (6,11) (6,17) (6,19) (6,13) (7,21) (7,22) (7,20) (7,18) (7,15) (7,12) (7,23) (7,14) (8,9) (8,10) (8,16) (8,11) (8,17) (8,19) (8,13) (9,10) (9,16) (9,11) (9,17) (9,19) (9,13) (10,16) (10,11) (10,17) (10,19) (10,13) (11,16) (11,17) (11,19) (11,13) (12,21) (12,22) (12,20) (12,18) (12,15) (12,23) (12,14) (13,16) (13,17) (13,19) (14,21) (14,22) (14,20) (14,18) (14,15) (14,23) (15,21) (15,22) (15,20) (15,18) (15,23) (16,17) (16,19) (17,19) (18,21) (18,22) (18,20) (18,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph104-3_9", + "image": "data/connectivity/graph_visual/medium/graph104.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,15) (0,11) (0,12) (0,14) (0,8) (0,1) (0,5) (0,3) (0,13) (1,15) (1,11) (1,12) (1,7) (1,8) (1,3) (1,13) (2,4) (2,10) (2,9) (3,15) (3,12) (3,7) (3,5) (3,13) (4,6) (5,15) (5,12) (5,14) (5,7) (5,8) (6,10) (7,15) (7,11) (7,14) (7,8) (7,13) (8,15) (8,11) (8,12) (8,14) (8,13) (11,12) (12,15) (12,14) (12,13) (13,15) (13,14) (14,15)\nIs there a path between node 3 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph366-0_13", + "image": "data/connectivity/graph_visual/medium/graph366.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,7) (0,6) (0,3) (0,18) (0,1) (0,15) (0,12) (0,14) (0,9) (0,16) (0,8) (0,2) (0,11) (0,19) (1,7) (1,6) (1,3) (1,18) (1,15) (1,9) (1,8) (1,2) (1,20) (2,7) (2,3) (2,18) (2,15) (2,12) (2,14) (2,9) (2,16) (2,8) (2,11) (2,19) (2,20) (3,18) (3,15) (3,12) (3,9) (3,16) (3,8) (3,19) (3,20) (4,13) (4,17) (5,17) (6,7) (6,18) (6,15) (6,14) (6,9) (6,16) (6,11) (6,19) (6,20) (7,15) (7,12) (7,14) (7,9) (7,16) (8,18) (8,12) (8,14) (8,9) (8,16) (8,11) (8,19) (8,20) (9,18) (9,15) (9,12) (9,11) (9,19) (9,20) (10,13) (11,18) (11,12) (11,14) (11,16) (11,19) (11,20) (12,18) (12,15) (12,14) (12,19) (12,20) (13,17) (14,19) (16,18) (16,19) (18,20)\nIs there a path between node 0 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph722-9_17", + "image": "data/connectivity/graph_visual/medium/graph722.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,1) (0,8) (0,17) (0,3) (0,9) (0,2) (0,12) (1,8) (1,17) (1,3) (1,9) (1,2) (1,12) (2,8) (2,17) (2,3) (2,9) (2,12) (3,8) (3,17) (3,9) (3,12) (4,7) (4,19) (4,22) (4,14) (4,16) (4,24) (4,6) (4,5) (5,7) (5,19) (5,22) (5,14) (5,16) (5,24) (5,6) (6,7) (6,19) (6,22) (6,14) (6,16) (6,24) (7,19) (7,22) (7,14) (7,16) (7,24) (8,17) (8,9) (8,12) (9,17) (9,12) (10,20) (10,13) (10,15) (10,11) (10,23) (10,21) (10,18) (11,20) (11,13) (11,15) (11,23) (11,21) (11,18) (12,17) (13,20) (13,15) (13,23) (13,21) (13,18) (14,19) (14,22) (14,16) (14,24) (15,20) (15,23) (15,21) (15,18) (16,19) (16,22) (16,24) (18,20) (18,23) (18,21) (19,22) (19,24) (20,23) (20,21) (21,23) (22,24)\nIs there a path between node 9 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph275-19_8", + "image": "data/connectivity/graph_visual/medium/graph275.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,7) (0,4) (0,9) (0,12) (0,11) (0,5) (1,6) (1,17) (1,8) (1,15) (1,3) (1,2) (1,18) (1,19) (1,13) (1,14) (1,10) (2,6) (2,17) (2,8) (2,15) (2,3) (2,18) (2,19) (2,13) (2,14) (2,10) (3,6) (3,17) (3,8) (3,15) (3,18) (3,19) (3,13) (3,14) (3,10) (4,7) (4,9) (4,12) (4,11) (4,5) (5,7) (5,9) (5,12) (5,11) (6,17) (6,8) (6,15) (6,18) (6,19) (6,13) (6,14) (6,10) (7,9) (7,12) (7,11) (8,17) (8,15) (8,18) (8,19) (8,13) (8,14) (8,10) (9,12) (9,11) (10,17) (10,15) (10,18) (10,19) (10,13) (10,14) (11,12) (13,17) (13,15) (13,18) (13,19) (13,14) (14,17) (14,15) (14,18) (14,19) (15,17) (15,18) (15,19) (17,18) (17,19) (18,19)\nIs there a path between node 19 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph280-4_9", + "image": "data/connectivity/graph_visual/medium/graph280.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,7) (0,14) (0,13) (0,18) (0,6) (0,19) (1,8) (1,11) (1,10) (1,15) (1,2) (1,3) (1,12) (1,5) (2,8) (2,11) (2,10) (2,15) (2,3) (2,12) (2,5) (3,8) (3,11) (3,10) (3,15) (3,12) (3,5) (4,16) (4,9) (5,8) (5,11) (5,10) (5,15) (5,12) (6,17) (6,7) (6,14) (6,13) (6,18) (6,19) (7,17) (7,14) (7,13) (7,18) (7,19) (8,11) (8,10) (8,15) (8,12) (9,16) (10,11) (10,15) (10,12) (11,15) (11,12) (12,15) (13,17) (13,14) (13,18) (13,19) (14,17) (14,18) (14,19) (17,18) (17,19) (18,19)\nIs there a path between node 4 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph435-17_18", + "image": "data/connectivity/graph_visual/medium/graph435.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,21) (0,10) (0,6) (0,17) (0,11) (1,6) (1,16) (1,4) (1,11) (1,8) (2,3) (4,21) (4,12) (4,17) (4,7) (4,11) (4,13) (5,21) (5,10) (5,16) (5,12) (5,19) (5,14) (5,9) (5,13) (5,8) (6,12) (6,19) (6,14) (6,13) (7,18) (7,12) (7,17) (7,19) (7,9) (8,12) (8,17) (8,19) (8,14) (8,11) (9,21) (9,10) (9,16) (9,17) (9,19) (9,11) (10,18) (10,21) (10,16) (11,18) (11,21) (11,19) (12,17) (13,17) (14,21) (14,19) (16,19)\nIs there a path between node 17 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph832-2_19", + "image": "data/connectivity/graph_visual/medium/graph832.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,7) (0,13) (0,24) (0,19) (0,5) (0,10) (0,4) (0,2) (0,21) (0,17) (0,23) (0,9) (0,20) (0,15) (0,22) (1,3) (1,18) (1,6) (1,14) (1,8) (1,11) (2,12) (2,7) (2,13) (2,24) (2,19) (2,5) (2,10) (2,4) (2,21) (2,17) (2,23) (2,9) (2,20) (2,15) (2,22) (3,18) (3,6) (3,14) (3,8) (3,11) (4,12) (4,7) (4,13) (4,24) (4,19) (4,5) (4,10) (4,21) (4,17) (4,23) (4,9) (4,20) (4,15) (4,22) (5,12) (5,7) (5,13) (5,24) (5,19) (5,10) (5,21) (5,17) (5,23) (5,9) (5,20) (5,15) (5,22) (6,18) (6,14) (6,8) (6,11) (7,12) (7,13) (7,24) (7,19) (7,10) (7,21) (7,17) (7,23) (7,9) (7,20) (7,15) (7,22) (8,18) (8,14) (8,11) (9,12) (9,13) (9,24) (9,19) (9,10) (9,21) (9,17) (9,23) (9,20) (9,15) (9,22) (10,12) (10,13) (10,24) (10,19) (10,21) (10,17) (10,23) (10,20) (10,15) (10,22) (11,18) (11,14) (12,13) (12,24) (12,19) (12,21) (12,17) (12,23) (12,20) (12,15) (12,22) (13,24) (13,19) (13,21) (13,17) (13,23) (13,20) (13,15) (13,22) (14,18) (15,24) (15,19) (15,21) (15,17) (15,23) (15,20) (15,22) (17,24) (17,19) (17,21) (17,23) (17,20) (17,22) (19,24) (19,21) (19,23) (19,20) (19,22) (20,24) (20,21) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nIs there a path between node 2 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph513-12_2", + "image": "data/connectivity/graph_visual/medium/graph513.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,3) (0,12) (0,7) (0,14) (0,2) (0,4) (0,19) (0,10) (0,16) (0,8) (0,6) (0,20) (0,1) (1,5) (1,21) (1,3) (1,14) (1,11) (1,2) (1,4) (1,8) (1,6) (1,20) (2,5) (2,21) (2,3) (2,12) (2,14) (2,11) (2,4) (2,19) (2,10) (2,16) (2,6) (3,5) (3,21) (3,7) (3,11) (3,4) (3,19) (3,10) (3,16) (3,8) (3,6) (3,20) (4,21) (4,7) (4,14) (4,11) (4,19) (4,10) (4,16) (4,8) (4,6) (5,21) (5,12) (5,7) (5,14) (5,11) (5,19) (5,10) (5,16) (5,8) (5,6) (5,20) (6,12) (6,7) (6,11) (6,10) (6,16) (6,8) (6,20) (7,21) (7,11) (7,10) (7,8) (7,20) (8,12) (8,14) (8,10) (8,16) (8,20) (9,13) (9,15) (9,18) (10,12) (10,14) (10,11) (10,16) (10,20) (11,12) (11,14) (11,20) (12,19) (12,16) (12,20) (13,15) (14,21) (14,16) (14,20) (16,21) (16,19) (16,20) (19,21) (19,20)\nIs there a path between node 12 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph71-9_7", + "image": "data/connectivity/graph_visual/medium/graph71.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,2) (0,5) (0,12) (0,11) (0,8) (0,1) (0,13) (0,10) (0,3) (1,2) (1,5) (1,12) (1,11) (1,8) (1,13) (1,10) (1,3) (2,5) (2,12) (2,11) (2,8) (2,13) (2,10) (2,3) (3,5) (3,12) (3,11) (3,8) (3,13) (3,10) (4,9) (4,6) (4,7) (4,14) (5,12) (5,11) (5,8) (5,13) (5,10) (6,9) (6,7) (6,14) (7,9) (7,14) (8,12) (8,11) (8,13) (8,10) (9,14) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nIs there a path between node 9 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph791-12_6", + "image": "data/connectivity/graph_visual/medium/graph791.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (1,16) (1,5) (1,10) (1,18) (2,7) (2,14) (2,11) (2,15) (3,16) (3,5) (3,12) (3,15) (3,10) (5,20) (5,24) (5,12) (5,7) (5,14) (7,20) (7,24) (7,18) (8,21) (8,23) (9,20) (9,16) (9,24) (10,20) (10,24) (10,15) (10,18) (11,16) (11,22) (12,24) (12,14) (12,15) (13,24) (13,14) (13,22) (15,18) (15,22) (16,24) (16,18) (17,19) (18,20) (19,21) (19,23) (21,23)\nIs there a path between node 12 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph237-1_6", + "image": "data/connectivity/graph_visual/medium/graph237.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,11) (0,17) (0,16) (1,2) (1,12) (1,7) (1,3) (2,15) (2,5) (2,7) (2,3) (3,15) (3,5) (3,12) (3,7) (4,8) (4,10) (4,18) (4,6) (4,11) (4,9) (4,17) (4,14) (4,16) (5,15) (5,7) (6,8) (6,10) (6,18) (6,11) (6,9) (6,17) (6,16) (7,15) (7,12) (8,11) (8,9) (8,17) (8,14) (9,18) (9,11) (10,18) (10,11) (10,14) (10,16) (11,18) (11,17) (11,16) (14,18) (14,16) (16,18) (16,17) (17,18)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph338-20_10", + "image": "data/connectivity/graph_visual/medium/graph338.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,8) (0,2) (0,7) (0,9) (0,15) (0,18) (1,8) (1,2) (1,9) (1,15) (1,18) (2,8) (2,7) (2,9) (2,18) (3,17) (3,6) (3,5) (3,16) (3,20) (4,13) (4,11) (5,17) (5,14) (5,10) (5,16) (5,20) (6,17) (6,14) (6,20) (7,8) (7,9) (7,15) (7,12) (8,9) (8,15) (8,12) (8,18) (9,15) (9,18) (10,17) (10,14) (10,16) (10,20) (11,13) (12,18) (13,19) (14,17) (15,18) (16,20)\nIs there a path between node 20 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph264-18_11", + "image": "data/connectivity/graph_visual/medium/graph264.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,7) (0,18) (0,16) (1,4) (1,2) (1,13) (1,11) (1,7) (2,19) (2,15) (2,3) (2,7) (2,18) (3,19) (3,17) (3,13) (3,14) (3,18) (3,16) (4,17) (4,11) (4,5) (5,17) (5,15) (5,13) (5,14) (5,11) (5,7) (5,18) (5,12) (5,16) (6,10) (7,19) (7,8) (7,14) (7,12) (8,17) (8,13) (8,14) (8,12) (11,18) (11,12) (12,13) (13,19) (13,15) (13,14) (13,18) (15,17) (16,19) (16,18) (17,19) (18,19)\nIs there a path between node 18 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph562-20_4", + "image": "data/connectivity/graph_visual/medium/graph562.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,5) (0,6) (0,13) (0,17) (0,23) (0,9) (0,10) (0,22) (0,2) (0,20) (0,21) (0,12) (1,14) (1,18) (1,3) (1,4) (1,11) (1,16) (1,7) (2,5) (2,13) (2,17) (2,23) (2,9) (2,10) (2,20) (2,21) (2,12) (3,18) (3,4) (3,11) (3,16) (3,7) (4,18) (4,11) (4,16) (4,8) (5,19) (5,13) (5,17) (5,23) (5,9) (5,10) (5,22) (5,15) (5,12) (6,19) (6,13) (6,23) (6,9) (6,22) (6,15) (6,20) (6,12) (7,14) (7,11) (7,16) (8,14) (8,11) (9,19) (9,13) (9,17) (9,23) (9,10) (9,15) (9,20) (9,21) (10,19) (10,13) (10,23) (10,15) (10,20) (11,18) (12,19) (12,23) (12,22) (12,15) (12,20) (12,21) (13,19) (13,23) (13,22) (13,20) (14,18) (15,19) (15,17) (15,22) (15,20) (17,23) (17,22) (17,21) (19,21) (20,23) (20,22) (21,23) (22,23)\nIs there a path between node 20 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph828-6_9", + "image": "data/connectivity/graph_visual/medium/graph828.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,6) (0,8) (0,9) (0,7) (0,20) (0,24) (0,3) (0,2) (1,15) (1,6) (1,8) (1,9) (1,7) (1,11) (1,20) (1,10) (1,24) (1,22) (1,2) (2,15) (2,6) (2,9) (2,11) (2,20) (2,5) (2,22) (2,3) (2,23) (3,15) (3,20) (3,10) (3,24) (3,22) (3,23) (4,17) (4,13) (4,16) (4,12) (4,19) (5,6) (5,8) (5,9) (5,7) (5,11) (5,10) (5,22) (5,23) (6,15) (6,8) (6,11) (6,20) (6,24) (6,22) (7,15) (7,8) (7,9) (7,11) (7,20) (7,10) (7,24) (7,22) (8,15) (8,11) (8,20) (8,10) (8,24) (8,22) (9,20) (9,10) (9,24) (9,22) (9,23) (10,15) (10,11) (10,24) (10,22) (10,23) (11,20) (11,23) (12,17) (12,13) (12,18) (12,21) (12,16) (12,14) (12,19) (13,17) (13,18) (13,21) (13,14) (13,19) (14,17) (14,18) (14,21) (14,16) (14,19) (15,20) (15,24) (15,22) (16,17) (16,18) (16,21) (18,21) (18,19) (19,21) (20,24) (20,22) (20,23) (22,24) (22,23)\nIs there a path between node 6 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph329-5_16", + "image": "data/connectivity/graph_visual/medium/graph329.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,14) (0,11) (0,7) (1,12) (1,9) (1,6) (1,20) (2,12) (2,9) (2,13) (2,14) (2,19) (2,11) (2,7) (4,5) (6,16) (6,20) (6,7) (7,12) (7,18) (7,8) (7,16) (7,10) (7,11) (8,12) (8,18) (8,16) (8,20) (8,10) (8,17) (9,18) (9,16) (9,14) (9,10) (9,19) (9,11) (10,18) (10,19) (10,17) (12,16) (13,16) (13,17) (16,18)\nIs there a path between node 5 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph466-10_17", + "image": "data/connectivity/graph_visual/medium/graph466.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,10) (0,14) (0,1) (0,11) (0,17) (0,13) (1,2) (1,10) (1,14) (1,11) (1,17) (1,13) (2,10) (2,14) (2,11) (2,17) (2,13) (3,19) (3,9) (3,12) (3,16) (3,5) (3,7) (3,18) (3,21) (4,15) (4,20) (4,6) (4,8) (5,19) (5,9) (5,12) (5,16) (5,7) (5,18) (5,21) (6,15) (6,20) (6,8) (7,19) (7,9) (7,12) (7,16) (7,18) (7,21) (8,15) (8,20) (9,19) (9,12) (9,16) (9,18) (9,21) (10,14) (10,11) (10,17) (10,13) (11,14) (11,17) (11,13) (12,19) (12,16) (12,18) (12,21) (13,14) (13,17) (14,17) (15,20) (16,19) (16,18) (16,21) (18,19) (18,21) (19,21)\nIs there a path between node 10 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph181-13_10", + "image": "data/connectivity/graph_visual/medium/graph181.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,17) (0,16) (0,5) (0,12) (0,13) (0,14) (0,7) (0,1) (1,5) (1,12) (1,9) (3,11) (3,6) (3,15) (5,17) (5,16) (5,12) (5,14) (5,7) (6,8) (7,16) (7,12) (7,14) (7,10) (7,9) (9,17) (9,16) (9,12) (9,14) (10,17) (10,16) (10,12) (10,13) (10,14) (11,15) (12,17) (12,16) (13,16) (13,14) (14,17) (14,16) (16,17)\nIs there a path between node 13 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph500-7_19", + "image": "data/connectivity/graph_visual/medium/graph500.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,12) (0,22) (0,14) (0,16) (0,19) (0,4) (0,11) (0,20) (0,13) (0,18) (0,5) (1,22) (1,15) (1,9) (2,7) (3,15) (3,16) (3,9) (3,11) (3,10) (3,5) (4,12) (4,22) (4,14) (4,15) (4,11) (4,13) (4,18) (4,6) (4,17) (5,15) (5,18) (5,6) (6,12) (6,15) (6,11) (6,20) (6,17) (8,22) (8,20) (9,14) (9,15) (9,11) (9,20) (10,19) (11,22) (11,19) (12,14) (12,16) (12,19) (12,17) (13,14) (13,15) (14,22) (14,19) (16,18) (16,17) (18,22) (18,19) (20,22)\nIs there a path between node 7 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph15-3_1", + "image": "data/connectivity/graph_visual/medium/graph15.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,4) (0,8) (1,5) (2,3) (3,5) (3,11) (4,8) (5,9) (5,7) (5,10) (6,11)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph549-8_18", + "image": "data/connectivity/graph_visual/medium/graph549.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (1,10) (2,11) (2,9) (3,21) (4,10) (4,23) (5,7) (5,9) (7,11) (7,9) (8,18) (8,17) (10,22) (13,19) (14,16) (15,19) (16,17) (17,19)\nIs there a path between node 8 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph137-7_12", + "image": "data/connectivity/graph_visual/medium/graph137.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,2) (0,13) (1,15) (1,14) (1,13) (2,5) (2,4) (4,15) (4,13) (5,14) (5,9) (5,13) (6,7) (6,12) (9,14) (10,16) (11,16) (12,17)\nIs there a path between node 7 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph168-12_0", + "image": "data/connectivity/graph_visual/medium/graph168.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,1) (0,5) (1,11) (1,6) (1,17) (1,10) (2,11) (2,17) (5,6) (5,9) (6,16) (6,8) (6,17) (6,10) (6,14) (8,10) (9,10) (10,11) (10,17) (10,15) (11,15) (14,16) (14,17)\nIs there a path between node 12 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph813-21_2", + "image": "data/connectivity/graph_visual/medium/graph813.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (1,9) (1,14) (1,11) (1,19) (1,8) (1,2) (1,15) (1,5) (1,24) (2,14) (2,22) (2,3) (2,8) (2,15) (2,18) (2,5) (2,24) (3,14) (3,11) (3,8) (3,15) (3,5) (4,16) (4,13) (4,17) (4,23) (4,10) (4,7) (5,9) (5,12) (5,22) (5,11) (5,19) (5,8) (5,15) (5,6) (6,9) (6,12) (6,22) (6,11) (6,19) (6,8) (6,15) (6,18) (6,24) (7,21) (7,16) (7,17) (7,10) (8,9) (8,14) (8,12) (8,19) (8,15) (8,18) (8,24) (9,14) (9,12) (9,22) (9,11) (9,19) (9,15) (9,18) (9,24) (10,21) (10,16) (10,13) (10,23) (11,12) (11,19) (11,15) (12,14) (12,22) (12,15) (12,18) (12,24) (13,16) (13,23) (14,22) (14,19) (14,18) (14,24) (15,22) (15,19) (15,18) (15,24) (16,21) (16,17) (17,21) (17,23) (18,22) (18,19) (18,24) (21,23) (22,24)\nIs there a path between node 21 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph336-8_11", + "image": "data/connectivity/graph_visual/medium/graph336.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,10) (0,3) (0,13) (0,7) (0,1) (0,9) (0,17) (0,15) (0,14) (0,18) (0,6) (0,12) (1,10) (1,7) (1,20) (1,11) (1,9) (1,15) (1,14) (1,18) (1,4) (1,12) (2,19) (3,16) (3,13) (3,7) (3,11) (3,17) (3,15) (3,18) (3,6) (4,16) (4,10) (4,13) (4,7) (4,20) (4,11) (4,9) (4,17) (4,14) (4,18) (4,6) (4,12) (5,8) (5,19) (6,16) (6,10) (6,13) (6,20) (6,9) (6,18) (6,12) (7,16) (7,10) (7,13) (7,20) (7,11) (7,9) (7,17) (7,15) (7,14) (7,18) (7,12) (8,19) (9,10) (9,13) (9,11) (9,17) (9,15) (9,14) (10,20) (10,17) (10,14) (11,16) (11,20) (11,17) (11,18) (12,15) (12,14) (13,16) (13,17) (13,14) (13,18) (14,16) (14,20) (14,17) (14,15) (14,18) (15,16) (15,20) (15,18) (16,20) (16,17) (16,18) (17,20) (17,18) (18,20)\nIs there a path between node 8 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph78-10_8", + "image": "data/connectivity/graph_visual/medium/graph78.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,14) (0,9) (0,13) (0,3) (0,1) (0,2) (0,7) (0,8) (0,11) (1,14) (1,13) (1,8) (1,10) (1,11) (1,5) (2,9) (2,13) (2,3) (2,7) (2,8) (2,10) (3,14) (3,9) (3,13) (3,8) (3,11) (3,5) (4,6) (4,12) (5,14) (5,9) (5,7) (5,8) (5,10) (5,11) (6,12) (7,14) (7,13) (7,8) (7,10) (8,14) (8,9) (8,10) (9,14) (9,13) (10,14) (10,13) (11,14) (13,14)\nIs there a path between node 10 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph546-20_7", + "image": "data/connectivity/graph_visual/medium/graph546.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,19) (0,17) (0,7) (0,16) (0,21) (1,22) (1,19) (1,20) (1,21) (2,23) (2,6) (3,13) (3,18) (3,4) (3,10) (3,21) (4,19) (4,10) (4,16) (5,14) (5,12) (5,9) (5,11) (6,14) (6,23) (7,15) (7,22) (7,18) (7,8) (7,17) (7,20) (8,13) (8,21) (9,12) (9,11) (10,17) (13,19) (13,17) (13,21) (15,20) (16,18) (16,20) (19,20) (19,21)\nIs there a path between node 20 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph618-23_21", + "image": "data/connectivity/graph_visual/medium/graph618.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,20) (0,21) (0,22) (0,9) (0,17) (0,12) (0,15) (0,7) (0,16) (0,6) (0,3) (0,1) (0,4) (1,10) (1,19) (1,20) (1,21) (1,22) (1,9) (1,17) (1,12) (1,15) (1,7) (1,16) (1,6) (1,3) (1,4) (2,23) (2,8) (2,5) (2,18) (2,11) (2,13) (2,14) (3,10) (3,19) (3,20) (3,21) (3,22) (3,9) (3,17) (3,12) (3,15) (3,7) (3,16) (3,6) (3,4) (4,10) (4,19) (4,20) (4,21) (4,22) (4,9) (4,17) (4,12) (4,15) (4,7) (4,16) (4,6) (5,23) (5,8) (5,18) (5,11) (5,13) (5,14) (6,10) (6,19) (6,20) (6,21) (6,22) (6,9) (6,17) (6,12) (6,15) (6,7) (6,16) (7,10) (7,19) (7,20) (7,21) (7,22) (7,9) (7,17) (7,12) (7,15) (7,16) (8,23) (8,18) (8,11) (8,13) (8,14) (9,10) (9,19) (9,20) (9,21) (9,22) (9,17) (9,12) (9,15) (9,16) (10,19) (10,20) (10,21) (10,22) (10,17) (10,12) (10,15) (10,16) (11,23) (11,18) (11,13) (11,14) (12,19) (12,20) (12,21) (12,22) (12,17) (12,15) (12,16) (13,23) (13,18) (13,14) (14,23) (14,18) (15,19) (15,20) (15,21) (15,22) (15,17) (15,16) (16,19) (16,20) (16,21) (16,22) (16,17) (17,19) (17,20) (17,21) (17,22) (18,23) (19,20) (19,21) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 23 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph400-21_4", + "image": "data/connectivity/graph_visual/medium/graph400.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,3) (0,4) (0,10) (1,18) (1,11) (1,16) (1,21) (1,10) (2,5) (2,20) (2,13) (3,11) (3,16) (3,13) (3,10) (4,20) (4,13) (4,6) (4,10) (5,11) (5,16) (5,13) (6,20) (6,16) (6,13) (6,19) (7,9) (8,17) (8,14) (10,18) (10,11) (10,16) (10,21) (11,20) (11,16) (13,21) (15,17) (16,21) (16,19) (18,20)\nIs there a path between node 21 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph762-18_0", + "image": "data/connectivity/graph_visual/medium/graph762.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,24) (0,4) (0,17) (0,22) (0,7) (0,23) (0,9) (0,8) (0,3) (0,1) (0,10) (0,19) (0,6) (1,12) (1,24) (1,4) (1,17) (1,5) (1,22) (1,16) (1,23) (1,9) (1,14) (1,3) (1,13) (1,21) (1,10) (1,19) (1,6) (2,15) (2,18) (2,11) (3,12) (3,24) (3,4) (3,17) (3,22) (3,7) (3,16) (3,20) (3,13) (3,21) (4,12) (4,24) (4,5) (4,16) (4,20) (4,23) (4,13) (4,21) (4,10) (4,19) (4,6) (5,12) (5,24) (5,17) (5,22) (5,16) (5,20) (5,23) (5,9) (5,8) (5,13) (5,10) (5,6) (6,12) (6,24) (6,17) (6,22) (6,7) (6,20) (6,23) (6,8) (6,14) (6,13) (6,21) (7,12) (7,24) (7,17) (7,16) (7,23) (7,14) (7,13) (7,21) (7,10) (7,19) (8,12) (8,24) (8,17) (8,22) (8,16) (8,20) (8,23) (8,14) (8,13) (8,21) (8,10) (9,12) (9,24) (9,17) (9,22) (9,20) (9,14) (9,13) (9,21) (9,10) (9,19) (10,17) (10,16) (10,23) (10,14) (10,13) (11,18) (12,17) (12,22) (12,16) (12,23) (12,13) (12,19) (13,24) (13,16) (13,20) (13,21) (13,19) (14,24) (14,17) (14,22) (14,16) (14,21) (16,24) (16,20) (16,23) (16,19) (17,24) (17,22) (17,20) (17,23) (17,21) (17,19) (19,24) (19,22) (19,21) (20,24) (20,22) (20,23) (20,21) (21,24) (21,23) (22,24)\nIs there a path between node 18 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph43-6_9", + "image": "data/connectivity/graph_visual/medium/graph43.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,11) (0,3) (0,10) (1,4) (1,9) (1,6) (2,10) (3,5) (3,10) (4,7) (4,9) (4,6) (4,12) (5,10) (6,7) (6,12) (7,9) (8,9) (8,12) (9,12) (10,11)\nIs there a path between node 6 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph8-5_4", + "image": "data/connectivity/graph_visual/medium/graph8.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,2) (0,8) (1,9) (1,3) (1,4) (1,7) (1,5) (1,10) (3,9) (3,7) (3,5) (3,10) (4,9) (4,6) (4,10) (5,9) (5,6) (6,9) (6,7) (6,10) (7,9) (9,10)\nIs there a path between node 5 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph633-20_17", + "image": "data/connectivity/graph_visual/medium/graph633.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,10) (1,9) (3,17) (3,8) (3,23) (4,17) (4,15) (4,22) (4,8) (4,23) (4,16) (6,11) (6,10) (7,21) (8,17) (8,23) (8,16) (10,18) (10,19) (11,18) (11,14) (15,23) (16,17) (16,23) (19,20) (21,22) (21,23)\nIs there a path between node 20 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph327-1_4", + "image": "data/connectivity/graph_visual/medium/graph327.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,4) (1,13) (2,11) (3,4) (3,6) (3,19) (4,20) (4,12) (4,16) (5,14) (5,9) (6,18) (6,8) (7,13) (7,8) (7,19) (7,15) (8,18) (8,20) (8,15) (11,14) (12,20) (12,13) (12,19) (12,16) (13,18) (13,15) (15,18) (15,19) (18,20) (18,19)\nIs there a path between node 1 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph445-12_18", + "image": "data/connectivity/graph_visual/medium/graph445.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,12) (0,21) (0,2) (0,17) (0,3) (0,7) (0,8) (0,14) (0,19) (0,13) (0,20) (1,9) (1,6) (1,18) (1,10) (1,16) (2,4) (2,12) (2,21) (2,3) (2,7) (2,8) (2,13) (3,12) (3,21) (3,17) (3,7) (3,8) (3,14) (3,19) (3,13) (3,20) (4,21) (4,17) (4,7) (4,8) (4,19) (4,13) (5,9) (5,6) (5,11) (5,18) (5,10) (6,9) (6,15) (6,11) (6,18) (6,10) (7,12) (7,17) (7,8) (7,14) (7,19) (7,20) (8,12) (8,21) (8,17) (9,15) (9,11) (9,18) (9,10) (10,15) (10,11) (10,18) (11,18) (11,16) (12,17) (12,14) (12,19) (12,13) (12,20) (13,17) (13,14) (13,19) (13,20) (14,17) (14,19) (14,20) (15,18) (15,16) (17,21) (17,20) (19,21) (19,20) (20,21)\nIs there a path between node 12 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph6-4_2", + "image": "data/connectivity/graph_visual/medium/graph6.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (0,1) (1,2) (1,8) (3,7) (5,10) (6,9)\nIs there a path between node 4 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph221-13_15", + "image": "data/connectivity/graph_visual/medium/graph221.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,11) (0,15) (1,12) (1,2) (1,8) (1,3) (1,15) (2,13) (2,3) (2,14) (2,15) (3,6) (3,12) (3,13) (3,11) (3,14) (3,9) (3,7) (4,8) (4,11) (4,14) (4,16) (5,6) (5,17) (5,15) (5,7) (6,8) (6,11) (6,17) (6,16) (7,13) (7,16) (8,12) (8,17) (8,14) (9,13) (9,15) (11,15) (12,17) (13,17) (14,16) (15,17) (16,17)\nIs there a path between node 13 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph394-15_0", + "image": "data/connectivity/graph_visual/medium/graph394.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,5) (0,6) (0,14) (0,7) (0,9) (0,19) (0,17) (0,20) (0,15) (0,11) (0,3) (0,1) (0,13) (0,16) (0,18) (0,2) (1,10) (1,5) (1,6) (1,14) (1,7) (1,9) (1,19) (1,17) (1,20) (1,15) (1,11) (1,3) (1,13) (1,16) (1,18) (1,2) (2,10) (2,5) (2,6) (2,14) (2,7) (2,9) (2,19) (2,17) (2,20) (2,15) (2,11) (2,3) (2,13) (2,16) (2,18) (3,10) (3,5) (3,6) (3,14) (3,7) (3,9) (3,19) (3,17) (3,20) (3,15) (3,11) (3,13) (3,16) (3,18) (4,12) (4,8) (5,10) (5,6) (5,14) (5,7) (5,9) (5,19) (5,17) (5,20) (5,15) (5,11) (5,13) (5,16) (5,18) (6,10) (6,14) (6,7) (6,9) (6,19) (6,17) (6,20) (6,15) (6,11) (6,13) (6,16) (6,18) (7,10) (7,14) (7,9) (7,19) (7,17) (7,20) (7,15) (7,11) (7,13) (7,16) (7,18) (8,12) (9,10) (9,14) (9,19) (9,17) (9,20) (9,15) (9,11) (9,13) (9,16) (9,18) (10,14) (10,19) (10,17) (10,20) (10,15) (10,11) (10,13) (10,16) (10,18) (11,14) (11,19) (11,17) (11,20) (11,15) (11,13) (11,16) (11,18) (13,14) (13,19) (13,17) (13,20) (13,15) (13,16) (13,18) (14,19) (14,17) (14,20) (14,15) (14,16) (14,18) (15,19) (15,17) (15,20) (15,16) (15,18) (16,19) (16,17) (16,20) (16,18) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20)\nIs there a path between node 15 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph691-9_15", + "image": "data/connectivity/graph_visual/medium/graph691.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,23) (0,3) (0,7) (0,9) (0,21) (0,13) (0,16) (0,6) (0,8) (0,12) (1,5) (1,22) (1,15) (1,14) (1,18) (1,17) (1,20) (1,11) (1,2) (2,5) (2,22) (2,15) (2,14) (2,18) (2,17) (2,20) (2,11) (3,10) (3,19) (3,23) (3,7) (3,9) (3,21) (3,13) (3,16) (3,6) (3,8) (3,12) (5,22) (5,15) (5,14) (5,18) (5,17) (5,20) (5,11) (6,10) (6,19) (6,23) (6,7) (6,9) (6,21) (6,13) (6,16) (6,8) (6,12) (7,10) (7,19) (7,23) (7,9) (7,21) (7,13) (7,16) (7,8) (7,12) (8,10) (8,19) (8,23) (8,9) (8,21) (8,13) (8,16) (8,12) (9,10) (9,19) (9,23) (9,21) (9,13) (9,16) (9,12) (10,19) (10,23) (10,21) (10,13) (10,16) (10,12) (11,22) (11,15) (11,14) (11,18) (11,17) (11,20) (12,19) (12,23) (12,21) (12,13) (12,16) (13,19) (13,23) (13,21) (13,16) (14,22) (14,15) (14,18) (14,17) (14,20) (15,22) (15,18) (15,17) (15,20) (16,19) (16,23) (16,21) (17,22) (17,18) (17,20) (18,22) (18,20) (19,23) (19,21) (20,22) (21,23)\nIs there a path between node 9 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph611-11_15", + "image": "data/connectivity/graph_visual/medium/graph611.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (0,19) (0,1) (0,14) (0,16) (0,4) (1,17) (1,19) (1,14) (1,16) (1,4) (2,11) (2,15) (3,18) (3,7) (3,9) (3,22) (3,23) (3,21) (3,10) (4,17) (4,19) (4,14) (4,16) (5,6) (5,20) (5,13) (5,8) (5,12) (6,20) (6,13) (6,8) (6,12) (7,18) (7,9) (7,22) (7,23) (7,21) (7,10) (8,20) (8,13) (8,12) (9,18) (9,22) (9,23) (9,21) (9,10) (10,18) (10,22) (10,23) (10,21) (11,15) (12,20) (12,13) (13,20) (14,17) (14,19) (14,16) (16,17) (16,19) (17,19) (18,22) (18,23) (18,21) (21,22) (21,23) (22,23)\nIs there a path between node 11 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph690-1_8", + "image": "data/connectivity/graph_visual/medium/graph690.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,11) (0,1) (0,4) (0,15) (0,10) (0,22) (0,14) (0,8) (1,21) (1,11) (1,4) (1,15) (1,10) (1,22) (1,14) (1,8) (2,3) (2,13) (2,5) (2,7) (3,13) (3,5) (3,7) (4,21) (4,11) (4,15) (4,10) (4,22) (4,14) (4,8) (5,13) (5,7) (6,20) (6,19) (6,16) (6,17) (6,9) (6,18) (6,12) (6,23) (7,13) (8,21) (8,11) (8,15) (8,10) (8,22) (8,14) (9,20) (9,19) (9,16) (9,17) (9,18) (9,12) (9,23) (10,21) (10,11) (10,15) (10,22) (10,14) (11,21) (11,15) (11,22) (11,14) (12,20) (12,19) (12,16) (12,17) (12,18) (12,23) (14,21) (14,15) (14,22) (15,21) (15,22) (16,20) (16,19) (16,17) (16,18) (16,23) (17,20) (17,19) (17,18) (17,23) (18,20) (18,19) (18,23) (19,20) (19,23) (20,23) (21,22)\nIs there a path between node 1 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph471-14_20", + "image": "data/connectivity/graph_visual/medium/graph471.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,19) (1,12) (1,19) (2,13) (3,20) (3,11) (4,7) (4,16) (4,18) (5,17) (5,7) (6,15) (6,20) (6,11) (7,20) (7,11) (8,12) (8,13) (8,19) (11,17) (11,15) (12,19) (16,17) (16,20) (17,20) (18,20)\nIs there a path between node 14 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph315-17_14", + "image": "data/connectivity/graph_visual/medium/graph315.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,16) (0,8) (0,12) (0,9) (0,4) (0,6) (0,11) (1,19) (1,15) (2,7) (2,10) (2,13) (2,3) (2,5) (2,18) (2,17) (2,14) (3,7) (3,10) (3,13) (3,5) (3,18) (3,17) (3,14) (4,16) (4,8) (4,12) (4,9) (4,6) (4,11) (5,7) (5,10) (5,13) (5,18) (5,17) (5,14) (6,16) (6,8) (6,12) (6,9) (6,11) (7,10) (7,13) (7,18) (7,17) (7,14) (8,16) (8,12) (8,9) (8,11) (9,16) (9,12) (9,11) (10,13) (10,18) (10,17) (10,14) (11,16) (11,12) (12,16) (13,18) (13,17) (13,14) (14,18) (14,17) (15,19) (17,18)\nIs there a path between node 17 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph416-19_14", + "image": "data/connectivity/graph_visual/medium/graph416.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,4) (0,21) (0,7) (0,11) (0,1) (0,12) (0,10) (0,6) (0,9) (0,17) (0,20) (0,15) (0,13) (1,2) (1,4) (1,21) (1,7) (1,11) (1,12) (1,10) (1,6) (1,9) (1,17) (1,20) (1,15) (1,13) (2,4) (2,21) (2,7) (2,11) (2,12) (2,10) (2,6) (2,9) (2,17) (2,20) (2,15) (2,13) (3,8) (3,16) (3,14) (3,18) (3,5) (3,19) (4,21) (4,7) (4,11) (4,12) (4,10) (4,6) (4,9) (4,17) (4,20) (4,15) (4,13) (5,8) (5,16) (5,14) (5,18) (5,19) (6,21) (6,7) (6,11) (6,12) (6,10) (6,9) (6,17) (6,20) (6,15) (6,13) (7,21) (7,11) (7,12) (7,10) (7,9) (7,17) (7,20) (7,15) (7,13) (8,16) (8,14) (8,18) (8,19) (9,21) (9,11) (9,12) (9,10) (9,17) (9,20) (9,15) (9,13) (10,21) (10,11) (10,12) (10,17) (10,20) (10,15) (10,13) (11,21) (11,12) (11,17) (11,20) (11,15) (11,13) (12,21) (12,17) (12,20) (12,15) (12,13) (13,21) (13,17) (13,20) (13,15) (14,16) (14,18) (14,19) (15,21) (15,17) (15,20) (16,18) (16,19) (17,21) (17,20) (18,19) (20,21)\nIs there a path between node 19 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph330-18_14", + "image": "data/connectivity/graph_visual/medium/graph330.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,5) (1,17) (2,16) (3,18) (3,14) (4,20) (5,17) (6,16) (6,12) (6,8) (8,15) (8,17) (10,13) (10,11) (11,20) (12,15) (12,17) (14,18) (14,19) (16,17)\nIs there a path between node 18 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph853-24_15", + "image": "data/connectivity/graph_visual/medium/graph853.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,15) (0,6) (0,16) (0,2) (1,5) (1,21) (1,19) (1,11) (1,18) (1,12) (1,8) (1,14) (1,20) (1,24) (1,9) (1,10) (2,7) (2,15) (2,6) (2,16) (3,22) (3,17) (3,13) (3,4) (3,23) (4,22) (4,17) (4,13) (4,23) (5,21) (5,19) (5,11) (5,18) (5,12) (5,8) (5,14) (5,20) (5,24) (5,9) (5,10) (6,7) (6,15) (6,16) (7,15) (7,16) (8,21) (8,19) (8,11) (8,18) (8,12) (8,14) (8,20) (8,24) (8,9) (8,10) (9,21) (9,19) (9,11) (9,18) (9,12) (9,14) (9,20) (9,24) (9,10) (10,21) (10,19) (10,11) (10,18) (10,12) (10,14) (10,20) (10,24) (11,21) (11,19) (11,18) (11,12) (11,14) (11,20) (11,24) (12,21) (12,19) (12,18) (12,14) (12,20) (12,24) (13,22) (13,17) (13,23) (14,21) (14,19) (14,18) (14,20) (14,24) (15,16) (17,22) (17,23) (18,21) (18,19) (18,20) (18,24) (19,21) (19,20) (19,24) (20,21) (20,24) (21,24) (22,23)\nIs there a path between node 24 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph715-5_11", + "image": "data/connectivity/graph_visual/medium/graph715.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,8) (0,13) (0,5) (0,2) (0,19) (0,22) (0,17) (0,16) (0,3) (0,24) (0,20) (0,10) (0,15) (0,7) (0,4) (0,23) (0,6) (0,1) (1,8) (1,13) (1,19) (1,11) (1,22) (1,17) (1,3) (1,24) (1,20) (1,10) (1,15) (1,7) (1,4) (1,23) (1,6) (2,14) (2,8) (2,13) (2,22) (2,17) (2,16) (2,3) (2,24) (2,10) (2,15) (2,7) (2,4) (2,23) (2,6) (3,14) (3,13) (3,19) (3,11) (3,22) (3,17) (3,24) (3,10) (3,15) (3,4) (3,9) (4,13) (4,5) (4,22) (4,17) (4,10) (4,15) (4,7) (4,9) (4,23) (4,6) (5,8) (5,13) (5,19) (5,22) (5,24) (5,20) (5,10) (5,7) (5,23) (6,14) (6,8) (6,13) (6,19) (6,11) (6,22) (6,17) (6,16) (6,20) (6,7) (6,9) (7,14) (7,8) (7,13) (7,19) (7,11) (7,22) (7,20) (7,9) (8,19) (8,11) (8,22) (8,17) (8,20) (8,10) (8,15) (8,9) (9,17) (9,16) (9,24) (9,20) (9,10) (9,15) (9,23) (10,14) (10,13) (10,19) (10,11) (10,22) (10,17) (10,15) (10,23) (11,13) (11,22) (11,16) (12,18) (13,14) (13,19) (13,22) (13,16) (13,24) (13,20) (13,15) (13,23) (14,19) (14,17) (14,16) (14,15) (14,23) (15,19) (15,22) (15,17) (15,24) (15,20) (16,22) (16,17) (16,24) (17,19) (17,24) (17,20) (17,23) (18,21) (19,24) (19,20) (19,23) (20,22) (20,24) (20,23)\nIs there a path between node 5 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph235-9_6", + "image": "data/connectivity/graph_visual/medium/graph235.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,16) (0,11) (0,14) (0,7) (0,5) (0,15) (0,13) (0,18) (0,2) (1,16) (1,11) (1,5) (1,18) (1,4) (1,2) (2,11) (2,12) (2,14) (2,7) (2,5) (2,15) (2,13) (2,4) (3,8) (4,16) (4,12) (4,14) (4,5) (4,15) (4,13) (4,18) (5,16) (5,11) (5,12) (5,14) (5,7) (5,15) (5,18) (5,17) (6,10) (6,8) (6,9) (7,11) (7,12) (7,14) (7,15) (7,18) (7,17) (8,10) (8,9) (9,10) (11,16) (11,15) (11,13) (11,18) (12,16) (12,15) (12,13) (12,17) (13,16) (13,14) (13,18) (14,16) (14,18) (14,17) (15,18) (15,17) (16,18) (16,17) (17,18)\nIs there a path between node 9 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph483-8_13", + "image": "data/connectivity/graph_visual/medium/graph483.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,12) (0,5) (0,19) (0,17) (0,10) (0,2) (1,4) (1,6) (1,15) (1,18) (1,14) (1,3) (1,16) (1,20) (1,8) (1,21) (1,13) (2,12) (2,5) (2,19) (2,22) (2,9) (3,6) (3,15) (3,18) (3,14) (3,20) (3,21) (3,13) (4,11) (4,14) (4,16) (4,20) (4,8) (4,21) (5,12) (5,19) (5,7) (5,17) (5,10) (5,9) (6,11) (6,18) (6,14) (6,16) (6,20) (6,13) (7,12) (7,19) (7,22) (7,17) (7,10) (7,9) (8,11) (8,15) (8,14) (8,16) (8,13) (9,12) (9,22) (9,17) (9,10) (10,17) (11,15) (11,18) (11,14) (11,16) (11,20) (12,19) (12,22) (13,15) (13,18) (13,14) (13,16) (13,20) (13,21) (14,18) (14,16) (14,20) (14,21) (15,18) (15,16) (15,20) (15,21) (16,18) (18,20) (19,22) (20,21)\nIs there a path between node 8 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph736-4_24", + "image": "data/connectivity/graph_visual/medium/graph736.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,9) (2,24) (2,5) (2,21) (2,19) (2,23) (2,4) (3,17) (3,7) (4,14) (4,5) (4,21) (4,15) (4,23) (5,10) (5,24) (5,6) (5,15) (6,15) (6,23) (7,16) (8,11) (8,13) (10,14) (11,22) (11,12) (13,22) (13,18) (13,20) (14,15) (14,23) (15,24) (15,21) (16,17) (18,20)\nIs there a path between node 4 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph7-0_7", + "image": "data/connectivity/graph_visual/medium/graph7.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,6) (1,4) (1,3) (1,2) (1,7) (2,10) (2,4) (2,8) (3,10) (3,6) (3,4) (3,8) (3,5) (4,6) (4,8) (4,5) (4,7) (5,10) (5,8) (6,10) (6,8) (7,10)\nIs there a path between node 0 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph186-9_12", + "image": "data/connectivity/graph_visual/medium/graph186.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,8) (0,7) (0,14) (0,17) (0,4) (0,1) (0,15) (0,2) (0,6) (0,16) (0,9) (0,12) (0,11) (0,3) (0,10) (1,8) (1,7) (1,14) (1,17) (1,4) (1,15) (1,2) (1,6) (1,16) (1,9) (1,12) (1,11) (1,3) (1,10) (2,8) (2,7) (2,14) (2,17) (2,4) (2,15) (2,6) (2,16) (2,9) (2,12) (2,11) (2,3) (2,10) (3,8) (3,7) (3,14) (3,17) (3,4) (3,15) (3,6) (3,16) (3,9) (3,12) (3,11) (3,10) (4,8) (4,7) (4,14) (4,17) (4,15) (4,6) (4,16) (4,9) (4,12) (4,11) (4,10) (5,13) (6,8) (6,7) (6,14) (6,17) (6,15) (6,16) (6,9) (6,12) (6,11) (6,10) (7,8) (7,14) (7,17) (7,15) (7,16) (7,9) (7,12) (7,11) (7,10) (8,14) (8,17) (8,15) (8,16) (8,9) (8,12) (8,11) (8,10) (9,14) (9,17) (9,15) (9,16) (9,12) (9,11) (9,10) (10,14) (10,17) (10,15) (10,16) (10,12) (10,11) (11,14) (11,17) (11,15) (11,16) (11,12) (12,14) (12,17) (12,15) (12,16) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 9 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph774-1_0", + "image": "data/connectivity/graph_visual/medium/graph774.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,7) (0,1) (0,9) (0,13) (0,24) (0,8) (0,11) (1,14) (1,7) (1,9) (1,13) (1,24) (1,8) (1,11) (2,19) (2,18) (2,12) (2,16) (2,4) (2,17) (2,3) (2,21) (2,20) (2,23) (2,22) (2,10) (2,6) (2,5) (2,15) (3,19) (3,18) (3,12) (3,16) (3,4) (3,17) (3,21) (3,20) (3,23) (3,22) (3,10) (3,6) (3,5) (3,15) (4,19) (4,18) (4,12) (4,16) (4,17) (4,21) (4,20) (4,23) (4,22) (4,10) (4,6) (4,5) (4,15) (5,19) (5,18) (5,12) (5,16) (5,17) (5,21) (5,20) (5,23) (5,22) (5,10) (5,6) (5,15) (6,19) (6,18) (6,12) (6,16) (6,17) (6,21) (6,20) (6,23) (6,22) (6,10) (6,15) (7,14) (7,9) (7,13) (7,24) (7,8) (7,11) (8,14) (8,9) (8,13) (8,24) (8,11) (9,14) (9,13) (9,24) (9,11) (10,19) (10,18) (10,12) (10,16) (10,17) (10,21) (10,20) (10,23) (10,22) (10,15) (11,14) (11,13) (11,24) (12,19) (12,18) (12,16) (12,17) (12,21) (12,20) (12,23) (12,22) (12,15) (13,14) (13,24) (14,24) (15,19) (15,18) (15,16) (15,17) (15,21) (15,20) (15,23) (15,22) (16,19) (16,18) (16,17) (16,21) (16,20) (16,23) (16,22) (17,19) (17,18) (17,21) (17,20) (17,23) (17,22) (18,19) (18,21) (18,20) (18,23) (18,22) (19,21) (19,20) (19,23) (19,22) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 1 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph191-16_11", + "image": "data/connectivity/graph_visual/medium/graph191.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,5) (0,10) (0,11) (0,6) (0,2) (0,15) (0,4) (0,8) (0,7) (0,17) (0,16) (0,12) (0,9) (0,3) (0,14) (1,13) (2,5) (2,10) (2,11) (2,6) (2,15) (2,4) (2,8) (2,7) (2,17) (2,16) (2,12) (2,9) (2,3) (2,14) (3,5) (3,10) (3,11) (3,6) (3,15) (3,4) (3,8) (3,7) (3,17) (3,16) (3,12) (3,9) (3,14) (4,5) (4,10) (4,11) (4,6) (4,15) (4,8) (4,7) (4,17) (4,16) (4,12) (4,9) (4,14) (5,10) (5,11) (5,6) (5,15) (5,8) (5,7) (5,17) (5,16) (5,12) (5,9) (5,14) (6,10) (6,11) (6,15) (6,8) (6,7) (6,17) (6,16) (6,12) (6,9) (6,14) (7,10) (7,11) (7,15) (7,8) (7,17) (7,16) (7,12) (7,9) (7,14) (8,10) (8,11) (8,15) (8,17) (8,16) (8,12) (8,9) (8,14) (9,10) (9,11) (9,15) (9,17) (9,16) (9,12) (9,14) (10,11) (10,15) (10,17) (10,16) (10,12) (10,14) (11,15) (11,17) (11,16) (11,12) (11,14) (12,15) (12,17) (12,16) (12,14) (14,15) (14,17) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 16 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph365-9_6", + "image": "data/connectivity/graph_visual/medium/graph365.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (0,11) (0,5) (1,6) (1,19) (1,9) (1,10) (1,13) (2,18) (2,4) (2,6) (3,17) (3,7) (3,11) (3,20) (3,13) (4,6) (4,19) (4,10) (4,11) (4,13) (5,19) (5,11) (5,14) (6,19) (6,10) (6,7) (7,19) (7,14) (7,13) (9,13) (10,11) (11,18) (14,18) (14,19) (16,20)\nIs there a path between node 9 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph425-1_0", + "image": "data/connectivity/graph_visual/medium/graph425.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,16) (0,8) (0,11) (0,20) (1,14) (1,19) (2,7) (2,16) (2,4) (2,10) (2,11) (2,3) (3,4) (3,10) (4,12) (4,8) (4,17) (5,8) (5,6) (5,10) (5,11) (5,13) (6,7) (6,15) (6,18) (7,13) (8,16) (8,18) (8,20) (10,12) (10,17) (10,20) (11,15) (11,13) (12,16) (12,18) (15,16) (16,20) (19,21)\nIs there a path between node 1 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph189-3_4", + "image": "data/connectivity/graph_visual/medium/graph189.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,15) (0,9) (0,1) (0,17) (0,12) (0,11) (0,13) (0,7) (1,15) (1,9) (1,17) (1,12) (1,11) (1,13) (1,7) (2,3) (2,5) (2,10) (2,14) (2,6) (2,8) (2,4) (3,5) (3,10) (3,14) (3,6) (3,8) (3,4) (4,5) (4,10) (4,14) (4,6) (4,8) (5,10) (5,14) (5,6) (5,8) (6,10) (6,14) (6,8) (7,15) (7,9) (7,17) (7,12) (7,11) (7,13) (8,10) (8,14) (9,15) (9,17) (9,12) (9,11) (9,13) (10,14) (11,15) (11,17) (11,12) (11,13) (12,15) (12,17) (12,13) (13,15) (13,17) (15,17)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph757-4_10", + "image": "data/connectivity/graph_visual/medium/graph757.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,5) (0,22) (0,20) (0,1) (0,7) (0,9) (0,23) (0,4) (0,8) (0,17) (0,6) (0,21) (0,12) (0,3) (0,16) (0,18) (1,5) (1,20) (1,13) (1,7) (1,9) (1,23) (1,14) (1,4) (1,8) (1,6) (1,21) (1,12) (1,3) (1,24) (1,16) (1,2) (1,11) (2,5) (2,20) (2,13) (2,9) (2,23) (2,14) (2,8) (2,21) (2,12) (2,3) (2,11) (2,18) (3,5) (3,22) (3,20) (3,13) (3,9) (3,14) (3,4) (3,8) (3,6) (3,24) (3,16) (3,11) (3,18) (4,5) (4,22) (4,20) (4,7) (4,9) (4,23) (4,14) (4,17) (4,21) (4,12) (4,24) (5,22) (5,20) (5,7) (5,23) (5,14) (5,8) (5,17) (5,12) (5,16) (5,11) (5,18) (6,20) (6,13) (6,7) (6,23) (6,14) (6,17) (6,24) (6,16) (6,11) (6,18) (7,22) (7,13) (7,23) (7,14) (7,8) (7,17) (7,12) (7,24) (7,16) (7,11) (7,18) (8,14) (8,12) (8,24) (8,16) (8,11) (8,18) (9,22) (9,20) (9,13) (9,23) (9,14) (9,17) (9,21) (9,12) (9,16) (9,11) (9,18) (10,15) (10,19) (11,22) (11,13) (11,23) (11,17) (11,12) (11,16) (12,22) (12,20) (12,14) (12,17) (12,21) (12,24) (12,16) (12,18) (13,22) (13,23) (13,14) (13,17) (13,21) (13,24) (13,16) (13,18) (14,20) (14,23) (14,24) (14,18) (15,19) (16,22) (16,20) (16,23) (16,24) (16,18) (17,22) (17,20) (17,23) (17,21) (17,24) (18,22) (18,20) (18,23) (18,21) (18,24) (20,22) (20,23) (20,24) (21,22) (21,23) (21,24)\nIs there a path between node 4 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph599-1_23", + "image": "data/connectivity/graph_visual/medium/graph599.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,16) (0,9) (0,8) (0,15) (0,3) (0,12) (0,2) (0,21) (0,11) (0,14) (0,19) (1,13) (1,7) (1,18) (1,5) (1,23) (1,22) (1,10) (1,4) (2,20) (2,9) (2,15) (2,3) (2,11) (2,19) (2,17) (3,6) (3,9) (3,8) (3,12) (3,11) (3,14) (3,19) (3,17) (4,18) (4,10) (5,13) (5,7) (5,18) (5,23) (5,22) (5,10) (6,20) (6,9) (6,8) (6,15) (6,11) (6,14) (6,19) (6,17) (7,13) (7,18) (7,23) (7,22) (8,9) (8,15) (8,12) (8,21) (8,11) (8,19) (8,17) (9,15) (9,21) (9,11) (9,14) (9,19) (9,17) (10,13) (10,18) (10,22) (11,16) (11,20) (11,12) (11,21) (11,19) (12,16) (12,20) (12,21) (12,17) (13,23) (13,22) (14,20) (14,15) (14,17) (15,20) (15,21) (15,19) (16,20) (16,21) (16,19) (16,17) (17,20) (17,21) (18,22) (19,20) (19,21) (20,21) (22,23)\nIs there a path between node 1 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph717-12_10", + "image": "data/connectivity/graph_visual/medium/graph717.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,13) (0,6) (0,16) (0,20) (1,21) (1,18) (1,2) (1,23) (1,7) (1,5) (1,11) (1,9) (1,3) (1,19) (1,14) (1,24) (2,4) (2,22) (2,18) (2,23) (2,5) (2,11) (2,19) (3,18) (3,5) (3,11) (3,19) (3,24) (4,21) (4,22) (4,8) (4,18) (4,23) (4,7) (4,5) (4,9) (4,14) (5,8) (5,7) (5,11) (5,9) (5,19) (6,10) (6,13) (6,16) (6,20) (6,12) (6,15) (7,21) (7,8) (7,23) (7,11) (7,9) (7,19) (8,18) (8,11) (8,14) (8,24) (9,21) (9,22) (9,18) (9,19) (9,14) (9,24) (10,13) (10,20) (10,15) (11,21) (11,22) (11,18) (11,23) (11,14) (12,13) (12,16) (12,20) (13,16) (13,15) (14,22) (14,18) (14,19) (14,24) (15,16) (15,20) (16,20) (18,22) (18,23) (18,19) (18,24) (19,22) (19,23) (19,24) (21,22) (22,23) (22,24) (23,24)\nIs there a path between node 12 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph196-6_15", + "image": "data/connectivity/graph_visual/medium/graph196.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,2) (0,14) (0,7) (0,13) (1,17) (1,3) (1,10) (1,6) (2,11) (2,12) (2,14) (2,13) (3,17) (3,10) (3,6) (4,9) (4,5) (5,9) (5,16) (6,17) (6,8) (6,10) (7,11) (7,12) (7,14) (7,13) (8,17) (8,15) (9,18) (9,16) (10,17) (12,14) (12,13) (13,14) (15,17)\nIs there a path between node 6 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph665-11_5", + "image": "data/connectivity/graph_visual/medium/graph665.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,10) (0,14) (0,2) (0,8) (1,18) (1,23) (1,5) (1,4) (1,11) (1,9) (1,20) (1,17) (1,7) (2,10) (2,14) (2,16) (2,3) (2,8) (2,22) (3,12) (3,10) (3,14) (3,16) (3,8) (4,18) (4,15) (4,20) (4,17) (4,7) (5,23) (5,15) (5,21) (5,11) (5,9) (5,19) (5,17) (5,7) (7,23) (7,21) (7,11) (7,9) (7,20) (7,17) (8,12) (8,10) (8,14) (8,22) (9,18) (9,23) (9,15) (9,21) (9,11) (9,20) (9,19) (10,16) (10,22) (11,18) (11,15) (11,21) (11,20) (11,19) (11,17) (12,14) (12,16) (14,22) (15,18) (15,20) (17,20) (18,23) (18,19) (19,23) (19,21) (21,23)\nIs there a path between node 11 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph53-8_5", + "image": "data/connectivity/graph_visual/medium/graph53.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,10) (0,5) (0,7) (0,2) (0,8) (0,4) (0,9) (0,1) (0,12) (0,3) (0,11) (0,13) (1,10) (1,5) (1,7) (1,2) (1,8) (1,4) (1,9) (1,12) (1,3) (1,11) (1,13) (2,10) (2,5) (2,7) (2,8) (2,4) (2,9) (2,12) (2,3) (2,11) (2,13) (3,10) (3,5) (3,7) (3,8) (3,4) (3,9) (3,12) (3,11) (3,13) (4,10) (4,5) (4,7) (4,8) (4,9) (4,12) (4,11) (4,13) (5,10) (5,7) (5,8) (5,9) (5,12) (5,11) (5,13) (7,10) (7,8) (7,9) (7,12) (7,11) (7,13) (8,10) (8,9) (8,12) (8,11) (8,13) (9,10) (9,12) (9,11) (9,13) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nIs there a path between node 8 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph415-9_6", + "image": "data/connectivity/graph_visual/medium/graph415.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,13) (0,17) (0,10) (0,5) (0,4) (0,16) (0,19) (0,20) (0,7) (0,8) (0,15) (0,1) (0,18) (0,9) (0,12) (1,13) (1,17) (1,10) (1,5) (1,4) (1,16) (1,19) (1,20) (1,7) (1,8) (1,15) (1,18) (1,9) (1,12) (2,11) (2,21) (2,3) (2,14) (3,11) (3,21) (3,14) (4,13) (4,17) (4,10) (4,5) (4,16) (4,19) (4,20) (4,7) (4,8) (4,15) (4,18) (4,9) (4,12) (5,13) (5,17) (5,10) (5,16) (5,19) (5,20) (5,7) (5,8) (5,15) (5,18) (5,9) (5,12) (7,13) (7,17) (7,10) (7,16) (7,19) (7,20) (7,8) (7,15) (7,18) (7,9) (7,12) (8,13) (8,17) (8,10) (8,16) (8,19) (8,20) (8,15) (8,18) (8,9) (8,12) (9,13) (9,17) (9,10) (9,16) (9,19) (9,20) (9,15) (9,18) (9,12) (10,13) (10,17) (10,16) (10,19) (10,20) (10,15) (10,18) (10,12) (11,21) (11,14) (12,13) (12,17) (12,16) (12,19) (12,20) (12,15) (12,18) (13,17) (13,16) (13,19) (13,20) (13,15) (13,18) (14,21) (15,17) (15,16) (15,19) (15,20) (15,18) (16,17) (16,19) (16,20) (16,18) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20)\nIs there a path between node 9 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph707-24_18", + "image": "data/connectivity/graph_visual/medium/graph707.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,8) (0,5) (0,13) (0,19) (0,17) (1,7) (1,12) (1,2) (1,16) (2,8) (2,10) (2,6) (3,7) (3,13) (3,4) (3,10) (3,16) (3,17) (3,6) (4,8) (4,10) (4,21) (4,17) (4,6) (5,7) (5,8) (5,21) (5,16) (5,17) (6,8) (6,10) (6,19) (8,12) (8,10) (8,16) (9,12) (9,10) (9,21) (9,17) (10,19) (10,16) (11,14) (12,17) (13,21) (14,15) (14,18) (15,22) (15,24) (15,23) (17,19) (17,21)\nIs there a path between node 24 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph505-17_15", + "image": "data/connectivity/graph_visual/medium/graph505.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,13) (0,9) (0,10) (1,2) (1,15) (1,7) (1,11) (1,16) (2,3) (2,18) (2,7) (2,11) (2,14) (3,8) (3,4) (4,20) (4,15) (4,22) (4,7) (4,16) (4,14) (5,21) (5,9) (5,10) (7,17) (7,15) (8,20) (8,14) (9,12) (9,21) (9,13) (9,10) (10,12) (10,21) (11,20) (11,15) (11,22) (14,18) (15,16) (16,17) (16,22) (17,22) (18,20)\nIs there a path between node 17 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph637-18_6", + "image": "data/connectivity/graph_visual/medium/graph637.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,12) (0,2) (1,13) (1,20) (1,6) (1,8) (1,3) (2,22) (3,10) (3,13) (3,20) (3,15) (3,6) (3,12) (3,14) (4,5) (4,23) (5,16) (5,23) (5,11) (6,12) (6,14) (6,21) (7,22) (7,8) (8,18) (8,22) (8,14) (9,16) (9,23) (9,19) (10,18) (10,15) (10,12) (10,22) (11,16) (12,18) (13,18) (13,14) (14,21) (15,21) (16,19) (17,20) (17,18) (20,22) (21,22)\nIs there a path between node 18 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph231-15_17", + "image": "data/connectivity/graph_visual/medium/graph231.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,10) (1,15) (2,16) (3,18) (3,8) (5,15) (5,14) (7,9) (8,18) (8,12) (10,17) (12,13) (12,17) (13,14) (14,18) (14,15) (17,18)\nIs there a path between node 15 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph812-5_11", + "image": "data/connectivity/graph_visual/medium/graph812.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,22) (0,18) (0,21) (0,12) (0,16) (0,14) (0,17) (0,6) (1,3) (2,20) (2,13) (2,4) (2,7) (3,10) (4,20) (4,13) (4,7) (5,19) (5,9) (5,24) (6,15) (6,22) (6,18) (6,21) (6,12) (6,16) (6,17) (7,20) (7,13) (8,15) (8,23) (8,12) (8,16) (8,14) (8,17) (9,19) (9,24) (11,23) (11,18) (11,21) (11,12) (11,16) (11,14) (11,17) (12,23) (12,22) (12,21) (12,16) (12,14) (14,15) (14,22) (14,18) (14,16) (14,17) (15,22) (15,17) (16,23) (16,21) (16,17) (17,23) (17,18) (17,21) (18,23) (18,21) (19,24) (21,23) (21,22) (22,23)\nIs there a path between node 5 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph13-5_3", + "image": "data/connectivity/graph_visual/medium/graph13.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (0,7) (0,10) (0,2) (1,8) (1,4) (1,9) (1,3) (1,5) (2,6) (2,7) (2,10) (3,8) (3,4) (3,9) (3,5) (4,8) (4,9) (4,5) (5,8) (5,9) (6,7) (6,10) (7,10) (8,9)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph684-0_12", + "image": "data/connectivity/graph_visual/medium/graph684.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,21) (0,12) (0,9) (0,2) (0,6) (0,4) (0,5) (0,14) (0,17) (0,8) (0,20) (0,13) (0,19) (0,22) (0,1) (0,15) (0,10) (0,18) (1,7) (1,21) (1,12) (1,9) (1,2) (1,6) (1,4) (1,5) (1,14) (1,17) (1,8) (1,20) (1,13) (1,19) (1,22) (1,15) (1,10) (1,18) (2,7) (2,21) (2,12) (2,9) (2,6) (2,4) (2,5) (2,14) (2,17) (2,8) (2,20) (2,13) (2,19) (2,22) (2,15) (2,10) (2,18) (3,11) (3,23) (4,7) (4,21) (4,12) (4,9) (4,6) (4,5) (4,14) (4,17) (4,8) (4,20) (4,13) (4,19) (4,22) (4,15) (4,10) (4,18) (5,7) (5,21) (5,12) (5,9) (5,6) (5,14) (5,17) (5,8) (5,20) (5,13) (5,19) (5,22) (5,15) (5,10) (5,18) (6,7) (6,21) (6,12) (6,9) (6,14) (6,17) (6,8) (6,20) (6,13) (6,19) (6,22) (6,15) (6,10) (6,18) (7,21) (7,12) (7,9) (7,14) (7,17) (7,8) (7,20) (7,13) (7,19) (7,22) (7,15) (7,10) (7,18) (8,21) (8,12) (8,9) (8,14) (8,17) (8,20) (8,13) (8,19) (8,22) (8,15) (8,10) (8,18) (9,21) (9,12) (9,14) (9,17) (9,20) (9,13) (9,19) (9,22) (9,15) (9,10) (9,18) (10,21) (10,12) (10,14) (10,17) (10,20) (10,13) (10,19) (10,22) (10,15) (10,18) (11,23) (12,21) (12,14) (12,17) (12,20) (12,13) (12,19) (12,22) (12,15) (12,18) (13,21) (13,14) (13,17) (13,20) (13,19) (13,22) (13,15) (13,18) (14,21) (14,17) (14,20) (14,19) (14,22) (14,15) (14,18) (15,21) (15,17) (15,20) (15,19) (15,22) (15,18) (17,21) (17,20) (17,19) (17,22) (17,18) (18,21) (18,20) (18,19) (18,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 0 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph619-12_14", + "image": "data/connectivity/graph_visual/medium/graph619.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,18) (0,8) (0,2) (0,12) (0,22) (0,19) (0,10) (0,21) (0,3) (0,14) (0,20) (0,6) (0,15) (0,23) (0,16) (0,4) (0,17) (0,1) (1,18) (1,8) (1,2) (1,12) (1,22) (1,19) (1,10) (1,21) (1,3) (1,14) (1,20) (1,6) (1,15) (1,23) (1,16) (1,4) (1,17) (2,18) (2,8) (2,12) (2,22) (2,19) (2,10) (2,21) (2,3) (2,14) (2,20) (2,6) (2,15) (2,23) (2,16) (2,4) (2,17) (3,18) (3,8) (3,12) (3,22) (3,19) (3,10) (3,21) (3,14) (3,20) (3,6) (3,15) (3,23) (3,16) (3,4) (3,17) (4,18) (4,8) (4,12) (4,22) (4,19) (4,10) (4,21) (4,14) (4,20) (4,6) (4,15) (4,23) (4,16) (4,17) (5,9) (5,11) (5,7) (5,13) (6,18) (6,8) (6,12) (6,22) (6,19) (6,10) (6,21) (6,14) (6,20) (6,15) (6,23) (6,16) (6,17) (7,9) (7,11) (7,13) (8,18) (8,12) (8,22) (8,19) (8,10) (8,21) (8,14) (8,20) (8,15) (8,23) (8,16) (8,17) (9,11) (9,13) (10,18) (10,12) (10,22) (10,19) (10,21) (10,14) (10,20) (10,15) (10,23) (10,16) (10,17) (11,13) (12,18) (12,22) (12,19) (12,21) (12,14) (12,20) (12,15) (12,23) (12,16) (12,17) (14,18) (14,22) (14,19) (14,21) (14,20) (14,15) (14,23) (14,16) (14,17) (15,18) (15,22) (15,19) (15,21) (15,20) (15,23) (15,16) (15,17) (16,18) (16,22) (16,19) (16,21) (16,20) (16,23) (16,17) (17,18) (17,22) (17,19) (17,21) (17,20) (17,23) (18,22) (18,19) (18,21) (18,20) (18,23) (19,22) (19,21) (19,20) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 12 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph28-5_4", + "image": "data/connectivity/graph_visual/medium/graph28.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,1) (0,4) (0,3) (0,6) (0,2) (0,8) (0,5) (0,11) (1,4) (1,3) (1,6) (1,2) (1,8) (1,5) (1,11) (2,4) (2,3) (2,6) (2,8) (2,5) (2,11) (3,4) (3,6) (3,8) (3,5) (3,11) (4,6) (4,8) (4,5) (4,11) (5,6) (5,8) (5,11) (6,8) (6,11) (7,9) (7,10) (8,11) (9,10)\nIs there a path between node 5 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph271-11_19", + "image": "data/connectivity/graph_visual/medium/graph271.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,11) (1,2) (1,3) (1,19) (2,19) (2,18) (3,19) (3,9) (3,18) (4,8) (4,12) (4,10) (4,6) (4,13) (4,14) (4,15) (5,8) (5,6) (5,14) (5,15) (6,8) (6,12) (6,10) (6,14) (6,16) (7,8) (7,12) (7,14) (7,15) (7,16) (8,12) (8,10) (8,13) (8,14) (8,15) (8,16) (9,19) (9,18) (10,12) (10,14) (10,15) (10,16) (12,13) (12,15) (12,16) (14,16) (15,16) (18,19)\nIs there a path between node 11 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph334-2_12", + "image": "data/connectivity/graph_visual/medium/graph334.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,7) (0,3) (0,20) (1,13) (2,9) (2,12) (2,13) (3,7) (3,20) (5,6) (5,10) (5,11) (5,15) (5,17) (5,12) (6,9) (6,10) (6,11) (8,16) (9,17) (9,13) (10,17) (11,16) (11,18) (12,16) (13,15) (13,17) (13,18) (14,19) (19,20)\nIs there a path between node 2 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph410-12_6", + "image": "data/connectivity/graph_visual/medium/graph410.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,16) (0,10) (0,15) (0,14) (0,21) (0,7) (0,5) (0,4) (0,2) (1,16) (1,14) (1,21) (1,20) (1,5) (2,16) (2,10) (2,15) (2,14) (2,21) (2,7) (2,20) (2,4) (3,13) (3,12) (3,11) (3,9) (4,16) (4,10) (4,15) (4,14) (4,21) (4,7) (4,20) (5,16) (5,15) (5,14) (5,7) (5,20) (5,6) (6,16) (6,10) (6,14) (6,21) (6,20) (7,16) (7,10) (7,15) (7,21) (8,18) (8,19) (8,13) (8,12) (8,9) (8,17) (9,18) (9,19) (9,12) (9,11) (9,17) (10,14) (11,18) (11,19) (11,13) (11,12) (12,19) (12,13) (12,17) (13,17) (14,16) (14,15) (14,21) (14,20) (15,21) (15,20) (16,20) (17,19) (20,21)\nIs there a path between node 12 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph155-11_6", + "image": "data/connectivity/graph_visual/medium/graph155.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,9) (0,1) (0,6) (0,10) (0,3) (0,13) (0,8) (0,14) (0,15) (0,2) (0,7) (0,11) (1,9) (1,6) (1,10) (1,3) (1,13) (1,8) (1,14) (1,15) (1,2) (1,7) (1,11) (2,9) (2,6) (2,10) (2,3) (2,13) (2,8) (2,14) (2,15) (2,7) (2,11) (3,9) (3,6) (3,10) (3,13) (3,8) (3,14) (3,15) (3,7) (3,11) (4,12) (4,5) (4,16) (5,12) (5,16) (6,9) (6,10) (6,13) (6,8) (6,14) (6,15) (6,7) (6,11) (7,9) (7,10) (7,13) (7,8) (7,14) (7,15) (7,11) (8,9) (8,10) (8,13) (8,14) (8,15) (8,11) (9,10) (9,13) (9,14) (9,15) (9,11) (10,13) (10,14) (10,15) (10,11) (11,13) (11,14) (11,15) (12,16) (13,14) (13,15) (14,15)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph505-11_19", + "image": "data/connectivity/graph_visual/medium/graph505.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,13) (0,9) (0,10) (1,2) (1,15) (1,7) (1,11) (1,16) (2,3) (2,18) (2,7) (2,11) (2,14) (3,8) (3,4) (4,20) (4,15) (4,22) (4,7) (4,16) (4,14) (5,21) (5,9) (5,10) (7,17) (7,15) (8,20) (8,14) (9,12) (9,21) (9,13) (9,10) (10,12) (10,21) (11,20) (11,15) (11,22) (14,18) (15,16) (16,17) (16,22) (17,22) (18,20)\nIs there a path between node 11 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph166-2_0", + "image": "data/connectivity/graph_visual/medium/graph166.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,7) (1,11) (1,16) (1,2) (1,9) (1,4) (2,10) (2,7) (2,11) (2,5) (3,12) (3,5) (3,16) (3,8) (4,16) (4,17) (5,13) (5,15) (5,11) (5,16) (5,6) (5,17) (6,9) (7,10) (7,11) (8,11) (8,9) (9,15) (9,11) (9,17) (10,11) (10,12) (11,15) (12,16) (13,15) (13,16) (15,17) (16,17)\nIs there a path between node 2 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph786-21_11", + "image": "data/connectivity/graph_visual/medium/graph786.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,12) (0,1) (0,9) (0,10) (0,21) (1,10) (1,16) (1,21) (2,4) (3,5) (5,11) (6,24) (7,14) (7,24) (7,8) (8,14) (8,24) (9,12) (9,16) (9,21) (10,16) (10,21) (12,15) (12,21) (18,20) (19,24) (22,23)\nIs there a path between node 21 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph358-3_9", + "image": "data/connectivity/graph_visual/medium/graph358.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,1) (0,19) (0,18) (0,16) (1,6) (1,15) (2,18) (2,20) (2,11) (3,12) (4,6) (4,16) (4,15) (4,11) (6,9) (6,18) (6,20) (6,11) (9,14) (9,19) (9,18) (9,20) (9,16) (9,11) (10,14) (10,20) (10,16) (11,14) (11,20) (14,19) (14,15) (15,18) (15,16) (16,18) (18,20)\nIs there a path between node 3 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph91-6_3", + "image": "data/connectivity/graph_visual/medium/graph91.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,15) (1,14) (1,3) (1,9) (1,10) (1,4) (1,7) (1,6) (1,13) (1,12) (1,11) (2,15) (3,14) (3,8) (3,9) (3,10) (3,4) (3,12) (3,11) (4,8) (4,9) (4,10) (4,7) (4,5) (4,11) (5,9) (5,7) (5,13) (5,12) (5,11) (6,14) (6,8) (6,7) (6,13) (6,11) (7,8) (7,9) (7,10) (7,11) (8,14) (8,10) (8,12) (8,11) (9,14) (9,10) (9,13) (9,12) (10,14) (10,13) (10,12) (11,14) (11,13) (11,12) (12,14)\nIs there a path between node 6 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph98-3_5", + "image": "data/connectivity/graph_visual/medium/graph98.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,14) (1,13) (1,6) (1,4) (1,11) (1,9) (2,13) (2,6) (2,4) (2,11) (2,9) (3,15) (4,8) (4,13) (4,11) (5,8) (5,6) (5,15) (10,12) (11,13)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph574-20_13", + "image": "data/connectivity/graph_visual/medium/graph574.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,11) (0,20) (0,12) (0,23) (0,9) (1,3) (2,13) (2,6) (2,8) (2,5) (2,17) (3,18) (3,22) (4,21) (5,6) (5,16) (5,10) (5,17) (6,15) (6,11) (6,12) (6,17) (8,16) (8,9) (9,20) (9,12) (9,10) (9,23) (10,15) (11,15) (11,12) (11,16) (12,13) (13,20) (15,20) (16,20) (16,23) (16,17) (18,19) (18,21) (21,22)\nIs there a path between node 20 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph685-4_14", + "image": "data/connectivity/graph_visual/medium/graph685.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,21) (0,7) (0,18) (0,8) (0,11) (0,4) (0,6) (0,13) (0,17) (0,9) (0,22) (0,14) (0,2) (1,21) (1,7) (1,18) (1,8) (1,11) (1,4) (1,6) (1,13) (1,17) (1,9) (1,22) (1,14) (1,2) (2,21) (2,7) (2,18) (2,8) (2,11) (2,4) (2,6) (2,13) (2,17) (2,9) (2,22) (2,14) (3,5) (3,10) (3,15) (3,12) (3,16) (3,20) (4,21) (4,7) (4,18) (4,8) (4,11) (4,6) (4,13) (4,17) (4,9) (4,22) (4,14) (5,10) (5,15) (5,12) (5,16) (5,20) (6,21) (6,7) (6,18) (6,8) (6,11) (6,13) (6,17) (6,9) (6,22) (6,14) (7,21) (7,18) (7,8) (7,11) (7,13) (7,17) (7,9) (7,22) (7,14) (8,21) (8,18) (8,11) (8,13) (8,17) (8,9) (8,22) (8,14) (9,21) (9,18) (9,11) (9,13) (9,17) (9,22) (9,14) (10,15) (10,12) (10,16) (10,20) (11,21) (11,18) (11,13) (11,17) (11,22) (11,14) (12,15) (12,16) (12,20) (13,21) (13,18) (13,17) (13,22) (13,14) (14,21) (14,18) (14,17) (14,22) (15,16) (15,20) (16,20) (17,21) (17,18) (17,22) (18,21) (18,22) (19,23) (21,22)\nIs there a path between node 4 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph395-2_4", + "image": "data/connectivity/graph_visual/medium/graph395.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,1) (0,14) (0,3) (0,19) (0,11) (0,12) (0,7) (0,20) (0,6) (0,2) (0,4) (1,5) (1,14) (1,3) (1,19) (1,11) (1,12) (1,7) (1,20) (1,6) (1,2) (1,4) (2,5) (2,14) (2,3) (2,19) (2,11) (2,12) (2,7) (2,20) (2,6) (2,4) (3,5) (3,14) (3,19) (3,11) (3,12) (3,7) (3,20) (3,6) (3,4) (4,5) (4,14) (4,19) (4,11) (4,12) (4,7) (4,20) (4,6) (5,14) (5,19) (5,11) (5,12) (5,7) (5,20) (5,6) (6,14) (6,19) (6,11) (6,12) (6,7) (6,20) (7,14) (7,19) (7,11) (7,12) (7,20) (8,18) (8,17) (8,13) (8,16) (8,15) (9,10) (11,14) (11,19) (11,12) (11,20) (12,14) (12,19) (12,20) (13,18) (13,17) (13,16) (13,15) (14,19) (14,20) (15,18) (15,17) (15,16) (16,18) (16,17) (17,18) (19,20)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph486-22_16", + "image": "data/connectivity/graph_visual/medium/graph486.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,19) (0,1) (0,11) (0,21) (0,13) (1,11) (1,6) (1,21) (1,22) (2,14) (2,7) (2,8) (2,10) (2,9) (2,4) (3,18) (3,17) (3,20) (3,15) (4,14) (4,16) (4,7) (4,8) (4,9) (4,5) (5,14) (5,8) (5,10) (5,9) (6,19) (6,12) (6,11) (6,21) (6,13) (7,14) (7,16) (7,8) (7,10) (8,14) (8,16) (8,10) (9,10) (10,14) (10,16) (11,12) (11,21) (12,19) (12,21) (12,22) (12,13) (13,21) (13,22) (14,16) (15,18) (15,17) (17,18) (17,20) (19,21) (19,22) (21,22)\nIs there a path between node 22 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph579-8_18", + "image": "data/connectivity/graph_visual/medium/graph579.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,3) (0,8) (0,10) (0,2) (0,13) (0,19) (1,23) (2,6) (2,20) (2,11) (2,12) (2,8) (2,17) (2,22) (2,5) (2,19) (3,11) (3,12) (3,21) (3,22) (5,16) (5,6) (5,8) (5,17) (5,13) (5,19) (6,20) (6,22) (6,7) (7,8) (7,10) (7,13) (8,11) (8,10) (8,13) (9,20) (9,10) (10,16) (10,11) (11,16) (12,17) (12,22) (12,13) (13,21) (14,23) (14,15) (17,20) (17,21) (21,22)\nIs there a path between node 8 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph532-10_0", + "image": "data/connectivity/graph_visual/medium/graph532.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,17) (0,19) (0,4) (0,6) (0,18) (0,20) (0,22) (0,16) (0,12) (0,10) (1,13) (1,5) (1,21) (1,7) (2,8) (2,3) (2,9) (2,14) (2,15) (2,11) (3,8) (3,9) (3,14) (3,15) (3,11) (4,17) (4,19) (4,6) (4,18) (4,20) (4,22) (4,16) (4,12) (4,10) (5,13) (5,21) (5,7) (6,17) (6,19) (6,18) (6,20) (6,22) (6,16) (6,12) (6,10) (7,13) (7,21) (8,9) (8,14) (8,15) (8,11) (9,14) (9,15) (9,11) (10,17) (10,19) (10,18) (10,20) (10,22) (10,16) (10,12) (11,14) (11,15) (12,17) (12,19) (12,18) (12,20) (12,22) (12,16) (13,21) (14,15) (16,17) (16,19) (16,18) (16,20) (16,22) (17,19) (17,18) (17,20) (17,22) (18,19) (18,20) (18,22) (19,20) (19,22) (20,22)\nIs there a path between node 10 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph851-0_24", + "image": "data/connectivity/graph_visual/medium/graph851.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,24) (0,15) (0,7) (0,16) (1,3) (1,6) (1,8) (1,14) (1,23) (1,10) (1,11) (2,17) (2,9) (2,21) (2,13) (2,18) (2,4) (2,5) (2,20) (2,22) (2,19) (3,6) (3,8) (3,14) (3,23) (3,10) (3,11) (4,17) (4,9) (4,21) (4,13) (4,18) (4,5) (4,20) (4,22) (4,19) (5,17) (5,9) (5,21) (5,13) (5,18) (5,20) (5,22) (5,19) (6,8) (6,14) (6,23) (6,10) (6,11) (7,12) (7,24) (7,15) (7,16) (8,14) (8,23) (8,10) (8,11) (9,17) (9,21) (9,13) (9,18) (9,20) (9,22) (9,19) (10,14) (10,23) (10,11) (11,14) (11,23) (12,24) (12,15) (12,16) (13,17) (13,21) (13,18) (13,20) (13,22) (13,19) (14,23) (15,24) (15,16) (16,24) (17,21) (17,18) (17,20) (17,22) (17,19) (18,21) (18,20) (18,22) (18,19) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 0 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph305-3_16", + "image": "data/connectivity/graph_visual/medium/graph305.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,1) (0,18) (1,11) (1,18) (2,15) (2,14) (2,7) (2,5) (2,4) (2,3) (2,8) (2,6) (2,16) (3,15) (3,14) (3,5) (3,13) (3,4) (3,9) (3,6) (4,15) (4,7) (4,5) (4,12) (4,8) (4,9) (4,16) (5,14) (5,12) (5,17) (5,9) (5,6) (5,16) (6,15) (6,14) (6,7) (6,17) (6,16) (7,15) (7,14) (7,13) (7,12) (7,9) (7,16) (8,15) (8,14) (8,13) (8,12) (8,17) (8,16) (9,15) (9,14) (9,12) (11,19) (11,18) (12,15) (12,14) (12,13) (12,17) (13,15) (13,14) (14,15) (15,17) (15,16) (16,17) (18,19)\nIs there a path between node 3 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph721-20_7", + "image": "data/connectivity/graph_visual/medium/graph721.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,3) (0,9) (0,20) (0,15) (1,21) (1,11) (1,13) (1,23) (1,19) (1,17) (1,5) (1,4) (1,22) (1,2) (1,16) (1,24) (1,7) (1,18) (1,6) (1,12) (1,8) (1,10) (2,21) (2,11) (2,13) (2,23) (2,19) (2,17) (2,5) (2,4) (2,22) (2,16) (2,24) (2,7) (2,18) (2,6) (2,12) (2,8) (2,10) (3,14) (3,9) (3,20) (3,15) (4,21) (4,11) (4,13) (4,23) (4,19) (4,17) (4,5) (4,22) (4,16) (4,24) (4,7) (4,18) (4,6) (4,12) (4,8) (4,10) (5,21) (5,11) (5,13) (5,23) (5,19) (5,17) (5,22) (5,16) (5,24) (5,7) (5,18) (5,6) (5,12) (5,8) (5,10) (6,21) (6,11) (6,13) (6,23) (6,19) (6,17) (6,22) (6,16) (6,24) (6,7) (6,18) (6,12) (6,8) (6,10) (7,21) (7,11) (7,13) (7,23) (7,19) (7,17) (7,22) (7,16) (7,24) (7,18) (7,12) (7,8) (7,10) (8,21) (8,11) (8,13) (8,23) (8,19) (8,17) (8,22) (8,16) (8,24) (8,18) (8,12) (8,10) (9,14) (9,20) (9,15) (10,21) (10,11) (10,13) (10,23) (10,19) (10,17) (10,22) (10,16) (10,24) (10,18) (10,12) (11,21) (11,13) (11,23) (11,19) (11,17) (11,22) (11,16) (11,24) (11,18) (11,12) (12,21) (12,13) (12,23) (12,19) (12,17) (12,22) (12,16) (12,24) (12,18) (13,21) (13,23) (13,19) (13,17) (13,22) (13,16) (13,24) (13,18) (14,20) (14,15) (15,20) (16,21) (16,23) (16,19) (16,17) (16,22) (16,24) (16,18) (17,21) (17,23) (17,19) (17,22) (17,24) (17,18) (18,21) (18,23) (18,19) (18,22) (18,24) (19,21) (19,23) (19,22) (19,24) (21,23) (21,22) (21,24) (22,23) (22,24) (23,24)\nIs there a path between node 20 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph354-16_17", + "image": "data/connectivity/graph_visual/medium/graph354.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,9) (1,15) (1,18) (2,12) (2,10) (2,4) (2,19) (2,5) (2,6) (4,13) (4,11) (4,16) (4,6) (5,7) (5,16) (5,10) (5,19) (6,7) (6,10) (7,8) (7,13) (7,16) (7,10) (8,16) (9,20) (10,11) (10,12) (10,16) (11,16) (11,17) (12,16) (12,17) (14,15) (17,19)\nIs there a path between node 16 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph398-4_19", + "image": "data/connectivity/graph_visual/medium/graph398.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,12) (0,3) (0,11) (0,18) (0,7) (0,8) (0,9) (0,1) (0,10) (0,15) (0,17) (0,13) (0,16) (0,19) (0,2) (0,6) (0,5) (0,14) (1,12) (1,3) (1,11) (1,18) (1,7) (1,8) (1,9) (1,10) (1,15) (1,17) (1,13) (1,16) (1,19) (1,2) (1,6) (1,5) (1,14) (2,12) (2,3) (2,11) (2,18) (2,7) (2,8) (2,9) (2,10) (2,15) (2,17) (2,13) (2,16) (2,19) (2,6) (2,5) (2,14) (3,12) (3,11) (3,18) (3,7) (3,8) (3,9) (3,10) (3,15) (3,17) (3,13) (3,16) (3,19) (3,6) (3,5) (3,14) (4,20) (4,21) (5,12) (5,11) (5,18) (5,7) (5,8) (5,9) (5,10) (5,15) (5,17) (5,13) (5,16) (5,19) (5,6) (5,14) (6,12) (6,11) (6,18) (6,7) (6,8) (6,9) (6,10) (6,15) (6,17) (6,13) (6,16) (6,19) (6,14) (7,12) (7,11) (7,18) (7,8) (7,9) (7,10) (7,15) (7,17) (7,13) (7,16) (7,19) (7,14) (8,12) (8,11) (8,18) (8,9) (8,10) (8,15) (8,17) (8,13) (8,16) (8,19) (8,14) (9,12) (9,11) (9,18) (9,10) (9,15) (9,17) (9,13) (9,16) (9,19) (9,14) (10,12) (10,11) (10,18) (10,15) (10,17) (10,13) (10,16) (10,19) (10,14) (11,12) (11,18) (11,15) (11,17) (11,13) (11,16) (11,19) (11,14) (12,18) (12,15) (12,17) (12,13) (12,16) (12,19) (12,14) (13,18) (13,15) (13,17) (13,16) (13,19) (13,14) (14,18) (14,15) (14,17) (14,16) (14,19) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19) (20,21)\nIs there a path between node 4 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph527-2_20", + "image": "data/connectivity/graph_visual/medium/graph527.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,20) (0,4) (0,15) (0,19) (0,8) (0,17) (0,13) (0,3) (0,14) (0,5) (0,2) (0,16) (0,1) (0,10) (1,20) (1,4) (1,15) (1,19) (1,8) (1,17) (1,13) (1,3) (1,14) (1,5) (1,2) (1,16) (1,10) (2,20) (2,4) (2,15) (2,19) (2,8) (2,17) (2,13) (2,3) (2,14) (2,5) (2,16) (2,10) (3,20) (3,4) (3,15) (3,19) (3,8) (3,17) (3,13) (3,14) (3,5) (3,16) (3,10) (4,20) (4,15) (4,19) (4,8) (4,17) (4,13) (4,14) (4,5) (4,16) (4,10) (5,20) (5,15) (5,19) (5,8) (5,17) (5,13) (5,14) (5,16) (5,10) (6,12) (6,22) (6,9) (6,18) (6,21) (6,7) (6,11) (7,12) (7,22) (7,9) (7,18) (7,21) (7,11) (8,20) (8,15) (8,19) (8,17) (8,13) (8,14) (8,16) (8,10) (9,12) (9,22) (9,18) (9,21) (9,11) (10,20) (10,15) (10,19) (10,17) (10,13) (10,14) (10,16) (11,12) (11,22) (11,18) (11,21) (12,22) (12,18) (12,21) (13,20) (13,15) (13,19) (13,17) (13,14) (13,16) (14,20) (14,15) (14,19) (14,17) (14,16) (15,20) (15,19) (15,17) (15,16) (16,20) (16,19) (16,17) (17,20) (17,19) (18,22) (18,21) (19,20) (21,22)\nIs there a path between node 2 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph233-6_17", + "image": "data/connectivity/graph_visual/medium/graph233.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,7) (0,4) (0,1) (0,2) (0,14) (0,15) (0,8) (0,11) (0,9) (0,16) (1,17) (1,2) (1,15) (1,8) (1,9) (1,18) (2,7) (2,4) (2,14) (2,15) (2,12) (2,8) (2,18) (3,5) (3,13) (4,17) (4,15) (4,12) (4,6) (4,11) (4,16) (4,18) (6,17) (6,7) (6,14) (6,12) (6,11) (6,9) (6,16) (6,18) (7,17) (7,14) (7,15) (7,11) (7,9) (7,16) (8,17) (8,15) (8,18) (9,17) (9,14) (9,15) (9,12) (9,11) (9,18) (10,13) (11,17) (11,14) (11,15) (11,12) (11,16) (11,18) (12,17) (12,14) (12,16) (12,18) (14,17) (14,15) (14,16) (15,16) (15,18) (17,18)\nIs there a path between node 6 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph18-10_3", + "image": "data/connectivity/graph_visual/medium/graph18.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (0,2) (1,5) (1,2) (2,5) (2,10) (3,10) (3,4) (3,8) (4,5) (5,10) (5,8) (7,11) (8,10) (9,11)\nIs there a path between node 10 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph504-3_22", + "image": "data/connectivity/graph_visual/medium/graph504.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,3) (0,20) (0,18) (0,14) (0,10) (0,11) (1,16) (1,2) (1,18) (1,13) (1,4) (1,8) (2,11) (2,8) (2,12) (3,16) (3,14) (3,9) (3,10) (3,12) (4,20) (4,6) (4,8) (6,20) (6,14) (6,11) (6,12) (7,21) (7,13) (7,12) (8,21) (8,10) (8,11) (9,16) (9,20) (9,10) (10,15) (10,14) (10,17) (10,12) (11,16) (11,20) (11,21) (11,13) (12,14) (14,21) (14,17) (15,20) (15,17) (17,20) (18,21)\nIs there a path between node 3 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph401-21_11", + "image": "data/connectivity/graph_visual/medium/graph401.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,11) (0,1) (1,11) (2,4) (2,14) (3,21) (3,18) (3,6) (3,12) (3,13) (5,6) (6,21) (6,20) (6,8) (6,12) (6,13) (7,16) (7,12) (8,20) (9,20) (9,13) (10,11) (12,17) (12,16) (13,20) (13,17) (13,19) (15,21) (15,16) (15,19) (16,21) (16,19) (17,19) (18,19) (19,20) (20,21)\nIs there a path between node 21 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph86-3_1", + "image": "data/connectivity/graph_visual/medium/graph86.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,3) (0,1) (0,14) (0,13) (0,4) (0,10) (0,5) (1,3) (1,14) (1,13) (1,4) (1,10) (1,5) (2,8) (2,11) (2,7) (2,12) (2,6) (2,9) (3,14) (3,13) (3,4) (3,10) (3,5) (4,14) (4,13) (4,10) (4,5) (5,14) (5,13) (5,10) (6,8) (6,11) (6,7) (6,12) (6,9) (7,8) (7,11) (7,12) (7,9) (8,11) (8,12) (8,9) (9,11) (9,12) (10,14) (10,13) (11,12) (13,14)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph437-14_19", + "image": "data/connectivity/graph_visual/medium/graph437.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,12) (0,5) (1,21) (1,6) (2,7) (2,3) (4,8) (5,8) (5,12) (6,16) (6,21) (6,20) (6,13) (7,17) (7,11) (9,11) (9,10) (10,17) (13,18) (13,15) (15,19) (15,21) (16,19) (16,20) (20,21)\nIs there a path between node 14 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph40-12_3", + "image": "data/connectivity/graph_visual/medium/graph40.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,1) (0,4) (1,11) (2,3) (2,12) (4,6) (4,7) (5,9) (6,7) (7,9) (7,11) (8,10) (8,12) (9,11)\nIs there a path between node 12 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph407-1_15", + "image": "data/connectivity/graph_visual/medium/graph407.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,8) (0,11) (0,17) (0,1) (0,2) (0,12) (0,6) (0,18) (0,7) (0,15) (1,19) (1,8) (1,9) (1,11) (1,2) (1,12) (1,6) (1,7) (1,15) (2,19) (2,4) (2,9) (2,11) (2,17) (2,12) (2,6) (2,18) (2,15) (3,5) (3,13) (3,10) (4,19) (4,8) (4,9) (4,11) (4,17) (4,12) (4,6) (4,7) (4,15) (5,13) (5,10) (6,9) (6,11) (6,12) (6,18) (7,19) (7,8) (7,9) (7,11) (7,17) (7,15) (8,19) (8,11) (8,17) (8,12) (9,17) (9,12) (9,18) (10,13) (11,17) (11,15) (12,19) (12,17) (12,18) (12,15) (14,20) (14,21) (15,17) (15,18) (17,19) (17,18) (18,19) (20,21)\nIs there a path between node 1 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph635-8_14", + "image": "data/connectivity/graph_visual/medium/graph635.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (1,2) (1,14) (1,20) (1,18) (2,7) (3,17) (3,9) (3,16) (3,8) (3,5) (4,23) (4,7) (4,18) (5,19) (5,6) (5,16) (5,15) (6,21) (6,8) (6,10) (7,14) (7,12) (9,19) (9,13) (9,16) (10,13) (10,16) (11,19) (12,14) (13,16) (13,21) (15,17) (15,19) (16,21) (17,21) (20,23)\nIs there a path between node 8 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph767-11_20", + "image": "data/connectivity/graph_visual/medium/graph767.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (0,24) (0,15) (0,2) (0,1) (0,7) (0,8) (0,18) (0,23) (0,5) (0,20) (1,19) (1,24) (1,15) (1,2) (1,7) (1,8) (1,18) (1,23) (1,5) (1,20) (2,19) (2,24) (2,15) (2,7) (2,8) (2,18) (2,23) (2,5) (2,20) (3,12) (3,16) (3,9) (3,14) (3,22) (3,13) (3,4) (3,11) (3,10) (3,17) (3,21) (3,6) (4,12) (4,16) (4,9) (4,14) (4,22) (4,13) (4,11) (4,10) (4,17) (4,21) (4,6) (5,19) (5,24) (5,15) (5,7) (5,8) (5,18) (5,23) (5,20) (6,12) (6,16) (6,9) (6,14) (6,22) (6,13) (6,11) (6,10) (6,17) (6,21) (7,19) (7,24) (7,15) (7,8) (7,18) (7,23) (7,20) (8,19) (8,24) (8,15) (8,18) (8,23) (8,20) (9,12) (9,16) (9,14) (9,22) (9,13) (9,11) (9,10) (9,17) (9,21) (10,12) (10,16) (10,14) (10,22) (10,13) (10,11) (10,17) (10,21) (11,12) (11,16) (11,14) (11,22) (11,13) (11,17) (11,21) (12,16) (12,14) (12,22) (12,13) (12,17) (12,21) (13,16) (13,14) (13,22) (13,17) (13,21) (14,16) (14,22) (14,17) (14,21) (15,19) (15,24) (15,18) (15,23) (15,20) (16,22) (16,17) (16,21) (17,22) (17,21) (18,19) (18,24) (18,23) (18,20) (19,24) (19,23) (19,20) (20,24) (20,23) (21,22) (23,24)\nIs there a path between node 11 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph99-2_13", + "image": "data/connectivity/graph_visual/medium/graph99.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,14) (0,2) (0,4) (0,5) (0,15) (0,7) (1,9) (1,13) (1,12) (1,3) (2,14) (2,10) (2,4) (2,8) (2,15) (2,7) (3,9) (3,13) (3,12) (3,11) (4,14) (4,6) (4,10) (4,8) (4,15) (5,6) (5,8) (5,7) (6,14) (6,8) (6,15) (7,14) (7,10) (7,8) (7,15) (8,14) (8,10) (8,15) (9,13) (9,12) (9,11) (10,14) (10,15) (11,13) (11,12) (12,13) (14,15)\nIs there a path between node 2 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph401-14_20", + "image": "data/connectivity/graph_visual/medium/graph401.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,11) (0,1) (1,11) (2,4) (2,14) (3,21) (3,18) (3,6) (3,12) (3,13) (5,6) (6,21) (6,20) (6,8) (6,12) (6,13) (7,16) (7,12) (8,20) (9,20) (9,13) (10,11) (12,17) (12,16) (13,20) (13,17) (13,19) (15,21) (15,16) (15,19) (16,21) (16,19) (17,19) (18,19) (19,20) (20,21)\nIs there a path between node 14 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph697-15_11", + "image": "data/connectivity/graph_visual/medium/graph697.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,6) (0,21) (0,17) (0,16) (0,20) (0,7) (0,12) (0,14) (0,22) (0,15) (1,18) (1,4) (1,2) (1,10) (1,3) (1,23) (1,19) (1,11) (1,9) (1,13) (1,8) (2,18) (2,4) (2,10) (2,3) (2,23) (2,19) (2,11) (2,9) (2,13) (2,8) (3,18) (3,4) (3,10) (3,23) (3,19) (3,11) (3,9) (3,13) (3,8) (4,18) (4,10) (4,23) (4,19) (4,11) (4,9) (4,13) (4,8) (5,6) (5,21) (5,17) (5,16) (5,20) (5,7) (5,12) (5,14) (5,22) (5,15) (6,21) (6,17) (6,16) (6,20) (6,7) (6,12) (6,14) (6,22) (6,15) (7,21) (7,17) (7,16) (7,20) (7,12) (7,14) (7,22) (7,15) (8,18) (8,10) (8,23) (8,19) (8,11) (8,9) (8,13) (9,18) (9,10) (9,23) (9,19) (9,11) (9,13) (10,18) (10,23) (10,19) (10,11) (10,13) (11,18) (11,23) (11,19) (11,13) (12,21) (12,17) (12,16) (12,20) (12,14) (12,22) (12,15) (13,18) (13,23) (13,19) (14,21) (14,17) (14,16) (14,20) (14,22) (14,15) (15,21) (15,17) (15,16) (15,20) (15,22) (16,21) (16,17) (16,20) (16,22) (17,21) (17,20) (17,22) (18,23) (18,19) (19,23) (20,21) (20,22) (21,22)\nIs there a path between node 15 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph266-5_9", + "image": "data/connectivity/graph_visual/medium/graph266.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,6) (0,7) (1,8) (1,14) (2,6) (3,4) (3,7) (4,16) (4,7) (5,19) (6,13) (8,9) (8,14) (9,12) (9,11) (11,12) (12,18) (12,14) (15,17)\nIs there a path between node 5 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph779-24_15", + "image": "data/connectivity/graph_visual/medium/graph779.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,8) (0,19) (0,17) (0,22) (0,12) (0,16) (0,1) (0,10) (0,23) (0,14) (0,15) (0,6) (0,11) (0,21) (0,3) (0,20) (0,18) (0,24) (0,4) (0,2) (1,7) (1,8) (1,19) (1,17) (1,22) (1,12) (1,16) (1,10) (1,23) (1,14) (1,15) (1,6) (1,11) (1,21) (1,3) (1,20) (1,18) (1,24) (1,4) (1,2) (2,7) (2,8) (2,19) (2,17) (2,22) (2,12) (2,16) (2,10) (2,23) (2,14) (2,15) (2,6) (2,11) (2,21) (2,3) (2,20) (2,18) (2,24) (2,4) (3,7) (3,8) (3,19) (3,17) (3,22) (3,12) (3,16) (3,10) (3,23) (3,14) (3,15) (3,6) (3,11) (3,21) (3,20) (3,18) (3,24) (3,4) (4,7) (4,8) (4,19) (4,17) (4,22) (4,12) (4,16) (4,10) (4,23) (4,14) (4,15) (4,6) (4,11) (4,21) (4,20) (4,18) (4,24) (5,13) (5,9) (6,7) (6,8) (6,19) (6,17) (6,22) (6,12) (6,16) (6,10) (6,23) (6,14) (6,15) (6,11) (6,21) (6,20) (6,18) (6,24) (7,8) (7,19) (7,17) (7,22) (7,12) (7,16) (7,10) (7,23) (7,14) (7,15) (7,11) (7,21) (7,20) (7,18) (7,24) (8,19) (8,17) (8,22) (8,12) (8,16) (8,10) (8,23) (8,14) (8,15) (8,11) (8,21) (8,20) (8,18) (8,24) (9,13) (10,19) (10,17) (10,22) (10,12) (10,16) (10,23) (10,14) (10,15) (10,11) (10,21) (10,20) (10,18) (10,24) (11,19) (11,17) (11,22) (11,12) (11,16) (11,23) (11,14) (11,15) (11,21) (11,20) (11,18) (11,24) (12,19) (12,17) (12,22) (12,16) (12,23) (12,14) (12,15) (12,21) (12,20) (12,18) (12,24) (14,19) (14,17) (14,22) (14,16) (14,23) (14,15) (14,21) (14,20) (14,18) (14,24) (15,19) (15,17) (15,22) (15,16) (15,23) (15,21) (15,20) (15,18) (15,24) (16,19) (16,17) (16,22) (16,23) (16,21) (16,20) (16,18) (16,24) (17,19) (17,22) (17,23) (17,21) (17,20) (17,18) (17,24) (18,19) (18,22) (18,23) (18,21) (18,20) (18,24) (19,22) (19,23) (19,21) (19,20) (19,24) (20,22) (20,23) (20,21) (20,24) (21,22) (21,23) (21,24) (22,23) (22,24) (23,24)\nIs there a path between node 24 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph481-1_15", + "image": "data/connectivity/graph_visual/medium/graph481.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,14) (0,2) (0,17) (0,18) (0,9) (0,21) (0,8) (0,13) (0,10) (0,15) (0,12) (1,14) (1,17) (1,22) (1,18) (1,9) (1,21) (1,8) (1,13) (1,7) (1,15) (1,12) (1,19) (2,17) (2,18) (2,9) (2,21) (2,13) (2,7) (2,15) (2,19) (3,16) (5,6) (5,16) (6,16) (7,17) (7,18) (7,9) (7,21) (7,8) (7,10) (7,15) (7,20) (7,12) (7,19) (8,17) (8,22) (8,18) (8,21) (8,13) (8,10) (8,11) (8,20) (8,12) (8,19) (9,14) (9,17) (9,22) (9,18) (9,21) (9,13) (9,10) (9,15) (9,20) (10,14) (10,17) (10,22) (10,13) (10,15) (10,11) (10,20) (10,12) (10,19) (11,14) (11,18) (11,13) (11,15) (11,19) (12,14) (12,22) (12,21) (12,20) (13,17) (13,22) (13,18) (13,21) (13,15) (13,19) (14,17) (14,22) (14,18) (14,21) (14,15) (14,20) (14,19) (15,22) (15,18) (15,19) (17,18) (17,21) (17,19) (18,22) (18,21) (18,20) (18,19) (19,22) (20,22) (20,21) (21,22)\nIs there a path between node 1 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph639-3_5", + "image": "data/connectivity/graph_visual/medium/graph639.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,12) (1,4) (1,21) (2,19) (2,23) (2,12) (3,16) (3,21) (4,22) (4,16) (5,18) (5,17) (5,8) (5,6) (5,15) (5,19) (5,23) (6,14) (6,23) (7,13) (8,17) (8,15) (8,12) (9,20) (10,20) (10,21) (11,16) (12,17) (12,15) (14,23) (15,18) (15,19) (15,23) (16,21) (17,19) (18,19) (19,23)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph317-17_0", + "image": "data/connectivity/graph_visual/medium/graph317.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,1) (0,18) (0,8) (0,7) (1,18) (1,8) (1,7) (2,17) (2,16) (2,11) (2,5) (2,9) (2,19) (2,6) (2,10) (2,14) (2,4) (2,12) (2,3) (2,15) (2,13) (3,17) (3,16) (3,11) (3,5) (3,9) (3,19) (3,6) (3,10) (3,14) (3,4) (3,12) (3,15) (3,13) (4,17) (4,16) (4,11) (4,5) (4,9) (4,19) (4,6) (4,10) (4,14) (4,12) (4,15) (4,13) (5,17) (5,16) (5,11) (5,9) (5,19) (5,6) (5,10) (5,14) (5,12) (5,15) (5,13) (6,17) (6,16) (6,11) (6,9) (6,19) (6,10) (6,14) (6,12) (6,15) (6,13) (7,18) (7,8) (8,18) (9,17) (9,16) (9,11) (9,19) (9,10) (9,14) (9,12) (9,15) (9,13) (10,17) (10,16) (10,11) (10,19) (10,14) (10,12) (10,15) (10,13) (11,17) (11,16) (11,19) (11,14) (11,12) (11,15) (11,13) (12,17) (12,16) (12,19) (12,14) (12,15) (12,13) (13,17) (13,16) (13,19) (13,14) (13,15) (14,17) (14,16) (14,19) (14,15) (15,17) (15,16) (15,19) (16,17) (16,19) (17,19)\nIs there a path between node 17 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph510-12_11", + "image": "data/connectivity/graph_visual/medium/graph510.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,16) (0,13) (0,7) (0,18) (0,8) (0,20) (0,15) (1,22) (1,21) (1,8) (1,20) (1,15) (2,11) (2,20) (3,17) (4,16) (4,11) (4,7) (4,9) (4,8) (4,20) (5,22) (5,7) (5,18) (5,9) (7,22) (7,20) (8,9) (8,20) (9,16) (9,19) (9,20) (10,17) (11,16) (11,13) (11,18) (12,17) (13,16) (13,22) (13,14) (13,21) (14,22) (14,19) (15,16) (16,19) (16,18) (16,21)\nIs there a path between node 12 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph831-8_18", + "image": "data/connectivity/graph_visual/medium/graph831.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (1,14) (1,20) (2,3) (2,17) (2,18) (2,9) (2,23) (2,6) (2,21) (2,11) (3,24) (3,13) (3,18) (3,9) (3,23) (3,21) (3,16) (3,10) (3,8) (4,12) (4,7) (4,22) (4,20) (4,5) (5,14) (5,12) (5,7) (5,22) (5,20) (6,13) (6,17) (6,15) (6,21) (6,11) (6,10) (6,8) (7,14) (7,12) (7,22) (8,24) (8,13) (8,15) (8,18) (8,23) (8,11) (8,16) (8,10) (9,24) (9,15) (9,23) (9,11) (9,16) (9,10) (10,24) (10,13) (10,17) (10,15) (10,18) (10,23) (10,11) (10,16) (11,24) (11,13) (11,18) (11,23) (11,21) (12,22) (12,20) (13,24) (13,17) (13,18) (13,23) (13,21) (13,16) (14,20) (15,24) (15,17) (15,18) (15,21) (16,24) (16,17) (16,23) (17,24) (17,18) (17,23) (18,24) (20,22) (21,24) (21,23) (23,24)\nIs there a path between node 8 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph36-10_3", + "image": "data/connectivity/graph_visual/medium/graph36.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,2) (0,12) (0,11) (0,4) (2,10) (2,8) (2,4) (4,6) (4,11) (5,9) (6,7) (6,10) (6,11) (7,8) (8,10) (8,9) (9,12) (10,11)\nIs there a path between node 10 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph791-9_15", + "image": "data/connectivity/graph_visual/medium/graph791.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (1,16) (1,5) (1,10) (1,18) (2,7) (2,14) (2,11) (2,15) (3,16) (3,5) (3,12) (3,15) (3,10) (5,20) (5,24) (5,12) (5,7) (5,14) (7,20) (7,24) (7,18) (8,21) (8,23) (9,20) (9,16) (9,24) (10,20) (10,24) (10,15) (10,18) (11,16) (11,22) (12,24) (12,14) (12,15) (13,24) (13,14) (13,22) (15,18) (15,22) (16,24) (16,18) (17,19) (18,20) (19,21) (19,23) (21,23)\nIs there a path between node 9 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph665-1_20", + "image": "data/connectivity/graph_visual/medium/graph665.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,10) (0,14) (0,2) (0,8) (1,18) (1,23) (1,5) (1,4) (1,11) (1,9) (1,20) (1,17) (1,7) (2,10) (2,14) (2,16) (2,3) (2,8) (2,22) (3,12) (3,10) (3,14) (3,16) (3,8) (4,18) (4,15) (4,20) (4,17) (4,7) (5,23) (5,15) (5,21) (5,11) (5,9) (5,19) (5,17) (5,7) (7,23) (7,21) (7,11) (7,9) (7,20) (7,17) (8,12) (8,10) (8,14) (8,22) (9,18) (9,23) (9,15) (9,21) (9,11) (9,20) (9,19) (10,16) (10,22) (11,18) (11,15) (11,21) (11,20) (11,19) (11,17) (12,14) (12,16) (14,22) (15,18) (15,20) (17,20) (18,23) (18,19) (19,23) (19,21) (21,23)\nIs there a path between node 1 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph190-7_3", + "image": "data/connectivity/graph_visual/medium/graph190.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,10) (0,11) (0,5) (0,8) (0,12) (0,17) (0,13) (0,16) (0,6) (0,2) (0,9) (1,10) (1,11) (1,5) (1,8) (1,12) (1,17) (1,13) (1,16) (1,6) (1,2) (1,9) (2,10) (2,11) (2,5) (2,8) (2,12) (2,17) (2,13) (2,16) (2,6) (2,9) (3,15) (3,4) (3,7) (3,14) (4,15) (4,7) (4,14) (5,10) (5,11) (5,8) (5,12) (5,17) (5,13) (5,16) (5,6) (5,9) (6,10) (6,11) (6,8) (6,12) (6,17) (6,13) (6,16) (6,9) (7,15) (7,14) (8,10) (8,11) (8,12) (8,17) (8,13) (8,16) (8,9) (9,10) (9,11) (9,12) (9,17) (9,13) (9,16) (10,11) (10,12) (10,17) (10,13) (10,16) (11,12) (11,17) (11,13) (11,16) (12,17) (12,13) (12,16) (13,17) (13,16) (14,15) (16,17)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph328-10_13", + "image": "data/connectivity/graph_visual/medium/graph328.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,6) (0,1) (0,19) (1,14) (1,6) (1,2) (1,13) (2,5) (2,12) (2,3) (2,9) (3,8) (3,12) (3,13) (3,17) (3,7) (4,16) (4,10) (5,11) (5,20) (5,6) (5,7) (6,17) (6,7) (7,11) (7,14) (7,13) (7,19) (8,20) (8,19) (9,12) (9,13) (11,14) (11,12) (11,13) (12,14) (12,17) (12,19) (13,20) (13,17) (13,15) (14,19) (14,15) (15,20) (15,18) (17,19) (18,20) (19,20)\nIs there a path between node 10 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph452-15_5", + "image": "data/connectivity/graph_visual/medium/graph452.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,5) (0,13) (0,16) (0,4) (0,12) (1,5) (1,13) (1,9) (1,16) (1,4) (1,2) (2,13) (2,14) (2,4) (3,11) (3,19) (3,18) (3,15) (3,20) (3,6) (3,8) (3,10) (3,21) (4,13) (4,14) (4,9) (4,12) (5,13) (5,14) (5,9) (5,16) (6,11) (6,19) (6,18) (6,15) (6,17) (6,10) (6,21) (6,7) (7,11) (7,19) (7,18) (7,15) (7,20) (7,17) (7,8) (7,10) (7,21) (8,11) (8,18) (8,15) (8,20) (8,21) (9,13) (9,14) (9,16) (9,12) (10,11) (10,19) (10,18) (10,20) (10,17) (10,21) (11,18) (11,20) (14,16) (15,19) (15,18) (15,20) (15,17) (15,21) (17,19) (17,18) (17,20) (17,21) (18,19) (18,20) (19,20) (19,21) (20,21)\nIs there a path between node 15 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph144-13_12", + "image": "data/connectivity/graph_visual/medium/graph144.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,14) (0,8) (0,3) (0,12) (0,17) (0,2) (0,15) (1,13) (1,8) (1,17) (1,16) (1,2) (1,9) (2,3) (2,12) (2,16) (3,6) (3,14) (3,8) (3,17) (3,16) (3,15) (4,7) (4,5) (4,11) (5,11) (6,10) (6,13) (6,14) (6,8) (6,17) (6,9) (7,11) (8,13) (8,14) (8,12) (8,17) (8,16) (8,9) (9,10) (9,13) (9,14) (9,12) (9,17) (9,16) (9,15) (10,12) (10,17) (10,16) (10,15) (12,13) (12,14) (12,17) (12,16) (12,15) (13,17) (13,16) (13,15) (14,17) (14,15) (15,16) (16,17)\nIs there a path between node 13 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph790-18_21", + "image": "data/connectivity/graph_visual/medium/graph790.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,23) (1,9) (2,13) (2,16) (2,24) (3,5) (3,7) (3,11) (4,6) (4,12) (4,5) (4,14) (4,7) (5,6) (5,12) (5,14) (5,11) (6,17) (6,20) (6,7) (10,19) (10,23) (10,16) (10,18) (11,12) (11,20) (11,15) (13,16) (13,22) (13,24) (14,17) (14,20) (15,20) (16,23) (17,20) (18,22) (22,23) (23,24)\nIs there a path between node 18 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph547-23_8", + "image": "data/connectivity/graph_visual/medium/graph547.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,8) (1,15) (1,14) (1,20) (1,23) (2,5) (2,12) (2,10) (2,19) (2,7) (3,16) (4,12) (4,7) (5,7) (6,15) (6,18) (6,22) (6,20) (6,23) (7,12) (8,16) (8,14) (8,18) (8,13) (9,12) (9,10) (12,19) (13,18) (13,20) (14,23) (15,16) (16,22) (16,23) (20,22)\nIs there a path between node 23 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph210-12_16", + "image": "data/connectivity/graph_visual/medium/graph210.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,5) (0,9) (0,1) (0,2) (0,18) (0,10) (0,7) (0,8) (0,16) (1,11) (1,14) (1,13) (1,17) (1,3) (1,9) (1,10) (1,8) (1,16) (1,12) (2,11) (2,14) (2,13) (2,17) (2,5) (2,9) (2,18) (2,6) (2,10) (2,7) (2,8) (2,16) (2,12) (3,11) (3,14) (3,13) (3,5) (3,18) (3,6) (3,10) (3,7) (3,16) (3,12) (4,15) (5,11) (5,14) (5,13) (5,9) (5,18) (5,6) (5,10) (5,7) (5,16) (5,12) (6,14) (6,13) (6,9) (6,18) (6,7) (7,11) (7,14) (7,9) (7,18) (7,10) (7,8) (7,16) (7,12) (8,13) (8,17) (8,10) (8,16) (8,12) (9,11) (9,13) (9,17) (9,18) (9,10) (9,12) (10,11) (10,14) (10,13) (10,18) (10,16) (11,14) (11,13) (11,17) (11,18) (12,14) (12,13) (12,18) (12,16) (13,17) (13,18) (13,16) (14,17) (14,18) (14,16) (16,17)\nIs there a path between node 12 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph502-8_14", + "image": "data/connectivity/graph_visual/medium/graph502.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,3) (0,7) (0,6) (1,19) (1,12) (1,9) (1,22) (1,21) (1,17) (1,2) (1,11) (2,14) (2,21) (2,4) (2,11) (4,10) (4,20) (4,21) (4,13) (4,17) (5,7) (8,19) (8,21) (8,17) (8,11) (9,16) (9,12) (9,15) (10,14) (11,19) (12,22) (12,21) (12,17) (13,14) (13,19) (13,15) (13,21) (14,20) (14,15) (15,16) (15,20) (15,19) (15,21) (16,22) (17,20) (17,19) (17,22) (20,21) (21,22)\nIs there a path between node 8 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph195-5_11", + "image": "data/connectivity/graph_visual/medium/graph195.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,1) (1,2) (3,11) (3,15) (3,8) (5,18) (5,7) (6,17) (6,7) (7,13) (7,8) (7,14) (8,18) (8,12) (9,11) (9,15) (9,13) (9,17) (10,18) (11,13) (11,17) (12,18) (12,17) (12,14) (13,17) (14,17) (17,18)\nIs there a path between node 5 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph606-4_6", + "image": "data/connectivity/graph_visual/medium/graph606.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,23) (1,16) (2,10) (2,11) (2,20) (2,21) (2,3) (3,15) (3,20) (3,21) (4,22) (4,7) (4,9) (4,12) (4,8) (4,14) (4,19) (5,22) (5,7) (5,9) (5,12) (5,8) (5,14) (5,19) (7,13) (7,22) (7,9) (7,12) (7,18) (7,19) (8,13) (8,9) (8,12) (8,18) (8,14) (8,19) (9,13) (9,12) (9,14) (10,15) (10,11) (11,15) (11,20) (11,21) (12,13) (12,22) (12,18) (12,14) (13,22) (13,18) (13,19) (14,22) (14,18) (14,19) (15,21) (16,17) (18,19) (19,22)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph692-3_21", + "image": "data/connectivity/graph_visual/medium/graph692.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,22) (0,23) (0,10) (0,16) (0,18) (0,3) (0,13) (0,5) (0,8) (0,17) (0,12) (0,6) (0,9) (0,4) (0,1) (0,14) (1,19) (1,22) (1,23) (1,10) (1,16) (1,18) (1,3) (1,13) (1,5) (1,8) (1,17) (1,12) (1,6) (1,9) (1,4) (1,14) (2,20) (2,7) (2,11) (2,15) (2,21) (3,19) (3,22) (3,23) (3,10) (3,16) (3,18) (3,13) (3,5) (3,8) (3,17) (3,12) (3,6) (3,9) (3,4) (3,14) (4,19) (4,22) (4,23) (4,10) (4,16) (4,18) (4,13) (4,5) (4,8) (4,17) (4,12) (4,6) (4,9) (4,14) (5,19) (5,22) (5,23) (5,10) (5,16) (5,18) (5,13) (5,8) (5,17) (5,12) (5,6) (5,9) (5,14) (6,19) (6,22) (6,23) (6,10) (6,16) (6,18) (6,13) (6,8) (6,17) (6,12) (6,9) (6,14) (7,20) (7,11) (7,15) (7,21) (8,19) (8,22) (8,23) (8,10) (8,16) (8,18) (8,13) (8,17) (8,12) (8,9) (8,14) (9,19) (9,22) (9,23) (9,10) (9,16) (9,18) (9,13) (9,17) (9,12) (9,14) (10,19) (10,22) (10,23) (10,16) (10,18) (10,13) (10,17) (10,12) (10,14) (11,20) (11,15) (11,21) (12,19) (12,22) (12,23) (12,16) (12,18) (12,13) (12,17) (12,14) (13,19) (13,22) (13,23) (13,16) (13,18) (13,17) (13,14) (14,19) (14,22) (14,23) (14,16) (14,18) (14,17) (15,20) (15,21) (16,19) (16,22) (16,23) (16,18) (16,17) (17,19) (17,22) (17,23) (17,18) (18,19) (18,22) (18,23) (19,22) (19,23) (20,21) (22,23)\nIs there a path between node 3 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph675-9_17", + "image": "data/connectivity/graph_visual/medium/graph675.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,22) (0,21) (0,14) (0,19) (0,13) (0,18) (0,12) (0,15) (0,6) (0,7) (0,10) (0,20) (0,2) (0,4) (0,8) (0,17) (0,23) (1,3) (1,16) (1,11) (1,9) (2,5) (2,22) (2,21) (2,14) (2,19) (2,13) (2,18) (2,12) (2,15) (2,6) (2,7) (2,10) (2,20) (2,4) (2,8) (2,17) (2,23) (3,16) (3,11) (3,9) (4,5) (4,22) (4,21) (4,14) (4,19) (4,13) (4,18) (4,12) (4,15) (4,6) (4,7) (4,10) (4,20) (4,8) (4,17) (4,23) (5,22) (5,21) (5,14) (5,19) (5,13) (5,18) (5,12) (5,15) (5,6) (5,7) (5,10) (5,20) (5,8) (5,17) (5,23) (6,22) (6,21) (6,14) (6,19) (6,13) (6,18) (6,12) (6,15) (6,7) (6,10) (6,20) (6,8) (6,17) (6,23) (7,22) (7,21) (7,14) (7,19) (7,13) (7,18) (7,12) (7,15) (7,10) (7,20) (7,8) (7,17) (7,23) (8,22) (8,21) (8,14) (8,19) (8,13) (8,18) (8,12) (8,15) (8,10) (8,20) (8,17) (8,23) (9,16) (9,11) (10,22) (10,21) (10,14) (10,19) (10,13) (10,18) (10,12) (10,15) (10,20) (10,17) (10,23) (11,16) (12,22) (12,21) (12,14) (12,19) (12,13) (12,18) (12,15) (12,20) (12,17) (12,23) (13,22) (13,21) (13,14) (13,19) (13,18) (13,15) (13,20) (13,17) (13,23) (14,22) (14,21) (14,19) (14,18) (14,15) (14,20) (14,17) (14,23) (15,22) (15,21) (15,19) (15,18) (15,20) (15,17) (15,23) (17,22) (17,21) (17,19) (17,18) (17,20) (17,23) (18,22) (18,21) (18,19) (18,20) (18,23) (19,22) (19,21) (19,20) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 9 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph495-5_14", + "image": "data/connectivity/graph_visual/medium/graph495.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,14) (1,21) (1,3) (1,15) (1,7) (3,12) (4,10) (5,10) (6,22) (7,21) (7,15) (9,12) (11,13) (11,21) (14,20) (15,17) (15,21) (16,18) (18,22)\nIs there a path between node 5 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph530-12_21", + "image": "data/connectivity/graph_visual/medium/graph530.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,5) (0,1) (0,18) (0,20) (0,19) (0,4) (0,10) (0,16) (0,12) (0,8) (0,21) (0,3) (0,9) (0,6) (0,11) (0,13) (1,5) (1,18) (1,20) (1,19) (1,4) (1,10) (1,16) (1,12) (1,8) (1,21) (1,3) (1,9) (1,6) (1,11) (1,13) (2,15) (2,22) (3,5) (3,18) (3,20) (3,19) (3,4) (3,10) (3,16) (3,12) (3,8) (3,21) (3,9) (3,6) (3,11) (3,13) (4,5) (4,18) (4,20) (4,19) (4,10) (4,16) (4,12) (4,8) (4,21) (4,9) (4,6) (4,11) (4,13) (5,18) (5,20) (5,19) (5,10) (5,16) (5,12) (5,8) (5,21) (5,9) (5,6) (5,11) (5,13) (6,18) (6,20) (6,19) (6,10) (6,16) (6,12) (6,8) (6,21) (6,9) (6,11) (6,13) (7,14) (7,17) (8,18) (8,20) (8,19) (8,10) (8,16) (8,12) (8,21) (8,9) (8,11) (8,13) (9,18) (9,20) (9,19) (9,10) (9,16) (9,12) (9,21) (9,11) (9,13) (10,18) (10,20) (10,19) (10,16) (10,12) (10,21) (10,11) (10,13) (11,18) (11,20) (11,19) (11,16) (11,12) (11,21) (11,13) (12,18) (12,20) (12,19) (12,16) (12,21) (12,13) (13,18) (13,20) (13,19) (13,16) (13,21) (14,17) (15,22) (16,18) (16,20) (16,19) (16,21) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 12 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph835-8_0", + "image": "data/connectivity/graph_visual/medium/graph835.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (0,3) (1,24) (1,12) (1,17) (1,9) (1,15) (1,16) (1,2) (1,10) (1,13) (1,4) (1,19) (1,7) (1,14) (2,24) (2,12) (2,17) (2,9) (2,15) (2,16) (2,10) (2,13) (2,4) (2,19) (2,7) (2,14) (3,18) (4,24) (4,12) (4,17) (4,9) (4,15) (4,16) (4,10) (4,13) (4,19) (4,7) (4,14) (5,11) (5,23) (5,20) (5,8) (6,22) (6,21) (7,24) (7,12) (7,17) (7,9) (7,15) (7,16) (7,10) (7,13) (7,19) (7,14) (8,11) (8,23) (8,20) (9,24) (9,12) (9,17) (9,15) (9,16) (9,10) (9,13) (9,19) (9,14) (10,24) (10,12) (10,17) (10,15) (10,16) (10,13) (10,19) (10,14) (11,23) (11,20) (12,24) (12,17) (12,15) (12,16) (12,13) (12,19) (12,14) (13,24) (13,17) (13,15) (13,16) (13,19) (13,14) (14,24) (14,17) (14,15) (14,16) (14,19) (15,24) (15,17) (15,16) (15,19) (16,24) (16,17) (16,19) (17,24) (17,19) (19,24) (20,23) (21,22)\nIs there a path between node 8 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph341-11_6", + "image": "data/connectivity/graph_visual/medium/graph341.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,20) (0,19) (1,16) (1,7) (1,2) (1,15) (1,17) (2,7) (3,5) (3,11) (3,8) (3,4) (3,13) (3,18) (3,9) (4,11) (4,8) (4,6) (4,18) (4,9) (4,12) (5,8) (5,13) (5,6) (6,13) (6,18) (6,9) (6,12) (7,16) (7,15) (7,17) (8,11) (8,13) (8,18) (8,9) (9,11) (9,12) (10,20) (10,19) (10,14) (11,18) (11,12) (12,13) (13,18) (14,20) (15,17) (19,20)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph593-14_9", + "image": "data/connectivity/graph_visual/medium/graph593.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,7) (0,14) (0,8) (0,5) (0,4) (0,3) (0,23) (0,12) (0,15) (0,13) (0,17) (0,2) (1,19) (1,7) (1,14) (1,8) (1,3) (1,23) (1,12) (1,15) (1,13) (1,17) (1,6) (2,21) (2,19) (2,7) (2,5) (2,4) (2,3) (2,13) (3,21) (3,19) (3,14) (3,5) (3,4) (3,23) (3,12) (3,15) (4,21) (4,19) (4,14) (4,8) (4,5) (4,23) (4,12) (4,15) (4,6) (5,21) (5,19) (5,7) (5,8) (5,12) (5,17) (6,19) (6,7) (6,23) (6,12) (6,15) (6,13) (6,17) (7,21) (7,14) (7,12) (7,15) (7,13) (7,17) (8,21) (8,19) (8,12) (8,13) (9,11) (9,22) (9,20) (11,22) (11,18) (11,20) (12,14) (12,23) (12,15) (12,13) (12,17) (13,21) (13,23) (14,21) (14,19) (14,23) (14,15) (14,17) (15,21) (15,19) (15,23) (15,17) (16,22) (16,20) (17,19) (17,23) (19,21) (19,23) (20,22)\nIs there a path between node 14 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph503-0_19", + "image": "data/connectivity/graph_visual/medium/graph503.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,7) (0,9) (0,16) (0,6) (0,13) (0,1) (1,2) (1,10) (1,16) (1,13) (2,16) (2,12) (4,21) (4,6) (4,13) (4,18) (5,22) (5,8) (5,15) (6,10) (6,13) (8,22) (8,15) (9,17) (9,10) (9,21) (9,13) (9,18) (10,19) (10,12) (10,13) (12,17) (12,19) (12,13) (12,18) (13,17) (13,18) (15,22) (15,20) (16,19) (17,19) (17,21) (18,21) (20,22)\nIs there a path between node 0 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph746-17_12", + "image": "data/connectivity/graph_visual/medium/graph746.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,21) (0,14) (0,1) (0,22) (0,16) (0,19) (0,5) (0,10) (0,20) (0,11) (0,24) (0,13) (1,21) (1,9) (1,3) (1,14) (1,22) (1,10) (1,20) (1,12) (1,11) (1,24) (1,13) (1,23) (2,8) (2,4) (2,18) (2,15) (3,9) (3,14) (3,16) (3,19) (3,7) (3,6) (3,5) (3,10) (3,11) (4,8) (4,17) (4,18) (4,15) (5,9) (5,14) (5,22) (5,7) (5,6) (5,10) (5,20) (5,12) (5,11) (5,13) (5,23) (6,21) (6,9) (6,22) (6,19) (6,7) (6,20) (6,12) (6,11) (6,13) (6,23) (7,21) (7,9) (7,14) (7,16) (7,19) (7,10) (7,20) (7,12) (7,11) (7,24) (7,13) (7,23) (8,17) (8,18) (8,15) (9,21) (9,16) (9,10) (9,20) (9,12) (9,11) (9,24) (9,13) (9,23) (10,22) (10,19) (10,12) (10,11) (10,13) (10,23) (11,21) (11,22) (11,19) (11,20) (11,12) (11,24) (11,13) (11,23) (12,21) (12,14) (12,22) (12,20) (12,24) (12,13) (12,23) (13,21) (13,14) (13,22) (13,16) (13,20) (13,23) (14,21) (14,16) (14,20) (14,24) (14,23) (15,18) (16,21) (16,22) (16,19) (16,20) (16,24) (16,23) (17,18) (19,21) (19,20) (19,24) (19,23) (20,21) (20,24) (20,23) (21,24) (21,23) (22,23) (23,24)\nIs there a path between node 17 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph443-8_11", + "image": "data/connectivity/graph_visual/medium/graph443.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,14) (0,16) (0,2) (0,3) (0,18) (0,13) (0,17) (0,15) (0,12) (0,6) (1,10) (1,16) (1,4) (1,2) (1,3) (1,9) (1,18) (1,21) (1,13) (1,15) (1,12) (1,8) (1,6) (2,10) (2,14) (2,16) (2,3) (2,9) (2,7) (2,18) (2,13) (2,17) (2,15) (2,12) (2,8) (2,6) (3,19) (3,10) (3,16) (3,4) (3,7) (3,21) (3,13) (3,12) (3,6) (4,19) (4,10) (4,14) (4,16) (4,21) (4,13) (4,17) (4,15) (4,6) (5,11) (6,19) (6,10) (6,7) (6,18) (6,13) (6,17) (6,15) (7,19) (7,10) (7,14) (7,16) (7,9) (7,18) (7,13) (7,17) (7,15) (7,12) (8,16) (8,9) (8,18) (8,21) (8,17) (8,12) (9,19) (9,18) (9,21) (9,17) (9,15) (9,12) (10,14) (10,16) (10,18) (10,13) (10,17) (10,15) (10,12) (12,14) (12,16) (12,21) (12,13) (12,17) (12,15) (13,16) (13,18) (13,17) (13,15) (14,19) (14,16) (14,18) (14,21) (14,17) (14,15) (15,16) (15,21) (16,19) (16,21) (16,17) (17,19) (17,18) (18,19) (18,21) (19,21)\nIs there a path between node 8 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph809-5_18", + "image": "data/connectivity/graph_visual/medium/graph809.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (1,23) (1,15) (1,8) (1,17) (1,19) (1,9) (1,12) (1,20) (1,10) (1,5) (1,22) (1,14) (1,4) (1,18) (1,21) (2,13) (2,3) (2,16) (3,16) (4,23) (4,15) (4,7) (4,17) (4,9) (4,12) (4,20) (4,5) (4,22) (4,14) (4,21) (5,23) (5,15) (5,8) (5,7) (5,19) (5,9) (5,20) (5,22) (5,14) (5,21) (6,24) (6,11) (7,15) (7,8) (7,17) (7,12) (7,20) (7,10) (7,18) (7,21) (8,15) (8,17) (8,19) (8,9) (8,22) (8,14) (8,18) (9,23) (9,15) (9,17) (9,19) (9,20) (9,10) (9,18) (9,21) (10,23) (10,19) (10,22) (10,14) (10,21) (12,23) (12,15) (12,17) (12,19) (12,22) (12,18) (14,15) (14,19) (14,20) (14,22) (14,18) (14,21) (15,19) (15,20) (15,22) (15,18) (17,23) (17,19) (17,20) (17,18) (17,21) (18,23) (18,22) (19,23) (19,20) (19,21) (20,22) (20,21) (21,22)\nIs there a path between node 5 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph696-12_22", + "image": "data/connectivity/graph_visual/medium/graph696.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,17) (0,12) (0,5) (0,7) (0,20) (0,13) (0,14) (0,8) (0,9) (0,19) (0,4) (0,21) (0,1) (1,15) (1,17) (1,12) (1,5) (1,7) (1,20) (1,13) (1,14) (1,8) (1,9) (1,19) (1,4) (1,21) (2,6) (2,18) (2,23) (2,3) (2,16) (2,11) (2,22) (2,10) (3,6) (3,18) (3,23) (3,16) (3,11) (3,22) (3,10) (4,15) (4,17) (4,12) (4,5) (4,7) (4,20) (4,13) (4,14) (4,8) (4,9) (4,19) (4,21) (5,15) (5,17) (5,12) (5,7) (5,20) (5,13) (5,14) (5,8) (5,9) (5,19) (5,21) (6,18) (6,23) (6,16) (6,11) (6,22) (6,10) (7,15) (7,17) (7,12) (7,20) (7,13) (7,14) (7,8) (7,9) (7,19) (7,21) (8,15) (8,17) (8,12) (8,20) (8,13) (8,14) (8,9) (8,19) (8,21) (9,15) (9,17) (9,12) (9,20) (9,13) (9,14) (9,19) (9,21) (10,18) (10,23) (10,16) (10,11) (10,22) (11,18) (11,23) (11,16) (11,22) (12,15) (12,17) (12,20) (12,13) (12,14) (12,19) (12,21) (13,15) (13,17) (13,20) (13,14) (13,19) (13,21) (14,15) (14,17) (14,20) (14,19) (14,21) (15,17) (15,20) (15,19) (15,21) (16,18) (16,23) (16,22) (17,20) (17,19) (17,21) (18,23) (18,22) (19,20) (19,21) (20,21) (22,23)\nIs there a path between node 12 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph149-4_10", + "image": "data/connectivity/graph_visual/medium/graph149.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,10) (0,17) (0,5) (0,13) (0,15) (0,16) (0,3) (0,7) (0,11) (0,1) (0,4) (0,14) (1,12) (1,10) (1,17) (1,5) (1,13) (1,15) (1,16) (1,3) (1,7) (1,11) (1,4) (1,14) (2,8) (2,6) (3,12) (3,10) (3,17) (3,5) (3,13) (3,15) (3,16) (3,7) (3,11) (3,4) (3,14) (4,12) (4,10) (4,17) (4,5) (4,13) (4,15) (4,16) (4,7) (4,11) (4,14) (5,12) (5,10) (5,17) (5,13) (5,15) (5,16) (5,7) (5,11) (5,14) (6,8) (7,12) (7,10) (7,17) (7,13) (7,15) (7,16) (7,11) (7,14) (10,12) (10,17) (10,13) (10,15) (10,16) (10,11) (10,14) (11,12) (11,17) (11,13) (11,15) (11,16) (11,14) (12,17) (12,13) (12,15) (12,16) (12,14) (13,17) (13,15) (13,16) (13,14) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 4 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph149-13_11", + "image": "data/connectivity/graph_visual/medium/graph149.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,10) (0,17) (0,5) (0,13) (0,15) (0,16) (0,3) (0,7) (0,11) (0,1) (0,4) (0,14) (1,12) (1,10) (1,17) (1,5) (1,13) (1,15) (1,16) (1,3) (1,7) (1,11) (1,4) (1,14) (2,8) (2,6) (3,12) (3,10) (3,17) (3,5) (3,13) (3,15) (3,16) (3,7) (3,11) (3,4) (3,14) (4,12) (4,10) (4,17) (4,5) (4,13) (4,15) (4,16) (4,7) (4,11) (4,14) (5,12) (5,10) (5,17) (5,13) (5,15) (5,16) (5,7) (5,11) (5,14) (6,8) (7,12) (7,10) (7,17) (7,13) (7,15) (7,16) (7,11) (7,14) (10,12) (10,17) (10,13) (10,15) (10,16) (10,11) (10,14) (11,12) (11,17) (11,13) (11,15) (11,16) (11,14) (12,17) (12,13) (12,15) (12,16) (12,14) (13,17) (13,15) (13,16) (13,14) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 13 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph108-2_11", + "image": "data/connectivity/graph_visual/medium/graph108.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,12) (0,13) (0,3) (0,4) (0,10) (1,6) (1,15) (1,9) (1,2) (1,7) (1,11) (1,5) (1,14) (1,8) (2,6) (2,15) (2,9) (2,7) (2,11) (2,5) (2,14) (2,8) (3,12) (3,13) (3,4) (3,10) (4,12) (4,13) (4,10) (5,6) (5,15) (5,9) (5,7) (5,11) (5,14) (5,8) (6,15) (6,9) (6,7) (6,11) (6,14) (6,8) (7,15) (7,9) (7,11) (7,14) (7,8) (8,15) (8,9) (8,11) (8,14) (9,15) (9,11) (9,14) (10,12) (10,13) (11,15) (11,14) (12,13) (14,15)\nIs there a path between node 2 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph367-14_17", + "image": "data/connectivity/graph_visual/medium/graph367.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,8) (0,14) (0,2) (0,17) (1,5) (1,9) (1,3) (1,11) (1,6) (1,19) (1,20) (1,4) (1,18) (1,10) (1,7) (2,16) (2,8) (2,14) (2,15) (2,12) (3,5) (3,13) (3,6) (3,20) (3,4) (3,18) (3,10) (3,7) (4,5) (4,9) (4,11) (4,19) (4,18) (4,10) (4,7) (5,13) (5,9) (5,11) (5,6) (5,19) (5,20) (5,18) (5,10) (6,13) (6,9) (6,11) (6,18) (6,10) (7,9) (7,11) (7,20) (8,12) (9,13) (9,11) (9,19) (9,20) (9,10) (10,13) (10,19) (10,20) (10,18) (11,19) (11,20) (12,16) (12,14) (12,15) (12,17) (13,18) (14,16) (14,15) (16,17) (18,19) (19,20)\nIs there a path between node 14 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph277-3_17", + "image": "data/connectivity/graph_visual/medium/graph277.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,12) (0,10) (0,16) (1,7) (1,18) (1,3) (1,14) (1,11) (1,5) (1,13) (1,19) (1,15) (1,6) (1,9) (1,8) (1,4) (3,7) (3,18) (3,14) (3,11) (3,5) (3,13) (3,19) (3,15) (3,6) (3,9) (3,8) (3,4) (4,7) (4,18) (4,14) (4,11) (4,5) (4,13) (4,19) (4,15) (4,6) (4,9) (4,8) (5,7) (5,18) (5,14) (5,11) (5,13) (5,19) (5,15) (5,6) (5,9) (5,8) (6,7) (6,18) (6,14) (6,11) (6,13) (6,19) (6,15) (6,9) (6,8) (7,18) (7,14) (7,11) (7,13) (7,19) (7,15) (7,9) (7,8) (8,18) (8,14) (8,11) (8,13) (8,19) (8,15) (8,9) (9,18) (9,14) (9,11) (9,13) (9,19) (9,15) (10,17) (10,12) (10,16) (11,18) (11,14) (11,13) (11,19) (11,15) (12,17) (12,16) (13,18) (13,14) (13,19) (13,15) (14,18) (14,19) (14,15) (15,18) (15,19) (16,17) (18,19)\nIs there a path between node 3 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph135-2_12", + "image": "data/connectivity/graph_visual/medium/graph135.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,14) (0,3) (0,5) (1,2) (1,10) (1,3) (1,5) (2,6) (2,10) (3,17) (3,14) (3,6) (3,9) (4,14) (4,7) (4,9) (5,17) (5,14) (5,6) (5,10) (5,7) (6,14) (6,16) (6,7) (9,17) (9,16) (9,10) (10,14) (11,15) (12,13) (14,17) (14,16) (14,15) (15,17)\nIs there a path between node 2 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph165-17_11", + "image": "data/connectivity/graph_visual/medium/graph165.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,2) (0,13) (0,11) (0,4) (0,17) (1,14) (1,12) (2,13) (2,10) (2,8) (2,4) (3,13) (3,10) (3,4) (4,5) (4,7) (5,10) (7,16) (9,15) (10,16) (10,13) (11,15) (11,17) (13,16) (13,15) (15,16)\nIs there a path between node 17 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph650-22_17", + "image": "data/connectivity/graph_visual/medium/graph650.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,22) (0,8) (0,16) (0,23) (0,21) (0,5) (1,14) (1,12) (1,9) (1,18) (1,17) (1,15) (1,10) (1,13) (2,20) (2,19) (2,22) (2,6) (2,8) (2,16) (2,21) (2,5) (2,4) (3,11) (3,14) (3,7) (3,18) (3,15) (3,10) (4,20) (4,22) (4,8) (4,23) (4,5) (5,20) (5,19) (5,22) (5,6) (5,8) (5,16) (5,21) (6,19) (6,22) (6,8) (6,16) (6,23) (6,21) (7,11) (7,12) (7,18) (7,17) (7,15) (7,10) (7,13) (8,20) (8,19) (8,22) (8,16) (8,21) (9,11) (9,14) (9,12) (9,18) (9,17) (9,13) (10,11) (10,12) (10,17) (10,15) (11,14) (11,12) (11,18) (11,17) (11,15) (11,13) (12,14) (12,17) (12,13) (13,14) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (16,20) (16,19) (16,22) (17,18) (19,20) (19,22) (19,23) (19,21) (20,22) (20,21) (21,22) (22,23)\nIs there a path between node 22 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph857-21_3", + "image": "data/connectivity/graph_visual/medium/graph857.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,21) (0,9) (0,1) (0,3) (0,4) (0,16) (0,24) (0,23) (0,22) (0,8) (0,11) (0,6) (0,14) (0,13) (1,2) (1,21) (1,9) (1,3) (1,4) (1,16) (1,24) (1,23) (1,22) (1,8) (1,11) (1,6) (1,14) (1,13) (2,21) (2,9) (2,3) (2,4) (2,16) (2,24) (2,23) (2,22) (2,8) (2,11) (2,6) (2,14) (2,13) (3,21) (3,9) (3,4) (3,16) (3,24) (3,23) (3,22) (3,8) (3,11) (3,6) (3,14) (3,13) (4,21) (4,9) (4,16) (4,24) (4,23) (4,22) (4,8) (4,11) (4,6) (4,14) (4,13) (6,21) (6,9) (6,16) (6,24) (6,23) (6,22) (6,8) (6,11) (6,14) (6,13) (7,19) (7,17) (7,12) (7,20) (7,10) (7,18) (7,15) (8,21) (8,9) (8,16) (8,24) (8,23) (8,22) (8,11) (8,14) (8,13) (9,21) (9,16) (9,24) (9,23) (9,22) (9,11) (9,14) (9,13) (10,19) (10,17) (10,12) (10,20) (10,18) (10,15) (11,21) (11,16) (11,24) (11,23) (11,22) (11,14) (11,13) (12,19) (12,17) (12,20) (12,18) (12,15) (13,21) (13,16) (13,24) (13,23) (13,22) (13,14) (14,21) (14,16) (14,24) (14,23) (14,22) (15,19) (15,17) (15,20) (15,18) (16,21) (16,24) (16,23) (16,22) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nIs there a path between node 21 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph844-19_24", + "image": "data/connectivity/graph_visual/medium/graph844.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,8) (0,10) (0,14) (0,24) (0,2) (0,3) (0,6) (0,7) (0,1) (0,11) (0,16) (0,9) (0,18) (0,23) (0,4) (0,22) (1,8) (1,10) (1,14) (1,24) (1,2) (1,3) (1,6) (1,7) (1,11) (1,16) (1,9) (1,18) (1,23) (1,4) (1,22) (2,8) (2,10) (2,14) (2,24) (2,3) (2,6) (2,7) (2,11) (2,16) (2,9) (2,18) (2,23) (2,4) (2,22) (3,8) (3,10) (3,14) (3,24) (3,6) (3,7) (3,11) (3,16) (3,9) (3,18) (3,23) (3,4) (3,22) (4,8) (4,10) (4,14) (4,24) (4,6) (4,7) (4,11) (4,16) (4,9) (4,18) (4,23) (4,22) (5,15) (5,21) (5,20) (5,17) (6,8) (6,10) (6,14) (6,24) (6,7) (6,11) (6,16) (6,9) (6,18) (6,23) (6,22) (7,8) (7,10) (7,14) (7,24) (7,11) (7,16) (7,9) (7,18) (7,23) (7,22) (8,10) (8,14) (8,24) (8,11) (8,16) (8,9) (8,18) (8,23) (8,22) (9,10) (9,14) (9,24) (9,11) (9,16) (9,18) (9,23) (9,22) (10,14) (10,24) (10,11) (10,16) (10,18) (10,23) (10,22) (11,14) (11,24) (11,16) (11,18) (11,23) (11,22) (12,19) (12,13) (13,19) (14,24) (14,16) (14,18) (14,23) (14,22) (15,21) (15,20) (15,17) (16,24) (16,18) (16,23) (16,22) (17,21) (17,20) (18,24) (18,23) (18,22) (20,21) (22,24) (22,23) (23,24)\nIs there a path between node 19 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph469-0_21", + "image": "data/connectivity/graph_visual/medium/graph469.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,3) (0,21) (0,8) (0,11) (0,16) (0,13) (0,10) (0,20) (0,6) (0,4) (1,14) (1,17) (1,18) (1,5) (1,19) (1,2) (2,22) (2,14) (2,5) (3,8) (3,11) (3,10) (3,12) (3,6) (4,11) (4,13) (4,20) (4,12) (5,22) (5,14) (5,17) (5,18) (5,9) (5,19) (6,8) (6,11) (6,16) (6,13) (6,10) (6,20) (6,12) (7,15) (8,11) (8,13) (8,10) (8,20) (8,12) (9,22) (9,14) (9,17) (9,18) (9,19) (10,21) (10,13) (11,16) (11,13) (11,20) (11,12) (12,21) (12,16) (12,13) (12,20) (13,21) (13,16) (13,20) (14,22) (14,18) (16,21) (16,20) (17,22) (17,18) (17,19) (18,19) (20,21)\nIs there a path between node 0 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph238-6_10", + "image": "data/connectivity/graph_visual/medium/graph238.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,2) (0,5) (0,7) (0,18) (0,13) (0,11) (0,17) (1,8) (1,7) (1,18) (1,13) (1,9) (1,15) (1,11) (1,10) (2,8) (2,5) (2,7) (2,15) (3,14) (3,4) (3,12) (4,12) (5,8) (5,18) (5,13) (5,9) (5,11) (5,17) (6,16) (7,18) (7,13) (7,9) (7,11) (7,17) (8,18) (8,13) (8,9) (8,15) (8,11) (8,17) (8,10) (9,18) (9,13) (9,15) (9,17) (10,15) (10,17) (11,18) (11,13) (11,15) (11,17) (12,14) (13,18) (13,15) (15,18) (15,17) (17,18)\nIs there a path between node 6 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph665-6_12", + "image": "data/connectivity/graph_visual/medium/graph665.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,10) (0,14) (0,2) (0,8) (1,18) (1,23) (1,5) (1,4) (1,11) (1,9) (1,20) (1,17) (1,7) (2,10) (2,14) (2,16) (2,3) (2,8) (2,22) (3,12) (3,10) (3,14) (3,16) (3,8) (4,18) (4,15) (4,20) (4,17) (4,7) (5,23) (5,15) (5,21) (5,11) (5,9) (5,19) (5,17) (5,7) (7,23) (7,21) (7,11) (7,9) (7,20) (7,17) (8,12) (8,10) (8,14) (8,22) (9,18) (9,23) (9,15) (9,21) (9,11) (9,20) (9,19) (10,16) (10,22) (11,18) (11,15) (11,21) (11,20) (11,19) (11,17) (12,14) (12,16) (14,22) (15,18) (15,20) (17,20) (18,23) (18,19) (19,23) (19,21) (21,23)\nIs there a path between node 6 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph616-13_5", + "image": "data/connectivity/graph_visual/medium/graph616.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,9) (0,12) (0,4) (0,11) (0,14) (0,3) (0,17) (0,22) (0,2) (0,19) (0,15) (0,20) (0,1) (0,16) (0,13) (0,7) (1,5) (1,9) (1,12) (1,4) (1,11) (1,14) (1,3) (1,17) (1,22) (1,2) (1,19) (1,15) (1,20) (1,16) (1,13) (1,7) (2,5) (2,9) (2,12) (2,4) (2,11) (2,14) (2,3) (2,17) (2,22) (2,19) (2,15) (2,20) (2,16) (2,13) (2,7) (3,5) (3,9) (3,12) (3,4) (3,11) (3,14) (3,17) (3,22) (3,19) (3,15) (3,20) (3,16) (3,13) (3,7) (4,5) (4,9) (4,12) (4,11) (4,14) (4,17) (4,22) (4,19) (4,15) (4,20) (4,16) (4,13) (4,7) (5,9) (5,12) (5,11) (5,14) (5,17) (5,22) (5,19) (5,15) (5,20) (5,16) (5,13) (5,7) (6,18) (6,21) (6,8) (6,10) (6,23) (7,9) (7,12) (7,11) (7,14) (7,17) (7,22) (7,19) (7,15) (7,20) (7,16) (7,13) (8,18) (8,21) (8,10) (8,23) (9,12) (9,11) (9,14) (9,17) (9,22) (9,19) (9,15) (9,20) (9,16) (9,13) (10,18) (10,21) (10,23) (11,12) (11,14) (11,17) (11,22) (11,19) (11,15) (11,20) (11,16) (11,13) (12,14) (12,17) (12,22) (12,19) (12,15) (12,20) (12,16) (12,13) (13,14) (13,17) (13,22) (13,19) (13,15) (13,20) (13,16) (14,17) (14,22) (14,19) (14,15) (14,20) (14,16) (15,17) (15,22) (15,19) (15,20) (15,16) (16,17) (16,22) (16,19) (16,20) (17,22) (17,19) (17,20) (18,21) (18,23) (19,22) (19,20) (20,22) (21,23)\nIs there a path between node 13 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph762-15_19", + "image": "data/connectivity/graph_visual/medium/graph762.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,24) (0,4) (0,17) (0,22) (0,7) (0,23) (0,9) (0,8) (0,3) (0,1) (0,10) (0,19) (0,6) (1,12) (1,24) (1,4) (1,17) (1,5) (1,22) (1,16) (1,23) (1,9) (1,14) (1,3) (1,13) (1,21) (1,10) (1,19) (1,6) (2,15) (2,18) (2,11) (3,12) (3,24) (3,4) (3,17) (3,22) (3,7) (3,16) (3,20) (3,13) (3,21) (4,12) (4,24) (4,5) (4,16) (4,20) (4,23) (4,13) (4,21) (4,10) (4,19) (4,6) (5,12) (5,24) (5,17) (5,22) (5,16) (5,20) (5,23) (5,9) (5,8) (5,13) (5,10) (5,6) (6,12) (6,24) (6,17) (6,22) (6,7) (6,20) (6,23) (6,8) (6,14) (6,13) (6,21) (7,12) (7,24) (7,17) (7,16) (7,23) (7,14) (7,13) (7,21) (7,10) (7,19) (8,12) (8,24) (8,17) (8,22) (8,16) (8,20) (8,23) (8,14) (8,13) (8,21) (8,10) (9,12) (9,24) (9,17) (9,22) (9,20) (9,14) (9,13) (9,21) (9,10) (9,19) (10,17) (10,16) (10,23) (10,14) (10,13) (11,18) (12,17) (12,22) (12,16) (12,23) (12,13) (12,19) (13,24) (13,16) (13,20) (13,21) (13,19) (14,24) (14,17) (14,22) (14,16) (14,21) (16,24) (16,20) (16,23) (16,19) (17,24) (17,22) (17,20) (17,23) (17,21) (17,19) (19,24) (19,22) (19,21) (20,24) (20,22) (20,23) (20,21) (21,24) (21,23) (22,24)\nIs there a path between node 15 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph432-12_16", + "image": "data/connectivity/graph_visual/medium/graph432.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,1) (0,20) (0,9) (1,2) (2,20) (2,9) (3,5) (3,19) (3,18) (3,14) (4,7) (4,12) (4,15) (5,7) (5,17) (5,15) (6,16) (7,17) (7,12) (7,14) (8,10) (10,16) (10,13) (11,19) (11,15) (12,19) (14,17) (14,18) (17,21) (18,19) (19,21)\nIs there a path between node 12 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph299-7_0", + "image": "data/connectivity/graph_visual/medium/graph299.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (1,3) (1,2) (1,7) (1,5) (1,18) (1,14) (1,17) (1,12) (1,11) (1,10) (1,19) (1,13) (1,4) (1,9) (2,7) (2,18) (2,16) (2,6) (2,11) (2,10) (2,19) (2,13) (2,4) (2,9) (2,15) (3,7) (3,18) (3,12) (3,6) (3,10) (3,19) (3,13) (3,4) (3,9) (4,7) (4,5) (4,14) (4,17) (4,16) (4,6) (4,11) (4,10) (4,19) (4,9) (5,7) (5,14) (5,17) (5,16) (5,12) (5,6) (5,11) (5,10) (5,13) (5,9) (5,15) (6,14) (6,17) (6,16) (6,12) (6,10) (6,19) (6,9) (7,18) (7,14) (7,17) (7,16) (7,12) (7,10) (7,19) (7,13) (7,9) (7,15) (9,18) (9,14) (9,17) (9,16) (9,12) (9,11) (9,19) (9,13) (9,15) (10,18) (10,14) (10,17) (10,12) (10,11) (10,19) (10,15) (11,18) (11,12) (11,19) (11,15) (12,18) (12,14) (12,17) (12,19) (12,13) (12,15) (13,18) (13,14) (13,17) (14,17) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19)\nIs there a path between node 7 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph750-13_2", + "image": "data/connectivity/graph_visual/medium/graph750.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,22) (0,19) (0,13) (0,3) (0,16) (0,24) (0,1) (0,4) (0,7) (0,6) (0,15) (0,9) (1,11) (1,2) (1,22) (1,10) (1,5) (1,14) (1,13) (1,3) (1,16) (1,24) (1,7) (1,6) (1,20) (1,9) (2,11) (2,22) (2,10) (2,5) (2,14) (2,13) (2,3) (2,16) (2,18) (2,24) (2,4) (2,7) (2,6) (2,15) (2,20) (2,9) (3,11) (3,22) (3,19) (3,10) (3,5) (3,13) (3,18) (3,24) (3,7) (3,6) (3,15) (3,20) (3,9) (4,22) (4,19) (4,5) (4,14) (4,13) (4,16) (4,18) (4,20) (4,9) (5,22) (5,19) (5,10) (5,13) (5,16) (5,18) (5,24) (5,6) (5,15) (6,11) (6,22) (6,19) (6,10) (6,16) (6,18) (6,24) (6,7) (6,15) (6,9) (7,11) (7,22) (7,19) (7,10) (7,14) (7,13) (7,18) (7,24) (7,15) (7,20) (7,9) (8,23) (8,17) (9,22) (9,19) (9,10) (9,14) (9,18) (9,24) (9,15) (9,20) (10,11) (10,22) (10,19) (10,14) (10,13) (10,16) (10,18) (10,24) (10,15) (10,20) (11,22) (11,19) (11,14) (11,13) (11,16) (11,24) (11,15) (11,20) (12,23) (12,21) (13,19) (13,16) (13,18) (13,24) (13,15) (13,20) (14,22) (14,16) (14,18) (14,15) (14,20) (15,16) (15,18) (15,24) (16,22) (16,19) (16,18) (16,24) (17,23) (17,21) (18,19) (19,22) (19,24) (19,20) (20,22) (20,24)\nIs there a path between node 13 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph642-12_8", + "image": "data/connectivity/graph_visual/medium/graph642.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,23) (0,10) (1,8) (1,2) (1,3) (1,6) (1,16) (2,5) (2,21) (2,6) (2,19) (2,10) (3,8) (3,5) (3,4) (4,17) (4,5) (4,9) (4,14) (5,17) (5,22) (5,11) (5,19) (5,13) (5,10) (6,9) (6,11) (6,21) (6,13) (7,12) (7,18) (7,20) (8,15) (8,13) (8,16) (9,17) (10,16) (11,17) (11,14) (11,13) (12,18) (13,17) (13,22) (13,14) (13,21) (14,22) (14,23) (14,19) (14,16) (16,22) (16,23) (17,23)\nIs there a path between node 12 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph120-1_6", + "image": "data/connectivity/graph_visual/medium/graph120.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,12) (0,7) (0,8) (0,9) (0,13) (0,14) (0,15) (0,5) (1,2) (1,12) (1,16) (1,11) (1,3) (1,6) (1,14) (1,4) (2,12) (2,7) (2,9) (2,13) (2,14) (3,16) (3,11) (3,7) (3,8) (3,14) (3,15) (3,5) (3,4) (4,12) (4,11) (4,8) (4,9) (4,13) (4,14) (4,5) (5,12) (5,16) (5,11) (5,7) (5,8) (5,13) (5,14) (5,15) (6,12) (6,16) (6,11) (6,7) (6,14) (6,15) (7,12) (7,16) (7,11) (7,8) (7,9) (7,13) (8,12) (8,16) (8,11) (8,9) (8,13) (8,14) (9,12) (9,16) (9,11) (9,14) (9,15) (11,12) (11,16) (11,14) (12,13) (12,15) (13,16) (13,15) (14,16)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph583-9_19", + "image": "data/connectivity/graph_visual/medium/graph583.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,17) (0,10) (0,22) (1,23) (1,19) (1,5) (1,18) (2,20) (2,12) (2,5) (2,16) (3,19) (3,5) (3,7) (3,15) (3,18) (4,21) (4,17) (4,22) (5,23) (5,19) (5,12) (5,18) (6,21) (7,23) (7,16) (7,18) (7,14) (8,9) (8,10) (8,22) (9,11) (12,23) (12,16) (12,14) (13,23) (13,16) (13,18) (14,23) (14,19) (14,15) (15,23) (16,23) (17,22) (18,20) (19,20)\nIs there a path between node 9 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph790-12_6", + "image": "data/connectivity/graph_visual/medium/graph790.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,23) (1,9) (2,13) (2,16) (2,24) (3,5) (3,7) (3,11) (4,6) (4,12) (4,5) (4,14) (4,7) (5,6) (5,12) (5,14) (5,11) (6,17) (6,20) (6,7) (10,19) (10,23) (10,16) (10,18) (11,12) (11,20) (11,15) (13,16) (13,22) (13,24) (14,17) (14,20) (15,20) (16,23) (17,20) (18,22) (22,23) (23,24)\nIs there a path between node 12 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph766-10_9", + "image": "data/connectivity/graph_visual/medium/graph766.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,24) (0,5) (0,14) (0,18) (0,1) (0,22) (0,2) (0,7) (0,13) (0,23) (0,9) (1,20) (1,24) (1,5) (1,14) (1,18) (1,22) (1,2) (1,7) (1,13) (1,23) (1,9) (2,20) (2,24) (2,5) (2,14) (2,18) (2,22) (2,7) (2,13) (2,23) (2,9) (3,16) (3,19) (3,8) (3,10) (3,21) (3,12) (3,11) (3,15) (4,17) (5,20) (5,24) (5,14) (5,18) (5,22) (5,7) (5,13) (5,23) (5,9) (7,20) (7,24) (7,14) (7,18) (7,22) (7,13) (7,23) (7,9) (8,16) (8,19) (8,10) (8,21) (8,12) (8,11) (8,15) (9,20) (9,24) (9,14) (9,18) (9,22) (9,13) (9,23) (10,16) (10,19) (10,21) (10,12) (10,11) (10,15) (11,16) (11,19) (11,21) (11,12) (11,15) (12,16) (12,19) (12,21) (12,15) (13,20) (13,24) (13,14) (13,18) (13,22) (13,23) (14,20) (14,24) (14,18) (14,22) (14,23) (15,16) (15,19) (15,21) (16,19) (16,21) (18,20) (18,24) (18,22) (18,23) (19,21) (20,24) (20,22) (20,23) (22,24) (22,23) (23,24)\nIs there a path between node 10 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph225-7_11", + "image": "data/connectivity/graph_visual/medium/graph225.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,1) (1,4) (1,2) (2,12) (2,3) (2,10) (3,10) (3,5) (3,4) (3,18) (4,12) (5,12) (5,11) (5,18) (6,11) (6,9) (9,17) (9,11) (9,18) (10,16) (10,18) (11,16) (11,12) (11,18) (14,15)\nIs there a path between node 7 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph289-11_18", + "image": "data/connectivity/graph_visual/medium/graph289.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,13) (0,17) (0,4) (1,14) (2,8) (3,15) (4,11) (4,18) (4,17) (5,19) (7,13) (7,12) (7,10) (8,16) (8,14) (9,12) (9,10) (10,18) (11,18) (11,12) (12,13) (13,18) (13,17) (14,16) (17,18)\nIs there a path between node 11 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph51-11_1", + "image": "data/connectivity/graph_visual/medium/graph51.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,6) (0,13) (1,6) (1,8) (1,3) (1,4) (2,5) (2,9) (3,12) (3,9) (3,13) (4,6) (4,10) (5,6) (5,9) (6,12) (6,8) (8,9) (9,10) (12,13)\nIs there a path between node 11 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph217-3_0", + "image": "data/connectivity/graph_visual/medium/graph217.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,2) (0,11) (0,14) (0,10) (0,5) (0,1) (0,16) (0,12) (0,18) (0,15) (1,2) (1,11) (1,14) (1,10) (1,5) (1,16) (1,12) (1,18) (1,15) (2,11) (2,14) (2,10) (2,5) (2,16) (2,12) (2,18) (2,15) (3,4) (3,7) (3,8) (3,13) (4,7) (4,8) (4,13) (5,11) (5,14) (5,10) (5,16) (5,12) (5,18) (5,15) (6,9) (6,17) (7,8) (7,13) (8,13) (9,17) (10,11) (10,14) (10,16) (10,12) (10,18) (10,15) (11,14) (11,16) (11,12) (11,18) (11,15) (12,14) (12,16) (12,18) (12,15) (14,16) (14,18) (14,15) (15,16) (15,18) (16,18)\nIs there a path between node 3 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph599-12_16", + "image": "data/connectivity/graph_visual/medium/graph599.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,16) (0,9) (0,8) (0,15) (0,3) (0,12) (0,2) (0,21) (0,11) (0,14) (0,19) (1,13) (1,7) (1,18) (1,5) (1,23) (1,22) (1,10) (1,4) (2,20) (2,9) (2,15) (2,3) (2,11) (2,19) (2,17) (3,6) (3,9) (3,8) (3,12) (3,11) (3,14) (3,19) (3,17) (4,18) (4,10) (5,13) (5,7) (5,18) (5,23) (5,22) (5,10) (6,20) (6,9) (6,8) (6,15) (6,11) (6,14) (6,19) (6,17) (7,13) (7,18) (7,23) (7,22) (8,9) (8,15) (8,12) (8,21) (8,11) (8,19) (8,17) (9,15) (9,21) (9,11) (9,14) (9,19) (9,17) (10,13) (10,18) (10,22) (11,16) (11,20) (11,12) (11,21) (11,19) (12,16) (12,20) (12,21) (12,17) (13,23) (13,22) (14,20) (14,15) (14,17) (15,20) (15,21) (15,19) (16,20) (16,21) (16,19) (16,17) (17,20) (17,21) (18,22) (19,20) (19,21) (20,21) (22,23)\nIs there a path between node 12 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph624-11_16", + "image": "data/connectivity/graph_visual/medium/graph624.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (0,11) (0,13) (0,3) (0,15) (0,4) (0,2) (1,7) (1,8) (2,14) (2,23) (2,21) (2,6) (2,10) (3,9) (3,17) (3,13) (3,5) (3,19) (3,4) (3,16) (3,10) (4,9) (4,22) (4,6) (5,11) (5,18) (5,23) (6,9) (6,14) (6,17) (6,20) (6,15) (6,21) (7,8) (9,17) (9,15) (9,21) (10,18) (10,12) (10,16) (11,17) (11,15) (11,22) (11,16) (12,15) (12,22) (13,23) (13,16) (14,17) (14,18) (14,20) (14,21) (14,22) (14,16) (15,20) (17,20) (17,19) (17,23) (18,19) (18,23) (19,20) (19,23) (21,23) (21,22)\nIs there a path between node 11 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph173-5_7", + "image": "data/connectivity/graph_visual/medium/graph173.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,7) (0,17) (0,11) (0,15) (0,12) (0,4) (0,14) (0,8) (0,16) (0,5) (1,7) (1,11) (1,15) (1,2) (1,9) (1,12) (1,14) (1,13) (1,5) (2,7) (2,11) (2,15) (2,9) (2,12) (2,4) (2,14) (2,13) (2,8) (2,16) (2,5) (4,7) (4,12) (5,17) (5,11) (5,15) (5,12) (5,13) (5,16) (6,10) (7,17) (7,11) (7,12) (7,14) (7,8) (8,11) (8,13) (8,16) (9,17) (9,11) (9,15) (9,12) (9,13) (9,16) (11,15) (11,12) (11,14) (11,13) (11,16) (12,17) (12,15) (12,14) (12,16) (13,17) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 5 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph111-3_1", + "image": "data/connectivity/graph_visual/medium/graph111.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,9) (0,10) (0,1) (1,8) (1,3) (1,14) (3,5) (3,6) (3,9) (3,12) (4,9) (4,16) (6,7) (6,12) (7,14) (8,16) (8,14) (10,11) (10,14) (10,12) (11,14) (12,14)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph778-0_12", + "image": "data/connectivity/graph_visual/medium/graph778.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,13) (0,16) (0,19) (0,12) (0,15) (0,22) (0,5) (0,4) (0,6) (0,11) (1,18) (1,14) (2,3) (2,8) (2,17) (2,24) (2,23) (2,21) (2,10) (2,20) (3,8) (3,17) (3,24) (3,23) (3,21) (3,10) (3,20) (4,9) (4,13) (4,16) (4,19) (4,12) (4,15) (4,22) (4,5) (4,6) (4,11) (5,9) (5,13) (5,16) (5,19) (5,12) (5,15) (5,22) (5,6) (5,11) (6,9) (6,13) (6,16) (6,19) (6,12) (6,15) (6,22) (6,11) (8,17) (8,24) (8,23) (8,21) (8,10) (8,20) (9,13) (9,16) (9,19) (9,12) (9,15) (9,22) (9,11) (10,17) (10,24) (10,23) (10,21) (10,20) (11,13) (11,16) (11,19) (11,12) (11,15) (11,22) (12,13) (12,16) (12,19) (12,15) (12,22) (13,16) (13,19) (13,15) (13,22) (14,18) (15,16) (15,19) (15,22) (16,19) (16,22) (17,24) (17,23) (17,21) (17,20) (19,22) (20,24) (20,23) (20,21) (21,24) (21,23) (23,24)\nIs there a path between node 0 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph198-0_8", + "image": "data/connectivity/graph_visual/medium/graph198.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,6) (0,3) (0,14) (1,8) (1,6) (1,14) (2,6) (2,12) (2,18) (3,8) (3,6) (3,12) (3,18) (4,12) (4,9) (4,14) (5,15) (5,16) (5,7) (6,8) (6,12) (6,14) (7,10) (9,11) (9,18) (15,17) (15,16)\nIs there a path between node 0 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph537-2_1", + "image": "data/connectivity/graph_visual/medium/graph537.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (0,16) (1,12) (1,10) (1,7) (1,6) (1,22) (1,13) (1,9) (1,2) (1,19) (1,14) (1,11) (1,21) (1,15) (1,5) (1,20) (1,4) (1,8) (1,17) (1,3) (2,12) (2,10) (2,7) (2,6) (2,22) (2,13) (2,9) (2,19) (2,14) (2,11) (2,21) (2,15) (2,5) (2,20) (2,4) (2,8) (2,17) (2,3) (3,12) (3,10) (3,7) (3,6) (3,22) (3,13) (3,9) (3,19) (3,14) (3,11) (3,21) (3,15) (3,5) (3,20) (3,4) (3,8) (3,17) (4,12) (4,10) (4,7) (4,6) (4,22) (4,13) (4,9) (4,19) (4,14) (4,11) (4,21) (4,15) (4,5) (4,20) (4,8) (4,17) (5,12) (5,10) (5,7) (5,6) (5,22) (5,13) (5,9) (5,19) (5,14) (5,11) (5,21) (5,15) (5,20) (5,8) (5,17) (6,12) (6,10) (6,7) (6,22) (6,13) (6,9) (6,19) (6,14) (6,11) (6,21) (6,15) (6,20) (6,8) (6,17) (7,12) (7,10) (7,22) (7,13) (7,9) (7,19) (7,14) (7,11) (7,21) (7,15) (7,20) (7,8) (7,17) (8,12) (8,10) (8,22) (8,13) (8,9) (8,19) (8,14) (8,11) (8,21) (8,15) (8,20) (8,17) (9,12) (9,10) (9,22) (9,13) (9,19) (9,14) (9,11) (9,21) (9,15) (9,20) (9,17) (10,12) (10,22) (10,13) (10,19) (10,14) (10,11) (10,21) (10,15) (10,20) (10,17) (11,12) (11,22) (11,13) (11,19) (11,14) (11,21) (11,15) (11,20) (11,17) (12,22) (12,13) (12,19) (12,14) (12,21) (12,15) (12,20) (12,17) (13,22) (13,19) (13,14) (13,21) (13,15) (13,20) (13,17) (14,22) (14,19) (14,21) (14,15) (14,20) (14,17) (15,22) (15,19) (15,21) (15,20) (15,17) (16,18) (17,22) (17,19) (17,21) (17,20) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 2 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph142-15_2", + "image": "data/connectivity/graph_visual/medium/graph142.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,11) (0,6) (1,5) (1,8) (1,10) (1,15) (1,17) (1,13) (1,16) (2,5) (2,4) (2,8) (2,10) (2,14) (2,17) (2,13) (2,16) (3,9) (3,6) (3,12) (4,8) (4,15) (4,14) (4,17) (4,13) (5,8) (5,15) (5,17) (6,7) (6,9) (7,11) (7,9) (8,15) (8,17) (8,13) (8,16) (9,11) (10,15) (10,14) (10,17) (11,12) (13,15) (13,14) (13,16) (14,15) (14,17) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 15 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph89-5_10", + "image": "data/connectivity/graph_visual/medium/graph89.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,14) (0,2) (0,7) (0,4) (0,1) (0,3) (0,11) (0,6) (0,9) (0,13) (0,8) (0,5) (0,10) (1,14) (1,2) (1,7) (1,4) (1,3) (1,11) (1,6) (1,9) (1,13) (1,8) (1,5) (1,10) (2,14) (2,7) (2,4) (2,3) (2,11) (2,6) (2,9) (2,13) (2,8) (2,5) (2,10) (3,14) (3,7) (3,4) (3,11) (3,6) (3,9) (3,13) (3,8) (3,5) (3,10) (4,14) (4,7) (4,11) (4,6) (4,9) (4,13) (4,8) (4,5) (4,10) (5,14) (5,7) (5,11) (5,6) (5,9) (5,13) (5,8) (5,10) (6,14) (6,7) (6,11) (6,9) (6,13) (6,8) (6,10) (7,14) (7,11) (7,9) (7,13) (7,8) (7,10) (8,14) (8,11) (8,9) (8,13) (8,10) (9,14) (9,11) (9,13) (9,10) (10,14) (10,11) (10,13) (11,14) (11,13) (13,14)\nIs there a path between node 5 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph521-11_8", + "image": "data/connectivity/graph_visual/medium/graph521.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,10) (0,12) (0,16) (0,9) (0,17) (0,11) (0,5) (0,13) (0,21) (0,4) (1,8) (1,18) (1,7) (3,6) (3,14) (3,10) (3,16) (3,9) (3,11) (3,5) (3,21) (3,4) (3,15) (4,6) (4,10) (4,12) (4,16) (4,9) (4,17) (4,11) (4,13) (4,21) (4,15) (5,6) (5,12) (5,9) (5,19) (5,17) (5,13) (5,21) (5,15) (6,14) (6,10) (6,12) (6,16) (6,19) (6,17) (6,13) (6,21) (6,15) (7,20) (7,8) (7,18) (8,20) (9,14) (9,10) (9,16) (9,19) (9,17) (9,11) (9,13) (9,21) (10,12) (10,19) (10,17) (10,11) (10,15) (11,14) (11,16) (11,19) (11,17) (11,21) (12,14) (12,17) (12,13) (12,21) (13,14) (13,16) (13,17) (13,21) (14,16) (14,21) (15,19) (15,17) (15,21) (16,17) (16,21) (17,19) (17,21) (18,20) (19,21)\nIs there a path between node 11 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph607-0_7", + "image": "data/connectivity/graph_visual/medium/graph607.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,11) (0,8) (0,17) (0,13) (0,6) (0,3) (0,15) (0,7) (1,14) (1,19) (1,9) (1,21) (1,12) (1,22) (1,4) (1,18) (1,5) (1,10) (1,20) (2,16) (3,23) (3,11) (3,8) (3,17) (3,13) (3,6) (3,15) (3,7) (4,14) (4,19) (4,9) (4,21) (4,12) (4,22) (4,18) (4,5) (4,10) (4,20) (5,14) (5,19) (5,9) (5,21) (5,12) (5,22) (5,18) (5,10) (5,20) (6,23) (6,11) (6,8) (6,17) (6,13) (6,15) (6,7) (7,23) (7,11) (7,8) (7,17) (7,13) (7,15) (8,23) (8,11) (8,17) (8,13) (8,15) (9,14) (9,19) (9,21) (9,12) (9,22) (9,18) (9,10) (9,20) (10,14) (10,19) (10,21) (10,12) (10,22) (10,18) (10,20) (11,23) (11,17) (11,13) (11,15) (12,14) (12,19) (12,21) (12,22) (12,18) (12,20) (13,23) (13,17) (13,15) (14,19) (14,21) (14,22) (14,18) (14,20) (15,23) (15,17) (17,23) (18,19) (18,21) (18,22) (18,20) (19,21) (19,22) (19,20) (20,21) (20,22) (21,22)\nIs there a path between node 0 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph262-13_1", + "image": "data/connectivity/graph_visual/medium/graph262.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (0,13) (0,12) (0,2) (1,8) (1,13) (1,11) (1,12) (1,4) (2,15) (2,19) (2,4) (3,13) (3,11) (4,8) (4,17) (4,19) (4,16) (5,14) (5,6) (5,9) (5,18) (6,10) (7,18) (8,11) (8,17) (8,16) (9,14) (9,10) (10,14) (11,17) (11,19) (11,16) (12,16) (13,17) (16,19)\nIs there a path between node 13 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph24-0_9", + "image": "data/connectivity/graph_visual/medium/graph24.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,1) (0,8) (0,9) (0,3) (1,11) (1,5) (1,4) (1,6) (1,3) (2,10) (3,11) (3,5) (3,8) (3,4) (4,11) (4,6) (4,9) (5,11) (5,8) (5,6) (5,9) (6,11) (7,10) (9,11)\nIs there a path between node 0 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph732-5_3", + "image": "data/connectivity/graph_visual/medium/graph732.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (0,1) (0,11) (0,22) (0,12) (1,18) (1,21) (1,11) (1,4) (1,20) (1,22) (1,12) (2,15) (2,21) (2,4) (2,6) (2,22) (3,19) (4,24) (4,14) (4,8) (4,21) (4,20) (4,7) (4,22) (4,12) (5,23) (5,15) (5,20) (5,9) (5,7) (6,14) (6,8) (6,21) (6,20) (6,10) (7,23) (7,8) (7,11) (7,22) (8,15) (8,21) (9,23) (9,21) (9,20) (9,12) (10,17) (10,14) (10,15) (10,21) (10,20) (10,22) (10,12) (10,16) (11,20) (11,12) (11,16) (12,24) (12,14) (12,23) (14,24) (14,17) (14,15) (14,21) (15,24) (16,24) (16,23) (17,24) (17,18) (17,20) (17,22) (18,24) (18,22) (22,24)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph195-18_10", + "image": "data/connectivity/graph_visual/medium/graph195.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,1) (1,2) (3,11) (3,15) (3,8) (5,18) (5,7) (6,17) (6,7) (7,13) (7,8) (7,14) (8,18) (8,12) (9,11) (9,15) (9,13) (9,17) (10,18) (11,13) (11,17) (12,18) (12,17) (12,14) (13,17) (14,17) (17,18)\nIs there a path between node 18 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph549-17_13", + "image": "data/connectivity/graph_visual/medium/graph549.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (1,10) (2,11) (2,9) (3,21) (4,10) (4,23) (5,7) (5,9) (7,11) (7,9) (8,18) (8,17) (10,22) (13,19) (14,16) (15,19) (16,17) (17,19)\nIs there a path between node 17 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph320-12_10", + "image": "data/connectivity/graph_visual/medium/graph320.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,1) (0,18) (1,19) (1,18) (2,6) (2,10) (2,7) (2,5) (2,16) (2,11) (2,15) (2,4) (3,8) (3,9) (3,13) (3,12) (3,14) (3,17) (4,6) (4,10) (4,7) (4,5) (4,16) (4,11) (4,15) (5,6) (5,10) (5,7) (5,16) (5,11) (5,15) (6,10) (6,7) (6,16) (6,11) (6,15) (7,10) (7,16) (7,11) (7,15) (8,9) (8,13) (8,12) (8,14) (8,17) (9,13) (9,12) (9,14) (9,17) (10,16) (10,11) (10,15) (11,16) (11,15) (12,13) (12,14) (12,17) (13,14) (13,17) (14,17) (15,16) (18,19)\nIs there a path between node 12 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph625-4_22", + "image": "data/connectivity/graph_visual/medium/graph625.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (1,11) (1,7) (1,13) (1,21) (1,19) (1,5) (2,17) (2,20) (2,5) (4,9) (4,22) (5,21) (5,19) (6,23) (7,11) (8,11) (8,13) (8,19) (8,18) (11,23) (11,13) (11,18) (13,20) (13,21) (13,19) (13,18) (14,16) (14,15) (18,20) (19,20) (19,21) (20,23)\nIs there a path between node 4 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph285-16_17", + "image": "data/connectivity/graph_visual/medium/graph285.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,14) (1,9) (1,2) (1,8) (2,18) (2,6) (2,5) (2,8) (2,11) (3,7) (5,13) (5,6) (5,9) (5,8) (6,12) (6,13) (6,18) (6,10) (6,9) (6,8) (6,11) (7,15) (8,16) (8,9) (9,13) (9,10) (10,16) (10,11) (11,12) (11,16) (12,16) (13,16) (14,15)\nIs there a path between node 16 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph158-16_17", + "image": "data/connectivity/graph_visual/medium/graph158.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,9) (1,14) (1,8) (2,11) (2,16) (2,7) (2,6) (3,17) (3,11) (3,4) (3,13) (3,6) (4,10) (5,15) (5,10) (6,17) (6,15) (7,17) (7,16) (8,9) (10,17) (10,16) (11,17) (11,15) (11,16) (12,17) (12,16) (15,17) (15,16)\nIs there a path between node 16 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph168-8_13", + "image": "data/connectivity/graph_visual/medium/graph168.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,1) (0,5) (1,11) (1,6) (1,17) (1,10) (2,11) (2,17) (5,6) (5,9) (6,16) (6,8) (6,17) (6,10) (6,14) (8,10) (9,10) (10,11) (10,17) (10,15) (11,15) (14,16) (14,17)\nIs there a path between node 8 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph663-9_21", + "image": "data/connectivity/graph_visual/medium/graph663.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,8) (0,23) (0,19) (0,9) (0,21) (1,14) (2,7) (2,11) (2,4) (3,5) (3,7) (3,16) (3,17) (3,18) (3,11) (3,4) (4,5) (4,7) (4,10) (4,16) (4,18) (5,7) (5,10) (5,11) (6,22) (6,8) (6,12) (6,19) (7,10) (7,16) (7,17) (7,13) (7,18) (7,11) (8,22) (8,23) (8,15) (8,21) (9,22) (9,23) (9,19) (9,15) (10,18) (11,16) (11,17) (11,13) (12,22) (12,23) (12,15) (12,21) (13,16) (13,17) (13,18) (14,20) (15,23) (15,19) (15,21) (16,18) (17,18) (19,22) (19,21) (21,22) (21,23)\nIs there a path between node 9 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph44-4_1", + "image": "data/connectivity/graph_visual/medium/graph44.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,7) (0,5) (0,4) (0,6) (0,11) (1,10) (1,2) (2,10) (3,9) (3,8) (3,7) (3,5) (3,12) (3,6) (3,11) (4,7) (4,5) (4,12) (4,11) (5,9) (5,8) (5,7) (5,11) (6,9) (6,8) (6,7) (6,12) (7,12) (7,11) (8,9) (8,12) (9,12) (9,11) (11,12)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph126-6_14", + "image": "data/connectivity/graph_visual/medium/graph126.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,11) (0,3) (0,7) (0,10) (0,13) (0,12) (0,16) (1,14) (1,2) (1,5) (1,9) (1,8) (1,15) (1,4) (1,6) (2,14) (2,5) (2,9) (2,8) (2,15) (2,4) (2,6) (3,11) (3,7) (3,10) (3,13) (3,12) (3,16) (4,14) (4,5) (4,9) (4,8) (4,15) (4,6) (5,14) (5,9) (5,8) (5,15) (5,6) (6,14) (6,9) (6,8) (6,15) (7,11) (7,10) (7,13) (7,12) (7,16) (8,14) (8,9) (8,15) (9,14) (9,15) (10,11) (10,13) (10,12) (10,16) (11,13) (11,12) (11,16) (12,13) (12,16) (13,16) (14,15)\nIs there a path between node 6 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph272-14_10", + "image": "data/connectivity/graph_visual/medium/graph272.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,13) (0,9) (0,7) (0,12) (0,4) (0,5) (0,19) (0,6) (0,1) (0,17) (1,14) (1,9) (1,3) (1,7) (1,12) (1,4) (1,5) (1,19) (1,15) (1,17) (2,11) (2,8) (2,10) (3,13) (3,14) (3,9) (3,7) (3,12) (3,4) (3,5) (3,6) (3,18) (3,15) (4,13) (4,9) (4,12) (4,19) (4,6) (4,18) (4,15) (4,17) (5,13) (5,14) (5,7) (5,12) (5,19) (5,15) (5,17) (6,13) (6,9) (6,7) (6,19) (6,15) (6,17) (7,13) (7,14) (7,9) (7,12) (7,19) (7,18) (7,17) (8,11) (8,16) (8,10) (9,14) (9,18) (9,17) (10,11) (11,16) (12,14) (12,19) (12,18) (12,15) (12,17) (13,14) (13,19) (13,18) (13,17) (14,19) (14,18) (14,15) (14,17) (15,17) (17,19) (17,18) (18,19)\nIs there a path between node 14 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph250-17_5", + "image": "data/connectivity/graph_visual/medium/graph250.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,15) (0,1) (0,9) (0,7) (0,18) (0,3) (0,13) (0,14) (0,11) (0,6) (0,17) (0,10) (0,2) (0,12) (1,15) (1,9) (1,7) (1,18) (1,3) (1,13) (1,14) (1,11) (1,6) (1,17) (1,10) (1,2) (1,12) (2,15) (2,9) (2,7) (2,18) (2,3) (2,13) (2,14) (2,11) (2,6) (2,17) (2,10) (2,12) (3,15) (3,9) (3,7) (3,18) (3,13) (3,14) (3,11) (3,6) (3,17) (3,10) (3,12) (4,16) (4,5) (4,8) (5,16) (5,8) (6,15) (6,9) (6,7) (6,18) (6,13) (6,14) (6,11) (6,17) (6,10) (6,12) (7,15) (7,9) (7,18) (7,13) (7,14) (7,11) (7,17) (7,10) (7,12) (8,16) (9,15) (9,18) (9,13) (9,14) (9,11) (9,17) (9,10) (9,12) (10,15) (10,18) (10,13) (10,14) (10,11) (10,17) (10,12) (11,15) (11,18) (11,13) (11,14) (11,17) (11,12) (12,15) (12,18) (12,13) (12,14) (12,17) (13,15) (13,18) (13,14) (13,17) (14,15) (14,18) (14,17) (15,18) (15,17) (17,18)\nIs there a path between node 17 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph98-5_13", + "image": "data/connectivity/graph_visual/medium/graph98.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,14) (1,13) (1,6) (1,4) (1,11) (1,9) (2,13) (2,6) (2,4) (2,11) (2,9) (3,15) (4,8) (4,13) (4,11) (5,8) (5,6) (5,15) (10,12) (11,13)\nIs there a path between node 5 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph231-9_7", + "image": "data/connectivity/graph_visual/medium/graph231.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,10) (1,15) (2,16) (3,18) (3,8) (5,15) (5,14) (7,9) (8,18) (8,12) (10,17) (12,13) (12,17) (13,14) (14,18) (14,15) (17,18)\nIs there a path between node 9 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph158-16_8", + "image": "data/connectivity/graph_visual/medium/graph158.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,9) (1,14) (1,8) (2,11) (2,16) (2,7) (2,6) (3,17) (3,11) (3,4) (3,13) (3,6) (4,10) (5,15) (5,10) (6,17) (6,15) (7,17) (7,16) (8,9) (10,17) (10,16) (11,17) (11,15) (11,16) (12,17) (12,16) (15,17) (15,16)\nIs there a path between node 16 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph400-8_4", + "image": "data/connectivity/graph_visual/medium/graph400.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,3) (0,4) (0,10) (1,18) (1,11) (1,16) (1,21) (1,10) (2,5) (2,20) (2,13) (3,11) (3,16) (3,13) (3,10) (4,20) (4,13) (4,6) (4,10) (5,11) (5,16) (5,13) (6,20) (6,16) (6,13) (6,19) (7,9) (8,17) (8,14) (10,18) (10,11) (10,16) (10,21) (11,20) (11,16) (13,21) (15,17) (16,21) (16,19) (18,20)\nIs there a path between node 8 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph84-14_12", + "image": "data/connectivity/graph_visual/medium/graph84.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,4) (0,13) (0,12) (0,14) (0,8) (0,3) (0,6) (0,2) (0,9) (0,5) (1,10) (1,7) (1,11) (2,4) (2,13) (2,12) (2,14) (2,8) (2,3) (2,6) (2,9) (2,5) (3,4) (3,13) (3,12) (3,14) (3,8) (3,6) (3,9) (3,5) (4,13) (4,12) (4,14) (4,8) (4,6) (4,9) (4,5) (5,13) (5,12) (5,14) (5,8) (5,6) (5,9) (6,13) (6,12) (6,14) (6,8) (6,9) (7,10) (7,11) (8,13) (8,12) (8,14) (8,9) (9,13) (9,12) (9,14) (10,11) (12,13) (12,14) (13,14)\nIs there a path between node 14 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph561-9_21", + "image": "data/connectivity/graph_visual/medium/graph561.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,3) (0,20) (0,6) (0,11) (0,4) (0,7) (0,23) (0,14) (0,21) (1,5) (1,10) (2,9) (2,3) (2,20) (2,4) (2,23) (2,14) (2,21) (3,8) (3,9) (3,20) (3,6) (3,11) (3,4) (3,22) (4,9) (4,20) (4,6) (4,7) (4,22) (4,23) (4,14) (4,21) (5,10) (6,8) (6,9) (6,20) (6,11) (6,22) (6,23) (6,14) (7,8) (7,9) (7,22) (7,23) (7,21) (8,20) (8,11) (8,22) (8,14) (8,21) (9,20) (9,22) (9,14) (9,21) (11,20) (11,22) (11,23) (11,14) (13,16) (13,18) (13,15) (13,19) (13,17) (14,20) (14,22) (14,23) (15,16) (15,19) (15,17) (16,18) (16,19) (16,17) (17,19) (18,19) (20,22) (20,23) (20,21) (21,22) (21,23) (22,23)\nIs there a path between node 9 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph404-13_16", + "image": "data/connectivity/graph_visual/medium/graph404.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,19) (2,11) (3,4) (3,6) (3,9) (4,20) (4,5) (4,15) (4,12) (5,6) (6,11) (6,20) (6,19) (6,15) (7,14) (7,18) (7,21) (7,13) (7,12) (8,10) (9,12) (10,18) (10,15) (11,20) (12,18) (13,20) (14,21) (15,18) (15,21) (15,19) (18,21)\nIs there a path between node 13 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph678-14_23", + "image": "data/connectivity/graph_visual/medium/graph678.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,16) (0,15) (0,3) (0,1) (0,8) (1,23) (1,16) (1,15) (1,3) (1,8) (2,7) (2,4) (2,20) (2,14) (3,23) (3,16) (3,15) (3,8) (4,7) (4,20) (4,14) (5,12) (5,10) (5,18) (5,9) (5,22) (5,13) (5,17) (6,19) (6,11) (6,21) (7,20) (7,14) (8,23) (8,16) (8,15) (9,12) (9,10) (9,18) (9,22) (9,13) (9,17) (10,12) (10,18) (10,22) (10,13) (10,17) (11,19) (11,21) (12,18) (12,22) (12,13) (12,17) (13,18) (13,22) (13,17) (14,20) (15,23) (15,16) (16,23) (17,18) (17,22) (18,22) (19,21)\nIs there a path between node 14 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph522-16_11", + "image": "data/connectivity/graph_visual/medium/graph522.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,19) (0,15) (0,8) (0,16) (0,11) (0,12) (1,19) (1,5) (1,9) (1,21) (1,16) (1,11) (1,12) (2,7) (2,20) (2,3) (2,6) (3,4) (3,20) (3,6) (4,13) (4,7) (4,18) (4,17) (4,10) (5,8) (5,12) (6,13) (6,7) (6,18) (6,17) (6,10) (7,20) (7,17) (7,10) (8,19) (8,15) (8,9) (8,21) (8,16) (9,19) (9,15) (9,21) (10,13) (10,20) (11,19) (11,12) (12,19) (12,21) (12,16) (13,20) (13,18) (13,17) (15,19) (15,21) (15,16) (16,19) (17,20) (17,18)\nIs there a path between node 16 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph139-2_6", + "image": "data/connectivity/graph_visual/medium/graph139.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,10) (0,17) (1,13) (1,14) (2,11) (3,11) (5,6) (5,13) (6,12) (6,14) (7,16) (8,17) (10,17) (12,13) (12,15) (12,14) (13,15)\nIs there a path between node 2 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph641-0_11", + "image": "data/connectivity/graph_visual/medium/graph641.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,14) (0,16) (0,22) (1,3) (1,8) (2,10) (3,20) (3,7) (3,13) (3,15) (3,18) (4,14) (4,16) (4,11) (5,16) (6,9) (8,17) (9,12) (9,11) (10,14) (10,11) (11,14) (11,19) (12,14) (13,23) (13,15) (13,18) (14,22) (15,21) (16,22) (17,23) (17,18) (19,22)\nIs there a path between node 0 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph842-6_1", + "image": "data/connectivity/graph_visual/medium/graph842.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,16) (0,23) (0,22) (0,13) (0,7) (0,2) (0,8) (0,9) (0,12) (0,10) (0,4) (0,20) (0,11) (0,18) (0,1) (0,15) (0,19) (1,6) (1,16) (1,23) (1,22) (1,13) (1,7) (1,2) (1,8) (1,9) (1,12) (1,10) (1,4) (1,20) (1,11) (1,18) (1,15) (1,19) (2,6) (2,16) (2,23) (2,22) (2,13) (2,7) (2,8) (2,9) (2,12) (2,10) (2,4) (2,20) (2,11) (2,18) (2,15) (2,19) (3,24) (3,5) (3,14) (4,6) (4,16) (4,23) (4,22) (4,13) (4,7) (4,8) (4,9) (4,12) (4,10) (4,20) (4,11) (4,18) (4,15) (4,19) (5,24) (5,14) (6,16) (6,23) (6,22) (6,13) (6,7) (6,8) (6,9) (6,12) (6,10) (6,20) (6,11) (6,18) (6,15) (6,19) (7,16) (7,23) (7,22) (7,13) (7,8) (7,9) (7,12) (7,10) (7,20) (7,11) (7,18) (7,15) (7,19) (8,16) (8,23) (8,22) (8,13) (8,9) (8,12) (8,10) (8,20) (8,11) (8,18) (8,15) (8,19) (9,16) (9,23) (9,22) (9,13) (9,12) (9,10) (9,20) (9,11) (9,18) (9,15) (9,19) (10,16) (10,23) (10,22) (10,13) (10,12) (10,20) (10,11) (10,18) (10,15) (10,19) (11,16) (11,23) (11,22) (11,13) (11,12) (11,20) (11,18) (11,15) (11,19) (12,16) (12,23) (12,22) (12,13) (12,20) (12,18) (12,15) (12,19) (13,16) (13,23) (13,22) (13,20) (13,18) (13,15) (13,19) (14,24) (15,16) (15,23) (15,22) (15,20) (15,18) (15,19) (16,23) (16,22) (16,20) (16,18) (16,19) (17,21) (18,23) (18,22) (18,20) (18,19) (19,23) (19,22) (19,20) (20,23) (20,22) (22,23)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph712-8_17", + "image": "data/connectivity/graph_visual/medium/graph712.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (0,15) (0,1) (0,11) (0,7) (0,17) (0,12) (0,4) (0,3) (0,5) (0,19) (0,9) (0,6) (0,22) (1,18) (1,15) (1,10) (1,2) (1,7) (1,8) (1,17) (1,12) (1,3) (1,5) (1,6) (1,22) (1,21) (2,18) (2,15) (2,24) (2,8) (2,17) (2,12) (2,4) (2,3) (2,19) (2,9) (2,22) (2,21) (3,24) (3,10) (3,11) (3,7) (3,12) (3,5) (3,9) (3,6) (3,22) (3,20) (3,21) (4,15) (4,10) (4,11) (4,7) (4,8) (4,17) (4,12) (4,5) (4,19) (4,9) (4,22) (5,15) (5,24) (5,7) (5,17) (5,19) (5,6) (5,20) (6,18) (6,15) (6,10) (6,7) (6,8) (6,17) (6,12) (6,19) (6,9) (6,22) (6,21) (7,15) (7,10) (7,11) (7,8) (7,12) (7,19) (7,22) (7,20) (7,21) (8,18) (8,15) (8,24) (8,11) (8,17) (8,9) (8,22) (8,20) (8,21) (9,18) (9,24) (9,11) (9,19) (9,20) (9,21) (10,24) (10,11) (10,17) (10,19) (10,22) (10,21) (11,18) (11,15) (11,24) (11,17) (11,12) (11,19) (11,22) (11,20) (11,21) (12,18) (12,24) (12,17) (12,19) (12,22) (12,20) (13,16) (14,16) (15,17) (15,19) (15,20) (16,23) (17,18) (17,19) (17,22) (17,21) (18,22) (18,20) (18,21) (19,24) (19,20) (19,21) (20,24) (20,21) (22,24)\nIs there a path between node 8 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph797-24_6", + "image": "data/connectivity/graph_visual/medium/graph797.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,17) (0,2) (0,10) (0,3) (0,11) (0,12) (2,9) (2,23) (2,18) (2,13) (2,16) (3,4) (4,20) (4,21) (4,24) (5,13) (5,11) (5,16) (6,21) (9,16) (10,18) (10,20) (10,12) (10,21) (11,14) (12,20) (12,14) (12,13) (13,14) (13,19) (14,17) (14,20) (14,16) (14,24) (16,23) (16,17) (16,18) (17,19) (18,23) (18,20) (18,21) (18,24) (19,20) (19,21) (20,23) (22,24)\nIs there a path between node 24 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph27-3_11", + "image": "data/connectivity/graph_visual/medium/graph27.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,2) (0,9) (0,1) (0,11) (0,4) (0,3) (1,6) (1,2) (1,9) (1,8) (1,11) (2,6) (2,8) (2,11) (2,3) (3,6) (3,9) (3,8) (3,10) (3,11) (3,4) (4,6) (4,8) (4,10) (5,7) (6,9) (6,8) (6,10) (6,11) (8,10) (9,11) (10,11)\nIs there a path between node 3 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph767-10_2", + "image": "data/connectivity/graph_visual/medium/graph767.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (0,24) (0,15) (0,2) (0,1) (0,7) (0,8) (0,18) (0,23) (0,5) (0,20) (1,19) (1,24) (1,15) (1,2) (1,7) (1,8) (1,18) (1,23) (1,5) (1,20) (2,19) (2,24) (2,15) (2,7) (2,8) (2,18) (2,23) (2,5) (2,20) (3,12) (3,16) (3,9) (3,14) (3,22) (3,13) (3,4) (3,11) (3,10) (3,17) (3,21) (3,6) (4,12) (4,16) (4,9) (4,14) (4,22) (4,13) (4,11) (4,10) (4,17) (4,21) (4,6) (5,19) (5,24) (5,15) (5,7) (5,8) (5,18) (5,23) (5,20) (6,12) (6,16) (6,9) (6,14) (6,22) (6,13) (6,11) (6,10) (6,17) (6,21) (7,19) (7,24) (7,15) (7,8) (7,18) (7,23) (7,20) (8,19) (8,24) (8,15) (8,18) (8,23) (8,20) (9,12) (9,16) (9,14) (9,22) (9,13) (9,11) (9,10) (9,17) (9,21) (10,12) (10,16) (10,14) (10,22) (10,13) (10,11) (10,17) (10,21) (11,12) (11,16) (11,14) (11,22) (11,13) (11,17) (11,21) (12,16) (12,14) (12,22) (12,13) (12,17) (12,21) (13,16) (13,14) (13,22) (13,17) (13,21) (14,16) (14,22) (14,17) (14,21) (15,19) (15,24) (15,18) (15,23) (15,20) (16,22) (16,17) (16,21) (17,22) (17,21) (18,19) (18,24) (18,23) (18,20) (19,24) (19,23) (19,20) (20,24) (20,23) (21,22) (23,24)\nIs there a path between node 10 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph293-6_11", + "image": "data/connectivity/graph_visual/medium/graph293.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,17) (2,4) (2,3) (2,13) (2,8) (2,16) (3,13) (3,7) (3,19) (3,11) (3,14) (4,11) (5,18) (5,11) (5,14) (6,7) (7,19) (7,16) (7,14) (8,18) (8,13) (10,18) (10,13) (10,11) (10,16) (11,13) (11,19) (11,16) (12,15) (13,16) (16,18) (18,19)\nIs there a path between node 6 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph369-13_19", + "image": "data/connectivity/graph_visual/medium/graph369.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (1,2) (1,16) (1,19) (1,10) (1,13) (1,18) (1,14) (1,20) (1,5) (1,4) (1,15) (1,6) (1,8) (1,12) (2,16) (2,19) (2,7) (2,9) (2,18) (2,11) (2,14) (2,20) (2,5) (2,6) (2,12) (3,17) (4,16) (4,19) (4,10) (4,7) (4,9) (4,13) (4,14) (4,15) (4,6) (4,8) (4,12) (5,19) (5,10) (5,7) (5,9) (5,13) (5,18) (5,14) (5,20) (5,15) (5,6) (5,8) (5,12) (6,16) (6,19) (6,10) (6,13) (6,18) (6,15) (6,8) (6,12) (7,16) (7,19) (7,9) (7,13) (7,18) (7,14) (7,20) (7,15) (8,16) (8,19) (8,9) (8,13) (8,18) (8,14) (8,15) (8,12) (9,16) (9,10) (9,13) (9,18) (9,11) (9,20) (10,16) (10,19) (10,13) (10,11) (10,14) (10,20) (10,15) (10,12) (11,13) (11,18) (11,14) (11,20) (11,15) (12,16) (12,14) (12,20) (12,15) (13,16) (13,19) (13,18) (13,14) (13,20) (13,15) (14,19) (14,20) (15,16) (15,19) (15,18) (15,20) (16,19) (16,20) (18,20) (19,20)\nIs there a path between node 13 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph790-7_22", + "image": "data/connectivity/graph_visual/medium/graph790.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,23) (1,9) (2,13) (2,16) (2,24) (3,5) (3,7) (3,11) (4,6) (4,12) (4,5) (4,14) (4,7) (5,6) (5,12) (5,14) (5,11) (6,17) (6,20) (6,7) (10,19) (10,23) (10,16) (10,18) (11,12) (11,20) (11,15) (13,16) (13,22) (13,24) (14,17) (14,20) (15,20) (16,23) (17,20) (18,22) (22,23) (23,24)\nIs there a path between node 7 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph741-19_16", + "image": "data/connectivity/graph_visual/medium/graph741.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,20) (0,17) (0,15) (3,5) (3,6) (3,8) (4,11) (4,16) (4,24) (5,10) (5,8) (5,14) (11,16) (13,20) (13,16) (13,15) (13,19) (14,18) (15,16) (15,22) (15,24) (17,20) (17,22) (17,21) (19,24) (20,22) (20,21) (21,22)\nIs there a path between node 19 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph790-19_24", + "image": "data/connectivity/graph_visual/medium/graph790.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,23) (1,9) (2,13) (2,16) (2,24) (3,5) (3,7) (3,11) (4,6) (4,12) (4,5) (4,14) (4,7) (5,6) (5,12) (5,14) (5,11) (6,17) (6,20) (6,7) (10,19) (10,23) (10,16) (10,18) (11,12) (11,20) (11,15) (13,16) (13,22) (13,24) (14,17) (14,20) (15,20) (16,23) (17,20) (18,22) (22,23) (23,24)\nIs there a path between node 19 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph760-3_18", + "image": "data/connectivity/graph_visual/medium/graph760.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,1) (0,19) (0,21) (1,9) (1,19) (1,21) (2,7) (3,11) (3,14) (3,6) (3,18) (4,23) (4,16) (4,10) (4,17) (4,13) (5,9) (5,21) (6,11) (6,12) (6,14) (6,15) (6,8) (8,12) (8,14) (8,15) (8,18) (9,19) (9,21) (10,23) (10,16) (10,20) (10,13) (11,12) (11,14) (11,15) (11,18) (12,14) (12,18) (13,23) (13,16) (13,20) (13,24) (14,15) (15,18) (16,23) (16,20) (16,24) (17,20) (20,23) (20,24) (23,24)\nIs there a path between node 3 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph661-0_9", + "image": "data/connectivity/graph_visual/medium/graph661.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,4) (1,8) (1,17) (1,20) (1,13) (1,18) (1,19) (1,2) (1,23) (1,21) (1,16) (1,7) (2,10) (2,8) (2,6) (2,15) (2,9) (2,17) (2,20) (2,13) (2,18) (2,19) (2,12) (2,21) (2,16) (3,10) (3,8) (3,6) (3,15) (3,9) (3,20) (3,13) (3,18) (3,5) (3,19) (3,12) (3,16) (3,14) (4,11) (5,8) (5,6) (5,15) (5,9) (5,17) (5,20) (5,13) (5,18) (5,19) (5,21) (5,7) (6,10) (6,8) (6,15) (6,17) (6,20) (6,13) (6,18) (6,19) (6,12) (6,21) (6,16) (6,22) (7,15) (7,9) (7,13) (7,18) (7,12) (7,23) (7,14) (7,22) (8,10) (8,20) (8,13) (8,12) (8,21) (8,16) (8,14) (8,22) (9,10) (9,15) (9,20) (9,13) (9,12) (9,16) (9,14) (9,22) (10,15) (10,17) (10,13) (10,18) (10,12) (10,16) (10,14) (10,22) (12,15) (12,17) (12,13) (12,18) (12,23) (12,21) (12,16) (12,14) (12,22) (13,17) (13,20) (13,19) (13,21) (13,14) (13,22) (14,15) (14,17) (14,18) (14,16) (14,22) (15,17) (15,19) (15,16) (15,22) (16,17) (16,20) (16,19) (16,21) (17,19) (17,23) (17,21) (17,22) (18,23) (18,21) (18,22) (19,20) (19,23) (19,21) (19,22) (20,21) (20,22) (21,23) (22,23)\nIs there a path between node 0 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph837-3_6", + "image": "data/connectivity/graph_visual/medium/graph837.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,24) (0,6) (1,2) (1,21) (1,9) (1,8) (1,17) (1,5) (1,3) (1,11) (1,4) (1,15) (2,21) (2,9) (2,8) (2,17) (2,5) (2,3) (2,11) (2,4) (2,15) (3,21) (3,9) (3,8) (3,17) (3,5) (3,11) (3,4) (3,15) (4,21) (4,9) (4,8) (4,17) (4,5) (4,11) (4,15) (5,21) (5,9) (5,8) (5,17) (5,11) (5,15) (6,10) (6,24) (7,12) (7,18) (7,16) (7,23) (7,13) (7,20) (7,22) (7,14) (7,19) (8,21) (8,9) (8,17) (8,11) (8,15) (9,21) (9,17) (9,11) (9,15) (10,24) (11,21) (11,17) (11,15) (12,18) (12,16) (12,23) (12,13) (12,20) (12,22) (12,14) (12,19) (13,18) (13,16) (13,23) (13,20) (13,22) (13,14) (13,19) (14,18) (14,16) (14,23) (14,20) (14,22) (14,19) (15,21) (15,17) (16,18) (16,23) (16,20) (16,22) (16,19) (17,21) (18,23) (18,20) (18,22) (18,19) (19,23) (19,20) (19,22) (20,23) (20,22) (22,23)\nIs there a path between node 3 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph6-6_1", + "image": "data/connectivity/graph_visual/medium/graph6.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (0,1) (1,2) (1,8) (3,7) (5,10) (6,9)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph311-15_5", + "image": "data/connectivity/graph_visual/medium/graph311.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,19) (0,16) (0,18) (0,2) (0,17) (0,7) (0,12) (1,8) (1,3) (1,10) (1,13) (1,6) (1,11) (1,15) (1,5) (1,4) (1,14) (2,9) (2,19) (2,16) (2,18) (2,17) (2,7) (2,12) (3,8) (3,10) (3,13) (3,6) (3,11) (3,15) (3,5) (3,4) (3,14) (4,8) (4,10) (4,13) (4,6) (4,11) (4,15) (4,5) (4,14) (5,8) (5,10) (5,13) (5,6) (5,11) (5,15) (5,14) (6,8) (6,10) (6,13) (6,11) (6,15) (6,14) (7,9) (7,19) (7,16) (7,18) (7,17) (7,12) (8,10) (8,13) (8,11) (8,15) (8,14) (9,19) (9,16) (9,18) (9,17) (9,12) (10,13) (10,11) (10,15) (10,14) (11,13) (11,15) (11,14) (12,19) (12,16) (12,18) (12,17) (13,15) (13,14) (14,15) (16,19) (16,18) (16,17) (17,19) (17,18) (18,19)\nIs there a path between node 15 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph286-19_11", + "image": "data/connectivity/graph_visual/medium/graph286.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (0,9) (1,11) (1,4) (2,6) (2,14) (2,19) (3,15) (4,18) (4,17) (4,9) (4,19) (5,6) (5,11) (5,10) (6,11) (6,18) (8,10) (8,14) (9,18) (9,10) (9,14) (10,18) (10,19) (11,14) (11,19) (12,15) (12,13) (16,19)\nIs there a path between node 19 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph44-12_9", + "image": "data/connectivity/graph_visual/medium/graph44.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,7) (0,5) (0,4) (0,6) (0,11) (1,10) (1,2) (2,10) (3,9) (3,8) (3,7) (3,5) (3,12) (3,6) (3,11) (4,7) (4,5) (4,12) (4,11) (5,9) (5,8) (5,7) (5,11) (6,9) (6,8) (6,7) (6,12) (7,12) (7,11) (8,9) (8,12) (9,12) (9,11) (11,12)\nIs there a path between node 12 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph214-5_6", + "image": "data/connectivity/graph_visual/medium/graph214.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,1) (0,6) (0,17) (0,10) (0,16) (0,13) (1,11) (1,6) (1,17) (1,10) (1,16) (1,13) (2,12) (2,8) (2,15) (2,14) (2,3) (2,9) (2,7) (2,4) (2,18) (2,5) (3,12) (3,8) (3,15) (3,14) (3,9) (3,7) (3,4) (3,18) (3,5) (4,12) (4,8) (4,15) (4,14) (4,9) (4,7) (4,18) (4,5) (5,12) (5,8) (5,15) (5,14) (5,9) (5,7) (5,18) (6,11) (6,17) (6,10) (6,16) (6,13) (7,12) (7,8) (7,15) (7,14) (7,9) (7,18) (8,12) (8,15) (8,14) (8,9) (8,18) (9,12) (9,15) (9,14) (9,18) (10,11) (10,17) (10,16) (10,13) (11,17) (11,16) (11,13) (12,15) (12,14) (12,18) (13,17) (13,16) (14,15) (14,18) (15,18) (16,17)\nIs there a path between node 5 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph160-16_9", + "image": "data/connectivity/graph_visual/medium/graph160.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,6) (0,13) (0,15) (0,8) (0,14) (0,2) (1,7) (2,10) (2,13) (2,11) (2,14) (2,17) (3,6) (3,12) (3,11) (4,16) (4,5) (4,7) (6,15) (8,13) (8,14) (10,12) (10,13) (10,17) (11,14) (12,13) (12,15) (14,17) (15,17)\nIs there a path between node 16 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph175-12_9", + "image": "data/connectivity/graph_visual/medium/graph175.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,2) (0,5) (1,13) (1,4) (1,8) (1,17) (1,9) (1,3) (1,6) (1,14) (1,10) (2,7) (2,5) (3,4) (3,8) (3,15) (3,11) (3,6) (3,14) (3,10) (4,13) (4,16) (4,8) (4,17) (4,11) (4,9) (4,6) (4,10) (5,7) (5,12) (6,15) (6,17) (6,11) (6,9) (6,14) (6,10) (8,13) (8,16) (8,15) (8,17) (8,9) (8,14) (8,10) (9,13) (9,15) (9,17) (9,11) (9,14) (9,10) (10,15) (10,17) (10,11) (10,14) (11,13) (11,16) (11,15) (11,14) (13,16) (13,15) (14,16) (14,15) (14,17) (15,16)\nIs there a path between node 12 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph136-12_8", + "image": "data/connectivity/graph_visual/medium/graph136.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,17) (1,14) (1,8) (3,14) (4,10) (5,17) (6,15) (7,14) (8,12) (8,15) (9,17) (9,10) (9,16) (12,15) (13,17) (14,15)\nIs there a path between node 12 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph672-15_1", + "image": "data/connectivity/graph_visual/medium/graph672.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,14) (0,10) (0,4) (0,9) (0,20) (1,8) (1,6) (1,16) (1,11) (3,7) (3,22) (3,19) (3,21) (3,15) (3,17) (4,23) (4,14) (4,9) (5,8) (5,13) (5,11) (6,8) (6,13) (6,11) (7,22) (7,19) (7,17) (8,13) (8,16) (8,11) (9,23) (9,12) (9,10) (9,18) (9,20) (10,23) (10,14) (10,18) (11,13) (11,16) (12,23) (12,18) (14,23) (14,18) (14,20) (15,19) (15,21) (15,17) (17,22) (17,19) (17,21) (18,23) (18,20) (19,21) (20,23) (21,22)\nIs there a path between node 15 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph115-5_1", + "image": "data/connectivity/graph_visual/medium/graph115.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,14) (0,10) (0,16) (0,12) (0,11) (2,7) (3,10) (3,16) (3,13) (3,9) (4,10) (4,16) (5,8) (5,16) (5,13) (5,12) (5,11) (5,9) (6,13) (6,11) (8,10) (8,16) (8,13) (8,15) (9,16) (10,12) (12,14) (13,16) (13,15) (14,15)\nIs there a path between node 5 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph737-12_23", + "image": "data/connectivity/graph_visual/medium/graph737.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,3) (0,16) (0,24) (0,7) (1,17) (1,2) (2,9) (2,20) (2,8) (3,22) (3,12) (3,23) (3,21) (4,9) (4,13) (4,18) (5,11) (5,23) (5,21) (6,15) (6,7) (7,11) (7,22) (7,12) (7,16) (7,23) (7,14) (7,21) (8,20) (8,17) (8,18) (10,20) (10,17) (10,18) (11,21) (12,22) (12,14) (14,22) (15,16) (15,24) (16,23) (17,18) (19,21) (21,24) (22,24)\nIs there a path between node 12 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph297-15_18", + "image": "data/connectivity/graph_visual/medium/graph297.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,12) (0,19) (1,2) (1,13) (1,7) (1,6) (1,3) (1,9) (1,16) (1,4) (2,13) (2,7) (2,6) (2,10) (2,9) (2,16) (2,8) (2,15) (3,17) (3,6) (3,5) (3,10) (3,16) (3,4) (4,13) (4,17) (4,6) (4,5) (4,10) (4,9) (4,15) (5,13) (5,7) (5,6) (5,9) (5,16) (5,8) (6,13) (6,7) (6,9) (6,16) (6,8) (6,15) (7,13) (7,10) (7,9) (8,17) (8,10) (8,9) (8,16) (8,15) (9,17) (9,10) (9,16) (9,15) (10,13) (10,17) (10,16) (10,15) (12,19) (12,18) (13,15) (15,17) (15,16) (16,17) (18,19)\nIs there a path between node 15 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph408-11_5", + "image": "data/connectivity/graph_visual/medium/graph408.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,17) (0,7) (0,18) (0,14) (0,8) (0,19) (0,15) (0,4) (0,21) (1,3) (1,6) (1,11) (2,7) (2,9) (2,14) (2,8) (2,19) (2,13) (2,15) (2,10) (3,5) (3,20) (3,6) (3,11) (4,17) (4,7) (4,18) (4,9) (4,21) (5,12) (5,6) (5,11) (6,12) (6,20) (7,17) (7,18) (7,9) (7,14) (7,8) (7,13) (7,15) (8,17) (8,18) (8,14) (8,13) (8,15) (8,21) (8,10) (9,17) (9,18) (9,14) (9,13) (9,21) (10,17) (10,18) (10,14) (10,13) (10,15) (11,12) (11,20) (12,20) (12,16) (13,18) (13,14) (13,19) (13,15) (13,21) (14,18) (14,15) (14,21) (15,17) (15,18) (15,19) (15,21) (17,18) (17,19) (18,19) (19,21)\nIs there a path between node 11 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph136-7_14", + "image": "data/connectivity/graph_visual/medium/graph136.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,17) (1,14) (1,8) (3,14) (4,10) (5,17) (6,15) (7,14) (8,12) (8,15) (9,17) (9,10) (9,16) (12,15) (13,17) (14,15)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph824-11_16", + "image": "data/connectivity/graph_visual/medium/graph824.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,8) (0,12) (0,5) (0,14) (0,15) (0,17) (0,11) (0,16) (0,1) (1,9) (1,8) (1,12) (1,5) (1,14) (1,15) (1,11) (1,16) (1,22) (2,9) (2,8) (2,15) (2,17) (2,11) (2,16) (2,6) (3,20) (3,24) (3,4) (3,13) (3,18) (3,19) (4,24) (4,21) (4,10) (4,18) (4,7) (5,9) (5,12) (5,15) (5,6) (5,22) (6,9) (6,8) (6,12) (6,14) (6,15) (6,17) (6,11) (7,20) (7,24) (7,23) (7,13) (7,21) (7,18) (7,19) (8,12) (8,14) (8,15) (8,11) (8,16) (8,22) (9,12) (9,17) (9,16) (9,22) (10,20) (10,23) (10,13) (10,19) (11,12) (11,14) (11,15) (11,17) (11,16) (12,15) (12,16) (12,22) (13,20) (13,24) (13,21) (13,18) (14,15) (14,17) (14,22) (15,17) (15,22) (16,17) (16,22) (18,20) (18,24) (18,23) (18,21) (18,19) (19,24) (20,24) (20,23) (20,21) (21,24) (21,23) (23,24)\nIs there a path between node 11 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph468-5_4", + "image": "data/connectivity/graph_visual/medium/graph468.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,14) (0,20) (0,13) (1,2) (1,8) (1,9) (2,9) (4,10) (4,20) (5,21) (5,17) (5,9) (6,10) (6,14) (6,13) (7,21) (7,22) (8,9) (10,19) (10,18) (10,12) (10,13) (11,16) (11,18) (12,16) (12,19) (12,18) (13,19) (14,19) (16,18) (17,22) (18,19)\nIs there a path between node 5 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph675-2_16", + "image": "data/connectivity/graph_visual/medium/graph675.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,22) (0,21) (0,14) (0,19) (0,13) (0,18) (0,12) (0,15) (0,6) (0,7) (0,10) (0,20) (0,2) (0,4) (0,8) (0,17) (0,23) (1,3) (1,16) (1,11) (1,9) (2,5) (2,22) (2,21) (2,14) (2,19) (2,13) (2,18) (2,12) (2,15) (2,6) (2,7) (2,10) (2,20) (2,4) (2,8) (2,17) (2,23) (3,16) (3,11) (3,9) (4,5) (4,22) (4,21) (4,14) (4,19) (4,13) (4,18) (4,12) (4,15) (4,6) (4,7) (4,10) (4,20) (4,8) (4,17) (4,23) (5,22) (5,21) (5,14) (5,19) (5,13) (5,18) (5,12) (5,15) (5,6) (5,7) (5,10) (5,20) (5,8) (5,17) (5,23) (6,22) (6,21) (6,14) (6,19) (6,13) (6,18) (6,12) (6,15) (6,7) (6,10) (6,20) (6,8) (6,17) (6,23) (7,22) (7,21) (7,14) (7,19) (7,13) (7,18) (7,12) (7,15) (7,10) (7,20) (7,8) (7,17) (7,23) (8,22) (8,21) (8,14) (8,19) (8,13) (8,18) (8,12) (8,15) (8,10) (8,20) (8,17) (8,23) (9,16) (9,11) (10,22) (10,21) (10,14) (10,19) (10,13) (10,18) (10,12) (10,15) (10,20) (10,17) (10,23) (11,16) (12,22) (12,21) (12,14) (12,19) (12,13) (12,18) (12,15) (12,20) (12,17) (12,23) (13,22) (13,21) (13,14) (13,19) (13,18) (13,15) (13,20) (13,17) (13,23) (14,22) (14,21) (14,19) (14,18) (14,15) (14,20) (14,17) (14,23) (15,22) (15,21) (15,19) (15,18) (15,20) (15,17) (15,23) (17,22) (17,21) (17,19) (17,18) (17,20) (17,23) (18,22) (18,21) (18,19) (18,20) (18,23) (19,22) (19,21) (19,20) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 2 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph752-24_13", + "image": "data/connectivity/graph_visual/medium/graph752.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,20) (0,17) (0,1) (0,21) (1,10) (1,20) (1,21) (3,20) (3,21) (4,5) (4,12) (4,14) (4,16) (4,6) (4,15) (5,7) (5,14) (5,16) (5,19) (5,11) (5,8) (5,15) (6,24) (6,14) (6,16) (6,19) (6,9) (6,13) (6,11) (6,8) (7,24) (7,12) (7,14) (7,19) (7,9) (7,13) (7,11) (7,8) (7,15) (8,24) (8,12) (8,16) (8,19) (8,9) (8,11) (8,15) (9,24) (9,12) (9,14) (9,11) (9,15) (10,20) (10,17) (10,21) (11,24) (11,12) (11,14) (11,16) (11,19) (11,13) (11,15) (12,14) (12,16) (12,19) (12,15) (13,24) (13,14) (13,16) (13,19) (14,24) (14,16) (14,15) (15,24) (15,16) (16,24) (16,19) (17,20) (17,21) (18,23) (19,24) (22,23)\nIs there a path between node 24 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph347-8_19", + "image": "data/connectivity/graph_visual/medium/graph347.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,13) (0,3) (0,19) (0,12) (0,15) (0,17) (1,20) (1,6) (1,2) (1,7) (2,20) (2,6) (2,7) (3,10) (3,13) (3,19) (3,12) (3,15) (3,17) (4,11) (4,9) (4,18) (4,16) (4,14) (4,8) (4,5) (5,11) (5,9) (5,18) (5,16) (5,14) (5,8) (6,20) (6,7) (7,20) (8,11) (8,9) (8,18) (8,16) (8,14) (9,11) (9,18) (9,16) (9,14) (10,13) (10,19) (10,12) (10,15) (10,17) (11,18) (11,16) (11,14) (12,13) (12,19) (12,15) (12,17) (13,19) (13,15) (13,17) (14,18) (14,16) (15,19) (15,17) (16,18) (17,19)\nIs there a path between node 8 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph255-4_7", + "image": "data/connectivity/graph_visual/medium/graph255.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,10) (0,15) (0,5) (0,1) (0,6) (0,9) (0,2) (0,8) (1,10) (1,15) (1,5) (1,6) (1,9) (1,2) (1,8) (2,10) (2,15) (2,5) (2,6) (2,9) (2,8) (3,17) (3,16) (3,12) (3,4) (3,18) (3,11) (3,13) (4,17) (4,16) (4,12) (4,18) (4,11) (4,13) (5,10) (5,15) (5,6) (5,9) (5,8) (6,10) (6,15) (6,9) (6,8) (7,14) (8,10) (8,15) (8,9) (9,10) (9,15) (10,15) (11,17) (11,16) (11,12) (11,18) (11,13) (12,17) (12,16) (12,18) (12,13) (13,17) (13,16) (13,18) (16,17) (16,18) (17,18)\nIs there a path between node 4 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph391-13_9", + "image": "data/connectivity/graph_visual/medium/graph391.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,9) (0,20) (0,8) (0,14) (0,2) (0,11) (0,1) (0,10) (0,7) (0,12) (0,4) (0,5) (0,15) (0,16) (1,18) (1,9) (1,20) (1,8) (1,14) (1,2) (1,11) (1,10) (1,7) (1,12) (1,4) (1,5) (1,15) (1,16) (2,18) (2,9) (2,20) (2,8) (2,14) (2,11) (2,10) (2,7) (2,12) (2,4) (2,5) (2,15) (2,16) (3,13) (3,19) (4,18) (4,9) (4,20) (4,8) (4,14) (4,11) (4,10) (4,7) (4,12) (4,5) (4,15) (4,16) (5,18) (5,9) (5,20) (5,8) (5,14) (5,11) (5,10) (5,7) (5,12) (5,15) (5,16) (6,17) (7,18) (7,9) (7,20) (7,8) (7,14) (7,11) (7,10) (7,12) (7,15) (7,16) (8,18) (8,9) (8,20) (8,14) (8,11) (8,10) (8,12) (8,15) (8,16) (9,18) (9,20) (9,14) (9,11) (9,10) (9,12) (9,15) (9,16) (10,18) (10,20) (10,14) (10,11) (10,12) (10,15) (10,16) (11,18) (11,20) (11,14) (11,12) (11,15) (11,16) (12,18) (12,20) (12,14) (12,15) (12,16) (13,19) (14,18) (14,20) (14,15) (14,16) (15,18) (15,20) (15,16) (16,18) (16,20) (18,20)\nIs there a path between node 13 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph741-18_17", + "image": "data/connectivity/graph_visual/medium/graph741.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,20) (0,17) (0,15) (3,5) (3,6) (3,8) (4,11) (4,16) (4,24) (5,10) (5,8) (5,14) (11,16) (13,20) (13,16) (13,15) (13,19) (14,18) (15,16) (15,22) (15,24) (17,20) (17,22) (17,21) (19,24) (20,22) (20,21) (21,22)\nIs there a path between node 18 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph369-18_11", + "image": "data/connectivity/graph_visual/medium/graph369.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (1,2) (1,16) (1,19) (1,10) (1,13) (1,18) (1,14) (1,20) (1,5) (1,4) (1,15) (1,6) (1,8) (1,12) (2,16) (2,19) (2,7) (2,9) (2,18) (2,11) (2,14) (2,20) (2,5) (2,6) (2,12) (3,17) (4,16) (4,19) (4,10) (4,7) (4,9) (4,13) (4,14) (4,15) (4,6) (4,8) (4,12) (5,19) (5,10) (5,7) (5,9) (5,13) (5,18) (5,14) (5,20) (5,15) (5,6) (5,8) (5,12) (6,16) (6,19) (6,10) (6,13) (6,18) (6,15) (6,8) (6,12) (7,16) (7,19) (7,9) (7,13) (7,18) (7,14) (7,20) (7,15) (8,16) (8,19) (8,9) (8,13) (8,18) (8,14) (8,15) (8,12) (9,16) (9,10) (9,13) (9,18) (9,11) (9,20) (10,16) (10,19) (10,13) (10,11) (10,14) (10,20) (10,15) (10,12) (11,13) (11,18) (11,14) (11,20) (11,15) (12,16) (12,14) (12,20) (12,15) (13,16) (13,19) (13,18) (13,14) (13,20) (13,15) (14,19) (14,20) (15,16) (15,19) (15,18) (15,20) (16,19) (16,20) (18,20) (19,20)\nIs there a path between node 18 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph458-14_15", + "image": "data/connectivity/graph_visual/medium/graph458.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,7) (0,5) (0,11) (0,3) (0,10) (0,6) (0,18) (0,15) (0,2) (0,13) (0,16) (0,8) (0,20) (1,12) (1,14) (1,21) (1,9) (1,4) (1,17) (2,19) (2,7) (2,5) (2,11) (2,3) (2,10) (2,6) (2,18) (2,15) (2,13) (2,16) (2,8) (2,20) (3,19) (3,7) (3,5) (3,11) (3,10) (3,6) (3,18) (3,15) (3,13) (3,16) (3,8) (3,20) (4,12) (4,14) (4,21) (4,9) (4,17) (5,19) (5,7) (5,11) (5,10) (5,6) (5,18) (5,15) (5,13) (5,16) (5,8) (5,20) (6,19) (6,7) (6,11) (6,10) (6,18) (6,15) (6,13) (6,16) (6,8) (6,20) (7,19) (7,11) (7,10) (7,18) (7,15) (7,13) (7,16) (7,8) (7,20) (8,19) (8,11) (8,10) (8,18) (8,15) (8,13) (8,16) (8,20) (9,12) (9,14) (9,21) (9,17) (10,19) (10,11) (10,18) (10,15) (10,13) (10,16) (10,20) (11,19) (11,18) (11,15) (11,13) (11,16) (11,20) (12,14) (12,21) (12,17) (13,19) (13,18) (13,15) (13,16) (13,20) (14,21) (14,17) (15,19) (15,18) (15,16) (15,20) (16,19) (16,18) (16,20) (17,21) (18,19) (18,20) (19,20)\nIs there a path between node 14 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph361-11_9", + "image": "data/connectivity/graph_visual/medium/graph361.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,8) (0,14) (0,2) (0,16) (1,5) (1,7) (1,18) (1,15) (1,2) (1,10) (2,19) (2,12) (3,5) (3,15) (3,4) (3,6) (4,13) (4,15) (4,8) (4,14) (4,12) (4,10) (5,13) (5,18) (5,14) (5,16) (5,10) (6,13) (6,18) (6,10) (7,15) (7,10) (8,14) (8,12) (10,19) (10,16) (12,16) (13,18) (15,19) (15,16)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph633-22_13", + "image": "data/connectivity/graph_visual/medium/graph633.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,10) (1,9) (3,17) (3,8) (3,23) (4,17) (4,15) (4,22) (4,8) (4,23) (4,16) (6,11) (6,10) (7,21) (8,17) (8,23) (8,16) (10,18) (10,19) (11,18) (11,14) (15,23) (16,17) (16,23) (19,20) (21,22) (21,23)\nIs there a path between node 22 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph800-14_10", + "image": "data/connectivity/graph_visual/medium/graph800.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,4) (0,22) (1,13) (1,4) (1,6) (1,2) (1,10) (1,3) (2,10) (2,23) (2,5) (3,4) (3,17) (3,23) (3,12) (4,12) (5,18) (5,15) (5,12) (5,22) (6,17) (7,19) (10,17) (10,23) (10,14) (10,15) (11,13) (12,18) (12,14) (13,17) (13,23) (13,22) (14,23) (14,15) (15,23) (16,20) (17,18) (17,23) (18,23) (19,24) (19,21) (20,21)\nIs there a path between node 14 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph428-2_18", + "image": "data/connectivity/graph_visual/medium/graph428.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,13) (0,7) (0,9) (0,19) (0,10) (1,16) (1,14) (1,7) (1,19) (1,3) (2,21) (3,18) (3,13) (3,9) (3,19) (4,21) (5,6) (5,13) (5,7) (5,9) (5,11) (5,12) (5,10) (6,15) (6,10) (7,14) (7,11) (9,15) (9,18) (9,14) (10,12) (11,13) (12,19) (14,16) (17,20) (20,21)\nIs there a path between node 2 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph692-1_22", + "image": "data/connectivity/graph_visual/medium/graph692.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,22) (0,23) (0,10) (0,16) (0,18) (0,3) (0,13) (0,5) (0,8) (0,17) (0,12) (0,6) (0,9) (0,4) (0,1) (0,14) (1,19) (1,22) (1,23) (1,10) (1,16) (1,18) (1,3) (1,13) (1,5) (1,8) (1,17) (1,12) (1,6) (1,9) (1,4) (1,14) (2,20) (2,7) (2,11) (2,15) (2,21) (3,19) (3,22) (3,23) (3,10) (3,16) (3,18) (3,13) (3,5) (3,8) (3,17) (3,12) (3,6) (3,9) (3,4) (3,14) (4,19) (4,22) (4,23) (4,10) (4,16) (4,18) (4,13) (4,5) (4,8) (4,17) (4,12) (4,6) (4,9) (4,14) (5,19) (5,22) (5,23) (5,10) (5,16) (5,18) (5,13) (5,8) (5,17) (5,12) (5,6) (5,9) (5,14) (6,19) (6,22) (6,23) (6,10) (6,16) (6,18) (6,13) (6,8) (6,17) (6,12) (6,9) (6,14) (7,20) (7,11) (7,15) (7,21) (8,19) (8,22) (8,23) (8,10) (8,16) (8,18) (8,13) (8,17) (8,12) (8,9) (8,14) (9,19) (9,22) (9,23) (9,10) (9,16) (9,18) (9,13) (9,17) (9,12) (9,14) (10,19) (10,22) (10,23) (10,16) (10,18) (10,13) (10,17) (10,12) (10,14) (11,20) (11,15) (11,21) (12,19) (12,22) (12,23) (12,16) (12,18) (12,13) (12,17) (12,14) (13,19) (13,22) (13,23) (13,16) (13,18) (13,17) (13,14) (14,19) (14,22) (14,23) (14,16) (14,18) (14,17) (15,20) (15,21) (16,19) (16,22) (16,23) (16,18) (16,17) (17,19) (17,22) (17,23) (17,18) (18,19) (18,22) (18,23) (19,22) (19,23) (20,21) (22,23)\nIs there a path between node 1 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph453-6_3", + "image": "data/connectivity/graph_visual/medium/graph453.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,3) (1,20) (1,21) (1,8) (1,5) (1,16) (1,17) (1,19) (1,6) (1,12) (1,14) (1,9) (1,13) (1,18) (1,7) (1,11) (1,15) (1,2) (1,10) (2,20) (2,21) (2,8) (2,5) (2,16) (2,17) (2,19) (2,6) (2,12) (2,14) (2,9) (2,13) (2,18) (2,7) (2,11) (2,15) (2,10) (3,4) (5,20) (5,21) (5,8) (5,16) (5,17) (5,19) (5,6) (5,12) (5,14) (5,9) (5,13) (5,18) (5,7) (5,11) (5,15) (5,10) (6,20) (6,21) (6,8) (6,16) (6,17) (6,19) (6,12) (6,14) (6,9) (6,13) (6,18) (6,7) (6,11) (6,15) (6,10) (7,20) (7,21) (7,8) (7,16) (7,17) (7,19) (7,12) (7,14) (7,9) (7,13) (7,18) (7,11) (7,15) (7,10) (8,20) (8,21) (8,16) (8,17) (8,19) (8,12) (8,14) (8,9) (8,13) (8,18) (8,11) (8,15) (8,10) (9,20) (9,21) (9,16) (9,17) (9,19) (9,12) (9,14) (9,13) (9,18) (9,11) (9,15) (9,10) (10,20) (10,21) (10,16) (10,17) (10,19) (10,12) (10,14) (10,13) (10,18) (10,11) (10,15) (11,20) (11,21) (11,16) (11,17) (11,19) (11,12) (11,14) (11,13) (11,18) (11,15) (12,20) (12,21) (12,16) (12,17) (12,19) (12,14) (12,13) (12,18) (12,15) (13,20) (13,21) (13,16) (13,17) (13,19) (13,14) (13,18) (13,15) (14,20) (14,21) (14,16) (14,17) (14,19) (14,18) (14,15) (15,20) (15,21) (15,16) (15,17) (15,19) (15,18) (16,20) (16,21) (16,17) (16,19) (16,18) (17,20) (17,21) (17,19) (17,18) (18,20) (18,21) (18,19) (19,20) (19,21) (20,21)\nIs there a path between node 6 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph493-12_6", + "image": "data/connectivity/graph_visual/medium/graph493.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,9) (0,19) (0,7) (0,2) (0,14) (0,12) (0,15) (0,22) (0,20) (1,16) (1,10) (1,3) (1,11) (1,4) (1,17) (1,5) (2,6) (2,9) (2,19) (2,7) (2,14) (2,12) (2,15) (2,22) (2,20) (3,16) (3,10) (3,11) (3,4) (3,17) (3,5) (4,16) (4,10) (4,11) (4,17) (4,5) (5,16) (5,10) (5,11) (5,17) (6,9) (6,19) (6,7) (6,14) (6,12) (6,15) (6,22) (6,20) (7,9) (7,19) (7,14) (7,12) (7,15) (7,22) (7,20) (8,13) (8,21) (8,18) (9,19) (9,14) (9,12) (9,15) (9,22) (9,20) (10,16) (10,11) (10,17) (11,16) (11,17) (12,19) (12,14) (12,15) (12,22) (12,20) (13,21) (13,18) (14,19) (14,15) (14,22) (14,20) (15,19) (15,22) (15,20) (16,17) (18,21) (19,22) (19,20) (20,22)\nIs there a path between node 12 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph804-13_19", + "image": "data/connectivity/graph_visual/medium/graph804.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,4) (1,19) (2,4) (2,10) (2,20) (3,20) (3,19) (4,13) (4,9) (4,7) (4,19) (5,6) (7,12) (7,20) (9,14) (9,13) (9,23) (9,12) (9,10) (10,15) (12,15) (12,20) (13,19) (14,20) (16,17) (18,22) (20,23)\nIs there a path between node 13 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph188-12_3", + "image": "data/connectivity/graph_visual/medium/graph188.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,11) (0,1) (0,9) (0,17) (0,3) (0,14) (0,15) (0,4) (0,10) (0,2) (0,6) (1,16) (1,11) (1,9) (1,17) (1,3) (1,14) (1,15) (1,4) (1,10) (1,2) (1,6) (2,16) (2,11) (2,9) (2,17) (2,3) (2,14) (2,15) (2,4) (2,10) (2,6) (3,16) (3,11) (3,9) (3,17) (3,14) (3,15) (3,4) (3,10) (3,6) (4,16) (4,11) (4,9) (4,17) (4,14) (4,15) (4,10) (4,6) (5,8) (5,12) (5,7) (5,13) (6,16) (6,11) (6,9) (6,17) (6,14) (6,15) (6,10) (7,8) (7,12) (7,13) (8,12) (8,13) (9,16) (9,11) (9,17) (9,14) (9,15) (9,10) (10,16) (10,11) (10,17) (10,14) (10,15) (11,16) (11,17) (11,14) (11,15) (12,13) (14,16) (14,17) (14,15) (15,16) (15,17) (16,17)\nIs there a path between node 12 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph63-9_13", + "image": "data/connectivity/graph_visual/medium/graph63.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,12) (0,9) (0,6) (1,10) (1,5) (1,2) (1,8) (1,7) (2,5) (2,3) (3,8) (3,11) (3,7) (4,12) (4,6) (4,13) (5,8) (5,11) (6,9) (6,13) (7,10) (7,8) (8,11) (9,13)\nIs there a path between node 9 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph294-5_19", + "image": "data/connectivity/graph_visual/medium/graph294.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,1) (0,19) (1,13) (1,19) (1,11) (1,14) (1,2) (2,4) (2,18) (3,10) (4,13) (4,11) (5,6) (5,10) (5,7) (6,12) (6,7) (7,10) (8,18) (9,15) (10,12) (11,19) (12,15) (13,18)\nIs there a path between node 5 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph711-15_21", + "image": "data/connectivity/graph_visual/medium/graph711.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,2) (0,7) (0,15) (0,14) (0,22) (0,10) (0,18) (0,5) (0,9) (0,4) (0,11) (0,8) (0,20) (0,13) (1,2) (1,7) (1,15) (1,14) (1,18) (1,5) (1,16) (1,9) (1,4) (1,11) (1,8) (1,13) (2,24) (2,7) (2,15) (2,14) (2,22) (2,18) (2,16) (2,9) (2,4) (2,11) (2,8) (2,20) (2,23) (3,21) (4,7) (4,14) (4,22) (4,18) (4,16) (4,13) (4,23) (5,24) (5,7) (5,15) (5,14) (5,22) (5,10) (5,18) (5,20) (5,23) (6,12) (7,24) (7,15) (7,14) (7,10) (7,18) (7,16) (7,9) (7,11) (7,8) (7,20) (7,13) (7,23) (8,24) (8,14) (8,10) (8,18) (8,9) (8,13) (8,23) (9,24) (9,15) (9,14) (9,22) (9,10) (9,16) (9,20) (9,23) (10,24) (10,15) (10,14) (10,22) (10,18) (10,16) (10,20) (11,15) (11,14) (11,18) (11,16) (11,20) (11,13) (11,23) (13,24) (13,15) (13,18) (13,16) (13,23) (14,24) (14,15) (14,22) (14,18) (14,16) (14,23) (15,24) (15,22) (15,18) (15,16) (15,20) (15,23) (16,24) (16,20) (16,23) (18,22) (18,20) (18,23) (19,21) (20,22) (22,24) (22,23) (23,24)\nIs there a path between node 15 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph163-10_0", + "image": "data/connectivity/graph_visual/medium/graph163.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,6) (1,13) (1,5) (2,17) (3,5) (3,15) (3,7) (4,8) (5,6) (5,16) (5,11) (5,15) (7,11) (10,16) (10,12) (10,13) (12,13)\nIs there a path between node 10 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph42-2_6", + "image": "data/connectivity/graph_visual/medium/graph42.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,6) (0,7) (0,10) (0,8) (0,11) (0,12) (1,3) (1,4) (1,9) (2,6) (2,7) (2,10) (2,8) (2,11) (2,12) (3,4) (3,5) (3,9) (4,5) (4,9) (5,9) (6,7) (6,10) (6,12) (7,10) (7,12) (8,10) (8,11) (8,12) (10,11) (11,12)\nIs there a path between node 2 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph24-2_0", + "image": "data/connectivity/graph_visual/medium/graph24.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,1) (0,8) (0,9) (0,3) (1,11) (1,5) (1,4) (1,6) (1,3) (2,10) (3,11) (3,5) (3,8) (3,4) (4,11) (4,6) (4,9) (5,11) (5,8) (5,6) (5,9) (6,11) (7,10) (9,11)\nIs there a path between node 2 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph222-2_5", + "image": "data/connectivity/graph_visual/medium/graph222.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,2) (0,3) (0,7) (0,10) (0,16) (1,18) (1,17) (1,7) (1,10) (1,16) (1,8) (2,17) (2,10) (2,8) (3,6) (3,15) (3,9) (3,4) (4,12) (4,18) (4,17) (4,9) (4,7) (4,10) (4,13) (6,9) (6,11) (6,16) (7,9) (8,9) (9,15) (9,10) (10,15) (10,18) (10,11) (12,16) (13,16) (15,17) (15,16) (16,18) (16,17) (17,18)\nIs there a path between node 2 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph335-6_9", + "image": "data/connectivity/graph_visual/medium/graph335.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,6) (0,19) (0,17) (0,3) (0,10) (0,14) (1,7) (1,8) (1,15) (1,13) (2,9) (2,12) (2,18) (2,4) (3,6) (3,19) (3,17) (3,16) (3,10) (3,14) (4,12) (4,18) (5,9) (5,18) (6,19) (6,17) (6,16) (6,14) (6,20) (7,8) (7,15) (7,13) (9,12) (9,18) (10,16) (10,14) (10,20) (11,15) (12,18) (13,15) (14,19) (14,17) (14,20) (16,19) (16,17) (17,20) (19,20)\nIs there a path between node 6 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph141-7_14", + "image": "data/connectivity/graph_visual/medium/graph141.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,12) (1,10) (3,14) (4,10) (5,12) (6,11) (6,16) (7,14) (8,14) (9,10) (10,15) (16,17)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph485-12_7", + "image": "data/connectivity/graph_visual/medium/graph485.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,2) (0,8) (0,7) (0,15) (1,9) (1,14) (1,19) (1,20) (1,5) (1,22) (1,10) (1,6) (1,17) (2,16) (2,8) (2,7) (3,16) (3,8) (3,7) (3,15) (4,14) (4,20) (4,5) (4,22) (4,18) (4,13) (4,10) (4,17) (5,14) (5,19) (5,22) (5,18) (5,13) (5,10) (5,6) (5,17) (6,9) (6,14) (6,19) (6,20) (6,22) (6,18) (6,13) (6,10) (6,17) (7,16) (7,8) (8,16) (8,15) (9,19) (9,20) (9,11) (9,22) (9,18) (9,10) (9,17) (10,19) (10,20) (10,11) (10,13) (10,17) (11,14) (11,19) (11,20) (11,22) (11,18) (11,13) (11,17) (12,21) (13,14) (13,19) (13,22) (13,18) (13,17) (14,20) (14,18) (14,17) (15,16) (17,20) (17,22) (18,19) (18,20) (18,22) (20,22)\nIs there a path between node 12 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph669-14_3", + "image": "data/connectivity/graph_visual/medium/graph669.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,7) (0,2) (0,9) (0,1) (0,17) (0,14) (0,18) (0,4) (0,5) (0,16) (0,15) (0,10) (0,22) (1,12) (1,3) (1,7) (1,14) (1,18) (1,5) (1,15) (1,10) (1,22) (2,3) (2,7) (2,9) (2,17) (2,18) (2,5) (2,16) (2,15) (2,10) (2,22) (3,7) (3,21) (3,9) (3,17) (3,14) (3,18) (3,4) (3,5) (3,15) (3,22) (4,6) (4,12) (4,7) (4,21) (4,9) (4,23) (4,16) (4,15) (4,22) (5,6) (5,12) (5,7) (5,17) (5,23) (5,16) (5,15) (5,10) (6,12) (6,7) (6,21) (6,18) (6,15) (6,10) (6,22) (7,9) (7,14) (7,18) (7,23) (7,16) (7,10) (7,22) (8,19) (8,20) (8,13) (8,11) (9,21) (9,14) (9,23) (9,16) (9,15) (9,10) (9,22) (10,12) (10,21) (10,17) (10,14) (10,23) (10,16) (10,15) (10,22) (11,19) (11,20) (11,13) (12,21) (12,14) (12,23) (12,16) (12,22) (14,17) (14,18) (14,23) (14,15) (14,22) (15,21) (15,17) (15,18) (15,23) (15,16) (16,21) (16,18) (16,23) (17,21) (17,18) (17,23) (17,22) (18,23) (19,20) (21,23) (21,22) (22,23)\nIs there a path between node 14 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph591-11_6", + "image": "data/connectivity/graph_visual/medium/graph591.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,2) (0,1) (0,16) (0,17) (1,12) (1,2) (1,16) (1,21) (1,5) (1,17) (2,12) (2,8) (2,21) (2,17) (3,6) (3,23) (3,18) (3,14) (4,10) (4,7) (4,22) (4,19) (4,11) (4,15) (4,20) (5,12) (5,8) (5,16) (6,23) (6,18) (7,13) (7,22) (7,19) (7,11) (8,16) (8,17) (10,22) (10,19) (10,11) (10,15) (10,20) (11,13) (11,22) (11,15) (11,20) (12,21) (13,19) (13,15) (13,20) (14,23) (14,18) (15,22) (15,19) (16,21) (16,17) (18,23) (19,22) (20,22)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph488-22_18", + "image": "data/connectivity/graph_visual/medium/graph488.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,10) (0,17) (0,16) (0,11) (0,4) (0,6) (0,5) (0,3) (0,19) (0,18) (0,9) (0,14) (0,22) (0,2) (0,13) (1,8) (1,12) (1,7) (1,20) (1,15) (2,21) (2,10) (2,17) (2,16) (2,11) (2,4) (2,6) (2,5) (2,3) (2,19) (2,18) (2,9) (2,14) (2,22) (2,13) (3,21) (3,10) (3,17) (3,16) (3,11) (3,4) (3,6) (3,5) (3,19) (3,18) (3,9) (3,14) (3,22) (3,13) (4,21) (4,10) (4,17) (4,16) (4,11) (4,6) (4,5) (4,19) (4,18) (4,9) (4,14) (4,22) (4,13) (5,21) (5,10) (5,17) (5,16) (5,11) (5,6) (5,19) (5,18) (5,9) (5,14) (5,22) (5,13) (6,21) (6,10) (6,17) (6,16) (6,11) (6,19) (6,18) (6,9) (6,14) (6,22) (6,13) (7,8) (7,12) (7,20) (7,15) (8,12) (8,20) (8,15) (9,21) (9,10) (9,17) (9,16) (9,11) (9,19) (9,18) (9,14) (9,22) (9,13) (10,21) (10,17) (10,16) (10,11) (10,19) (10,18) (10,14) (10,22) (10,13) (11,21) (11,17) (11,16) (11,19) (11,18) (11,14) (11,22) (11,13) (12,20) (12,15) (13,21) (13,17) (13,16) (13,19) (13,18) (13,14) (13,22) (14,21) (14,17) (14,16) (14,19) (14,18) (14,22) (15,20) (16,21) (16,17) (16,19) (16,18) (16,22) (17,21) (17,19) (17,18) (17,22) (18,21) (18,19) (18,22) (19,21) (19,22) (21,22)\nIs there a path between node 22 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph109-3_7", + "image": "data/connectivity/graph_visual/medium/graph109.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,6) (0,3) (0,13) (0,10) (0,9) (0,15) (0,14) (1,5) (1,7) (1,11) (1,4) (1,8) (1,2) (1,12) (2,5) (2,7) (2,11) (2,4) (2,8) (2,12) (3,6) (3,13) (3,10) (3,9) (3,15) (3,14) (4,5) (4,7) (4,11) (4,8) (4,12) (5,7) (5,11) (5,8) (5,12) (6,13) (6,10) (6,9) (6,15) (6,14) (7,11) (7,8) (7,12) (8,11) (8,12) (9,13) (9,10) (9,15) (9,14) (10,13) (10,15) (10,14) (11,12) (13,15) (13,14) (14,15)\nIs there a path between node 3 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph798-10_22", + "image": "data/connectivity/graph_visual/medium/graph798.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (0,12) (0,11) (0,10) (1,23) (2,24) (2,22) (2,6) (3,21) (3,7) (4,24) (4,12) (4,6) (4,14) (4,15) (4,9) (4,5) (5,18) (5,12) (5,14) (5,11) (6,15) (6,9) (7,17) (7,13) (8,14) (8,9) (9,22) (9,12) (10,19) (10,24) (10,22) (10,14) (10,11) (11,22) (12,24) (13,21) (13,20) (14,19) (14,16) (14,15) (15,19) (17,23) (18,19) (18,24) (19,22)\nIs there a path between node 10 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph165-16_0", + "image": "data/connectivity/graph_visual/medium/graph165.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,2) (0,13) (0,11) (0,4) (0,17) (1,14) (1,12) (2,13) (2,10) (2,8) (2,4) (3,13) (3,10) (3,4) (4,5) (4,7) (5,10) (7,16) (9,15) (10,16) (10,13) (11,15) (11,17) (13,16) (13,15) (15,16)\nIs there a path between node 16 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph316-18_11", + "image": "data/connectivity/graph_visual/medium/graph316.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,13) (0,18) (1,10) (1,9) (1,11) (1,8) (1,5) (1,17) (1,19) (1,4) (1,6) (1,12) (1,14) (1,7) (1,3) (1,15) (1,2) (1,16) (2,10) (2,9) (2,11) (2,8) (2,5) (2,17) (2,19) (2,4) (2,6) (2,12) (2,14) (2,7) (2,3) (2,15) (2,16) (3,10) (3,9) (3,11) (3,8) (3,5) (3,17) (3,19) (3,4) (3,6) (3,12) (3,14) (3,7) (3,15) (3,16) (4,10) (4,9) (4,11) (4,8) (4,5) (4,17) (4,19) (4,6) (4,12) (4,14) (4,7) (4,15) (4,16) (5,10) (5,9) (5,11) (5,8) (5,17) (5,19) (5,6) (5,12) (5,14) (5,7) (5,15) (5,16) (6,10) (6,9) (6,11) (6,8) (6,17) (6,19) (6,12) (6,14) (6,7) (6,15) (6,16) (7,10) (7,9) (7,11) (7,8) (7,17) (7,19) (7,12) (7,14) (7,15) (7,16) (8,10) (8,9) (8,11) (8,17) (8,19) (8,12) (8,14) (8,15) (8,16) (9,10) (9,11) (9,17) (9,19) (9,12) (9,14) (9,15) (9,16) (10,11) (10,17) (10,19) (10,12) (10,14) (10,15) (10,16) (11,17) (11,19) (11,12) (11,14) (11,15) (11,16) (12,17) (12,19) (12,14) (12,15) (12,16) (13,18) (14,17) (14,19) (14,15) (14,16) (15,17) (15,19) (15,16) (16,17) (16,19) (17,19)\nIs there a path between node 18 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph619-0_9", + "image": "data/connectivity/graph_visual/medium/graph619.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,18) (0,8) (0,2) (0,12) (0,22) (0,19) (0,10) (0,21) (0,3) (0,14) (0,20) (0,6) (0,15) (0,23) (0,16) (0,4) (0,17) (0,1) (1,18) (1,8) (1,2) (1,12) (1,22) (1,19) (1,10) (1,21) (1,3) (1,14) (1,20) (1,6) (1,15) (1,23) (1,16) (1,4) (1,17) (2,18) (2,8) (2,12) (2,22) (2,19) (2,10) (2,21) (2,3) (2,14) (2,20) (2,6) (2,15) (2,23) (2,16) (2,4) (2,17) (3,18) (3,8) (3,12) (3,22) (3,19) (3,10) (3,21) (3,14) (3,20) (3,6) (3,15) (3,23) (3,16) (3,4) (3,17) (4,18) (4,8) (4,12) (4,22) (4,19) (4,10) (4,21) (4,14) (4,20) (4,6) (4,15) (4,23) (4,16) (4,17) (5,9) (5,11) (5,7) (5,13) (6,18) (6,8) (6,12) (6,22) (6,19) (6,10) (6,21) (6,14) (6,20) (6,15) (6,23) (6,16) (6,17) (7,9) (7,11) (7,13) (8,18) (8,12) (8,22) (8,19) (8,10) (8,21) (8,14) (8,20) (8,15) (8,23) (8,16) (8,17) (9,11) (9,13) (10,18) (10,12) (10,22) (10,19) (10,21) (10,14) (10,20) (10,15) (10,23) (10,16) (10,17) (11,13) (12,18) (12,22) (12,19) (12,21) (12,14) (12,20) (12,15) (12,23) (12,16) (12,17) (14,18) (14,22) (14,19) (14,21) (14,20) (14,15) (14,23) (14,16) (14,17) (15,18) (15,22) (15,19) (15,21) (15,20) (15,23) (15,16) (15,17) (16,18) (16,22) (16,19) (16,21) (16,20) (16,23) (16,17) (17,18) (17,22) (17,19) (17,21) (17,20) (17,23) (18,22) (18,19) (18,21) (18,20) (18,23) (19,22) (19,21) (19,20) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 0 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph538-3_21", + "image": "data/connectivity/graph_visual/medium/graph538.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,4) (0,11) (0,17) (0,18) (0,6) (0,10) (0,7) (0,12) (0,5) (0,21) (0,8) (0,13) (0,9) (0,3) (0,15) (0,14) (0,20) (0,2) (1,19) (1,16) (2,22) (2,4) (2,11) (2,17) (2,18) (2,6) (2,10) (2,7) (2,12) (2,5) (2,21) (2,8) (2,13) (2,9) (2,3) (2,15) (2,14) (2,20) (3,22) (3,4) (3,11) (3,17) (3,18) (3,6) (3,10) (3,7) (3,12) (3,5) (3,21) (3,8) (3,13) (3,9) (3,15) (3,14) (3,20) (4,22) (4,11) (4,17) (4,18) (4,6) (4,10) (4,7) (4,12) (4,5) (4,21) (4,8) (4,13) (4,9) (4,15) (4,14) (4,20) (5,22) (5,11) (5,17) (5,18) (5,6) (5,10) (5,7) (5,12) (5,21) (5,8) (5,13) (5,9) (5,15) (5,14) (5,20) (6,22) (6,11) (6,17) (6,18) (6,10) (6,7) (6,12) (6,21) (6,8) (6,13) (6,9) (6,15) (6,14) (6,20) (7,22) (7,11) (7,17) (7,18) (7,10) (7,12) (7,21) (7,8) (7,13) (7,9) (7,15) (7,14) (7,20) (8,22) (8,11) (8,17) (8,18) (8,10) (8,12) (8,21) (8,13) (8,9) (8,15) (8,14) (8,20) (9,22) (9,11) (9,17) (9,18) (9,10) (9,12) (9,21) (9,13) (9,15) (9,14) (9,20) (10,22) (10,11) (10,17) (10,18) (10,12) (10,21) (10,13) (10,15) (10,14) (10,20) (11,22) (11,17) (11,18) (11,12) (11,21) (11,13) (11,15) (11,14) (11,20) (12,22) (12,17) (12,18) (12,21) (12,13) (12,15) (12,14) (12,20) (13,22) (13,17) (13,18) (13,21) (13,15) (13,14) (13,20) (14,22) (14,17) (14,18) (14,21) (14,15) (14,20) (15,22) (15,17) (15,18) (15,21) (15,20) (16,19) (17,22) (17,18) (17,21) (17,20) (18,22) (18,21) (18,20) (20,22) (20,21) (21,22)\nIs there a path between node 3 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph815-0_15", + "image": "data/connectivity/graph_visual/medium/graph815.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,16) (0,22) (0,3) (0,20) (0,14) (0,6) (0,19) (0,15) (0,13) (1,18) (1,9) (1,24) (1,2) (1,21) (1,23) (2,9) (2,24) (2,12) (2,10) (2,23) (2,4) (3,11) (3,16) (3,20) (3,14) (3,6) (3,7) (3,8) (3,15) (3,13) (4,9) (4,24) (4,12) (4,10) (4,21) (4,17) (4,23) (5,9) (5,24) (5,12) (5,10) (5,21) (5,17) (6,16) (6,22) (6,20) (6,7) (6,19) (6,8) (6,15) (6,13) (7,11) (7,16) (7,22) (7,20) (7,19) (7,8) (7,13) (8,22) (8,20) (8,19) (8,15) (8,13) (9,18) (9,10) (9,21) (9,23) (10,18) (10,24) (10,12) (10,17) (10,23) (11,16) (11,22) (11,20) (11,14) (11,19) (12,24) (12,21) (12,17) (12,23) (13,16) (13,22) (13,20) (13,19) (13,15) (14,16) (14,22) (14,19) (14,15) (15,16) (15,22) (15,19) (16,22) (16,20) (16,19) (18,24) (18,21) (19,20) (20,22) (21,24)\nIs there a path between node 0 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph30-11_9", + "image": "data/connectivity/graph_visual/medium/graph30.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,5) (0,6) (0,4) (0,9) (0,11) (0,1) (0,7) (1,5) (1,6) (1,4) (1,9) (1,11) (1,7) (2,10) (2,3) (2,8) (3,10) (3,8) (4,5) (4,6) (4,9) (4,11) (4,7) (5,6) (5,9) (5,11) (5,7) (6,9) (6,11) (6,7) (7,9) (7,11) (8,10) (9,11)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph246-3_15", + "image": "data/connectivity/graph_visual/medium/graph246.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,7) (0,16) (0,1) (0,13) (0,9) (0,12) (0,4) (0,14) (0,10) (0,18) (0,15) (0,6) (1,8) (1,7) (1,16) (1,13) (1,9) (1,12) (1,4) (1,14) (1,10) (1,18) (1,15) (1,6) (2,5) (3,17) (3,11) (4,8) (4,7) (4,16) (4,13) (4,9) (4,12) (4,14) (4,10) (4,18) (4,15) (4,6) (6,8) (6,7) (6,16) (6,13) (6,9) (6,12) (6,14) (6,10) (6,18) (6,15) (7,8) (7,16) (7,13) (7,9) (7,12) (7,14) (7,10) (7,18) (7,15) (8,16) (8,13) (8,9) (8,12) (8,14) (8,10) (8,18) (8,15) (9,16) (9,13) (9,12) (9,14) (9,10) (9,18) (9,15) (10,16) (10,13) (10,12) (10,14) (10,18) (10,15) (11,17) (12,16) (12,13) (12,14) (12,18) (12,15) (13,16) (13,14) (13,18) (13,15) (14,16) (14,18) (14,15) (15,16) (15,18) (16,18)\nIs there a path between node 3 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph638-0_1", + "image": "data/connectivity/graph_visual/medium/graph638.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (1,2) (1,16) (2,19) (2,21) (2,10) (2,23) (2,22) (3,15) (3,17) (3,18) (3,8) (5,15) (7,21) (7,10) (7,23) (7,16) (7,12) (8,20) (8,14) (8,17) (10,21) (10,11) (11,16) (11,22) (12,23) (12,16) (12,22) (13,19) (13,21) (13,23) (13,22) (14,17) (14,18) (15,17) (16,19) (16,23) (18,20)\nIs there a path between node 0 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph364-6_16", + "image": "data/connectivity/graph_visual/medium/graph364.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,2) (1,11) (1,7) (2,11) (2,15) (2,12) (2,3) (3,9) (3,7) (4,19) (4,7) (6,16) (6,13) (6,18) (8,17) (8,15) (8,12) (9,17) (9,19) (9,11) (10,19) (10,11) (11,20) (15,19) (17,20)\nIs there a path between node 6 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph434-2_17", + "image": "data/connectivity/graph_visual/medium/graph434.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,1) (0,17) (0,2) (0,3) (1,2) (2,20) (3,17) (3,7) (4,18) (4,11) (4,9) (5,12) (6,18) (6,11) (6,9) (7,19) (8,17) (8,14) (9,10) (9,18) (9,11) (11,15) (11,18) (11,21) (14,19) (14,17) (16,17) (17,19) (19,20)\nIs there a path between node 2 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph323-5_0", + "image": "data/connectivity/graph_visual/medium/graph323.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,15) (0,7) (0,3) (0,19) (0,14) (0,18) (0,16) (1,2) (1,8) (1,6) (1,17) (1,5) (1,4) (1,9) (1,10) (1,13) (1,12) (1,11) (2,8) (2,6) (2,17) (2,5) (2,4) (2,9) (2,10) (2,13) (2,12) (2,11) (3,15) (3,7) (3,19) (3,14) (3,18) (3,16) (4,8) (4,6) (4,17) (4,5) (4,9) (4,10) (4,13) (4,12) (4,11) (5,8) (5,6) (5,17) (5,9) (5,10) (5,13) (5,12) (5,11) (6,8) (6,17) (6,9) (6,10) (6,13) (6,12) (6,11) (7,15) (7,19) (7,14) (7,18) (7,16) (8,17) (8,9) (8,10) (8,13) (8,12) (8,11) (9,17) (9,10) (9,13) (9,12) (9,11) (10,17) (10,13) (10,12) (10,11) (11,17) (11,13) (11,12) (12,17) (12,13) (13,17) (14,15) (14,19) (14,18) (14,16) (15,19) (15,18) (15,16) (16,19) (16,18) (18,19)\nIs there a path between node 5 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph751-24_9", + "image": "data/connectivity/graph_visual/medium/graph751.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,21) (0,20) (0,18) (0,23) (0,11) (0,14) (0,22) (0,7) (0,10) (0,15) (0,13) (1,4) (1,17) (1,24) (1,12) (1,8) (1,9) (2,3) (2,21) (2,18) (2,23) (2,11) (2,14) (2,22) (2,7) (2,10) (2,15) (2,13) (3,21) (3,20) (3,19) (3,23) (3,11) (3,14) (3,7) (3,10) (3,13) (4,16) (4,5) (4,24) (4,6) (4,8) (5,16) (5,17) (5,24) (5,12) (5,6) (5,8) (5,9) (6,16) (6,17) (6,24) (6,12) (7,21) (7,20) (7,11) (7,22) (7,13) (8,16) (8,24) (8,12) (8,9) (9,16) (9,17) (9,24) (9,12) (10,19) (10,18) (10,23) (10,14) (10,15) (10,13) (11,21) (11,19) (11,23) (11,14) (11,15) (12,16) (12,24) (13,18) (13,23) (13,14) (13,15) (14,21) (14,20) (14,19) (14,18) (14,23) (14,22) (15,21) (15,20) (15,18) (15,23) (15,22) (16,17) (16,24) (17,24) (18,21) (18,20) (18,19) (18,23) (18,22) (19,20) (19,23) (20,21) (20,23) (20,22) (21,23) (22,23)\nIs there a path between node 24 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph280-4_6", + "image": "data/connectivity/graph_visual/medium/graph280.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,7) (0,14) (0,13) (0,18) (0,6) (0,19) (1,8) (1,11) (1,10) (1,15) (1,2) (1,3) (1,12) (1,5) (2,8) (2,11) (2,10) (2,15) (2,3) (2,12) (2,5) (3,8) (3,11) (3,10) (3,15) (3,12) (3,5) (4,16) (4,9) (5,8) (5,11) (5,10) (5,15) (5,12) (6,17) (6,7) (6,14) (6,13) (6,18) (6,19) (7,17) (7,14) (7,13) (7,18) (7,19) (8,11) (8,10) (8,15) (8,12) (9,16) (10,11) (10,15) (10,12) (11,15) (11,12) (12,15) (13,17) (13,14) (13,18) (13,19) (14,17) (14,18) (14,19) (17,18) (17,19) (18,19)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph89-12_13", + "image": "data/connectivity/graph_visual/medium/graph89.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,14) (0,2) (0,7) (0,4) (0,1) (0,3) (0,11) (0,6) (0,9) (0,13) (0,8) (0,5) (0,10) (1,14) (1,2) (1,7) (1,4) (1,3) (1,11) (1,6) (1,9) (1,13) (1,8) (1,5) (1,10) (2,14) (2,7) (2,4) (2,3) (2,11) (2,6) (2,9) (2,13) (2,8) (2,5) (2,10) (3,14) (3,7) (3,4) (3,11) (3,6) (3,9) (3,13) (3,8) (3,5) (3,10) (4,14) (4,7) (4,11) (4,6) (4,9) (4,13) (4,8) (4,5) (4,10) (5,14) (5,7) (5,11) (5,6) (5,9) (5,13) (5,8) (5,10) (6,14) (6,7) (6,11) (6,9) (6,13) (6,8) (6,10) (7,14) (7,11) (7,9) (7,13) (7,8) (7,10) (8,14) (8,11) (8,9) (8,13) (8,10) (9,14) (9,11) (9,13) (9,10) (10,14) (10,11) (10,13) (11,14) (11,13) (13,14)\nIs there a path between node 12 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph623-18_4", + "image": "data/connectivity/graph_visual/medium/graph623.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,17) (0,18) (0,4) (0,10) (0,21) (0,8) (0,22) (0,9) (0,19) (0,23) (0,5) (0,1) (0,14) (0,6) (0,15) (0,16) (1,20) (1,17) (1,18) (1,4) (1,10) (1,21) (1,8) (1,22) (1,9) (1,19) (1,23) (1,5) (1,14) (1,6) (1,15) (1,16) (2,12) (2,13) (2,11) (2,7) (2,3) (3,12) (3,13) (3,11) (3,7) (4,20) (4,17) (4,18) (4,10) (4,21) (4,8) (4,22) (4,9) (4,19) (4,23) (4,5) (4,14) (4,6) (4,15) (4,16) (5,20) (5,17) (5,18) (5,10) (5,21) (5,8) (5,22) (5,9) (5,19) (5,23) (5,14) (5,6) (5,15) (5,16) (6,20) (6,17) (6,18) (6,10) (6,21) (6,8) (6,22) (6,9) (6,19) (6,23) (6,14) (6,15) (6,16) (7,12) (7,13) (7,11) (8,20) (8,17) (8,18) (8,10) (8,21) (8,22) (8,9) (8,19) (8,23) (8,14) (8,15) (8,16) (9,20) (9,17) (9,18) (9,10) (9,21) (9,22) (9,19) (9,23) (9,14) (9,15) (9,16) (10,20) (10,17) (10,18) (10,21) (10,22) (10,19) (10,23) (10,14) (10,15) (10,16) (11,12) (11,13) (12,13) (14,20) (14,17) (14,18) (14,21) (14,22) (14,19) (14,23) (14,15) (14,16) (15,20) (15,17) (15,18) (15,21) (15,22) (15,19) (15,23) (15,16) (16,20) (16,17) (16,18) (16,21) (16,22) (16,19) (16,23) (17,20) (17,18) (17,21) (17,22) (17,19) (17,23) (18,20) (18,21) (18,22) (18,19) (18,23) (19,20) (19,21) (19,22) (19,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 18 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph122-10_2", + "image": "data/connectivity/graph_visual/medium/graph122.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,5) (0,3) (1,13) (1,4) (1,12) (1,16) (1,9) (1,15) (1,11) (1,8) (1,6) (1,7) (1,10) (2,5) (3,14) (4,16) (4,9) (4,11) (4,8) (4,7) (4,10) (6,13) (6,16) (6,11) (6,7) (6,10) (7,13) (7,9) (7,11) (7,8) (7,10) (8,13) (8,12) (8,16) (8,9) (8,15) (8,10) (9,13) (9,16) (9,15) (9,10) (10,16) (10,11) (11,13) (11,16) (11,15) (12,13) (12,15) (13,16) (15,16)\nIs there a path between node 10 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph461-9_1", + "image": "data/connectivity/graph_visual/medium/graph461.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,11) (0,17) (0,16) (0,3) (0,9) (0,15) (0,12) (0,1) (0,20) (0,19) (0,6) (0,21) (0,7) (0,8) (0,14) (0,5) (0,2) (1,18) (1,11) (1,17) (1,16) (1,3) (1,9) (1,15) (1,12) (1,20) (1,19) (1,6) (1,21) (1,7) (1,8) (1,14) (1,5) (1,2) (2,18) (2,11) (2,17) (2,16) (2,3) (2,9) (2,15) (2,12) (2,20) (2,19) (2,6) (2,21) (2,7) (2,8) (2,14) (2,5) (3,18) (3,11) (3,17) (3,16) (3,9) (3,15) (3,12) (3,20) (3,19) (3,6) (3,21) (3,7) (3,8) (3,14) (3,5) (5,18) (5,11) (5,17) (5,16) (5,9) (5,15) (5,12) (5,20) (5,19) (5,6) (5,21) (5,7) (5,8) (5,14) (6,18) (6,11) (6,17) (6,16) (6,9) (6,15) (6,12) (6,20) (6,19) (6,21) (6,7) (6,8) (6,14) (7,18) (7,11) (7,17) (7,16) (7,9) (7,15) (7,12) (7,20) (7,19) (7,21) (7,8) (7,14) (8,18) (8,11) (8,17) (8,16) (8,9) (8,15) (8,12) (8,20) (8,19) (8,21) (8,14) (9,18) (9,11) (9,17) (9,16) (9,15) (9,12) (9,20) (9,19) (9,21) (9,14) (10,13) (11,18) (11,17) (11,16) (11,15) (11,12) (11,20) (11,19) (11,21) (11,14) (12,18) (12,17) (12,16) (12,15) (12,20) (12,19) (12,21) (12,14) (14,18) (14,17) (14,16) (14,15) (14,20) (14,19) (14,21) (15,18) (15,17) (15,16) (15,20) (15,19) (15,21) (16,18) (16,17) (16,20) (16,19) (16,21) (17,18) (17,20) (17,19) (17,21) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 9 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph252-13_18", + "image": "data/connectivity/graph_visual/medium/graph252.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,5) (0,16) (0,1) (0,14) (0,4) (0,15) (0,3) (0,9) (0,10) (0,6) (0,17) (0,18) (0,11) (1,8) (1,5) (1,16) (1,14) (1,4) (1,15) (1,3) (1,9) (1,10) (1,6) (1,17) (1,18) (1,11) (3,8) (3,5) (3,16) (3,14) (3,4) (3,15) (3,9) (3,10) (3,6) (3,17) (3,18) (3,11) (4,8) (4,5) (4,16) (4,14) (4,15) (4,9) (4,10) (4,6) (4,17) (4,18) (4,11) (5,8) (5,16) (5,14) (5,15) (5,9) (5,10) (5,6) (5,17) (5,18) (5,11) (6,8) (6,16) (6,14) (6,15) (6,9) (6,10) (6,17) (6,18) (6,11) (7,12) (7,13) (8,16) (8,14) (8,15) (8,9) (8,10) (8,17) (8,18) (8,11) (9,16) (9,14) (9,15) (9,10) (9,17) (9,18) (9,11) (10,16) (10,14) (10,15) (10,17) (10,18) (10,11) (11,16) (11,14) (11,15) (11,17) (11,18) (12,13) (14,16) (14,15) (14,17) (14,18) (15,16) (15,17) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 13 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph168-3_15", + "image": "data/connectivity/graph_visual/medium/graph168.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,1) (0,5) (1,11) (1,6) (1,17) (1,10) (2,11) (2,17) (5,6) (5,9) (6,16) (6,8) (6,17) (6,10) (6,14) (8,10) (9,10) (10,11) (10,17) (10,15) (11,15) (14,16) (14,17)\nIs there a path between node 3 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph645-1_13", + "image": "data/connectivity/graph_visual/medium/graph645.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,5) (4,19) (4,5) (6,23) (8,9) (8,20) (8,23) (8,22) (8,13) (8,10) (9,15) (9,20) (9,23) (9,22) (9,13) (9,11) (10,23) (10,22) (10,12) (10,11) (10,14) (11,23) (12,15) (12,20) (12,23) (12,16) (13,15) (13,23) (14,18) (14,16) (15,21) (15,22) (15,16) (16,20) (16,21) (20,22) (21,23) (21,22)\nIs there a path between node 1 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph678-23_5", + "image": "data/connectivity/graph_visual/medium/graph678.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,16) (0,15) (0,3) (0,1) (0,8) (1,23) (1,16) (1,15) (1,3) (1,8) (2,7) (2,4) (2,20) (2,14) (3,23) (3,16) (3,15) (3,8) (4,7) (4,20) (4,14) (5,12) (5,10) (5,18) (5,9) (5,22) (5,13) (5,17) (6,19) (6,11) (6,21) (7,20) (7,14) (8,23) (8,16) (8,15) (9,12) (9,10) (9,18) (9,22) (9,13) (9,17) (10,12) (10,18) (10,22) (10,13) (10,17) (11,19) (11,21) (12,18) (12,22) (12,13) (12,17) (13,18) (13,22) (13,17) (14,20) (15,23) (15,16) (16,23) (17,18) (17,22) (18,22) (19,21)\nIs there a path between node 23 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph486-20_7", + "image": "data/connectivity/graph_visual/medium/graph486.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,19) (0,1) (0,11) (0,21) (0,13) (1,11) (1,6) (1,21) (1,22) (2,14) (2,7) (2,8) (2,10) (2,9) (2,4) (3,18) (3,17) (3,20) (3,15) (4,14) (4,16) (4,7) (4,8) (4,9) (4,5) (5,14) (5,8) (5,10) (5,9) (6,19) (6,12) (6,11) (6,21) (6,13) (7,14) (7,16) (7,8) (7,10) (8,14) (8,16) (8,10) (9,10) (10,14) (10,16) (11,12) (11,21) (12,19) (12,21) (12,22) (12,13) (13,21) (13,22) (14,16) (15,18) (15,17) (17,18) (17,20) (19,21) (19,22) (21,22)\nIs there a path between node 20 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph339-9_7", + "image": "data/connectivity/graph_visual/medium/graph339.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (0,12) (0,18) (0,5) (0,16) (0,10) (0,2) (0,11) (1,17) (1,12) (1,18) (1,4) (1,5) (1,16) (1,10) (1,11) (2,17) (2,12) (2,18) (2,4) (2,5) (2,10) (2,11) (3,15) (3,13) (3,6) (3,20) (3,7) (3,19) (3,8) (3,14) (4,17) (4,12) (4,18) (4,10) (5,17) (5,12) (5,16) (5,10) (5,11) (6,15) (6,20) (6,7) (6,14) (6,9) (7,15) (7,13) (7,20) (7,19) (7,8) (8,15) (8,13) (8,19) (8,9) (9,15) (9,13) (9,19) (9,14) (10,17) (10,12) (10,18) (10,11) (11,17) (12,17) (12,18) (13,19) (13,14) (14,20) (14,19) (15,20) (15,19) (16,17) (16,18) (19,20)\nIs there a path between node 9 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph273-4_12", + "image": "data/connectivity/graph_visual/medium/graph273.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,18) (0,5) (0,19) (0,11) (0,8) (0,6) (0,14) (0,10) (1,7) (1,2) (2,7) (2,17) (3,9) (3,18) (3,13) (3,19) (3,11) (3,16) (3,8) (3,6) (3,14) (3,10) (4,9) (4,13) (4,5) (4,15) (4,19) (4,11) (4,16) (4,8) (4,6) (4,10) (5,9) (5,18) (5,13) (5,15) (5,19) (5,11) (5,8) (5,14) (5,10) (6,13) (6,12) (6,15) (6,19) (6,11) (6,16) (6,8) (6,10) (7,17) (8,9) (8,13) (8,12) (8,15) (8,14) (8,10) (9,18) (9,12) (9,19) (9,16) (9,14) (9,10) (10,18) (10,13) (10,12) (10,15) (10,19) (10,16) (10,14) (11,15) (11,19) (11,16) (12,13) (12,19) (13,15) (13,19) (13,16) (14,18) (14,16) (15,18) (15,16) (16,18) (16,19)\nIs there a path between node 4 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph422-9_16", + "image": "data/connectivity/graph_visual/medium/graph422.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,20) (0,18) (0,4) (0,8) (0,1) (0,17) (0,15) (0,11) (0,21) (0,9) (0,12) (0,14) (0,3) (1,19) (1,20) (1,18) (1,4) (1,8) (1,17) (1,15) (1,11) (1,21) (1,9) (1,12) (1,14) (1,3) (2,5) (2,7) (2,13) (2,6) (2,10) (2,16) (3,19) (3,20) (3,18) (3,4) (3,8) (3,17) (3,15) (3,11) (3,21) (3,9) (3,12) (3,14) (4,19) (4,20) (4,18) (4,8) (4,17) (4,15) (4,11) (4,21) (4,9) (4,12) (4,14) (5,7) (5,13) (5,6) (5,10) (5,16) (6,7) (6,13) (6,10) (6,16) (7,13) (7,10) (7,16) (8,19) (8,20) (8,18) (8,17) (8,15) (8,11) (8,21) (8,9) (8,12) (8,14) (9,19) (9,20) (9,18) (9,17) (9,15) (9,11) (9,21) (9,12) (9,14) (10,13) (10,16) (11,19) (11,20) (11,18) (11,17) (11,15) (11,21) (11,12) (11,14) (12,19) (12,20) (12,18) (12,17) (12,15) (12,21) (12,14) (13,16) (14,19) (14,20) (14,18) (14,17) (14,15) (14,21) (15,19) (15,20) (15,18) (15,17) (15,21) (17,19) (17,20) (17,18) (17,21) (18,19) (18,20) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 9 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph185-2_10", + "image": "data/connectivity/graph_visual/medium/graph185.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,7) (0,9) (0,6) (0,16) (0,3) (0,13) (0,15) (0,4) (0,8) (1,5) (1,17) (1,12) (1,14) (1,2) (2,5) (2,17) (2,12) (2,14) (3,7) (3,9) (3,6) (3,16) (3,13) (3,15) (3,4) (3,8) (4,7) (4,9) (4,6) (4,16) (4,13) (4,15) (4,8) (5,17) (5,12) (5,14) (6,7) (6,9) (6,16) (6,13) (6,15) (6,8) (7,9) (7,16) (7,13) (7,15) (7,8) (8,9) (8,16) (8,13) (8,15) (9,16) (9,13) (9,15) (10,11) (12,17) (12,14) (13,16) (13,15) (14,17) (15,16)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph591-11_19", + "image": "data/connectivity/graph_visual/medium/graph591.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,2) (0,1) (0,16) (0,17) (1,12) (1,2) (1,16) (1,21) (1,5) (1,17) (2,12) (2,8) (2,21) (2,17) (3,6) (3,23) (3,18) (3,14) (4,10) (4,7) (4,22) (4,19) (4,11) (4,15) (4,20) (5,12) (5,8) (5,16) (6,23) (6,18) (7,13) (7,22) (7,19) (7,11) (8,16) (8,17) (10,22) (10,19) (10,11) (10,15) (10,20) (11,13) (11,22) (11,15) (11,20) (12,21) (13,19) (13,15) (13,20) (14,23) (14,18) (15,22) (15,19) (16,21) (16,17) (18,23) (19,22) (20,22)\nIs there a path between node 11 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph509-18_1", + "image": "data/connectivity/graph_visual/medium/graph509.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,15) (0,10) (0,1) (0,7) (0,13) (0,3) (0,2) (0,11) (0,12) (1,7) (1,22) (1,12) (2,6) (2,10) (2,18) (2,16) (2,5) (2,7) (2,13) (2,3) (2,11) (3,10) (3,16) (3,5) (4,8) (4,21) (5,18) (5,7) (5,11) (5,12) (6,10) (6,16) (6,17) (6,7) (6,20) (7,20) (7,13) (7,12) (8,21) (9,14) (10,16) (10,11) (11,15) (11,16) (11,17) (12,15) (12,20) (13,17) (13,22) (15,18) (15,16) (15,17) (17,18) (18,20) (19,21) (20,22)\nIs there a path between node 18 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph72-4_10", + "image": "data/connectivity/graph_visual/medium/graph72.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (0,9) (1,10) (1,3) (2,6) (2,4) (2,7) (3,6) (3,10) (3,9) (3,12) (4,8) (5,9) (5,12) (6,9) (6,12) (6,7) (7,10) (7,9) (7,14) (8,10) (8,9) (8,14) (12,14)\nIs there a path between node 4 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph13-3_9", + "image": "data/connectivity/graph_visual/medium/graph13.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (0,7) (0,10) (0,2) (1,8) (1,4) (1,9) (1,3) (1,5) (2,6) (2,7) (2,10) (3,8) (3,4) (3,9) (3,5) (4,8) (4,9) (4,5) (5,8) (5,9) (6,7) (6,10) (7,10) (8,9)\nIs there a path between node 3 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph329-7_19", + "image": "data/connectivity/graph_visual/medium/graph329.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,14) (0,11) (0,7) (1,12) (1,9) (1,6) (1,20) (2,12) (2,9) (2,13) (2,14) (2,19) (2,11) (2,7) (4,5) (6,16) (6,20) (6,7) (7,12) (7,18) (7,8) (7,16) (7,10) (7,11) (8,12) (8,18) (8,16) (8,20) (8,10) (8,17) (9,18) (9,16) (9,14) (9,10) (9,19) (9,11) (10,18) (10,19) (10,17) (12,16) (13,16) (13,17) (16,18)\nIs there a path between node 7 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph498-6_18", + "image": "data/connectivity/graph_visual/medium/graph498.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,8) (0,22) (0,9) (0,19) (0,12) (1,7) (1,15) (1,6) (1,21) (1,9) (1,2) (1,19) (1,12) (1,10) (2,8) (2,3) (2,17) (3,22) (3,6) (3,21) (3,5) (3,10) (4,8) (4,6) (4,21) (4,9) (5,7) (5,8) (5,17) (5,6) (5,9) (5,12) (5,10) (6,7) (6,15) (6,14) (6,17) (7,15) (7,12) (7,10) (9,15) (9,14) (9,22) (10,14) (10,17) (11,16) (12,17) (12,21) (14,18) (15,19) (17,18) (18,21)\nIs there a path between node 6 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph764-3_19", + "image": "data/connectivity/graph_visual/medium/graph764.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,4) (0,24) (1,22) (1,13) (1,2) (1,18) (1,5) (1,3) (1,19) (1,7) (1,9) (1,21) (1,8) (1,10) (1,23) (1,6) (1,20) (1,14) (1,11) (1,16) (1,17) (1,15) (2,22) (2,13) (2,18) (2,5) (2,3) (2,19) (2,7) (2,9) (2,21) (2,8) (2,10) (2,23) (2,6) (2,20) (2,14) (2,11) (2,16) (2,17) (2,15) (3,22) (3,13) (3,18) (3,5) (3,19) (3,7) (3,9) (3,21) (3,8) (3,10) (3,23) (3,6) (3,20) (3,14) (3,11) (3,16) (3,17) (3,15) (4,12) (4,24) (5,22) (5,13) (5,18) (5,19) (5,7) (5,9) (5,21) (5,8) (5,10) (5,23) (5,6) (5,20) (5,14) (5,11) (5,16) (5,17) (5,15) (6,22) (6,13) (6,18) (6,19) (6,7) (6,9) (6,21) (6,8) (6,10) (6,23) (6,20) (6,14) (6,11) (6,16) (6,17) (6,15) (7,22) (7,13) (7,18) (7,19) (7,9) (7,21) (7,8) (7,10) (7,23) (7,20) (7,14) (7,11) (7,16) (7,17) (7,15) (8,22) (8,13) (8,18) (8,19) (8,9) (8,21) (8,10) (8,23) (8,20) (8,14) (8,11) (8,16) (8,17) (8,15) (9,22) (9,13) (9,18) (9,19) (9,21) (9,10) (9,23) (9,20) (9,14) (9,11) (9,16) (9,17) (9,15) (10,22) (10,13) (10,18) (10,19) (10,21) (10,23) (10,20) (10,14) (10,11) (10,16) (10,17) (10,15) (11,22) (11,13) (11,18) (11,19) (11,21) (11,23) (11,20) (11,14) (11,16) (11,17) (11,15) (12,24) (13,22) (13,18) (13,19) (13,21) (13,23) (13,20) (13,14) (13,16) (13,17) (13,15) (14,22) (14,18) (14,19) (14,21) (14,23) (14,20) (14,16) (14,17) (14,15) (15,22) (15,18) (15,19) (15,21) (15,23) (15,20) (15,16) (15,17) (16,22) (16,18) (16,19) (16,21) (16,23) (16,20) (16,17) (17,22) (17,18) (17,19) (17,21) (17,23) (17,20) (18,22) (18,19) (18,21) (18,23) (18,20) (19,22) (19,21) (19,23) (19,20) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 3 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph314-0_14", + "image": "data/connectivity/graph_visual/medium/graph314.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,2) (0,18) (0,4) (0,12) (0,1) (0,19) (0,14) (0,16) (0,13) (0,15) (0,11) (0,8) (1,2) (1,18) (1,4) (1,12) (1,19) (1,14) (1,16) (1,13) (1,15) (1,11) (1,8) (2,18) (2,4) (2,12) (2,19) (2,14) (2,16) (2,13) (2,15) (2,11) (2,8) (3,6) (3,9) (3,10) (3,17) (4,18) (4,12) (4,19) (4,14) (4,16) (4,13) (4,15) (4,11) (4,8) (5,7) (6,9) (6,10) (6,17) (8,18) (8,12) (8,19) (8,14) (8,16) (8,13) (8,15) (8,11) (9,10) (9,17) (10,17) (11,18) (11,12) (11,19) (11,14) (11,16) (11,13) (11,15) (12,18) (12,19) (12,14) (12,16) (12,13) (12,15) (13,18) (13,19) (13,14) (13,16) (13,15) (14,18) (14,19) (14,16) (14,15) (15,18) (15,19) (15,16) (16,18) (16,19) (18,19)\nIs there a path between node 0 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph208-16_10", + "image": "data/connectivity/graph_visual/medium/graph208.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,15) (0,13) (0,3) (0,16) (0,10) (1,18) (1,7) (1,2) (1,4) (1,9) (1,12) (1,11) (1,5) (2,18) (2,7) (2,4) (2,9) (2,12) (2,6) (2,11) (2,5) (3,15) (3,17) (4,18) (4,9) (4,12) (4,6) (4,5) (5,18) (5,7) (5,12) (5,6) (5,11) (6,18) (6,7) (6,12) (7,18) (7,12) (9,12) (9,11) (10,15) (10,14) (11,18) (11,12) (13,16) (13,14) (13,17) (14,15) (14,16) (15,16) (16,17)\nIs there a path between node 16 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph554-10_0", + "image": "data/connectivity/graph_visual/medium/graph554.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,8) (0,4) (0,10) (2,13) (3,17) (4,12) (4,14) (4,19) (6,22) (7,18) (7,23) (7,16) (7,17) (7,13) (8,12) (8,20) (9,21) (9,19) (10,14) (11,21) (11,15) (12,20) (13,18) (13,23) (14,15) (16,18) (17,23) (19,20)\nIs there a path between node 10 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph88-10_11", + "image": "data/connectivity/graph_visual/medium/graph88.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,14) (0,6) (0,12) (0,3) (0,5) (0,13) (0,4) (0,2) (0,9) (0,1) (0,10) (0,7) (0,8) (1,14) (1,6) (1,12) (1,3) (1,5) (1,13) (1,4) (1,2) (1,9) (1,10) (1,7) (1,8) (2,14) (2,6) (2,12) (2,3) (2,5) (2,13) (2,4) (2,9) (2,10) (2,7) (2,8) (3,14) (3,6) (3,12) (3,5) (3,13) (3,4) (3,9) (3,10) (3,7) (3,8) (4,14) (4,6) (4,12) (4,5) (4,13) (4,9) (4,10) (4,7) (4,8) (5,14) (5,6) (5,12) (5,13) (5,9) (5,10) (5,7) (5,8) (6,14) (6,12) (6,13) (6,9) (6,10) (6,7) (6,8) (7,14) (7,12) (7,13) (7,9) (7,10) (7,8) (8,14) (8,12) (8,13) (8,9) (8,10) (9,14) (9,12) (9,13) (9,10) (10,14) (10,12) (10,13) (12,14) (12,13) (13,14)\nIs there a path between node 10 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph815-8_10", + "image": "data/connectivity/graph_visual/medium/graph815.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,16) (0,22) (0,3) (0,20) (0,14) (0,6) (0,19) (0,15) (0,13) (1,18) (1,9) (1,24) (1,2) (1,21) (1,23) (2,9) (2,24) (2,12) (2,10) (2,23) (2,4) (3,11) (3,16) (3,20) (3,14) (3,6) (3,7) (3,8) (3,15) (3,13) (4,9) (4,24) (4,12) (4,10) (4,21) (4,17) (4,23) (5,9) (5,24) (5,12) (5,10) (5,21) (5,17) (6,16) (6,22) (6,20) (6,7) (6,19) (6,8) (6,15) (6,13) (7,11) (7,16) (7,22) (7,20) (7,19) (7,8) (7,13) (8,22) (8,20) (8,19) (8,15) (8,13) (9,18) (9,10) (9,21) (9,23) (10,18) (10,24) (10,12) (10,17) (10,23) (11,16) (11,22) (11,20) (11,14) (11,19) (12,24) (12,21) (12,17) (12,23) (13,16) (13,22) (13,20) (13,19) (13,15) (14,16) (14,22) (14,19) (14,15) (15,16) (15,22) (15,19) (16,22) (16,20) (16,19) (18,24) (18,21) (19,20) (20,22) (21,24)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph637-18_0", + "image": "data/connectivity/graph_visual/medium/graph637.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,12) (0,2) (1,13) (1,20) (1,6) (1,8) (1,3) (2,22) (3,10) (3,13) (3,20) (3,15) (3,6) (3,12) (3,14) (4,5) (4,23) (5,16) (5,23) (5,11) (6,12) (6,14) (6,21) (7,22) (7,8) (8,18) (8,22) (8,14) (9,16) (9,23) (9,19) (10,18) (10,15) (10,12) (10,22) (11,16) (12,18) (13,18) (13,14) (14,21) (15,21) (16,19) (17,20) (17,18) (20,22) (21,22)\nIs there a path between node 18 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph352-8_7", + "image": "data/connectivity/graph_visual/medium/graph352.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,3) (2,11) (2,19) (2,5) (2,17) (2,10) (3,4) (3,6) (3,18) (3,7) (4,6) (4,19) (5,13) (5,19) (5,10) (6,7) (6,10) (7,13) (7,17) (7,10) (8,9) (10,18) (10,19) (10,17) (11,13)\nIs there a path between node 8 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph350-3_11", + "image": "data/connectivity/graph_visual/medium/graph350.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,20) (0,4) (0,9) (0,18) (0,12) (0,5) (0,1) (0,17) (0,13) (0,2) (0,10) (0,7) (0,19) (0,15) (0,11) (0,8) (1,16) (1,20) (1,4) (1,9) (1,18) (1,12) (1,5) (1,17) (1,13) (1,2) (1,10) (1,7) (1,19) (1,15) (1,11) (1,8) (2,16) (2,20) (2,4) (2,9) (2,18) (2,12) (2,5) (2,17) (2,13) (2,10) (2,7) (2,19) (2,15) (2,11) (2,8) (3,14) (3,6) (4,16) (4,20) (4,9) (4,18) (4,12) (4,5) (4,17) (4,13) (4,10) (4,7) (4,19) (4,15) (4,11) (4,8) (5,16) (5,20) (5,9) (5,18) (5,12) (5,17) (5,13) (5,10) (5,7) (5,19) (5,15) (5,11) (5,8) (6,14) (7,16) (7,20) (7,9) (7,18) (7,12) (7,17) (7,13) (7,10) (7,19) (7,15) (7,11) (7,8) (8,16) (8,20) (8,9) (8,18) (8,12) (8,17) (8,13) (8,10) (8,19) (8,15) (8,11) (9,16) (9,20) (9,18) (9,12) (9,17) (9,13) (9,10) (9,19) (9,15) (9,11) (10,16) (10,20) (10,18) (10,12) (10,17) (10,13) (10,19) (10,15) (10,11) (11,16) (11,20) (11,18) (11,12) (11,17) (11,13) (11,19) (11,15) (12,16) (12,20) (12,18) (12,17) (12,13) (12,19) (12,15) (13,16) (13,20) (13,18) (13,17) (13,19) (13,15) (15,16) (15,20) (15,18) (15,17) (15,19) (16,20) (16,18) (16,17) (16,19) (17,20) (17,18) (17,19) (18,20) (18,19) (19,20)\nIs there a path between node 3 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph721-21_8", + "image": "data/connectivity/graph_visual/medium/graph721.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,3) (0,9) (0,20) (0,15) (1,21) (1,11) (1,13) (1,23) (1,19) (1,17) (1,5) (1,4) (1,22) (1,2) (1,16) (1,24) (1,7) (1,18) (1,6) (1,12) (1,8) (1,10) (2,21) (2,11) (2,13) (2,23) (2,19) (2,17) (2,5) (2,4) (2,22) (2,16) (2,24) (2,7) (2,18) (2,6) (2,12) (2,8) (2,10) (3,14) (3,9) (3,20) (3,15) (4,21) (4,11) (4,13) (4,23) (4,19) (4,17) (4,5) (4,22) (4,16) (4,24) (4,7) (4,18) (4,6) (4,12) (4,8) (4,10) (5,21) (5,11) (5,13) (5,23) (5,19) (5,17) (5,22) (5,16) (5,24) (5,7) (5,18) (5,6) (5,12) (5,8) (5,10) (6,21) (6,11) (6,13) (6,23) (6,19) (6,17) (6,22) (6,16) (6,24) (6,7) (6,18) (6,12) (6,8) (6,10) (7,21) (7,11) (7,13) (7,23) (7,19) (7,17) (7,22) (7,16) (7,24) (7,18) (7,12) (7,8) (7,10) (8,21) (8,11) (8,13) (8,23) (8,19) (8,17) (8,22) (8,16) (8,24) (8,18) (8,12) (8,10) (9,14) (9,20) (9,15) (10,21) (10,11) (10,13) (10,23) (10,19) (10,17) (10,22) (10,16) (10,24) (10,18) (10,12) (11,21) (11,13) (11,23) (11,19) (11,17) (11,22) (11,16) (11,24) (11,18) (11,12) (12,21) (12,13) (12,23) (12,19) (12,17) (12,22) (12,16) (12,24) (12,18) (13,21) (13,23) (13,19) (13,17) (13,22) (13,16) (13,24) (13,18) (14,20) (14,15) (15,20) (16,21) (16,23) (16,19) (16,17) (16,22) (16,24) (16,18) (17,21) (17,23) (17,19) (17,22) (17,24) (17,18) (18,21) (18,23) (18,19) (18,22) (18,24) (19,21) (19,23) (19,22) (19,24) (21,23) (21,22) (21,24) (22,23) (22,24) (23,24)\nIs there a path between node 21 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph560-3_15", + "image": "data/connectivity/graph_visual/medium/graph560.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,15) (0,22) (0,18) (0,2) (1,7) (1,19) (1,23) (1,3) (1,10) (1,13) (1,16) (1,11) (1,12) (1,21) (1,5) (2,9) (2,15) (2,22) (2,17) (2,8) (3,7) (3,19) (3,10) (3,13) (3,16) (3,11) (3,6) (3,20) (3,21) (4,19) (4,23) (4,10) (4,13) (4,16) (4,11) (4,6) (4,20) (4,5) (5,7) (5,19) (5,23) (5,13) (5,16) (5,11) (5,12) (5,6) (5,20) (5,21) (6,7) (6,23) (6,10) (6,13) (6,16) (6,12) (6,20) (6,21) (7,19) (7,23) (7,10) (7,13) (7,16) (7,11) (7,21) (8,15) (8,14) (9,15) (9,22) (9,14) (9,17) (10,13) (10,16) (10,11) (10,12) (11,19) (11,23) (11,12) (11,20) (11,21) (12,16) (12,21) (13,19) (13,16) (13,20) (13,21) (14,22) (14,18) (14,17) (15,22) (15,17) (16,19) (16,23) (16,20) (16,21) (17,18) (18,22) (19,20) (19,21) (20,23) (20,21)\nIs there a path between node 3 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph660-6_16", + "image": "data/connectivity/graph_visual/medium/graph660.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,11) (0,3) (0,2) (0,9) (0,5) (0,10) (0,23) (1,13) (1,17) (1,20) (1,8) (1,14) (1,4) (2,22) (2,11) (2,9) (2,10) (2,23) (3,21) (3,11) (3,5) (3,15) (3,23) (3,12) (4,18) (4,19) (4,13) (4,8) (4,16) (5,11) (5,9) (5,10) (5,15) (6,18) (6,19) (6,13) (6,20) (6,8) (6,16) (6,14) (7,19) (7,20) (7,8) (7,16) (7,14) (8,18) (8,19) (8,13) (8,17) (8,16) (8,14) (9,22) (9,21) (9,10) (9,15) (9,23) (9,12) (10,22) (10,21) (10,15) (10,12) (11,22) (11,15) (11,23) (11,12) (12,22) (12,15) (12,23) (13,18) (13,19) (13,20) (13,16) (13,14) (14,18) (14,19) (14,17) (14,20) (14,16) (15,22) (15,21) (16,18) (16,19) (16,17) (17,18) (17,19) (17,20) (18,19) (18,20) (19,20) (21,22) (21,23) (22,23)\nIs there a path between node 6 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph333-10_8", + "image": "data/connectivity/graph_visual/medium/graph333.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,14) (0,7) (0,2) (1,9) (1,13) (2,19) (2,3) (3,16) (3,17) (3,19) (3,6) (4,16) (4,20) (4,17) (4,14) (4,18) (5,12) (5,13) (6,12) (6,19) (6,10) (6,9) (6,7) (6,13) (7,16) (9,16) (9,12) (9,18) (10,12) (10,17) (10,15) (10,14) (10,13) (12,16) (13,17) (13,18) (14,17) (14,18) (15,19) (16,19) (17,20) (17,18)\nIs there a path between node 10 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph211-5_7", + "image": "data/connectivity/graph_visual/medium/graph211.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,14) (0,1) (0,8) (0,11) (0,7) (1,14) (1,15) (1,17) (1,7) (2,3) (2,6) (2,5) (2,13) (2,16) (2,4) (2,9) (3,6) (3,5) (3,12) (3,13) (3,16) (3,4) (3,9) (4,6) (4,5) (4,12) (4,13) (4,16) (4,9) (5,6) (5,12) (5,13) (5,16) (6,9) (7,14) (7,8) (7,15) (7,17) (7,11) (8,14) (8,17) (8,11) (9,12) (9,13) (10,18) (11,14) (11,15) (11,17) (12,13) (12,16) (13,16) (14,17) (15,17)\nIs there a path between node 5 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph574-23_4", + "image": "data/connectivity/graph_visual/medium/graph574.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,11) (0,20) (0,12) (0,23) (0,9) (1,3) (2,13) (2,6) (2,8) (2,5) (2,17) (3,18) (3,22) (4,21) (5,6) (5,16) (5,10) (5,17) (6,15) (6,11) (6,12) (6,17) (8,16) (8,9) (9,20) (9,12) (9,10) (9,23) (10,15) (11,15) (11,12) (11,16) (12,13) (13,20) (15,20) (16,20) (16,23) (16,17) (18,19) (18,21) (21,22)\nIs there a path between node 23 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph546-16_2", + "image": "data/connectivity/graph_visual/medium/graph546.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,19) (0,17) (0,7) (0,16) (0,21) (1,22) (1,19) (1,20) (1,21) (2,23) (2,6) (3,13) (3,18) (3,4) (3,10) (3,21) (4,19) (4,10) (4,16) (5,14) (5,12) (5,9) (5,11) (6,14) (6,23) (7,15) (7,22) (7,18) (7,8) (7,17) (7,20) (8,13) (8,21) (9,12) (9,11) (10,17) (13,19) (13,17) (13,21) (15,20) (16,18) (16,20) (19,20) (19,21)\nIs there a path between node 16 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph280-5_10", + "image": "data/connectivity/graph_visual/medium/graph280.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,7) (0,14) (0,13) (0,18) (0,6) (0,19) (1,8) (1,11) (1,10) (1,15) (1,2) (1,3) (1,12) (1,5) (2,8) (2,11) (2,10) (2,15) (2,3) (2,12) (2,5) (3,8) (3,11) (3,10) (3,15) (3,12) (3,5) (4,16) (4,9) (5,8) (5,11) (5,10) (5,15) (5,12) (6,17) (6,7) (6,14) (6,13) (6,18) (6,19) (7,17) (7,14) (7,13) (7,18) (7,19) (8,11) (8,10) (8,15) (8,12) (9,16) (10,11) (10,15) (10,12) (11,15) (11,12) (12,15) (13,17) (13,14) (13,18) (13,19) (14,17) (14,18) (14,19) (17,18) (17,19) (18,19)\nIs there a path between node 5 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph802-0_14", + "image": "data/connectivity/graph_visual/medium/graph802.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,12) (1,6) (1,18) (4,24) (4,16) (4,15) (4,12) (5,23) (5,6) (6,23) (6,18) (7,9) (7,13) (7,11) (8,14) (9,14) (9,11) (11,17) (11,14) (12,24) (12,22) (12,18) (14,21) (16,22) (16,18) (19,20) (22,23) (23,24)\nIs there a path between node 0 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph843-4_3", + "image": "data/connectivity/graph_visual/medium/graph843.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,21) (0,4) (0,1) (0,23) (0,19) (0,2) (0,18) (0,16) (0,5) (0,12) (0,20) (0,14) (1,15) (1,21) (1,4) (1,23) (1,19) (1,2) (1,18) (1,16) (1,5) (1,12) (1,20) (1,14) (2,15) (2,21) (2,4) (2,23) (2,19) (2,18) (2,16) (2,5) (2,12) (2,20) (2,14) (3,10) (3,8) (3,6) (3,17) (3,13) (3,7) (3,11) (3,22) (3,9) (3,24) (4,15) (4,21) (4,23) (4,19) (4,18) (4,16) (4,5) (4,12) (4,20) (4,14) (5,15) (5,21) (5,23) (5,19) (5,18) (5,16) (5,12) (5,20) (5,14) (6,10) (6,8) (6,17) (6,13) (6,7) (6,11) (6,22) (6,9) (6,24) (7,10) (7,8) (7,17) (7,13) (7,11) (7,22) (7,9) (7,24) (8,10) (8,17) (8,13) (8,11) (8,22) (8,9) (8,24) (9,10) (9,17) (9,13) (9,11) (9,22) (9,24) (10,17) (10,13) (10,11) (10,22) (10,24) (11,17) (11,13) (11,22) (11,24) (12,15) (12,21) (12,23) (12,19) (12,18) (12,16) (12,20) (12,14) (13,17) (13,22) (13,24) (14,15) (14,21) (14,23) (14,19) (14,18) (14,16) (14,20) (15,21) (15,23) (15,19) (15,18) (15,16) (15,20) (16,21) (16,23) (16,19) (16,18) (16,20) (17,22) (17,24) (18,21) (18,23) (18,19) (18,20) (19,21) (19,23) (19,20) (20,21) (20,23) (21,23) (22,24)\nIs there a path between node 4 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph52-1_0", + "image": "data/connectivity/graph_visual/medium/graph52.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (0,5) (0,11) (0,8) (0,6) (0,1) (1,10) (1,3) (1,5) (1,9) (1,6) (1,2) (2,10) (2,3) (2,5) (2,9) (2,8) (2,7) (2,6) (2,13) (3,9) (3,11) (3,8) (3,7) (4,12) (5,10) (5,9) (5,8) (5,7) (5,6) (6,10) (6,9) (6,11) (6,8) (7,10) (7,11) (7,8) (7,13) (8,10) (8,11) (8,13) (9,10) (9,11) (9,13) (10,11) (10,13)\nIs there a path between node 1 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph788-21_3", + "image": "data/connectivity/graph_visual/medium/graph788.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,2) (0,20) (0,18) (0,19) (0,7) (0,1) (0,9) (0,24) (1,15) (1,10) (1,2) (1,5) (1,7) (1,12) (1,3) (1,9) (1,22) (1,17) (1,11) (2,6) (2,18) (2,16) (2,3) (2,11) (3,15) (3,20) (3,18) (3,5) (3,22) (3,11) (5,18) (5,9) (5,11) (6,15) (6,23) (6,18) (6,8) (6,12) (6,22) (7,10) (7,20) (7,18) (7,16) (7,9) (8,15) (8,20) (8,24) (9,15) (9,17) (9,11) (10,23) (10,18) (10,13) (10,24) (10,11) (11,23) (11,13) (11,12) (11,17) (12,15) (12,23) (12,19) (12,16) (12,17) (13,23) (13,17) (14,21) (15,23) (15,20) (15,19) (15,22) (16,24) (18,23) (18,20) (19,23) (19,20) (20,22) (20,24)\nIs there a path between node 21 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph98-14_2", + "image": "data/connectivity/graph_visual/medium/graph98.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,14) (1,13) (1,6) (1,4) (1,11) (1,9) (2,13) (2,6) (2,4) (2,11) (2,9) (3,15) (4,8) (4,13) (4,11) (5,8) (5,6) (5,15) (10,12) (11,13)\nIs there a path between node 14 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph727-17_23", + "image": "data/connectivity/graph_visual/medium/graph727.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,2) (1,12) (1,21) (1,18) (1,15) (1,10) (1,13) (1,19) (1,16) (1,22) (1,7) (1,24) (1,14) (1,9) (1,6) (1,17) (1,3) (1,11) (1,20) (1,5) (1,8) (2,12) (2,21) (2,18) (2,15) (2,10) (2,13) (2,19) (2,16) (2,22) (2,7) (2,24) (2,14) (2,9) (2,6) (2,17) (2,3) (2,11) (2,20) (2,5) (2,8) (3,12) (3,21) (3,18) (3,15) (3,10) (3,13) (3,19) (3,16) (3,22) (3,7) (3,24) (3,14) (3,9) (3,6) (3,17) (3,11) (3,20) (3,5) (3,8) (4,23) (5,12) (5,21) (5,18) (5,15) (5,10) (5,13) (5,19) (5,16) (5,22) (5,7) (5,24) (5,14) (5,9) (5,6) (5,17) (5,11) (5,20) (5,8) (6,12) (6,21) (6,18) (6,15) (6,10) (6,13) (6,19) (6,16) (6,22) (6,7) (6,24) (6,14) (6,9) (6,17) (6,11) (6,20) (6,8) (7,12) (7,21) (7,18) (7,15) (7,10) (7,13) (7,19) (7,16) (7,22) (7,24) (7,14) (7,9) (7,17) (7,11) (7,20) (7,8) (8,12) (8,21) (8,18) (8,15) (8,10) (8,13) (8,19) (8,16) (8,22) (8,24) (8,14) (8,9) (8,17) (8,11) (8,20) (9,12) (9,21) (9,18) (9,15) (9,10) (9,13) (9,19) (9,16) (9,22) (9,24) (9,14) (9,17) (9,11) (9,20) (10,12) (10,21) (10,18) (10,15) (10,13) (10,19) (10,16) (10,22) (10,24) (10,14) (10,17) (10,11) (10,20) (11,12) (11,21) (11,18) (11,15) (11,13) (11,19) (11,16) (11,22) (11,24) (11,14) (11,17) (11,20) (12,21) (12,18) (12,15) (12,13) (12,19) (12,16) (12,22) (12,24) (12,14) (12,17) (12,20) (13,21) (13,18) (13,15) (13,19) (13,16) (13,22) (13,24) (13,14) (13,17) (13,20) (14,21) (14,18) (14,15) (14,19) (14,16) (14,22) (14,24) (14,17) (14,20) (15,21) (15,18) (15,19) (15,16) (15,22) (15,24) (15,17) (15,20) (16,21) (16,18) (16,19) (16,22) (16,24) (16,17) (16,20) (17,21) (17,18) (17,19) (17,22) (17,24) (17,20) (18,21) (18,19) (18,22) (18,24) (18,20) (19,21) (19,22) (19,24) (19,20) (20,21) (20,22) (20,24) (21,22) (21,24) (22,24)\nIs there a path between node 17 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph576-5_11", + "image": "data/connectivity/graph_visual/medium/graph576.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,18) (0,11) (0,23) (0,17) (0,7) (0,16) (0,1) (1,18) (1,6) (1,11) (1,21) (1,22) (1,2) (2,8) (2,16) (3,9) (3,13) (5,18) (5,6) (5,21) (5,17) (6,8) (6,11) (6,17) (6,19) (7,20) (7,8) (7,15) (7,19) (8,18) (8,22) (8,15) (11,14) (11,20) (11,22) (11,17) (11,16) (12,13) (14,18) (14,21) (14,23) (14,19) (15,21) (15,23) (16,21) (16,23) (18,20) (18,21) (18,23) (21,22)\nIs there a path between node 5 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph646-10_16", + "image": "data/connectivity/graph_visual/medium/graph646.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,14) (1,22) (1,12) (2,11) (2,7) (2,18) (2,3) (2,20) (3,11) (3,7) (3,18) (3,16) (4,20) (5,20) (5,10) (6,20) (6,16) (6,10) (7,11) (7,16) (8,17) (8,13) (9,23) (10,18) (10,16) (11,16) (12,19) (13,14) (13,22) (13,19) (14,19) (17,22) (17,19) (19,22)\nIs there a path between node 10 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph311-16_19", + "image": "data/connectivity/graph_visual/medium/graph311.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,19) (0,16) (0,18) (0,2) (0,17) (0,7) (0,12) (1,8) (1,3) (1,10) (1,13) (1,6) (1,11) (1,15) (1,5) (1,4) (1,14) (2,9) (2,19) (2,16) (2,18) (2,17) (2,7) (2,12) (3,8) (3,10) (3,13) (3,6) (3,11) (3,15) (3,5) (3,4) (3,14) (4,8) (4,10) (4,13) (4,6) (4,11) (4,15) (4,5) (4,14) (5,8) (5,10) (5,13) (5,6) (5,11) (5,15) (5,14) (6,8) (6,10) (6,13) (6,11) (6,15) (6,14) (7,9) (7,19) (7,16) (7,18) (7,17) (7,12) (8,10) (8,13) (8,11) (8,15) (8,14) (9,19) (9,16) (9,18) (9,17) (9,12) (10,13) (10,11) (10,15) (10,14) (11,13) (11,15) (11,14) (12,19) (12,16) (12,18) (12,17) (13,15) (13,14) (14,15) (16,19) (16,18) (16,17) (17,19) (17,18) (18,19)\nIs there a path between node 16 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph427-14_3", + "image": "data/connectivity/graph_visual/medium/graph427.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,8) (1,11) (1,9) (1,17) (3,21) (3,11) (3,18) (3,6) (3,10) (3,15) (4,8) (5,18) (5,6) (5,9) (5,15) (6,16) (6,21) (6,11) (6,10) (7,14) (7,9) (7,17) (7,15) (8,12) (8,13) (9,21) (9,17) (9,10) (9,19) (11,14) (11,21) (11,19) (13,20) (14,16) (14,18) (14,17) (14,15) (14,19) (15,16) (16,18) (16,17) (18,21)\nIs there a path between node 14 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph687-2_16", + "image": "data/connectivity/graph_visual/medium/graph687.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,2) (0,4) (0,11) (0,8) (0,3) (0,20) (0,15) (0,13) (0,6) (0,7) (0,12) (0,14) (0,18) (0,23) (0,16) (0,9) (1,2) (1,4) (1,11) (1,8) (1,3) (1,20) (1,15) (1,13) (1,6) (1,7) (1,12) (1,14) (1,18) (1,23) (1,16) (1,9) (2,4) (2,11) (2,8) (2,3) (2,20) (2,15) (2,13) (2,6) (2,7) (2,12) (2,14) (2,18) (2,23) (2,16) (2,9) (3,4) (3,11) (3,8) (3,20) (3,15) (3,13) (3,6) (3,7) (3,12) (3,14) (3,18) (3,23) (3,16) (3,9) (4,11) (4,8) (4,20) (4,15) (4,13) (4,6) (4,7) (4,12) (4,14) (4,18) (4,23) (4,16) (4,9) (5,21) (5,19) (5,17) (5,22) (6,11) (6,8) (6,20) (6,15) (6,13) (6,7) (6,12) (6,14) (6,18) (6,23) (6,16) (6,9) (7,11) (7,8) (7,20) (7,15) (7,13) (7,12) (7,14) (7,18) (7,23) (7,16) (7,9) (8,11) (8,20) (8,15) (8,13) (8,12) (8,14) (8,18) (8,23) (8,16) (8,9) (9,11) (9,20) (9,15) (9,13) (9,12) (9,14) (9,18) (9,23) (9,16) (11,20) (11,15) (11,13) (11,12) (11,14) (11,18) (11,23) (11,16) (12,20) (12,15) (12,13) (12,14) (12,18) (12,23) (12,16) (13,20) (13,15) (13,14) (13,18) (13,23) (13,16) (14,20) (14,15) (14,18) (14,23) (14,16) (15,20) (15,18) (15,23) (15,16) (16,20) (16,18) (16,23) (17,21) (17,19) (17,22) (18,20) (18,23) (19,21) (19,22) (20,23) (21,22)\nIs there a path between node 2 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph837-2_19", + "image": "data/connectivity/graph_visual/medium/graph837.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,24) (0,6) (1,2) (1,21) (1,9) (1,8) (1,17) (1,5) (1,3) (1,11) (1,4) (1,15) (2,21) (2,9) (2,8) (2,17) (2,5) (2,3) (2,11) (2,4) (2,15) (3,21) (3,9) (3,8) (3,17) (3,5) (3,11) (3,4) (3,15) (4,21) (4,9) (4,8) (4,17) (4,5) (4,11) (4,15) (5,21) (5,9) (5,8) (5,17) (5,11) (5,15) (6,10) (6,24) (7,12) (7,18) (7,16) (7,23) (7,13) (7,20) (7,22) (7,14) (7,19) (8,21) (8,9) (8,17) (8,11) (8,15) (9,21) (9,17) (9,11) (9,15) (10,24) (11,21) (11,17) (11,15) (12,18) (12,16) (12,23) (12,13) (12,20) (12,22) (12,14) (12,19) (13,18) (13,16) (13,23) (13,20) (13,22) (13,14) (13,19) (14,18) (14,16) (14,23) (14,20) (14,22) (14,19) (15,21) (15,17) (16,18) (16,23) (16,20) (16,22) (16,19) (17,21) (18,23) (18,20) (18,22) (18,19) (19,23) (19,20) (19,22) (20,23) (20,22) (22,23)\nIs there a path between node 2 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph133-17_8", + "image": "data/connectivity/graph_visual/medium/graph133.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,15) (0,8) (0,4) (0,5) (0,13) (0,2) (0,17) (1,15) (1,8) (1,3) (1,4) (1,5) (1,13) (1,17) (2,15) (2,8) (2,3) (2,4) (2,5) (2,13) (3,8) (3,5) (3,17) (4,15) (4,13) (4,17) (5,15) (5,8) (5,17) (6,14) (6,7) (6,10) (6,16) (6,9) (6,12) (7,14) (7,16) (7,9) (8,13) (9,14) (9,10) (9,11) (9,16) (9,12) (10,14) (10,12) (11,14) (11,12) (12,14) (12,16) (13,17) (15,17)\nIs there a path between node 17 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph367-17_18", + "image": "data/connectivity/graph_visual/medium/graph367.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,8) (0,14) (0,2) (0,17) (1,5) (1,9) (1,3) (1,11) (1,6) (1,19) (1,20) (1,4) (1,18) (1,10) (1,7) (2,16) (2,8) (2,14) (2,15) (2,12) (3,5) (3,13) (3,6) (3,20) (3,4) (3,18) (3,10) (3,7) (4,5) (4,9) (4,11) (4,19) (4,18) (4,10) (4,7) (5,13) (5,9) (5,11) (5,6) (5,19) (5,20) (5,18) (5,10) (6,13) (6,9) (6,11) (6,18) (6,10) (7,9) (7,11) (7,20) (8,12) (9,13) (9,11) (9,19) (9,20) (9,10) (10,13) (10,19) (10,20) (10,18) (11,19) (11,20) (12,16) (12,14) (12,15) (12,17) (13,18) (14,16) (14,15) (16,17) (18,19) (19,20)\nIs there a path between node 17 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph123-6_12", + "image": "data/connectivity/graph_visual/medium/graph123.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,8) (0,10) (0,6) (0,2) (0,5) (0,7) (0,9) (0,13) (1,10) (1,6) (1,14) (1,2) (1,5) (1,4) (1,7) (1,3) (1,9) (1,13) (2,8) (2,10) (2,14) (2,5) (2,4) (2,7) (2,3) (2,15) (2,13) (3,10) (3,6) (3,9) (3,13) (4,10) (4,6) (4,14) (4,15) (4,9) (4,13) (5,10) (5,7) (5,15) (5,9) (5,13) (6,8) (6,15) (6,9) (6,13) (7,14) (7,15) (8,10) (8,15) (8,9) (8,13) (9,14) (10,14) (10,15) (11,12) (11,16) (14,15)\nIs there a path between node 6 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph702-21_6", + "image": "data/connectivity/graph_visual/medium/graph702.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,1) (0,6) (0,21) (0,18) (1,24) (1,3) (3,24) (3,14) (4,6) (4,5) (4,23) (6,14) (6,21) (6,23) (7,11) (8,19) (8,13) (9,15) (9,19) (10,11) (10,12) (10,16) (10,17) (11,12) (11,16) (12,17) (13,15) (13,22) (14,23) (15,22) (16,17) (18,24) (18,21)\nIs there a path between node 21 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph834-20_12", + "image": "data/connectivity/graph_visual/medium/graph834.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,5) (0,17) (0,4) (0,7) (0,21) (0,8) (0,22) (0,3) (0,16) (0,23) (0,13) (1,24) (1,15) (1,11) (1,20) (1,10) (1,18) (1,12) (1,14) (1,9) (1,19) (1,6) (2,5) (2,17) (2,4) (2,7) (2,21) (2,8) (2,22) (2,3) (2,16) (2,23) (2,13) (3,5) (3,17) (3,4) (3,7) (3,21) (3,8) (3,22) (3,16) (3,23) (3,13) (4,5) (4,17) (4,7) (4,21) (4,8) (4,22) (4,16) (4,23) (4,13) (5,17) (5,7) (5,21) (5,8) (5,22) (5,16) (5,23) (5,13) (6,24) (6,15) (6,11) (6,20) (6,10) (6,18) (6,12) (6,14) (6,9) (6,19) (7,17) (7,21) (7,8) (7,22) (7,16) (7,23) (7,13) (8,17) (8,21) (8,22) (8,16) (8,23) (8,13) (9,24) (9,15) (9,11) (9,20) (9,10) (9,18) (9,12) (9,14) (9,19) (10,24) (10,15) (10,11) (10,20) (10,18) (10,12) (10,14) (10,19) (11,24) (11,15) (11,20) (11,18) (11,12) (11,14) (11,19) (12,24) (12,15) (12,20) (12,18) (12,14) (12,19) (13,17) (13,21) (13,22) (13,16) (13,23) (14,24) (14,15) (14,20) (14,18) (14,19) (15,24) (15,20) (15,18) (15,19) (16,17) (16,21) (16,22) (16,23) (17,21) (17,22) (17,23) (18,24) (18,20) (18,19) (19,24) (19,20) (20,24) (21,22) (21,23) (22,23)\nIs there a path between node 20 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph363-20_2", + "image": "data/connectivity/graph_visual/medium/graph363.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,9) (0,8) (0,17) (0,6) (1,14) (1,7) (2,8) (2,17) (2,3) (2,11) (2,10) (2,6) (3,9) (3,19) (3,10) (3,16) (4,18) (4,14) (5,8) (5,17) (5,10) (6,9) (6,11) (6,16) (7,20) (7,15) (8,9) (8,13) (8,19) (9,13) (10,17) (10,13) (12,16) (13,17) (14,18) (14,20) (15,20) (16,19)\nIs there a path between node 20 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph828-0_4", + "image": "data/connectivity/graph_visual/medium/graph828.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,6) (0,8) (0,9) (0,7) (0,20) (0,24) (0,3) (0,2) (1,15) (1,6) (1,8) (1,9) (1,7) (1,11) (1,20) (1,10) (1,24) (1,22) (1,2) (2,15) (2,6) (2,9) (2,11) (2,20) (2,5) (2,22) (2,3) (2,23) (3,15) (3,20) (3,10) (3,24) (3,22) (3,23) (4,17) (4,13) (4,16) (4,12) (4,19) (5,6) (5,8) (5,9) (5,7) (5,11) (5,10) (5,22) (5,23) (6,15) (6,8) (6,11) (6,20) (6,24) (6,22) (7,15) (7,8) (7,9) (7,11) (7,20) (7,10) (7,24) (7,22) (8,15) (8,11) (8,20) (8,10) (8,24) (8,22) (9,20) (9,10) (9,24) (9,22) (9,23) (10,15) (10,11) (10,24) (10,22) (10,23) (11,20) (11,23) (12,17) (12,13) (12,18) (12,21) (12,16) (12,14) (12,19) (13,17) (13,18) (13,21) (13,14) (13,19) (14,17) (14,18) (14,21) (14,16) (14,19) (15,20) (15,24) (15,22) (16,17) (16,18) (16,21) (18,21) (18,19) (19,21) (20,24) (20,22) (20,23) (22,24) (22,23)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph428-21_13", + "image": "data/connectivity/graph_visual/medium/graph428.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,13) (0,7) (0,9) (0,19) (0,10) (1,16) (1,14) (1,7) (1,19) (1,3) (2,21) (3,18) (3,13) (3,9) (3,19) (4,21) (5,6) (5,13) (5,7) (5,9) (5,11) (5,12) (5,10) (6,15) (6,10) (7,14) (7,11) (9,15) (9,18) (9,14) (10,12) (11,13) (12,19) (14,16) (17,20) (20,21)\nIs there a path between node 21 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph413-4_15", + "image": "data/connectivity/graph_visual/medium/graph413.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,13) (0,19) (0,21) (0,4) (0,2) (0,16) (0,6) (0,7) (0,8) (0,3) (0,20) (0,14) (1,9) (1,10) (2,13) (2,19) (2,21) (2,12) (2,16) (2,5) (2,8) (2,20) (2,14) (3,13) (3,21) (3,4) (3,12) (3,16) (3,7) (3,8) (3,20) (3,14) (4,21) (4,12) (4,16) (4,6) (4,5) (4,8) (5,13) (5,19) (5,21) (5,12) (5,6) (5,7) (5,8) (5,14) (6,13) (6,19) (6,12) (6,16) (6,7) (6,8) (6,20) (6,14) (7,13) (7,21) (7,12) (7,16) (7,20) (7,14) (8,19) (8,12) (8,20) (8,14) (9,11) (9,10) (9,15) (9,18) (9,17) (10,11) (10,15) (10,17) (11,15) (11,18) (11,17) (12,21) (12,16) (12,20) (13,19) (13,16) (13,20) (13,14) (14,19) (14,21) (14,16) (14,20) (15,18) (15,17) (16,19) (16,21) (17,18) (19,21) (19,20) (20,21)\nIs there a path between node 4 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph566-21_3", + "image": "data/connectivity/graph_visual/medium/graph566.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (0,9) (0,15) (0,23) (0,4) (0,22) (0,8) (0,7) (0,16) (0,19) (0,3) (0,21) (0,17) (1,6) (1,10) (1,12) (1,2) (1,18) (1,11) (1,14) (1,20) (1,5) (2,6) (2,10) (2,12) (2,18) (2,11) (2,14) (2,20) (2,5) (3,13) (3,9) (3,15) (3,23) (3,4) (3,22) (3,8) (3,7) (3,16) (3,19) (3,21) (3,17) (4,13) (4,9) (4,15) (4,23) (4,22) (4,8) (4,7) (4,16) (4,19) (4,21) (4,17) (5,6) (5,10) (5,12) (5,18) (5,11) (5,14) (5,20) (6,10) (6,12) (6,18) (6,11) (6,14) (6,20) (7,13) (7,9) (7,15) (7,23) (7,22) (7,8) (7,16) (7,19) (7,21) (7,17) (8,13) (8,9) (8,15) (8,23) (8,22) (8,16) (8,19) (8,21) (8,17) (9,13) (9,15) (9,23) (9,22) (9,16) (9,19) (9,21) (9,17) (10,12) (10,18) (10,11) (10,14) (10,20) (11,12) (11,18) (11,14) (11,20) (12,18) (12,14) (12,20) (13,15) (13,23) (13,22) (13,16) (13,19) (13,21) (13,17) (14,18) (14,20) (15,23) (15,22) (15,16) (15,19) (15,21) (15,17) (16,23) (16,22) (16,19) (16,21) (16,17) (17,23) (17,22) (17,19) (17,21) (18,20) (19,23) (19,22) (19,21) (21,23) (21,22) (22,23)\nIs there a path between node 21 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph625-20_21", + "image": "data/connectivity/graph_visual/medium/graph625.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (1,11) (1,7) (1,13) (1,21) (1,19) (1,5) (2,17) (2,20) (2,5) (4,9) (4,22) (5,21) (5,19) (6,23) (7,11) (8,11) (8,13) (8,19) (8,18) (11,23) (11,13) (11,18) (13,20) (13,21) (13,19) (13,18) (14,16) (14,15) (18,20) (19,20) (19,21) (20,23)\nIs there a path between node 20 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph472-0_15", + "image": "data/connectivity/graph_visual/medium/graph472.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,5) (0,9) (0,21) (0,19) (1,2) (1,13) (2,22) (2,10) (3,12) (3,21) (4,12) (5,8) (5,9) (5,21) (5,14) (6,18) (6,7) (7,17) (8,11) (8,9) (8,15) (8,19) (9,11) (9,21) (9,15) (9,14) (10,18) (10,17) (10,20) (12,16) (12,21) (12,19) (13,17) (14,21) (16,21) (16,19) (17,20) (20,22)\nIs there a path between node 0 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph69-9_10", + "image": "data/connectivity/graph_visual/medium/graph69.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,5) (0,9) (1,8) (1,4) (2,8) (2,4) (2,3) (3,7) (3,6) (3,10) (3,12) (3,11) (4,10) (4,12) (6,14) (6,8) (6,10) (7,14) (7,11) (8,14) (8,12) (10,14) (11,14) (12,14)\nIs there a path between node 9 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph1-0_2", + "image": "data/connectivity/graph_visual/medium/graph1.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,7) (0,3) (0,2) (0,9) (0,8) (1,6) (1,4) (2,7) (2,10) (2,3) (2,8) (2,5) (3,10) (3,9) (3,8) (4,6) (5,7) (5,10) (5,9) (7,8) (8,9)\nIs there a path between node 0 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph522-0_17", + "image": "data/connectivity/graph_visual/medium/graph522.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,19) (0,15) (0,8) (0,16) (0,11) (0,12) (1,19) (1,5) (1,9) (1,21) (1,16) (1,11) (1,12) (2,7) (2,20) (2,3) (2,6) (3,4) (3,20) (3,6) (4,13) (4,7) (4,18) (4,17) (4,10) (5,8) (5,12) (6,13) (6,7) (6,18) (6,17) (6,10) (7,20) (7,17) (7,10) (8,19) (8,15) (8,9) (8,21) (8,16) (9,19) (9,15) (9,21) (10,13) (10,20) (11,19) (11,12) (12,19) (12,21) (12,16) (13,20) (13,18) (13,17) (15,19) (15,21) (15,16) (16,19) (17,20) (17,18)\nIs there a path between node 0 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph748-6_8", + "image": "data/connectivity/graph_visual/medium/graph748.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,8) (0,22) (0,20) (0,17) (0,19) (1,6) (1,9) (1,4) (1,23) (1,14) (1,21) (1,2) (1,13) (2,6) (2,9) (2,4) (2,23) (2,14) (2,5) (2,21) (2,13) (3,9) (3,14) (3,5) (3,21) (4,15) (4,6) (4,9) (4,23) (4,5) (4,21) (4,13) (5,15) (5,6) (5,9) (5,23) (5,10) (5,14) (5,21) (6,15) (6,9) (6,23) (6,10) (6,14) (6,21) (7,18) (7,22) (7,20) (7,17) (7,12) (7,19) (8,11) (8,22) (8,17) (8,12) (8,19) (9,23) (9,10) (9,14) (9,21) (9,13) (10,15) (10,21) (10,13) (11,18) (11,22) (11,24) (11,12) (12,18) (12,22) (12,20) (12,24) (12,19) (13,15) (13,23) (13,14) (14,23) (14,21) (15,23) (15,21) (17,20) (18,20) (18,24) (18,19) (19,22) (19,20) (20,22) (20,24) (21,23) (22,24)\nIs there a path between node 6 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph167-9_13", + "image": "data/connectivity/graph_visual/medium/graph167.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,17) (0,8) (0,6) (0,12) (0,16) (0,3) (1,17) (1,2) (1,8) (1,9) (1,4) (1,12) (1,3) (2,17) (2,11) (2,9) (2,16) (2,14) (2,5) (3,13) (3,9) (3,14) (4,17) (4,7) (4,13) (4,16) (4,5) (5,7) (5,13) (5,9) (5,14) (6,8) (6,11) (6,9) (6,12) (6,16) (6,14) (7,8) (7,13) (8,13) (9,13) (9,12) (11,13) (11,12) (11,14) (13,14)\nIs there a path between node 9 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph125-13_15", + "image": "data/connectivity/graph_visual/medium/graph125.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,14) (0,8) (0,6) (0,10) (0,12) (0,16) (0,2) (0,3) (0,5) (0,13) (1,11) (1,9) (1,4) (1,14) (1,8) (1,6) (1,10) (1,12) (1,16) (1,2) (1,3) (1,5) (1,7) (1,13) (2,11) (2,9) (2,4) (2,14) (2,6) (2,16) (2,3) (2,5) (2,7) (2,13) (3,11) (3,9) (3,14) (3,8) (3,6) (3,10) (3,12) (3,16) (3,13) (4,11) (4,9) (4,14) (4,8) (4,10) (4,12) (4,16) (4,5) (4,7) (4,13) (5,11) (5,14) (5,8) (5,6) (5,10) (5,12) (5,16) (6,11) (6,9) (6,8) (6,10) (6,12) (6,7) (6,13) (7,11) (7,9) (7,14) (7,10) (7,12) (7,16) (8,9) (8,10) (8,12) (8,16) (8,13) (9,11) (9,14) (9,16) (9,13) (10,14) (10,12) (10,16) (10,13) (11,13) (12,14) (12,16) (12,13) (13,14) (13,16) (14,16)\nIs there a path between node 13 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph201-12_10", + "image": "data/connectivity/graph_visual/medium/graph201.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,7) (1,4) (3,9) (3,12) (4,15) (5,10) (8,10) (8,16)\nIs there a path between node 12 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph26-9_7", + "image": "data/connectivity/graph_visual/medium/graph26.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,10) (0,5) (0,8) (0,11) (0,2) (0,6) (0,9) (1,5) (1,8) (1,9) (2,8) (2,3) (2,11) (2,9) (3,5) (3,8) (3,11) (3,6) (3,9) (4,7) (5,10) (5,8) (6,8) (6,9) (8,10) (9,10) (9,11) (10,11)\nIs there a path between node 9 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph270-9_8", + "image": "data/connectivity/graph_visual/medium/graph270.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,16) (0,3) (0,5) (1,6) (1,7) (1,2) (1,8) (1,14) (1,13) (1,9) (1,4) (1,12) (1,19) (2,6) (2,11) (2,8) (2,14) (2,13) (2,9) (2,12) (2,19) (3,17) (3,16) (3,15) (3,5) (3,18) (4,7) (4,8) (4,14) (4,9) (4,12) (5,17) (5,16) (5,10) (5,15) (6,7) (6,11) (6,8) (6,14) (6,12) (6,19) (7,11) (7,19) (8,11) (8,13) (8,9) (8,19) (9,11) (9,14) (9,13) (9,12) (9,19) (10,17) (10,16) (10,15) (11,14) (11,13) (11,12) (12,13) (12,19) (13,14) (13,19) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 9 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph9-9_4", + "image": "data/connectivity/graph_visual/medium/graph9.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,7) (0,5) (0,9) (0,6) (0,1) (1,2) (1,7) (1,3) (1,6) (2,7) (2,4) (2,9) (2,6) (3,7) (3,5) (4,9) (4,6) (6,7) (6,9) (8,10)\nIs there a path between node 9 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph276-11_17", + "image": "data/connectivity/graph_visual/medium/graph276.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,10) (1,9) (1,16) (1,4) (1,12) (2,8) (2,19) (2,7) (2,14) (2,17) (2,5) (2,18) (2,6) (2,11) (2,3) (2,13) (2,15) (3,8) (3,19) (3,7) (3,14) (3,17) (3,5) (3,18) (3,6) (3,11) (3,13) (3,15) (4,10) (4,9) (4,16) (4,12) (5,8) (5,19) (5,7) (5,14) (5,17) (5,18) (5,6) (5,11) (5,13) (5,15) (6,8) (6,19) (6,7) (6,14) (6,17) (6,18) (6,11) (6,13) (6,15) (7,8) (7,19) (7,14) (7,17) (7,18) (7,11) (7,13) (7,15) (8,19) (8,14) (8,17) (8,18) (8,11) (8,13) (8,15) (9,10) (9,16) (9,12) (10,16) (10,12) (11,19) (11,14) (11,17) (11,18) (11,13) (11,15) (12,16) (13,19) (13,14) (13,17) (13,18) (13,15) (14,19) (14,17) (14,18) (14,15) (15,19) (15,17) (15,18) (17,19) (17,18) (18,19)\nIs there a path between node 11 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph109-10_0", + "image": "data/connectivity/graph_visual/medium/graph109.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,6) (0,3) (0,13) (0,10) (0,9) (0,15) (0,14) (1,5) (1,7) (1,11) (1,4) (1,8) (1,2) (1,12) (2,5) (2,7) (2,11) (2,4) (2,8) (2,12) (3,6) (3,13) (3,10) (3,9) (3,15) (3,14) (4,5) (4,7) (4,11) (4,8) (4,12) (5,7) (5,11) (5,8) (5,12) (6,13) (6,10) (6,9) (6,15) (6,14) (7,11) (7,8) (7,12) (8,11) (8,12) (9,13) (9,10) (9,15) (9,14) (10,13) (10,15) (10,14) (11,12) (13,15) (13,14) (14,15)\nIs there a path between node 10 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph742-17_13", + "image": "data/connectivity/graph_visual/medium/graph742.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,4) (0,5) (0,10) (0,22) (0,8) (3,9) (3,24) (3,11) (4,21) (4,13) (5,13) (7,9) (8,21) (8,17) (8,18) (9,20) (10,21) (10,22) (13,14) (13,18) (14,18) (15,19) (15,16) (21,22)\nIs there a path between node 17 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph310-18_12", + "image": "data/connectivity/graph_visual/medium/graph310.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,10) (0,19) (0,16) (0,7) (0,8) (0,4) (0,3) (0,11) (0,1) (0,18) (0,9) (0,5) (0,2) (0,13) (1,17) (1,10) (1,19) (1,16) (1,7) (1,8) (1,4) (1,3) (1,11) (1,18) (1,9) (1,5) (1,2) (1,13) (2,17) (2,10) (2,19) (2,16) (2,7) (2,8) (2,4) (2,3) (2,11) (2,18) (2,9) (2,5) (2,13) (3,17) (3,10) (3,19) (3,16) (3,7) (3,8) (3,4) (3,11) (3,18) (3,9) (3,5) (3,13) (4,17) (4,10) (4,19) (4,16) (4,7) (4,8) (4,11) (4,18) (4,9) (4,5) (4,13) (5,17) (5,10) (5,19) (5,16) (5,7) (5,8) (5,11) (5,18) (5,9) (5,13) (6,15) (7,17) (7,10) (7,19) (7,16) (7,8) (7,11) (7,18) (7,9) (7,13) (8,17) (8,10) (8,19) (8,16) (8,11) (8,18) (8,9) (8,13) (9,17) (9,10) (9,19) (9,16) (9,11) (9,18) (9,13) (10,17) (10,19) (10,16) (10,11) (10,18) (10,13) (11,17) (11,19) (11,16) (11,18) (11,13) (12,14) (13,17) (13,19) (13,16) (13,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nIs there a path between node 18 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph92-3_9", + "image": "data/connectivity/graph_visual/medium/graph92.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,12) (0,13) (0,6) (0,5) (0,15) (0,14) (0,1) (0,10) (0,8) (0,7) (0,2) (0,11) (0,3) (1,12) (1,13) (1,6) (1,5) (1,15) (1,14) (1,10) (1,8) (1,7) (1,2) (1,11) (1,3) (2,12) (2,13) (2,6) (2,5) (2,15) (2,14) (2,10) (2,8) (2,7) (2,11) (2,3) (3,12) (3,13) (3,6) (3,5) (3,15) (3,14) (3,10) (3,8) (3,7) (3,11) (4,9) (5,12) (5,13) (5,6) (5,15) (5,14) (5,10) (5,8) (5,7) (5,11) (6,12) (6,13) (6,15) (6,14) (6,10) (6,8) (6,7) (6,11) (7,12) (7,13) (7,15) (7,14) (7,10) (7,8) (7,11) (8,12) (8,13) (8,15) (8,14) (8,10) (8,11) (10,12) (10,13) (10,15) (10,14) (10,11) (11,12) (11,13) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nIs there a path between node 3 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph698-9_12", + "image": "data/connectivity/graph_visual/medium/graph698.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,2) (1,22) (1,7) (1,20) (1,13) (1,10) (1,16) (2,11) (3,6) (3,21) (3,18) (3,4) (3,12) (3,9) (3,5) (3,8) (3,19) (3,15) (3,23) (3,17) (3,14) (4,6) (4,21) (4,18) (4,12) (4,9) (4,5) (4,8) (4,19) (4,15) (4,23) (4,17) (4,14) (5,6) (5,21) (5,18) (5,12) (5,9) (5,8) (5,19) (5,15) (5,23) (5,17) (5,14) (6,21) (6,18) (6,12) (6,9) (6,8) (6,19) (6,15) (6,23) (6,17) (6,14) (7,22) (7,20) (7,13) (7,10) (7,16) (8,21) (8,18) (8,12) (8,9) (8,19) (8,15) (8,23) (8,17) (8,14) (9,21) (9,18) (9,12) (9,19) (9,15) (9,23) (9,17) (9,14) (10,22) (10,20) (10,13) (10,16) (12,21) (12,18) (12,19) (12,15) (12,23) (12,17) (12,14) (13,22) (13,20) (13,16) (14,21) (14,18) (14,19) (14,15) (14,23) (14,17) (15,21) (15,18) (15,19) (15,23) (15,17) (16,22) (16,20) (17,21) (17,18) (17,19) (17,23) (18,21) (18,19) (18,23) (19,21) (19,23) (20,22) (21,23)\nIs there a path between node 9 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph108-3_7", + "image": "data/connectivity/graph_visual/medium/graph108.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,12) (0,13) (0,3) (0,4) (0,10) (1,6) (1,15) (1,9) (1,2) (1,7) (1,11) (1,5) (1,14) (1,8) (2,6) (2,15) (2,9) (2,7) (2,11) (2,5) (2,14) (2,8) (3,12) (3,13) (3,4) (3,10) (4,12) (4,13) (4,10) (5,6) (5,15) (5,9) (5,7) (5,11) (5,14) (5,8) (6,15) (6,9) (6,7) (6,11) (6,14) (6,8) (7,15) (7,9) (7,11) (7,14) (7,8) (8,15) (8,9) (8,11) (8,14) (9,15) (9,11) (9,14) (10,12) (10,13) (11,15) (11,14) (12,13) (14,15)\nIs there a path between node 3 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph285-13_18", + "image": "data/connectivity/graph_visual/medium/graph285.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,14) (1,9) (1,2) (1,8) (2,18) (2,6) (2,5) (2,8) (2,11) (3,7) (5,13) (5,6) (5,9) (5,8) (6,12) (6,13) (6,18) (6,10) (6,9) (6,8) (6,11) (7,15) (8,16) (8,9) (9,13) (9,10) (10,16) (10,11) (11,12) (11,16) (12,16) (13,16) (14,15)\nIs there a path between node 13 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph269-0_13", + "image": "data/connectivity/graph_visual/medium/graph269.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,5) (0,8) (0,10) (0,4) (1,9) (1,18) (2,7) (2,16) (2,12) (2,3) (2,15) (2,19) (3,6) (3,16) (4,17) (4,5) (4,8) (4,14) (5,17) (5,14) (6,16) (7,16) (7,12) (7,15) (7,19) (8,14) (9,11) (9,13) (10,17) (10,14) (11,18) (11,13) (12,16) (12,15) (15,16) (15,19) (16,19)\nIs there a path between node 0 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph509-6_19", + "image": "data/connectivity/graph_visual/medium/graph509.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,15) (0,10) (0,1) (0,7) (0,13) (0,3) (0,2) (0,11) (0,12) (1,7) (1,22) (1,12) (2,6) (2,10) (2,18) (2,16) (2,5) (2,7) (2,13) (2,3) (2,11) (3,10) (3,16) (3,5) (4,8) (4,21) (5,18) (5,7) (5,11) (5,12) (6,10) (6,16) (6,17) (6,7) (6,20) (7,20) (7,13) (7,12) (8,21) (9,14) (10,16) (10,11) (11,15) (11,16) (11,17) (12,15) (12,20) (13,17) (13,22) (15,18) (15,16) (15,17) (17,18) (18,20) (19,21) (20,22)\nIs there a path between node 6 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph809-16_7", + "image": "data/connectivity/graph_visual/medium/graph809.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (1,23) (1,15) (1,8) (1,17) (1,19) (1,9) (1,12) (1,20) (1,10) (1,5) (1,22) (1,14) (1,4) (1,18) (1,21) (2,13) (2,3) (2,16) (3,16) (4,23) (4,15) (4,7) (4,17) (4,9) (4,12) (4,20) (4,5) (4,22) (4,14) (4,21) (5,23) (5,15) (5,8) (5,7) (5,19) (5,9) (5,20) (5,22) (5,14) (5,21) (6,24) (6,11) (7,15) (7,8) (7,17) (7,12) (7,20) (7,10) (7,18) (7,21) (8,15) (8,17) (8,19) (8,9) (8,22) (8,14) (8,18) (9,23) (9,15) (9,17) (9,19) (9,20) (9,10) (9,18) (9,21) (10,23) (10,19) (10,22) (10,14) (10,21) (12,23) (12,15) (12,17) (12,19) (12,22) (12,18) (14,15) (14,19) (14,20) (14,22) (14,18) (14,21) (15,19) (15,20) (15,22) (15,18) (17,23) (17,19) (17,20) (17,18) (17,21) (18,23) (18,22) (19,23) (19,20) (19,21) (20,22) (20,21) (21,22)\nIs there a path between node 16 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph750-6_1", + "image": "data/connectivity/graph_visual/medium/graph750.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,22) (0,19) (0,13) (0,3) (0,16) (0,24) (0,1) (0,4) (0,7) (0,6) (0,15) (0,9) (1,11) (1,2) (1,22) (1,10) (1,5) (1,14) (1,13) (1,3) (1,16) (1,24) (1,7) (1,6) (1,20) (1,9) (2,11) (2,22) (2,10) (2,5) (2,14) (2,13) (2,3) (2,16) (2,18) (2,24) (2,4) (2,7) (2,6) (2,15) (2,20) (2,9) (3,11) (3,22) (3,19) (3,10) (3,5) (3,13) (3,18) (3,24) (3,7) (3,6) (3,15) (3,20) (3,9) (4,22) (4,19) (4,5) (4,14) (4,13) (4,16) (4,18) (4,20) (4,9) (5,22) (5,19) (5,10) (5,13) (5,16) (5,18) (5,24) (5,6) (5,15) (6,11) (6,22) (6,19) (6,10) (6,16) (6,18) (6,24) (6,7) (6,15) (6,9) (7,11) (7,22) (7,19) (7,10) (7,14) (7,13) (7,18) (7,24) (7,15) (7,20) (7,9) (8,23) (8,17) (9,22) (9,19) (9,10) (9,14) (9,18) (9,24) (9,15) (9,20) (10,11) (10,22) (10,19) (10,14) (10,13) (10,16) (10,18) (10,24) (10,15) (10,20) (11,22) (11,19) (11,14) (11,13) (11,16) (11,24) (11,15) (11,20) (12,23) (12,21) (13,19) (13,16) (13,18) (13,24) (13,15) (13,20) (14,22) (14,16) (14,18) (14,15) (14,20) (15,16) (15,18) (15,24) (16,22) (16,19) (16,18) (16,24) (17,23) (17,21) (18,19) (19,22) (19,24) (19,20) (20,22) (20,24)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph417-3_21", + "image": "data/connectivity/graph_visual/medium/graph417.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,14) (0,9) (0,11) (0,4) (0,5) (0,15) (0,18) (0,20) (1,17) (1,16) (1,19) (1,3) (1,21) (1,6) (1,13) (1,8) (1,10) (1,7) (2,14) (2,9) (2,11) (2,4) (2,5) (2,15) (2,18) (2,20) (3,17) (3,16) (3,19) (3,21) (3,6) (3,13) (3,8) (3,10) (3,7) (4,14) (4,9) (4,11) (4,5) (4,15) (4,18) (4,20) (5,14) (5,9) (5,11) (5,15) (5,18) (5,20) (6,17) (6,16) (6,19) (6,21) (6,13) (6,8) (6,10) (6,7) (7,17) (7,16) (7,19) (7,21) (7,13) (7,8) (7,10) (8,17) (8,16) (8,19) (8,21) (8,13) (8,10) (9,14) (9,11) (9,15) (9,18) (9,20) (10,17) (10,16) (10,19) (10,21) (10,13) (11,14) (11,15) (11,18) (11,20) (13,17) (13,16) (13,19) (13,21) (14,15) (14,18) (14,20) (15,18) (15,20) (16,17) (16,19) (16,21) (17,19) (17,21) (18,20) (19,21)\nIs there a path between node 3 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph243-16_18", + "image": "data/connectivity/graph_visual/medium/graph243.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,3) (0,4) (0,8) (0,13) (0,7) (0,2) (0,14) (0,18) (0,1) (0,10) (0,5) (1,15) (1,4) (1,9) (1,8) (1,7) (1,17) (1,2) (1,10) (1,12) (1,5) (2,15) (2,4) (2,8) (2,17) (2,14) (2,18) (2,10) (2,5) (3,15) (3,4) (3,9) (3,13) (3,7) (3,14) (3,18) (3,10) (4,9) (4,8) (4,7) (4,17) (4,14) (4,18) (4,12) (4,5) (5,15) (5,8) (5,13) (5,11) (5,14) (5,18) (6,16) (7,15) (7,8) (7,13) (7,18) (7,10) (8,15) (8,9) (8,13) (8,11) (8,14) (8,18) (8,10) (8,12) (9,15) (9,13) (9,17) (9,11) (9,14) (9,18) (9,10) (9,12) (10,15) (10,18) (11,15) (11,13) (11,18) (11,12) (12,15) (12,17) (12,18) (13,15) (13,17) (13,18) (14,15) (14,18) (15,17) (17,18)\nIs there a path between node 16 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph171-9_2", + "image": "data/connectivity/graph_visual/medium/graph171.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,10) (0,7) (0,15) (0,17) (0,6) (1,12) (1,3) (1,4) (1,14) (1,16) (2,8) (2,5) (2,4) (2,9) (2,14) (2,16) (3,12) (3,11) (3,8) (3,4) (3,9) (3,14) (3,16) (4,12) (4,11) (4,8) (4,5) (4,14) (4,16) (5,12) (5,8) (5,9) (5,14) (5,16) (6,10) (6,13) (6,7) (6,15) (6,17) (7,10) (7,13) (7,15) (7,17) (8,11) (8,9) (9,14) (9,16) (10,15) (10,17) (11,12) (11,14) (12,14) (12,16) (13,15) (13,17) (15,17)\nIs there a path between node 9 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph286-16_9", + "image": "data/connectivity/graph_visual/medium/graph286.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (0,9) (1,11) (1,4) (2,6) (2,14) (2,19) (3,15) (4,18) (4,17) (4,9) (4,19) (5,6) (5,11) (5,10) (6,11) (6,18) (8,10) (8,14) (9,18) (9,10) (9,14) (10,18) (10,19) (11,14) (11,19) (12,15) (12,13) (16,19)\nIs there a path between node 16 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph340-18_6", + "image": "data/connectivity/graph_visual/medium/graph340.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,9) (0,11) (0,6) (0,14) (0,8) (0,19) (0,16) (0,4) (0,13) (0,17) (0,15) (1,9) (1,5) (1,14) (1,8) (1,16) (1,12) (1,13) (1,17) (1,15) (2,9) (2,11) (2,6) (2,20) (2,5) (2,14) (2,16) (2,4) (2,17) (2,15) (3,18) (4,9) (4,11) (4,6) (4,5) (4,14) (4,8) (4,19) (4,16) (4,12) (5,11) (5,6) (5,20) (5,8) (5,17) (5,15) (6,9) (6,20) (6,14) (6,8) (6,19) (6,16) (6,12) (6,13) (6,17) (6,15) (8,11) (8,20) (8,14) (8,19) (8,16) (8,12) (8,13) (8,17) (8,15) (9,11) (9,20) (9,14) (9,19) (9,16) (9,13) (9,17) (9,15) (11,20) (11,16) (11,13) (11,17) (11,15) (12,20) (12,14) (12,19) (12,13) (12,17) (12,15) (13,20) (13,14) (13,19) (13,17) (13,15) (14,19) (14,16) (14,17) (15,20) (15,19) (15,17) (16,19) (16,17) (17,19) (19,20)\nIs there a path between node 18 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph683-6_20", + "image": "data/connectivity/graph_visual/medium/graph683.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (1,22) (1,14) (1,5) (1,9) (1,13) (1,16) (1,17) (1,12) (1,19) (1,3) (1,8) (1,10) (1,23) (1,15) (1,18) (1,7) (1,20) (2,21) (2,11) (3,22) (3,14) (3,5) (3,9) (3,13) (3,16) (3,17) (3,12) (3,19) (3,8) (3,10) (3,23) (3,15) (3,18) (3,7) (3,20) (5,22) (5,14) (5,9) (5,13) (5,16) (5,17) (5,12) (5,19) (5,8) (5,10) (5,23) (5,15) (5,18) (5,7) (5,20) (7,22) (7,14) (7,9) (7,13) (7,16) (7,17) (7,12) (7,19) (7,8) (7,10) (7,23) (7,15) (7,18) (7,20) (8,22) (8,14) (8,9) (8,13) (8,16) (8,17) (8,12) (8,19) (8,10) (8,23) (8,15) (8,18) (8,20) (9,22) (9,14) (9,13) (9,16) (9,17) (9,12) (9,19) (9,10) (9,23) (9,15) (9,18) (9,20) (10,22) (10,14) (10,13) (10,16) (10,17) (10,12) (10,19) (10,23) (10,15) (10,18) (10,20) (11,21) (12,22) (12,14) (12,13) (12,16) (12,17) (12,19) (12,23) (12,15) (12,18) (12,20) (13,22) (13,14) (13,16) (13,17) (13,19) (13,23) (13,15) (13,18) (13,20) (14,22) (14,16) (14,17) (14,19) (14,23) (14,15) (14,18) (14,20) (15,22) (15,16) (15,17) (15,19) (15,23) (15,18) (15,20) (16,22) (16,17) (16,19) (16,23) (16,18) (16,20) (17,22) (17,19) (17,23) (17,18) (17,20) (18,22) (18,19) (18,23) (18,20) (19,22) (19,23) (19,20) (20,22) (20,23) (22,23)\nIs there a path between node 6 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph796-12_9", + "image": "data/connectivity/graph_visual/medium/graph796.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,1) (1,16) (1,12) (1,19) (1,21) (4,16) (4,9) (4,17) (4,15) (4,23) (4,21) (6,10) (7,13) (8,23) (8,19) (8,21) (8,18) (8,22) (9,16) (9,24) (9,15) (9,23) (9,12) (9,19) (9,21) (12,15) (15,16) (15,24) (15,23) (15,19) (15,21) (15,18) (16,24) (16,18) (17,23) (18,19) (18,21) (19,23) (21,24) (21,23)\nIs there a path between node 12 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph321-7_19", + "image": "data/connectivity/graph_visual/medium/graph321.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,15) (0,19) (0,18) (0,2) (0,17) (0,16) (0,4) (0,10) (0,14) (0,1) (0,5) (0,7) (0,9) (1,15) (1,19) (1,18) (1,2) (1,17) (1,16) (1,4) (1,10) (1,14) (1,5) (1,7) (1,9) (2,15) (2,19) (2,18) (2,17) (2,16) (2,4) (2,10) (2,14) (2,5) (2,7) (2,9) (3,8) (3,6) (3,13) (4,15) (4,19) (4,18) (4,17) (4,16) (4,10) (4,14) (4,5) (4,7) (4,9) (5,15) (5,19) (5,18) (5,17) (5,16) (5,10) (5,14) (5,7) (5,9) (6,8) (6,13) (7,15) (7,19) (7,18) (7,17) (7,16) (7,10) (7,14) (7,9) (8,13) (9,15) (9,19) (9,18) (9,17) (9,16) (9,10) (9,14) (10,15) (10,19) (10,18) (10,17) (10,16) (10,14) (11,12) (14,15) (14,19) (14,18) (14,17) (14,16) (15,19) (15,18) (15,17) (15,16) (16,19) (16,18) (16,17) (17,19) (17,18) (18,19)\nIs there a path between node 7 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph745-20_0", + "image": "data/connectivity/graph_visual/medium/graph745.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,1) (0,11) (0,2) (1,6) (1,16) (1,2) (2,6) (2,23) (2,19) (3,13) (3,4) (3,17) (3,7) (3,10) (3,24) (4,17) (4,8) (4,24) (5,9) (5,12) (5,17) (5,18) (5,8) (5,10) (6,22) (6,21) (7,14) (7,12) (7,18) (8,14) (8,13) (8,12) (8,17) (8,18) (8,24) (9,14) (9,12) (9,20) (9,10) (9,24) (10,20) (11,15) (11,16) (13,18) (15,22) (15,19) (16,19) (19,22)\nIs there a path between node 20 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph264-17_14", + "image": "data/connectivity/graph_visual/medium/graph264.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,7) (0,18) (0,16) (1,4) (1,2) (1,13) (1,11) (1,7) (2,19) (2,15) (2,3) (2,7) (2,18) (3,19) (3,17) (3,13) (3,14) (3,18) (3,16) (4,17) (4,11) (4,5) (5,17) (5,15) (5,13) (5,14) (5,11) (5,7) (5,18) (5,12) (5,16) (6,10) (7,19) (7,8) (7,14) (7,12) (8,17) (8,13) (8,14) (8,12) (11,18) (11,12) (12,13) (13,19) (13,15) (13,14) (13,18) (15,17) (16,19) (16,18) (17,19) (18,19)\nIs there a path between node 17 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph26-2_10", + "image": "data/connectivity/graph_visual/medium/graph26.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,10) (0,5) (0,8) (0,11) (0,2) (0,6) (0,9) (1,5) (1,8) (1,9) (2,8) (2,3) (2,11) (2,9) (3,5) (3,8) (3,11) (3,6) (3,9) (4,7) (5,10) (5,8) (6,8) (6,9) (8,10) (9,10) (9,11) (10,11)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph565-19_2", + "image": "data/connectivity/graph_visual/medium/graph565.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,21) (0,5) (0,19) (0,7) (1,20) (1,10) (1,11) (1,9) (1,18) (1,12) (1,16) (1,23) (1,3) (1,13) (1,22) (1,6) (1,14) (2,21) (2,5) (2,19) (2,7) (3,20) (3,10) (3,11) (3,9) (3,18) (3,12) (3,16) (3,23) (3,13) (3,22) (3,6) (3,14) (4,17) (4,8) (4,15) (5,21) (5,19) (5,7) (6,20) (6,10) (6,11) (6,9) (6,18) (6,12) (6,16) (6,23) (6,13) (6,22) (6,14) (7,21) (7,19) (8,17) (8,15) (9,20) (9,10) (9,11) (9,18) (9,12) (9,16) (9,23) (9,13) (9,22) (9,14) (10,20) (10,11) (10,18) (10,12) (10,16) (10,23) (10,13) (10,22) (10,14) (11,20) (11,18) (11,12) (11,16) (11,23) (11,13) (11,22) (11,14) (12,20) (12,18) (12,16) (12,23) (12,13) (12,22) (12,14) (13,20) (13,18) (13,16) (13,23) (13,22) (13,14) (14,20) (14,18) (14,16) (14,23) (14,22) (15,17) (16,20) (16,18) (16,23) (16,22) (18,20) (18,23) (18,22) (19,21) (20,23) (20,22) (22,23)\nIs there a path between node 19 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph771-17_12", + "image": "data/connectivity/graph_visual/medium/graph771.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,21) (0,18) (0,10) (0,11) (0,4) (0,24) (0,1) (0,5) (0,12) (0,6) (0,23) (1,7) (1,21) (1,18) (1,10) (1,11) (1,4) (1,24) (1,5) (1,12) (1,6) (1,23) (2,22) (2,17) (2,19) (2,14) (2,3) (2,13) (2,15) (2,9) (2,8) (2,20) (2,16) (3,22) (3,17) (3,19) (3,14) (3,13) (3,15) (3,9) (3,8) (3,20) (3,16) (4,7) (4,21) (4,18) (4,10) (4,11) (4,24) (4,5) (4,12) (4,6) (4,23) (5,7) (5,21) (5,18) (5,10) (5,11) (5,24) (5,12) (5,6) (5,23) (6,7) (6,21) (6,18) (6,10) (6,11) (6,24) (6,12) (6,23) (7,21) (7,18) (7,10) (7,11) (7,24) (7,12) (7,23) (8,22) (8,17) (8,19) (8,14) (8,13) (8,15) (8,9) (8,20) (8,16) (9,22) (9,17) (9,19) (9,14) (9,13) (9,15) (9,20) (9,16) (10,21) (10,18) (10,11) (10,24) (10,12) (10,23) (11,21) (11,18) (11,24) (11,12) (11,23) (12,21) (12,18) (12,24) (12,23) (13,22) (13,17) (13,19) (13,14) (13,15) (13,20) (13,16) (14,22) (14,17) (14,19) (14,15) (14,20) (14,16) (15,22) (15,17) (15,19) (15,20) (15,16) (16,22) (16,17) (16,19) (16,20) (17,22) (17,19) (17,20) (18,21) (18,24) (18,23) (19,22) (19,20) (20,22) (21,24) (21,23) (23,24)\nIs there a path between node 17 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph637-2_3", + "image": "data/connectivity/graph_visual/medium/graph637.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,12) (0,2) (1,13) (1,20) (1,6) (1,8) (1,3) (2,22) (3,10) (3,13) (3,20) (3,15) (3,6) (3,12) (3,14) (4,5) (4,23) (5,16) (5,23) (5,11) (6,12) (6,14) (6,21) (7,22) (7,8) (8,18) (8,22) (8,14) (9,16) (9,23) (9,19) (10,18) (10,15) (10,12) (10,22) (11,16) (12,18) (13,18) (13,14) (14,21) (15,21) (16,19) (17,20) (17,18) (20,22) (21,22)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph595-7_23", + "image": "data/connectivity/graph_visual/medium/graph595.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,5) (0,23) (0,17) (1,16) (1,11) (1,6) (2,7) (2,12) (2,5) (3,11) (3,6) (4,15) (4,19) (4,10) (4,9) (4,21) (4,14) (4,8) (5,12) (5,18) (5,23) (5,17) (6,11) (7,18) (7,17) (8,19) (8,10) (8,21) (8,14) (9,15) (9,19) (9,13) (9,14) (10,15) (10,19) (10,21) (10,14) (11,16) (12,18) (12,23) (12,17) (13,15) (13,21) (13,14) (14,15) (14,19) (14,21) (15,19) (15,21) (17,18) (17,23) (18,23) (19,21)\nIs there a path between node 7 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph458-8_13", + "image": "data/connectivity/graph_visual/medium/graph458.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,7) (0,5) (0,11) (0,3) (0,10) (0,6) (0,18) (0,15) (0,2) (0,13) (0,16) (0,8) (0,20) (1,12) (1,14) (1,21) (1,9) (1,4) (1,17) (2,19) (2,7) (2,5) (2,11) (2,3) (2,10) (2,6) (2,18) (2,15) (2,13) (2,16) (2,8) (2,20) (3,19) (3,7) (3,5) (3,11) (3,10) (3,6) (3,18) (3,15) (3,13) (3,16) (3,8) (3,20) (4,12) (4,14) (4,21) (4,9) (4,17) (5,19) (5,7) (5,11) (5,10) (5,6) (5,18) (5,15) (5,13) (5,16) (5,8) (5,20) (6,19) (6,7) (6,11) (6,10) (6,18) (6,15) (6,13) (6,16) (6,8) (6,20) (7,19) (7,11) (7,10) (7,18) (7,15) (7,13) (7,16) (7,8) (7,20) (8,19) (8,11) (8,10) (8,18) (8,15) (8,13) (8,16) (8,20) (9,12) (9,14) (9,21) (9,17) (10,19) (10,11) (10,18) (10,15) (10,13) (10,16) (10,20) (11,19) (11,18) (11,15) (11,13) (11,16) (11,20) (12,14) (12,21) (12,17) (13,19) (13,18) (13,15) (13,16) (13,20) (14,21) (14,17) (15,19) (15,18) (15,16) (15,20) (16,19) (16,18) (16,20) (17,21) (18,19) (18,20) (19,20)\nIs there a path between node 8 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph261-1_13", + "image": "data/connectivity/graph_visual/medium/graph261.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,2) (0,19) (1,11) (2,4) (2,13) (3,17) (3,10) (3,11) (5,8) (5,13) (6,10) (6,12) (7,18) (7,9) (10,17) (10,12) (11,12) (12,17) (13,16) (13,15) (14,18)\nIs there a path between node 1 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph763-9_6", + "image": "data/connectivity/graph_visual/medium/graph763.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,20) (0,13) (0,24) (0,4) (1,21) (1,3) (1,11) (1,10) (1,23) (1,8) (1,2) (1,22) (1,19) (1,18) (2,21) (2,3) (2,11) (2,10) (2,23) (2,8) (2,22) (2,19) (2,18) (3,21) (3,11) (3,10) (3,23) (3,8) (3,22) (3,19) (3,18) (4,14) (4,20) (4,13) (4,24) (5,7) (5,9) (5,12) (5,16) (5,15) (5,17) (5,6) (6,7) (6,9) (6,12) (6,16) (6,15) (6,17) (7,9) (7,12) (7,16) (7,15) (7,17) (8,21) (8,11) (8,10) (8,23) (8,22) (8,19) (8,18) (9,12) (9,16) (9,15) (9,17) (10,21) (10,11) (10,23) (10,22) (10,19) (10,18) (11,21) (11,23) (11,22) (11,19) (11,18) (12,16) (12,15) (12,17) (13,14) (13,20) (13,24) (14,20) (14,24) (15,16) (15,17) (16,17) (18,21) (18,23) (18,22) (18,19) (19,21) (19,23) (19,22) (20,24) (21,23) (21,22) (22,23)\nIs there a path between node 9 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph30-10_5", + "image": "data/connectivity/graph_visual/medium/graph30.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,5) (0,6) (0,4) (0,9) (0,11) (0,1) (0,7) (1,5) (1,6) (1,4) (1,9) (1,11) (1,7) (2,10) (2,3) (2,8) (3,10) (3,8) (4,5) (4,6) (4,9) (4,11) (4,7) (5,6) (5,9) (5,11) (5,7) (6,9) (6,11) (6,7) (7,9) (7,11) (8,10) (9,11)\nIs there a path between node 10 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph816-5_17", + "image": "data/connectivity/graph_visual/medium/graph816.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,8) (0,1) (0,13) (0,10) (0,22) (0,9) (1,12) (1,8) (1,17) (1,10) (1,5) (1,22) (1,9) (2,18) (2,3) (2,14) (2,6) (2,7) (2,19) (2,24) (2,11) (2,23) (3,16) (3,20) (3,14) (3,6) (3,7) (3,19) (3,4) (3,23) (4,18) (4,14) (4,6) (4,11) (4,23) (5,12) (5,8) (5,21) (5,17) (5,22) (6,18) (6,16) (6,20) (6,14) (6,7) (6,19) (6,24) (6,11) (6,23) (7,18) (7,16) (7,14) (7,19) (7,11) (8,12) (8,21) (8,17) (8,22) (8,9) (9,12) (9,21) (9,13) (9,17) (9,10) (9,22) (10,12) (10,21) (10,13) (10,17) (11,16) (11,20) (11,24) (11,23) (12,21) (12,13) (12,17) (12,22) (13,21) (13,17) (13,22) (14,18) (14,16) (14,19) (14,23) (16,19) (16,23) (17,22) (18,20) (18,24) (18,23) (19,20) (19,24) (19,23) (20,23) (21,22)\nIs there a path between node 5 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph578-15_11", + "image": "data/connectivity/graph_visual/medium/graph578.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,16) (2,17) (2,19) (2,7) (2,15) (2,13) (2,21) (2,11) (2,8) (4,7) (4,14) (4,9) (4,5) (5,19) (5,7) (5,9) (5,20) (6,17) (6,19) (6,22) (6,20) (6,8) (7,17) (7,19) (7,9) (7,11) (7,20) (7,10) (8,14) (8,9) (9,13) (9,11) (9,10) (10,17) (11,19) (11,22) (11,15) (11,13) (11,18) (11,12) (12,17) (12,15) (12,18) (14,19) (14,22) (15,21) (15,18) (17,20) (19,21)\nIs there a path between node 15 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph681-23_8", + "image": "data/connectivity/graph_visual/medium/graph681.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,22) (0,16) (0,2) (0,6) (0,17) (0,20) (0,1) (0,12) (0,8) (0,11) (0,4) (0,18) (0,7) (0,3) (0,23) (0,9) (1,21) (1,22) (1,16) (1,2) (1,6) (1,17) (1,20) (1,12) (1,8) (1,11) (1,4) (1,18) (1,7) (1,3) (1,23) (1,9) (2,21) (2,22) (2,16) (2,6) (2,17) (2,20) (2,12) (2,8) (2,11) (2,4) (2,18) (2,7) (2,3) (2,23) (2,9) (3,21) (3,22) (3,16) (3,6) (3,17) (3,20) (3,12) (3,8) (3,11) (3,4) (3,18) (3,7) (3,23) (3,9) (4,21) (4,22) (4,16) (4,6) (4,17) (4,20) (4,12) (4,8) (4,11) (4,18) (4,7) (4,23) (4,9) (5,13) (6,21) (6,22) (6,16) (6,17) (6,20) (6,12) (6,8) (6,11) (6,18) (6,7) (6,23) (6,9) (7,21) (7,22) (7,16) (7,17) (7,20) (7,12) (7,8) (7,11) (7,18) (7,23) (7,9) (8,21) (8,22) (8,16) (8,17) (8,20) (8,12) (8,11) (8,18) (8,23) (8,9) (9,21) (9,22) (9,16) (9,17) (9,20) (9,12) (9,11) (9,18) (9,23) (10,14) (10,19) (10,15) (11,21) (11,22) (11,16) (11,17) (11,20) (11,12) (11,18) (11,23) (12,21) (12,22) (12,16) (12,17) (12,20) (12,18) (12,23) (14,19) (14,15) (15,19) (16,21) (16,22) (16,17) (16,20) (16,18) (16,23) (17,21) (17,22) (17,20) (17,18) (17,23) (18,21) (18,22) (18,20) (18,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 23 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph77-4_6", + "image": "data/connectivity/graph_visual/medium/graph77.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,11) (0,10) (1,8) (1,9) (2,13) (2,7) (2,12) (3,11) (4,14) (4,5) (6,14) (7,11) (7,12) (8,14)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph110-14_3", + "image": "data/connectivity/graph_visual/medium/graph110.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,12) (0,14) (0,10) (0,3) (0,2) (0,8) (0,15) (0,4) (0,11) (0,13) (0,5) (1,6) (1,9) (1,7) (2,12) (2,14) (2,10) (2,3) (2,8) (2,15) (2,4) (2,11) (2,13) (2,5) (3,12) (3,14) (3,10) (3,8) (3,15) (3,4) (3,11) (3,13) (3,5) (4,12) (4,14) (4,10) (4,8) (4,15) (4,11) (4,13) (4,5) (5,12) (5,14) (5,10) (5,8) (5,15) (5,11) (5,13) (6,9) (6,7) (7,9) (8,12) (8,14) (8,10) (8,15) (8,11) (8,13) (10,12) (10,14) (10,15) (10,11) (10,13) (11,12) (11,14) (11,15) (11,13) (12,14) (12,15) (12,13) (13,14) (13,15) (14,15)\nIs there a path between node 14 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph479-17_19", + "image": "data/connectivity/graph_visual/medium/graph479.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,4) (0,10) (0,12) (0,20) (0,14) (0,8) (0,3) (0,6) (0,5) (0,15) (0,19) (0,7) (0,9) (0,22) (0,2) (0,21) (0,18) (1,4) (1,10) (1,12) (1,20) (1,8) (1,5) (1,15) (1,16) (1,19) (1,7) (1,9) (1,22) (1,2) (1,18) (2,4) (2,10) (2,12) (2,14) (2,3) (2,5) (2,15) (2,19) (2,7) (2,22) (2,21) (2,18) (3,4) (3,12) (3,20) (3,14) (3,6) (3,5) (3,15) (3,16) (3,19) (3,7) (3,9) (3,22) (3,21) (3,18) (4,10) (4,12) (4,8) (4,6) (4,5) (4,15) (4,16) (4,19) (4,7) (4,9) (4,21) (4,18) (5,12) (5,14) (5,8) (5,6) (5,15) (5,16) (5,19) (5,7) (5,9) (5,22) (5,18) (6,10) (6,12) (6,20) (6,14) (6,16) (6,19) (6,7) (6,9) (6,22) (6,21) (6,18) (7,10) (7,12) (7,14) (7,8) (7,16) (7,9) (7,22) (7,21) (7,18) (8,10) (8,12) (8,14) (8,15) (8,16) (8,19) (8,9) (8,21) (9,12) (9,20) (9,15) (9,16) (9,22) (9,21) (9,18) (10,12) (10,20) (10,14) (10,15) (10,16) (10,18) (12,16) (12,19) (13,17) (14,20) (14,16) (15,16) (15,22) (15,21) (16,20) (16,21) (16,18) (18,22) (18,21) (19,20) (19,22) (19,21) (21,22)\nIs there a path between node 17 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph466-4_20", + "image": "data/connectivity/graph_visual/medium/graph466.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,10) (0,14) (0,1) (0,11) (0,17) (0,13) (1,2) (1,10) (1,14) (1,11) (1,17) (1,13) (2,10) (2,14) (2,11) (2,17) (2,13) (3,19) (3,9) (3,12) (3,16) (3,5) (3,7) (3,18) (3,21) (4,15) (4,20) (4,6) (4,8) (5,19) (5,9) (5,12) (5,16) (5,7) (5,18) (5,21) (6,15) (6,20) (6,8) (7,19) (7,9) (7,12) (7,16) (7,18) (7,21) (8,15) (8,20) (9,19) (9,12) (9,16) (9,18) (9,21) (10,14) (10,11) (10,17) (10,13) (11,14) (11,17) (11,13) (12,19) (12,16) (12,18) (12,21) (13,14) (13,17) (14,17) (15,20) (16,19) (16,18) (16,21) (18,19) (18,21) (19,21)\nIs there a path between node 4 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph773-16_18", + "image": "data/connectivity/graph_visual/medium/graph773.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,5) (0,20) (0,13) (0,12) (0,24) (0,18) (0,7) (0,15) (0,6) (0,4) (0,22) (0,2) (0,8) (0,1) (0,23) (0,10) (0,9) (0,3) (0,19) (1,5) (1,20) (1,13) (1,12) (1,24) (1,18) (1,7) (1,15) (1,6) (1,4) (1,22) (1,2) (1,8) (1,23) (1,10) (1,9) (1,3) (1,19) (2,5) (2,20) (2,13) (2,12) (2,24) (2,18) (2,7) (2,15) (2,6) (2,4) (2,22) (2,8) (2,23) (2,10) (2,9) (2,3) (2,19) (3,5) (3,20) (3,13) (3,12) (3,24) (3,18) (3,7) (3,15) (3,6) (3,4) (3,22) (3,8) (3,23) (3,10) (3,9) (3,19) (4,5) (4,20) (4,13) (4,12) (4,24) (4,18) (4,7) (4,15) (4,6) (4,22) (4,8) (4,23) (4,10) (4,9) (4,19) (5,20) (5,13) (5,12) (5,24) (5,18) (5,7) (5,15) (5,6) (5,22) (5,8) (5,23) (5,10) (5,9) (5,19) (6,20) (6,13) (6,12) (6,24) (6,18) (6,7) (6,15) (6,22) (6,8) (6,23) (6,10) (6,9) (6,19) (7,20) (7,13) (7,12) (7,24) (7,18) (7,15) (7,22) (7,8) (7,23) (7,10) (7,9) (7,19) (8,20) (8,13) (8,12) (8,24) (8,18) (8,15) (8,22) (8,23) (8,10) (8,9) (8,19) (9,20) (9,13) (9,12) (9,24) (9,18) (9,15) (9,22) (9,23) (9,10) (9,19) (10,20) (10,13) (10,12) (10,24) (10,18) (10,15) (10,22) (10,23) (10,19) (11,21) (11,17) (11,14) (11,16) (12,20) (12,13) (12,24) (12,18) (12,15) (12,22) (12,23) (12,19) (13,20) (13,24) (13,18) (13,15) (13,22) (13,23) (13,19) (14,21) (14,17) (14,16) (15,20) (15,24) (15,18) (15,22) (15,23) (15,19) (16,21) (16,17) (17,21) (18,20) (18,24) (18,22) (18,23) (18,19) (19,20) (19,24) (19,22) (19,23) (20,24) (20,22) (20,23) (22,24) (22,23) (23,24)\nIs there a path between node 16 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph53-12_6", + "image": "data/connectivity/graph_visual/medium/graph53.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,10) (0,5) (0,7) (0,2) (0,8) (0,4) (0,9) (0,1) (0,12) (0,3) (0,11) (0,13) (1,10) (1,5) (1,7) (1,2) (1,8) (1,4) (1,9) (1,12) (1,3) (1,11) (1,13) (2,10) (2,5) (2,7) (2,8) (2,4) (2,9) (2,12) (2,3) (2,11) (2,13) (3,10) (3,5) (3,7) (3,8) (3,4) (3,9) (3,12) (3,11) (3,13) (4,10) (4,5) (4,7) (4,8) (4,9) (4,12) (4,11) (4,13) (5,10) (5,7) (5,8) (5,9) (5,12) (5,11) (5,13) (7,10) (7,8) (7,9) (7,12) (7,11) (7,13) (8,10) (8,9) (8,12) (8,11) (8,13) (9,10) (9,12) (9,11) (9,13) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nIs there a path between node 12 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph527-16_3", + "image": "data/connectivity/graph_visual/medium/graph527.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,20) (0,4) (0,15) (0,19) (0,8) (0,17) (0,13) (0,3) (0,14) (0,5) (0,2) (0,16) (0,1) (0,10) (1,20) (1,4) (1,15) (1,19) (1,8) (1,17) (1,13) (1,3) (1,14) (1,5) (1,2) (1,16) (1,10) (2,20) (2,4) (2,15) (2,19) (2,8) (2,17) (2,13) (2,3) (2,14) (2,5) (2,16) (2,10) (3,20) (3,4) (3,15) (3,19) (3,8) (3,17) (3,13) (3,14) (3,5) (3,16) (3,10) (4,20) (4,15) (4,19) (4,8) (4,17) (4,13) (4,14) (4,5) (4,16) (4,10) (5,20) (5,15) (5,19) (5,8) (5,17) (5,13) (5,14) (5,16) (5,10) (6,12) (6,22) (6,9) (6,18) (6,21) (6,7) (6,11) (7,12) (7,22) (7,9) (7,18) (7,21) (7,11) (8,20) (8,15) (8,19) (8,17) (8,13) (8,14) (8,16) (8,10) (9,12) (9,22) (9,18) (9,21) (9,11) (10,20) (10,15) (10,19) (10,17) (10,13) (10,14) (10,16) (11,12) (11,22) (11,18) (11,21) (12,22) (12,18) (12,21) (13,20) (13,15) (13,19) (13,17) (13,14) (13,16) (14,20) (14,15) (14,19) (14,17) (14,16) (15,20) (15,19) (15,17) (15,16) (16,20) (16,19) (16,17) (17,20) (17,19) (18,22) (18,21) (19,20) (21,22)\nIs there a path between node 16 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph4-8_1", + "image": "data/connectivity/graph_visual/medium/graph4.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,7) (0,10) (1,8) (2,9) (3,6) (3,4) (5,7) (5,8) (7,8) (7,10)\nIs there a path between node 8 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph357-17_4", + "image": "data/connectivity/graph_visual/medium/graph357.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,12) (1,6) (1,2) (1,14) (1,3) (1,10) (2,6) (2,4) (2,9) (2,14) (2,10) (3,4) (3,13) (3,14) (4,9) (5,19) (5,15) (6,17) (6,9) (6,20) (6,10) (7,17) (7,9) (8,19) (8,18) (10,17) (10,13) (10,14) (12,16) (13,14) (17,20) (18,19)\nIs there a path between node 17 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph27-0_10", + "image": "data/connectivity/graph_visual/medium/graph27.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,2) (0,9) (0,1) (0,11) (0,4) (0,3) (1,6) (1,2) (1,9) (1,8) (1,11) (2,6) (2,8) (2,11) (2,3) (3,6) (3,9) (3,8) (3,10) (3,11) (3,4) (4,6) (4,8) (4,10) (5,7) (6,9) (6,8) (6,10) (6,11) (8,10) (9,11) (10,11)\nIs there a path between node 0 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph538-19_7", + "image": "data/connectivity/graph_visual/medium/graph538.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,4) (0,11) (0,17) (0,18) (0,6) (0,10) (0,7) (0,12) (0,5) (0,21) (0,8) (0,13) (0,9) (0,3) (0,15) (0,14) (0,20) (0,2) (1,19) (1,16) (2,22) (2,4) (2,11) (2,17) (2,18) (2,6) (2,10) (2,7) (2,12) (2,5) (2,21) (2,8) (2,13) (2,9) (2,3) (2,15) (2,14) (2,20) (3,22) (3,4) (3,11) (3,17) (3,18) (3,6) (3,10) (3,7) (3,12) (3,5) (3,21) (3,8) (3,13) (3,9) (3,15) (3,14) (3,20) (4,22) (4,11) (4,17) (4,18) (4,6) (4,10) (4,7) (4,12) (4,5) (4,21) (4,8) (4,13) (4,9) (4,15) (4,14) (4,20) (5,22) (5,11) (5,17) (5,18) (5,6) (5,10) (5,7) (5,12) (5,21) (5,8) (5,13) (5,9) (5,15) (5,14) (5,20) (6,22) (6,11) (6,17) (6,18) (6,10) (6,7) (6,12) (6,21) (6,8) (6,13) (6,9) (6,15) (6,14) (6,20) (7,22) (7,11) (7,17) (7,18) (7,10) (7,12) (7,21) (7,8) (7,13) (7,9) (7,15) (7,14) (7,20) (8,22) (8,11) (8,17) (8,18) (8,10) (8,12) (8,21) (8,13) (8,9) (8,15) (8,14) (8,20) (9,22) (9,11) (9,17) (9,18) (9,10) (9,12) (9,21) (9,13) (9,15) (9,14) (9,20) (10,22) (10,11) (10,17) (10,18) (10,12) (10,21) (10,13) (10,15) (10,14) (10,20) (11,22) (11,17) (11,18) (11,12) (11,21) (11,13) (11,15) (11,14) (11,20) (12,22) (12,17) (12,18) (12,21) (12,13) (12,15) (12,14) (12,20) (13,22) (13,17) (13,18) (13,21) (13,15) (13,14) (13,20) (14,22) (14,17) (14,18) (14,21) (14,15) (14,20) (15,22) (15,17) (15,18) (15,21) (15,20) (16,19) (17,22) (17,18) (17,21) (17,20) (18,22) (18,21) (18,20) (20,22) (20,21) (21,22)\nIs there a path between node 19 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph27-7_10", + "image": "data/connectivity/graph_visual/medium/graph27.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,2) (0,9) (0,1) (0,11) (0,4) (0,3) (1,6) (1,2) (1,9) (1,8) (1,11) (2,6) (2,8) (2,11) (2,3) (3,6) (3,9) (3,8) (3,10) (3,11) (3,4) (4,6) (4,8) (4,10) (5,7) (6,9) (6,8) (6,10) (6,11) (8,10) (9,11) (10,11)\nIs there a path between node 7 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph165-4_6", + "image": "data/connectivity/graph_visual/medium/graph165.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,2) (0,13) (0,11) (0,4) (0,17) (1,14) (1,12) (2,13) (2,10) (2,8) (2,4) (3,13) (3,10) (3,4) (4,5) (4,7) (5,10) (7,16) (9,15) (10,16) (10,13) (11,15) (11,17) (13,16) (13,15) (15,16)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph175-3_4", + "image": "data/connectivity/graph_visual/medium/graph175.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,2) (0,5) (1,13) (1,4) (1,8) (1,17) (1,9) (1,3) (1,6) (1,14) (1,10) (2,7) (2,5) (3,4) (3,8) (3,15) (3,11) (3,6) (3,14) (3,10) (4,13) (4,16) (4,8) (4,17) (4,11) (4,9) (4,6) (4,10) (5,7) (5,12) (6,15) (6,17) (6,11) (6,9) (6,14) (6,10) (8,13) (8,16) (8,15) (8,17) (8,9) (8,14) (8,10) (9,13) (9,15) (9,17) (9,11) (9,14) (9,10) (10,15) (10,17) (10,11) (10,14) (11,13) (11,16) (11,15) (11,14) (13,16) (13,15) (14,16) (14,15) (14,17) (15,16)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph438-20_0", + "image": "data/connectivity/graph_visual/medium/graph438.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,10) (0,5) (0,20) (0,7) (0,19) (0,1) (0,14) (0,12) (0,15) (0,18) (0,4) (1,10) (1,5) (1,7) (1,2) (1,14) (1,12) (1,3) (1,15) (1,16) (1,4) (2,10) (2,5) (2,20) (2,7) (2,19) (2,14) (2,12) (2,15) (2,16) (2,17) (2,18) (2,4) (3,5) (3,20) (3,7) (3,19) (3,14) (3,16) (3,17) (3,18) (4,10) (4,5) (4,20) (4,7) (4,19) (4,14) (4,12) (4,15) (4,16) (4,17) (5,20) (5,7) (5,19) (5,14) (5,12) (5,16) (5,17) (5,18) (6,11) (6,8) (7,10) (7,19) (7,14) (7,12) (7,15) (7,16) (7,17) (7,18) (8,11) (9,21) (9,13) (10,19) (10,14) (10,12) (10,16) (10,18) (12,20) (12,19) (12,14) (12,15) (12,16) (12,17) (14,20) (14,19) (14,15) (14,16) (14,17) (15,20) (15,19) (15,16) (15,17) (15,18) (16,20) (16,19) (16,17) (16,18) (17,20) (17,19) (17,18) (18,19) (19,20)\nIs there a path between node 20 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph28-6_7", + "image": "data/connectivity/graph_visual/medium/graph28.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,1) (0,4) (0,3) (0,6) (0,2) (0,8) (0,5) (0,11) (1,4) (1,3) (1,6) (1,2) (1,8) (1,5) (1,11) (2,4) (2,3) (2,6) (2,8) (2,5) (2,11) (3,4) (3,6) (3,8) (3,5) (3,11) (4,6) (4,8) (4,5) (4,11) (5,6) (5,8) (5,11) (6,8) (6,11) (7,9) (7,10) (8,11) (9,10)\nIs there a path between node 6 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph724-3_24", + "image": "data/connectivity/graph_visual/medium/graph724.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,10) (0,23) (0,13) (0,12) (0,18) (0,8) (0,4) (0,11) (0,9) (0,20) (0,5) (0,14) (0,24) (0,21) (0,1) (0,16) (0,2) (0,7) (0,22) (0,19) (1,15) (1,10) (1,23) (1,13) (1,12) (1,18) (1,8) (1,4) (1,11) (1,9) (1,20) (1,5) (1,14) (1,24) (1,21) (1,16) (1,2) (1,7) (1,22) (1,19) (2,15) (2,10) (2,23) (2,13) (2,12) (2,18) (2,8) (2,4) (2,11) (2,9) (2,20) (2,5) (2,14) (2,24) (2,21) (2,16) (2,7) (2,22) (2,19) (3,17) (3,6) (4,15) (4,10) (4,23) (4,13) (4,12) (4,18) (4,8) (4,11) (4,9) (4,20) (4,5) (4,14) (4,24) (4,21) (4,16) (4,7) (4,22) (4,19) (5,15) (5,10) (5,23) (5,13) (5,12) (5,18) (5,8) (5,11) (5,9) (5,20) (5,14) (5,24) (5,21) (5,16) (5,7) (5,22) (5,19) (6,17) (7,15) (7,10) (7,23) (7,13) (7,12) (7,18) (7,8) (7,11) (7,9) (7,20) (7,14) (7,24) (7,21) (7,16) (7,22) (7,19) (8,15) (8,10) (8,23) (8,13) (8,12) (8,18) (8,11) (8,9) (8,20) (8,14) (8,24) (8,21) (8,16) (8,22) (8,19) (9,15) (9,10) (9,23) (9,13) (9,12) (9,18) (9,11) (9,20) (9,14) (9,24) (9,21) (9,16) (9,22) (9,19) (10,15) (10,23) (10,13) (10,12) (10,18) (10,11) (10,20) (10,14) (10,24) (10,21) (10,16) (10,22) (10,19) (11,15) (11,23) (11,13) (11,12) (11,18) (11,20) (11,14) (11,24) (11,21) (11,16) (11,22) (11,19) (12,15) (12,23) (12,13) (12,18) (12,20) (12,14) (12,24) (12,21) (12,16) (12,22) (12,19) (13,15) (13,23) (13,18) (13,20) (13,14) (13,24) (13,21) (13,16) (13,22) (13,19) (14,15) (14,23) (14,18) (14,20) (14,24) (14,21) (14,16) (14,22) (14,19) (15,23) (15,18) (15,20) (15,24) (15,21) (15,16) (15,22) (15,19) (16,23) (16,18) (16,20) (16,24) (16,21) (16,22) (16,19) (18,23) (18,20) (18,24) (18,21) (18,22) (18,19) (19,23) (19,20) (19,24) (19,21) (19,22) (20,23) (20,24) (20,21) (20,22) (21,23) (21,24) (21,22) (22,23) (22,24) (23,24)\nIs there a path between node 3 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph311-10_0", + "image": "data/connectivity/graph_visual/medium/graph311.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,19) (0,16) (0,18) (0,2) (0,17) (0,7) (0,12) (1,8) (1,3) (1,10) (1,13) (1,6) (1,11) (1,15) (1,5) (1,4) (1,14) (2,9) (2,19) (2,16) (2,18) (2,17) (2,7) (2,12) (3,8) (3,10) (3,13) (3,6) (3,11) (3,15) (3,5) (3,4) (3,14) (4,8) (4,10) (4,13) (4,6) (4,11) (4,15) (4,5) (4,14) (5,8) (5,10) (5,13) (5,6) (5,11) (5,15) (5,14) (6,8) (6,10) (6,13) (6,11) (6,15) (6,14) (7,9) (7,19) (7,16) (7,18) (7,17) (7,12) (8,10) (8,13) (8,11) (8,15) (8,14) (9,19) (9,16) (9,18) (9,17) (9,12) (10,13) (10,11) (10,15) (10,14) (11,13) (11,15) (11,14) (12,19) (12,16) (12,18) (12,17) (13,15) (13,14) (14,15) (16,19) (16,18) (16,17) (17,19) (17,18) (18,19)\nIs there a path between node 10 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph422-6_17", + "image": "data/connectivity/graph_visual/medium/graph422.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,20) (0,18) (0,4) (0,8) (0,1) (0,17) (0,15) (0,11) (0,21) (0,9) (0,12) (0,14) (0,3) (1,19) (1,20) (1,18) (1,4) (1,8) (1,17) (1,15) (1,11) (1,21) (1,9) (1,12) (1,14) (1,3) (2,5) (2,7) (2,13) (2,6) (2,10) (2,16) (3,19) (3,20) (3,18) (3,4) (3,8) (3,17) (3,15) (3,11) (3,21) (3,9) (3,12) (3,14) (4,19) (4,20) (4,18) (4,8) (4,17) (4,15) (4,11) (4,21) (4,9) (4,12) (4,14) (5,7) (5,13) (5,6) (5,10) (5,16) (6,7) (6,13) (6,10) (6,16) (7,13) (7,10) (7,16) (8,19) (8,20) (8,18) (8,17) (8,15) (8,11) (8,21) (8,9) (8,12) (8,14) (9,19) (9,20) (9,18) (9,17) (9,15) (9,11) (9,21) (9,12) (9,14) (10,13) (10,16) (11,19) (11,20) (11,18) (11,17) (11,15) (11,21) (11,12) (11,14) (12,19) (12,20) (12,18) (12,17) (12,15) (12,21) (12,14) (13,16) (14,19) (14,20) (14,18) (14,17) (14,15) (14,21) (15,19) (15,20) (15,18) (15,17) (15,21) (17,19) (17,20) (17,18) (17,21) (18,19) (18,20) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 6 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph193-15_6", + "image": "data/connectivity/graph_visual/medium/graph193.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,5) (0,7) (0,14) (0,2) (0,16) (0,13) (0,3) (0,12) (0,4) (1,9) (1,15) (1,6) (1,10) (1,17) (2,5) (2,7) (2,14) (2,16) (2,13) (2,3) (2,12) (2,4) (3,5) (3,7) (3,14) (3,16) (3,13) (3,12) (3,4) (4,5) (4,7) (4,14) (4,16) (4,13) (4,12) (5,7) (5,14) (5,16) (5,13) (5,12) (6,9) (6,15) (6,10) (6,17) (7,14) (7,16) (7,13) (7,12) (8,11) (9,15) (9,10) (9,17) (10,15) (10,17) (12,14) (12,16) (12,13) (13,14) (13,16) (14,16) (15,17)\nIs there a path between node 15 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph431-14_4", + "image": "data/connectivity/graph_visual/medium/graph431.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,16) (0,3) (0,5) (0,19) (1,21) (2,21) (2,10) (2,19) (3,4) (3,19) (4,15) (4,10) (4,19) (5,16) (6,8) (8,13) (10,17) (11,13) (14,20) (15,17) (16,17) (17,19)\nIs there a path between node 14 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph703-12_4", + "image": "data/connectivity/graph_visual/medium/graph703.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,13) (0,17) (0,11) (0,16) (0,14) (0,8) (1,3) (1,20) (2,3) (2,20) (2,21) (3,23) (3,20) (3,18) (6,13) (6,22) (6,14) (6,9) (7,17) (7,22) (7,14) (7,24) (7,9) (8,13) (8,17) (8,22) (8,16) (8,14) (8,24) (9,15) (9,17) (9,11) (9,19) (9,10) (9,24) (9,12) (10,15) (10,17) (10,11) (11,15) (11,22) (12,22) (12,24) (13,15) (13,22) (13,16) (13,24) (14,15) (14,19) (15,24) (16,22) (16,24) (18,20) (18,21) (21,23) (22,24)\nIs there a path between node 12 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph379-18_14", + "image": "data/connectivity/graph_visual/medium/graph379.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,10) (1,4) (1,12) (1,15) (1,7) (1,17) (1,16) (2,18) (3,19) (3,14) (4,12) (4,13) (4,11) (4,15) (4,7) (4,17) (4,16) (4,20) (5,12) (5,13) (5,11) (5,15) (5,7) (5,9) (5,16) (6,12) (6,13) (6,11) (6,15) (6,7) (6,17) (6,16) (6,20) (7,12) (7,13) (7,11) (7,16) (7,20) (8,19) (9,12) (9,13) (9,15) (9,16) (9,20) (10,18) (11,12) (11,13) (11,17) (11,16) (11,20) (12,17) (12,16) (12,20) (13,15) (13,17) (13,16) (13,20) (14,19) (15,17) (15,16) (16,17) (16,20) (17,20)\nIs there a path between node 18 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph57-3_2", + "image": "data/connectivity/graph_visual/medium/graph57.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,5) (1,6) (1,8) (1,13) (3,9) (5,6) (5,11) (5,13) (5,10) (6,11) (6,12) (6,13) (7,12) (10,12) (11,12)\nIs there a path between node 3 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph645-14_6", + "image": "data/connectivity/graph_visual/medium/graph645.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,5) (4,19) (4,5) (6,23) (8,9) (8,20) (8,23) (8,22) (8,13) (8,10) (9,15) (9,20) (9,23) (9,22) (9,13) (9,11) (10,23) (10,22) (10,12) (10,11) (10,14) (11,23) (12,15) (12,20) (12,23) (12,16) (13,15) (13,23) (14,18) (14,16) (15,21) (15,22) (15,16) (16,20) (16,21) (20,22) (21,23) (21,22)\nIs there a path between node 14 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph152-9_0", + "image": "data/connectivity/graph_visual/medium/graph152.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,11) (1,13) (1,16) (1,8) (1,5) (1,4) (1,9) (1,3) (1,15) (1,17) (1,7) (1,6) (1,14) (1,2) (2,13) (2,16) (2,8) (2,5) (2,4) (2,9) (2,3) (2,15) (2,17) (2,7) (2,6) (2,14) (3,13) (3,16) (3,8) (3,5) (3,4) (3,9) (3,15) (3,17) (3,7) (3,6) (3,14) (4,13) (4,16) (4,8) (4,5) (4,9) (4,15) (4,17) (4,7) (4,6) (4,14) (5,13) (5,16) (5,8) (5,9) (5,15) (5,17) (5,7) (5,6) (5,14) (6,13) (6,16) (6,8) (6,9) (6,15) (6,17) (6,7) (6,14) (7,13) (7,16) (7,8) (7,9) (7,15) (7,17) (7,14) (8,13) (8,16) (8,9) (8,15) (8,17) (8,14) (9,13) (9,16) (9,15) (9,17) (9,14) (11,12) (13,16) (13,15) (13,17) (13,14) (14,16) (14,15) (14,17) (15,16) (15,17) (16,17)\nIs there a path between node 9 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph632-8_12", + "image": "data/connectivity/graph_visual/medium/graph632.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,10) (0,1) (0,14) (0,16) (0,4) (1,10) (1,20) (1,4) (2,3) (3,13) (3,21) (3,17) (3,4) (4,20) (4,17) (5,20) (5,15) (6,21) (6,8) (6,15) (6,11) (6,17) (7,13) (7,21) (7,8) (7,15) (7,12) (8,23) (8,9) (8,20) (8,15) (9,13) (9,10) (9,20) (9,14) (10,20) (10,11) (11,15) (11,12) (11,16) (12,23) (12,14) (12,17) (13,20) (15,21) (16,21) (16,17) (17,23) (17,21)\nIs there a path between node 8 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph616-22_21", + "image": "data/connectivity/graph_visual/medium/graph616.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,9) (0,12) (0,4) (0,11) (0,14) (0,3) (0,17) (0,22) (0,2) (0,19) (0,15) (0,20) (0,1) (0,16) (0,13) (0,7) (1,5) (1,9) (1,12) (1,4) (1,11) (1,14) (1,3) (1,17) (1,22) (1,2) (1,19) (1,15) (1,20) (1,16) (1,13) (1,7) (2,5) (2,9) (2,12) (2,4) (2,11) (2,14) (2,3) (2,17) (2,22) (2,19) (2,15) (2,20) (2,16) (2,13) (2,7) (3,5) (3,9) (3,12) (3,4) (3,11) (3,14) (3,17) (3,22) (3,19) (3,15) (3,20) (3,16) (3,13) (3,7) (4,5) (4,9) (4,12) (4,11) (4,14) (4,17) (4,22) (4,19) (4,15) (4,20) (4,16) (4,13) (4,7) (5,9) (5,12) (5,11) (5,14) (5,17) (5,22) (5,19) (5,15) (5,20) (5,16) (5,13) (5,7) (6,18) (6,21) (6,8) (6,10) (6,23) (7,9) (7,12) (7,11) (7,14) (7,17) (7,22) (7,19) (7,15) (7,20) (7,16) (7,13) (8,18) (8,21) (8,10) (8,23) (9,12) (9,11) (9,14) (9,17) (9,22) (9,19) (9,15) (9,20) (9,16) (9,13) (10,18) (10,21) (10,23) (11,12) (11,14) (11,17) (11,22) (11,19) (11,15) (11,20) (11,16) (11,13) (12,14) (12,17) (12,22) (12,19) (12,15) (12,20) (12,16) (12,13) (13,14) (13,17) (13,22) (13,19) (13,15) (13,20) (13,16) (14,17) (14,22) (14,19) (14,15) (14,20) (14,16) (15,17) (15,22) (15,19) (15,20) (15,16) (16,17) (16,22) (16,19) (16,20) (17,22) (17,19) (17,20) (18,21) (18,23) (19,22) (19,20) (20,22) (21,23)\nIs there a path between node 22 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph188-10_0", + "image": "data/connectivity/graph_visual/medium/graph188.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,11) (0,1) (0,9) (0,17) (0,3) (0,14) (0,15) (0,4) (0,10) (0,2) (0,6) (1,16) (1,11) (1,9) (1,17) (1,3) (1,14) (1,15) (1,4) (1,10) (1,2) (1,6) (2,16) (2,11) (2,9) (2,17) (2,3) (2,14) (2,15) (2,4) (2,10) (2,6) (3,16) (3,11) (3,9) (3,17) (3,14) (3,15) (3,4) (3,10) (3,6) (4,16) (4,11) (4,9) (4,17) (4,14) (4,15) (4,10) (4,6) (5,8) (5,12) (5,7) (5,13) (6,16) (6,11) (6,9) (6,17) (6,14) (6,15) (6,10) (7,8) (7,12) (7,13) (8,12) (8,13) (9,16) (9,11) (9,17) (9,14) (9,15) (9,10) (10,16) (10,11) (10,17) (10,14) (10,15) (11,16) (11,17) (11,14) (11,15) (12,13) (14,16) (14,17) (14,15) (15,16) (15,17) (16,17)\nIs there a path between node 10 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph649-18_2", + "image": "data/connectivity/graph_visual/medium/graph649.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (1,5) (1,18) (1,7) (1,22) (1,11) (1,20) (1,4) (1,23) (2,14) (2,10) (2,21) (2,15) (2,16) (2,3) (3,14) (3,10) (3,15) (3,16) (3,6) (3,19) (4,18) (4,7) (4,22) (4,11) (4,20) (4,23) (5,13) (5,7) (5,22) (5,11) (5,20) (5,23) (6,10) (6,21) (6,15) (6,16) (6,9) (6,8) (6,19) (7,13) (7,22) (7,20) (7,23) (8,10) (8,9) (8,19) (9,21) (9,15) (9,19) (10,21) (10,16) (10,19) (11,18) (11,13) (11,22) (11,23) (12,17) (13,22) (13,20) (14,15) (14,16) (14,19) (15,16) (15,19) (16,21) (16,19) (18,20) (18,23) (19,21) (20,22) (20,23) (22,23)\nIs there a path between node 18 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph557-0_4", + "image": "data/connectivity/graph_visual/medium/graph557.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,2) (0,18) (0,23) (0,21) (0,13) (0,16) (0,15) (0,22) (0,6) (0,14) (1,17) (1,11) (1,10) (1,4) (1,19) (1,9) (2,8) (2,18) (2,23) (2,21) (2,22) (2,14) (2,20) (3,17) (3,11) (3,10) (3,4) (3,19) (3,9) (4,7) (4,10) (4,9) (5,8) (5,21) (5,13) (5,16) (5,15) (5,22) (5,6) (5,14) (5,20) (6,8) (6,18) (6,13) (6,15) (6,14) (6,20) (7,17) (7,10) (7,19) (7,9) (8,18) (8,23) (8,21) (8,13) (8,16) (8,14) (8,20) (9,17) (9,10) (9,19) (10,17) (10,19) (11,19) (13,18) (13,23) (13,21) (13,16) (13,22) (13,14) (13,20) (14,18) (14,23) (14,21) (14,16) (14,22) (14,20) (15,18) (15,21) (15,22) (16,23) (16,21) (17,19) (18,22) (20,23) (20,21) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph850-9_19", + "image": "data/connectivity/graph_visual/medium/graph850.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,4) (0,11) (0,16) (0,5) (0,2) (0,22) (0,15) (0,8) (0,21) (0,7) (0,9) (0,23) (0,12) (0,3) (0,14) (0,20) (1,19) (1,18) (1,24) (1,17) (1,13) (1,10) (2,6) (2,4) (2,11) (2,16) (2,5) (2,22) (2,15) (2,8) (2,21) (2,7) (2,9) (2,23) (2,12) (2,3) (2,14) (2,20) (3,6) (3,4) (3,11) (3,16) (3,5) (3,22) (3,15) (3,8) (3,21) (3,7) (3,9) (3,23) (3,12) (3,14) (3,20) (4,6) (4,11) (4,16) (4,5) (4,22) (4,15) (4,8) (4,21) (4,7) (4,9) (4,23) (4,12) (4,14) (4,20) (5,6) (5,11) (5,16) (5,22) (5,15) (5,8) (5,21) (5,7) (5,9) (5,23) (5,12) (5,14) (5,20) (6,11) (6,16) (6,22) (6,15) (6,8) (6,21) (6,7) (6,9) (6,23) (6,12) (6,14) (6,20) (7,11) (7,16) (7,22) (7,15) (7,8) (7,21) (7,9) (7,23) (7,12) (7,14) (7,20) (8,11) (8,16) (8,22) (8,15) (8,21) (8,9) (8,23) (8,12) (8,14) (8,20) (9,11) (9,16) (9,22) (9,15) (9,21) (9,23) (9,12) (9,14) (9,20) (10,19) (10,18) (10,24) (10,17) (10,13) (11,16) (11,22) (11,15) (11,21) (11,23) (11,12) (11,14) (11,20) (12,16) (12,22) (12,15) (12,21) (12,23) (12,14) (12,20) (13,19) (13,18) (13,24) (13,17) (14,16) (14,22) (14,15) (14,21) (14,23) (14,20) (15,16) (15,22) (15,21) (15,23) (15,20) (16,22) (16,21) (16,23) (16,20) (17,19) (17,18) (17,24) (18,19) (18,24) (19,24) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 9 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph391-17_14", + "image": "data/connectivity/graph_visual/medium/graph391.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,9) (0,20) (0,8) (0,14) (0,2) (0,11) (0,1) (0,10) (0,7) (0,12) (0,4) (0,5) (0,15) (0,16) (1,18) (1,9) (1,20) (1,8) (1,14) (1,2) (1,11) (1,10) (1,7) (1,12) (1,4) (1,5) (1,15) (1,16) (2,18) (2,9) (2,20) (2,8) (2,14) (2,11) (2,10) (2,7) (2,12) (2,4) (2,5) (2,15) (2,16) (3,13) (3,19) (4,18) (4,9) (4,20) (4,8) (4,14) (4,11) (4,10) (4,7) (4,12) (4,5) (4,15) (4,16) (5,18) (5,9) (5,20) (5,8) (5,14) (5,11) (5,10) (5,7) (5,12) (5,15) (5,16) (6,17) (7,18) (7,9) (7,20) (7,8) (7,14) (7,11) (7,10) (7,12) (7,15) (7,16) (8,18) (8,9) (8,20) (8,14) (8,11) (8,10) (8,12) (8,15) (8,16) (9,18) (9,20) (9,14) (9,11) (9,10) (9,12) (9,15) (9,16) (10,18) (10,20) (10,14) (10,11) (10,12) (10,15) (10,16) (11,18) (11,20) (11,14) (11,12) (11,15) (11,16) (12,18) (12,20) (12,14) (12,15) (12,16) (13,19) (14,18) (14,20) (14,15) (14,16) (15,18) (15,20) (15,16) (16,18) (16,20) (18,20)\nIs there a path between node 17 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph700-16_13", + "image": "data/connectivity/graph_visual/medium/graph700.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,22) (0,6) (0,11) (0,10) (0,4) (0,5) (0,9) (0,1) (0,13) (0,21) (0,20) (0,12) (1,22) (1,11) (1,10) (1,5) (1,16) (1,9) (1,13) (1,21) (1,20) (2,8) (2,19) (2,3) (2,18) (2,24) (3,19) (3,17) (3,24) (3,23) (4,22) (4,6) (4,16) (4,9) (4,21) (4,20) (5,22) (5,6) (5,14) (5,11) (5,16) (5,15) (5,9) (5,13) (5,21) (5,20) (6,22) (6,11) (6,10) (6,16) (6,13) (6,21) (6,12) (7,8) (7,17) (7,18) (7,24) (7,23) (8,17) (8,24) (9,14) (9,11) (9,10) (9,16) (9,15) (9,21) (9,20) (9,12) (10,22) (10,14) (10,11) (10,16) (10,15) (10,21) (10,20) (11,22) (11,16) (11,15) (11,20) (12,22) (12,14) (12,15) (12,13) (12,21) (12,20) (13,14) (13,16) (13,15) (13,21) (13,20) (14,22) (14,16) (14,15) (14,21) (15,16) (15,21) (16,22) (16,21) (16,20) (17,19) (17,18) (17,24) (17,23) (18,23) (19,24) (23,24)\nIs there a path between node 16 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph250-1_2", + "image": "data/connectivity/graph_visual/medium/graph250.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,15) (0,1) (0,9) (0,7) (0,18) (0,3) (0,13) (0,14) (0,11) (0,6) (0,17) (0,10) (0,2) (0,12) (1,15) (1,9) (1,7) (1,18) (1,3) (1,13) (1,14) (1,11) (1,6) (1,17) (1,10) (1,2) (1,12) (2,15) (2,9) (2,7) (2,18) (2,3) (2,13) (2,14) (2,11) (2,6) (2,17) (2,10) (2,12) (3,15) (3,9) (3,7) (3,18) (3,13) (3,14) (3,11) (3,6) (3,17) (3,10) (3,12) (4,16) (4,5) (4,8) (5,16) (5,8) (6,15) (6,9) (6,7) (6,18) (6,13) (6,14) (6,11) (6,17) (6,10) (6,12) (7,15) (7,9) (7,18) (7,13) (7,14) (7,11) (7,17) (7,10) (7,12) (8,16) (9,15) (9,18) (9,13) (9,14) (9,11) (9,17) (9,10) (9,12) (10,15) (10,18) (10,13) (10,14) (10,11) (10,17) (10,12) (11,15) (11,18) (11,13) (11,14) (11,17) (11,12) (12,15) (12,18) (12,13) (12,14) (12,17) (13,15) (13,18) (13,14) (13,17) (14,15) (14,18) (14,17) (15,18) (15,17) (17,18)\nIs there a path between node 1 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph759-12_13", + "image": "data/connectivity/graph_visual/medium/graph759.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,4) (0,17) (0,13) (0,21) (0,2) (0,1) (0,24) (0,10) (0,5) (0,14) (0,12) (0,19) (1,4) (1,24) (1,5) (1,18) (1,14) (1,12) (1,19) (1,15) (2,17) (2,13) (2,21) (2,8) (2,14) (2,19) (2,15) (3,11) (3,20) (3,9) (3,6) (3,22) (3,16) (4,17) (4,13) (4,21) (4,24) (4,8) (4,10) (4,5) (4,18) (4,14) (4,12) (4,19) (4,15) (5,17) (5,13) (5,21) (5,8) (5,10) (5,14) (5,12) (5,19) (5,15) (6,11) (6,20) (6,22) (6,7) (6,23) (7,11) (7,9) (7,22) (7,16) (7,23) (8,17) (8,13) (8,18) (8,14) (8,12) (8,19) (8,15) (9,11) (9,20) (9,16) (9,23) (10,13) (10,21) (10,24) (10,18) (10,15) (11,22) (11,16) (12,17) (12,21) (12,24) (12,14) (12,19) (12,15) (13,21) (13,24) (13,18) (13,14) (13,19) (13,15) (14,17) (14,21) (14,24) (14,18) (14,19) (14,15) (15,21) (15,24) (15,18) (15,19) (16,20) (16,23) (17,21) (17,19) (18,21) (18,24) (18,19) (19,21) (19,24) (20,22) (20,23) (22,23)\nIs there a path between node 12 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph538-16_13", + "image": "data/connectivity/graph_visual/medium/graph538.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,4) (0,11) (0,17) (0,18) (0,6) (0,10) (0,7) (0,12) (0,5) (0,21) (0,8) (0,13) (0,9) (0,3) (0,15) (0,14) (0,20) (0,2) (1,19) (1,16) (2,22) (2,4) (2,11) (2,17) (2,18) (2,6) (2,10) (2,7) (2,12) (2,5) (2,21) (2,8) (2,13) (2,9) (2,3) (2,15) (2,14) (2,20) (3,22) (3,4) (3,11) (3,17) (3,18) (3,6) (3,10) (3,7) (3,12) (3,5) (3,21) (3,8) (3,13) (3,9) (3,15) (3,14) (3,20) (4,22) (4,11) (4,17) (4,18) (4,6) (4,10) (4,7) (4,12) (4,5) (4,21) (4,8) (4,13) (4,9) (4,15) (4,14) (4,20) (5,22) (5,11) (5,17) (5,18) (5,6) (5,10) (5,7) (5,12) (5,21) (5,8) (5,13) (5,9) (5,15) (5,14) (5,20) (6,22) (6,11) (6,17) (6,18) (6,10) (6,7) (6,12) (6,21) (6,8) (6,13) (6,9) (6,15) (6,14) (6,20) (7,22) (7,11) (7,17) (7,18) (7,10) (7,12) (7,21) (7,8) (7,13) (7,9) (7,15) (7,14) (7,20) (8,22) (8,11) (8,17) (8,18) (8,10) (8,12) (8,21) (8,13) (8,9) (8,15) (8,14) (8,20) (9,22) (9,11) (9,17) (9,18) (9,10) (9,12) (9,21) (9,13) (9,15) (9,14) (9,20) (10,22) (10,11) (10,17) (10,18) (10,12) (10,21) (10,13) (10,15) (10,14) (10,20) (11,22) (11,17) (11,18) (11,12) (11,21) (11,13) (11,15) (11,14) (11,20) (12,22) (12,17) (12,18) (12,21) (12,13) (12,15) (12,14) (12,20) (13,22) (13,17) (13,18) (13,21) (13,15) (13,14) (13,20) (14,22) (14,17) (14,18) (14,21) (14,15) (14,20) (15,22) (15,17) (15,18) (15,21) (15,20) (16,19) (17,22) (17,18) (17,21) (17,20) (18,22) (18,21) (18,20) (20,22) (20,21) (21,22)\nIs there a path between node 16 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph336-0_6", + "image": "data/connectivity/graph_visual/medium/graph336.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,10) (0,3) (0,13) (0,7) (0,1) (0,9) (0,17) (0,15) (0,14) (0,18) (0,6) (0,12) (1,10) (1,7) (1,20) (1,11) (1,9) (1,15) (1,14) (1,18) (1,4) (1,12) (2,19) (3,16) (3,13) (3,7) (3,11) (3,17) (3,15) (3,18) (3,6) (4,16) (4,10) (4,13) (4,7) (4,20) (4,11) (4,9) (4,17) (4,14) (4,18) (4,6) (4,12) (5,8) (5,19) (6,16) (6,10) (6,13) (6,20) (6,9) (6,18) (6,12) (7,16) (7,10) (7,13) (7,20) (7,11) (7,9) (7,17) (7,15) (7,14) (7,18) (7,12) (8,19) (9,10) (9,13) (9,11) (9,17) (9,15) (9,14) (10,20) (10,17) (10,14) (11,16) (11,20) (11,17) (11,18) (12,15) (12,14) (13,16) (13,17) (13,14) (13,18) (14,16) (14,20) (14,17) (14,15) (14,18) (15,16) (15,20) (15,18) (16,20) (16,17) (16,18) (17,20) (17,18) (18,20)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph609-5_13", + "image": "data/connectivity/graph_visual/medium/graph609.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,4) (0,2) (0,20) (0,6) (0,1) (0,15) (0,17) (0,11) (0,12) (0,21) (0,7) (0,14) (0,9) (0,10) (0,22) (0,23) (1,3) (1,4) (1,2) (1,20) (1,6) (1,15) (1,17) (1,11) (1,12) (1,21) (1,7) (1,14) (1,9) (1,10) (1,22) (1,23) (2,3) (2,4) (2,20) (2,6) (2,15) (2,17) (2,11) (2,12) (2,21) (2,7) (2,14) (2,9) (2,10) (2,22) (2,23) (3,4) (3,20) (3,6) (3,15) (3,17) (3,11) (3,12) (3,21) (3,7) (3,14) (3,9) (3,10) (3,22) (3,23) (4,20) (4,6) (4,15) (4,17) (4,11) (4,12) (4,21) (4,7) (4,14) (4,9) (4,10) (4,22) (4,23) (5,18) (6,20) (6,15) (6,17) (6,11) (6,12) (6,21) (6,7) (6,14) (6,9) (6,10) (6,22) (6,23) (7,20) (7,15) (7,17) (7,11) (7,12) (7,21) (7,14) (7,9) (7,10) (7,22) (7,23) (8,16) (8,19) (8,13) (9,20) (9,15) (9,17) (9,11) (9,12) (9,21) (9,14) (9,10) (9,22) (9,23) (10,20) (10,15) (10,17) (10,11) (10,12) (10,21) (10,14) (10,22) (10,23) (11,20) (11,15) (11,17) (11,12) (11,21) (11,14) (11,22) (11,23) (12,20) (12,15) (12,17) (12,21) (12,14) (12,22) (12,23) (13,16) (13,19) (14,20) (14,15) (14,17) (14,21) (14,22) (14,23) (15,20) (15,17) (15,21) (15,22) (15,23) (16,19) (17,20) (17,21) (17,22) (17,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 5 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph516-11_3", + "image": "data/connectivity/graph_visual/medium/graph516.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,2) (0,11) (0,3) (0,19) (0,9) (0,1) (0,22) (0,13) (0,20) (0,4) (0,7) (0,10) (0,6) (0,14) (1,2) (1,11) (1,19) (1,18) (1,9) (1,21) (1,22) (1,13) (1,4) (1,7) (1,17) (1,14) (2,3) (2,19) (2,9) (2,21) (2,13) (2,12) (2,20) (2,4) (2,10) (2,17) (2,14) (3,11) (3,19) (3,18) (3,9) (3,21) (3,22) (3,13) (3,7) (3,10) (3,17) (3,6) (3,14) (4,19) (4,18) (4,9) (4,13) (4,12) (4,20) (4,7) (4,10) (4,14) (5,8) (5,15) (6,19) (6,18) (6,9) (6,21) (6,22) (6,13) (6,12) (6,20) (6,7) (7,11) (7,18) (7,9) (7,21) (7,22) (7,12) (7,10) (7,17) (7,14) (8,16) (8,15) (9,11) (9,19) (9,18) (9,21) (9,20) (9,10) (9,17) (9,14) (10,11) (10,21) (10,22) (10,13) (10,12) (10,20) (10,17) (10,14) (11,19) (11,18) (11,21) (11,22) (11,13) (11,12) (11,20) (11,17) (11,14) (12,18) (12,21) (12,13) (12,20) (12,17) (13,19) (13,22) (13,14) (14,19) (14,18) (14,21) (14,17) (15,16) (17,19) (17,21) (17,22) (17,20) (18,19) (18,21) (18,22) (18,20) (19,20) (20,21) (20,22) (21,22)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph384-9_11", + "image": "data/connectivity/graph_visual/medium/graph384.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,6) (1,7) (1,5) (1,16) (1,15) (1,3) (1,13) (1,10) (1,12) (1,4) (1,17) (1,20) (1,18) (1,8) (1,2) (1,19) (1,9) (1,11) (1,14) (2,7) (2,5) (2,16) (2,15) (2,3) (2,13) (2,10) (2,12) (2,4) (2,17) (2,20) (2,18) (2,8) (2,19) (2,9) (2,11) (2,14) (3,7) (3,5) (3,16) (3,15) (3,13) (3,10) (3,12) (3,4) (3,17) (3,20) (3,18) (3,8) (3,19) (3,9) (3,11) (3,14) (4,7) (4,5) (4,16) (4,15) (4,13) (4,10) (4,12) (4,17) (4,20) (4,18) (4,8) (4,19) (4,9) (4,11) (4,14) (5,7) (5,16) (5,15) (5,13) (5,10) (5,12) (5,17) (5,20) (5,18) (5,8) (5,19) (5,9) (5,11) (5,14) (7,16) (7,15) (7,13) (7,10) (7,12) (7,17) (7,20) (7,18) (7,8) (7,19) (7,9) (7,11) (7,14) (8,16) (8,15) (8,13) (8,10) (8,12) (8,17) (8,20) (8,18) (8,19) (8,9) (8,11) (8,14) (9,16) (9,15) (9,13) (9,10) (9,12) (9,17) (9,20) (9,18) (9,19) (9,11) (9,14) (10,16) (10,15) (10,13) (10,12) (10,17) (10,20) (10,18) (10,19) (10,11) (10,14) (11,16) (11,15) (11,13) (11,12) (11,17) (11,20) (11,18) (11,19) (11,14) (12,16) (12,15) (12,13) (12,17) (12,20) (12,18) (12,19) (12,14) (13,16) (13,15) (13,17) (13,20) (13,18) (13,19) (13,14) (14,16) (14,15) (14,17) (14,20) (14,18) (14,19) (15,16) (15,17) (15,20) (15,18) (15,19) (16,17) (16,20) (16,18) (16,19) (17,20) (17,18) (17,19) (18,20) (18,19) (19,20)\nIs there a path between node 9 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph170-3_7", + "image": "data/connectivity/graph_visual/medium/graph170.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,9) (0,17) (0,12) (0,8) (0,14) (0,10) (0,11) (0,4) (1,6) (1,7) (2,13) (2,17) (2,12) (2,8) (2,10) (2,11) (2,15) (2,4) (3,6) (3,5) (4,9) (4,8) (4,10) (4,11) (6,7) (6,16) (7,16) (8,13) (8,17) (8,12) (8,14) (8,10) (8,11) (9,17) (9,14) (9,15) (10,17) (10,12) (10,14) (10,15) (11,17) (11,14) (11,15) (12,13) (13,14) (13,15) (14,17) (15,17)\nIs there a path between node 3 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph87-2_13", + "image": "data/connectivity/graph_visual/medium/graph87.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (0,13) (0,7) (0,3) (0,14) (0,6) (0,10) (0,1) (0,12) (1,9) (1,13) (1,7) (1,3) (1,14) (1,6) (1,10) (1,12) (2,5) (2,11) (2,8) (2,4) (3,9) (3,13) (3,7) (3,14) (3,6) (3,10) (3,12) (4,5) (4,11) (4,8) (5,11) (5,8) (6,9) (6,13) (6,7) (6,14) (6,10) (6,12) (7,9) (7,13) (7,14) (7,10) (7,12) (8,11) (9,13) (9,14) (9,10) (9,12) (10,13) (10,14) (10,12) (12,13) (12,14) (13,14)\nIs there a path between node 2 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph349-4_20", + "image": "data/connectivity/graph_visual/medium/graph349.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,11) (0,12) (0,14) (0,1) (0,8) (0,2) (0,9) (0,7) (0,6) (0,18) (0,19) (1,10) (1,11) (1,12) (1,14) (1,8) (1,2) (1,9) (1,7) (1,6) (1,18) (1,19) (2,10) (2,11) (2,12) (2,14) (2,8) (2,9) (2,7) (2,6) (2,18) (2,19) (3,5) (3,4) (3,16) (3,20) (3,13) (3,17) (4,5) (4,16) (4,20) (4,13) (4,17) (5,16) (5,20) (5,13) (5,17) (6,10) (6,11) (6,12) (6,14) (6,8) (6,9) (6,7) (6,18) (6,19) (7,10) (7,11) (7,12) (7,14) (7,8) (7,9) (7,18) (7,19) (8,10) (8,11) (8,12) (8,14) (8,9) (8,18) (8,19) (9,10) (9,11) (9,12) (9,14) (9,18) (9,19) (10,11) (10,12) (10,14) (10,18) (10,19) (11,12) (11,14) (11,18) (11,19) (12,14) (12,18) (12,19) (13,16) (13,20) (13,17) (14,18) (14,19) (16,20) (16,17) (17,20) (18,19)\nIs there a path between node 4 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph830-11_1", + "image": "data/connectivity/graph_visual/medium/graph830.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,18) (1,15) (1,5) (1,23) (1,10) (1,2) (1,20) (1,6) (1,22) (1,13) (1,21) (2,18) (2,14) (2,24) (2,15) (2,5) (2,23) (2,10) (2,20) (2,22) (2,13) (3,19) (4,17) (4,12) (4,7) (5,14) (5,23) (5,10) (5,22) (5,21) (6,18) (6,14) (6,24) (6,15) (6,10) (6,20) (6,22) (6,13) (6,21) (7,16) (7,11) (7,17) (7,12) (7,9) (9,11) (9,17) (9,12) (10,24) (10,23) (10,20) (10,22) (10,13) (10,21) (11,16) (11,17) (11,12) (12,16) (12,17) (13,18) (13,14) (13,24) (13,15) (13,23) (13,20) (13,22) (13,21) (14,18) (14,24) (14,15) (14,23) (14,20) (14,21) (15,23) (15,22) (15,21) (16,17) (18,24) (18,23) (18,22) (18,21) (20,24) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (23,24)\nIs there a path between node 11 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph416-19_4", + "image": "data/connectivity/graph_visual/medium/graph416.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,4) (0,21) (0,7) (0,11) (0,1) (0,12) (0,10) (0,6) (0,9) (0,17) (0,20) (0,15) (0,13) (1,2) (1,4) (1,21) (1,7) (1,11) (1,12) (1,10) (1,6) (1,9) (1,17) (1,20) (1,15) (1,13) (2,4) (2,21) (2,7) (2,11) (2,12) (2,10) (2,6) (2,9) (2,17) (2,20) (2,15) (2,13) (3,8) (3,16) (3,14) (3,18) (3,5) (3,19) (4,21) (4,7) (4,11) (4,12) (4,10) (4,6) (4,9) (4,17) (4,20) (4,15) (4,13) (5,8) (5,16) (5,14) (5,18) (5,19) (6,21) (6,7) (6,11) (6,12) (6,10) (6,9) (6,17) (6,20) (6,15) (6,13) (7,21) (7,11) (7,12) (7,10) (7,9) (7,17) (7,20) (7,15) (7,13) (8,16) (8,14) (8,18) (8,19) (9,21) (9,11) (9,12) (9,10) (9,17) (9,20) (9,15) (9,13) (10,21) (10,11) (10,12) (10,17) (10,20) (10,15) (10,13) (11,21) (11,12) (11,17) (11,20) (11,15) (11,13) (12,21) (12,17) (12,20) (12,15) (12,13) (13,21) (13,17) (13,20) (13,15) (14,16) (14,18) (14,19) (15,21) (15,17) (15,20) (16,18) (16,19) (17,21) (17,20) (18,19) (20,21)\nIs there a path between node 19 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph238-8_1", + "image": "data/connectivity/graph_visual/medium/graph238.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,2) (0,5) (0,7) (0,18) (0,13) (0,11) (0,17) (1,8) (1,7) (1,18) (1,13) (1,9) (1,15) (1,11) (1,10) (2,8) (2,5) (2,7) (2,15) (3,14) (3,4) (3,12) (4,12) (5,8) (5,18) (5,13) (5,9) (5,11) (5,17) (6,16) (7,18) (7,13) (7,9) (7,11) (7,17) (8,18) (8,13) (8,9) (8,15) (8,11) (8,17) (8,10) (9,18) (9,13) (9,15) (9,17) (10,15) (10,17) (11,18) (11,13) (11,15) (11,17) (12,14) (13,18) (13,15) (15,18) (15,17) (17,18)\nIs there a path between node 8 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph421-13_11", + "image": "data/connectivity/graph_visual/medium/graph421.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,18) (0,10) (0,17) (0,14) (0,16) (0,3) (0,7) (0,15) (0,9) (0,11) (0,20) (0,1) (0,12) (0,4) (0,21) (0,8) (1,19) (1,18) (1,10) (1,17) (1,14) (1,16) (1,3) (1,7) (1,15) (1,9) (1,11) (1,20) (1,12) (1,4) (1,21) (1,8) (2,6) (2,5) (2,13) (3,19) (3,18) (3,10) (3,17) (3,14) (3,16) (3,7) (3,15) (3,9) (3,11) (3,20) (3,12) (3,4) (3,21) (3,8) (4,19) (4,18) (4,10) (4,17) (4,14) (4,16) (4,7) (4,15) (4,9) (4,11) (4,20) (4,12) (4,21) (4,8) (5,6) (5,13) (6,13) (7,19) (7,18) (7,10) (7,17) (7,14) (7,16) (7,15) (7,9) (7,11) (7,20) (7,12) (7,21) (7,8) (8,19) (8,18) (8,10) (8,17) (8,14) (8,16) (8,15) (8,9) (8,11) (8,20) (8,12) (8,21) (9,19) (9,18) (9,10) (9,17) (9,14) (9,16) (9,15) (9,11) (9,20) (9,12) (9,21) (10,19) (10,18) (10,17) (10,14) (10,16) (10,15) (10,11) (10,20) (10,12) (10,21) (11,19) (11,18) (11,17) (11,14) (11,16) (11,15) (11,20) (11,12) (11,21) (12,19) (12,18) (12,17) (12,14) (12,16) (12,15) (12,20) (12,21) (14,19) (14,18) (14,17) (14,16) (14,15) (14,20) (14,21) (15,19) (15,18) (15,17) (15,16) (15,20) (15,21) (16,19) (16,18) (16,17) (16,20) (16,21) (17,19) (17,18) (17,20) (17,21) (18,19) (18,20) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 13 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph334-18_16", + "image": "data/connectivity/graph_visual/medium/graph334.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,7) (0,3) (0,20) (1,13) (2,9) (2,12) (2,13) (3,7) (3,20) (5,6) (5,10) (5,11) (5,15) (5,17) (5,12) (6,9) (6,10) (6,11) (8,16) (9,17) (9,13) (10,17) (11,16) (11,18) (12,16) (13,15) (13,17) (13,18) (14,19) (19,20)\nIs there a path between node 18 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph9-0_8", + "image": "data/connectivity/graph_visual/medium/graph9.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,7) (0,5) (0,9) (0,6) (0,1) (1,2) (1,7) (1,3) (1,6) (2,7) (2,4) (2,9) (2,6) (3,7) (3,5) (4,9) (4,6) (6,7) (6,9) (8,10)\nIs there a path between node 0 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph664-21_5", + "image": "data/connectivity/graph_visual/medium/graph664.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,4) (0,14) (0,9) (0,19) (0,7) (0,20) (0,17) (0,16) (1,11) (1,12) (1,2) (1,15) (1,3) (1,23) (1,5) (1,21) (2,12) (2,15) (2,3) (2,23) (2,13) (2,10) (3,22) (3,12) (3,15) (3,23) (3,5) (3,21) (3,13) (4,14) (4,18) (4,9) (4,19) (4,16) (5,22) (5,11) (5,12) (5,23) (5,21) (5,10) (6,18) (6,9) (6,7) (6,20) (6,17) (6,16) (7,14) (7,9) (7,19) (7,20) (7,17) (7,8) (8,14) (8,18) (8,9) (8,19) (8,20) (8,17) (8,16) (9,14) (9,19) (10,11) (10,15) (10,23) (10,21) (10,13) (11,22) (11,12) (11,15) (11,13) (12,22) (12,15) (12,23) (12,21) (12,13) (13,15) (13,21) (14,18) (14,19) (14,20) (14,16) (15,22) (16,20) (16,17) (18,19) (18,20) (19,20) (21,22) (22,23)\nIs there a path between node 21 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph128-13_7", + "image": "data/connectivity/graph_visual/medium/graph128.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,10) (0,5) (0,16) (0,1) (0,12) (0,15) (0,11) (0,9) (0,7) (0,6) (0,3) (0,2) (0,4) (1,10) (1,5) (1,16) (1,12) (1,15) (1,11) (1,9) (1,7) (1,6) (1,3) (1,2) (1,4) (2,10) (2,5) (2,16) (2,12) (2,15) (2,11) (2,9) (2,7) (2,6) (2,3) (2,4) (3,10) (3,5) (3,16) (3,12) (3,15) (3,11) (3,9) (3,7) (3,6) (3,4) (4,10) (4,5) (4,16) (4,12) (4,15) (4,11) (4,9) (4,7) (4,6) (5,10) (5,16) (5,12) (5,15) (5,11) (5,9) (5,7) (5,6) (6,10) (6,16) (6,12) (6,15) (6,11) (6,9) (6,7) (7,10) (7,16) (7,12) (7,15) (7,11) (7,9) (8,13) (8,14) (9,10) (9,16) (9,12) (9,15) (9,11) (10,16) (10,12) (10,15) (10,11) (11,16) (11,12) (11,15) (12,16) (12,15) (13,14) (15,16)\nIs there a path between node 13 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph761-24_0", + "image": "data/connectivity/graph_visual/medium/graph761.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,16) (0,17) (0,9) (1,18) (1,8) (1,22) (1,21) (1,19) (1,6) (1,24) (1,13) (1,3) (1,7) (1,2) (1,15) (1,10) (1,11) (1,23) (2,8) (2,22) (2,21) (2,19) (2,6) (2,24) (2,13) (2,15) (2,14) (2,4) (2,12) (2,23) (3,18) (3,21) (3,24) (3,15) (3,10) (3,11) (3,14) (3,12) (3,23) (4,20) (4,8) (4,21) (4,6) (4,24) (4,13) (4,7) (4,15) (4,10) (4,11) (4,14) (4,12) (4,23) (5,16) (5,9) (6,20) (6,18) (6,8) (6,21) (6,19) (6,24) (6,13) (6,7) (6,15) (6,11) (6,14) (6,12) (6,23) (7,20) (7,18) (7,22) (7,21) (7,24) (7,13) (7,15) (7,11) (7,12) (7,23) (8,20) (8,18) (8,22) (8,21) (8,19) (8,24) (8,13) (8,15) (8,10) (8,11) (8,14) (8,23) (9,16) (9,17) (10,20) (10,18) (10,22) (10,21) (10,19) (10,13) (10,15) (10,14) (10,12) (11,20) (11,18) (11,22) (11,21) (11,19) (11,24) (11,13) (11,14) (11,12) (11,23) (12,18) (12,22) (12,21) (12,19) (12,24) (12,14) (12,23) (13,22) (13,21) (13,24) (13,15) (13,14) (13,23) (14,20) (14,18) (14,22) (14,21) (14,19) (14,23) (15,21) (16,17) (18,20) (18,21) (18,19) (18,23) (19,20) (19,24) (19,23) (20,21) (20,24) (20,23) (21,24) (21,23) (22,24) (22,23)\nIs there a path between node 24 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph727-3_11", + "image": "data/connectivity/graph_visual/medium/graph727.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,2) (1,12) (1,21) (1,18) (1,15) (1,10) (1,13) (1,19) (1,16) (1,22) (1,7) (1,24) (1,14) (1,9) (1,6) (1,17) (1,3) (1,11) (1,20) (1,5) (1,8) (2,12) (2,21) (2,18) (2,15) (2,10) (2,13) (2,19) (2,16) (2,22) (2,7) (2,24) (2,14) (2,9) (2,6) (2,17) (2,3) (2,11) (2,20) (2,5) (2,8) (3,12) (3,21) (3,18) (3,15) (3,10) (3,13) (3,19) (3,16) (3,22) (3,7) (3,24) (3,14) (3,9) (3,6) (3,17) (3,11) (3,20) (3,5) (3,8) (4,23) (5,12) (5,21) (5,18) (5,15) (5,10) (5,13) (5,19) (5,16) (5,22) (5,7) (5,24) (5,14) (5,9) (5,6) (5,17) (5,11) (5,20) (5,8) (6,12) (6,21) (6,18) (6,15) (6,10) (6,13) (6,19) (6,16) (6,22) (6,7) (6,24) (6,14) (6,9) (6,17) (6,11) (6,20) (6,8) (7,12) (7,21) (7,18) (7,15) (7,10) (7,13) (7,19) (7,16) (7,22) (7,24) (7,14) (7,9) (7,17) (7,11) (7,20) (7,8) (8,12) (8,21) (8,18) (8,15) (8,10) (8,13) (8,19) (8,16) (8,22) (8,24) (8,14) (8,9) (8,17) (8,11) (8,20) (9,12) (9,21) (9,18) (9,15) (9,10) (9,13) (9,19) (9,16) (9,22) (9,24) (9,14) (9,17) (9,11) (9,20) (10,12) (10,21) (10,18) (10,15) (10,13) (10,19) (10,16) (10,22) (10,24) (10,14) (10,17) (10,11) (10,20) (11,12) (11,21) (11,18) (11,15) (11,13) (11,19) (11,16) (11,22) (11,24) (11,14) (11,17) (11,20) (12,21) (12,18) (12,15) (12,13) (12,19) (12,16) (12,22) (12,24) (12,14) (12,17) (12,20) (13,21) (13,18) (13,15) (13,19) (13,16) (13,22) (13,24) (13,14) (13,17) (13,20) (14,21) (14,18) (14,15) (14,19) (14,16) (14,22) (14,24) (14,17) (14,20) (15,21) (15,18) (15,19) (15,16) (15,22) (15,24) (15,17) (15,20) (16,21) (16,18) (16,19) (16,22) (16,24) (16,17) (16,20) (17,21) (17,18) (17,19) (17,22) (17,24) (17,20) (18,21) (18,19) (18,22) (18,24) (18,20) (19,21) (19,22) (19,24) (19,20) (20,21) (20,22) (20,24) (21,22) (21,24) (22,24)\nIs there a path between node 3 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph461-1_17", + "image": "data/connectivity/graph_visual/medium/graph461.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,11) (0,17) (0,16) (0,3) (0,9) (0,15) (0,12) (0,1) (0,20) (0,19) (0,6) (0,21) (0,7) (0,8) (0,14) (0,5) (0,2) (1,18) (1,11) (1,17) (1,16) (1,3) (1,9) (1,15) (1,12) (1,20) (1,19) (1,6) (1,21) (1,7) (1,8) (1,14) (1,5) (1,2) (2,18) (2,11) (2,17) (2,16) (2,3) (2,9) (2,15) (2,12) (2,20) (2,19) (2,6) (2,21) (2,7) (2,8) (2,14) (2,5) (3,18) (3,11) (3,17) (3,16) (3,9) (3,15) (3,12) (3,20) (3,19) (3,6) (3,21) (3,7) (3,8) (3,14) (3,5) (5,18) (5,11) (5,17) (5,16) (5,9) (5,15) (5,12) (5,20) (5,19) (5,6) (5,21) (5,7) (5,8) (5,14) (6,18) (6,11) (6,17) (6,16) (6,9) (6,15) (6,12) (6,20) (6,19) (6,21) (6,7) (6,8) (6,14) (7,18) (7,11) (7,17) (7,16) (7,9) (7,15) (7,12) (7,20) (7,19) (7,21) (7,8) (7,14) (8,18) (8,11) (8,17) (8,16) (8,9) (8,15) (8,12) (8,20) (8,19) (8,21) (8,14) (9,18) (9,11) (9,17) (9,16) (9,15) (9,12) (9,20) (9,19) (9,21) (9,14) (10,13) (11,18) (11,17) (11,16) (11,15) (11,12) (11,20) (11,19) (11,21) (11,14) (12,18) (12,17) (12,16) (12,15) (12,20) (12,19) (12,21) (12,14) (14,18) (14,17) (14,16) (14,15) (14,20) (14,19) (14,21) (15,18) (15,17) (15,16) (15,20) (15,19) (15,21) (16,18) (16,17) (16,20) (16,19) (16,21) (17,18) (17,20) (17,19) (17,21) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 1 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph577-22_17", + "image": "data/connectivity/graph_visual/medium/graph577.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (0,12) (0,18) (1,3) (1,16) (1,17) (1,14) (1,9) (1,8) (2,18) (2,9) (2,13) (2,22) (3,17) (3,14) (4,5) (4,21) (5,11) (5,6) (5,10) (6,11) (6,21) (7,19) (8,16) (8,22) (9,20) (9,18) (9,23) (11,19) (11,21) (12,14) (12,23) (12,22) (13,16) (13,20) (13,17) (13,22) (14,16) (15,18) (15,23) (16,18) (17,20) (17,18) (17,23) (17,22) (19,21) (20,23)\nIs there a path between node 22 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph2-1_5", + "image": "data/connectivity/graph_visual/medium/graph2.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,3) (0,7) (0,10) (0,6) (0,2) (0,8) (0,4) (0,1) (1,3) (1,7) (1,10) (1,6) (1,2) (1,8) (1,4) (2,3) (2,7) (2,10) (2,6) (2,8) (2,4) (3,7) (3,10) (3,6) (3,8) (3,4) (4,7) (4,10) (4,6) (4,8) (5,9) (6,7) (6,10) (6,8) (7,10) (7,8) (8,10)\nIs there a path between node 1 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph542-8_10", + "image": "data/connectivity/graph_visual/medium/graph542.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,14) (0,9) (0,13) (0,4) (0,12) (0,5) (0,3) (0,15) (0,21) (0,2) (0,18) (0,17) (1,14) (1,9) (1,13) (1,4) (1,12) (1,5) (1,3) (1,15) (1,21) (1,2) (1,18) (1,17) (2,14) (2,9) (2,13) (2,4) (2,12) (2,5) (2,3) (2,15) (2,21) (2,18) (2,17) (3,14) (3,9) (3,13) (3,4) (3,12) (3,5) (3,15) (3,21) (3,18) (3,17) (4,14) (4,9) (4,13) (4,12) (4,5) (4,15) (4,21) (4,18) (4,17) (5,14) (5,9) (5,13) (5,12) (5,15) (5,21) (5,18) (5,17) (6,22) (6,8) (6,11) (6,10) (6,19) (6,20) (6,7) (7,22) (7,8) (7,11) (7,10) (7,19) (7,20) (8,22) (8,11) (8,10) (8,19) (8,20) (9,14) (9,13) (9,12) (9,15) (9,21) (9,18) (9,17) (10,22) (10,11) (10,19) (10,20) (11,22) (11,19) (11,20) (12,14) (12,13) (12,15) (12,21) (12,18) (12,17) (13,14) (13,15) (13,21) (13,18) (13,17) (14,15) (14,21) (14,18) (14,17) (15,21) (15,18) (15,17) (17,21) (17,18) (18,21) (19,22) (19,20) (20,22)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph428-4_19", + "image": "data/connectivity/graph_visual/medium/graph428.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,13) (0,7) (0,9) (0,19) (0,10) (1,16) (1,14) (1,7) (1,19) (1,3) (2,21) (3,18) (3,13) (3,9) (3,19) (4,21) (5,6) (5,13) (5,7) (5,9) (5,11) (5,12) (5,10) (6,15) (6,10) (7,14) (7,11) (9,15) (9,18) (9,14) (10,12) (11,13) (12,19) (14,16) (17,20) (20,21)\nIs there a path between node 4 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph823-13_21", + "image": "data/connectivity/graph_visual/medium/graph823.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (0,21) (0,3) (0,7) (0,20) (0,17) (0,8) (1,19) (1,21) (1,7) (1,20) (1,8) (1,6) (2,16) (2,23) (3,7) (3,20) (3,17) (3,8) (3,6) (4,5) (4,15) (4,22) (4,24) (4,11) (5,15) (5,22) (5,11) (6,19) (6,13) (6,20) (6,17) (6,8) (7,19) (7,20) (7,17) (7,8) (8,19) (8,21) (8,17) (9,12) (9,18) (9,14) (10,12) (11,15) (11,24) (12,18) (12,14) (13,19) (13,21) (13,20) (13,17) (14,18) (17,19) (17,21) (19,21) (19,20)\nIs there a path between node 13 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph658-22_13", + "image": "data/connectivity/graph_visual/medium/graph658.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,5) (0,18) (0,14) (0,15) (0,22) (0,3) (0,2) (0,13) (0,8) (1,23) (1,6) (1,10) (2,5) (2,9) (2,18) (2,4) (2,12) (2,15) (2,22) (2,19) (2,3) (2,13) (3,7) (3,5) (3,12) (3,14) (3,20) (3,15) (3,22) (3,16) (3,8) (4,17) (4,7) (4,9) (4,18) (4,12) (4,20) (4,22) (4,19) (4,13) (4,8) (5,17) (5,7) (5,9) (5,18) (5,12) (5,14) (5,20) (5,22) (5,19) (5,16) (5,13) (6,11) (6,23) (6,21) (6,10) (7,17) (7,9) (7,18) (7,12) (7,14) (7,22) (7,13) (7,8) (8,17) (8,9) (8,18) (8,12) (8,14) (8,20) (8,15) (8,22) (8,19) (8,16) (8,13) (9,12) (9,14) (9,20) (9,15) (9,22) (9,16) (10,11) (10,23) (10,21) (11,23) (11,21) (12,18) (12,14) (12,20) (12,15) (12,22) (12,19) (12,16) (13,17) (13,18) (13,14) (13,20) (13,15) (13,19) (14,17) (14,18) (14,20) (14,15) (14,22) (14,19) (14,16) (15,17) (15,20) (15,22) (16,17) (16,18) (16,20) (16,22) (16,19) (17,18) (17,20) (17,22) (17,19) (18,20) (18,19) (19,20) (20,22) (21,23)\nIs there a path between node 22 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph681-18_15", + "image": "data/connectivity/graph_visual/medium/graph681.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,22) (0,16) (0,2) (0,6) (0,17) (0,20) (0,1) (0,12) (0,8) (0,11) (0,4) (0,18) (0,7) (0,3) (0,23) (0,9) (1,21) (1,22) (1,16) (1,2) (1,6) (1,17) (1,20) (1,12) (1,8) (1,11) (1,4) (1,18) (1,7) (1,3) (1,23) (1,9) (2,21) (2,22) (2,16) (2,6) (2,17) (2,20) (2,12) (2,8) (2,11) (2,4) (2,18) (2,7) (2,3) (2,23) (2,9) (3,21) (3,22) (3,16) (3,6) (3,17) (3,20) (3,12) (3,8) (3,11) (3,4) (3,18) (3,7) (3,23) (3,9) (4,21) (4,22) (4,16) (4,6) (4,17) (4,20) (4,12) (4,8) (4,11) (4,18) (4,7) (4,23) (4,9) (5,13) (6,21) (6,22) (6,16) (6,17) (6,20) (6,12) (6,8) (6,11) (6,18) (6,7) (6,23) (6,9) (7,21) (7,22) (7,16) (7,17) (7,20) (7,12) (7,8) (7,11) (7,18) (7,23) (7,9) (8,21) (8,22) (8,16) (8,17) (8,20) (8,12) (8,11) (8,18) (8,23) (8,9) (9,21) (9,22) (9,16) (9,17) (9,20) (9,12) (9,11) (9,18) (9,23) (10,14) (10,19) (10,15) (11,21) (11,22) (11,16) (11,17) (11,20) (11,12) (11,18) (11,23) (12,21) (12,22) (12,16) (12,17) (12,20) (12,18) (12,23) (14,19) (14,15) (15,19) (16,21) (16,22) (16,17) (16,20) (16,18) (16,23) (17,21) (17,22) (17,20) (17,18) (17,23) (18,21) (18,22) (18,20) (18,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 18 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph545-4_23", + "image": "data/connectivity/graph_visual/medium/graph545.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,17) (0,23) (0,22) (0,1) (0,9) (0,11) (0,14) (0,19) (0,12) (0,18) (0,8) (0,4) (0,16) (0,15) (0,10) (0,6) (1,20) (1,17) (1,23) (1,22) (1,9) (1,11) (1,14) (1,19) (1,12) (1,18) (1,8) (1,4) (1,16) (1,15) (1,10) (1,6) (2,13) (2,5) (2,3) (2,21) (2,7) (3,13) (3,5) (3,21) (3,7) (4,20) (4,17) (4,23) (4,22) (4,9) (4,11) (4,14) (4,19) (4,12) (4,18) (4,8) (4,16) (4,15) (4,10) (4,6) (5,13) (5,21) (5,7) (6,20) (6,17) (6,23) (6,22) (6,9) (6,11) (6,14) (6,19) (6,12) (6,18) (6,8) (6,16) (6,15) (6,10) (7,13) (7,21) (8,20) (8,17) (8,23) (8,22) (8,9) (8,11) (8,14) (8,19) (8,12) (8,18) (8,16) (8,15) (8,10) (9,20) (9,17) (9,23) (9,22) (9,11) (9,14) (9,19) (9,12) (9,18) (9,16) (9,15) (9,10) (10,20) (10,17) (10,23) (10,22) (10,11) (10,14) (10,19) (10,12) (10,18) (10,16) (10,15) (11,20) (11,17) (11,23) (11,22) (11,14) (11,19) (11,12) (11,18) (11,16) (11,15) (12,20) (12,17) (12,23) (12,22) (12,14) (12,19) (12,18) (12,16) (12,15) (13,21) (14,20) (14,17) (14,23) (14,22) (14,19) (14,18) (14,16) (14,15) (15,20) (15,17) (15,23) (15,22) (15,19) (15,18) (15,16) (16,20) (16,17) (16,23) (16,22) (16,19) (16,18) (17,20) (17,23) (17,22) (17,19) (17,18) (18,20) (18,23) (18,22) (18,19) (19,20) (19,23) (19,22) (20,23) (20,22) (22,23)\nIs there a path between node 4 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph207-1_7", + "image": "data/connectivity/graph_visual/medium/graph207.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,9) (0,12) (1,9) (1,7) (1,12) (2,17) (2,13) (2,18) (2,15) (2,5) (2,16) (2,4) (2,3) (2,6) (2,14) (2,11) (2,10) (2,8) (3,13) (3,18) (3,5) (3,16) (3,4) (3,6) (3,14) (3,11) (3,10) (3,8) (4,13) (4,5) (4,16) (4,6) (4,14) (4,11) (4,10) (4,8) (5,17) (5,13) (5,16) (5,14) (5,10) (5,8) (6,17) (6,13) (6,18) (6,15) (6,14) (6,11) (6,10) (6,8) (7,12) (8,13) (8,18) (8,15) (8,14) (8,10) (10,13) (10,18) (10,16) (10,14) (10,11) (11,17) (11,13) (11,18) (11,15) (11,14) (13,18) (13,15) (13,16) (14,17) (14,15) (14,16) (16,17) (17,18)\nIs there a path between node 1 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph66-12_1", + "image": "data/connectivity/graph_visual/medium/graph66.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (0,1) (0,13) (0,7) (0,4) (0,10) (0,12) (0,5) (0,11) (0,6) (0,9) (0,8) (1,3) (1,13) (1,7) (1,4) (1,10) (1,12) (1,5) (1,11) (1,6) (1,9) (1,8) (3,13) (3,7) (3,4) (3,10) (3,12) (3,5) (3,11) (3,6) (3,9) (3,8) (4,13) (4,7) (4,10) (4,12) (4,5) (4,11) (4,6) (4,9) (4,8) (5,13) (5,7) (5,10) (5,12) (5,11) (5,6) (5,9) (5,8) (6,13) (6,7) (6,10) (6,12) (6,11) (6,9) (6,8) (7,13) (7,10) (7,12) (7,11) (7,9) (7,8) (8,13) (8,10) (8,12) (8,11) (8,9) (9,13) (9,10) (9,12) (9,11) (10,13) (10,12) (10,11) (11,13) (11,12) (12,13)\nIs there a path between node 12 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph243-18_2", + "image": "data/connectivity/graph_visual/medium/graph243.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,3) (0,4) (0,8) (0,13) (0,7) (0,2) (0,14) (0,18) (0,1) (0,10) (0,5) (1,15) (1,4) (1,9) (1,8) (1,7) (1,17) (1,2) (1,10) (1,12) (1,5) (2,15) (2,4) (2,8) (2,17) (2,14) (2,18) (2,10) (2,5) (3,15) (3,4) (3,9) (3,13) (3,7) (3,14) (3,18) (3,10) (4,9) (4,8) (4,7) (4,17) (4,14) (4,18) (4,12) (4,5) (5,15) (5,8) (5,13) (5,11) (5,14) (5,18) (6,16) (7,15) (7,8) (7,13) (7,18) (7,10) (8,15) (8,9) (8,13) (8,11) (8,14) (8,18) (8,10) (8,12) (9,15) (9,13) (9,17) (9,11) (9,14) (9,18) (9,10) (9,12) (10,15) (10,18) (11,15) (11,13) (11,18) (11,12) (12,15) (12,17) (12,18) (13,15) (13,17) (13,18) (14,15) (14,18) (15,17) (17,18)\nIs there a path between node 18 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph581-15_3", + "image": "data/connectivity/graph_visual/medium/graph581.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,11) (0,20) (1,22) (1,12) (1,16) (1,6) (1,18) (1,13) (1,17) (1,14) (1,15) (2,11) (2,20) (3,11) (3,7) (4,23) (4,16) (4,18) (4,13) (5,22) (5,23) (5,16) (5,18) (6,12) (6,23) (6,16) (7,20) (8,11) (8,20) (8,9) (9,10) (12,22) (12,21) (12,16) (12,18) (12,13) (12,14) (13,23) (13,16) (13,17) (13,14) (14,19) (14,15) (15,22) (15,19) (16,21) (16,18) (17,22) (17,21) (17,23) (17,19) (19,21) (21,22)\nIs there a path between node 15 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph365-19_8", + "image": "data/connectivity/graph_visual/medium/graph365.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (0,11) (0,5) (1,6) (1,19) (1,9) (1,10) (1,13) (2,18) (2,4) (2,6) (3,17) (3,7) (3,11) (3,20) (3,13) (4,6) (4,19) (4,10) (4,11) (4,13) (5,19) (5,11) (5,14) (6,19) (6,10) (6,7) (7,19) (7,14) (7,13) (9,13) (10,11) (11,18) (14,18) (14,19) (16,20)\nIs there a path between node 19 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph286-8_16", + "image": "data/connectivity/graph_visual/medium/graph286.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (0,9) (1,11) (1,4) (2,6) (2,14) (2,19) (3,15) (4,18) (4,17) (4,9) (4,19) (5,6) (5,11) (5,10) (6,11) (6,18) (8,10) (8,14) (9,18) (9,10) (9,14) (10,18) (10,19) (11,14) (11,19) (12,15) (12,13) (16,19)\nIs there a path between node 8 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph816-11_7", + "image": "data/connectivity/graph_visual/medium/graph816.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,8) (0,1) (0,13) (0,10) (0,22) (0,9) (1,12) (1,8) (1,17) (1,10) (1,5) (1,22) (1,9) (2,18) (2,3) (2,14) (2,6) (2,7) (2,19) (2,24) (2,11) (2,23) (3,16) (3,20) (3,14) (3,6) (3,7) (3,19) (3,4) (3,23) (4,18) (4,14) (4,6) (4,11) (4,23) (5,12) (5,8) (5,21) (5,17) (5,22) (6,18) (6,16) (6,20) (6,14) (6,7) (6,19) (6,24) (6,11) (6,23) (7,18) (7,16) (7,14) (7,19) (7,11) (8,12) (8,21) (8,17) (8,22) (8,9) (9,12) (9,21) (9,13) (9,17) (9,10) (9,22) (10,12) (10,21) (10,13) (10,17) (11,16) (11,20) (11,24) (11,23) (12,21) (12,13) (12,17) (12,22) (13,21) (13,17) (13,22) (14,18) (14,16) (14,19) (14,23) (16,19) (16,23) (17,22) (18,20) (18,24) (18,23) (19,20) (19,24) (19,23) (20,23) (21,22)\nIs there a path between node 11 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph536-17_21", + "image": "data/connectivity/graph_visual/medium/graph536.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,4) (0,7) (0,15) (0,8) (0,16) (0,12) (0,14) (1,17) (1,2) (1,22) (1,5) (1,21) (1,3) (2,17) (2,22) (2,5) (2,21) (2,3) (3,17) (3,22) (3,5) (3,21) (4,7) (4,15) (4,8) (4,16) (4,12) (4,14) (5,17) (5,22) (5,21) (6,20) (6,19) (6,11) (6,10) (6,13) (6,18) (6,9) (7,15) (7,8) (7,16) (7,12) (7,14) (8,15) (8,16) (8,12) (8,14) (9,20) (9,19) (9,11) (9,10) (9,13) (9,18) (10,20) (10,19) (10,11) (10,13) (10,18) (11,20) (11,19) (11,13) (11,18) (12,15) (12,16) (12,14) (13,20) (13,19) (13,18) (14,15) (14,16) (15,16) (17,22) (17,21) (18,20) (18,19) (19,20) (21,22)\nIs there a path between node 17 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph583-4_23", + "image": "data/connectivity/graph_visual/medium/graph583.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,17) (0,10) (0,22) (1,23) (1,19) (1,5) (1,18) (2,20) (2,12) (2,5) (2,16) (3,19) (3,5) (3,7) (3,15) (3,18) (4,21) (4,17) (4,22) (5,23) (5,19) (5,12) (5,18) (6,21) (7,23) (7,16) (7,18) (7,14) (8,9) (8,10) (8,22) (9,11) (12,23) (12,16) (12,14) (13,23) (13,16) (13,18) (14,23) (14,19) (14,15) (15,23) (16,23) (17,22) (18,20) (19,20)\nIs there a path between node 4 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph348-16_8", + "image": "data/connectivity/graph_visual/medium/graph348.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,2) (0,7) (0,20) (0,1) (0,18) (0,11) (0,5) (0,15) (0,13) (0,14) (0,3) (0,9) (0,6) (0,4) (0,12) (0,17) (0,16) (1,10) (1,2) (1,7) (1,20) (1,18) (1,11) (1,5) (1,15) (1,13) (1,14) (1,3) (1,9) (1,6) (1,4) (1,12) (1,17) (1,16) (2,10) (2,7) (2,20) (2,18) (2,11) (2,5) (2,15) (2,13) (2,14) (2,3) (2,9) (2,6) (2,4) (2,12) (2,17) (2,16) (3,10) (3,7) (3,20) (3,18) (3,11) (3,5) (3,15) (3,13) (3,14) (3,9) (3,6) (3,4) (3,12) (3,17) (3,16) (4,10) (4,7) (4,20) (4,18) (4,11) (4,5) (4,15) (4,13) (4,14) (4,9) (4,6) (4,12) (4,17) (4,16) (5,10) (5,7) (5,20) (5,18) (5,11) (5,15) (5,13) (5,14) (5,9) (5,6) (5,12) (5,17) (5,16) (6,10) (6,7) (6,20) (6,18) (6,11) (6,15) (6,13) (6,14) (6,9) (6,12) (6,17) (6,16) (7,10) (7,20) (7,18) (7,11) (7,15) (7,13) (7,14) (7,9) (7,12) (7,17) (7,16) (8,19) (9,10) (9,20) (9,18) (9,11) (9,15) (9,13) (9,14) (9,12) (9,17) (9,16) (10,20) (10,18) (10,11) (10,15) (10,13) (10,14) (10,12) (10,17) (10,16) (11,20) (11,18) (11,15) (11,13) (11,14) (11,12) (11,17) (11,16) (12,20) (12,18) (12,15) (12,13) (12,14) (12,17) (12,16) (13,20) (13,18) (13,15) (13,14) (13,17) (13,16) (14,20) (14,18) (14,15) (14,17) (14,16) (15,20) (15,18) (15,17) (15,16) (16,20) (16,18) (16,17) (17,20) (17,18) (18,20)\nIs there a path between node 16 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph270-5_19", + "image": "data/connectivity/graph_visual/medium/graph270.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,16) (0,3) (0,5) (1,6) (1,7) (1,2) (1,8) (1,14) (1,13) (1,9) (1,4) (1,12) (1,19) (2,6) (2,11) (2,8) (2,14) (2,13) (2,9) (2,12) (2,19) (3,17) (3,16) (3,15) (3,5) (3,18) (4,7) (4,8) (4,14) (4,9) (4,12) (5,17) (5,16) (5,10) (5,15) (6,7) (6,11) (6,8) (6,14) (6,12) (6,19) (7,11) (7,19) (8,11) (8,13) (8,9) (8,19) (9,11) (9,14) (9,13) (9,12) (9,19) (10,17) (10,16) (10,15) (11,14) (11,13) (11,12) (12,13) (12,19) (13,14) (13,19) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 5 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph541-22_10", + "image": "data/connectivity/graph_visual/medium/graph541.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,10) (0,11) (0,12) (0,6) (0,14) (0,21) (1,10) (1,11) (1,12) (1,6) (1,14) (1,21) (2,4) (2,20) (2,5) (2,13) (3,15) (3,8) (3,18) (3,17) (3,22) (3,9) (3,16) (3,7) (3,19) (4,20) (4,5) (4,13) (5,20) (5,13) (6,10) (6,11) (6,12) (6,14) (6,21) (7,15) (7,8) (7,18) (7,17) (7,22) (7,9) (7,16) (7,19) (8,15) (8,18) (8,17) (8,22) (8,9) (8,16) (8,19) (9,15) (9,18) (9,17) (9,22) (9,16) (9,19) (10,11) (10,12) (10,14) (10,21) (11,12) (11,14) (11,21) (12,14) (12,21) (13,20) (14,21) (15,18) (15,17) (15,22) (15,16) (15,19) (16,18) (16,17) (16,22) (16,19) (17,18) (17,22) (17,19) (18,22) (18,19) (19,22)\nIs there a path between node 22 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph760-24_23", + "image": "data/connectivity/graph_visual/medium/graph760.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,1) (0,19) (0,21) (1,9) (1,19) (1,21) (2,7) (3,11) (3,14) (3,6) (3,18) (4,23) (4,16) (4,10) (4,17) (4,13) (5,9) (5,21) (6,11) (6,12) (6,14) (6,15) (6,8) (8,12) (8,14) (8,15) (8,18) (9,19) (9,21) (10,23) (10,16) (10,20) (10,13) (11,12) (11,14) (11,15) (11,18) (12,14) (12,18) (13,23) (13,16) (13,20) (13,24) (14,15) (15,18) (16,23) (16,20) (16,24) (17,20) (20,23) (20,24) (23,24)\nIs there a path between node 24 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph676-11_7", + "image": "data/connectivity/graph_visual/medium/graph676.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,1) (0,3) (0,20) (0,21) (0,6) (0,11) (0,23) (0,8) (0,9) (0,14) (0,19) (1,10) (1,3) (1,20) (1,21) (1,6) (1,11) (1,23) (1,8) (1,9) (1,14) (1,19) (2,15) (2,18) (2,7) (2,22) (2,13) (2,17) (2,16) (2,12) (2,4) (2,5) (3,10) (3,20) (3,21) (3,6) (3,11) (3,23) (3,8) (3,9) (3,14) (3,19) (4,15) (4,18) (4,7) (4,22) (4,13) (4,17) (4,16) (4,12) (4,5) (5,15) (5,18) (5,7) (5,22) (5,13) (5,17) (5,16) (5,12) (6,10) (6,20) (6,21) (6,11) (6,23) (6,8) (6,9) (6,14) (6,19) (7,15) (7,18) (7,22) (7,13) (7,17) (7,16) (7,12) (8,10) (8,20) (8,21) (8,11) (8,23) (8,9) (8,14) (8,19) (9,10) (9,20) (9,21) (9,11) (9,23) (9,14) (9,19) (10,20) (10,21) (10,11) (10,23) (10,14) (10,19) (11,20) (11,21) (11,23) (11,14) (11,19) (12,15) (12,18) (12,22) (12,13) (12,17) (12,16) (13,15) (13,18) (13,22) (13,17) (13,16) (14,20) (14,21) (14,23) (14,19) (15,18) (15,22) (15,17) (15,16) (16,18) (16,22) (16,17) (17,18) (17,22) (18,22) (19,20) (19,21) (19,23) (20,21) (20,23) (21,23)\nIs there a path between node 11 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph86-6_10", + "image": "data/connectivity/graph_visual/medium/graph86.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,3) (0,1) (0,14) (0,13) (0,4) (0,10) (0,5) (1,3) (1,14) (1,13) (1,4) (1,10) (1,5) (2,8) (2,11) (2,7) (2,12) (2,6) (2,9) (3,14) (3,13) (3,4) (3,10) (3,5) (4,14) (4,13) (4,10) (4,5) (5,14) (5,13) (5,10) (6,8) (6,11) (6,7) (6,12) (6,9) (7,8) (7,11) (7,12) (7,9) (8,11) (8,12) (8,9) (9,11) (9,12) (10,14) (10,13) (11,12) (13,14)\nIs there a path between node 6 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph531-5_2", + "image": "data/connectivity/graph_visual/medium/graph531.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,13) (0,7) (0,4) (0,9) (0,21) (0,16) (0,1) (0,18) (0,11) (0,8) (0,6) (0,15) (0,14) (0,12) (0,20) (0,2) (0,22) (1,10) (1,13) (1,7) (1,4) (1,9) (1,21) (1,16) (1,18) (1,11) (1,8) (1,6) (1,15) (1,14) (1,12) (1,20) (1,2) (1,22) (2,10) (2,13) (2,7) (2,4) (2,9) (2,21) (2,16) (2,18) (2,11) (2,8) (2,6) (2,15) (2,14) (2,12) (2,20) (2,22) (3,17) (3,19) (3,5) (4,10) (4,13) (4,7) (4,9) (4,21) (4,16) (4,18) (4,11) (4,8) (4,6) (4,15) (4,14) (4,12) (4,20) (4,22) (5,17) (5,19) (6,10) (6,13) (6,7) (6,9) (6,21) (6,16) (6,18) (6,11) (6,8) (6,15) (6,14) (6,12) (6,20) (6,22) (7,10) (7,13) (7,9) (7,21) (7,16) (7,18) (7,11) (7,8) (7,15) (7,14) (7,12) (7,20) (7,22) (8,10) (8,13) (8,9) (8,21) (8,16) (8,18) (8,11) (8,15) (8,14) (8,12) (8,20) (8,22) (9,10) (9,13) (9,21) (9,16) (9,18) (9,11) (9,15) (9,14) (9,12) (9,20) (9,22) (10,13) (10,21) (10,16) (10,18) (10,11) (10,15) (10,14) (10,12) (10,20) (10,22) (11,13) (11,21) (11,16) (11,18) (11,15) (11,14) (11,12) (11,20) (11,22) (12,13) (12,21) (12,16) (12,18) (12,15) (12,14) (12,20) (12,22) (13,21) (13,16) (13,18) (13,15) (13,14) (13,20) (13,22) (14,21) (14,16) (14,18) (14,15) (14,20) (14,22) (15,21) (15,16) (15,18) (15,20) (15,22) (16,21) (16,18) (16,20) (16,22) (17,19) (18,21) (18,20) (18,22) (20,21) (20,22) (21,22)\nIs there a path between node 5 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph116-14_15", + "image": "data/connectivity/graph_visual/medium/graph116.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,5) (3,13) (3,7) (4,16) (4,10) (4,12) (4,7) (4,15) (4,6) (6,9) (6,12) (6,13) (7,16) (7,14) (7,10) (7,9) (7,12) (9,12) (9,13) (9,15) (10,16) (11,14) (11,12) (11,13) (13,14)\nIs there a path between node 14 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph675-14_13", + "image": "data/connectivity/graph_visual/medium/graph675.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,22) (0,21) (0,14) (0,19) (0,13) (0,18) (0,12) (0,15) (0,6) (0,7) (0,10) (0,20) (0,2) (0,4) (0,8) (0,17) (0,23) (1,3) (1,16) (1,11) (1,9) (2,5) (2,22) (2,21) (2,14) (2,19) (2,13) (2,18) (2,12) (2,15) (2,6) (2,7) (2,10) (2,20) (2,4) (2,8) (2,17) (2,23) (3,16) (3,11) (3,9) (4,5) (4,22) (4,21) (4,14) (4,19) (4,13) (4,18) (4,12) (4,15) (4,6) (4,7) (4,10) (4,20) (4,8) (4,17) (4,23) (5,22) (5,21) (5,14) (5,19) (5,13) (5,18) (5,12) (5,15) (5,6) (5,7) (5,10) (5,20) (5,8) (5,17) (5,23) (6,22) (6,21) (6,14) (6,19) (6,13) (6,18) (6,12) (6,15) (6,7) (6,10) (6,20) (6,8) (6,17) (6,23) (7,22) (7,21) (7,14) (7,19) (7,13) (7,18) (7,12) (7,15) (7,10) (7,20) (7,8) (7,17) (7,23) (8,22) (8,21) (8,14) (8,19) (8,13) (8,18) (8,12) (8,15) (8,10) (8,20) (8,17) (8,23) (9,16) (9,11) (10,22) (10,21) (10,14) (10,19) (10,13) (10,18) (10,12) (10,15) (10,20) (10,17) (10,23) (11,16) (12,22) (12,21) (12,14) (12,19) (12,13) (12,18) (12,15) (12,20) (12,17) (12,23) (13,22) (13,21) (13,14) (13,19) (13,18) (13,15) (13,20) (13,17) (13,23) (14,22) (14,21) (14,19) (14,18) (14,15) (14,20) (14,17) (14,23) (15,22) (15,21) (15,19) (15,18) (15,20) (15,17) (15,23) (17,22) (17,21) (17,19) (17,18) (17,20) (17,23) (18,22) (18,21) (18,19) (18,20) (18,23) (19,22) (19,21) (19,20) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 14 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph710-24_7", + "image": "data/connectivity/graph_visual/medium/graph710.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,4) (1,18) (1,8) (1,10) (2,4) (3,14) (3,5) (3,22) (4,11) (4,13) (5,22) (6,10) (8,9) (8,18) (8,16) (10,21) (13,20) (14,19) (15,19) (15,22) (17,21) (18,21)\nIs there a path between node 24 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph728-12_6", + "image": "data/connectivity/graph_visual/medium/graph728.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,17) (0,10) (0,7) (0,19) (0,22) (0,13) (0,12) (0,5) (0,4) (0,24) (0,16) (0,1) (0,3) (0,11) (1,2) (1,17) (1,10) (1,7) (1,19) (1,22) (1,13) (1,12) (1,5) (1,4) (1,24) (1,16) (1,3) (1,11) (2,17) (2,10) (2,7) (2,19) (2,22) (2,13) (2,12) (2,5) (2,4) (2,24) (2,16) (2,3) (2,11) (3,17) (3,10) (3,7) (3,19) (3,22) (3,13) (3,12) (3,5) (3,4) (3,24) (3,16) (3,11) (4,17) (4,10) (4,7) (4,19) (4,22) (4,13) (4,12) (4,5) (4,24) (4,16) (4,11) (5,17) (5,10) (5,7) (5,19) (5,22) (5,13) (5,12) (5,24) (5,16) (5,11) (6,8) (6,14) (6,9) (6,23) (7,17) (7,10) (7,19) (7,22) (7,13) (7,12) (7,24) (7,16) (7,11) (8,14) (8,9) (8,23) (9,14) (9,23) (10,17) (10,19) (10,22) (10,13) (10,12) (10,24) (10,16) (10,11) (11,17) (11,19) (11,22) (11,13) (11,12) (11,24) (11,16) (12,17) (12,19) (12,22) (12,13) (12,24) (12,16) (13,17) (13,19) (13,22) (13,24) (13,16) (14,23) (15,20) (15,18) (15,21) (16,17) (16,19) (16,22) (16,24) (17,19) (17,22) (17,24) (18,20) (18,21) (19,22) (19,24) (20,21) (22,24)\nIs there a path between node 12 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph835-7_16", + "image": "data/connectivity/graph_visual/medium/graph835.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (0,3) (1,24) (1,12) (1,17) (1,9) (1,15) (1,16) (1,2) (1,10) (1,13) (1,4) (1,19) (1,7) (1,14) (2,24) (2,12) (2,17) (2,9) (2,15) (2,16) (2,10) (2,13) (2,4) (2,19) (2,7) (2,14) (3,18) (4,24) (4,12) (4,17) (4,9) (4,15) (4,16) (4,10) (4,13) (4,19) (4,7) (4,14) (5,11) (5,23) (5,20) (5,8) (6,22) (6,21) (7,24) (7,12) (7,17) (7,9) (7,15) (7,16) (7,10) (7,13) (7,19) (7,14) (8,11) (8,23) (8,20) (9,24) (9,12) (9,17) (9,15) (9,16) (9,10) (9,13) (9,19) (9,14) (10,24) (10,12) (10,17) (10,15) (10,16) (10,13) (10,19) (10,14) (11,23) (11,20) (12,24) (12,17) (12,15) (12,16) (12,13) (12,19) (12,14) (13,24) (13,17) (13,15) (13,16) (13,19) (13,14) (14,24) (14,17) (14,15) (14,16) (14,19) (15,24) (15,17) (15,16) (15,19) (16,24) (16,17) (16,19) (17,24) (17,19) (19,24) (20,23) (21,22)\nIs there a path between node 7 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph490-11_9", + "image": "data/connectivity/graph_visual/medium/graph490.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (2,17) (2,19) (2,18) (2,8) (2,12) (2,21) (2,7) (2,13) (2,11) (2,10) (2,20) (2,5) (2,22) (3,15) (3,4) (3,16) (3,9) (3,6) (3,14) (4,15) (4,16) (4,9) (4,6) (4,14) (5,17) (5,19) (5,18) (5,8) (5,12) (5,21) (5,7) (5,13) (5,11) (5,10) (5,20) (5,22) (6,15) (6,16) (6,9) (6,14) (7,17) (7,19) (7,18) (7,8) (7,12) (7,21) (7,13) (7,11) (7,10) (7,20) (7,22) (8,17) (8,19) (8,18) (8,12) (8,21) (8,13) (8,11) (8,10) (8,20) (8,22) (9,15) (9,16) (9,14) (10,17) (10,19) (10,18) (10,12) (10,21) (10,13) (10,11) (10,20) (10,22) (11,17) (11,19) (11,18) (11,12) (11,21) (11,13) (11,20) (11,22) (12,17) (12,19) (12,18) (12,21) (12,13) (12,20) (12,22) (13,17) (13,19) (13,18) (13,21) (13,20) (13,22) (14,15) (14,16) (15,16) (17,19) (17,18) (17,21) (17,20) (17,22) (18,19) (18,21) (18,20) (18,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph772-19_1", + "image": "data/connectivity/graph_visual/medium/graph772.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,18) (0,22) (0,4) (0,12) (0,21) (0,24) (0,16) (1,3) (1,11) (1,10) (1,5) (1,8) (1,19) (1,9) (1,17) (1,7) (1,2) (1,20) (2,3) (2,11) (2,10) (2,5) (2,8) (2,19) (2,9) (2,17) (2,7) (2,20) (3,11) (3,10) (3,5) (3,8) (3,19) (3,9) (3,17) (3,7) (3,20) (4,15) (4,18) (4,22) (4,12) (4,21) (4,24) (4,16) (5,11) (5,10) (5,8) (5,19) (5,9) (5,17) (5,7) (5,20) (6,23) (6,14) (6,13) (7,11) (7,10) (7,8) (7,19) (7,9) (7,17) (7,20) (8,11) (8,10) (8,19) (8,9) (8,17) (8,20) (9,11) (9,10) (9,19) (9,17) (9,20) (10,11) (10,19) (10,17) (10,20) (11,19) (11,17) (11,20) (12,15) (12,18) (12,22) (12,21) (12,24) (12,16) (13,23) (13,14) (14,23) (15,18) (15,22) (15,21) (15,24) (15,16) (16,18) (16,22) (16,21) (16,24) (17,19) (17,20) (18,22) (18,21) (18,24) (19,20) (21,22) (21,24) (22,24)\nIs there a path between node 19 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph708-3_9", + "image": "data/connectivity/graph_visual/medium/graph708.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,14) (0,4) (1,9) (1,2) (1,15) (1,23) (2,9) (2,10) (2,18) (3,5) (3,8) (3,15) (3,18) (4,24) (4,13) (5,8) (5,15) (5,10) (5,23) (6,15) (6,10) (7,20) (8,15) (9,21) (10,15) (10,21) (10,18) (11,22) (11,13) (11,14) (12,22) (12,24) (12,13) (12,14) (13,17) (13,19) (13,22) (13,24) (14,24) (14,20) (15,18) (17,19) (17,20) (19,20)\nIs there a path between node 3 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph319-19_6", + "image": "data/connectivity/graph_visual/medium/graph319.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,1) (0,10) (0,2) (0,8) (0,4) (0,6) (0,11) (0,9) (0,5) (0,18) (0,7) (1,17) (1,10) (1,2) (1,8) (1,4) (1,6) (1,11) (1,9) (1,5) (1,18) (1,7) (2,17) (2,10) (2,8) (2,4) (2,6) (2,11) (2,9) (2,5) (2,18) (2,7) (3,16) (3,13) (3,14) (3,15) (3,19) (3,12) (4,17) (4,10) (4,8) (4,6) (4,11) (4,9) (4,5) (4,18) (4,7) (5,17) (5,10) (5,8) (5,6) (5,11) (5,9) (5,18) (5,7) (6,17) (6,10) (6,8) (6,11) (6,9) (6,18) (6,7) (7,17) (7,10) (7,8) (7,11) (7,9) (7,18) (8,17) (8,10) (8,11) (8,9) (8,18) (9,17) (9,10) (9,11) (9,18) (10,17) (10,11) (10,18) (11,17) (11,18) (12,16) (12,13) (12,14) (12,15) (12,19) (13,16) (13,14) (13,15) (13,19) (14,16) (14,15) (14,19) (15,16) (15,19) (16,19) (17,18)\nIs there a path between node 19 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph855-11_5", + "image": "data/connectivity/graph_visual/medium/graph855.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,13) (0,18) (0,21) (0,5) (0,12) (0,10) (0,7) (0,20) (0,17) (0,8) (0,24) (0,3) (0,9) (0,22) (0,16) (0,6) (0,19) (0,15) (1,4) (1,11) (1,23) (1,14) (2,13) (2,18) (2,21) (2,5) (2,12) (2,10) (2,7) (2,20) (2,17) (2,8) (2,24) (2,3) (2,9) (2,22) (2,16) (2,6) (2,19) (2,15) (3,13) (3,18) (3,21) (3,5) (3,12) (3,10) (3,7) (3,20) (3,17) (3,8) (3,24) (3,9) (3,22) (3,16) (3,6) (3,19) (3,15) (4,11) (4,23) (4,14) (5,13) (5,18) (5,21) (5,12) (5,10) (5,7) (5,20) (5,17) (5,8) (5,24) (5,9) (5,22) (5,16) (5,6) (5,19) (5,15) (6,13) (6,18) (6,21) (6,12) (6,10) (6,7) (6,20) (6,17) (6,8) (6,24) (6,9) (6,22) (6,16) (6,19) (6,15) (7,13) (7,18) (7,21) (7,12) (7,10) (7,20) (7,17) (7,8) (7,24) (7,9) (7,22) (7,16) (7,19) (7,15) (8,13) (8,18) (8,21) (8,12) (8,10) (8,20) (8,17) (8,24) (8,9) (8,22) (8,16) (8,19) (8,15) (9,13) (9,18) (9,21) (9,12) (9,10) (9,20) (9,17) (9,24) (9,22) (9,16) (9,19) (9,15) (10,13) (10,18) (10,21) (10,12) (10,20) (10,17) (10,24) (10,22) (10,16) (10,19) (10,15) (11,23) (11,14) (12,13) (12,18) (12,21) (12,20) (12,17) (12,24) (12,22) (12,16) (12,19) (12,15) (13,18) (13,21) (13,20) (13,17) (13,24) (13,22) (13,16) (13,19) (13,15) (14,23) (15,18) (15,21) (15,20) (15,17) (15,24) (15,22) (15,16) (15,19) (16,18) (16,21) (16,20) (16,17) (16,24) (16,22) (16,19) (17,18) (17,21) (17,20) (17,24) (17,22) (17,19) (18,21) (18,20) (18,24) (18,22) (18,19) (19,21) (19,20) (19,24) (19,22) (20,21) (20,24) (20,22) (21,24) (21,22) (22,24)\nIs there a path between node 11 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph724-1_2", + "image": "data/connectivity/graph_visual/medium/graph724.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,10) (0,23) (0,13) (0,12) (0,18) (0,8) (0,4) (0,11) (0,9) (0,20) (0,5) (0,14) (0,24) (0,21) (0,1) (0,16) (0,2) (0,7) (0,22) (0,19) (1,15) (1,10) (1,23) (1,13) (1,12) (1,18) (1,8) (1,4) (1,11) (1,9) (1,20) (1,5) (1,14) (1,24) (1,21) (1,16) (1,2) (1,7) (1,22) (1,19) (2,15) (2,10) (2,23) (2,13) (2,12) (2,18) (2,8) (2,4) (2,11) (2,9) (2,20) (2,5) (2,14) (2,24) (2,21) (2,16) (2,7) (2,22) (2,19) (3,17) (3,6) (4,15) (4,10) (4,23) (4,13) (4,12) (4,18) (4,8) (4,11) (4,9) (4,20) (4,5) (4,14) (4,24) (4,21) (4,16) (4,7) (4,22) (4,19) (5,15) (5,10) (5,23) (5,13) (5,12) (5,18) (5,8) (5,11) (5,9) (5,20) (5,14) (5,24) (5,21) (5,16) (5,7) (5,22) (5,19) (6,17) (7,15) (7,10) (7,23) (7,13) (7,12) (7,18) (7,8) (7,11) (7,9) (7,20) (7,14) (7,24) (7,21) (7,16) (7,22) (7,19) (8,15) (8,10) (8,23) (8,13) (8,12) (8,18) (8,11) (8,9) (8,20) (8,14) (8,24) (8,21) (8,16) (8,22) (8,19) (9,15) (9,10) (9,23) (9,13) (9,12) (9,18) (9,11) (9,20) (9,14) (9,24) (9,21) (9,16) (9,22) (9,19) (10,15) (10,23) (10,13) (10,12) (10,18) (10,11) (10,20) (10,14) (10,24) (10,21) (10,16) (10,22) (10,19) (11,15) (11,23) (11,13) (11,12) (11,18) (11,20) (11,14) (11,24) (11,21) (11,16) (11,22) (11,19) (12,15) (12,23) (12,13) (12,18) (12,20) (12,14) (12,24) (12,21) (12,16) (12,22) (12,19) (13,15) (13,23) (13,18) (13,20) (13,14) (13,24) (13,21) (13,16) (13,22) (13,19) (14,15) (14,23) (14,18) (14,20) (14,24) (14,21) (14,16) (14,22) (14,19) (15,23) (15,18) (15,20) (15,24) (15,21) (15,16) (15,22) (15,19) (16,23) (16,18) (16,20) (16,24) (16,21) (16,22) (16,19) (18,23) (18,20) (18,24) (18,21) (18,22) (18,19) (19,23) (19,20) (19,24) (19,21) (19,22) (20,23) (20,24) (20,21) (20,22) (21,23) (21,24) (21,22) (22,23) (22,24) (23,24)\nIs there a path between node 1 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph460-13_11", + "image": "data/connectivity/graph_visual/medium/graph460.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,8) (0,1) (0,15) (0,12) (0,6) (0,14) (0,5) (0,2) (0,3) (0,16) (0,17) (0,11) (0,9) (0,7) (0,4) (0,20) (0,13) (0,10) (1,8) (1,15) (1,12) (1,6) (1,14) (1,5) (1,2) (1,3) (1,16) (1,17) (1,11) (1,9) (1,7) (1,4) (1,20) (1,13) (1,10) (2,8) (2,15) (2,12) (2,6) (2,14) (2,5) (2,3) (2,16) (2,17) (2,11) (2,9) (2,7) (2,4) (2,20) (2,13) (2,10) (3,8) (3,15) (3,12) (3,6) (3,14) (3,5) (3,16) (3,17) (3,11) (3,9) (3,7) (3,4) (3,20) (3,13) (3,10) (4,8) (4,15) (4,12) (4,6) (4,14) (4,5) (4,16) (4,17) (4,11) (4,9) (4,7) (4,20) (4,13) (4,10) (5,8) (5,15) (5,12) (5,6) (5,14) (5,16) (5,17) (5,11) (5,9) (5,7) (5,20) (5,13) (5,10) (6,8) (6,15) (6,12) (6,14) (6,16) (6,17) (6,11) (6,9) (6,7) (6,20) (6,13) (6,10) (7,8) (7,15) (7,12) (7,14) (7,16) (7,17) (7,11) (7,9) (7,20) (7,13) (7,10) (8,15) (8,12) (8,14) (8,16) (8,17) (8,11) (8,9) (8,20) (8,13) (8,10) (9,15) (9,12) (9,14) (9,16) (9,17) (9,11) (9,20) (9,13) (9,10) (10,15) (10,12) (10,14) (10,16) (10,17) (10,11) (10,20) (10,13) (11,15) (11,12) (11,14) (11,16) (11,17) (11,20) (11,13) (12,15) (12,14) (12,16) (12,17) (12,20) (12,13) (13,15) (13,14) (13,16) (13,17) (13,20) (14,15) (14,16) (14,17) (14,20) (15,16) (15,17) (15,20) (16,17) (16,20) (17,20) (18,21)\nIs there a path between node 13 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph15-5_3", + "image": "data/connectivity/graph_visual/medium/graph15.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,4) (0,8) (1,5) (2,3) (3,5) (3,11) (4,8) (5,9) (5,7) (5,10) (6,11)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph531-16_17", + "image": "data/connectivity/graph_visual/medium/graph531.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,13) (0,7) (0,4) (0,9) (0,21) (0,16) (0,1) (0,18) (0,11) (0,8) (0,6) (0,15) (0,14) (0,12) (0,20) (0,2) (0,22) (1,10) (1,13) (1,7) (1,4) (1,9) (1,21) (1,16) (1,18) (1,11) (1,8) (1,6) (1,15) (1,14) (1,12) (1,20) (1,2) (1,22) (2,10) (2,13) (2,7) (2,4) (2,9) (2,21) (2,16) (2,18) (2,11) (2,8) (2,6) (2,15) (2,14) (2,12) (2,20) (2,22) (3,17) (3,19) (3,5) (4,10) (4,13) (4,7) (4,9) (4,21) (4,16) (4,18) (4,11) (4,8) (4,6) (4,15) (4,14) (4,12) (4,20) (4,22) (5,17) (5,19) (6,10) (6,13) (6,7) (6,9) (6,21) (6,16) (6,18) (6,11) (6,8) (6,15) (6,14) (6,12) (6,20) (6,22) (7,10) (7,13) (7,9) (7,21) (7,16) (7,18) (7,11) (7,8) (7,15) (7,14) (7,12) (7,20) (7,22) (8,10) (8,13) (8,9) (8,21) (8,16) (8,18) (8,11) (8,15) (8,14) (8,12) (8,20) (8,22) (9,10) (9,13) (9,21) (9,16) (9,18) (9,11) (9,15) (9,14) (9,12) (9,20) (9,22) (10,13) (10,21) (10,16) (10,18) (10,11) (10,15) (10,14) (10,12) (10,20) (10,22) (11,13) (11,21) (11,16) (11,18) (11,15) (11,14) (11,12) (11,20) (11,22) (12,13) (12,21) (12,16) (12,18) (12,15) (12,14) (12,20) (12,22) (13,21) (13,16) (13,18) (13,15) (13,14) (13,20) (13,22) (14,21) (14,16) (14,18) (14,15) (14,20) (14,22) (15,21) (15,16) (15,18) (15,20) (15,22) (16,21) (16,18) (16,20) (16,22) (17,19) (18,21) (18,20) (18,22) (20,21) (20,22) (21,22)\nIs there a path between node 16 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph18-0_3", + "image": "data/connectivity/graph_visual/medium/graph18.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (0,2) (1,5) (1,2) (2,5) (2,10) (3,10) (3,4) (3,8) (4,5) (5,10) (5,8) (7,11) (8,10) (9,11)\nIs there a path between node 0 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph382-12_4", + "image": "data/connectivity/graph_visual/medium/graph382.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,20) (0,10) (0,13) (0,17) (1,7) (1,5) (1,16) (1,6) (2,14) (2,18) (2,11) (2,9) (2,4) (2,15) (2,19) (2,12) (2,3) (2,8) (3,14) (3,18) (3,11) (3,9) (3,4) (3,15) (3,19) (3,12) (3,8) (4,14) (4,18) (4,11) (4,9) (4,15) (4,19) (4,12) (4,8) (5,7) (5,16) (5,6) (6,7) (6,16) (7,16) (8,14) (8,18) (8,11) (8,9) (8,15) (8,19) (8,12) (9,14) (9,18) (9,11) (9,15) (9,19) (9,12) (10,20) (10,13) (10,17) (11,14) (11,18) (11,15) (11,19) (11,12) (12,14) (12,18) (12,15) (12,19) (13,20) (13,17) (14,18) (14,15) (14,19) (15,18) (15,19) (17,20) (18,19)\nIs there a path between node 12 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph543-8_10", + "image": "data/connectivity/graph_visual/medium/graph543.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,15) (0,8) (0,12) (0,14) (0,2) (0,9) (0,1) (1,15) (1,20) (1,12) (2,20) (2,12) (2,7) (2,16) (3,15) (3,7) (3,16) (3,13) (3,14) (3,17) (3,21) (4,22) (4,8) (4,12) (4,17) (4,11) (6,23) (7,15) (7,17) (7,11) (7,21) (7,18) (8,22) (8,15) (8,20) (8,16) (8,9) (9,22) (9,13) (9,11) (9,21) (9,18) (10,22) (10,13) (10,21) (11,22) (11,15) (11,20) (11,12) (11,21) (11,18) (12,15) (12,13) (13,20) (13,18) (14,20) (17,22) (17,18) (18,20) (19,23) (20,22) (21,22)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph449-9_13", + "image": "data/connectivity/graph_visual/medium/graph449.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,10) (0,9) (0,12) (0,15) (1,8) (1,11) (1,5) (1,10) (1,17) (1,9) (1,12) (1,20) (1,15) (2,8) (2,11) (2,10) (2,17) (2,12) (3,11) (3,5) (3,17) (3,9) (3,12) (3,15) (5,11) (5,12) (5,20) (5,15) (6,16) (6,14) (6,18) (7,16) (7,13) (7,21) (7,14) (7,19) (7,18) (8,11) (8,17) (8,20) (9,11) (9,10) (9,17) (9,12) (9,20) (9,15) (10,11) (10,17) (10,12) (10,20) (10,15) (11,12) (11,20) (12,17) (12,20) (13,16) (13,21) (13,14) (13,18) (14,19) (14,18) (15,17) (15,20) (16,19) (16,18) (18,21) (18,19)\nIs there a path between node 9 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph804-12_2", + "image": "data/connectivity/graph_visual/medium/graph804.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,4) (1,19) (2,4) (2,10) (2,20) (3,20) (3,19) (4,13) (4,9) (4,7) (4,19) (5,6) (7,12) (7,20) (9,14) (9,13) (9,23) (9,12) (9,10) (10,15) (12,15) (12,20) (13,19) (14,20) (16,17) (18,22) (20,23)\nIs there a path between node 12 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph838-16_8", + "image": "data/connectivity/graph_visual/medium/graph838.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,22) (1,18) (1,7) (1,23) (1,2) (1,24) (1,9) (1,21) (1,14) (1,17) (1,16) (1,3) (1,15) (1,6) (1,19) (2,18) (2,7) (2,23) (2,24) (2,9) (2,21) (2,14) (2,17) (2,16) (2,3) (2,15) (2,6) (2,19) (3,18) (3,7) (3,23) (3,24) (3,9) (3,21) (3,14) (3,17) (3,16) (3,15) (3,6) (3,19) (4,11) (4,20) (4,13) (4,5) (4,8) (4,10) (4,12) (5,11) (5,20) (5,13) (5,8) (5,10) (5,12) (6,18) (6,7) (6,23) (6,24) (6,9) (6,21) (6,14) (6,17) (6,16) (6,15) (6,19) (7,18) (7,23) (7,24) (7,9) (7,21) (7,14) (7,17) (7,16) (7,15) (7,19) (8,11) (8,20) (8,13) (8,10) (8,12) (9,18) (9,23) (9,24) (9,21) (9,14) (9,17) (9,16) (9,15) (9,19) (10,11) (10,20) (10,13) (10,12) (11,20) (11,13) (11,12) (12,20) (12,13) (13,20) (14,18) (14,23) (14,24) (14,21) (14,17) (14,16) (14,15) (14,19) (15,18) (15,23) (15,24) (15,21) (15,17) (15,16) (15,19) (16,18) (16,23) (16,24) (16,21) (16,17) (16,19) (17,18) (17,23) (17,24) (17,21) (17,19) (18,23) (18,24) (18,21) (18,19) (19,23) (19,24) (19,21) (21,23) (21,24) (23,24)\nIs there a path between node 16 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph402-17_21", + "image": "data/connectivity/graph_visual/medium/graph402.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,16) (0,1) (0,8) (2,6) (2,17) (2,20) (3,7) (3,13) (5,20) (5,13) (6,17) (6,10) (6,13) (7,10) (7,11) (7,9) (8,19) (8,14) (9,10) (12,17) (12,20) (12,13) (14,21)\nIs there a path between node 17 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph782-1_21", + "image": "data/connectivity/graph_visual/medium/graph782.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,11) (0,5) (1,9) (1,17) (2,6) (2,22) (2,15) (2,11) (2,18) (2,7) (3,12) (3,11) (4,12) (4,14) (4,15) (4,13) (5,10) (5,14) (5,22) (5,11) (5,7) (6,8) (6,15) (7,8) (7,10) (7,22) (7,13) (7,16) (8,20) (8,14) (8,19) (8,15) (8,11) (9,24) (9,23) (9,17) (10,14) (10,11) (10,18) (11,20) (12,15) (12,13) (13,22) (13,15) (13,18) (13,16) (14,20) (14,22) (14,18) (15,20) (15,19) (15,18) (17,23) (20,21) (21,22) (23,24)\nIs there a path between node 1 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph241-0_16", + "image": "data/connectivity/graph_visual/medium/graph241.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,10) (1,14) (1,18) (1,4) (1,11) (1,15) (1,7) (1,5) (1,3) (2,14) (2,18) (2,16) (2,6) (2,4) (2,9) (2,11) (2,15) (2,7) (2,5) (2,3) (3,14) (3,16) (3,6) (3,4) (3,9) (3,11) (3,15) (3,7) (3,5) (4,14) (4,8) (4,9) (4,11) (4,15) (5,18) (5,16) (5,8) (5,6) (5,9) (5,11) (5,15) (5,7) (6,14) (6,16) (6,12) (6,15) (6,7) (7,14) (7,18) (7,16) (7,12) (7,8) (7,9) (7,15) (8,14) (8,18) (8,16) (8,9) (8,11) (8,15) (9,18) (9,16) (9,11) (11,18) (11,16) (11,12) (11,15) (12,14) (12,18) (12,16) (12,15) (14,18) (14,16) (14,15) (15,16) (16,18)\nIs there a path between node 0 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph720-6_5", + "image": "data/connectivity/graph_visual/medium/graph720.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,21) (0,11) (0,15) (0,4) (0,22) (0,5) (0,3) (0,6) (0,20) (0,13) (0,18) (0,9) (0,1) (0,12) (0,24) (0,16) (0,8) (0,23) (0,2) (1,21) (1,11) (1,15) (1,4) (1,22) (1,5) (1,3) (1,6) (1,20) (1,13) (1,18) (1,9) (1,12) (1,24) (1,16) (1,8) (1,23) (1,2) (2,21) (2,11) (2,15) (2,4) (2,22) (2,5) (2,3) (2,6) (2,20) (2,13) (2,18) (2,9) (2,12) (2,24) (2,16) (2,8) (2,23) (3,21) (3,11) (3,15) (3,4) (3,22) (3,5) (3,6) (3,20) (3,13) (3,18) (3,9) (3,12) (3,24) (3,16) (3,8) (3,23) (4,21) (4,11) (4,15) (4,22) (4,5) (4,6) (4,20) (4,13) (4,18) (4,9) (4,12) (4,24) (4,16) (4,8) (4,23) (5,21) (5,11) (5,15) (5,22) (5,6) (5,20) (5,13) (5,18) (5,9) (5,12) (5,24) (5,16) (5,8) (5,23) (6,21) (6,11) (6,15) (6,22) (6,20) (6,13) (6,18) (6,9) (6,12) (6,24) (6,16) (6,8) (6,23) (7,10) (7,14) (7,17) (7,19) (8,21) (8,11) (8,15) (8,22) (8,20) (8,13) (8,18) (8,9) (8,12) (8,24) (8,16) (8,23) (9,21) (9,11) (9,15) (9,22) (9,20) (9,13) (9,18) (9,12) (9,24) (9,16) (9,23) (10,14) (10,17) (10,19) (11,21) (11,15) (11,22) (11,20) (11,13) (11,18) (11,12) (11,24) (11,16) (11,23) (12,21) (12,15) (12,22) (12,20) (12,13) (12,18) (12,24) (12,16) (12,23) (13,21) (13,15) (13,22) (13,20) (13,18) (13,24) (13,16) (13,23) (14,17) (14,19) (15,21) (15,22) (15,20) (15,18) (15,24) (15,16) (15,23) (16,21) (16,22) (16,20) (16,18) (16,24) (16,23) (17,19) (18,21) (18,22) (18,20) (18,24) (18,23) (20,21) (20,22) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph614-11_9", + "image": "data/connectivity/graph_visual/medium/graph614.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,18) (0,1) (0,6) (0,10) (1,8) (1,18) (1,6) (1,10) (2,21) (2,20) (2,19) (2,14) (2,16) (2,13) (2,3) (2,12) (2,4) (2,22) (2,11) (2,9) (2,17) (2,15) (3,21) (3,20) (3,19) (3,14) (3,16) (3,13) (3,12) (3,4) (3,22) (3,11) (3,9) (3,17) (3,15) (4,21) (4,20) (4,19) (4,14) (4,16) (4,13) (4,12) (4,22) (4,11) (4,9) (4,17) (4,15) (5,7) (6,8) (6,18) (6,10) (8,18) (8,10) (9,21) (9,20) (9,19) (9,14) (9,16) (9,13) (9,12) (9,22) (9,11) (9,17) (9,15) (10,18) (11,21) (11,20) (11,19) (11,14) (11,16) (11,13) (11,12) (11,22) (11,17) (11,15) (12,21) (12,20) (12,19) (12,14) (12,16) (12,13) (12,22) (12,17) (12,15) (13,21) (13,20) (13,19) (13,14) (13,16) (13,22) (13,17) (13,15) (14,21) (14,20) (14,19) (14,16) (14,22) (14,17) (14,15) (15,21) (15,20) (15,19) (15,16) (15,22) (15,17) (16,21) (16,20) (16,19) (16,22) (16,17) (17,21) (17,20) (17,19) (17,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph446-6_18", + "image": "data/connectivity/graph_visual/medium/graph446.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,13) (0,2) (0,5) (0,4) (0,18) (0,9) (0,3) (0,12) (0,21) (0,8) (0,20) (1,16) (1,17) (1,14) (1,19) (2,11) (2,13) (2,5) (2,4) (2,3) (2,21) (2,10) (2,8) (3,11) (3,5) (3,18) (3,12) (3,21) (3,10) (3,8) (3,20) (4,11) (4,13) (4,5) (4,18) (4,9) (4,12) (4,21) (4,10) (4,8) (4,20) (5,11) (5,13) (5,18) (5,12) (5,21) (5,10) (5,8) (5,20) (6,15) (7,15) (8,13) (8,12) (8,10) (9,11) (9,18) (9,12) (9,21) (9,10) (10,11) (10,13) (10,18) (10,21) (10,20) (11,12) (11,20) (12,13) (12,21) (12,20) (13,21) (14,16) (14,17) (14,19) (16,17) (16,19) (18,21) (18,20) (20,21)\nIs there a path between node 6 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph384-0_19", + "image": "data/connectivity/graph_visual/medium/graph384.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,6) (1,7) (1,5) (1,16) (1,15) (1,3) (1,13) (1,10) (1,12) (1,4) (1,17) (1,20) (1,18) (1,8) (1,2) (1,19) (1,9) (1,11) (1,14) (2,7) (2,5) (2,16) (2,15) (2,3) (2,13) (2,10) (2,12) (2,4) (2,17) (2,20) (2,18) (2,8) (2,19) (2,9) (2,11) (2,14) (3,7) (3,5) (3,16) (3,15) (3,13) (3,10) (3,12) (3,4) (3,17) (3,20) (3,18) (3,8) (3,19) (3,9) (3,11) (3,14) (4,7) (4,5) (4,16) (4,15) (4,13) (4,10) (4,12) (4,17) (4,20) (4,18) (4,8) (4,19) (4,9) (4,11) (4,14) (5,7) (5,16) (5,15) (5,13) (5,10) (5,12) (5,17) (5,20) (5,18) (5,8) (5,19) (5,9) (5,11) (5,14) (7,16) (7,15) (7,13) (7,10) (7,12) (7,17) (7,20) (7,18) (7,8) (7,19) (7,9) (7,11) (7,14) (8,16) (8,15) (8,13) (8,10) (8,12) (8,17) (8,20) (8,18) (8,19) (8,9) (8,11) (8,14) (9,16) (9,15) (9,13) (9,10) (9,12) (9,17) (9,20) (9,18) (9,19) (9,11) (9,14) (10,16) (10,15) (10,13) (10,12) (10,17) (10,20) (10,18) (10,19) (10,11) (10,14) (11,16) (11,15) (11,13) (11,12) (11,17) (11,20) (11,18) (11,19) (11,14) (12,16) (12,15) (12,13) (12,17) (12,20) (12,18) (12,19) (12,14) (13,16) (13,15) (13,17) (13,20) (13,18) (13,19) (13,14) (14,16) (14,15) (14,17) (14,20) (14,18) (14,19) (15,16) (15,17) (15,20) (15,18) (15,19) (16,17) (16,20) (16,18) (16,19) (17,20) (17,18) (17,19) (18,20) (18,19) (19,20)\nIs there a path between node 0 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph678-14_4", + "image": "data/connectivity/graph_visual/medium/graph678.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,16) (0,15) (0,3) (0,1) (0,8) (1,23) (1,16) (1,15) (1,3) (1,8) (2,7) (2,4) (2,20) (2,14) (3,23) (3,16) (3,15) (3,8) (4,7) (4,20) (4,14) (5,12) (5,10) (5,18) (5,9) (5,22) (5,13) (5,17) (6,19) (6,11) (6,21) (7,20) (7,14) (8,23) (8,16) (8,15) (9,12) (9,10) (9,18) (9,22) (9,13) (9,17) (10,12) (10,18) (10,22) (10,13) (10,17) (11,19) (11,21) (12,18) (12,22) (12,13) (12,17) (13,18) (13,22) (13,17) (14,20) (15,23) (15,16) (16,23) (17,18) (17,22) (18,22) (19,21)\nIs there a path between node 14 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph323-11_0", + "image": "data/connectivity/graph_visual/medium/graph323.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,15) (0,7) (0,3) (0,19) (0,14) (0,18) (0,16) (1,2) (1,8) (1,6) (1,17) (1,5) (1,4) (1,9) (1,10) (1,13) (1,12) (1,11) (2,8) (2,6) (2,17) (2,5) (2,4) (2,9) (2,10) (2,13) (2,12) (2,11) (3,15) (3,7) (3,19) (3,14) (3,18) (3,16) (4,8) (4,6) (4,17) (4,5) (4,9) (4,10) (4,13) (4,12) (4,11) (5,8) (5,6) (5,17) (5,9) (5,10) (5,13) (5,12) (5,11) (6,8) (6,17) (6,9) (6,10) (6,13) (6,12) (6,11) (7,15) (7,19) (7,14) (7,18) (7,16) (8,17) (8,9) (8,10) (8,13) (8,12) (8,11) (9,17) (9,10) (9,13) (9,12) (9,11) (10,17) (10,13) (10,12) (10,11) (11,17) (11,13) (11,12) (12,17) (12,13) (13,17) (14,15) (14,19) (14,18) (14,16) (15,19) (15,18) (15,16) (16,19) (16,18) (18,19)\nIs there a path between node 11 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph56-9_5", + "image": "data/connectivity/graph_visual/medium/graph56.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,8) (1,7) (1,11) (2,12) (3,8) (3,4) (4,5) (5,7) (5,6) (5,11) (6,11) (9,12) (10,12) (12,13)\nIs there a path between node 9 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph577-21_4", + "image": "data/connectivity/graph_visual/medium/graph577.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (0,12) (0,18) (1,3) (1,16) (1,17) (1,14) (1,9) (1,8) (2,18) (2,9) (2,13) (2,22) (3,17) (3,14) (4,5) (4,21) (5,11) (5,6) (5,10) (6,11) (6,21) (7,19) (8,16) (8,22) (9,20) (9,18) (9,23) (11,19) (11,21) (12,14) (12,23) (12,22) (13,16) (13,20) (13,17) (13,22) (14,16) (15,18) (15,23) (16,18) (17,20) (17,18) (17,23) (17,22) (19,21) (20,23)\nIs there a path between node 21 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph172-9_0", + "image": "data/connectivity/graph_visual/medium/graph172.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,15) (0,3) (1,10) (1,2) (1,5) (1,9) (2,10) (2,7) (2,9) (4,17) (4,12) (4,8) (4,13) (5,10) (5,7) (5,9) (6,17) (6,14) (6,11) (6,8) (6,13) (8,17) (8,11) (8,12) (8,13) (9,10) (11,14) (11,13) (12,17) (12,14) (12,13) (13,17) (13,14) (14,17) (15,16)\nIs there a path between node 9 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph402-13_8", + "image": "data/connectivity/graph_visual/medium/graph402.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,16) (0,1) (0,8) (2,6) (2,17) (2,20) (3,7) (3,13) (5,20) (5,13) (6,17) (6,10) (6,13) (7,10) (7,11) (7,9) (8,19) (8,14) (9,10) (12,17) (12,20) (12,13) (14,21)\nIs there a path between node 13 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph135-17_13", + "image": "data/connectivity/graph_visual/medium/graph135.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,14) (0,3) (0,5) (1,2) (1,10) (1,3) (1,5) (2,6) (2,10) (3,17) (3,14) (3,6) (3,9) (4,14) (4,7) (4,9) (5,17) (5,14) (5,6) (5,10) (5,7) (6,14) (6,16) (6,7) (9,17) (9,16) (9,10) (10,14) (11,15) (12,13) (14,17) (14,16) (14,15) (15,17)\nIs there a path between node 17 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph83-3_4", + "image": "data/connectivity/graph_visual/medium/graph83.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,6) (0,9) (0,10) (0,2) (0,11) (0,12) (1,13) (1,5) (2,6) (2,9) (2,8) (2,7) (2,10) (2,14) (2,12) (4,6) (4,9) (4,8) (4,7) (4,10) (4,14) (4,11) (4,12) (5,13) (6,8) (6,7) (6,10) (6,14) (6,11) (6,12) (7,9) (7,10) (7,14) (8,9) (8,10) (8,11) (8,12) (9,14) (9,11) (10,11) (11,14) (12,14)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph208-8_10", + "image": "data/connectivity/graph_visual/medium/graph208.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,15) (0,13) (0,3) (0,16) (0,10) (1,18) (1,7) (1,2) (1,4) (1,9) (1,12) (1,11) (1,5) (2,18) (2,7) (2,4) (2,9) (2,12) (2,6) (2,11) (2,5) (3,15) (3,17) (4,18) (4,9) (4,12) (4,6) (4,5) (5,18) (5,7) (5,12) (5,6) (5,11) (6,18) (6,7) (6,12) (7,18) (7,12) (9,12) (9,11) (10,15) (10,14) (11,18) (11,12) (13,16) (13,14) (13,17) (14,15) (14,16) (15,16) (16,17)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph626-20_12", + "image": "data/connectivity/graph_visual/medium/graph626.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,17) (0,15) (0,9) (1,21) (1,22) (2,7) (2,21) (2,12) (2,23) (3,7) (3,8) (3,17) (3,12) (4,11) (5,14) (5,13) (6,17) (6,15) (6,18) (7,17) (7,12) (7,20) (7,22) (7,18) (8,17) (8,18) (9,17) (10,16) (11,19) (13,16) (17,21) (17,20) (17,18) (18,23) (18,20) (21,23)\nIs there a path between node 20 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph566-21_18", + "image": "data/connectivity/graph_visual/medium/graph566.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (0,9) (0,15) (0,23) (0,4) (0,22) (0,8) (0,7) (0,16) (0,19) (0,3) (0,21) (0,17) (1,6) (1,10) (1,12) (1,2) (1,18) (1,11) (1,14) (1,20) (1,5) (2,6) (2,10) (2,12) (2,18) (2,11) (2,14) (2,20) (2,5) (3,13) (3,9) (3,15) (3,23) (3,4) (3,22) (3,8) (3,7) (3,16) (3,19) (3,21) (3,17) (4,13) (4,9) (4,15) (4,23) (4,22) (4,8) (4,7) (4,16) (4,19) (4,21) (4,17) (5,6) (5,10) (5,12) (5,18) (5,11) (5,14) (5,20) (6,10) (6,12) (6,18) (6,11) (6,14) (6,20) (7,13) (7,9) (7,15) (7,23) (7,22) (7,8) (7,16) (7,19) (7,21) (7,17) (8,13) (8,9) (8,15) (8,23) (8,22) (8,16) (8,19) (8,21) (8,17) (9,13) (9,15) (9,23) (9,22) (9,16) (9,19) (9,21) (9,17) (10,12) (10,18) (10,11) (10,14) (10,20) (11,12) (11,18) (11,14) (11,20) (12,18) (12,14) (12,20) (13,15) (13,23) (13,22) (13,16) (13,19) (13,21) (13,17) (14,18) (14,20) (15,23) (15,22) (15,16) (15,19) (15,21) (15,17) (16,23) (16,22) (16,19) (16,21) (16,17) (17,23) (17,22) (17,19) (17,21) (18,20) (19,23) (19,22) (19,21) (21,23) (21,22) (22,23)\nIs there a path between node 21 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph634-0_11", + "image": "data/connectivity/graph_visual/medium/graph634.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,9) (0,18) (0,2) (0,14) (0,20) (0,22) (0,4) (0,1) (0,19) (1,23) (1,2) (1,16) (1,20) (1,22) (1,11) (1,4) (1,12) (2,3) (2,5) (2,7) (2,9) (2,18) (2,16) (2,14) (2,20) (2,8) (2,4) (2,19) (3,15) (3,5) (3,18) (3,16) (3,8) (3,22) (3,11) (4,15) (4,5) (4,18) (4,11) (4,12) (4,19) (5,23) (5,15) (5,16) (5,12) (5,19) (6,17) (7,18) (7,14) (7,20) (8,15) (8,18) (8,21) (12,21) (12,22) (12,19) (14,23) (14,19) (15,19) (16,18) (18,19) (19,23) (19,20) (19,22) (20,23)\nIs there a path between node 0 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph173-5_6", + "image": "data/connectivity/graph_visual/medium/graph173.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,7) (0,17) (0,11) (0,15) (0,12) (0,4) (0,14) (0,8) (0,16) (0,5) (1,7) (1,11) (1,15) (1,2) (1,9) (1,12) (1,14) (1,13) (1,5) (2,7) (2,11) (2,15) (2,9) (2,12) (2,4) (2,14) (2,13) (2,8) (2,16) (2,5) (4,7) (4,12) (5,17) (5,11) (5,15) (5,12) (5,13) (5,16) (6,10) (7,17) (7,11) (7,12) (7,14) (7,8) (8,11) (8,13) (8,16) (9,17) (9,11) (9,15) (9,12) (9,13) (9,16) (11,15) (11,12) (11,14) (11,13) (11,16) (12,17) (12,15) (12,14) (12,16) (13,17) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 5 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph405-2_12", + "image": "data/connectivity/graph_visual/medium/graph405.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,12) (0,8) (1,21) (1,5) (1,14) (2,17) (3,15) (3,21) (3,9) (3,5) (3,20) (3,19) (4,16) (4,7) (4,18) (5,15) (5,13) (6,9) (6,10) (6,20) (7,12) (9,10) (9,20) (9,14) (9,13) (10,21) (10,11) (11,15) (11,14) (13,14) (14,21) (15,19) (16,18) (20,21)\nIs there a path between node 2 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph481-5_19", + "image": "data/connectivity/graph_visual/medium/graph481.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,14) (0,2) (0,17) (0,18) (0,9) (0,21) (0,8) (0,13) (0,10) (0,15) (0,12) (1,14) (1,17) (1,22) (1,18) (1,9) (1,21) (1,8) (1,13) (1,7) (1,15) (1,12) (1,19) (2,17) (2,18) (2,9) (2,21) (2,13) (2,7) (2,15) (2,19) (3,16) (5,6) (5,16) (6,16) (7,17) (7,18) (7,9) (7,21) (7,8) (7,10) (7,15) (7,20) (7,12) (7,19) (8,17) (8,22) (8,18) (8,21) (8,13) (8,10) (8,11) (8,20) (8,12) (8,19) (9,14) (9,17) (9,22) (9,18) (9,21) (9,13) (9,10) (9,15) (9,20) (10,14) (10,17) (10,22) (10,13) (10,15) (10,11) (10,20) (10,12) (10,19) (11,14) (11,18) (11,13) (11,15) (11,19) (12,14) (12,22) (12,21) (12,20) (13,17) (13,22) (13,18) (13,21) (13,15) (13,19) (14,17) (14,22) (14,18) (14,21) (14,15) (14,20) (14,19) (15,22) (15,18) (15,19) (17,18) (17,21) (17,19) (18,22) (18,21) (18,20) (18,19) (19,22) (20,22) (20,21) (21,22)\nIs there a path between node 5 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph243-11_6", + "image": "data/connectivity/graph_visual/medium/graph243.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,3) (0,4) (0,8) (0,13) (0,7) (0,2) (0,14) (0,18) (0,1) (0,10) (0,5) (1,15) (1,4) (1,9) (1,8) (1,7) (1,17) (1,2) (1,10) (1,12) (1,5) (2,15) (2,4) (2,8) (2,17) (2,14) (2,18) (2,10) (2,5) (3,15) (3,4) (3,9) (3,13) (3,7) (3,14) (3,18) (3,10) (4,9) (4,8) (4,7) (4,17) (4,14) (4,18) (4,12) (4,5) (5,15) (5,8) (5,13) (5,11) (5,14) (5,18) (6,16) (7,15) (7,8) (7,13) (7,18) (7,10) (8,15) (8,9) (8,13) (8,11) (8,14) (8,18) (8,10) (8,12) (9,15) (9,13) (9,17) (9,11) (9,14) (9,18) (9,10) (9,12) (10,15) (10,18) (11,15) (11,13) (11,18) (11,12) (12,15) (12,17) (12,18) (13,15) (13,17) (13,18) (14,15) (14,18) (15,17) (17,18)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph416-4_16", + "image": "data/connectivity/graph_visual/medium/graph416.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,4) (0,21) (0,7) (0,11) (0,1) (0,12) (0,10) (0,6) (0,9) (0,17) (0,20) (0,15) (0,13) (1,2) (1,4) (1,21) (1,7) (1,11) (1,12) (1,10) (1,6) (1,9) (1,17) (1,20) (1,15) (1,13) (2,4) (2,21) (2,7) (2,11) (2,12) (2,10) (2,6) (2,9) (2,17) (2,20) (2,15) (2,13) (3,8) (3,16) (3,14) (3,18) (3,5) (3,19) (4,21) (4,7) (4,11) (4,12) (4,10) (4,6) (4,9) (4,17) (4,20) (4,15) (4,13) (5,8) (5,16) (5,14) (5,18) (5,19) (6,21) (6,7) (6,11) (6,12) (6,10) (6,9) (6,17) (6,20) (6,15) (6,13) (7,21) (7,11) (7,12) (7,10) (7,9) (7,17) (7,20) (7,15) (7,13) (8,16) (8,14) (8,18) (8,19) (9,21) (9,11) (9,12) (9,10) (9,17) (9,20) (9,15) (9,13) (10,21) (10,11) (10,12) (10,17) (10,20) (10,15) (10,13) (11,21) (11,12) (11,17) (11,20) (11,15) (11,13) (12,21) (12,17) (12,20) (12,15) (12,13) (13,21) (13,17) (13,20) (13,15) (14,16) (14,18) (14,19) (15,21) (15,17) (15,20) (16,18) (16,19) (17,21) (17,20) (18,19) (20,21)\nIs there a path between node 4 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph169-1_7", + "image": "data/connectivity/graph_visual/medium/graph169.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,17) (0,13) (0,12) (0,4) (0,1) (1,3) (1,17) (1,16) (1,14) (1,4) (2,5) (2,7) (2,9) (2,11) (2,8) (3,15) (3,13) (3,16) (3,12) (3,14) (3,6) (4,15) (4,13) (4,16) (4,12) (4,6) (5,9) (5,11) (5,10) (6,17) (6,13) (6,12) (7,11) (7,10) (7,8) (8,9) (8,11) (9,10) (10,11) (12,15) (12,17) (12,16) (12,14) (13,17) (13,16) (14,15) (14,17) (15,17) (15,16) (16,17)\nIs there a path between node 1 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph103-12_4", + "image": "data/connectivity/graph_visual/medium/graph103.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (0,5) (0,8) (0,4) (0,12) (0,2) (0,7) (0,14) (0,3) (0,6) (1,13) (1,5) (1,8) (1,4) (1,12) (1,2) (1,9) (1,14) (1,3) (2,13) (2,5) (2,10) (2,4) (2,9) (2,14) (3,5) (3,8) (3,10) (3,4) (3,9) (3,14) (3,6) (4,13) (4,5) (4,10) (4,9) (4,6) (5,13) (5,8) (5,10) (5,12) (5,9) (6,8) (6,10) (6,9) (6,7) (6,14) (7,13) (7,8) (7,10) (7,12) (8,10) (8,12) (8,9) (8,14) (9,13) (9,10) (9,12) (9,14) (10,12) (10,14) (11,15) (12,13)\nIs there a path between node 12 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph483-11_3", + "image": "data/connectivity/graph_visual/medium/graph483.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,12) (0,5) (0,19) (0,17) (0,10) (0,2) (1,4) (1,6) (1,15) (1,18) (1,14) (1,3) (1,16) (1,20) (1,8) (1,21) (1,13) (2,12) (2,5) (2,19) (2,22) (2,9) (3,6) (3,15) (3,18) (3,14) (3,20) (3,21) (3,13) (4,11) (4,14) (4,16) (4,20) (4,8) (4,21) (5,12) (5,19) (5,7) (5,17) (5,10) (5,9) (6,11) (6,18) (6,14) (6,16) (6,20) (6,13) (7,12) (7,19) (7,22) (7,17) (7,10) (7,9) (8,11) (8,15) (8,14) (8,16) (8,13) (9,12) (9,22) (9,17) (9,10) (10,17) (11,15) (11,18) (11,14) (11,16) (11,20) (12,19) (12,22) (13,15) (13,18) (13,14) (13,16) (13,20) (13,21) (14,18) (14,16) (14,20) (14,21) (15,18) (15,16) (15,20) (15,21) (16,18) (18,20) (19,22) (20,21)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph749-15_21", + "image": "data/connectivity/graph_visual/medium/graph749.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,24) (0,22) (0,18) (0,2) (0,6) (0,23) (0,12) (0,15) (0,19) (0,16) (0,10) (0,8) (0,20) (1,5) (1,22) (1,23) (1,9) (1,12) (1,15) (1,16) (1,8) (1,20) (2,24) (2,5) (2,22) (2,18) (2,6) (2,23) (2,9) (2,3) (2,15) (2,19) (2,16) (2,10) (2,8) (2,20) (3,24) (3,5) (3,22) (3,18) (3,6) (3,9) (3,15) (3,10) (3,17) (3,20) (4,13) (4,7) (4,14) (5,11) (5,24) (5,23) (5,12) (5,15) (5,19) (5,10) (5,8) (5,17) (6,11) (6,24) (6,22) (6,18) (6,23) (6,9) (6,19) (6,10) (6,8) (6,17) (6,20) (7,13) (8,11) (8,24) (8,22) (8,18) (8,12) (8,15) (8,17) (8,20) (9,11) (9,24) (9,23) (9,15) (9,19) (9,10) (9,17) (9,20) (10,24) (10,22) (10,18) (10,23) (10,19) (10,16) (10,20) (11,24) (11,22) (11,18) (11,12) (11,19) (11,16) (11,17) (11,20) (12,18) (12,23) (12,19) (12,16) (12,20) (13,14) (15,22) (15,16) (15,17) (15,20) (16,24) (16,22) (16,18) (16,23) (16,19) (16,20) (17,24) (17,18) (17,23) (17,20) (18,22) (18,19) (18,20) (19,24) (19,23) (20,22) (20,23) (22,24) (23,24)\nIs there a path between node 15 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph625-4_13", + "image": "data/connectivity/graph_visual/medium/graph625.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (1,11) (1,7) (1,13) (1,21) (1,19) (1,5) (2,17) (2,20) (2,5) (4,9) (4,22) (5,21) (5,19) (6,23) (7,11) (8,11) (8,13) (8,19) (8,18) (11,23) (11,13) (11,18) (13,20) (13,21) (13,19) (13,18) (14,16) (14,15) (18,20) (19,20) (19,21) (20,23)\nIs there a path between node 4 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph639-4_13", + "image": "data/connectivity/graph_visual/medium/graph639.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,12) (1,4) (1,21) (2,19) (2,23) (2,12) (3,16) (3,21) (4,22) (4,16) (5,18) (5,17) (5,8) (5,6) (5,15) (5,19) (5,23) (6,14) (6,23) (7,13) (8,17) (8,15) (8,12) (9,20) (10,20) (10,21) (11,16) (12,17) (12,15) (14,23) (15,18) (15,19) (15,23) (16,21) (17,19) (18,19) (19,23)\nIs there a path between node 4 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph281-14_6", + "image": "data/connectivity/graph_visual/medium/graph281.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,16) (0,13) (0,5) (0,1) (0,18) (0,8) (0,10) (0,4) (0,12) (0,14) (0,9) (0,15) (1,16) (1,13) (1,5) (1,18) (1,8) (1,10) (1,4) (1,12) (1,14) (1,9) (1,15) (2,11) (2,19) (2,6) (2,3) (2,7) (2,17) (3,11) (3,19) (3,6) (3,7) (3,17) (4,16) (4,13) (4,5) (4,18) (4,8) (4,10) (4,12) (4,14) (4,9) (4,15) (5,16) (5,13) (5,18) (5,8) (5,10) (5,12) (5,14) (5,9) (5,15) (6,11) (6,19) (6,7) (6,17) (7,11) (7,19) (7,17) (8,16) (8,13) (8,18) (8,10) (8,12) (8,14) (8,9) (8,15) (9,16) (9,13) (9,18) (9,10) (9,12) (9,14) (9,15) (10,16) (10,13) (10,18) (10,12) (10,14) (10,15) (11,19) (11,17) (12,16) (12,13) (12,18) (12,14) (12,15) (13,16) (13,18) (13,14) (13,15) (14,16) (14,18) (14,15) (15,16) (15,18) (16,18) (17,19)\nIs there a path between node 14 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph494-0_20", + "image": "data/connectivity/graph_visual/medium/graph494.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,13) (1,13) (2,14) (2,17) (2,4) (2,18) (2,15) (2,22) (2,5) (2,21) (2,7) (2,20) (2,12) (2,16) (2,10) (2,9) (2,6) (2,11) (2,19) (2,8) (2,3) (3,14) (3,17) (3,4) (3,18) (3,15) (3,22) (3,5) (3,21) (3,7) (3,20) (3,12) (3,16) (3,10) (3,9) (3,6) (3,11) (3,19) (3,8) (4,14) (4,17) (4,18) (4,15) (4,22) (4,5) (4,21) (4,7) (4,20) (4,12) (4,16) (4,10) (4,9) (4,6) (4,11) (4,19) (4,8) (5,14) (5,17) (5,18) (5,15) (5,22) (5,21) (5,7) (5,20) (5,12) (5,16) (5,10) (5,9) (5,6) (5,11) (5,19) (5,8) (6,14) (6,17) (6,18) (6,15) (6,22) (6,21) (6,7) (6,20) (6,12) (6,16) (6,10) (6,9) (6,11) (6,19) (6,8) (7,14) (7,17) (7,18) (7,15) (7,22) (7,21) (7,20) (7,12) (7,16) (7,10) (7,9) (7,11) (7,19) (7,8) (8,14) (8,17) (8,18) (8,15) (8,22) (8,21) (8,20) (8,12) (8,16) (8,10) (8,9) (8,11) (8,19) (9,14) (9,17) (9,18) (9,15) (9,22) (9,21) (9,20) (9,12) (9,16) (9,10) (9,11) (9,19) (10,14) (10,17) (10,18) (10,15) (10,22) (10,21) (10,20) (10,12) (10,16) (10,11) (10,19) (11,14) (11,17) (11,18) (11,15) (11,22) (11,21) (11,20) (11,12) (11,16) (11,19) (12,14) (12,17) (12,18) (12,15) (12,22) (12,21) (12,20) (12,16) (12,19) (14,17) (14,18) (14,15) (14,22) (14,21) (14,20) (14,16) (14,19) (15,17) (15,18) (15,22) (15,21) (15,20) (15,16) (15,19) (16,17) (16,18) (16,22) (16,21) (16,20) (16,19) (17,18) (17,22) (17,21) (17,20) (17,19) (18,22) (18,21) (18,20) (18,19) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 0 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph107-10_12", + "image": "data/connectivity/graph_visual/medium/graph107.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (0,7) (0,14) (0,5) (0,13) (0,10) (1,7) (1,14) (1,5) (1,13) (1,10) (2,6) (2,12) (2,4) (2,8) (2,15) (2,3) (2,9) (2,11) (3,6) (3,12) (3,4) (3,8) (3,15) (3,9) (3,11) (4,6) (4,12) (4,8) (4,15) (4,9) (4,11) (5,7) (5,14) (5,13) (5,10) (6,12) (6,8) (6,15) (6,9) (6,11) (7,14) (7,13) (7,10) (8,12) (8,15) (8,9) (8,11) (9,12) (9,15) (9,11) (10,14) (10,13) (11,12) (11,15) (12,15) (13,14)\nIs there a path between node 10 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph192-8_15", + "image": "data/connectivity/graph_visual/medium/graph192.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,11) (0,14) (0,5) (0,7) (0,9) (0,1) (0,12) (1,11) (1,14) (1,5) (1,7) (1,9) (1,12) (2,6) (2,10) (2,15) (2,8) (2,17) (2,13) (2,16) (2,3) (2,4) (3,6) (3,10) (3,15) (3,8) (3,17) (3,13) (3,16) (3,4) (4,6) (4,10) (4,15) (4,8) (4,17) (4,13) (4,16) (5,11) (5,14) (5,7) (5,9) (5,12) (6,10) (6,15) (6,8) (6,17) (6,13) (6,16) (7,11) (7,14) (7,9) (7,12) (8,10) (8,15) (8,17) (8,13) (8,16) (9,11) (9,14) (9,12) (10,15) (10,17) (10,13) (10,16) (11,14) (11,12) (12,14) (13,15) (13,17) (13,16) (15,17) (15,16) (16,17)\nIs there a path between node 8 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph43-7_8", + "image": "data/connectivity/graph_visual/medium/graph43.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,11) (0,3) (0,10) (1,4) (1,9) (1,6) (2,10) (3,5) (3,10) (4,7) (4,9) (4,6) (4,12) (5,10) (6,7) (6,12) (7,9) (8,9) (8,12) (9,12) (10,11)\nIs there a path between node 7 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph84-14_7", + "image": "data/connectivity/graph_visual/medium/graph84.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,4) (0,13) (0,12) (0,14) (0,8) (0,3) (0,6) (0,2) (0,9) (0,5) (1,10) (1,7) (1,11) (2,4) (2,13) (2,12) (2,14) (2,8) (2,3) (2,6) (2,9) (2,5) (3,4) (3,13) (3,12) (3,14) (3,8) (3,6) (3,9) (3,5) (4,13) (4,12) (4,14) (4,8) (4,6) (4,9) (4,5) (5,13) (5,12) (5,14) (5,8) (5,6) (5,9) (6,13) (6,12) (6,14) (6,8) (6,9) (7,10) (7,11) (8,13) (8,12) (8,14) (8,9) (9,13) (9,12) (9,14) (10,11) (12,13) (12,14) (13,14)\nIs there a path between node 14 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph69-7_8", + "image": "data/connectivity/graph_visual/medium/graph69.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,5) (0,9) (1,8) (1,4) (2,8) (2,4) (2,3) (3,7) (3,6) (3,10) (3,12) (3,11) (4,10) (4,12) (6,14) (6,8) (6,10) (7,14) (7,11) (8,14) (8,12) (10,14) (11,14) (12,14)\nIs there a path between node 7 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph43-0_9", + "image": "data/connectivity/graph_visual/medium/graph43.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,11) (0,3) (0,10) (1,4) (1,9) (1,6) (2,10) (3,5) (3,10) (4,7) (4,9) (4,6) (4,12) (5,10) (6,7) (6,12) (7,9) (8,9) (8,12) (9,12) (10,11)\nIs there a path between node 0 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph390-2_10", + "image": "data/connectivity/graph_visual/medium/graph390.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,20) (0,11) (0,2) (0,10) (0,8) (0,17) (0,6) (0,7) (0,9) (0,5) (1,13) (1,19) (1,14) (1,18) (1,12) (1,3) (1,4) (1,16) (1,15) (2,20) (2,11) (2,10) (2,8) (2,17) (2,6) (2,7) (2,9) (2,5) (3,13) (3,19) (3,14) (3,18) (3,12) (3,4) (3,16) (3,15) (4,13) (4,19) (4,14) (4,18) (4,12) (4,16) (4,15) (5,20) (5,11) (5,10) (5,8) (5,17) (5,6) (5,7) (5,9) (6,20) (6,11) (6,10) (6,8) (6,17) (6,7) (6,9) (7,20) (7,11) (7,10) (7,8) (7,17) (7,9) (8,20) (8,11) (8,10) (8,17) (8,9) (9,20) (9,11) (9,10) (9,17) (10,20) (10,11) (10,17) (11,20) (11,17) (12,13) (12,19) (12,14) (12,18) (12,16) (12,15) (13,19) (13,14) (13,18) (13,16) (13,15) (14,19) (14,18) (14,16) (14,15) (15,19) (15,18) (15,16) (16,19) (16,18) (17,20) (18,19)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph826-10_6", + "image": "data/connectivity/graph_visual/medium/graph826.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,15) (4,23) (4,8) (4,9) (4,21) (4,16) (4,10) (4,20) (4,17) (4,11) (4,24) (4,12) (4,22) (5,18) (5,23) (5,8) (5,9) (5,7) (5,21) (5,16) (5,10) (5,17) (5,11) (5,24) (5,12) (6,18) (6,8) (6,9) (6,14) (6,21) (6,16) (6,10) (6,20) (6,11) (6,24) (6,12) (6,22) (7,18) (7,23) (7,8) (7,14) (7,21) (7,10) (7,17) (7,11) (8,18) (8,14) (8,10) (8,24) (8,12) (8,22) (9,18) (9,23) (9,16) (9,10) (9,20) (9,24) (9,12) (9,22) (10,18) (10,23) (10,21) (10,16) (10,20) (10,17) (10,24) (10,12) (11,18) (11,24) (11,12) (11,22) (12,18) (12,14) (12,21) (12,17) (12,24) (12,22) (14,18) (14,16) (14,20) (14,24) (16,18) (16,23) (16,21) (16,20) (16,17) (16,24) (16,22) (17,18) (17,24) (18,23) (18,21) (18,24) (20,21) (20,24) (21,22) (22,23) (22,24) (23,24)\nIs there a path between node 10 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph293-15_2", + "image": "data/connectivity/graph_visual/medium/graph293.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,17) (2,4) (2,3) (2,13) (2,8) (2,16) (3,13) (3,7) (3,19) (3,11) (3,14) (4,11) (5,18) (5,11) (5,14) (6,7) (7,19) (7,16) (7,14) (8,18) (8,13) (10,18) (10,13) (10,11) (10,16) (11,13) (11,19) (11,16) (12,15) (13,16) (16,18) (18,19)\nIs there a path between node 15 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph152-1_2", + "image": "data/connectivity/graph_visual/medium/graph152.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,11) (1,13) (1,16) (1,8) (1,5) (1,4) (1,9) (1,3) (1,15) (1,17) (1,7) (1,6) (1,14) (1,2) (2,13) (2,16) (2,8) (2,5) (2,4) (2,9) (2,3) (2,15) (2,17) (2,7) (2,6) (2,14) (3,13) (3,16) (3,8) (3,5) (3,4) (3,9) (3,15) (3,17) (3,7) (3,6) (3,14) (4,13) (4,16) (4,8) (4,5) (4,9) (4,15) (4,17) (4,7) (4,6) (4,14) (5,13) (5,16) (5,8) (5,9) (5,15) (5,17) (5,7) (5,6) (5,14) (6,13) (6,16) (6,8) (6,9) (6,15) (6,17) (6,7) (6,14) (7,13) (7,16) (7,8) (7,9) (7,15) (7,17) (7,14) (8,13) (8,16) (8,9) (8,15) (8,17) (8,14) (9,13) (9,16) (9,15) (9,17) (9,14) (11,12) (13,16) (13,15) (13,17) (13,14) (14,16) (14,15) (14,17) (15,16) (15,17) (16,17)\nIs there a path between node 1 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph403-5_4", + "image": "data/connectivity/graph_visual/medium/graph403.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,3) (0,10) (1,13) (1,4) (1,12) (1,9) (2,20) (2,3) (3,6) (4,12) (5,14) (6,10) (6,14) (7,15) (8,18) (8,15) (9,18) (10,20) (10,16) (10,11) (10,21) (11,14) (12,15) (13,18) (14,20) (17,19) (17,18) (18,19)\nIs there a path between node 5 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph310-17_12", + "image": "data/connectivity/graph_visual/medium/graph310.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,10) (0,19) (0,16) (0,7) (0,8) (0,4) (0,3) (0,11) (0,1) (0,18) (0,9) (0,5) (0,2) (0,13) (1,17) (1,10) (1,19) (1,16) (1,7) (1,8) (1,4) (1,3) (1,11) (1,18) (1,9) (1,5) (1,2) (1,13) (2,17) (2,10) (2,19) (2,16) (2,7) (2,8) (2,4) (2,3) (2,11) (2,18) (2,9) (2,5) (2,13) (3,17) (3,10) (3,19) (3,16) (3,7) (3,8) (3,4) (3,11) (3,18) (3,9) (3,5) (3,13) (4,17) (4,10) (4,19) (4,16) (4,7) (4,8) (4,11) (4,18) (4,9) (4,5) (4,13) (5,17) (5,10) (5,19) (5,16) (5,7) (5,8) (5,11) (5,18) (5,9) (5,13) (6,15) (7,17) (7,10) (7,19) (7,16) (7,8) (7,11) (7,18) (7,9) (7,13) (8,17) (8,10) (8,19) (8,16) (8,11) (8,18) (8,9) (8,13) (9,17) (9,10) (9,19) (9,16) (9,11) (9,18) (9,13) (10,17) (10,19) (10,16) (10,11) (10,18) (10,13) (11,17) (11,19) (11,16) (11,18) (11,13) (12,14) (13,17) (13,19) (13,16) (13,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nIs there a path between node 17 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph492-8_5", + "image": "data/connectivity/graph_visual/medium/graph492.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,6) (0,17) (0,18) (0,8) (0,10) (0,12) (0,14) (0,16) (0,13) (0,9) (0,19) (0,15) (0,4) (0,20) (0,7) (0,5) (0,21) (0,3) (0,2) (1,6) (1,17) (1,18) (1,8) (1,10) (1,12) (1,14) (1,16) (1,13) (1,9) (1,19) (1,15) (1,4) (1,20) (1,7) (1,5) (1,21) (1,3) (1,2) (2,6) (2,17) (2,18) (2,8) (2,10) (2,12) (2,14) (2,16) (2,13) (2,9) (2,19) (2,15) (2,4) (2,20) (2,7) (2,5) (2,21) (2,3) (3,6) (3,17) (3,18) (3,8) (3,10) (3,12) (3,14) (3,16) (3,13) (3,9) (3,19) (3,15) (3,4) (3,20) (3,7) (3,5) (3,21) (4,6) (4,17) (4,18) (4,8) (4,10) (4,12) (4,14) (4,16) (4,13) (4,9) (4,19) (4,15) (4,20) (4,7) (4,5) (4,21) (5,6) (5,17) (5,18) (5,8) (5,10) (5,12) (5,14) (5,16) (5,13) (5,9) (5,19) (5,15) (5,20) (5,7) (5,21) (6,17) (6,18) (6,8) (6,10) (6,12) (6,14) (6,16) (6,13) (6,9) (6,19) (6,15) (6,20) (6,7) (6,21) (7,17) (7,18) (7,8) (7,10) (7,12) (7,14) (7,16) (7,13) (7,9) (7,19) (7,15) (7,20) (7,21) (8,17) (8,18) (8,10) (8,12) (8,14) (8,16) (8,13) (8,9) (8,19) (8,15) (8,20) (8,21) (9,17) (9,18) (9,10) (9,12) (9,14) (9,16) (9,13) (9,19) (9,15) (9,20) (9,21) (10,17) (10,18) (10,12) (10,14) (10,16) (10,13) (10,19) (10,15) (10,20) (10,21) (11,22) (12,17) (12,18) (12,14) (12,16) (12,13) (12,19) (12,15) (12,20) (12,21) (13,17) (13,18) (13,14) (13,16) (13,19) (13,15) (13,20) (13,21) (14,17) (14,18) (14,16) (14,19) (14,15) (14,20) (14,21) (15,17) (15,18) (15,16) (15,19) (15,20) (15,21) (16,17) (16,18) (16,19) (16,20) (16,21) (17,18) (17,19) (17,20) (17,21) (18,19) (18,20) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 8 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph63-2_0", + "image": "data/connectivity/graph_visual/medium/graph63.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,12) (0,9) (0,6) (1,10) (1,5) (1,2) (1,8) (1,7) (2,5) (2,3) (3,8) (3,11) (3,7) (4,12) (4,6) (4,13) (5,8) (5,11) (6,9) (6,13) (7,10) (7,8) (8,11) (9,13)\nIs there a path between node 2 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph235-6_2", + "image": "data/connectivity/graph_visual/medium/graph235.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,16) (0,11) (0,14) (0,7) (0,5) (0,15) (0,13) (0,18) (0,2) (1,16) (1,11) (1,5) (1,18) (1,4) (1,2) (2,11) (2,12) (2,14) (2,7) (2,5) (2,15) (2,13) (2,4) (3,8) (4,16) (4,12) (4,14) (4,5) (4,15) (4,13) (4,18) (5,16) (5,11) (5,12) (5,14) (5,7) (5,15) (5,18) (5,17) (6,10) (6,8) (6,9) (7,11) (7,12) (7,14) (7,15) (7,18) (7,17) (8,10) (8,9) (9,10) (11,16) (11,15) (11,13) (11,18) (12,16) (12,15) (12,13) (12,17) (13,16) (13,14) (13,18) (14,16) (14,18) (14,17) (15,18) (15,17) (16,18) (16,17) (17,18)\nIs there a path between node 6 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph516-22_8", + "image": "data/connectivity/graph_visual/medium/graph516.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,2) (0,11) (0,3) (0,19) (0,9) (0,1) (0,22) (0,13) (0,20) (0,4) (0,7) (0,10) (0,6) (0,14) (1,2) (1,11) (1,19) (1,18) (1,9) (1,21) (1,22) (1,13) (1,4) (1,7) (1,17) (1,14) (2,3) (2,19) (2,9) (2,21) (2,13) (2,12) (2,20) (2,4) (2,10) (2,17) (2,14) (3,11) (3,19) (3,18) (3,9) (3,21) (3,22) (3,13) (3,7) (3,10) (3,17) (3,6) (3,14) (4,19) (4,18) (4,9) (4,13) (4,12) (4,20) (4,7) (4,10) (4,14) (5,8) (5,15) (6,19) (6,18) (6,9) (6,21) (6,22) (6,13) (6,12) (6,20) (6,7) (7,11) (7,18) (7,9) (7,21) (7,22) (7,12) (7,10) (7,17) (7,14) (8,16) (8,15) (9,11) (9,19) (9,18) (9,21) (9,20) (9,10) (9,17) (9,14) (10,11) (10,21) (10,22) (10,13) (10,12) (10,20) (10,17) (10,14) (11,19) (11,18) (11,21) (11,22) (11,13) (11,12) (11,20) (11,17) (11,14) (12,18) (12,21) (12,13) (12,20) (12,17) (13,19) (13,22) (13,14) (14,19) (14,18) (14,21) (14,17) (15,16) (17,19) (17,21) (17,22) (17,20) (18,19) (18,21) (18,22) (18,20) (19,20) (20,21) (20,22) (21,22)\nIs there a path between node 22 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph370-1_18", + "image": "data/connectivity/graph_visual/medium/graph370.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,13) (0,5) (0,16) (0,1) (0,3) (1,13) (1,5) (1,9) (1,20) (1,2) (1,16) (1,3) (2,13) (2,5) (2,12) (2,8) (2,9) (2,20) (2,16) (2,3) (3,8) (3,9) (3,16) (4,7) (4,15) (4,19) (4,6) (4,11) (4,18) (4,10) (4,14) (5,13) (5,12) (5,9) (5,16) (6,7) (6,17) (6,19) (6,11) (6,10) (6,14) (7,15) (7,17) (7,19) (7,11) (7,10) (7,14) (8,13) (8,9) (8,20) (9,13) (9,12) (10,15) (10,19) (10,11) (11,15) (11,17) (11,19) (11,18) (11,14) (12,13) (12,20) (14,15) (14,18) (15,18) (16,20) (17,19) (17,18) (18,19)\nIs there a path between node 1 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph47-0_6", + "image": "data/connectivity/graph_visual/medium/graph47.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,12) (0,7) (0,10) (0,8) (0,9) (0,2) (0,4) (0,3) (1,5) (1,6) (1,11) (2,12) (2,7) (2,10) (2,8) (2,9) (2,4) (2,3) (3,12) (3,7) (3,10) (3,8) (3,9) (3,4) (4,12) (4,7) (4,10) (4,8) (4,9) (5,6) (5,11) (6,11) (7,12) (7,10) (7,8) (7,9) (8,12) (8,10) (8,9) (9,12) (9,10) (10,12)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph768-24_4", + "image": "data/connectivity/graph_visual/medium/graph768.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,8) (0,1) (0,20) (0,7) (0,24) (0,14) (0,5) (0,9) (0,18) (0,10) (0,4) (0,22) (0,16) (0,21) (0,11) (0,19) (0,6) (1,8) (1,20) (1,7) (1,24) (1,14) (1,5) (1,9) (1,18) (1,10) (1,4) (1,22) (1,16) (1,21) (1,11) (1,19) (1,6) (2,12) (2,3) (2,17) (2,15) (2,23) (3,12) (3,17) (3,15) (3,23) (4,8) (4,20) (4,7) (4,24) (4,14) (4,5) (4,9) (4,18) (4,10) (4,22) (4,16) (4,21) (4,11) (4,19) (4,6) (5,8) (5,20) (5,7) (5,24) (5,14) (5,9) (5,18) (5,10) (5,22) (5,16) (5,21) (5,11) (5,19) (5,6) (6,8) (6,20) (6,7) (6,24) (6,14) (6,9) (6,18) (6,10) (6,22) (6,16) (6,21) (6,11) (6,19) (7,8) (7,20) (7,24) (7,14) (7,9) (7,18) (7,10) (7,22) (7,16) (7,21) (7,11) (7,19) (8,20) (8,24) (8,14) (8,9) (8,18) (8,10) (8,22) (8,16) (8,21) (8,11) (8,19) (9,20) (9,24) (9,14) (9,18) (9,10) (9,22) (9,16) (9,21) (9,11) (9,19) (10,20) (10,24) (10,14) (10,18) (10,22) (10,16) (10,21) (10,11) (10,19) (11,20) (11,24) (11,14) (11,18) (11,22) (11,16) (11,21) (11,19) (12,17) (12,15) (12,23) (14,20) (14,24) (14,18) (14,22) (14,16) (14,21) (14,19) (15,17) (15,23) (16,20) (16,24) (16,18) (16,22) (16,21) (16,19) (17,23) (18,20) (18,24) (18,22) (18,21) (18,19) (19,20) (19,24) (19,22) (19,21) (20,24) (20,22) (20,21) (21,24) (21,22) (22,24)\nIs there a path between node 24 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph856-14_20", + "image": "data/connectivity/graph_visual/medium/graph856.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (1,23) (1,21) (1,10) (1,20) (1,4) (1,6) (1,24) (1,22) (1,13) (1,19) (1,9) (1,2) (1,14) (1,16) (1,12) (1,11) (1,18) (1,8) (1,5) (2,23) (2,21) (2,10) (2,20) (2,4) (2,6) (2,24) (2,22) (2,13) (2,19) (2,9) (2,14) (2,16) (2,12) (2,11) (2,18) (2,8) (2,5) (3,15) (3,17) (4,23) (4,21) (4,10) (4,20) (4,6) (4,24) (4,22) (4,13) (4,19) (4,9) (4,14) (4,16) (4,12) (4,11) (4,18) (4,8) (4,5) (5,23) (5,21) (5,10) (5,20) (5,6) (5,24) (5,22) (5,13) (5,19) (5,9) (5,14) (5,16) (5,12) (5,11) (5,18) (5,8) (6,23) (6,21) (6,10) (6,20) (6,24) (6,22) (6,13) (6,19) (6,9) (6,14) (6,16) (6,12) (6,11) (6,18) (6,8) (8,23) (8,21) (8,10) (8,20) (8,24) (8,22) (8,13) (8,19) (8,9) (8,14) (8,16) (8,12) (8,11) (8,18) (9,23) (9,21) (9,10) (9,20) (9,24) (9,22) (9,13) (9,19) (9,14) (9,16) (9,12) (9,11) (9,18) (10,23) (10,21) (10,20) (10,24) (10,22) (10,13) (10,19) (10,14) (10,16) (10,12) (10,11) (10,18) (11,23) (11,21) (11,20) (11,24) (11,22) (11,13) (11,19) (11,14) (11,16) (11,12) (11,18) (12,23) (12,21) (12,20) (12,24) (12,22) (12,13) (12,19) (12,14) (12,16) (12,18) (13,23) (13,21) (13,20) (13,24) (13,22) (13,19) (13,14) (13,16) (13,18) (14,23) (14,21) (14,20) (14,24) (14,22) (14,19) (14,16) (14,18) (15,17) (16,23) (16,21) (16,20) (16,24) (16,22) (16,19) (16,18) (18,23) (18,21) (18,20) (18,24) (18,22) (18,19) (19,23) (19,21) (19,20) (19,24) (19,22) (20,23) (20,21) (20,24) (20,22) (21,23) (21,24) (21,22) (22,23) (22,24) (23,24)\nIs there a path between node 14 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph269-5_17", + "image": "data/connectivity/graph_visual/medium/graph269.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,5) (0,8) (0,10) (0,4) (1,9) (1,18) (2,7) (2,16) (2,12) (2,3) (2,15) (2,19) (3,6) (3,16) (4,17) (4,5) (4,8) (4,14) (5,17) (5,14) (6,16) (7,16) (7,12) (7,15) (7,19) (8,14) (9,11) (9,13) (10,17) (10,14) (11,18) (11,13) (12,16) (12,15) (15,16) (15,19) (16,19)\nIs there a path between node 5 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph609-3_22", + "image": "data/connectivity/graph_visual/medium/graph609.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,4) (0,2) (0,20) (0,6) (0,1) (0,15) (0,17) (0,11) (0,12) (0,21) (0,7) (0,14) (0,9) (0,10) (0,22) (0,23) (1,3) (1,4) (1,2) (1,20) (1,6) (1,15) (1,17) (1,11) (1,12) (1,21) (1,7) (1,14) (1,9) (1,10) (1,22) (1,23) (2,3) (2,4) (2,20) (2,6) (2,15) (2,17) (2,11) (2,12) (2,21) (2,7) (2,14) (2,9) (2,10) (2,22) (2,23) (3,4) (3,20) (3,6) (3,15) (3,17) (3,11) (3,12) (3,21) (3,7) (3,14) (3,9) (3,10) (3,22) (3,23) (4,20) (4,6) (4,15) (4,17) (4,11) (4,12) (4,21) (4,7) (4,14) (4,9) (4,10) (4,22) (4,23) (5,18) (6,20) (6,15) (6,17) (6,11) (6,12) (6,21) (6,7) (6,14) (6,9) (6,10) (6,22) (6,23) (7,20) (7,15) (7,17) (7,11) (7,12) (7,21) (7,14) (7,9) (7,10) (7,22) (7,23) (8,16) (8,19) (8,13) (9,20) (9,15) (9,17) (9,11) (9,12) (9,21) (9,14) (9,10) (9,22) (9,23) (10,20) (10,15) (10,17) (10,11) (10,12) (10,21) (10,14) (10,22) (10,23) (11,20) (11,15) (11,17) (11,12) (11,21) (11,14) (11,22) (11,23) (12,20) (12,15) (12,17) (12,21) (12,14) (12,22) (12,23) (13,16) (13,19) (14,20) (14,15) (14,17) (14,21) (14,22) (14,23) (15,20) (15,17) (15,21) (15,22) (15,23) (16,19) (17,20) (17,21) (17,22) (17,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 3 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph700-2_12", + "image": "data/connectivity/graph_visual/medium/graph700.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,22) (0,6) (0,11) (0,10) (0,4) (0,5) (0,9) (0,1) (0,13) (0,21) (0,20) (0,12) (1,22) (1,11) (1,10) (1,5) (1,16) (1,9) (1,13) (1,21) (1,20) (2,8) (2,19) (2,3) (2,18) (2,24) (3,19) (3,17) (3,24) (3,23) (4,22) (4,6) (4,16) (4,9) (4,21) (4,20) (5,22) (5,6) (5,14) (5,11) (5,16) (5,15) (5,9) (5,13) (5,21) (5,20) (6,22) (6,11) (6,10) (6,16) (6,13) (6,21) (6,12) (7,8) (7,17) (7,18) (7,24) (7,23) (8,17) (8,24) (9,14) (9,11) (9,10) (9,16) (9,15) (9,21) (9,20) (9,12) (10,22) (10,14) (10,11) (10,16) (10,15) (10,21) (10,20) (11,22) (11,16) (11,15) (11,20) (12,22) (12,14) (12,15) (12,13) (12,21) (12,20) (13,14) (13,16) (13,15) (13,21) (13,20) (14,22) (14,16) (14,15) (14,21) (15,16) (15,21) (16,22) (16,21) (16,20) (17,19) (17,18) (17,24) (17,23) (18,23) (19,24) (23,24)\nIs there a path between node 2 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph218-15_12", + "image": "data/connectivity/graph_visual/medium/graph218.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,14) (0,3) (0,13) (0,18) (0,16) (0,4) (0,10) (0,8) (0,12) (0,15) (0,11) (0,1) (1,14) (1,3) (1,13) (1,18) (1,16) (1,4) (1,10) (1,8) (1,12) (1,15) (1,11) (2,17) (2,6) (2,7) (2,5) (2,9) (3,14) (3,13) (3,18) (3,16) (3,4) (3,10) (3,8) (3,12) (3,15) (3,11) (4,14) (4,13) (4,18) (4,16) (4,10) (4,8) (4,12) (4,15) (4,11) (5,17) (5,6) (5,7) (5,9) (6,17) (6,7) (6,9) (7,17) (7,9) (8,14) (8,13) (8,18) (8,16) (8,10) (8,12) (8,15) (8,11) (9,17) (10,14) (10,13) (10,18) (10,16) (10,12) (10,15) (10,11) (11,14) (11,13) (11,18) (11,16) (11,12) (11,15) (12,14) (12,13) (12,18) (12,16) (12,15) (13,14) (13,18) (13,16) (13,15) (14,18) (14,16) (14,15) (15,18) (15,16) (16,18)\nIs there a path between node 15 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph297-18_10", + "image": "data/connectivity/graph_visual/medium/graph297.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,12) (0,19) (1,2) (1,13) (1,7) (1,6) (1,3) (1,9) (1,16) (1,4) (2,13) (2,7) (2,6) (2,10) (2,9) (2,16) (2,8) (2,15) (3,17) (3,6) (3,5) (3,10) (3,16) (3,4) (4,13) (4,17) (4,6) (4,5) (4,10) (4,9) (4,15) (5,13) (5,7) (5,6) (5,9) (5,16) (5,8) (6,13) (6,7) (6,9) (6,16) (6,8) (6,15) (7,13) (7,10) (7,9) (8,17) (8,10) (8,9) (8,16) (8,15) (9,17) (9,10) (9,16) (9,15) (10,13) (10,17) (10,16) (10,15) (12,19) (12,18) (13,15) (15,17) (15,16) (16,17) (18,19)\nIs there a path between node 18 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph54-13_2", + "image": "data/connectivity/graph_visual/medium/graph54.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,9) (0,3) (0,5) (1,2) (1,8) (1,7) (2,8) (2,7) (3,11) (3,9) (3,13) (5,11) (5,12) (10,11) (11,12) (12,13)\nIs there a path between node 13 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph516-16_0", + "image": "data/connectivity/graph_visual/medium/graph516.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,2) (0,11) (0,3) (0,19) (0,9) (0,1) (0,22) (0,13) (0,20) (0,4) (0,7) (0,10) (0,6) (0,14) (1,2) (1,11) (1,19) (1,18) (1,9) (1,21) (1,22) (1,13) (1,4) (1,7) (1,17) (1,14) (2,3) (2,19) (2,9) (2,21) (2,13) (2,12) (2,20) (2,4) (2,10) (2,17) (2,14) (3,11) (3,19) (3,18) (3,9) (3,21) (3,22) (3,13) (3,7) (3,10) (3,17) (3,6) (3,14) (4,19) (4,18) (4,9) (4,13) (4,12) (4,20) (4,7) (4,10) (4,14) (5,8) (5,15) (6,19) (6,18) (6,9) (6,21) (6,22) (6,13) (6,12) (6,20) (6,7) (7,11) (7,18) (7,9) (7,21) (7,22) (7,12) (7,10) (7,17) (7,14) (8,16) (8,15) (9,11) (9,19) (9,18) (9,21) (9,20) (9,10) (9,17) (9,14) (10,11) (10,21) (10,22) (10,13) (10,12) (10,20) (10,17) (10,14) (11,19) (11,18) (11,21) (11,22) (11,13) (11,12) (11,20) (11,17) (11,14) (12,18) (12,21) (12,13) (12,20) (12,17) (13,19) (13,22) (13,14) (14,19) (14,18) (14,21) (14,17) (15,16) (17,19) (17,21) (17,22) (17,20) (18,19) (18,21) (18,22) (18,20) (19,20) (20,21) (20,22) (21,22)\nIs there a path between node 16 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph593-19_13", + "image": "data/connectivity/graph_visual/medium/graph593.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,7) (0,14) (0,8) (0,5) (0,4) (0,3) (0,23) (0,12) (0,15) (0,13) (0,17) (0,2) (1,19) (1,7) (1,14) (1,8) (1,3) (1,23) (1,12) (1,15) (1,13) (1,17) (1,6) (2,21) (2,19) (2,7) (2,5) (2,4) (2,3) (2,13) (3,21) (3,19) (3,14) (3,5) (3,4) (3,23) (3,12) (3,15) (4,21) (4,19) (4,14) (4,8) (4,5) (4,23) (4,12) (4,15) (4,6) (5,21) (5,19) (5,7) (5,8) (5,12) (5,17) (6,19) (6,7) (6,23) (6,12) (6,15) (6,13) (6,17) (7,21) (7,14) (7,12) (7,15) (7,13) (7,17) (8,21) (8,19) (8,12) (8,13) (9,11) (9,22) (9,20) (11,22) (11,18) (11,20) (12,14) (12,23) (12,15) (12,13) (12,17) (13,21) (13,23) (14,21) (14,19) (14,23) (14,15) (14,17) (15,21) (15,19) (15,23) (15,17) (16,22) (16,20) (17,19) (17,23) (19,21) (19,23) (20,22)\nIs there a path between node 19 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph375-10_12", + "image": "data/connectivity/graph_visual/medium/graph375.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,15) (0,5) (0,3) (0,11) (0,9) (0,8) (0,13) (1,15) (1,5) (1,3) (1,11) (1,4) (1,9) (1,10) (1,8) (3,15) (3,4) (3,10) (3,8) (4,15) (4,12) (4,9) (4,10) (4,8) (4,13) (5,15) (5,11) (5,9) (5,10) (6,7) (6,20) (6,17) (6,18) (6,14) (7,19) (7,20) (7,18) (8,12) (8,11) (8,9) (8,10) (8,13) (9,15) (9,12) (9,11) (9,10) (10,15) (10,11) (10,13) (11,12) (12,13) (14,19) (14,20) (14,17) (14,18) (17,19) (17,20) (17,18) (18,19) (18,20)\nIs there a path between node 10 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph307-0_15", + "image": "data/connectivity/graph_visual/medium/graph307.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,11) (0,12) (0,1) (0,6) (0,2) (1,3) (1,11) (1,13) (1,12) (1,6) (1,19) (1,2) (2,3) (2,11) (2,13) (2,12) (2,19) (3,13) (3,12) (3,10) (3,19) (4,18) (5,16) (5,17) (5,9) (5,15) (5,7) (6,13) (6,12) (6,10) (7,14) (8,18) (9,16) (9,14) (9,17) (9,15) (10,11) (10,12) (10,19) (11,13) (11,12) (11,19) (12,13) (12,19) (13,19) (14,15) (15,16) (15,17) (16,17)\nIs there a path between node 0 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph440-3_21", + "image": "data/connectivity/graph_visual/medium/graph440.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,5) (0,4) (0,14) (0,8) (0,20) (0,3) (0,12) (0,10) (0,2) (0,9) (1,16) (1,7) (1,21) (1,17) (2,5) (2,11) (2,18) (2,4) (2,8) (2,20) (2,12) (2,9) (3,5) (3,11) (3,18) (3,4) (3,20) (3,13) (3,12) (3,15) (3,9) (4,5) (4,18) (4,14) (4,8) (4,20) (4,13) (4,12) (4,10) (4,15) (4,9) (5,11) (5,18) (5,14) (5,8) (5,12) (5,10) (5,15) (6,11) (6,18) (6,8) (6,20) (6,13) (6,10) (6,15) (7,16) (7,21) (7,19) (7,17) (8,11) (8,18) (8,14) (8,20) (8,12) (8,10) (8,15) (8,9) (9,11) (9,14) (9,20) (9,13) (9,15) (10,11) (10,18) (10,14) (10,20) (10,13) (10,12) (10,15) (11,14) (11,20) (11,13) (11,12) (11,15) (12,18) (12,14) (12,20) (12,13) (13,14) (13,20) (13,15) (14,18) (14,15) (15,20) (16,21) (16,19) (17,21) (17,19) (18,20)\nIs there a path between node 3 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph111-7_3", + "image": "data/connectivity/graph_visual/medium/graph111.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,9) (0,10) (0,1) (1,8) (1,3) (1,14) (3,5) (3,6) (3,9) (3,12) (4,9) (4,16) (6,7) (6,12) (7,14) (8,16) (8,14) (10,11) (10,14) (10,12) (11,14) (12,14)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph113-11_6", + "image": "data/connectivity/graph_visual/medium/graph113.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,11) (0,8) (0,10) (0,4) (0,16) (0,5) (0,2) (0,7) (0,9) (0,15) (0,13) (0,1) (0,12) (0,14) (0,3) (1,11) (1,8) (1,10) (1,4) (1,16) (1,5) (1,2) (1,7) (1,9) (1,15) (1,13) (1,12) (1,14) (1,3) (2,11) (2,8) (2,10) (2,4) (2,16) (2,5) (2,7) (2,9) (2,15) (2,13) (2,12) (2,14) (2,3) (3,11) (3,8) (3,10) (3,4) (3,16) (3,5) (3,7) (3,9) (3,15) (3,13) (3,12) (3,14) (4,11) (4,8) (4,10) (4,16) (4,5) (4,7) (4,9) (4,15) (4,13) (4,12) (4,14) (5,11) (5,8) (5,10) (5,16) (5,7) (5,9) (5,15) (5,13) (5,12) (5,14) (7,11) (7,8) (7,10) (7,16) (7,9) (7,15) (7,13) (7,12) (7,14) (8,11) (8,10) (8,16) (8,9) (8,15) (8,13) (8,12) (8,14) (9,11) (9,10) (9,16) (9,15) (9,13) (9,12) (9,14) (10,11) (10,16) (10,15) (10,13) (10,12) (10,14) (11,16) (11,15) (11,13) (11,12) (11,14) (12,16) (12,15) (12,13) (12,14) (13,16) (13,15) (13,14) (14,16) (14,15) (15,16)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph693-17_15", + "image": "data/connectivity/graph_visual/medium/graph693.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,18) (0,15) (0,19) (0,13) (0,10) (0,6) (0,1) (0,17) (0,22) (1,4) (1,18) (1,15) (1,19) (1,13) (1,10) (1,6) (1,17) (1,22) (2,7) (2,8) (2,5) (2,12) (2,21) (2,3) (2,23) (2,9) (2,11) (2,14) (2,20) (2,16) (3,7) (3,8) (3,5) (3,12) (3,21) (3,23) (3,9) (3,11) (3,14) (3,20) (3,16) (4,18) (4,15) (4,19) (4,13) (4,10) (4,6) (4,17) (4,22) (5,7) (5,8) (5,12) (5,21) (5,23) (5,9) (5,11) (5,14) (5,20) (5,16) (6,18) (6,15) (6,19) (6,13) (6,10) (6,17) (6,22) (7,8) (7,12) (7,21) (7,23) (7,9) (7,11) (7,14) (7,20) (7,16) (8,12) (8,21) (8,23) (8,9) (8,11) (8,14) (8,20) (8,16) (9,12) (9,21) (9,23) (9,11) (9,14) (9,20) (9,16) (10,18) (10,15) (10,19) (10,13) (10,17) (10,22) (11,12) (11,21) (11,23) (11,14) (11,20) (11,16) (12,21) (12,23) (12,14) (12,20) (12,16) (13,18) (13,15) (13,19) (13,17) (13,22) (14,21) (14,23) (14,20) (14,16) (15,18) (15,19) (15,17) (15,22) (16,21) (16,23) (16,20) (17,18) (17,19) (17,22) (18,19) (18,22) (19,22) (20,21) (20,23) (21,23)\nIs there a path between node 17 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph543-13_20", + "image": "data/connectivity/graph_visual/medium/graph543.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,15) (0,8) (0,12) (0,14) (0,2) (0,9) (0,1) (1,15) (1,20) (1,12) (2,20) (2,12) (2,7) (2,16) (3,15) (3,7) (3,16) (3,13) (3,14) (3,17) (3,21) (4,22) (4,8) (4,12) (4,17) (4,11) (6,23) (7,15) (7,17) (7,11) (7,21) (7,18) (8,22) (8,15) (8,20) (8,16) (8,9) (9,22) (9,13) (9,11) (9,21) (9,18) (10,22) (10,13) (10,21) (11,22) (11,15) (11,20) (11,12) (11,21) (11,18) (12,15) (12,13) (13,20) (13,18) (14,20) (17,22) (17,18) (18,20) (19,23) (20,22) (21,22)\nIs there a path between node 13 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph753-2_10", + "image": "data/connectivity/graph_visual/medium/graph753.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,3) (0,23) (0,18) (0,9) (0,5) (0,2) (0,4) (0,8) (0,24) (1,6) (1,3) (1,23) (1,16) (1,10) (1,12) (1,18) (1,9) (1,5) (1,2) (1,4) (1,22) (1,24) (2,6) (2,3) (2,13) (2,23) (2,16) (2,10) (2,12) (2,18) (2,15) (2,19) (2,9) (2,5) (2,11) (2,7) (2,22) (2,8) (2,24) (3,6) (3,13) (3,23) (3,10) (3,12) (3,18) (3,15) (3,9) (3,11) (3,7) (3,4) (3,22) (4,6) (4,13) (4,16) (4,12) (4,15) (4,19) (4,9) (4,5) (4,11) (4,7) (4,22) (4,8) (4,24) (5,6) (5,13) (5,23) (5,16) (5,10) (5,15) (5,19) (5,9) (5,11) (5,22) (6,23) (6,16) (6,10) (6,12) (6,18) (6,19) (6,9) (6,11) (6,7) (6,24) (7,13) (7,23) (7,16) (7,10) (7,12) (7,18) (7,15) (7,19) (7,11) (7,22) (7,24) (8,13) (8,23) (8,10) (8,12) (8,18) (8,15) (8,19) (8,9) (8,11) (8,24) (9,23) (9,16) (9,10) (9,12) (9,18) (9,15) (9,19) (9,22) (10,13) (10,23) (10,16) (10,12) (10,18) (10,15) (10,11) (10,22) (11,13) (11,23) (11,12) (11,18) (11,15) (11,19) (11,22) (11,24) (12,13) (12,23) (12,16) (12,18) (12,19) (13,23) (13,16) (13,18) (13,22) (15,23) (15,16) (15,18) (15,19) (15,24) (16,23) (16,18) (16,19) (16,22) (16,24) (18,23) (18,19) (18,22) (18,24) (19,23) (19,22) (19,24) (22,23) (22,24)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph831-19_12", + "image": "data/connectivity/graph_visual/medium/graph831.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (1,14) (1,20) (2,3) (2,17) (2,18) (2,9) (2,23) (2,6) (2,21) (2,11) (3,24) (3,13) (3,18) (3,9) (3,23) (3,21) (3,16) (3,10) (3,8) (4,12) (4,7) (4,22) (4,20) (4,5) (5,14) (5,12) (5,7) (5,22) (5,20) (6,13) (6,17) (6,15) (6,21) (6,11) (6,10) (6,8) (7,14) (7,12) (7,22) (8,24) (8,13) (8,15) (8,18) (8,23) (8,11) (8,16) (8,10) (9,24) (9,15) (9,23) (9,11) (9,16) (9,10) (10,24) (10,13) (10,17) (10,15) (10,18) (10,23) (10,11) (10,16) (11,24) (11,13) (11,18) (11,23) (11,21) (12,22) (12,20) (13,24) (13,17) (13,18) (13,23) (13,21) (13,16) (14,20) (15,24) (15,17) (15,18) (15,21) (16,24) (16,17) (16,23) (17,24) (17,18) (17,23) (18,24) (20,22) (21,24) (21,23) (23,24)\nIs there a path between node 19 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph454-3_0", + "image": "data/connectivity/graph_visual/medium/graph454.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,21) (0,11) (0,7) (0,1) (0,20) (0,14) (0,16) (0,17) (0,12) (0,9) (0,6) (0,19) (0,2) (0,8) (0,15) (0,10) (1,18) (1,21) (1,11) (1,7) (1,20) (1,14) (1,16) (1,17) (1,12) (1,9) (1,6) (1,19) (1,2) (1,8) (1,15) (1,10) (2,18) (2,21) (2,11) (2,7) (2,20) (2,14) (2,16) (2,17) (2,12) (2,9) (2,6) (2,19) (2,8) (2,15) (2,10) (3,13) (3,4) (3,5) (4,13) (4,5) (5,13) (6,18) (6,21) (6,11) (6,7) (6,20) (6,14) (6,16) (6,17) (6,12) (6,9) (6,19) (6,8) (6,15) (6,10) (7,18) (7,21) (7,11) (7,20) (7,14) (7,16) (7,17) (7,12) (7,9) (7,19) (7,8) (7,15) (7,10) (8,18) (8,21) (8,11) (8,20) (8,14) (8,16) (8,17) (8,12) (8,9) (8,19) (8,15) (8,10) (9,18) (9,21) (9,11) (9,20) (9,14) (9,16) (9,17) (9,12) (9,19) (9,15) (9,10) (10,18) (10,21) (10,11) (10,20) (10,14) (10,16) (10,17) (10,12) (10,19) (10,15) (11,18) (11,21) (11,20) (11,14) (11,16) (11,17) (11,12) (11,19) (11,15) (12,18) (12,21) (12,20) (12,14) (12,16) (12,17) (12,19) (12,15) (14,18) (14,21) (14,20) (14,16) (14,17) (14,19) (14,15) (15,18) (15,21) (15,20) (15,16) (15,17) (15,19) (16,18) (16,21) (16,20) (16,17) (16,19) (17,18) (17,21) (17,20) (17,19) (18,21) (18,20) (18,19) (19,21) (19,20) (20,21)\nIs there a path between node 3 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph69-14_0", + "image": "data/connectivity/graph_visual/medium/graph69.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,5) (0,9) (1,8) (1,4) (2,8) (2,4) (2,3) (3,7) (3,6) (3,10) (3,12) (3,11) (4,10) (4,12) (6,14) (6,8) (6,10) (7,14) (7,11) (8,14) (8,12) (10,14) (11,14) (12,14)\nIs there a path between node 14 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph134-3_1", + "image": "data/connectivity/graph_visual/medium/graph134.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,11) (0,6) (0,2) (0,5) (1,7) (1,16) (1,14) (1,17) (1,3) (1,9) (1,13) (1,10) (2,11) (2,6) (2,5) (3,7) (3,16) (3,14) (3,17) (3,9) (3,13) (3,10) (4,8) (4,15) (4,12) (5,11) (5,6) (6,11) (7,16) (7,14) (7,17) (7,9) (7,13) (7,10) (8,15) (8,12) (9,16) (9,14) (9,17) (9,13) (9,10) (10,16) (10,14) (10,17) (10,13) (12,15) (13,16) (13,14) (13,17) (14,16) (14,17) (16,17)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph563-0_13", + "image": "data/connectivity/graph_visual/medium/graph563.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,1) (0,9) (0,10) (1,19) (2,20) (2,3) (2,7) (2,12) (2,22) (2,5) (3,23) (3,12) (3,22) (3,17) (3,8) (3,11) (3,13) (3,16) (3,5) (4,15) (4,6) (4,14) (4,18) (5,20) (5,23) (5,12) (5,22) (5,8) (5,11) (5,13) (6,21) (6,15) (6,14) (6,18) (7,20) (7,23) (7,12) (7,22) (7,13) (7,16) (8,20) (8,23) (8,12) (8,22) (8,17) (8,11) (9,19) (9,10) (11,20) (11,23) (11,12) (11,22) (11,17) (12,20) (12,17) (12,13) (12,16) (13,20) (13,23) (13,22) (13,17) (14,21) (14,15) (16,20) (16,23) (16,22) (16,17) (17,23) (17,22) (18,21) (22,23)\nIs there a path between node 0 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph122-6_9", + "image": "data/connectivity/graph_visual/medium/graph122.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,5) (0,3) (1,13) (1,4) (1,12) (1,16) (1,9) (1,15) (1,11) (1,8) (1,6) (1,7) (1,10) (2,5) (3,14) (4,16) (4,9) (4,11) (4,8) (4,7) (4,10) (6,13) (6,16) (6,11) (6,7) (6,10) (7,13) (7,9) (7,11) (7,8) (7,10) (8,13) (8,12) (8,16) (8,9) (8,15) (8,10) (9,13) (9,16) (9,15) (9,10) (10,16) (10,11) (11,13) (11,16) (11,15) (12,13) (12,15) (13,16) (15,16)\nIs there a path between node 6 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph276-14_10", + "image": "data/connectivity/graph_visual/medium/graph276.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,10) (1,9) (1,16) (1,4) (1,12) (2,8) (2,19) (2,7) (2,14) (2,17) (2,5) (2,18) (2,6) (2,11) (2,3) (2,13) (2,15) (3,8) (3,19) (3,7) (3,14) (3,17) (3,5) (3,18) (3,6) (3,11) (3,13) (3,15) (4,10) (4,9) (4,16) (4,12) (5,8) (5,19) (5,7) (5,14) (5,17) (5,18) (5,6) (5,11) (5,13) (5,15) (6,8) (6,19) (6,7) (6,14) (6,17) (6,18) (6,11) (6,13) (6,15) (7,8) (7,19) (7,14) (7,17) (7,18) (7,11) (7,13) (7,15) (8,19) (8,14) (8,17) (8,18) (8,11) (8,13) (8,15) (9,10) (9,16) (9,12) (10,16) (10,12) (11,19) (11,14) (11,17) (11,18) (11,13) (11,15) (12,16) (13,19) (13,14) (13,17) (13,18) (13,15) (14,19) (14,17) (14,18) (14,15) (15,19) (15,17) (15,18) (17,19) (17,18) (18,19)\nIs there a path between node 14 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph213-7_1", + "image": "data/connectivity/graph_visual/medium/graph213.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (0,6) (0,7) (0,1) (1,4) (1,6) (1,7) (2,18) (2,12) (2,5) (2,17) (2,10) (2,8) (2,16) (2,3) (2,14) (2,11) (2,13) (3,18) (3,12) (3,5) (3,17) (3,10) (3,8) (3,16) (3,14) (3,11) (3,13) (4,6) (4,7) (5,18) (5,12) (5,17) (5,10) (5,8) (5,16) (5,14) (5,11) (5,13) (6,7) (8,18) (8,12) (8,17) (8,10) (8,16) (8,14) (8,11) (8,13) (9,15) (10,18) (10,12) (10,17) (10,16) (10,14) (10,11) (10,13) (11,18) (11,12) (11,17) (11,16) (11,14) (11,13) (12,18) (12,17) (12,16) (12,14) (12,13) (13,18) (13,17) (13,16) (13,14) (14,18) (14,17) (14,16) (16,18) (16,17) (17,18)\nIs there a path between node 7 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph828-0_13", + "image": "data/connectivity/graph_visual/medium/graph828.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,6) (0,8) (0,9) (0,7) (0,20) (0,24) (0,3) (0,2) (1,15) (1,6) (1,8) (1,9) (1,7) (1,11) (1,20) (1,10) (1,24) (1,22) (1,2) (2,15) (2,6) (2,9) (2,11) (2,20) (2,5) (2,22) (2,3) (2,23) (3,15) (3,20) (3,10) (3,24) (3,22) (3,23) (4,17) (4,13) (4,16) (4,12) (4,19) (5,6) (5,8) (5,9) (5,7) (5,11) (5,10) (5,22) (5,23) (6,15) (6,8) (6,11) (6,20) (6,24) (6,22) (7,15) (7,8) (7,9) (7,11) (7,20) (7,10) (7,24) (7,22) (8,15) (8,11) (8,20) (8,10) (8,24) (8,22) (9,20) (9,10) (9,24) (9,22) (9,23) (10,15) (10,11) (10,24) (10,22) (10,23) (11,20) (11,23) (12,17) (12,13) (12,18) (12,21) (12,16) (12,14) (12,19) (13,17) (13,18) (13,21) (13,14) (13,19) (14,17) (14,18) (14,21) (14,16) (14,19) (15,20) (15,24) (15,22) (16,17) (16,18) (16,21) (18,21) (18,19) (19,21) (20,24) (20,22) (20,23) (22,24) (22,23)\nIs there a path between node 0 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph747-22_20", + "image": "data/connectivity/graph_visual/medium/graph747.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,10) (1,8) (1,9) (1,18) (1,15) (1,23) (2,4) (2,22) (2,7) (2,16) (2,5) (2,3) (2,14) (2,17) (3,4) (3,22) (3,7) (3,19) (3,11) (3,14) (3,17) (4,22) (4,7) (4,19) (4,5) (4,11) (4,14) (4,17) (5,22) (5,7) (5,19) (5,11) (5,14) (6,20) (6,8) (6,9) (6,21) (6,18) (6,15) (6,23) (7,22) (7,16) (7,11) (8,20) (8,10) (8,21) (8,24) (9,20) (9,10) (9,24) (9,18) (9,15) (10,20) (10,24) (10,18) (10,15) (10,23) (11,22) (11,19) (14,22) (14,19) (14,17) (15,20) (15,21) (15,24) (15,18) (15,23) (16,22) (16,19) (16,17) (17,22) (18,20) (18,21) (20,21) (20,24) (20,23) (21,24)\nIs there a path between node 22 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph176-17_13", + "image": "data/connectivity/graph_visual/medium/graph176.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,7) (0,13) (0,10) (0,9) (1,16) (1,12) (1,17) (1,8) (2,3) (2,14) (2,15) (2,5) (2,11) (3,14) (3,5) (4,7) (4,10) (4,9) (5,15) (5,11) (6,7) (6,10) (7,13) (7,10) (7,9) (8,12) (9,13) (10,13) (11,14) (11,15) (12,16) (12,17) (14,15) (16,17)\nIs there a path between node 17 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph805-5_23", + "image": "data/connectivity/graph_visual/medium/graph805.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,1) (1,12) (1,15) (2,11) (2,19) (2,16) (2,10) (3,17) (3,11) (3,19) (3,7) (3,23) (3,10) (6,18) (7,11) (7,19) (7,23) (8,12) (8,15) (9,17) (9,11) (9,21) (9,22) (9,10) (10,24) (10,14) (11,17) (11,24) (11,14) (11,21) (11,22) (12,15) (14,23) (14,16) (16,24) (16,21) (17,24) (17,19) (19,24) (19,22) (21,24) (23,24)\nIs there a path between node 5 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph734-18_13", + "image": "data/connectivity/graph_visual/medium/graph734.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,8) (0,14) (0,10) (1,21) (1,22) (1,17) (1,12) (2,23) (2,3) (3,23) (3,10) (3,15) (4,23) (4,10) (4,15) (4,11) (5,16) (5,17) (6,21) (6,13) (6,17) (6,12) (7,9) (7,22) (7,18) (8,20) (8,15) (8,11) (9,24) (9,17) (9,12) (12,19) (12,17) (13,21) (13,22) (15,23) (16,24) (16,22) (16,17) (17,24) (17,21) (17,18) (21,22) (22,24)\nIs there a path between node 18 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph477-14_22", + "image": "data/connectivity/graph_visual/medium/graph477.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,15) (0,20) (0,21) (0,14) (1,17) (1,10) (1,7) (2,21) (3,10) (4,8) (4,9) (5,22) (5,13) (5,7) (5,12) (6,19) (7,22) (7,12) (9,11) (10,17) (10,12) (12,13) (14,18) (14,19) (15,18) (16,20)\nIs there a path between node 14 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph157-17_0", + "image": "data/connectivity/graph_visual/medium/graph157.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,6) (0,16) (0,3) (1,9) (2,10) (2,12) (2,3) (3,10) (3,12) (5,6) (6,8) (7,8) (8,10) (9,15) (9,13) (13,14)\nIs there a path between node 17 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph783-3_2", + "image": "data/connectivity/graph_visual/medium/graph783.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (0,18) (0,24) (0,2) (0,3) (0,20) (0,22) (0,10) (0,17) (1,9) (1,8) (1,20) (2,23) (2,9) (2,16) (2,11) (2,15) (3,23) (3,21) (3,4) (3,24) (3,17) (4,9) (4,18) (4,20) (4,10) (4,17) (5,14) (6,7) (8,21) (8,16) (8,22) (8,10) (8,17) (9,23) (9,21) (9,11) (9,20) (9,10) (9,17) (10,24) (10,20) (10,22) (10,17) (11,18) (11,12) (12,23) (12,21) (12,19) (12,18) (12,20) (15,23) (15,18) (15,24) (15,22) (15,17) (16,23) (16,19) (16,22) (17,18) (17,20) (18,22) (19,23) (19,20) (19,22) (20,22)\nIs there a path between node 3 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph193-5_2", + "image": "data/connectivity/graph_visual/medium/graph193.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,5) (0,7) (0,14) (0,2) (0,16) (0,13) (0,3) (0,12) (0,4) (1,9) (1,15) (1,6) (1,10) (1,17) (2,5) (2,7) (2,14) (2,16) (2,13) (2,3) (2,12) (2,4) (3,5) (3,7) (3,14) (3,16) (3,13) (3,12) (3,4) (4,5) (4,7) (4,14) (4,16) (4,13) (4,12) (5,7) (5,14) (5,16) (5,13) (5,12) (6,9) (6,15) (6,10) (6,17) (7,14) (7,16) (7,13) (7,12) (8,11) (9,15) (9,10) (9,17) (10,15) (10,17) (12,14) (12,16) (12,13) (13,14) (13,16) (14,16) (15,17)\nIs there a path between node 5 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph202-13_0", + "image": "data/connectivity/graph_visual/medium/graph202.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (0,13) (0,12) (0,3) (1,4) (1,13) (1,3) (2,10) (2,15) (2,18) (3,12) (3,14) (4,6) (4,9) (4,17) (6,14) (6,17) (7,14) (8,13) (10,16) (11,12) (11,14) (12,14) (14,17)\nIs there a path between node 13 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph822-14_4", + "image": "data/connectivity/graph_visual/medium/graph822.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (0,19) (0,5) (0,22) (0,2) (0,16) (0,10) (0,24) (0,20) (0,8) (0,15) (1,18) (1,19) (1,4) (1,23) (1,2) (1,10) (1,24) (1,21) (1,20) (1,15) (2,18) (2,6) (2,19) (2,23) (2,7) (2,22) (2,12) (2,16) (2,24) (2,21) (2,20) (2,15) (3,17) (3,13) (3,11) (4,18) (4,9) (4,19) (4,23) (4,7) (4,22) (4,16) (4,10) (4,24) (4,21) (4,20) (4,15) (5,18) (5,23) (5,7) (5,22) (5,12) (5,16) (5,10) (5,24) (5,8) (5,15) (6,18) (6,19) (6,7) (6,22) (6,12) (6,16) (6,10) (6,24) (6,21) (6,20) (6,15) (7,9) (7,19) (7,23) (7,12) (7,10) (7,21) (7,20) (7,15) (8,18) (8,9) (8,19) (8,23) (8,22) (8,12) (8,16) (8,10) (8,20) (8,15) (9,18) (9,19) (9,23) (9,12) (9,10) (9,24) (9,21) (9,20) (9,15) (10,18) (10,19) (10,23) (10,22) (10,12) (10,24) (10,21) (10,20) (10,15) (11,17) (12,18) (12,23) (12,22) (12,16) (12,24) (12,20) (13,17) (15,18) (15,19) (15,22) (15,24) (15,20) (16,18) (16,19) (16,23) (16,22) (16,24) (16,20) (18,23) (18,22) (18,21) (19,23) (19,22) (19,24) (19,20) (20,24) (20,21) (21,23) (21,22) (21,24) (22,24) (23,24)\nIs there a path between node 14 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph23-3_2", + "image": "data/connectivity/graph_visual/medium/graph23.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (0,5) (0,7) (0,6) (0,2) (0,4) (0,8) (0,9) (1,10) (2,3) (2,5) (2,7) (2,6) (2,4) (2,8) (2,9) (2,11) (3,5) (3,4) (3,8) (3,11) (4,5) (4,6) (4,9) (4,11) (5,6) (5,8) (5,9) (6,7) (6,8) (6,9) (6,11) (7,8) (7,11) (8,9) (9,11)\nIs there a path between node 3 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph75-8_7", + "image": "data/connectivity/graph_visual/medium/graph75.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,13) (1,6) (1,7) (1,4) (2,6) (2,7) (2,9) (2,10) (2,14) (3,6) (3,9) (3,4) (4,8) (4,9) (4,11) (5,6) (6,8) (6,7) (6,9) (6,10) (7,8) (7,14) (8,13) (9,13) (9,10) (10,13) (10,11)\nIs there a path between node 8 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph35-3_11", + "image": "data/connectivity/graph_visual/medium/graph35.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,5) (0,7) (0,8) (0,10) (0,3) (1,4) (1,11) (1,9) (1,6) (1,12) (1,2) (2,4) (2,11) (2,9) (2,6) (2,12) (3,5) (3,7) (3,8) (3,10) (4,11) (4,9) (4,6) (4,12) (5,7) (5,8) (5,10) (6,11) (6,9) (6,12) (7,8) (7,10) (8,10) (9,11) (9,12) (11,12)\nIs there a path between node 3 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph794-0_1", + "image": "data/connectivity/graph_visual/medium/graph794.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,13) (0,15) (1,17) (1,18) (1,7) (2,14) (2,6) (2,15) (2,10) (4,6) (4,15) (4,5) (5,13) (5,21) (5,23) (5,24) (6,13) (6,21) (6,23) (7,17) (10,23) (11,16) (11,18) (12,21) (13,23) (15,24) (21,24) (23,24)\nIs there a path between node 0 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph467-15_1", + "image": "data/connectivity/graph_visual/medium/graph467.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,7) (0,1) (0,18) (0,12) (0,2) (0,4) (0,21) (0,16) (0,20) (0,15) (0,10) (0,19) (0,17) (0,13) (1,11) (1,7) (1,18) (1,12) (1,2) (1,4) (1,21) (1,16) (1,20) (1,15) (1,10) (1,19) (1,17) (1,13) (2,11) (2,7) (2,18) (2,12) (2,4) (2,21) (2,16) (2,20) (2,15) (2,10) (2,19) (2,17) (2,13) (3,5) (4,11) (4,7) (4,18) (4,12) (4,21) (4,16) (4,20) (4,15) (4,10) (4,19) (4,17) (4,13) (6,9) (6,8) (6,14) (7,11) (7,18) (7,12) (7,21) (7,16) (7,20) (7,15) (7,10) (7,19) (7,17) (7,13) (8,9) (8,14) (9,14) (10,11) (10,18) (10,12) (10,21) (10,16) (10,20) (10,15) (10,19) (10,17) (10,13) (11,18) (11,12) (11,21) (11,16) (11,20) (11,15) (11,19) (11,17) (11,13) (12,18) (12,21) (12,16) (12,20) (12,15) (12,19) (12,17) (12,13) (13,18) (13,21) (13,16) (13,20) (13,15) (13,19) (13,17) (15,18) (15,21) (15,16) (15,20) (15,19) (15,17) (16,18) (16,21) (16,20) (16,19) (16,17) (17,18) (17,21) (17,20) (17,19) (18,21) (18,20) (18,19) (19,21) (19,20) (20,21)\nIs there a path between node 15 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph819-11_10", + "image": "data/connectivity/graph_visual/medium/graph819.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,10) (0,5) (0,7) (1,20) (1,4) (1,8) (1,16) (1,9) (1,23) (1,2) (2,20) (2,22) (2,15) (2,4) (2,19) (2,8) (2,16) (2,9) (2,23) (2,14) (2,17) (3,20) (3,4) (3,19) (3,8) (3,23) (3,14) (3,21) (4,20) (4,22) (4,15) (4,8) (4,16) (4,23) (4,14) (4,21) (5,11) (5,10) (5,7) (6,13) (6,12) (6,18) (7,11) (7,10) (8,20) (8,22) (8,15) (8,23) (8,14) (8,21) (9,22) (9,19) (9,16) (9,21) (9,17) (12,18) (13,24) (13,18) (14,20) (14,22) (14,15) (14,19) (14,23) (14,21) (14,17) (15,22) (15,19) (15,16) (15,21) (15,17) (16,20) (16,21) (17,20) (17,19) (17,23) (17,21) (18,24) (19,22) (19,21) (20,22) (20,23) (20,21) (21,22) (21,23) (22,23)\nIs there a path between node 11 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph593-11_17", + "image": "data/connectivity/graph_visual/medium/graph593.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,7) (0,14) (0,8) (0,5) (0,4) (0,3) (0,23) (0,12) (0,15) (0,13) (0,17) (0,2) (1,19) (1,7) (1,14) (1,8) (1,3) (1,23) (1,12) (1,15) (1,13) (1,17) (1,6) (2,21) (2,19) (2,7) (2,5) (2,4) (2,3) (2,13) (3,21) (3,19) (3,14) (3,5) (3,4) (3,23) (3,12) (3,15) (4,21) (4,19) (4,14) (4,8) (4,5) (4,23) (4,12) (4,15) (4,6) (5,21) (5,19) (5,7) (5,8) (5,12) (5,17) (6,19) (6,7) (6,23) (6,12) (6,15) (6,13) (6,17) (7,21) (7,14) (7,12) (7,15) (7,13) (7,17) (8,21) (8,19) (8,12) (8,13) (9,11) (9,22) (9,20) (11,22) (11,18) (11,20) (12,14) (12,23) (12,15) (12,13) (12,17) (13,21) (13,23) (14,21) (14,19) (14,23) (14,15) (14,17) (15,21) (15,19) (15,23) (15,17) (16,22) (16,20) (17,19) (17,23) (19,21) (19,23) (20,22)\nIs there a path between node 11 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph15-6_4", + "image": "data/connectivity/graph_visual/medium/graph15.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,4) (0,8) (1,5) (2,3) (3,5) (3,11) (4,8) (5,9) (5,7) (5,10) (6,11)\nIs there a path between node 6 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph215-1_10", + "image": "data/connectivity/graph_visual/medium/graph215.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,18) (0,17) (0,8) (0,14) (0,7) (0,6) (0,16) (0,13) (0,5) (1,2) (1,12) (1,4) (1,10) (1,11) (1,9) (1,3) (2,12) (2,4) (2,10) (2,11) (2,9) (2,3) (3,12) (3,4) (3,10) (3,11) (3,9) (4,12) (4,10) (4,11) (4,9) (5,18) (5,17) (5,8) (5,14) (5,7) (5,6) (5,16) (5,13) (6,18) (6,17) (6,8) (6,14) (6,7) (6,16) (6,13) (7,18) (7,17) (7,8) (7,14) (7,16) (7,13) (8,18) (8,17) (8,14) (8,16) (8,13) (9,12) (9,10) (9,11) (10,12) (10,11) (11,12) (13,18) (13,17) (13,14) (13,16) (14,18) (14,17) (14,16) (16,18) (16,17) (17,18)\nIs there a path between node 1 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph711-18_21", + "image": "data/connectivity/graph_visual/medium/graph711.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,2) (0,7) (0,15) (0,14) (0,22) (0,10) (0,18) (0,5) (0,9) (0,4) (0,11) (0,8) (0,20) (0,13) (1,2) (1,7) (1,15) (1,14) (1,18) (1,5) (1,16) (1,9) (1,4) (1,11) (1,8) (1,13) (2,24) (2,7) (2,15) (2,14) (2,22) (2,18) (2,16) (2,9) (2,4) (2,11) (2,8) (2,20) (2,23) (3,21) (4,7) (4,14) (4,22) (4,18) (4,16) (4,13) (4,23) (5,24) (5,7) (5,15) (5,14) (5,22) (5,10) (5,18) (5,20) (5,23) (6,12) (7,24) (7,15) (7,14) (7,10) (7,18) (7,16) (7,9) (7,11) (7,8) (7,20) (7,13) (7,23) (8,24) (8,14) (8,10) (8,18) (8,9) (8,13) (8,23) (9,24) (9,15) (9,14) (9,22) (9,10) (9,16) (9,20) (9,23) (10,24) (10,15) (10,14) (10,22) (10,18) (10,16) (10,20) (11,15) (11,14) (11,18) (11,16) (11,20) (11,13) (11,23) (13,24) (13,15) (13,18) (13,16) (13,23) (14,24) (14,15) (14,22) (14,18) (14,16) (14,23) (15,24) (15,22) (15,18) (15,16) (15,20) (15,23) (16,24) (16,20) (16,23) (18,22) (18,20) (18,23) (19,21) (20,22) (22,24) (22,23) (23,24)\nIs there a path between node 18 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph167-5_0", + "image": "data/connectivity/graph_visual/medium/graph167.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,17) (0,8) (0,6) (0,12) (0,16) (0,3) (1,17) (1,2) (1,8) (1,9) (1,4) (1,12) (1,3) (2,17) (2,11) (2,9) (2,16) (2,14) (2,5) (3,13) (3,9) (3,14) (4,17) (4,7) (4,13) (4,16) (4,5) (5,7) (5,13) (5,9) (5,14) (6,8) (6,11) (6,9) (6,12) (6,16) (6,14) (7,8) (7,13) (8,13) (9,13) (9,12) (11,13) (11,12) (11,14) (13,14)\nIs there a path between node 5 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph351-20_11", + "image": "data/connectivity/graph_visual/medium/graph351.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,10) (2,9) (2,5) (3,12) (3,14) (3,4) (3,8) (3,18) (4,19) (4,16) (4,11) (5,20) (5,12) (5,14) (5,11) (6,18) (6,16) (7,15) (8,20) (8,12) (8,18) (8,16) (9,20) (9,14) (9,19) (9,11) (11,13) (11,12) (11,18) (11,16) (12,18) (13,19) (13,18) (14,19) (16,20) (18,19)\nIs there a path between node 20 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph316-3_0", + "image": "data/connectivity/graph_visual/medium/graph316.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,13) (0,18) (1,10) (1,9) (1,11) (1,8) (1,5) (1,17) (1,19) (1,4) (1,6) (1,12) (1,14) (1,7) (1,3) (1,15) (1,2) (1,16) (2,10) (2,9) (2,11) (2,8) (2,5) (2,17) (2,19) (2,4) (2,6) (2,12) (2,14) (2,7) (2,3) (2,15) (2,16) (3,10) (3,9) (3,11) (3,8) (3,5) (3,17) (3,19) (3,4) (3,6) (3,12) (3,14) (3,7) (3,15) (3,16) (4,10) (4,9) (4,11) (4,8) (4,5) (4,17) (4,19) (4,6) (4,12) (4,14) (4,7) (4,15) (4,16) (5,10) (5,9) (5,11) (5,8) (5,17) (5,19) (5,6) (5,12) (5,14) (5,7) (5,15) (5,16) (6,10) (6,9) (6,11) (6,8) (6,17) (6,19) (6,12) (6,14) (6,7) (6,15) (6,16) (7,10) (7,9) (7,11) (7,8) (7,17) (7,19) (7,12) (7,14) (7,15) (7,16) (8,10) (8,9) (8,11) (8,17) (8,19) (8,12) (8,14) (8,15) (8,16) (9,10) (9,11) (9,17) (9,19) (9,12) (9,14) (9,15) (9,16) (10,11) (10,17) (10,19) (10,12) (10,14) (10,15) (10,16) (11,17) (11,19) (11,12) (11,14) (11,15) (11,16) (12,17) (12,19) (12,14) (12,15) (12,16) (13,18) (14,17) (14,19) (14,15) (14,16) (15,17) (15,19) (15,16) (16,17) (16,19) (17,19)\nIs there a path between node 3 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph618-17_1", + "image": "data/connectivity/graph_visual/medium/graph618.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,20) (0,21) (0,22) (0,9) (0,17) (0,12) (0,15) (0,7) (0,16) (0,6) (0,3) (0,1) (0,4) (1,10) (1,19) (1,20) (1,21) (1,22) (1,9) (1,17) (1,12) (1,15) (1,7) (1,16) (1,6) (1,3) (1,4) (2,23) (2,8) (2,5) (2,18) (2,11) (2,13) (2,14) (3,10) (3,19) (3,20) (3,21) (3,22) (3,9) (3,17) (3,12) (3,15) (3,7) (3,16) (3,6) (3,4) (4,10) (4,19) (4,20) (4,21) (4,22) (4,9) (4,17) (4,12) (4,15) (4,7) (4,16) (4,6) (5,23) (5,8) (5,18) (5,11) (5,13) (5,14) (6,10) (6,19) (6,20) (6,21) (6,22) (6,9) (6,17) (6,12) (6,15) (6,7) (6,16) (7,10) (7,19) (7,20) (7,21) (7,22) (7,9) (7,17) (7,12) (7,15) (7,16) (8,23) (8,18) (8,11) (8,13) (8,14) (9,10) (9,19) (9,20) (9,21) (9,22) (9,17) (9,12) (9,15) (9,16) (10,19) (10,20) (10,21) (10,22) (10,17) (10,12) (10,15) (10,16) (11,23) (11,18) (11,13) (11,14) (12,19) (12,20) (12,21) (12,22) (12,17) (12,15) (12,16) (13,23) (13,18) (13,14) (14,23) (14,18) (15,19) (15,20) (15,21) (15,22) (15,17) (15,16) (16,19) (16,20) (16,21) (16,22) (16,17) (17,19) (17,20) (17,21) (17,22) (18,23) (19,20) (19,21) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 17 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph716-19_11", + "image": "data/connectivity/graph_visual/medium/graph716.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,22) (0,23) (0,15) (0,21) (0,8) (0,12) (0,2) (0,1) (1,24) (1,14) (1,11) (1,22) (1,19) (1,15) (1,8) (1,12) (1,2) (1,17) (2,24) (2,11) (2,19) (2,15) (2,8) (2,7) (2,17) (3,16) (3,6) (3,13) (3,4) (4,16) (4,6) (4,10) (4,13) (4,9) (4,18) (5,16) (5,10) (5,13) (5,9) (5,18) (6,10) (6,9) (6,18) (7,24) (7,14) (7,22) (7,19) (7,21) (7,12) (7,20) (7,17) (8,24) (8,14) (8,23) (8,21) (8,20) (9,16) (9,10) (9,13) (9,18) (10,13) (10,18) (11,24) (11,14) (11,22) (11,19) (11,15) (11,21) (11,17) (12,24) (12,14) (12,19) (12,23) (12,21) (12,20) (12,17) (13,16) (13,18) (14,24) (14,22) (14,19) (14,23) (14,15) (14,21) (14,20) (14,17) (15,24) (15,22) (15,19) (15,20) (15,17) (16,18) (17,24) (17,22) (17,19) (17,21) (17,20) (19,24) (19,22) (19,21) (19,20) (20,24) (20,22) (21,24) (21,22) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 19 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph448-20_18", + "image": "data/connectivity/graph_visual/medium/graph448.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,17) (0,19) (0,1) (0,6) (0,5) (0,7) (0,2) (0,14) (0,4) (0,10) (1,17) (1,6) (1,5) (1,12) (1,7) (1,13) (1,2) (1,20) (1,14) (1,10) (2,9) (2,17) (2,16) (2,19) (2,6) (2,12) (2,7) (2,18) (2,13) (2,20) (2,14) (2,4) (2,10) (3,21) (3,15) (3,11) (4,9) (4,17) (4,16) (4,19) (4,6) (4,5) (4,12) (4,7) (4,13) (4,10) (5,9) (5,17) (5,16) (5,12) (5,18) (5,13) (5,20) (5,14) (6,17) (6,16) (6,12) (6,7) (6,18) (6,20) (6,10) (7,9) (7,17) (7,16) (7,19) (7,13) (7,20) (7,14) (7,10) (8,21) (8,15) (9,16) (9,19) (9,18) (9,13) (9,20) (9,14) (9,10) (10,17) (10,16) (10,18) (10,13) (10,20) (10,14) (11,21) (12,17) (12,16) (12,19) (13,17) (13,16) (13,19) (14,17) (14,19) (14,20) (15,21) (16,17) (16,18) (16,20) (17,19) (17,20) (18,19) (18,20) (19,20)\nIs there a path between node 20 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph669-20_12", + "image": "data/connectivity/graph_visual/medium/graph669.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,7) (0,2) (0,9) (0,1) (0,17) (0,14) (0,18) (0,4) (0,5) (0,16) (0,15) (0,10) (0,22) (1,12) (1,3) (1,7) (1,14) (1,18) (1,5) (1,15) (1,10) (1,22) (2,3) (2,7) (2,9) (2,17) (2,18) (2,5) (2,16) (2,15) (2,10) (2,22) (3,7) (3,21) (3,9) (3,17) (3,14) (3,18) (3,4) (3,5) (3,15) (3,22) (4,6) (4,12) (4,7) (4,21) (4,9) (4,23) (4,16) (4,15) (4,22) (5,6) (5,12) (5,7) (5,17) (5,23) (5,16) (5,15) (5,10) (6,12) (6,7) (6,21) (6,18) (6,15) (6,10) (6,22) (7,9) (7,14) (7,18) (7,23) (7,16) (7,10) (7,22) (8,19) (8,20) (8,13) (8,11) (9,21) (9,14) (9,23) (9,16) (9,15) (9,10) (9,22) (10,12) (10,21) (10,17) (10,14) (10,23) (10,16) (10,15) (10,22) (11,19) (11,20) (11,13) (12,21) (12,14) (12,23) (12,16) (12,22) (14,17) (14,18) (14,23) (14,15) (14,22) (15,21) (15,17) (15,18) (15,23) (15,16) (16,21) (16,18) (16,23) (17,21) (17,18) (17,23) (17,22) (18,23) (19,20) (21,23) (21,22) (22,23)\nIs there a path between node 20 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph632-19_15", + "image": "data/connectivity/graph_visual/medium/graph632.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,10) (0,1) (0,14) (0,16) (0,4) (1,10) (1,20) (1,4) (2,3) (3,13) (3,21) (3,17) (3,4) (4,20) (4,17) (5,20) (5,15) (6,21) (6,8) (6,15) (6,11) (6,17) (7,13) (7,21) (7,8) (7,15) (7,12) (8,23) (8,9) (8,20) (8,15) (9,13) (9,10) (9,20) (9,14) (10,20) (10,11) (11,15) (11,12) (11,16) (12,23) (12,14) (12,17) (13,20) (15,21) (16,21) (16,17) (17,23) (17,21)\nIs there a path between node 19 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph723-12_23", + "image": "data/connectivity/graph_visual/medium/graph723.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,22) (0,15) (0,6) (0,7) (0,11) (0,9) (0,1) (0,4) (0,14) (0,23) (0,17) (0,21) (0,20) (0,8) (0,24) (0,18) (1,3) (1,22) (1,15) (1,6) (1,7) (1,11) (1,9) (1,4) (1,14) (1,23) (1,17) (1,21) (1,20) (1,8) (1,24) (1,18) (2,12) (2,10) (2,13) (2,16) (3,22) (3,15) (3,6) (3,7) (3,11) (3,9) (3,4) (3,14) (3,23) (3,17) (3,21) (3,20) (3,8) (3,24) (3,18) (4,22) (4,15) (4,6) (4,7) (4,11) (4,9) (4,14) (4,23) (4,17) (4,21) (4,20) (4,8) (4,24) (4,18) (5,19) (6,22) (6,15) (6,7) (6,11) (6,9) (6,14) (6,23) (6,17) (6,21) (6,20) (6,8) (6,24) (6,18) (7,22) (7,15) (7,11) (7,9) (7,14) (7,23) (7,17) (7,21) (7,20) (7,8) (7,24) (7,18) (8,22) (8,15) (8,11) (8,9) (8,14) (8,23) (8,17) (8,21) (8,20) (8,24) (8,18) (9,22) (9,15) (9,11) (9,14) (9,23) (9,17) (9,21) (9,20) (9,24) (9,18) (10,12) (10,13) (10,16) (11,22) (11,15) (11,14) (11,23) (11,17) (11,21) (11,20) (11,24) (11,18) (12,13) (12,16) (13,16) (14,22) (14,15) (14,23) (14,17) (14,21) (14,20) (14,24) (14,18) (15,22) (15,23) (15,17) (15,21) (15,20) (15,24) (15,18) (17,22) (17,23) (17,21) (17,20) (17,24) (17,18) (18,22) (18,23) (18,21) (18,20) (18,24) (20,22) (20,23) (20,21) (20,24) (21,22) (21,23) (21,24) (22,23) (22,24) (23,24)\nIs there a path between node 12 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph706-8_17", + "image": "data/connectivity/graph_visual/medium/graph706.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (0,2) (0,23) (0,1) (1,16) (1,17) (1,5) (1,15) (1,19) (1,13) (1,4) (2,3) (2,13) (2,4) (2,10) (3,17) (3,15) (3,14) (3,9) (3,20) (3,6) (4,12) (4,18) (5,13) (5,14) (5,9) (6,19) (6,13) (6,23) (6,14) (6,20) (7,21) (9,16) (9,13) (9,23) (9,11) (9,18) (10,16) (10,13) (11,15) (11,23) (12,16) (12,17) (12,23) (13,17) (13,23) (14,16) (14,17) (14,19) (14,18) (15,16) (15,19) (15,23) (15,18) (15,20) (16,17) (17,18) (18,20)\nIs there a path between node 8 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph338-11_6", + "image": "data/connectivity/graph_visual/medium/graph338.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,8) (0,2) (0,7) (0,9) (0,15) (0,18) (1,8) (1,2) (1,9) (1,15) (1,18) (2,8) (2,7) (2,9) (2,18) (3,17) (3,6) (3,5) (3,16) (3,20) (4,13) (4,11) (5,17) (5,14) (5,10) (5,16) (5,20) (6,17) (6,14) (6,20) (7,8) (7,9) (7,15) (7,12) (8,9) (8,15) (8,12) (8,18) (9,15) (9,18) (10,17) (10,14) (10,16) (10,20) (11,13) (12,18) (13,19) (14,17) (15,18) (16,20)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph526-4_1", + "image": "data/connectivity/graph_visual/medium/graph526.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,16) (0,9) (0,20) (0,8) (0,18) (0,4) (0,3) (0,1) (0,12) (0,15) (0,10) (0,14) (1,11) (1,17) (1,5) (1,22) (1,21) (1,9) (1,20) (1,8) (1,18) (1,3) (1,2) (1,10) (2,17) (2,5) (2,22) (2,16) (2,21) (2,20) (2,8) (2,18) (2,3) (2,12) (2,15) (3,11) (3,17) (3,5) (3,22) (3,16) (3,21) (3,9) (3,8) (3,18) (3,4) (3,15) (3,10) (4,17) (4,5) (4,22) (4,16) (4,9) (4,20) (4,8) (4,12) (4,10) (4,14) (5,16) (5,9) (5,20) (5,18) (5,10) (5,14) (7,13) (8,11) (8,17) (8,22) (8,16) (8,21) (8,9) (8,18) (8,12) (8,15) (8,10) (8,14) (9,11) (9,17) (9,16) (9,21) (9,20) (9,18) (9,10) (9,14) (10,11) (10,17) (10,22) (10,16) (10,21) (10,20) (10,18) (10,12) (10,15) (10,14) (11,22) (11,16) (11,21) (11,18) (11,15) (11,14) (12,22) (12,18) (12,14) (14,17) (14,20) (14,18) (14,15) (15,17) (15,22) (15,21) (15,20) (15,18) (16,17) (16,21) (16,20) (16,18) (17,22) (17,20) (17,18) (18,22) (18,21) (20,22) (21,22)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph810-7_19", + "image": "data/connectivity/graph_visual/medium/graph810.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,6) (0,1) (0,21) (0,23) (0,16) (1,8) (1,6) (1,24) (1,5) (1,3) (1,15) (1,2) (1,21) (1,23) (1,7) (2,9) (2,24) (2,3) (2,15) (2,21) (2,16) (3,9) (3,8) (3,15) (3,7) (4,11) (4,14) (4,20) (5,9) (5,8) (5,17) (5,6) (5,15) (5,21) (5,23) (5,7) (6,9) (6,17) (6,24) (6,15) (6,21) (6,23) (6,7) (7,9) (7,8) (7,24) (7,15) (7,21) (7,16) (8,24) (8,15) (8,21) (8,23) (8,16) (9,24) (9,15) (9,21) (9,16) (10,19) (10,18) (11,14) (11,20) (12,18) (12,22) (14,20) (15,17) (15,24) (15,21) (15,23) (16,17) (16,24) (16,21) (16,23) (17,24) (17,21) (18,19) (19,22) (21,24) (23,24)\nIs there a path between node 7 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph248-16_13", + "image": "data/connectivity/graph_visual/medium/graph248.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,9) (0,4) (0,3) (0,6) (0,10) (0,17) (0,11) (1,13) (1,5) (1,18) (1,2) (1,8) (1,7) (1,12) (1,14) (2,13) (2,5) (2,18) (2,8) (2,7) (2,12) (2,14) (3,9) (3,4) (3,6) (3,10) (3,17) (3,11) (4,9) (4,6) (4,10) (4,17) (4,11) (5,13) (5,18) (5,8) (5,7) (5,12) (5,14) (6,9) (6,10) (6,17) (6,11) (7,13) (7,18) (7,8) (7,12) (7,14) (8,13) (8,18) (8,12) (8,14) (9,10) (9,17) (9,11) (10,17) (10,11) (11,17) (12,13) (12,18) (12,14) (13,18) (13,14) (14,18) (15,16)\nIs there a path between node 16 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph441-14_13", + "image": "data/connectivity/graph_visual/medium/graph441.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,17) (0,9) (1,21) (1,2) (1,13) (1,12) (1,11) (1,5) (2,19) (2,7) (2,18) (2,21) (2,13) (2,16) (2,20) (2,12) (3,15) (3,14) (3,10) (3,6) (4,21) (4,13) (4,16) (4,20) (4,12) (4,5) (5,7) (5,18) (5,21) (5,13) (5,16) (5,20) (5,12) (6,15) (6,14) (6,8) (7,19) (7,18) (7,13) (7,16) (7,20) (7,12) (7,11) (8,14) (8,10) (10,14) (11,18) (11,13) (11,16) (12,19) (12,18) (12,21) (12,13) (12,16) (13,19) (13,18) (13,21) (13,20) (14,15) (18,21) (19,21) (19,20)\nIs there a path between node 14 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph448-8_18", + "image": "data/connectivity/graph_visual/medium/graph448.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,17) (0,19) (0,1) (0,6) (0,5) (0,7) (0,2) (0,14) (0,4) (0,10) (1,17) (1,6) (1,5) (1,12) (1,7) (1,13) (1,2) (1,20) (1,14) (1,10) (2,9) (2,17) (2,16) (2,19) (2,6) (2,12) (2,7) (2,18) (2,13) (2,20) (2,14) (2,4) (2,10) (3,21) (3,15) (3,11) (4,9) (4,17) (4,16) (4,19) (4,6) (4,5) (4,12) (4,7) (4,13) (4,10) (5,9) (5,17) (5,16) (5,12) (5,18) (5,13) (5,20) (5,14) (6,17) (6,16) (6,12) (6,7) (6,18) (6,20) (6,10) (7,9) (7,17) (7,16) (7,19) (7,13) (7,20) (7,14) (7,10) (8,21) (8,15) (9,16) (9,19) (9,18) (9,13) (9,20) (9,14) (9,10) (10,17) (10,16) (10,18) (10,13) (10,20) (10,14) (11,21) (12,17) (12,16) (12,19) (13,17) (13,16) (13,19) (14,17) (14,19) (14,20) (15,21) (16,17) (16,18) (16,20) (17,19) (17,20) (18,19) (18,20) (19,20)\nIs there a path between node 8 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph586-9_1", + "image": "data/connectivity/graph_visual/medium/graph586.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,1) (1,22) (1,8) (1,9) (1,14) (2,18) (2,9) (4,6) (4,10) (4,19) (6,10) (7,23) (7,16) (7,10) (8,22) (8,15) (8,18) (8,20) (9,12) (9,14) (12,18) (13,14) (14,22) (14,20) (15,22) (15,20) (18,22)\nIs there a path between node 9 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph401-7_19", + "image": "data/connectivity/graph_visual/medium/graph401.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,11) (0,1) (1,11) (2,4) (2,14) (3,21) (3,18) (3,6) (3,12) (3,13) (5,6) (6,21) (6,20) (6,8) (6,12) (6,13) (7,16) (7,12) (8,20) (9,20) (9,13) (10,11) (12,17) (12,16) (13,20) (13,17) (13,19) (15,21) (15,16) (15,19) (16,21) (16,19) (17,19) (18,19) (19,20) (20,21)\nIs there a path between node 7 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph170-6_15", + "image": "data/connectivity/graph_visual/medium/graph170.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,9) (0,17) (0,12) (0,8) (0,14) (0,10) (0,11) (0,4) (1,6) (1,7) (2,13) (2,17) (2,12) (2,8) (2,10) (2,11) (2,15) (2,4) (3,6) (3,5) (4,9) (4,8) (4,10) (4,11) (6,7) (6,16) (7,16) (8,13) (8,17) (8,12) (8,14) (8,10) (8,11) (9,17) (9,14) (9,15) (10,17) (10,12) (10,14) (10,15) (11,17) (11,14) (11,15) (12,13) (13,14) (13,15) (14,17) (15,17)\nIs there a path between node 6 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph130-11_1", + "image": "data/connectivity/graph_visual/medium/graph130.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,10) (0,1) (0,5) (0,15) (0,6) (0,4) (0,7) (0,16) (0,13) (0,8) (0,2) (0,12) (0,14) (1,10) (1,5) (1,15) (1,6) (1,4) (1,7) (1,16) (1,13) (1,8) (1,2) (1,12) (1,14) (2,10) (2,5) (2,15) (2,6) (2,4) (2,7) (2,16) (2,13) (2,8) (2,12) (2,14) (3,11) (3,9) (4,10) (4,5) (4,15) (4,6) (4,7) (4,16) (4,13) (4,8) (4,12) (4,14) (5,10) (5,15) (5,6) (5,7) (5,16) (5,13) (5,8) (5,12) (5,14) (6,10) (6,15) (6,7) (6,16) (6,13) (6,8) (6,12) (6,14) (7,10) (7,15) (7,16) (7,13) (7,8) (7,12) (7,14) (8,10) (8,15) (8,16) (8,13) (8,12) (8,14) (9,11) (10,15) (10,16) (10,13) (10,12) (10,14) (12,15) (12,16) (12,13) (12,14) (13,15) (13,16) (13,14) (14,15) (14,16) (15,16)\nIs there a path between node 11 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph396-4_11", + "image": "data/connectivity/graph_visual/medium/graph396.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,12) (0,3) (0,13) (0,15) (0,7) (1,4) (1,6) (2,9) (2,18) (2,13) (3,12) (4,11) (6,8) (6,17) (7,16) (7,12) (7,13) (7,14) (8,11) (8,17) (8,20) (9,18) (9,21) (9,14) (9,15) (10,12) (12,16) (12,15) (13,18) (13,15) (14,16) (14,21) (15,16) (15,18) (16,18)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph325-17_14", + "image": "data/connectivity/graph_visual/medium/graph325.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,13) (0,5) (0,11) (0,15) (0,10) (0,16) (0,14) (0,8) (0,9) (1,18) (1,12) (1,7) (1,6) (2,13) (2,11) (2,15) (2,17) (2,16) (2,14) (2,3) (2,8) (2,9) (3,5) (3,11) (3,4) (3,15) (3,10) (3,14) (3,8) (3,9) (4,13) (4,5) (4,17) (4,16) (4,14) (4,8) (5,17) (5,16) (5,14) (6,12) (6,19) (6,20) (6,7) (7,18) (8,15) (8,17) (8,16) (8,14) (8,9) (9,13) (9,11) (9,17) (9,16) (9,14) (10,11) (10,15) (10,17) (10,16) (10,14) (11,13) (11,15) (11,16) (12,18) (12,19) (12,20) (13,17) (13,14) (14,15) (14,17) (14,16) (15,17) (16,17) (18,19) (18,20) (19,20)\nIs there a path between node 17 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph145-4_13", + "image": "data/connectivity/graph_visual/medium/graph145.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,12) (0,4) (0,11) (0,17) (0,2) (0,5) (0,9) (0,8) (0,16) (0,10) (1,3) (1,12) (1,4) (1,11) (1,17) (1,7) (1,2) (1,5) (1,9) (1,8) (1,10) (2,3) (2,12) (2,4) (2,11) (2,17) (2,7) (2,5) (2,8) (2,16) (3,12) (3,7) (3,9) (3,8) (4,12) (4,11) (4,17) (4,5) (4,9) (4,8) (4,16) (4,10) (5,12) (5,11) (5,17) (5,7) (5,14) (5,9) (5,16) (5,10) (6,15) (6,13) (7,12) (7,11) (7,17) (7,9) (7,16) (7,10) (8,11) (8,14) (8,9) (8,16) (8,10) (9,12) (9,17) (9,10) (10,11) (10,17) (10,14) (10,16) (11,17) (11,16) (14,16) (16,17)\nIs there a path between node 4 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph548-5_3", + "image": "data/connectivity/graph_visual/medium/graph548.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,9) (0,17) (0,7) (1,18) (1,3) (1,23) (1,19) (2,21) (2,14) (2,9) (2,16) (2,11) (2,5) (3,23) (3,6) (4,9) (4,11) (4,8) (4,20) (5,21) (5,8) (5,13) (6,10) (7,21) (7,17) (7,22) (8,14) (9,11) (9,13) (9,20) (9,22) (10,23) (11,16) (11,12) (12,21) (12,14) (13,21) (13,17) (14,16) (16,20) (19,23)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph250-16_7", + "image": "data/connectivity/graph_visual/medium/graph250.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,15) (0,1) (0,9) (0,7) (0,18) (0,3) (0,13) (0,14) (0,11) (0,6) (0,17) (0,10) (0,2) (0,12) (1,15) (1,9) (1,7) (1,18) (1,3) (1,13) (1,14) (1,11) (1,6) (1,17) (1,10) (1,2) (1,12) (2,15) (2,9) (2,7) (2,18) (2,3) (2,13) (2,14) (2,11) (2,6) (2,17) (2,10) (2,12) (3,15) (3,9) (3,7) (3,18) (3,13) (3,14) (3,11) (3,6) (3,17) (3,10) (3,12) (4,16) (4,5) (4,8) (5,16) (5,8) (6,15) (6,9) (6,7) (6,18) (6,13) (6,14) (6,11) (6,17) (6,10) (6,12) (7,15) (7,9) (7,18) (7,13) (7,14) (7,11) (7,17) (7,10) (7,12) (8,16) (9,15) (9,18) (9,13) (9,14) (9,11) (9,17) (9,10) (9,12) (10,15) (10,18) (10,13) (10,14) (10,11) (10,17) (10,12) (11,15) (11,18) (11,13) (11,14) (11,17) (11,12) (12,15) (12,18) (12,13) (12,14) (12,17) (13,15) (13,18) (13,14) (13,17) (14,15) (14,18) (14,17) (15,18) (15,17) (17,18)\nIs there a path between node 16 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph670-1_23", + "image": "data/connectivity/graph_visual/medium/graph670.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,21) (0,18) (0,20) (0,16) (1,14) (1,23) (1,7) (1,3) (2,23) (2,7) (2,3) (3,14) (3,23) (3,7) (3,22) (4,11) (5,6) (5,21) (5,20) (5,16) (5,15) (6,21) (6,20) (6,16) (6,15) (7,23) (7,22) (8,12) (8,19) (8,17) (9,13) (9,12) (9,19) (9,10) (10,13) (10,12) (10,19) (10,17) (12,13) (12,19) (12,17) (13,17) (14,23) (15,21) (15,18) (15,16) (16,21) (16,18) (16,20) (17,19) (18,21) (18,20)\nIs there a path between node 1 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph158-9_4", + "image": "data/connectivity/graph_visual/medium/graph158.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,9) (1,14) (1,8) (2,11) (2,16) (2,7) (2,6) (3,17) (3,11) (3,4) (3,13) (3,6) (4,10) (5,15) (5,10) (6,17) (6,15) (7,17) (7,16) (8,9) (10,17) (10,16) (11,17) (11,15) (11,16) (12,17) (12,16) (15,17) (15,16)\nIs there a path between node 9 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph444-6_9", + "image": "data/connectivity/graph_visual/medium/graph444.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,3) (0,15) (0,21) (0,17) (0,7) (0,12) (0,5) (0,9) (0,2) (0,19) (0,14) (0,20) (1,3) (1,15) (1,16) (1,17) (1,11) (1,7) (1,12) (1,13) (1,8) (1,18) (1,9) (1,2) (1,19) (1,14) (1,20) (2,15) (2,21) (2,17) (2,11) (2,7) (2,12) (2,5) (2,8) (2,19) (2,14) (2,10) (2,20) (3,15) (3,21) (3,16) (3,17) (3,11) (3,13) (3,5) (3,8) (3,18) (3,14) (3,10) (3,20) (5,15) (5,21) (5,16) (5,17) (5,11) (5,7) (5,12) (5,13) (5,9) (5,19) (5,14) (5,10) (5,20) (7,21) (7,17) (7,11) (7,12) (7,8) (7,18) (7,19) (7,10) (7,20) (8,15) (8,21) (8,16) (8,17) (8,9) (8,19) (8,14) (8,10) (8,20) (9,15) (9,21) (9,16) (9,13) (9,18) (9,14) (10,15) (10,21) (10,16) (10,17) (10,11) (10,12) (10,13) (10,18) (10,19) (10,14) (10,20) (11,15) (11,21) (11,16) (11,17) (11,13) (11,18) (11,14) (11,20) (12,16) (12,17) (12,13) (12,18) (12,20) (13,15) (13,21) (13,16) (13,17) (13,18) (13,14) (13,20) (14,16) (14,17) (14,19) (14,20) (15,16) (15,17) (15,19) (16,17) (16,18) (16,19) (16,20) (17,21) (17,18) (18,19) (18,20) (19,21) (20,21)\nIs there a path between node 6 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph368-13_12", + "image": "data/connectivity/graph_visual/medium/graph368.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,11) (0,9) (0,14) (0,7) (0,8) (0,15) (0,16) (0,1) (0,5) (1,9) (1,2) (1,14) (1,7) (1,16) (1,10) (1,17) (1,3) (1,6) (2,11) (2,14) (2,7) (2,8) (2,15) (2,16) (2,3) (2,5) (2,6) (3,11) (3,7) (3,8) (3,16) (3,10) (3,17) (3,6) (4,12) (4,19) (5,14) (5,8) (5,15) (5,16) (5,10) (5,17) (6,9) (6,14) (6,7) (6,8) (6,15) (6,10) (6,17) (7,11) (7,9) (7,14) (7,8) (7,16) (7,10) (8,11) (8,14) (8,15) (8,16) (8,17) (9,11) (9,14) (9,15) (9,16) (9,10) (10,11) (10,14) (10,15) (11,15) (11,16) (11,17) (12,18) (13,18) (14,15) (14,17) (15,16) (15,17) (18,19)\nIs there a path between node 13 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph779-9_19", + "image": "data/connectivity/graph_visual/medium/graph779.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,8) (0,19) (0,17) (0,22) (0,12) (0,16) (0,1) (0,10) (0,23) (0,14) (0,15) (0,6) (0,11) (0,21) (0,3) (0,20) (0,18) (0,24) (0,4) (0,2) (1,7) (1,8) (1,19) (1,17) (1,22) (1,12) (1,16) (1,10) (1,23) (1,14) (1,15) (1,6) (1,11) (1,21) (1,3) (1,20) (1,18) (1,24) (1,4) (1,2) (2,7) (2,8) (2,19) (2,17) (2,22) (2,12) (2,16) (2,10) (2,23) (2,14) (2,15) (2,6) (2,11) (2,21) (2,3) (2,20) (2,18) (2,24) (2,4) (3,7) (3,8) (3,19) (3,17) (3,22) (3,12) (3,16) (3,10) (3,23) (3,14) (3,15) (3,6) (3,11) (3,21) (3,20) (3,18) (3,24) (3,4) (4,7) (4,8) (4,19) (4,17) (4,22) (4,12) (4,16) (4,10) (4,23) (4,14) (4,15) (4,6) (4,11) (4,21) (4,20) (4,18) (4,24) (5,13) (5,9) (6,7) (6,8) (6,19) (6,17) (6,22) (6,12) (6,16) (6,10) (6,23) (6,14) (6,15) (6,11) (6,21) (6,20) (6,18) (6,24) (7,8) (7,19) (7,17) (7,22) (7,12) (7,16) (7,10) (7,23) (7,14) (7,15) (7,11) (7,21) (7,20) (7,18) (7,24) (8,19) (8,17) (8,22) (8,12) (8,16) (8,10) (8,23) (8,14) (8,15) (8,11) (8,21) (8,20) (8,18) (8,24) (9,13) (10,19) (10,17) (10,22) (10,12) (10,16) (10,23) (10,14) (10,15) (10,11) (10,21) (10,20) (10,18) (10,24) (11,19) (11,17) (11,22) (11,12) (11,16) (11,23) (11,14) (11,15) (11,21) (11,20) (11,18) (11,24) (12,19) (12,17) (12,22) (12,16) (12,23) (12,14) (12,15) (12,21) (12,20) (12,18) (12,24) (14,19) (14,17) (14,22) (14,16) (14,23) (14,15) (14,21) (14,20) (14,18) (14,24) (15,19) (15,17) (15,22) (15,16) (15,23) (15,21) (15,20) (15,18) (15,24) (16,19) (16,17) (16,22) (16,23) (16,21) (16,20) (16,18) (16,24) (17,19) (17,22) (17,23) (17,21) (17,20) (17,18) (17,24) (18,19) (18,22) (18,23) (18,21) (18,20) (18,24) (19,22) (19,23) (19,21) (19,20) (19,24) (20,22) (20,23) (20,21) (20,24) (21,22) (21,23) (21,24) (22,23) (22,24) (23,24)\nIs there a path between node 9 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph251-13_2", + "image": "data/connectivity/graph_visual/medium/graph251.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,3) (0,1) (0,15) (0,9) (0,2) (0,6) (0,14) (0,8) (0,11) (0,10) (0,7) (1,13) (1,3) (1,15) (1,9) (1,2) (1,6) (1,14) (1,8) (1,11) (1,10) (1,7) (2,13) (2,3) (2,15) (2,9) (2,6) (2,14) (2,8) (2,11) (2,10) (2,7) (3,13) (3,15) (3,9) (3,6) (3,14) (3,8) (3,11) (3,10) (3,7) (4,12) (5,16) (5,18) (5,17) (6,13) (6,15) (6,9) (6,14) (6,8) (6,11) (6,10) (6,7) (7,13) (7,15) (7,9) (7,14) (7,8) (7,11) (7,10) (8,13) (8,15) (8,9) (8,14) (8,11) (8,10) (9,13) (9,15) (9,14) (9,11) (9,10) (10,13) (10,15) (10,14) (10,11) (11,13) (11,15) (11,14) (13,15) (13,14) (14,15) (16,18) (16,17) (17,18)\nIs there a path between node 13 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph398-7_21", + "image": "data/connectivity/graph_visual/medium/graph398.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,12) (0,3) (0,11) (0,18) (0,7) (0,8) (0,9) (0,1) (0,10) (0,15) (0,17) (0,13) (0,16) (0,19) (0,2) (0,6) (0,5) (0,14) (1,12) (1,3) (1,11) (1,18) (1,7) (1,8) (1,9) (1,10) (1,15) (1,17) (1,13) (1,16) (1,19) (1,2) (1,6) (1,5) (1,14) (2,12) (2,3) (2,11) (2,18) (2,7) (2,8) (2,9) (2,10) (2,15) (2,17) (2,13) (2,16) (2,19) (2,6) (2,5) (2,14) (3,12) (3,11) (3,18) (3,7) (3,8) (3,9) (3,10) (3,15) (3,17) (3,13) (3,16) (3,19) (3,6) (3,5) (3,14) (4,20) (4,21) (5,12) (5,11) (5,18) (5,7) (5,8) (5,9) (5,10) (5,15) (5,17) (5,13) (5,16) (5,19) (5,6) (5,14) (6,12) (6,11) (6,18) (6,7) (6,8) (6,9) (6,10) (6,15) (6,17) (6,13) (6,16) (6,19) (6,14) (7,12) (7,11) (7,18) (7,8) (7,9) (7,10) (7,15) (7,17) (7,13) (7,16) (7,19) (7,14) (8,12) (8,11) (8,18) (8,9) (8,10) (8,15) (8,17) (8,13) (8,16) (8,19) (8,14) (9,12) (9,11) (9,18) (9,10) (9,15) (9,17) (9,13) (9,16) (9,19) (9,14) (10,12) (10,11) (10,18) (10,15) (10,17) (10,13) (10,16) (10,19) (10,14) (11,12) (11,18) (11,15) (11,17) (11,13) (11,16) (11,19) (11,14) (12,18) (12,15) (12,17) (12,13) (12,16) (12,19) (12,14) (13,18) (13,15) (13,17) (13,16) (13,19) (13,14) (14,18) (14,15) (14,17) (14,16) (14,19) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19) (20,21)\nIs there a path between node 7 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph606-5_7", + "image": "data/connectivity/graph_visual/medium/graph606.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,23) (1,16) (2,10) (2,11) (2,20) (2,21) (2,3) (3,15) (3,20) (3,21) (4,22) (4,7) (4,9) (4,12) (4,8) (4,14) (4,19) (5,22) (5,7) (5,9) (5,12) (5,8) (5,14) (5,19) (7,13) (7,22) (7,9) (7,12) (7,18) (7,19) (8,13) (8,9) (8,12) (8,18) (8,14) (8,19) (9,13) (9,12) (9,14) (10,15) (10,11) (11,15) (11,20) (11,21) (12,13) (12,22) (12,18) (12,14) (13,22) (13,18) (13,19) (14,22) (14,18) (14,19) (15,21) (16,17) (18,19) (19,22)\nIs there a path between node 5 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph7-0_3", + "image": "data/connectivity/graph_visual/medium/graph7.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,6) (1,4) (1,3) (1,2) (1,7) (2,10) (2,4) (2,8) (3,10) (3,6) (3,4) (3,8) (3,5) (4,6) (4,8) (4,5) (4,7) (5,10) (5,8) (6,10) (6,8) (7,10)\nIs there a path between node 0 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph337-9_15", + "image": "data/connectivity/graph_visual/medium/graph337.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,11) (0,3) (0,17) (1,13) (1,14) (2,13) (2,14) (2,20) (2,6) (3,5) (3,11) (3,18) (4,10) (4,12) (4,7) (5,19) (5,18) (5,17) (6,14) (6,20) (7,8) (7,12) (8,10) (8,9) (8,12) (8,15) (9,10) (10,12) (10,15) (11,16) (11,18) (12,15) (14,20) (16,19) (16,18) (17,19) (17,18) (18,19)\nIs there a path between node 9 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph706-5_0", + "image": "data/connectivity/graph_visual/medium/graph706.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (0,2) (0,23) (0,1) (1,16) (1,17) (1,5) (1,15) (1,19) (1,13) (1,4) (2,3) (2,13) (2,4) (2,10) (3,17) (3,15) (3,14) (3,9) (3,20) (3,6) (4,12) (4,18) (5,13) (5,14) (5,9) (6,19) (6,13) (6,23) (6,14) (6,20) (7,21) (9,16) (9,13) (9,23) (9,11) (9,18) (10,16) (10,13) (11,15) (11,23) (12,16) (12,17) (12,23) (13,17) (13,23) (14,16) (14,17) (14,19) (14,18) (15,16) (15,19) (15,23) (15,18) (15,20) (16,17) (17,18) (18,20)\nIs there a path between node 5 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph602-7_4", + "image": "data/connectivity/graph_visual/medium/graph602.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,7) (0,1) (0,21) (0,20) (0,9) (1,7) (1,21) (1,20) (1,9) (2,5) (2,11) (2,23) (2,12) (2,22) (2,6) (2,10) (2,19) (3,8) (3,15) (3,17) (4,21) (5,11) (5,12) (5,22) (5,13) (5,18) (5,10) (6,23) (6,22) (6,13) (6,18) (6,10) (6,19) (6,16) (7,21) (7,9) (8,15) (8,17) (9,21) (10,11) (10,12) (10,22) (10,13) (10,19) (11,23) (11,12) (11,22) (11,13) (11,18) (11,19) (11,16) (12,23) (12,22) (12,13) (12,18) (12,19) (12,16) (13,23) (13,22) (13,18) (13,19) (13,16) (14,15) (16,23) (16,22) (16,18) (18,23) (18,22) (18,19) (19,23) (19,22) (20,21) (22,23)\nIs there a path between node 7 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph640-16_9", + "image": "data/connectivity/graph_visual/medium/graph640.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,22) (0,16) (0,23) (1,8) (1,4) (1,22) (1,16) (1,18) (1,3) (2,19) (2,9) (2,17) (2,20) (3,14) (3,13) (3,7) (4,8) (4,12) (4,16) (4,23) (4,18) (5,10) (5,9) (5,20) (6,14) (6,13) (6,22) (6,7) (7,22) (7,18) (8,22) (8,18) (9,19) (9,11) (9,20) (9,21) (10,20) (10,21) (11,20) (12,18) (13,22) (13,16) (13,23) (13,18) (15,19) (15,17) (15,21) (16,23) (16,18) (17,19) (18,22)\nIs there a path between node 16 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph261-7_13", + "image": "data/connectivity/graph_visual/medium/graph261.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,2) (0,19) (1,11) (2,4) (2,13) (3,17) (3,10) (3,11) (5,8) (5,13) (6,10) (6,12) (7,18) (7,9) (10,17) (10,12) (11,12) (12,17) (13,16) (13,15) (14,18)\nIs there a path between node 7 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph583-5_2", + "image": "data/connectivity/graph_visual/medium/graph583.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,17) (0,10) (0,22) (1,23) (1,19) (1,5) (1,18) (2,20) (2,12) (2,5) (2,16) (3,19) (3,5) (3,7) (3,15) (3,18) (4,21) (4,17) (4,22) (5,23) (5,19) (5,12) (5,18) (6,21) (7,23) (7,16) (7,18) (7,14) (8,9) (8,10) (8,22) (9,11) (12,23) (12,16) (12,14) (13,23) (13,16) (13,18) (14,23) (14,19) (14,15) (15,23) (16,23) (17,22) (18,20) (19,20)\nIs there a path between node 5 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph677-12_3", + "image": "data/connectivity/graph_visual/medium/graph677.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,4) (0,9) (0,19) (0,14) (0,17) (0,7) (0,6) (0,5) (0,16) (0,13) (0,22) (0,12) (0,15) (0,23) (1,3) (1,2) (1,21) (1,8) (1,20) (2,3) (2,21) (2,8) (2,20) (3,21) (3,8) (3,20) (4,11) (4,9) (4,19) (4,14) (4,17) (4,7) (4,6) (4,5) (4,16) (4,13) (4,22) (4,12) (4,15) (4,23) (5,11) (5,9) (5,19) (5,14) (5,17) (5,7) (5,6) (5,16) (5,13) (5,22) (5,12) (5,15) (5,23) (6,11) (6,9) (6,19) (6,14) (6,17) (6,7) (6,16) (6,13) (6,22) (6,12) (6,15) (6,23) (7,11) (7,9) (7,19) (7,14) (7,17) (7,16) (7,13) (7,22) (7,12) (7,15) (7,23) (8,21) (8,20) (9,11) (9,19) (9,14) (9,17) (9,16) (9,13) (9,22) (9,12) (9,15) (9,23) (11,19) (11,14) (11,17) (11,16) (11,13) (11,22) (11,12) (11,15) (11,23) (12,19) (12,14) (12,17) (12,16) (12,13) (12,22) (12,15) (12,23) (13,19) (13,14) (13,17) (13,16) (13,22) (13,15) (13,23) (14,19) (14,17) (14,16) (14,22) (14,15) (14,23) (15,19) (15,17) (15,16) (15,22) (15,23) (16,19) (16,17) (16,22) (16,23) (17,19) (17,22) (17,23) (19,22) (19,23) (20,21) (22,23)\nIs there a path between node 12 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph423-20_5", + "image": "data/connectivity/graph_visual/medium/graph423.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,20) (0,15) (1,3) (1,20) (2,11) (3,12) (3,6) (3,16) (3,20) (5,14) (5,7) (6,20) (6,21) (7,13) (7,18) (8,14) (8,13) (9,12) (9,16) (9,21) (10,21) (11,17) (12,16) (14,18) (15,16) (15,21) (16,20) (20,21)\nIs there a path between node 20 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph815-2_10", + "image": "data/connectivity/graph_visual/medium/graph815.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,16) (0,22) (0,3) (0,20) (0,14) (0,6) (0,19) (0,15) (0,13) (1,18) (1,9) (1,24) (1,2) (1,21) (1,23) (2,9) (2,24) (2,12) (2,10) (2,23) (2,4) (3,11) (3,16) (3,20) (3,14) (3,6) (3,7) (3,8) (3,15) (3,13) (4,9) (4,24) (4,12) (4,10) (4,21) (4,17) (4,23) (5,9) (5,24) (5,12) (5,10) (5,21) (5,17) (6,16) (6,22) (6,20) (6,7) (6,19) (6,8) (6,15) (6,13) (7,11) (7,16) (7,22) (7,20) (7,19) (7,8) (7,13) (8,22) (8,20) (8,19) (8,15) (8,13) (9,18) (9,10) (9,21) (9,23) (10,18) (10,24) (10,12) (10,17) (10,23) (11,16) (11,22) (11,20) (11,14) (11,19) (12,24) (12,21) (12,17) (12,23) (13,16) (13,22) (13,20) (13,19) (13,15) (14,16) (14,22) (14,19) (14,15) (15,16) (15,22) (15,19) (16,22) (16,20) (16,19) (18,24) (18,21) (19,20) (20,22) (21,24)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph699-7_10", + "image": "data/connectivity/graph_visual/medium/graph699.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (1,20) (2,11) (2,23) (2,14) (2,8) (3,17) (3,14) (3,16) (4,7) (4,16) (4,8) (4,24) (5,6) (5,10) (5,20) (6,20) (7,12) (7,16) (7,8) (7,24) (8,12) (8,23) (8,21) (9,18) (10,18) (10,20) (11,17) (11,19) (11,24) (12,22) (12,17) (12,14) (13,24) (14,23) (14,24) (15,17) (15,19) (15,24) (16,22) (16,19) (17,19) (17,24) (19,24) (23,24)\nIs there a path between node 7 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph651-7_1", + "image": "data/connectivity/graph_visual/medium/graph651.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,4) (0,11) (0,18) (0,2) (0,8) (0,19) (0,23) (0,13) (0,7) (0,3) (0,16) (1,21) (1,22) (1,14) (1,17) (2,9) (2,4) (2,11) (2,18) (2,8) (2,19) (2,23) (2,13) (2,7) (2,3) (2,6) (3,9) (3,4) (3,11) (3,18) (3,8) (3,23) (3,13) (3,7) (3,6) (4,9) (4,11) (4,18) (4,23) (5,20) (5,10) (6,9) (6,18) (6,8) (6,13) (6,7) (6,16) (7,9) (7,11) (7,18) (7,8) (7,19) (7,23) (7,13) (7,16) (8,9) (8,11) (8,18) (8,19) (8,23) (8,13) (9,19) (9,23) (9,13) (11,18) (11,19) (11,23) (11,16) (12,21) (12,22) (12,15) (13,19) (13,23) (14,21) (14,22) (14,15) (15,21) (15,22) (16,18) (16,23) (17,21) (18,19) (19,23) (21,22)\nIs there a path between node 7 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph10-0_6", + "image": "data/connectivity/graph_visual/medium/graph10.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,1) (0,7) (0,4) (0,9) (0,3) (1,7) (1,2) (1,4) (1,9) (1,3) (2,8) (2,9) (2,3) (3,8) (3,6) (3,4) (3,9) (4,8) (4,6) (5,10) (6,9) (8,9)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph499-19_10", + "image": "data/connectivity/graph_visual/medium/graph499.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (0,15) (0,5) (1,10) (2,19) (2,14) (2,21) (4,22) (4,13) (4,6) (5,15) (6,22) (6,9) (8,13) (8,19) (8,21) (10,20) (11,20) (12,18) (13,14) (15,18) (17,19) (21,22)\nIs there a path between node 19 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph679-5_18", + "image": "data/connectivity/graph_visual/medium/graph679.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (0,20) (0,18) (0,16) (0,17) (0,12) (0,19) (0,9) (0,4) (0,14) (0,23) (0,7) (0,2) (0,5) (0,8) (0,1) (0,22) (0,6) (0,21) (0,11) (1,13) (1,20) (1,18) (1,16) (1,17) (1,12) (1,19) (1,9) (1,4) (1,14) (1,23) (1,7) (1,2) (1,5) (1,8) (1,22) (1,6) (1,21) (1,11) (2,13) (2,20) (2,18) (2,16) (2,17) (2,12) (2,19) (2,9) (2,4) (2,14) (2,23) (2,7) (2,5) (2,8) (2,22) (2,6) (2,21) (2,11) (3,15) (4,13) (4,20) (4,18) (4,16) (4,17) (4,12) (4,19) (4,9) (4,14) (4,23) (4,7) (4,5) (4,8) (4,22) (4,6) (4,21) (4,11) (5,13) (5,20) (5,18) (5,16) (5,17) (5,12) (5,19) (5,9) (5,14) (5,23) (5,7) (5,8) (5,22) (5,6) (5,21) (5,11) (6,13) (6,20) (6,18) (6,16) (6,17) (6,12) (6,19) (6,9) (6,14) (6,23) (6,7) (6,8) (6,22) (6,21) (6,11) (7,13) (7,20) (7,18) (7,16) (7,17) (7,12) (7,19) (7,9) (7,14) (7,23) (7,8) (7,22) (7,21) (7,11) (8,13) (8,20) (8,18) (8,16) (8,17) (8,12) (8,19) (8,9) (8,14) (8,23) (8,22) (8,21) (8,11) (9,13) (9,20) (9,18) (9,16) (9,17) (9,12) (9,19) (9,14) (9,23) (9,22) (9,21) (9,11) (11,13) (11,20) (11,18) (11,16) (11,17) (11,12) (11,19) (11,14) (11,23) (11,22) (11,21) (12,13) (12,20) (12,18) (12,16) (12,17) (12,19) (12,14) (12,23) (12,22) (12,21) (13,20) (13,18) (13,16) (13,17) (13,19) (13,14) (13,23) (13,22) (13,21) (14,20) (14,18) (14,16) (14,17) (14,19) (14,23) (14,22) (14,21) (16,20) (16,18) (16,17) (16,19) (16,23) (16,22) (16,21) (17,20) (17,18) (17,19) (17,23) (17,22) (17,21) (18,20) (18,19) (18,23) (18,22) (18,21) (19,20) (19,23) (19,22) (19,21) (20,23) (20,22) (20,21) (21,23) (21,22) (22,23)\nIs there a path between node 5 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph464-14_12", + "image": "data/connectivity/graph_visual/medium/graph464.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,16) (0,1) (0,9) (0,10) (0,18) (1,4) (1,16) (1,9) (1,10) (1,18) (2,3) (2,7) (2,11) (2,20) (2,8) (2,19) (2,13) (2,12) (2,5) (2,17) (2,6) (2,15) (2,21) (2,14) (3,7) (3,11) (3,20) (3,8) (3,19) (3,13) (3,12) (3,5) (3,17) (3,6) (3,15) (3,21) (3,14) (4,16) (4,9) (4,10) (4,18) (5,7) (5,11) (5,20) (5,8) (5,19) (5,13) (5,12) (5,17) (5,6) (5,15) (5,21) (5,14) (6,7) (6,11) (6,20) (6,8) (6,19) (6,13) (6,12) (6,17) (6,15) (6,21) (6,14) (7,11) (7,20) (7,8) (7,19) (7,13) (7,12) (7,17) (7,15) (7,21) (7,14) (8,11) (8,20) (8,19) (8,13) (8,12) (8,17) (8,15) (8,21) (8,14) (9,16) (9,10) (9,18) (10,16) (10,18) (11,20) (11,19) (11,13) (11,12) (11,17) (11,15) (11,21) (11,14) (12,20) (12,19) (12,13) (12,17) (12,15) (12,21) (12,14) (13,20) (13,19) (13,17) (13,15) (13,21) (13,14) (14,20) (14,19) (14,17) (14,15) (14,21) (15,20) (15,19) (15,17) (15,21) (16,18) (17,20) (17,19) (17,21) (19,20) (19,21) (20,21)\nIs there a path between node 14 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph215-18_12", + "image": "data/connectivity/graph_visual/medium/graph215.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,18) (0,17) (0,8) (0,14) (0,7) (0,6) (0,16) (0,13) (0,5) (1,2) (1,12) (1,4) (1,10) (1,11) (1,9) (1,3) (2,12) (2,4) (2,10) (2,11) (2,9) (2,3) (3,12) (3,4) (3,10) (3,11) (3,9) (4,12) (4,10) (4,11) (4,9) (5,18) (5,17) (5,8) (5,14) (5,7) (5,6) (5,16) (5,13) (6,18) (6,17) (6,8) (6,14) (6,7) (6,16) (6,13) (7,18) (7,17) (7,8) (7,14) (7,16) (7,13) (8,18) (8,17) (8,14) (8,16) (8,13) (9,12) (9,10) (9,11) (10,12) (10,11) (11,12) (13,18) (13,17) (13,14) (13,16) (14,18) (14,17) (14,16) (16,18) (16,17) (17,18)\nIs there a path between node 18 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph270-2_17", + "image": "data/connectivity/graph_visual/medium/graph270.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,16) (0,3) (0,5) (1,6) (1,7) (1,2) (1,8) (1,14) (1,13) (1,9) (1,4) (1,12) (1,19) (2,6) (2,11) (2,8) (2,14) (2,13) (2,9) (2,12) (2,19) (3,17) (3,16) (3,15) (3,5) (3,18) (4,7) (4,8) (4,14) (4,9) (4,12) (5,17) (5,16) (5,10) (5,15) (6,7) (6,11) (6,8) (6,14) (6,12) (6,19) (7,11) (7,19) (8,11) (8,13) (8,9) (8,19) (9,11) (9,14) (9,13) (9,12) (9,19) (10,17) (10,16) (10,15) (11,14) (11,13) (11,12) (12,13) (12,19) (13,14) (13,19) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 2 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph459-1_12", + "image": "data/connectivity/graph_visual/medium/graph459.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,9) (0,13) (0,10) (0,12) (0,1) (0,18) (0,8) (0,2) (0,15) (0,6) (0,4) (0,19) (0,21) (0,20) (0,17) (0,5) (1,9) (1,13) (1,10) (1,12) (1,18) (1,8) (1,2) (1,15) (1,6) (1,4) (1,19) (1,21) (1,20) (1,17) (1,5) (2,9) (2,13) (2,10) (2,12) (2,18) (2,8) (2,15) (2,6) (2,4) (2,19) (2,21) (2,20) (2,17) (2,5) (3,16) (3,14) (3,7) (3,11) (4,9) (4,13) (4,10) (4,12) (4,18) (4,8) (4,15) (4,6) (4,19) (4,21) (4,20) (4,17) (4,5) (5,9) (5,13) (5,10) (5,12) (5,18) (5,8) (5,15) (5,6) (5,19) (5,21) (5,20) (5,17) (6,9) (6,13) (6,10) (6,12) (6,18) (6,8) (6,15) (6,19) (6,21) (6,20) (6,17) (7,16) (7,14) (7,11) (8,9) (8,13) (8,10) (8,12) (8,18) (8,15) (8,19) (8,21) (8,20) (8,17) (9,13) (9,10) (9,12) (9,18) (9,15) (9,19) (9,21) (9,20) (9,17) (10,13) (10,12) (10,18) (10,15) (10,19) (10,21) (10,20) (10,17) (11,16) (11,14) (12,13) (12,18) (12,15) (12,19) (12,21) (12,20) (12,17) (13,18) (13,15) (13,19) (13,21) (13,20) (13,17) (14,16) (15,18) (15,19) (15,21) (15,20) (15,17) (17,18) (17,19) (17,21) (17,20) (18,19) (18,21) (18,20) (19,21) (19,20) (20,21)\nIs there a path between node 1 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph826-20_5", + "image": "data/connectivity/graph_visual/medium/graph826.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,15) (4,23) (4,8) (4,9) (4,21) (4,16) (4,10) (4,20) (4,17) (4,11) (4,24) (4,12) (4,22) (5,18) (5,23) (5,8) (5,9) (5,7) (5,21) (5,16) (5,10) (5,17) (5,11) (5,24) (5,12) (6,18) (6,8) (6,9) (6,14) (6,21) (6,16) (6,10) (6,20) (6,11) (6,24) (6,12) (6,22) (7,18) (7,23) (7,8) (7,14) (7,21) (7,10) (7,17) (7,11) (8,18) (8,14) (8,10) (8,24) (8,12) (8,22) (9,18) (9,23) (9,16) (9,10) (9,20) (9,24) (9,12) (9,22) (10,18) (10,23) (10,21) (10,16) (10,20) (10,17) (10,24) (10,12) (11,18) (11,24) (11,12) (11,22) (12,18) (12,14) (12,21) (12,17) (12,24) (12,22) (14,18) (14,16) (14,20) (14,24) (16,18) (16,23) (16,21) (16,20) (16,17) (16,24) (16,22) (17,18) (17,24) (18,23) (18,21) (18,24) (20,21) (20,24) (21,22) (22,23) (22,24) (23,24)\nIs there a path between node 20 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph333-17_6", + "image": "data/connectivity/graph_visual/medium/graph333.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,14) (0,7) (0,2) (1,9) (1,13) (2,19) (2,3) (3,16) (3,17) (3,19) (3,6) (4,16) (4,20) (4,17) (4,14) (4,18) (5,12) (5,13) (6,12) (6,19) (6,10) (6,9) (6,7) (6,13) (7,16) (9,16) (9,12) (9,18) (10,12) (10,17) (10,15) (10,14) (10,13) (12,16) (13,17) (13,18) (14,17) (14,18) (15,19) (16,19) (17,20) (17,18)\nIs there a path between node 17 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph68-2_9", + "image": "data/connectivity/graph_visual/medium/graph68.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (0,13) (0,8) (0,10) (0,11) (0,6) (0,1) (0,3) (0,12) (1,2) (1,13) (1,8) (1,10) (1,11) (1,6) (1,3) (1,12) (2,13) (2,8) (2,10) (2,11) (2,6) (2,3) (2,12) (3,13) (3,8) (3,10) (3,11) (3,6) (3,12) (4,7) (4,5) (4,9) (5,7) (5,9) (6,13) (6,8) (6,10) (6,11) (6,12) (7,9) (8,13) (8,10) (8,11) (8,12) (10,13) (10,11) (10,12) (11,13) (11,12) (12,13)\nIs there a path between node 2 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph127-4_11", + "image": "data/connectivity/graph_visual/medium/graph127.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,4) (0,2) (0,14) (0,5) (0,1) (0,7) (0,8) (0,15) (0,3) (0,10) (0,13) (0,9) (0,16) (0,12) (1,4) (1,2) (1,14) (1,5) (1,7) (1,8) (1,15) (1,3) (1,10) (1,13) (1,9) (1,16) (1,12) (2,4) (2,14) (2,5) (2,7) (2,8) (2,15) (2,3) (2,10) (2,13) (2,9) (2,16) (2,12) (3,4) (3,14) (3,5) (3,7) (3,8) (3,15) (3,10) (3,13) (3,9) (3,16) (3,12) (4,14) (4,5) (4,7) (4,8) (4,15) (4,10) (4,13) (4,9) (4,16) (4,12) (5,14) (5,7) (5,8) (5,15) (5,10) (5,13) (5,9) (5,16) (5,12) (6,11) (7,14) (7,8) (7,15) (7,10) (7,13) (7,9) (7,16) (7,12) (8,14) (8,15) (8,10) (8,13) (8,9) (8,16) (8,12) (9,14) (9,15) (9,10) (9,13) (9,16) (9,12) (10,14) (10,15) (10,13) (10,16) (10,12) (12,14) (12,15) (12,13) (12,16) (13,14) (13,15) (13,16) (14,15) (14,16) (15,16)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph455-5_2", + "image": "data/connectivity/graph_visual/medium/graph455.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,14) (1,19) (1,12) (1,18) (1,5) (1,13) (1,2) (1,17) (1,7) (1,15) (1,3) (1,16) (1,11) (1,9) (1,10) (1,20) (1,21) (1,4) (2,19) (2,12) (2,18) (2,5) (2,13) (2,17) (2,7) (2,15) (2,3) (2,16) (2,11) (2,9) (2,10) (2,20) (2,21) (2,4) (3,19) (3,12) (3,18) (3,5) (3,13) (3,17) (3,7) (3,15) (3,16) (3,11) (3,9) (3,10) (3,20) (3,21) (3,4) (4,19) (4,12) (4,18) (4,5) (4,13) (4,17) (4,7) (4,15) (4,16) (4,11) (4,9) (4,10) (4,20) (4,21) (5,19) (5,12) (5,18) (5,13) (5,17) (5,7) (5,15) (5,16) (5,11) (5,9) (5,10) (5,20) (5,21) (6,8) (7,19) (7,12) (7,18) (7,13) (7,17) (7,15) (7,16) (7,11) (7,9) (7,10) (7,20) (7,21) (9,19) (9,12) (9,18) (9,13) (9,17) (9,15) (9,16) (9,11) (9,10) (9,20) (9,21) (10,19) (10,12) (10,18) (10,13) (10,17) (10,15) (10,16) (10,11) (10,20) (10,21) (11,19) (11,12) (11,18) (11,13) (11,17) (11,15) (11,16) (11,20) (11,21) (12,19) (12,18) (12,13) (12,17) (12,15) (12,16) (12,20) (12,21) (13,19) (13,18) (13,17) (13,15) (13,16) (13,20) (13,21) (15,19) (15,18) (15,17) (15,16) (15,20) (15,21) (16,19) (16,18) (16,17) (16,20) (16,21) (17,19) (17,18) (17,20) (17,21) (18,19) (18,20) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 5 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph80-6_10", + "image": "data/connectivity/graph_visual/medium/graph80.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,2) (0,1) (0,13) (0,12) (0,6) (0,14) (0,11) (0,9) (1,2) (1,3) (1,8) (1,4) (1,6) (1,11) (1,5) (2,7) (2,3) (2,13) (2,12) (2,6) (2,14) (2,11) (2,5) (3,7) (3,12) (3,4) (3,6) (3,14) (3,5) (3,9) (4,7) (4,13) (4,12) (4,8) (4,14) (4,11) (5,7) (5,12) (5,8) (5,6) (5,14) (5,11) (5,9) (6,7) (6,13) (6,12) (6,14) (6,9) (7,12) (7,8) (7,14) (7,11) (8,13) (8,14) (8,11) (9,13) (9,12) (9,14) (9,11) (11,12) (12,13) (12,14) (13,14)\nIs there a path between node 6 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph529-6_12", + "image": "data/connectivity/graph_visual/medium/graph529.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,20) (0,19) (0,14) (0,2) (0,9) (0,13) (0,21) (0,12) (0,18) (0,16) (0,7) (1,17) (1,5) (1,4) (1,22) (1,11) (1,3) (1,8) (1,15) (1,10) (1,6) (2,20) (2,19) (2,14) (2,9) (2,13) (2,21) (2,12) (2,18) (2,16) (2,7) (3,17) (3,5) (3,4) (3,22) (3,11) (3,8) (3,15) (3,10) (3,6) (4,17) (4,5) (4,22) (4,11) (4,8) (4,15) (4,10) (4,6) (5,17) (5,22) (5,11) (5,8) (5,15) (5,10) (5,6) (6,17) (6,22) (6,11) (6,8) (6,15) (6,10) (7,20) (7,19) (7,14) (7,9) (7,13) (7,21) (7,12) (7,18) (7,16) (8,17) (8,22) (8,11) (8,15) (8,10) (9,20) (9,19) (9,14) (9,13) (9,21) (9,12) (9,18) (9,16) (10,17) (10,22) (10,11) (10,15) (11,17) (11,22) (11,15) (12,20) (12,19) (12,14) (12,13) (12,21) (12,18) (12,16) (13,20) (13,19) (13,14) (13,21) (13,18) (13,16) (14,20) (14,19) (14,21) (14,18) (14,16) (15,17) (15,22) (16,20) (16,19) (16,21) (16,18) (17,22) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 6 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph237-17_0", + "image": "data/connectivity/graph_visual/medium/graph237.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,11) (0,17) (0,16) (1,2) (1,12) (1,7) (1,3) (2,15) (2,5) (2,7) (2,3) (3,15) (3,5) (3,12) (3,7) (4,8) (4,10) (4,18) (4,6) (4,11) (4,9) (4,17) (4,14) (4,16) (5,15) (5,7) (6,8) (6,10) (6,18) (6,11) (6,9) (6,17) (6,16) (7,15) (7,12) (8,11) (8,9) (8,17) (8,14) (9,18) (9,11) (10,18) (10,11) (10,14) (10,16) (11,18) (11,17) (11,16) (14,18) (14,16) (16,18) (16,17) (17,18)\nIs there a path between node 17 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph7-9_3", + "image": "data/connectivity/graph_visual/medium/graph7.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,6) (1,4) (1,3) (1,2) (1,7) (2,10) (2,4) (2,8) (3,10) (3,6) (3,4) (3,8) (3,5) (4,6) (4,8) (4,5) (4,7) (5,10) (5,8) (6,10) (6,8) (7,10)\nIs there a path between node 9 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph414-14_9", + "image": "data/connectivity/graph_visual/medium/graph414.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,1) (0,18) (1,18) (1,14) (1,11) (2,4) (2,21) (2,15) (2,9) (2,12) (2,8) (2,3) (2,10) (3,4) (3,9) (3,12) (3,5) (3,20) (3,8) (3,17) (3,10) (3,19) (4,21) (4,15) (4,12) (4,6) (4,5) (4,17) (4,19) (5,21) (5,9) (5,6) (5,20) (5,8) (5,10) (6,15) (6,9) (6,12) (6,8) (6,10) (6,19) (7,13) (8,21) (8,15) (8,9) (8,12) (8,17) (8,10) (8,19) (9,21) (9,20) (9,19) (10,21) (10,20) (10,17) (11,14) (12,21) (12,15) (12,20) (12,19) (14,16) (15,20) (15,17) (17,21) (17,20) (17,19) (19,21)\nIs there a path between node 14 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph483-11_9", + "image": "data/connectivity/graph_visual/medium/graph483.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,12) (0,5) (0,19) (0,17) (0,10) (0,2) (1,4) (1,6) (1,15) (1,18) (1,14) (1,3) (1,16) (1,20) (1,8) (1,21) (1,13) (2,12) (2,5) (2,19) (2,22) (2,9) (3,6) (3,15) (3,18) (3,14) (3,20) (3,21) (3,13) (4,11) (4,14) (4,16) (4,20) (4,8) (4,21) (5,12) (5,19) (5,7) (5,17) (5,10) (5,9) (6,11) (6,18) (6,14) (6,16) (6,20) (6,13) (7,12) (7,19) (7,22) (7,17) (7,10) (7,9) (8,11) (8,15) (8,14) (8,16) (8,13) (9,12) (9,22) (9,17) (9,10) (10,17) (11,15) (11,18) (11,14) (11,16) (11,20) (12,19) (12,22) (13,15) (13,18) (13,14) (13,16) (13,20) (13,21) (14,18) (14,16) (14,20) (14,21) (15,18) (15,16) (15,20) (15,21) (16,18) (18,20) (19,22) (20,21)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph442-5_11", + "image": "data/connectivity/graph_visual/medium/graph442.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (1,11) (1,21) (1,5) (1,7) (1,17) (1,8) (2,18) (2,12) (2,19) (2,13) (2,11) (2,21) (2,9) (2,14) (2,17) (2,8) (3,10) (3,6) (5,18) (5,15) (5,12) (5,11) (5,7) (5,9) (5,14) (5,8) (6,20) (6,16) (7,18) (7,15) (7,19) (7,13) (7,9) (7,14) (7,17) (7,8) (8,15) (8,12) (8,19) (8,11) (8,21) (8,9) (8,14) (9,18) (9,15) (9,12) (9,19) (9,11) (9,14) (9,17) (10,16) (11,18) (11,15) (11,12) (11,19) (11,21) (12,18) (12,15) (12,13) (12,21) (12,17) (13,15) (13,19) (13,14) (14,18) (14,19) (14,21) (14,17) (15,18) (15,21) (15,17) (16,20) (17,18) (17,21) (18,19) (18,21) (19,21)\nIs there a path between node 5 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph59-10_0", + "image": "data/connectivity/graph_visual/medium/graph59.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,6) (0,4) (0,1) (0,11) (0,9) (0,12) (1,2) (1,4) (1,11) (1,9) (1,13) (1,8) (1,12) (2,6) (2,3) (2,4) (2,11) (2,9) (2,13) (2,8) (3,6) (3,9) (3,13) (3,8) (3,12) (4,6) (4,11) (4,9) (4,13) (4,8) (4,12) (5,7) (5,10) (6,11) (6,9) (6,8) (6,12) (8,9) (8,12) (9,11) (9,12) (11,13) (12,13)\nIs there a path between node 10 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph417-20_0", + "image": "data/connectivity/graph_visual/medium/graph417.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,14) (0,9) (0,11) (0,4) (0,5) (0,15) (0,18) (0,20) (1,17) (1,16) (1,19) (1,3) (1,21) (1,6) (1,13) (1,8) (1,10) (1,7) (2,14) (2,9) (2,11) (2,4) (2,5) (2,15) (2,18) (2,20) (3,17) (3,16) (3,19) (3,21) (3,6) (3,13) (3,8) (3,10) (3,7) (4,14) (4,9) (4,11) (4,5) (4,15) (4,18) (4,20) (5,14) (5,9) (5,11) (5,15) (5,18) (5,20) (6,17) (6,16) (6,19) (6,21) (6,13) (6,8) (6,10) (6,7) (7,17) (7,16) (7,19) (7,21) (7,13) (7,8) (7,10) (8,17) (8,16) (8,19) (8,21) (8,13) (8,10) (9,14) (9,11) (9,15) (9,18) (9,20) (10,17) (10,16) (10,19) (10,21) (10,13) (11,14) (11,15) (11,18) (11,20) (13,17) (13,16) (13,19) (13,21) (14,15) (14,18) (14,20) (15,18) (15,20) (16,17) (16,19) (16,21) (17,19) (17,21) (18,20) (19,21)\nIs there a path between node 20 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph666-21_7", + "image": "data/connectivity/graph_visual/medium/graph666.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,5) (0,23) (0,3) (0,4) (0,16) (0,12) (0,1) (0,20) (1,21) (1,15) (1,5) (1,23) (1,22) (1,4) (1,11) (1,12) (1,14) (1,17) (1,20) (2,9) (2,6) (2,13) (3,5) (3,23) (3,18) (3,22) (3,4) (3,16) (3,19) (3,14) (3,20) (4,21) (4,15) (4,5) (4,23) (4,18) (4,22) (4,11) (4,19) (4,14) (4,20) (5,21) (5,15) (5,23) (5,18) (5,22) (5,11) (5,16) (5,10) (5,19) (5,14) (5,17) (6,13) (8,9) (8,13) (9,13) (10,15) (10,23) (10,22) (10,16) (10,12) (10,14) (10,17) (10,20) (11,21) (11,15) (11,23) (11,18) (11,22) (11,16) (11,19) (11,14) (11,17) (11,20) (12,23) (12,22) (12,16) (12,19) (12,14) (12,17) (12,20) (14,21) (14,23) (14,18) (14,16) (14,19) (14,17) (14,20) (15,18) (15,22) (15,16) (15,19) (15,17) (15,20) (16,18) (16,19) (17,21) (17,18) (17,22) (17,19) (17,20) (18,21) (18,20) (19,22) (19,20) (20,21) (20,22) (21,22)\nIs there a path between node 21 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph547-18_20", + "image": "data/connectivity/graph_visual/medium/graph547.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,8) (1,15) (1,14) (1,20) (1,23) (2,5) (2,12) (2,10) (2,19) (2,7) (3,16) (4,12) (4,7) (5,7) (6,15) (6,18) (6,22) (6,20) (6,23) (7,12) (8,16) (8,14) (8,18) (8,13) (9,12) (9,10) (12,19) (13,18) (13,20) (14,23) (15,16) (16,22) (16,23) (20,22)\nIs there a path between node 18 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph393-1_12", + "image": "data/connectivity/graph_visual/medium/graph393.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,14) (0,11) (0,17) (0,5) (0,4) (1,20) (1,8) (1,13) (1,2) (1,16) (1,19) (1,7) (1,6) (1,12) (1,9) (2,20) (2,8) (2,13) (2,16) (2,19) (2,7) (2,6) (2,12) (2,9) (3,18) (3,10) (3,15) (4,14) (4,11) (4,17) (4,5) (5,14) (5,11) (5,17) (6,20) (6,8) (6,13) (6,16) (6,19) (6,7) (6,12) (6,9) (7,20) (7,8) (7,13) (7,16) (7,19) (7,12) (7,9) (8,20) (8,13) (8,16) (8,19) (8,12) (8,9) (9,20) (9,13) (9,16) (9,19) (9,12) (10,18) (10,15) (11,14) (11,17) (12,20) (12,13) (12,16) (12,19) (13,20) (13,16) (13,19) (14,17) (15,18) (16,20) (16,19) (19,20)\nIs there a path between node 1 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph493-10_18", + "image": "data/connectivity/graph_visual/medium/graph493.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,9) (0,19) (0,7) (0,2) (0,14) (0,12) (0,15) (0,22) (0,20) (1,16) (1,10) (1,3) (1,11) (1,4) (1,17) (1,5) (2,6) (2,9) (2,19) (2,7) (2,14) (2,12) (2,15) (2,22) (2,20) (3,16) (3,10) (3,11) (3,4) (3,17) (3,5) (4,16) (4,10) (4,11) (4,17) (4,5) (5,16) (5,10) (5,11) (5,17) (6,9) (6,19) (6,7) (6,14) (6,12) (6,15) (6,22) (6,20) (7,9) (7,19) (7,14) (7,12) (7,15) (7,22) (7,20) (8,13) (8,21) (8,18) (9,19) (9,14) (9,12) (9,15) (9,22) (9,20) (10,16) (10,11) (10,17) (11,16) (11,17) (12,19) (12,14) (12,15) (12,22) (12,20) (13,21) (13,18) (14,19) (14,15) (14,22) (14,20) (15,19) (15,22) (15,20) (16,17) (18,21) (19,22) (19,20) (20,22)\nIs there a path between node 10 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph561-13_7", + "image": "data/connectivity/graph_visual/medium/graph561.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,3) (0,20) (0,6) (0,11) (0,4) (0,7) (0,23) (0,14) (0,21) (1,5) (1,10) (2,9) (2,3) (2,20) (2,4) (2,23) (2,14) (2,21) (3,8) (3,9) (3,20) (3,6) (3,11) (3,4) (3,22) (4,9) (4,20) (4,6) (4,7) (4,22) (4,23) (4,14) (4,21) (5,10) (6,8) (6,9) (6,20) (6,11) (6,22) (6,23) (6,14) (7,8) (7,9) (7,22) (7,23) (7,21) (8,20) (8,11) (8,22) (8,14) (8,21) (9,20) (9,22) (9,14) (9,21) (11,20) (11,22) (11,23) (11,14) (13,16) (13,18) (13,15) (13,19) (13,17) (14,20) (14,22) (14,23) (15,16) (15,19) (15,17) (16,18) (16,19) (16,17) (17,19) (18,19) (20,22) (20,23) (20,21) (21,22) (21,23) (22,23)\nIs there a path between node 13 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph742-10_8", + "image": "data/connectivity/graph_visual/medium/graph742.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,4) (0,5) (0,10) (0,22) (0,8) (3,9) (3,24) (3,11) (4,21) (4,13) (5,13) (7,9) (8,21) (8,17) (8,18) (9,20) (10,21) (10,22) (13,14) (13,18) (14,18) (15,19) (15,16) (21,22)\nIs there a path between node 10 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph265-2_11", + "image": "data/connectivity/graph_visual/medium/graph265.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,12) (0,19) (0,11) (0,8) (0,10) (1,14) (1,13) (2,11) (2,6) (3,12) (3,19) (3,9) (4,7) (5,11) (5,10) (6,10) (7,16) (7,13) (8,19) (8,11) (9,12) (9,11) (9,18) (11,12) (11,19) (13,16) (13,17) (14,16) (14,17)\nIs there a path between node 2 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph607-13_18", + "image": "data/connectivity/graph_visual/medium/graph607.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,11) (0,8) (0,17) (0,13) (0,6) (0,3) (0,15) (0,7) (1,14) (1,19) (1,9) (1,21) (1,12) (1,22) (1,4) (1,18) (1,5) (1,10) (1,20) (2,16) (3,23) (3,11) (3,8) (3,17) (3,13) (3,6) (3,15) (3,7) (4,14) (4,19) (4,9) (4,21) (4,12) (4,22) (4,18) (4,5) (4,10) (4,20) (5,14) (5,19) (5,9) (5,21) (5,12) (5,22) (5,18) (5,10) (5,20) (6,23) (6,11) (6,8) (6,17) (6,13) (6,15) (6,7) (7,23) (7,11) (7,8) (7,17) (7,13) (7,15) (8,23) (8,11) (8,17) (8,13) (8,15) (9,14) (9,19) (9,21) (9,12) (9,22) (9,18) (9,10) (9,20) (10,14) (10,19) (10,21) (10,12) (10,22) (10,18) (10,20) (11,23) (11,17) (11,13) (11,15) (12,14) (12,19) (12,21) (12,22) (12,18) (12,20) (13,23) (13,17) (13,15) (14,19) (14,21) (14,22) (14,18) (14,20) (15,23) (15,17) (17,23) (18,19) (18,21) (18,22) (18,20) (19,21) (19,22) (19,20) (20,21) (20,22) (21,22)\nIs there a path between node 13 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph752-3_0", + "image": "data/connectivity/graph_visual/medium/graph752.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,20) (0,17) (0,1) (0,21) (1,10) (1,20) (1,21) (3,20) (3,21) (4,5) (4,12) (4,14) (4,16) (4,6) (4,15) (5,7) (5,14) (5,16) (5,19) (5,11) (5,8) (5,15) (6,24) (6,14) (6,16) (6,19) (6,9) (6,13) (6,11) (6,8) (7,24) (7,12) (7,14) (7,19) (7,9) (7,13) (7,11) (7,8) (7,15) (8,24) (8,12) (8,16) (8,19) (8,9) (8,11) (8,15) (9,24) (9,12) (9,14) (9,11) (9,15) (10,20) (10,17) (10,21) (11,24) (11,12) (11,14) (11,16) (11,19) (11,13) (11,15) (12,14) (12,16) (12,19) (12,15) (13,24) (13,14) (13,16) (13,19) (14,24) (14,16) (14,15) (15,24) (15,16) (16,24) (16,19) (17,20) (17,21) (18,23) (19,24) (22,23)\nIs there a path between node 3 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph324-5_14", + "image": "data/connectivity/graph_visual/medium/graph324.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (0,8) (0,18) (0,6) (0,1) (0,12) (0,3) (0,7) (0,14) (0,10) (0,19) (0,16) (0,13) (1,17) (1,8) (1,18) (1,2) (1,19) (2,8) (2,6) (2,20) (2,14) (3,17) (3,18) (3,6) (3,14) (3,10) (3,19) (4,17) (4,18) (4,6) (4,19) (4,13) (5,15) (6,17) (6,8) (6,18) (6,13) (7,17) (7,14) (7,10) (8,20) (9,15) (9,11) (10,17) (10,18) (11,15) (12,17) (12,18) (12,14) (12,19) (13,17) (13,18) (13,20) (14,17) (14,18) (14,20) (18,20) (19,20)\nIs there a path between node 5 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph103-7_12", + "image": "data/connectivity/graph_visual/medium/graph103.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (0,5) (0,8) (0,4) (0,12) (0,2) (0,7) (0,14) (0,3) (0,6) (1,13) (1,5) (1,8) (1,4) (1,12) (1,2) (1,9) (1,14) (1,3) (2,13) (2,5) (2,10) (2,4) (2,9) (2,14) (3,5) (3,8) (3,10) (3,4) (3,9) (3,14) (3,6) (4,13) (4,5) (4,10) (4,9) (4,6) (5,13) (5,8) (5,10) (5,12) (5,9) (6,8) (6,10) (6,9) (6,7) (6,14) (7,13) (7,8) (7,10) (7,12) (8,10) (8,12) (8,9) (8,14) (9,13) (9,10) (9,12) (9,14) (10,12) (10,14) (11,15) (12,13)\nIs there a path between node 7 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph208-12_9", + "image": "data/connectivity/graph_visual/medium/graph208.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,15) (0,13) (0,3) (0,16) (0,10) (1,18) (1,7) (1,2) (1,4) (1,9) (1,12) (1,11) (1,5) (2,18) (2,7) (2,4) (2,9) (2,12) (2,6) (2,11) (2,5) (3,15) (3,17) (4,18) (4,9) (4,12) (4,6) (4,5) (5,18) (5,7) (5,12) (5,6) (5,11) (6,18) (6,7) (6,12) (7,18) (7,12) (9,12) (9,11) (10,15) (10,14) (11,18) (11,12) (13,16) (13,14) (13,17) (14,15) (14,16) (15,16) (16,17)\nIs there a path between node 12 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph649-23_18", + "image": "data/connectivity/graph_visual/medium/graph649.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (1,5) (1,18) (1,7) (1,22) (1,11) (1,20) (1,4) (1,23) (2,14) (2,10) (2,21) (2,15) (2,16) (2,3) (3,14) (3,10) (3,15) (3,16) (3,6) (3,19) (4,18) (4,7) (4,22) (4,11) (4,20) (4,23) (5,13) (5,7) (5,22) (5,11) (5,20) (5,23) (6,10) (6,21) (6,15) (6,16) (6,9) (6,8) (6,19) (7,13) (7,22) (7,20) (7,23) (8,10) (8,9) (8,19) (9,21) (9,15) (9,19) (10,21) (10,16) (10,19) (11,18) (11,13) (11,22) (11,23) (12,17) (13,22) (13,20) (14,15) (14,16) (14,19) (15,16) (15,19) (16,21) (16,19) (18,20) (18,23) (19,21) (20,22) (20,23) (22,23)\nIs there a path between node 23 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph72-4_11", + "image": "data/connectivity/graph_visual/medium/graph72.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (0,9) (1,10) (1,3) (2,6) (2,4) (2,7) (3,6) (3,10) (3,9) (3,12) (4,8) (5,9) (5,12) (6,9) (6,12) (6,7) (7,10) (7,9) (7,14) (8,10) (8,9) (8,14) (12,14)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph100-5_6", + "image": "data/connectivity/graph_visual/medium/graph100.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,5) (0,1) (0,2) (0,9) (0,13) (0,4) (0,15) (1,5) (1,2) (1,3) (1,8) (1,7) (1,11) (2,8) (2,9) (2,13) (2,11) (3,5) (3,14) (3,13) (3,4) (3,15) (3,7) (4,5) (4,14) (4,8) (4,9) (4,13) (4,7) (4,11) (5,14) (5,9) (5,13) (5,7) (5,11) (6,10) (6,12) (7,14) (7,8) (7,9) (7,15) (8,9) (8,13) (8,15) (8,11) (9,15) (9,11) (10,12) (11,14) (11,13) (11,15)\nIs there a path between node 5 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph139-8_2", + "image": "data/connectivity/graph_visual/medium/graph139.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,10) (0,17) (1,13) (1,14) (2,11) (3,11) (5,6) (5,13) (6,12) (6,14) (7,16) (8,17) (10,17) (12,13) (12,15) (12,14) (13,15)\nIs there a path between node 8 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph134-11_12", + "image": "data/connectivity/graph_visual/medium/graph134.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,11) (0,6) (0,2) (0,5) (1,7) (1,16) (1,14) (1,17) (1,3) (1,9) (1,13) (1,10) (2,11) (2,6) (2,5) (3,7) (3,16) (3,14) (3,17) (3,9) (3,13) (3,10) (4,8) (4,15) (4,12) (5,11) (5,6) (6,11) (7,16) (7,14) (7,17) (7,9) (7,13) (7,10) (8,15) (8,12) (9,16) (9,14) (9,17) (9,13) (9,10) (10,16) (10,14) (10,17) (10,13) (12,15) (13,16) (13,14) (13,17) (14,16) (14,17) (16,17)\nIs there a path between node 11 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph412-13_6", + "image": "data/connectivity/graph_visual/medium/graph412.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,14) (0,15) (0,1) (0,7) (0,4) (0,8) (0,13) (0,12) (0,2) (0,16) (0,20) (0,18) (0,11) (0,21) (1,19) (1,14) (1,15) (1,7) (1,8) (1,6) (1,13) (1,12) (1,2) (1,16) (1,20) (1,18) (1,11) (1,21) (1,17) (2,19) (2,14) (2,15) (2,7) (2,4) (2,13) (2,12) (2,18) (2,21) (2,17) (2,5) (3,9) (3,10) (4,19) (4,15) (4,7) (4,8) (4,6) (4,12) (4,16) (4,11) (4,21) (4,17) (4,5) (5,14) (5,15) (5,7) (5,8) (5,13) (5,12) (5,20) (5,11) (5,21) (6,19) (6,14) (6,15) (6,13) (6,16) (6,20) (6,18) (6,11) (6,21) (6,17) (7,19) (7,14) (7,15) (7,8) (7,12) (7,16) (7,20) (7,18) (7,11) (7,21) (8,19) (8,14) (8,15) (8,13) (8,20) (8,11) (8,21) (9,10) (11,19) (11,14) (11,15) (11,13) (11,12) (11,16) (11,20) (11,18) (11,21) (12,14) (12,20) (12,21) (13,19) (13,14) (13,15) (13,16) (13,18) (13,21) (13,17) (14,19) (14,15) (14,21) (15,19) (15,20) (15,18) (16,19) (16,18) (16,21) (16,17) (17,19) (17,20) (17,18) (18,19) (19,20) (19,21)\nIs there a path between node 13 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph686-6_2", + "image": "data/connectivity/graph_visual/medium/graph686.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,18) (1,14) (1,6) (1,16) (1,4) (1,15) (1,19) (1,20) (1,23) (1,7) (1,13) (1,22) (1,9) (1,21) (1,2) (2,14) (2,6) (2,16) (2,4) (2,15) (2,19) (2,20) (2,23) (2,7) (2,13) (2,22) (2,9) (2,21) (3,5) (3,10) (3,12) (3,11) (3,17) (4,14) (4,6) (4,16) (4,15) (4,19) (4,20) (4,23) (4,7) (4,13) (4,22) (4,9) (4,21) (5,10) (5,12) (5,11) (5,17) (6,14) (6,16) (6,15) (6,19) (6,20) (6,23) (6,7) (6,13) (6,22) (6,9) (6,21) (7,14) (7,16) (7,15) (7,19) (7,20) (7,23) (7,13) (7,22) (7,9) (7,21) (8,18) (9,14) (9,16) (9,15) (9,19) (9,20) (9,23) (9,13) (9,22) (9,21) (10,12) (10,11) (10,17) (11,12) (11,17) (12,17) (13,14) (13,16) (13,15) (13,19) (13,20) (13,23) (13,22) (13,21) (14,16) (14,15) (14,19) (14,20) (14,23) (14,22) (14,21) (15,16) (15,19) (15,20) (15,23) (15,22) (15,21) (16,19) (16,20) (16,23) (16,22) (16,21) (19,20) (19,23) (19,22) (19,21) (20,23) (20,22) (20,21) (21,23) (21,22) (22,23)\nIs there a path between node 6 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph381-4_9", + "image": "data/connectivity/graph_visual/medium/graph381.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,20) (0,1) (0,15) (0,6) (0,9) (0,4) (0,16) (0,19) (1,20) (1,15) (1,6) (1,9) (1,4) (1,16) (1,19) (2,14) (2,10) (2,3) (2,11) (2,7) (2,18) (2,5) (2,12) (2,17) (2,8) (3,14) (3,10) (3,11) (3,7) (3,18) (3,5) (3,12) (3,17) (3,8) (4,20) (4,15) (4,6) (4,9) (4,16) (4,19) (5,14) (5,10) (5,11) (5,7) (5,18) (5,12) (5,17) (5,8) (6,20) (6,15) (6,9) (6,16) (6,19) (7,14) (7,10) (7,11) (7,18) (7,12) (7,17) (7,8) (8,14) (8,10) (8,11) (8,18) (8,12) (8,17) (9,20) (9,15) (9,16) (9,19) (10,14) (10,11) (10,18) (10,12) (10,17) (11,14) (11,18) (11,12) (11,17) (12,14) (12,18) (12,17) (14,18) (14,17) (15,20) (15,16) (15,19) (16,20) (16,19) (17,18) (19,20)\nIs there a path between node 4 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph627-11_2", + "image": "data/connectivity/graph_visual/medium/graph627.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (1,15) (1,14) (1,12) (2,15) (2,18) (2,4) (2,12) (3,16) (3,14) (3,8) (4,8) (7,21) (8,16) (8,11) (8,14) (8,12) (8,22) (9,21) (11,12) (12,15) (12,18) (13,16) (13,22) (14,15) (14,18) (15,16) (17,22) (19,23)\nIs there a path between node 11 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph362-0_4", + "image": "data/connectivity/graph_visual/medium/graph362.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,20) (0,3) (0,2) (0,16) (0,9) (0,18) (1,3) (1,13) (1,2) (1,12) (1,9) (1,18) (2,5) (2,6) (2,13) (2,4) (2,17) (3,11) (3,6) (3,8) (3,12) (4,20) (4,15) (4,6) (4,8) (5,20) (5,13) (5,7) (5,17) (6,15) (6,8) (6,13) (6,7) (6,9) (7,20) (7,13) (8,15) (8,12) (8,18) (9,20) (9,11) (9,13) (11,20) (11,16) (12,15) (12,18) (13,16) (15,18) (16,20) (17,18) (18,20)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph387-4_5", + "image": "data/connectivity/graph_visual/medium/graph387.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (0,2) (0,10) (0,1) (0,4) (0,9) (0,19) (0,8) (0,18) (0,14) (0,6) (1,3) (1,2) (1,10) (1,4) (1,9) (1,19) (1,8) (1,18) (1,14) (1,6) (2,3) (2,10) (2,4) (2,9) (2,19) (2,8) (2,18) (2,14) (2,6) (3,10) (3,4) (3,9) (3,19) (3,8) (3,18) (3,14) (3,6) (4,10) (4,9) (4,19) (4,8) (4,18) (4,14) (4,6) (5,17) (5,11) (5,16) (6,10) (6,9) (6,19) (6,8) (6,18) (6,14) (7,15) (7,20) (7,13) (7,12) (8,10) (8,9) (8,19) (8,18) (8,14) (9,10) (9,19) (9,18) (9,14) (10,19) (10,18) (10,14) (11,17) (11,16) (12,15) (12,20) (12,13) (13,15) (13,20) (14,19) (14,18) (15,20) (16,17) (18,19)\nIs there a path between node 4 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph417-14_13", + "image": "data/connectivity/graph_visual/medium/graph417.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,14) (0,9) (0,11) (0,4) (0,5) (0,15) (0,18) (0,20) (1,17) (1,16) (1,19) (1,3) (1,21) (1,6) (1,13) (1,8) (1,10) (1,7) (2,14) (2,9) (2,11) (2,4) (2,5) (2,15) (2,18) (2,20) (3,17) (3,16) (3,19) (3,21) (3,6) (3,13) (3,8) (3,10) (3,7) (4,14) (4,9) (4,11) (4,5) (4,15) (4,18) (4,20) (5,14) (5,9) (5,11) (5,15) (5,18) (5,20) (6,17) (6,16) (6,19) (6,21) (6,13) (6,8) (6,10) (6,7) (7,17) (7,16) (7,19) (7,21) (7,13) (7,8) (7,10) (8,17) (8,16) (8,19) (8,21) (8,13) (8,10) (9,14) (9,11) (9,15) (9,18) (9,20) (10,17) (10,16) (10,19) (10,21) (10,13) (11,14) (11,15) (11,18) (11,20) (13,17) (13,16) (13,19) (13,21) (14,15) (14,18) (14,20) (15,18) (15,20) (16,17) (16,19) (16,21) (17,19) (17,21) (18,20) (19,21)\nIs there a path between node 14 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph763-16_2", + "image": "data/connectivity/graph_visual/medium/graph763.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,20) (0,13) (0,24) (0,4) (1,21) (1,3) (1,11) (1,10) (1,23) (1,8) (1,2) (1,22) (1,19) (1,18) (2,21) (2,3) (2,11) (2,10) (2,23) (2,8) (2,22) (2,19) (2,18) (3,21) (3,11) (3,10) (3,23) (3,8) (3,22) (3,19) (3,18) (4,14) (4,20) (4,13) (4,24) (5,7) (5,9) (5,12) (5,16) (5,15) (5,17) (5,6) (6,7) (6,9) (6,12) (6,16) (6,15) (6,17) (7,9) (7,12) (7,16) (7,15) (7,17) (8,21) (8,11) (8,10) (8,23) (8,22) (8,19) (8,18) (9,12) (9,16) (9,15) (9,17) (10,21) (10,11) (10,23) (10,22) (10,19) (10,18) (11,21) (11,23) (11,22) (11,19) (11,18) (12,16) (12,15) (12,17) (13,14) (13,20) (13,24) (14,20) (14,24) (15,16) (15,17) (16,17) (18,21) (18,23) (18,22) (18,19) (19,21) (19,23) (19,22) (20,24) (21,23) (21,22) (22,23)\nIs there a path between node 16 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph594-22_19", + "image": "data/connectivity/graph_visual/medium/graph594.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,13) (0,4) (0,19) (0,9) (0,18) (0,17) (0,21) (0,10) (0,16) (0,2) (0,1) (0,23) (0,14) (0,7) (1,11) (1,13) (1,4) (1,9) (1,6) (1,17) (1,21) (1,10) (1,23) (1,14) (1,7) (2,11) (2,13) (2,19) (2,18) (2,17) (2,21) (2,10) (2,16) (2,23) (2,14) (3,8) (3,12) (3,5) (3,20) (3,22) (4,13) (4,19) (4,9) (4,18) (4,17) (4,21) (4,10) (4,14) (4,7) (5,8) (5,15) (5,20) (5,22) (6,13) (6,19) (6,18) (6,21) (6,10) (6,7) (7,13) (7,9) (7,18) (7,17) (7,10) (7,14) (8,15) (8,12) (8,22) (9,11) (9,19) (9,18) (9,17) (9,21) (9,10) (9,16) (9,23) (9,14) (10,11) (10,13) (10,19) (10,18) (10,17) (10,16) (10,23) (10,14) (11,13) (11,19) (11,17) (11,21) (11,16) (11,23) (11,14) (12,20) (12,22) (13,19) (13,18) (13,17) (13,16) (13,23) (13,14) (14,19) (14,18) (14,17) (14,16) (14,23) (15,22) (16,19) (16,17) (16,21) (16,23) (17,18) (18,23) (19,23) (20,22)\nIs there a path between node 22 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph279-11_12", + "image": "data/connectivity/graph_visual/medium/graph279.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,2) (0,14) (0,16) (0,7) (0,10) (1,12) (1,11) (1,13) (1,8) (1,17) (1,4) (2,19) (2,14) (2,16) (2,7) (2,10) (3,5) (3,15) (3,18) (3,6) (3,9) (4,12) (4,11) (4,13) (4,8) (4,17) (5,15) (5,18) (5,6) (5,9) (6,15) (6,18) (6,9) (7,19) (7,14) (7,16) (7,10) (8,12) (8,11) (8,13) (8,17) (9,15) (9,18) (10,19) (10,14) (10,16) (11,12) (11,13) (11,17) (12,13) (12,17) (13,17) (14,19) (14,16) (15,18) (16,19)\nIs there a path between node 11 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph35-12_10", + "image": "data/connectivity/graph_visual/medium/graph35.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,5) (0,7) (0,8) (0,10) (0,3) (1,4) (1,11) (1,9) (1,6) (1,12) (1,2) (2,4) (2,11) (2,9) (2,6) (2,12) (3,5) (3,7) (3,8) (3,10) (4,11) (4,9) (4,6) (4,12) (5,7) (5,8) (5,10) (6,11) (6,9) (6,12) (7,8) (7,10) (8,10) (9,11) (9,12) (11,12)\nIs there a path between node 12 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph61-4_6", + "image": "data/connectivity/graph_visual/medium/graph61.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,11) (0,9) (0,10) (0,6) (1,7) (2,11) (2,10) (3,5) (3,13) (3,7) (4,7) (5,13) (6,11) (6,9) (6,12) (7,8) (7,13) (8,13) (9,10) (9,12) (10,11) (10,12) (11,12)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph350-1_0", + "image": "data/connectivity/graph_visual/medium/graph350.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,20) (0,4) (0,9) (0,18) (0,12) (0,5) (0,1) (0,17) (0,13) (0,2) (0,10) (0,7) (0,19) (0,15) (0,11) (0,8) (1,16) (1,20) (1,4) (1,9) (1,18) (1,12) (1,5) (1,17) (1,13) (1,2) (1,10) (1,7) (1,19) (1,15) (1,11) (1,8) (2,16) (2,20) (2,4) (2,9) (2,18) (2,12) (2,5) (2,17) (2,13) (2,10) (2,7) (2,19) (2,15) (2,11) (2,8) (3,14) (3,6) (4,16) (4,20) (4,9) (4,18) (4,12) (4,5) (4,17) (4,13) (4,10) (4,7) (4,19) (4,15) (4,11) (4,8) (5,16) (5,20) (5,9) (5,18) (5,12) (5,17) (5,13) (5,10) (5,7) (5,19) (5,15) (5,11) (5,8) (6,14) (7,16) (7,20) (7,9) (7,18) (7,12) (7,17) (7,13) (7,10) (7,19) (7,15) (7,11) (7,8) (8,16) (8,20) (8,9) (8,18) (8,12) (8,17) (8,13) (8,10) (8,19) (8,15) (8,11) (9,16) (9,20) (9,18) (9,12) (9,17) (9,13) (9,10) (9,19) (9,15) (9,11) (10,16) (10,20) (10,18) (10,12) (10,17) (10,13) (10,19) (10,15) (10,11) (11,16) (11,20) (11,18) (11,12) (11,17) (11,13) (11,19) (11,15) (12,16) (12,20) (12,18) (12,17) (12,13) (12,19) (12,15) (13,16) (13,20) (13,18) (13,17) (13,19) (13,15) (15,16) (15,20) (15,18) (15,17) (15,19) (16,20) (16,18) (16,17) (16,19) (17,20) (17,18) (17,19) (18,20) (18,19) (19,20)\nIs there a path between node 1 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph122-14_16", + "image": "data/connectivity/graph_visual/medium/graph122.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,5) (0,3) (1,13) (1,4) (1,12) (1,16) (1,9) (1,15) (1,11) (1,8) (1,6) (1,7) (1,10) (2,5) (3,14) (4,16) (4,9) (4,11) (4,8) (4,7) (4,10) (6,13) (6,16) (6,11) (6,7) (6,10) (7,13) (7,9) (7,11) (7,8) (7,10) (8,13) (8,12) (8,16) (8,9) (8,15) (8,10) (9,13) (9,16) (9,15) (9,10) (10,16) (10,11) (11,13) (11,16) (11,15) (12,13) (12,15) (13,16) (15,16)\nIs there a path between node 14 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph240-10_0", + "image": "data/connectivity/graph_visual/medium/graph240.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,16) (0,6) (0,8) (0,13) (0,7) (0,12) (1,14) (1,15) (1,11) (2,14) (2,11) (3,16) (3,18) (3,13) (4,14) (4,15) (4,11) (5,17) (5,9) (6,16) (6,7) (6,12) (7,18) (7,8) (7,13) (7,12) (8,18) (8,13) (8,12) (9,17) (10,16) (10,18) (10,13) (11,14) (11,15) (12,16) (12,18) (13,18) (14,15) (16,18)\nIs there a path between node 10 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph767-19_12", + "image": "data/connectivity/graph_visual/medium/graph767.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (0,24) (0,15) (0,2) (0,1) (0,7) (0,8) (0,18) (0,23) (0,5) (0,20) (1,19) (1,24) (1,15) (1,2) (1,7) (1,8) (1,18) (1,23) (1,5) (1,20) (2,19) (2,24) (2,15) (2,7) (2,8) (2,18) (2,23) (2,5) (2,20) (3,12) (3,16) (3,9) (3,14) (3,22) (3,13) (3,4) (3,11) (3,10) (3,17) (3,21) (3,6) (4,12) (4,16) (4,9) (4,14) (4,22) (4,13) (4,11) (4,10) (4,17) (4,21) (4,6) (5,19) (5,24) (5,15) (5,7) (5,8) (5,18) (5,23) (5,20) (6,12) (6,16) (6,9) (6,14) (6,22) (6,13) (6,11) (6,10) (6,17) (6,21) (7,19) (7,24) (7,15) (7,8) (7,18) (7,23) (7,20) (8,19) (8,24) (8,15) (8,18) (8,23) (8,20) (9,12) (9,16) (9,14) (9,22) (9,13) (9,11) (9,10) (9,17) (9,21) (10,12) (10,16) (10,14) (10,22) (10,13) (10,11) (10,17) (10,21) (11,12) (11,16) (11,14) (11,22) (11,13) (11,17) (11,21) (12,16) (12,14) (12,22) (12,13) (12,17) (12,21) (13,16) (13,14) (13,22) (13,17) (13,21) (14,16) (14,22) (14,17) (14,21) (15,19) (15,24) (15,18) (15,23) (15,20) (16,22) (16,17) (16,21) (17,22) (17,21) (18,19) (18,24) (18,23) (18,20) (19,24) (19,23) (19,20) (20,24) (20,23) (21,22) (23,24)\nIs there a path between node 19 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph517-4_19", + "image": "data/connectivity/graph_visual/medium/graph517.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,9) (0,17) (0,20) (1,15) (1,22) (1,14) (1,3) (1,21) (1,5) (1,18) (1,7) (1,6) (1,13) (2,15) (2,3) (2,4) (2,11) (2,21) (2,18) (2,8) (2,13) (3,15) (3,22) (3,12) (3,14) (3,4) (3,11) (3,21) (3,5) (3,7) (3,6) (3,16) (4,15) (4,22) (4,12) (4,14) (4,11) (4,5) (4,7) (4,6) (4,16) (4,8) (4,13) (5,15) (5,22) (5,12) (5,11) (5,21) (5,7) (5,6) (5,8) (5,13) (6,15) (6,12) (6,11) (6,21) (6,18) (6,16) (6,8) (6,13) (7,22) (7,12) (7,14) (7,11) (7,21) (7,16) (7,8) (8,22) (8,14) (8,21) (8,18) (8,16) (8,13) (9,19) (9,10) (9,17) (10,17) (11,22) (11,14) (11,21) (11,18) (11,13) (12,22) (12,14) (12,21) (12,18) (12,16) (12,13) (13,14) (13,18) (13,16) (14,15) (14,21) (14,18) (14,16) (15,21) (16,18) (17,20) (18,22)\nIs there a path between node 4 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph375-12_11", + "image": "data/connectivity/graph_visual/medium/graph375.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,15) (0,5) (0,3) (0,11) (0,9) (0,8) (0,13) (1,15) (1,5) (1,3) (1,11) (1,4) (1,9) (1,10) (1,8) (3,15) (3,4) (3,10) (3,8) (4,15) (4,12) (4,9) (4,10) (4,8) (4,13) (5,15) (5,11) (5,9) (5,10) (6,7) (6,20) (6,17) (6,18) (6,14) (7,19) (7,20) (7,18) (8,12) (8,11) (8,9) (8,10) (8,13) (9,15) (9,12) (9,11) (9,10) (10,15) (10,11) (10,13) (11,12) (12,13) (14,19) (14,20) (14,17) (14,18) (17,19) (17,20) (17,18) (18,19) (18,20)\nIs there a path between node 12 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph363-8_18", + "image": "data/connectivity/graph_visual/medium/graph363.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,9) (0,8) (0,17) (0,6) (1,14) (1,7) (2,8) (2,17) (2,3) (2,11) (2,10) (2,6) (3,9) (3,19) (3,10) (3,16) (4,18) (4,14) (5,8) (5,17) (5,10) (6,9) (6,11) (6,16) (7,20) (7,15) (8,9) (8,13) (8,19) (9,13) (10,17) (10,13) (12,16) (13,17) (14,18) (14,20) (15,20) (16,19)\nIs there a path between node 8 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph560-7_11", + "image": "data/connectivity/graph_visual/medium/graph560.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,15) (0,22) (0,18) (0,2) (1,7) (1,19) (1,23) (1,3) (1,10) (1,13) (1,16) (1,11) (1,12) (1,21) (1,5) (2,9) (2,15) (2,22) (2,17) (2,8) (3,7) (3,19) (3,10) (3,13) (3,16) (3,11) (3,6) (3,20) (3,21) (4,19) (4,23) (4,10) (4,13) (4,16) (4,11) (4,6) (4,20) (4,5) (5,7) (5,19) (5,23) (5,13) (5,16) (5,11) (5,12) (5,6) (5,20) (5,21) (6,7) (6,23) (6,10) (6,13) (6,16) (6,12) (6,20) (6,21) (7,19) (7,23) (7,10) (7,13) (7,16) (7,11) (7,21) (8,15) (8,14) (9,15) (9,22) (9,14) (9,17) (10,13) (10,16) (10,11) (10,12) (11,19) (11,23) (11,12) (11,20) (11,21) (12,16) (12,21) (13,19) (13,16) (13,20) (13,21) (14,22) (14,18) (14,17) (15,22) (15,17) (16,19) (16,23) (16,20) (16,21) (17,18) (18,22) (19,20) (19,21) (20,23) (20,21)\nIs there a path between node 7 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph263-8_16", + "image": "data/connectivity/graph_visual/medium/graph263.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,12) (0,3) (1,18) (2,11) (2,17) (2,9) (3,12) (4,10) (4,17) (4,6) (4,7) (6,14) (6,11) (6,17) (6,7) (7,15) (7,14) (7,19) (8,16) (9,10) (10,15) (10,11) (10,13) (11,13) (13,15) (13,14) (13,19)\nIs there a path between node 8 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph785-19_5", + "image": "data/connectivity/graph_visual/medium/graph785.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,15) (0,24) (0,1) (0,10) (1,3) (1,8) (2,13) (3,15) (3,14) (3,10) (4,17) (5,15) (5,24) (7,13) (8,11) (8,16) (8,10) (9,22) (9,20) (10,14) (11,15) (11,24) (13,19) (14,15) (14,18) (15,24) (16,24) (20,22)\nIs there a path between node 19 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph579-22_19", + "image": "data/connectivity/graph_visual/medium/graph579.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,3) (0,8) (0,10) (0,2) (0,13) (0,19) (1,23) (2,6) (2,20) (2,11) (2,12) (2,8) (2,17) (2,22) (2,5) (2,19) (3,11) (3,12) (3,21) (3,22) (5,16) (5,6) (5,8) (5,17) (5,13) (5,19) (6,20) (6,22) (6,7) (7,8) (7,10) (7,13) (8,11) (8,10) (8,13) (9,20) (9,10) (10,16) (10,11) (11,16) (12,17) (12,22) (12,13) (13,21) (14,23) (14,15) (17,20) (17,21) (21,22)\nIs there a path between node 22 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph328-16_13", + "image": "data/connectivity/graph_visual/medium/graph328.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,6) (0,1) (0,19) (1,14) (1,6) (1,2) (1,13) (2,5) (2,12) (2,3) (2,9) (3,8) (3,12) (3,13) (3,17) (3,7) (4,16) (4,10) (5,11) (5,20) (5,6) (5,7) (6,17) (6,7) (7,11) (7,14) (7,13) (7,19) (8,20) (8,19) (9,12) (9,13) (11,14) (11,12) (11,13) (12,14) (12,17) (12,19) (13,20) (13,17) (13,15) (14,19) (14,15) (15,20) (15,18) (17,19) (18,20) (19,20)\nIs there a path between node 16 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph451-20_1", + "image": "data/connectivity/graph_visual/medium/graph451.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,19) (0,3) (0,1) (0,16) (0,2) (1,4) (1,19) (1,20) (1,16) (1,12) (2,15) (2,3) (2,20) (2,16) (2,18) (3,4) (3,20) (3,16) (3,18) (4,15) (4,20) (4,16) (5,11) (5,9) (5,17) (5,21) (5,7) (5,14) (5,6) (6,8) (6,17) (6,21) (6,7) (6,13) (7,11) (7,10) (7,9) (7,8) (7,21) (7,13) (7,14) (8,11) (8,9) (8,17) (8,21) (8,13) (8,14) (9,10) (9,17) (9,14) (10,21) (11,21) (11,13) (11,14) (12,19) (12,16) (12,18) (13,17) (13,21) (14,17) (15,19) (15,20) (15,16) (15,18) (16,19) (16,18) (18,19) (18,20) (19,20)\nIs there a path between node 20 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph555-17_16", + "image": "data/connectivity/graph_visual/medium/graph555.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,14) (0,5) (0,9) (0,8) (0,6) (0,21) (1,4) (1,15) (1,18) (1,11) (1,10) (1,12) (2,20) (2,14) (2,5) (2,9) (2,22) (2,6) (2,16) (3,9) (3,23) (3,22) (3,6) (3,21) (4,15) (4,11) (4,19) (4,13) (5,20) (5,14) (5,9) (5,8) (5,6) (5,21) (6,20) (6,14) (6,9) (6,23) (6,8) (6,16) (7,18) (7,11) (7,10) (7,12) (7,19) (7,13) (8,20) (8,14) (8,23) (8,21) (9,20) (9,23) (9,22) (9,21) (10,15) (10,18) (10,11) (10,12) (10,19) (10,13) (11,15) (11,13) (12,18) (12,19) (13,18) (13,19) (14,23) (14,22) (14,21) (15,19) (16,23) (16,22) (20,21) (22,23)\nIs there a path between node 17 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph395-3_18", + "image": "data/connectivity/graph_visual/medium/graph395.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,1) (0,14) (0,3) (0,19) (0,11) (0,12) (0,7) (0,20) (0,6) (0,2) (0,4) (1,5) (1,14) (1,3) (1,19) (1,11) (1,12) (1,7) (1,20) (1,6) (1,2) (1,4) (2,5) (2,14) (2,3) (2,19) (2,11) (2,12) (2,7) (2,20) (2,6) (2,4) (3,5) (3,14) (3,19) (3,11) (3,12) (3,7) (3,20) (3,6) (3,4) (4,5) (4,14) (4,19) (4,11) (4,12) (4,7) (4,20) (4,6) (5,14) (5,19) (5,11) (5,12) (5,7) (5,20) (5,6) (6,14) (6,19) (6,11) (6,12) (6,7) (6,20) (7,14) (7,19) (7,11) (7,12) (7,20) (8,18) (8,17) (8,13) (8,16) (8,15) (9,10) (11,14) (11,19) (11,12) (11,20) (12,14) (12,19) (12,20) (13,18) (13,17) (13,16) (13,15) (14,19) (14,20) (15,18) (15,17) (15,16) (16,18) (16,17) (17,18) (19,20)\nIs there a path between node 3 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph260-13_16", + "image": "data/connectivity/graph_visual/medium/graph260.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,18) (0,1) (0,8) (0,10) (0,11) (0,7) (0,4) (0,2) (0,6) (0,17) (0,14) (1,19) (1,18) (1,8) (1,10) (1,11) (1,7) (1,4) (1,2) (1,6) (1,17) (1,14) (2,19) (2,18) (2,8) (2,10) (2,11) (2,7) (2,4) (2,6) (2,17) (2,14) (3,13) (3,9) (3,15) (4,19) (4,18) (4,8) (4,10) (4,11) (4,7) (4,6) (4,17) (4,14) (5,12) (5,16) (6,19) (6,18) (6,8) (6,10) (6,11) (6,7) (6,17) (6,14) (7,19) (7,18) (7,8) (7,10) (7,11) (7,17) (7,14) (8,19) (8,18) (8,10) (8,11) (8,17) (8,14) (9,13) (9,15) (10,19) (10,18) (10,11) (10,17) (10,14) (11,19) (11,18) (11,17) (11,14) (12,16) (13,15) (14,19) (14,18) (14,17) (17,19) (17,18) (18,19)\nIs there a path between node 13 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph558-18_13", + "image": "data/connectivity/graph_visual/medium/graph558.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,6) (0,19) (0,8) (0,17) (0,23) (0,1) (0,18) (0,7) (0,14) (1,15) (1,17) (1,23) (1,18) (1,7) (1,11) (1,14) (2,6) (2,19) (2,17) (2,23) (2,7) (3,15) (3,9) (3,17) (3,23) (3,18) (3,7) (3,11) (3,14) (4,12) (4,21) (5,12) (5,13) (6,15) (6,9) (6,19) (6,8) (6,17) (6,23) (6,10) (6,18) (6,7) (6,11) (6,14) (7,15) (7,9) (7,19) (7,8) (7,17) (7,23) (7,14) (8,19) (8,17) (8,23) (8,18) (8,11) (8,14) (9,19) (9,17) (9,23) (9,10) (9,14) (10,19) (10,17) (10,23) (10,18) (11,15) (11,19) (11,23) (11,18) (11,14) (12,13) (12,21) (13,21) (13,22) (14,19) (14,17) (14,23) (15,19) (15,23) (15,18) (16,20) (17,23) (18,19) (18,23) (19,23) (21,22)\nIs there a path between node 18 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph141-6_15", + "image": "data/connectivity/graph_visual/medium/graph141.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,12) (1,10) (3,14) (4,10) (5,12) (6,11) (6,16) (7,14) (8,14) (9,10) (10,15) (16,17)\nIs there a path between node 6 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph672-5_16", + "image": "data/connectivity/graph_visual/medium/graph672.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,14) (0,10) (0,4) (0,9) (0,20) (1,8) (1,6) (1,16) (1,11) (3,7) (3,22) (3,19) (3,21) (3,15) (3,17) (4,23) (4,14) (4,9) (5,8) (5,13) (5,11) (6,8) (6,13) (6,11) (7,22) (7,19) (7,17) (8,13) (8,16) (8,11) (9,23) (9,12) (9,10) (9,18) (9,20) (10,23) (10,14) (10,18) (11,13) (11,16) (12,23) (12,18) (14,23) (14,18) (14,20) (15,19) (15,21) (15,17) (17,22) (17,19) (17,21) (18,23) (18,20) (19,21) (20,23) (21,22)\nIs there a path between node 5 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph165-17_9", + "image": "data/connectivity/graph_visual/medium/graph165.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,2) (0,13) (0,11) (0,4) (0,17) (1,14) (1,12) (2,13) (2,10) (2,8) (2,4) (3,13) (3,10) (3,4) (4,5) (4,7) (5,10) (7,16) (9,15) (10,16) (10,13) (11,15) (11,17) (13,16) (13,15) (15,16)\nIs there a path between node 17 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph397-20_2", + "image": "data/connectivity/graph_visual/medium/graph397.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,6) (0,10) (0,17) (0,4) (0,21) (0,1) (0,2) (0,18) (0,7) (0,19) (0,11) (0,3) (0,5) (0,14) (1,6) (1,10) (1,17) (1,21) (1,16) (1,18) (1,7) (1,8) (1,11) (2,6) (2,10) (2,17) (2,4) (2,21) (2,16) (2,13) (2,18) (2,7) (2,8) (2,19) (2,3) (2,5) (3,6) (3,10) (3,17) (3,4) (3,21) (3,16) (3,13) (3,18) (3,7) (3,19) (4,10) (4,16) (4,18) (4,7) (4,8) (4,19) (4,5) (5,6) (5,16) (5,13) (5,18) (5,7) (5,8) (5,19) (5,14) (6,10) (6,17) (6,21) (6,16) (6,13) (6,18) (6,7) (6,19) (6,11) (6,14) (7,10) (7,17) (7,21) (7,16) (7,13) (7,18) (7,8) (7,19) (7,11) (7,14) (8,10) (8,17) (8,21) (8,16) (8,13) (8,18) (8,19) (8,11) (9,20) (10,17) (10,21) (10,13) (10,18) (10,19) (10,11) (10,14) (11,17) (11,16) (11,13) (11,18) (11,19) (12,15) (13,21) (13,16) (13,18) (13,19) (13,14) (14,17) (14,21) (14,16) (14,18) (14,19) (16,17) (16,21) (16,18) (17,18) (18,21) (18,19) (19,21)\nIs there a path between node 20 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph588-9_4", + "image": "data/connectivity/graph_visual/medium/graph588.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (1,5) (1,12) (1,3) (1,17) (1,15) (1,16) (2,21) (2,9) (2,11) (2,13) (2,4) (2,14) (3,23) (3,13) (3,15) (3,19) (3,14) (4,5) (4,12) (4,9) (4,17) (4,11) (5,8) (5,12) (5,22) (5,16) (5,14) (6,10) (7,18) (7,10) (8,12) (8,17) (8,23) (8,11) (8,16) (9,22) (9,13) (11,21) (11,15) (12,17) (12,23) (12,16) (12,14) (13,22) (13,23) (13,19) (13,16) (14,20) (14,22) (14,17) (15,20) (15,19) (16,22) (16,17) (16,23) (16,19) (19,23) (20,22) (22,23)\nIs there a path between node 9 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph765-8_12", + "image": "data/connectivity/graph_visual/medium/graph765.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,4) (0,7) (0,6) (0,8) (0,2) (0,22) (0,11) (0,21) (0,10) (1,5) (1,19) (1,14) (1,23) (2,3) (2,4) (2,7) (2,6) (2,8) (2,22) (2,11) (2,21) (2,10) (3,4) (3,7) (3,6) (3,8) (3,22) (3,11) (3,21) (3,10) (4,7) (4,6) (4,8) (4,22) (4,11) (4,21) (4,10) (5,19) (5,14) (5,23) (6,7) (6,8) (6,22) (6,11) (6,21) (6,10) (7,8) (7,22) (7,11) (7,21) (7,10) (8,22) (8,11) (8,21) (8,10) (9,24) (9,15) (9,16) (9,20) (9,17) (10,22) (10,11) (10,21) (11,22) (11,21) (12,13) (12,18) (13,18) (14,19) (14,23) (15,24) (15,16) (15,20) (15,17) (16,24) (16,20) (16,17) (17,24) (17,20) (19,23) (20,24) (21,22)\nIs there a path between node 8 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph467-10_11", + "image": "data/connectivity/graph_visual/medium/graph467.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,7) (0,1) (0,18) (0,12) (0,2) (0,4) (0,21) (0,16) (0,20) (0,15) (0,10) (0,19) (0,17) (0,13) (1,11) (1,7) (1,18) (1,12) (1,2) (1,4) (1,21) (1,16) (1,20) (1,15) (1,10) (1,19) (1,17) (1,13) (2,11) (2,7) (2,18) (2,12) (2,4) (2,21) (2,16) (2,20) (2,15) (2,10) (2,19) (2,17) (2,13) (3,5) (4,11) (4,7) (4,18) (4,12) (4,21) (4,16) (4,20) (4,15) (4,10) (4,19) (4,17) (4,13) (6,9) (6,8) (6,14) (7,11) (7,18) (7,12) (7,21) (7,16) (7,20) (7,15) (7,10) (7,19) (7,17) (7,13) (8,9) (8,14) (9,14) (10,11) (10,18) (10,12) (10,21) (10,16) (10,20) (10,15) (10,19) (10,17) (10,13) (11,18) (11,12) (11,21) (11,16) (11,20) (11,15) (11,19) (11,17) (11,13) (12,18) (12,21) (12,16) (12,20) (12,15) (12,19) (12,17) (12,13) (13,18) (13,21) (13,16) (13,20) (13,15) (13,19) (13,17) (15,18) (15,21) (15,16) (15,20) (15,19) (15,17) (16,18) (16,21) (16,20) (16,19) (16,17) (17,18) (17,21) (17,20) (17,19) (18,21) (18,20) (18,19) (19,21) (19,20) (20,21)\nIs there a path between node 10 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph675-19_20", + "image": "data/connectivity/graph_visual/medium/graph675.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,22) (0,21) (0,14) (0,19) (0,13) (0,18) (0,12) (0,15) (0,6) (0,7) (0,10) (0,20) (0,2) (0,4) (0,8) (0,17) (0,23) (1,3) (1,16) (1,11) (1,9) (2,5) (2,22) (2,21) (2,14) (2,19) (2,13) (2,18) (2,12) (2,15) (2,6) (2,7) (2,10) (2,20) (2,4) (2,8) (2,17) (2,23) (3,16) (3,11) (3,9) (4,5) (4,22) (4,21) (4,14) (4,19) (4,13) (4,18) (4,12) (4,15) (4,6) (4,7) (4,10) (4,20) (4,8) (4,17) (4,23) (5,22) (5,21) (5,14) (5,19) (5,13) (5,18) (5,12) (5,15) (5,6) (5,7) (5,10) (5,20) (5,8) (5,17) (5,23) (6,22) (6,21) (6,14) (6,19) (6,13) (6,18) (6,12) (6,15) (6,7) (6,10) (6,20) (6,8) (6,17) (6,23) (7,22) (7,21) (7,14) (7,19) (7,13) (7,18) (7,12) (7,15) (7,10) (7,20) (7,8) (7,17) (7,23) (8,22) (8,21) (8,14) (8,19) (8,13) (8,18) (8,12) (8,15) (8,10) (8,20) (8,17) (8,23) (9,16) (9,11) (10,22) (10,21) (10,14) (10,19) (10,13) (10,18) (10,12) (10,15) (10,20) (10,17) (10,23) (11,16) (12,22) (12,21) (12,14) (12,19) (12,13) (12,18) (12,15) (12,20) (12,17) (12,23) (13,22) (13,21) (13,14) (13,19) (13,18) (13,15) (13,20) (13,17) (13,23) (14,22) (14,21) (14,19) (14,18) (14,15) (14,20) (14,17) (14,23) (15,22) (15,21) (15,19) (15,18) (15,20) (15,17) (15,23) (17,22) (17,21) (17,19) (17,18) (17,20) (17,23) (18,22) (18,21) (18,19) (18,20) (18,23) (19,22) (19,21) (19,20) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 19 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph782-22_17", + "image": "data/connectivity/graph_visual/medium/graph782.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,11) (0,5) (1,9) (1,17) (2,6) (2,22) (2,15) (2,11) (2,18) (2,7) (3,12) (3,11) (4,12) (4,14) (4,15) (4,13) (5,10) (5,14) (5,22) (5,11) (5,7) (6,8) (6,15) (7,8) (7,10) (7,22) (7,13) (7,16) (8,20) (8,14) (8,19) (8,15) (8,11) (9,24) (9,23) (9,17) (10,14) (10,11) (10,18) (11,20) (12,15) (12,13) (13,22) (13,15) (13,18) (13,16) (14,20) (14,22) (14,18) (15,20) (15,19) (15,18) (17,23) (20,21) (21,22) (23,24)\nIs there a path between node 22 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph710-10_19", + "image": "data/connectivity/graph_visual/medium/graph710.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,4) (1,18) (1,8) (1,10) (2,4) (3,14) (3,5) (3,22) (4,11) (4,13) (5,22) (6,10) (8,9) (8,18) (8,16) (10,21) (13,20) (14,19) (15,19) (15,22) (17,21) (18,21)\nIs there a path between node 10 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph394-16_1", + "image": "data/connectivity/graph_visual/medium/graph394.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,5) (0,6) (0,14) (0,7) (0,9) (0,19) (0,17) (0,20) (0,15) (0,11) (0,3) (0,1) (0,13) (0,16) (0,18) (0,2) (1,10) (1,5) (1,6) (1,14) (1,7) (1,9) (1,19) (1,17) (1,20) (1,15) (1,11) (1,3) (1,13) (1,16) (1,18) (1,2) (2,10) (2,5) (2,6) (2,14) (2,7) (2,9) (2,19) (2,17) (2,20) (2,15) (2,11) (2,3) (2,13) (2,16) (2,18) (3,10) (3,5) (3,6) (3,14) (3,7) (3,9) (3,19) (3,17) (3,20) (3,15) (3,11) (3,13) (3,16) (3,18) (4,12) (4,8) (5,10) (5,6) (5,14) (5,7) (5,9) (5,19) (5,17) (5,20) (5,15) (5,11) (5,13) (5,16) (5,18) (6,10) (6,14) (6,7) (6,9) (6,19) (6,17) (6,20) (6,15) (6,11) (6,13) (6,16) (6,18) (7,10) (7,14) (7,9) (7,19) (7,17) (7,20) (7,15) (7,11) (7,13) (7,16) (7,18) (8,12) (9,10) (9,14) (9,19) (9,17) (9,20) (9,15) (9,11) (9,13) (9,16) (9,18) (10,14) (10,19) (10,17) (10,20) (10,15) (10,11) (10,13) (10,16) (10,18) (11,14) (11,19) (11,17) (11,20) (11,15) (11,13) (11,16) (11,18) (13,14) (13,19) (13,17) (13,20) (13,15) (13,16) (13,18) (14,19) (14,17) (14,20) (14,15) (14,16) (14,18) (15,19) (15,17) (15,20) (15,16) (15,18) (16,19) (16,17) (16,20) (16,18) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20)\nIs there a path between node 16 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph649-12_3", + "image": "data/connectivity/graph_visual/medium/graph649.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (1,5) (1,18) (1,7) (1,22) (1,11) (1,20) (1,4) (1,23) (2,14) (2,10) (2,21) (2,15) (2,16) (2,3) (3,14) (3,10) (3,15) (3,16) (3,6) (3,19) (4,18) (4,7) (4,22) (4,11) (4,20) (4,23) (5,13) (5,7) (5,22) (5,11) (5,20) (5,23) (6,10) (6,21) (6,15) (6,16) (6,9) (6,8) (6,19) (7,13) (7,22) (7,20) (7,23) (8,10) (8,9) (8,19) (9,21) (9,15) (9,19) (10,21) (10,16) (10,19) (11,18) (11,13) (11,22) (11,23) (12,17) (13,22) (13,20) (14,15) (14,16) (14,19) (15,16) (15,19) (16,21) (16,19) (18,20) (18,23) (19,21) (20,22) (20,23) (22,23)\nIs there a path between node 12 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph347-1_6", + "image": "data/connectivity/graph_visual/medium/graph347.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,13) (0,3) (0,19) (0,12) (0,15) (0,17) (1,20) (1,6) (1,2) (1,7) (2,20) (2,6) (2,7) (3,10) (3,13) (3,19) (3,12) (3,15) (3,17) (4,11) (4,9) (4,18) (4,16) (4,14) (4,8) (4,5) (5,11) (5,9) (5,18) (5,16) (5,14) (5,8) (6,20) (6,7) (7,20) (8,11) (8,9) (8,18) (8,16) (8,14) (9,11) (9,18) (9,16) (9,14) (10,13) (10,19) (10,12) (10,15) (10,17) (11,18) (11,16) (11,14) (12,13) (12,19) (12,15) (12,17) (13,19) (13,15) (13,17) (14,18) (14,16) (15,19) (15,17) (16,18) (17,19)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph429-16_6", + "image": "data/connectivity/graph_visual/medium/graph429.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,10) (0,2) (0,8) (0,13) (1,11) (1,21) (1,7) (2,20) (2,6) (2,10) (2,3) (2,4) (2,12) (2,18) (3,17) (3,6) (3,4) (3,19) (3,18) (4,17) (4,19) (4,13) (6,17) (6,10) (6,19) (7,14) (8,15) (8,20) (9,20) (9,16) (9,18) (10,20) (10,16) (10,19) (12,19) (12,13) (13,17) (13,15) (13,16) (15,17) (15,19) (16,17) (17,20) (18,19) (19,20)\nIs there a path between node 16 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph394-14_12", + "image": "data/connectivity/graph_visual/medium/graph394.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,5) (0,6) (0,14) (0,7) (0,9) (0,19) (0,17) (0,20) (0,15) (0,11) (0,3) (0,1) (0,13) (0,16) (0,18) (0,2) (1,10) (1,5) (1,6) (1,14) (1,7) (1,9) (1,19) (1,17) (1,20) (1,15) (1,11) (1,3) (1,13) (1,16) (1,18) (1,2) (2,10) (2,5) (2,6) (2,14) (2,7) (2,9) (2,19) (2,17) (2,20) (2,15) (2,11) (2,3) (2,13) (2,16) (2,18) (3,10) (3,5) (3,6) (3,14) (3,7) (3,9) (3,19) (3,17) (3,20) (3,15) (3,11) (3,13) (3,16) (3,18) (4,12) (4,8) (5,10) (5,6) (5,14) (5,7) (5,9) (5,19) (5,17) (5,20) (5,15) (5,11) (5,13) (5,16) (5,18) (6,10) (6,14) (6,7) (6,9) (6,19) (6,17) (6,20) (6,15) (6,11) (6,13) (6,16) (6,18) (7,10) (7,14) (7,9) (7,19) (7,17) (7,20) (7,15) (7,11) (7,13) (7,16) (7,18) (8,12) (9,10) (9,14) (9,19) (9,17) (9,20) (9,15) (9,11) (9,13) (9,16) (9,18) (10,14) (10,19) (10,17) (10,20) (10,15) (10,11) (10,13) (10,16) (10,18) (11,14) (11,19) (11,17) (11,20) (11,15) (11,13) (11,16) (11,18) (13,14) (13,19) (13,17) (13,20) (13,15) (13,16) (13,18) (14,19) (14,17) (14,20) (14,15) (14,16) (14,18) (15,19) (15,17) (15,20) (15,16) (15,18) (16,19) (16,17) (16,20) (16,18) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20)\nIs there a path between node 14 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph480-5_15", + "image": "data/connectivity/graph_visual/medium/graph480.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,16) (1,4) (1,7) (1,13) (1,22) (1,19) (1,15) (1,8) (1,12) (1,9) (1,18) (2,10) (2,5) (2,21) (2,20) (3,5) (3,21) (3,20) (4,16) (4,7) (4,13) (4,6) (4,22) (4,19) (4,15) (4,12) (4,9) (5,17) (5,21) (6,14) (6,16) (6,22) (6,19) (6,15) (6,8) (6,12) (6,9) (6,18) (7,14) (7,13) (7,11) (7,22) (7,15) (7,9) (7,18) (8,14) (8,19) (8,15) (8,12) (8,18) (9,14) (9,13) (9,11) (9,22) (9,19) (9,15) (10,17) (10,21) (11,22) (11,15) (11,12) (11,18) (12,16) (12,19) (12,15) (12,18) (13,14) (13,16) (13,22) (13,15) (13,18) (14,22) (14,19) (14,15) (15,22) (15,19) (15,18) (16,22) (16,18) (18,22) (18,19) (19,22)\nIs there a path between node 5 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph22-6_9", + "image": "data/connectivity/graph_visual/medium/graph22.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,2) (2,9) (7,11) (10,11)\nIs there a path between node 6 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph655-12_23", + "image": "data/connectivity/graph_visual/medium/graph655.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,16) (0,3) (0,21) (0,23) (1,16) (1,7) (1,3) (1,4) (1,11) (1,23) (2,15) (2,18) (2,6) (2,8) (2,12) (2,14) (2,13) (2,5) (3,16) (3,7) (3,4) (3,21) (3,11) (3,23) (4,16) (4,7) (4,21) (4,11) (5,10) (5,15) (5,17) (5,18) (5,8) (5,19) (5,9) (5,14) (5,13) (6,15) (6,17) (6,12) (6,19) (6,9) (7,21) (7,11) (7,23) (8,10) (8,15) (8,9) (8,14) (8,13) (9,15) (9,18) (9,12) (9,19) (9,14) (10,15) (10,12) (10,14) (10,13) (11,16) (11,21) (11,23) (12,15) (12,17) (12,18) (12,19) (12,13) (13,15) (13,17) (13,18) (13,19) (13,14) (14,17) (15,18) (16,23) (17,18) (18,19) (20,22) (21,23)\nIs there a path between node 12 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph213-14_12", + "image": "data/connectivity/graph_visual/medium/graph213.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (0,6) (0,7) (0,1) (1,4) (1,6) (1,7) (2,18) (2,12) (2,5) (2,17) (2,10) (2,8) (2,16) (2,3) (2,14) (2,11) (2,13) (3,18) (3,12) (3,5) (3,17) (3,10) (3,8) (3,16) (3,14) (3,11) (3,13) (4,6) (4,7) (5,18) (5,12) (5,17) (5,10) (5,8) (5,16) (5,14) (5,11) (5,13) (6,7) (8,18) (8,12) (8,17) (8,10) (8,16) (8,14) (8,11) (8,13) (9,15) (10,18) (10,12) (10,17) (10,16) (10,14) (10,11) (10,13) (11,18) (11,12) (11,17) (11,16) (11,14) (11,13) (12,18) (12,17) (12,16) (12,14) (12,13) (13,18) (13,17) (13,16) (13,14) (14,18) (14,17) (14,16) (16,18) (16,17) (17,18)\nIs there a path between node 14 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph571-10_12", + "image": "data/connectivity/graph_visual/medium/graph571.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,22) (0,3) (0,15) (0,6) (0,5) (0,7) (0,2) (0,19) (0,4) (0,11) (0,9) (0,14) (0,21) (1,16) (1,12) (1,18) (1,17) (1,20) (1,23) (1,13) (1,10) (2,8) (2,22) (2,3) (2,15) (2,6) (2,5) (2,7) (2,19) (2,4) (2,11) (2,9) (2,14) (2,21) (3,8) (3,22) (3,15) (3,6) (3,5) (3,7) (3,19) (3,4) (3,11) (3,9) (3,14) (3,21) (4,8) (4,22) (4,15) (4,6) (4,5) (4,7) (4,19) (4,11) (4,9) (4,14) (4,21) (5,8) (5,22) (5,15) (5,6) (5,7) (5,19) (5,11) (5,9) (5,14) (5,21) (6,8) (6,22) (6,15) (6,7) (6,19) (6,11) (6,9) (6,14) (6,21) (7,8) (7,22) (7,15) (7,19) (7,11) (7,9) (7,14) (7,21) (8,22) (8,15) (8,19) (8,11) (8,9) (8,14) (8,21) (9,22) (9,15) (9,19) (9,11) (9,14) (9,21) (10,16) (10,12) (10,18) (10,17) (10,20) (10,23) (10,13) (11,22) (11,15) (11,19) (11,14) (11,21) (12,16) (12,18) (12,17) (12,20) (12,23) (12,13) (13,16) (13,18) (13,17) (13,20) (13,23) (14,22) (14,15) (14,19) (14,21) (15,22) (15,19) (15,21) (16,18) (16,17) (16,20) (16,23) (17,18) (17,20) (17,23) (18,20) (18,23) (19,22) (19,21) (20,23) (21,22)\nIs there a path between node 10 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph323-0_15", + "image": "data/connectivity/graph_visual/medium/graph323.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,15) (0,7) (0,3) (0,19) (0,14) (0,18) (0,16) (1,2) (1,8) (1,6) (1,17) (1,5) (1,4) (1,9) (1,10) (1,13) (1,12) (1,11) (2,8) (2,6) (2,17) (2,5) (2,4) (2,9) (2,10) (2,13) (2,12) (2,11) (3,15) (3,7) (3,19) (3,14) (3,18) (3,16) (4,8) (4,6) (4,17) (4,5) (4,9) (4,10) (4,13) (4,12) (4,11) (5,8) (5,6) (5,17) (5,9) (5,10) (5,13) (5,12) (5,11) (6,8) (6,17) (6,9) (6,10) (6,13) (6,12) (6,11) (7,15) (7,19) (7,14) (7,18) (7,16) (8,17) (8,9) (8,10) (8,13) (8,12) (8,11) (9,17) (9,10) (9,13) (9,12) (9,11) (10,17) (10,13) (10,12) (10,11) (11,17) (11,13) (11,12) (12,17) (12,13) (13,17) (14,15) (14,19) (14,18) (14,16) (15,19) (15,18) (15,16) (16,19) (16,18) (18,19)\nIs there a path between node 0 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph791-4_21", + "image": "data/connectivity/graph_visual/medium/graph791.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (1,16) (1,5) (1,10) (1,18) (2,7) (2,14) (2,11) (2,15) (3,16) (3,5) (3,12) (3,15) (3,10) (5,20) (5,24) (5,12) (5,7) (5,14) (7,20) (7,24) (7,18) (8,21) (8,23) (9,20) (9,16) (9,24) (10,20) (10,24) (10,15) (10,18) (11,16) (11,22) (12,24) (12,14) (12,15) (13,24) (13,14) (13,22) (15,18) (15,22) (16,24) (16,18) (17,19) (18,20) (19,21) (19,23) (21,23)\nIs there a path between node 4 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph493-15_4", + "image": "data/connectivity/graph_visual/medium/graph493.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,9) (0,19) (0,7) (0,2) (0,14) (0,12) (0,15) (0,22) (0,20) (1,16) (1,10) (1,3) (1,11) (1,4) (1,17) (1,5) (2,6) (2,9) (2,19) (2,7) (2,14) (2,12) (2,15) (2,22) (2,20) (3,16) (3,10) (3,11) (3,4) (3,17) (3,5) (4,16) (4,10) (4,11) (4,17) (4,5) (5,16) (5,10) (5,11) (5,17) (6,9) (6,19) (6,7) (6,14) (6,12) (6,15) (6,22) (6,20) (7,9) (7,19) (7,14) (7,12) (7,15) (7,22) (7,20) (8,13) (8,21) (8,18) (9,19) (9,14) (9,12) (9,15) (9,22) (9,20) (10,16) (10,11) (10,17) (11,16) (11,17) (12,19) (12,14) (12,15) (12,22) (12,20) (13,21) (13,18) (14,19) (14,15) (14,22) (14,20) (15,19) (15,22) (15,20) (16,17) (18,21) (19,22) (19,20) (20,22)\nIs there a path between node 15 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph536-5_19", + "image": "data/connectivity/graph_visual/medium/graph536.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,4) (0,7) (0,15) (0,8) (0,16) (0,12) (0,14) (1,17) (1,2) (1,22) (1,5) (1,21) (1,3) (2,17) (2,22) (2,5) (2,21) (2,3) (3,17) (3,22) (3,5) (3,21) (4,7) (4,15) (4,8) (4,16) (4,12) (4,14) (5,17) (5,22) (5,21) (6,20) (6,19) (6,11) (6,10) (6,13) (6,18) (6,9) (7,15) (7,8) (7,16) (7,12) (7,14) (8,15) (8,16) (8,12) (8,14) (9,20) (9,19) (9,11) (9,10) (9,13) (9,18) (10,20) (10,19) (10,11) (10,13) (10,18) (11,20) (11,19) (11,13) (11,18) (12,15) (12,16) (12,14) (13,20) (13,19) (13,18) (14,15) (14,16) (15,16) (17,22) (17,21) (18,20) (18,19) (19,20) (21,22)\nIs there a path between node 5 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph487-0_3", + "image": "data/connectivity/graph_visual/medium/graph487.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,14) (0,6) (0,11) (0,19) (0,20) (0,1) (0,15) (0,12) (0,7) (0,22) (0,5) (0,21) (0,3) (0,4) (0,18) (0,17) (1,14) (1,6) (1,11) (1,19) (1,20) (1,15) (1,12) (1,7) (1,22) (1,5) (1,21) (1,3) (1,4) (1,18) (1,17) (2,13) (2,10) (2,8) (2,16) (2,9) (3,14) (3,6) (3,11) (3,19) (3,20) (3,15) (3,12) (3,7) (3,22) (3,5) (3,21) (3,4) (3,18) (3,17) (4,14) (4,6) (4,11) (4,19) (4,20) (4,15) (4,12) (4,7) (4,22) (4,5) (4,21) (4,18) (4,17) (5,14) (5,6) (5,11) (5,19) (5,20) (5,15) (5,12) (5,7) (5,22) (5,21) (5,18) (5,17) (6,14) (6,11) (6,19) (6,20) (6,15) (6,12) (6,7) (6,22) (6,21) (6,18) (6,17) (7,14) (7,11) (7,19) (7,20) (7,15) (7,12) (7,22) (7,21) (7,18) (7,17) (8,13) (8,10) (8,16) (8,9) (9,13) (9,10) (9,16) (10,13) (10,16) (11,14) (11,19) (11,20) (11,15) (11,12) (11,22) (11,21) (11,18) (11,17) (12,14) (12,19) (12,20) (12,15) (12,22) (12,21) (12,18) (12,17) (13,16) (14,19) (14,20) (14,15) (14,22) (14,21) (14,18) (14,17) (15,19) (15,20) (15,22) (15,21) (15,18) (15,17) (17,19) (17,20) (17,22) (17,21) (17,18) (18,19) (18,20) (18,22) (18,21) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22)\nIs there a path between node 0 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph347-9_16", + "image": "data/connectivity/graph_visual/medium/graph347.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,13) (0,3) (0,19) (0,12) (0,15) (0,17) (1,20) (1,6) (1,2) (1,7) (2,20) (2,6) (2,7) (3,10) (3,13) (3,19) (3,12) (3,15) (3,17) (4,11) (4,9) (4,18) (4,16) (4,14) (4,8) (4,5) (5,11) (5,9) (5,18) (5,16) (5,14) (5,8) (6,20) (6,7) (7,20) (8,11) (8,9) (8,18) (8,16) (8,14) (9,11) (9,18) (9,16) (9,14) (10,13) (10,19) (10,12) (10,15) (10,17) (11,18) (11,16) (11,14) (12,13) (12,19) (12,15) (12,17) (13,19) (13,15) (13,17) (14,18) (14,16) (15,19) (15,17) (16,18) (17,19)\nIs there a path between node 9 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph659-22_12", + "image": "data/connectivity/graph_visual/medium/graph659.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,21) (0,14) (0,23) (0,11) (0,19) (0,17) (0,22) (0,8) (0,9) (0,16) (0,10) (0,4) (1,3) (1,14) (1,11) (1,17) (1,7) (1,16) (2,15) (2,13) (2,5) (3,21) (3,14) (3,11) (3,20) (3,19) (3,17) (3,22) (3,9) (3,16) (3,10) (4,6) (4,21) (4,14) (4,23) (4,20) (4,17) (4,22) (4,7) (4,8) (4,9) (4,10) (5,15) (5,12) (6,21) (6,14) (6,23) (6,11) (6,20) (6,18) (6,19) (6,17) (6,7) (6,9) (6,16) (6,10) (7,21) (7,23) (7,11) (7,20) (7,19) (7,17) (7,22) (7,8) (7,16) (8,14) (8,23) (8,20) (8,18) (8,17) (8,22) (8,9) (8,10) (9,21) (9,14) (9,23) (9,11) (9,18) (9,19) (9,17) (9,22) (9,16) (9,10) (10,21) (10,14) (10,23) (10,11) (10,20) (10,18) (10,19) (10,16) (11,23) (11,20) (11,19) (11,17) (11,16) (12,15) (12,13) (13,15) (14,21) (14,23) (14,20) (14,18) (14,19) (14,17) (16,21) (16,23) (16,20) (16,18) (16,17) (17,21) (17,23) (17,20) (17,18) (18,21) (18,23) (18,19) (18,22) (19,21) (19,23) (19,20) (19,22) (20,21) (20,23) (20,22) (21,23) (22,23)\nIs there a path between node 22 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph654-22_18", + "image": "data/connectivity/graph_visual/medium/graph654.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,8) (0,2) (0,17) (0,6) (0,11) (0,23) (0,4) (0,7) (0,14) (0,1) (0,21) (0,12) (0,10) (0,19) (1,20) (1,22) (1,8) (1,2) (1,17) (1,6) (1,9) (1,4) (1,14) (1,21) (1,12) (2,20) (2,22) (2,3) (2,16) (2,17) (2,6) (2,9) (2,11) (2,23) (2,7) (2,21) (2,12) (2,19) (3,20) (3,22) (3,8) (3,16) (3,17) (3,6) (3,11) (3,23) (3,4) (3,7) (3,14) (3,21) (3,12) (3,19) (4,8) (4,17) (4,11) (4,7) (4,12) (4,10) (4,19) (6,20) (6,22) (6,8) (6,16) (6,23) (6,7) (6,21) (6,12) (6,10) (6,19) (7,20) (7,22) (7,16) (7,17) (7,23) (7,21) (7,12) (7,19) (8,20) (8,22) (8,17) (8,9) (8,23) (8,14) (8,21) (8,12) (8,10) (8,19) (9,22) (9,16) (9,17) (9,11) (9,14) (9,21) (9,12) (10,20) (10,22) (10,16) (10,17) (10,11) (10,23) (10,21) (10,19) (11,20) (11,22) (11,23) (11,14) (11,21) (11,12) (11,19) (12,22) (12,16) (12,17) (12,21) (12,19) (13,15) (13,18) (14,20) (14,22) (14,16) (14,17) (14,23) (14,21) (14,19) (15,18) (16,22) (16,21) (17,22) (17,19) (19,20) (19,22) (19,21) (20,22) (20,23) (20,21) (21,22)\nIs there a path between node 22 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph103-11_14", + "image": "data/connectivity/graph_visual/medium/graph103.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (0,5) (0,8) (0,4) (0,12) (0,2) (0,7) (0,14) (0,3) (0,6) (1,13) (1,5) (1,8) (1,4) (1,12) (1,2) (1,9) (1,14) (1,3) (2,13) (2,5) (2,10) (2,4) (2,9) (2,14) (3,5) (3,8) (3,10) (3,4) (3,9) (3,14) (3,6) (4,13) (4,5) (4,10) (4,9) (4,6) (5,13) (5,8) (5,10) (5,12) (5,9) (6,8) (6,10) (6,9) (6,7) (6,14) (7,13) (7,8) (7,10) (7,12) (8,10) (8,12) (8,9) (8,14) (9,13) (9,10) (9,12) (9,14) (10,12) (10,14) (11,15) (12,13)\nIs there a path between node 11 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph777-24_12", + "image": "data/connectivity/graph_visual/medium/graph777.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,3) (0,9) (0,12) (0,24) (0,2) (0,17) (0,20) (0,14) (0,13) (0,21) (0,7) (0,8) (0,15) (0,18) (0,5) (0,23) (0,16) (1,4) (1,19) (1,11) (1,22) (1,6) (2,10) (2,3) (2,9) (2,12) (2,24) (2,17) (2,20) (2,14) (2,13) (2,21) (2,7) (2,8) (2,15) (2,18) (2,5) (2,23) (2,16) (3,10) (3,9) (3,12) (3,24) (3,17) (3,20) (3,14) (3,13) (3,21) (3,7) (3,8) (3,15) (3,18) (3,5) (3,23) (3,16) (4,19) (4,11) (4,22) (4,6) (5,10) (5,9) (5,12) (5,24) (5,17) (5,20) (5,14) (5,13) (5,21) (5,7) (5,8) (5,15) (5,18) (5,23) (5,16) (6,19) (6,11) (6,22) (7,10) (7,9) (7,12) (7,24) (7,17) (7,20) (7,14) (7,13) (7,21) (7,8) (7,15) (7,18) (7,23) (7,16) (8,10) (8,9) (8,12) (8,24) (8,17) (8,20) (8,14) (8,13) (8,21) (8,15) (8,18) (8,23) (8,16) (9,10) (9,12) (9,24) (9,17) (9,20) (9,14) (9,13) (9,21) (9,15) (9,18) (9,23) (9,16) (10,12) (10,24) (10,17) (10,20) (10,14) (10,13) (10,21) (10,15) (10,18) (10,23) (10,16) (11,19) (11,22) (12,24) (12,17) (12,20) (12,14) (12,13) (12,21) (12,15) (12,18) (12,23) (12,16) (13,24) (13,17) (13,20) (13,14) (13,21) (13,15) (13,18) (13,23) (13,16) (14,24) (14,17) (14,20) (14,21) (14,15) (14,18) (14,23) (14,16) (15,24) (15,17) (15,20) (15,21) (15,18) (15,23) (15,16) (16,24) (16,17) (16,20) (16,21) (16,18) (16,23) (17,24) (17,20) (17,21) (17,18) (17,23) (18,24) (18,20) (18,21) (18,23) (19,22) (20,24) (20,21) (20,23) (21,24) (21,23) (23,24)\nIs there a path between node 24 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph188-10_7", + "image": "data/connectivity/graph_visual/medium/graph188.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,11) (0,1) (0,9) (0,17) (0,3) (0,14) (0,15) (0,4) (0,10) (0,2) (0,6) (1,16) (1,11) (1,9) (1,17) (1,3) (1,14) (1,15) (1,4) (1,10) (1,2) (1,6) (2,16) (2,11) (2,9) (2,17) (2,3) (2,14) (2,15) (2,4) (2,10) (2,6) (3,16) (3,11) (3,9) (3,17) (3,14) (3,15) (3,4) (3,10) (3,6) (4,16) (4,11) (4,9) (4,17) (4,14) (4,15) (4,10) (4,6) (5,8) (5,12) (5,7) (5,13) (6,16) (6,11) (6,9) (6,17) (6,14) (6,15) (6,10) (7,8) (7,12) (7,13) (8,12) (8,13) (9,16) (9,11) (9,17) (9,14) (9,15) (9,10) (10,16) (10,11) (10,17) (10,14) (10,15) (11,16) (11,17) (11,14) (11,15) (12,13) (14,16) (14,17) (14,15) (15,16) (15,17) (16,17)\nIs there a path between node 10 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph769-1_3", + "image": "data/connectivity/graph_visual/medium/graph769.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,10) (0,7) (0,11) (0,9) (0,21) (0,12) (0,19) (0,17) (0,24) (0,23) (0,1) (0,4) (0,8) (0,6) (0,16) (0,14) (0,22) (0,20) (0,13) (1,2) (1,10) (1,7) (1,11) (1,9) (1,21) (1,12) (1,19) (1,17) (1,24) (1,23) (1,4) (1,8) (1,6) (1,16) (1,14) (1,22) (1,20) (1,13) (2,10) (2,7) (2,11) (2,9) (2,21) (2,12) (2,19) (2,17) (2,24) (2,23) (2,4) (2,8) (2,6) (2,16) (2,14) (2,22) (2,20) (2,13) (3,5) (3,15) (3,18) (4,10) (4,7) (4,11) (4,9) (4,21) (4,12) (4,19) (4,17) (4,24) (4,23) (4,8) (4,6) (4,16) (4,14) (4,22) (4,20) (4,13) (5,15) (5,18) (6,10) (6,7) (6,11) (6,9) (6,21) (6,12) (6,19) (6,17) (6,24) (6,23) (6,8) (6,16) (6,14) (6,22) (6,20) (6,13) (7,10) (7,11) (7,9) (7,21) (7,12) (7,19) (7,17) (7,24) (7,23) (7,8) (7,16) (7,14) (7,22) (7,20) (7,13) (8,10) (8,11) (8,9) (8,21) (8,12) (8,19) (8,17) (8,24) (8,23) (8,16) (8,14) (8,22) (8,20) (8,13) (9,10) (9,11) (9,21) (9,12) (9,19) (9,17) (9,24) (9,23) (9,16) (9,14) (9,22) (9,20) (9,13) (10,11) (10,21) (10,12) (10,19) (10,17) (10,24) (10,23) (10,16) (10,14) (10,22) (10,20) (10,13) (11,21) (11,12) (11,19) (11,17) (11,24) (11,23) (11,16) (11,14) (11,22) (11,20) (11,13) (12,21) (12,19) (12,17) (12,24) (12,23) (12,16) (12,14) (12,22) (12,20) (12,13) (13,21) (13,19) (13,17) (13,24) (13,23) (13,16) (13,14) (13,22) (13,20) (14,21) (14,19) (14,17) (14,24) (14,23) (14,16) (14,22) (14,20) (15,18) (16,21) (16,19) (16,17) (16,24) (16,23) (16,22) (16,20) (17,21) (17,19) (17,24) (17,23) (17,22) (17,20) (19,21) (19,24) (19,23) (19,22) (19,20) (20,21) (20,24) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nIs there a path between node 1 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph664-7_22", + "image": "data/connectivity/graph_visual/medium/graph664.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,4) (0,14) (0,9) (0,19) (0,7) (0,20) (0,17) (0,16) (1,11) (1,12) (1,2) (1,15) (1,3) (1,23) (1,5) (1,21) (2,12) (2,15) (2,3) (2,23) (2,13) (2,10) (3,22) (3,12) (3,15) (3,23) (3,5) (3,21) (3,13) (4,14) (4,18) (4,9) (4,19) (4,16) (5,22) (5,11) (5,12) (5,23) (5,21) (5,10) (6,18) (6,9) (6,7) (6,20) (6,17) (6,16) (7,14) (7,9) (7,19) (7,20) (7,17) (7,8) (8,14) (8,18) (8,9) (8,19) (8,20) (8,17) (8,16) (9,14) (9,19) (10,11) (10,15) (10,23) (10,21) (10,13) (11,22) (11,12) (11,15) (11,13) (12,22) (12,15) (12,23) (12,21) (12,13) (13,15) (13,21) (14,18) (14,19) (14,20) (14,16) (15,22) (16,20) (16,17) (18,19) (18,20) (19,20) (21,22) (22,23)\nIs there a path between node 7 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph557-4_17", + "image": "data/connectivity/graph_visual/medium/graph557.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,2) (0,18) (0,23) (0,21) (0,13) (0,16) (0,15) (0,22) (0,6) (0,14) (1,17) (1,11) (1,10) (1,4) (1,19) (1,9) (2,8) (2,18) (2,23) (2,21) (2,22) (2,14) (2,20) (3,17) (3,11) (3,10) (3,4) (3,19) (3,9) (4,7) (4,10) (4,9) (5,8) (5,21) (5,13) (5,16) (5,15) (5,22) (5,6) (5,14) (5,20) (6,8) (6,18) (6,13) (6,15) (6,14) (6,20) (7,17) (7,10) (7,19) (7,9) (8,18) (8,23) (8,21) (8,13) (8,16) (8,14) (8,20) (9,17) (9,10) (9,19) (10,17) (10,19) (11,19) (13,18) (13,23) (13,21) (13,16) (13,22) (13,14) (13,20) (14,18) (14,23) (14,21) (14,16) (14,22) (14,20) (15,18) (15,21) (15,22) (16,23) (16,21) (17,19) (18,22) (20,23) (20,21) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 4 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph53-6_2", + "image": "data/connectivity/graph_visual/medium/graph53.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,10) (0,5) (0,7) (0,2) (0,8) (0,4) (0,9) (0,1) (0,12) (0,3) (0,11) (0,13) (1,10) (1,5) (1,7) (1,2) (1,8) (1,4) (1,9) (1,12) (1,3) (1,11) (1,13) (2,10) (2,5) (2,7) (2,8) (2,4) (2,9) (2,12) (2,3) (2,11) (2,13) (3,10) (3,5) (3,7) (3,8) (3,4) (3,9) (3,12) (3,11) (3,13) (4,10) (4,5) (4,7) (4,8) (4,9) (4,12) (4,11) (4,13) (5,10) (5,7) (5,8) (5,9) (5,12) (5,11) (5,13) (7,10) (7,8) (7,9) (7,12) (7,11) (7,13) (8,10) (8,9) (8,12) (8,11) (8,13) (9,10) (9,12) (9,11) (9,13) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nIs there a path between node 6 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph783-23_20", + "image": "data/connectivity/graph_visual/medium/graph783.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (0,18) (0,24) (0,2) (0,3) (0,20) (0,22) (0,10) (0,17) (1,9) (1,8) (1,20) (2,23) (2,9) (2,16) (2,11) (2,15) (3,23) (3,21) (3,4) (3,24) (3,17) (4,9) (4,18) (4,20) (4,10) (4,17) (5,14) (6,7) (8,21) (8,16) (8,22) (8,10) (8,17) (9,23) (9,21) (9,11) (9,20) (9,10) (9,17) (10,24) (10,20) (10,22) (10,17) (11,18) (11,12) (12,23) (12,21) (12,19) (12,18) (12,20) (15,23) (15,18) (15,24) (15,22) (15,17) (16,23) (16,19) (16,22) (17,18) (17,20) (18,22) (19,23) (19,20) (19,22) (20,22)\nIs there a path between node 23 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph597-21_8", + "image": "data/connectivity/graph_visual/medium/graph597.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,1) (0,20) (0,19) (0,6) (0,23) (1,12) (1,15) (1,22) (1,20) (1,19) (1,6) (1,2) (1,23) (2,12) (2,15) (2,18) (2,22) (2,21) (2,20) (2,19) (2,6) (2,23) (3,5) (3,14) (3,11) (3,7) (4,16) (4,13) (4,9) (4,10) (4,8) (5,14) (5,11) (5,7) (6,12) (6,15) (6,18) (6,21) (6,19) (7,14) (7,11) (8,16) (8,17) (8,10) (9,17) (10,16) (12,18) (12,21) (12,20) (12,19) (13,16) (13,17) (15,22) (15,21) (15,20) (15,23) (16,17) (18,22) (18,20) (18,19) (18,23) (19,22) (19,21) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 21 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph762-6_5", + "image": "data/connectivity/graph_visual/medium/graph762.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,24) (0,4) (0,17) (0,22) (0,7) (0,23) (0,9) (0,8) (0,3) (0,1) (0,10) (0,19) (0,6) (1,12) (1,24) (1,4) (1,17) (1,5) (1,22) (1,16) (1,23) (1,9) (1,14) (1,3) (1,13) (1,21) (1,10) (1,19) (1,6) (2,15) (2,18) (2,11) (3,12) (3,24) (3,4) (3,17) (3,22) (3,7) (3,16) (3,20) (3,13) (3,21) (4,12) (4,24) (4,5) (4,16) (4,20) (4,23) (4,13) (4,21) (4,10) (4,19) (4,6) (5,12) (5,24) (5,17) (5,22) (5,16) (5,20) (5,23) (5,9) (5,8) (5,13) (5,10) (5,6) (6,12) (6,24) (6,17) (6,22) (6,7) (6,20) (6,23) (6,8) (6,14) (6,13) (6,21) (7,12) (7,24) (7,17) (7,16) (7,23) (7,14) (7,13) (7,21) (7,10) (7,19) (8,12) (8,24) (8,17) (8,22) (8,16) (8,20) (8,23) (8,14) (8,13) (8,21) (8,10) (9,12) (9,24) (9,17) (9,22) (9,20) (9,14) (9,13) (9,21) (9,10) (9,19) (10,17) (10,16) (10,23) (10,14) (10,13) (11,18) (12,17) (12,22) (12,16) (12,23) (12,13) (12,19) (13,24) (13,16) (13,20) (13,21) (13,19) (14,24) (14,17) (14,22) (14,16) (14,21) (16,24) (16,20) (16,23) (16,19) (17,24) (17,22) (17,20) (17,23) (17,21) (17,19) (19,24) (19,22) (19,21) (20,24) (20,22) (20,23) (20,21) (21,24) (21,23) (22,24)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph676-4_19", + "image": "data/connectivity/graph_visual/medium/graph676.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,1) (0,3) (0,20) (0,21) (0,6) (0,11) (0,23) (0,8) (0,9) (0,14) (0,19) (1,10) (1,3) (1,20) (1,21) (1,6) (1,11) (1,23) (1,8) (1,9) (1,14) (1,19) (2,15) (2,18) (2,7) (2,22) (2,13) (2,17) (2,16) (2,12) (2,4) (2,5) (3,10) (3,20) (3,21) (3,6) (3,11) (3,23) (3,8) (3,9) (3,14) (3,19) (4,15) (4,18) (4,7) (4,22) (4,13) (4,17) (4,16) (4,12) (4,5) (5,15) (5,18) (5,7) (5,22) (5,13) (5,17) (5,16) (5,12) (6,10) (6,20) (6,21) (6,11) (6,23) (6,8) (6,9) (6,14) (6,19) (7,15) (7,18) (7,22) (7,13) (7,17) (7,16) (7,12) (8,10) (8,20) (8,21) (8,11) (8,23) (8,9) (8,14) (8,19) (9,10) (9,20) (9,21) (9,11) (9,23) (9,14) (9,19) (10,20) (10,21) (10,11) (10,23) (10,14) (10,19) (11,20) (11,21) (11,23) (11,14) (11,19) (12,15) (12,18) (12,22) (12,13) (12,17) (12,16) (13,15) (13,18) (13,22) (13,17) (13,16) (14,20) (14,21) (14,23) (14,19) (15,18) (15,22) (15,17) (15,16) (16,18) (16,22) (16,17) (17,18) (17,22) (18,22) (19,20) (19,21) (19,23) (20,21) (20,23) (21,23)\nIs there a path between node 4 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph338-16_5", + "image": "data/connectivity/graph_visual/medium/graph338.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,8) (0,2) (0,7) (0,9) (0,15) (0,18) (1,8) (1,2) (1,9) (1,15) (1,18) (2,8) (2,7) (2,9) (2,18) (3,17) (3,6) (3,5) (3,16) (3,20) (4,13) (4,11) (5,17) (5,14) (5,10) (5,16) (5,20) (6,17) (6,14) (6,20) (7,8) (7,9) (7,15) (7,12) (8,9) (8,15) (8,12) (8,18) (9,15) (9,18) (10,17) (10,14) (10,16) (10,20) (11,13) (12,18) (13,19) (14,17) (15,18) (16,20)\nIs there a path between node 16 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph658-22_7", + "image": "data/connectivity/graph_visual/medium/graph658.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,5) (0,18) (0,14) (0,15) (0,22) (0,3) (0,2) (0,13) (0,8) (1,23) (1,6) (1,10) (2,5) (2,9) (2,18) (2,4) (2,12) (2,15) (2,22) (2,19) (2,3) (2,13) (3,7) (3,5) (3,12) (3,14) (3,20) (3,15) (3,22) (3,16) (3,8) (4,17) (4,7) (4,9) (4,18) (4,12) (4,20) (4,22) (4,19) (4,13) (4,8) (5,17) (5,7) (5,9) (5,18) (5,12) (5,14) (5,20) (5,22) (5,19) (5,16) (5,13) (6,11) (6,23) (6,21) (6,10) (7,17) (7,9) (7,18) (7,12) (7,14) (7,22) (7,13) (7,8) (8,17) (8,9) (8,18) (8,12) (8,14) (8,20) (8,15) (8,22) (8,19) (8,16) (8,13) (9,12) (9,14) (9,20) (9,15) (9,22) (9,16) (10,11) (10,23) (10,21) (11,23) (11,21) (12,18) (12,14) (12,20) (12,15) (12,22) (12,19) (12,16) (13,17) (13,18) (13,14) (13,20) (13,15) (13,19) (14,17) (14,18) (14,20) (14,15) (14,22) (14,19) (14,16) (15,17) (15,20) (15,22) (16,17) (16,18) (16,20) (16,22) (16,19) (17,18) (17,20) (17,22) (17,19) (18,20) (18,19) (19,20) (20,22) (21,23)\nIs there a path between node 22 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph830-11_16", + "image": "data/connectivity/graph_visual/medium/graph830.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,18) (1,15) (1,5) (1,23) (1,10) (1,2) (1,20) (1,6) (1,22) (1,13) (1,21) (2,18) (2,14) (2,24) (2,15) (2,5) (2,23) (2,10) (2,20) (2,22) (2,13) (3,19) (4,17) (4,12) (4,7) (5,14) (5,23) (5,10) (5,22) (5,21) (6,18) (6,14) (6,24) (6,15) (6,10) (6,20) (6,22) (6,13) (6,21) (7,16) (7,11) (7,17) (7,12) (7,9) (9,11) (9,17) (9,12) (10,24) (10,23) (10,20) (10,22) (10,13) (10,21) (11,16) (11,17) (11,12) (12,16) (12,17) (13,18) (13,14) (13,24) (13,15) (13,23) (13,20) (13,22) (13,21) (14,18) (14,24) (14,15) (14,23) (14,20) (14,21) (15,23) (15,22) (15,21) (16,17) (18,24) (18,23) (18,22) (18,21) (20,24) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (23,24)\nIs there a path between node 11 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph397-9_12", + "image": "data/connectivity/graph_visual/medium/graph397.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,6) (0,10) (0,17) (0,4) (0,21) (0,1) (0,2) (0,18) (0,7) (0,19) (0,11) (0,3) (0,5) (0,14) (1,6) (1,10) (1,17) (1,21) (1,16) (1,18) (1,7) (1,8) (1,11) (2,6) (2,10) (2,17) (2,4) (2,21) (2,16) (2,13) (2,18) (2,7) (2,8) (2,19) (2,3) (2,5) (3,6) (3,10) (3,17) (3,4) (3,21) (3,16) (3,13) (3,18) (3,7) (3,19) (4,10) (4,16) (4,18) (4,7) (4,8) (4,19) (4,5) (5,6) (5,16) (5,13) (5,18) (5,7) (5,8) (5,19) (5,14) (6,10) (6,17) (6,21) (6,16) (6,13) (6,18) (6,7) (6,19) (6,11) (6,14) (7,10) (7,17) (7,21) (7,16) (7,13) (7,18) (7,8) (7,19) (7,11) (7,14) (8,10) (8,17) (8,21) (8,16) (8,13) (8,18) (8,19) (8,11) (9,20) (10,17) (10,21) (10,13) (10,18) (10,19) (10,11) (10,14) (11,17) (11,16) (11,13) (11,18) (11,19) (12,15) (13,21) (13,16) (13,18) (13,19) (13,14) (14,17) (14,21) (14,16) (14,18) (14,19) (16,17) (16,21) (16,18) (17,18) (18,21) (18,19) (19,21)\nIs there a path between node 9 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph22-0_2", + "image": "data/connectivity/graph_visual/medium/graph22.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,2) (2,9) (7,11) (10,11)\nIs there a path between node 0 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph476-20_13", + "image": "data/connectivity/graph_visual/medium/graph476.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,17) (0,1) (0,19) (0,11) (1,18) (1,7) (1,2) (1,12) (2,17) (2,14) (2,7) (2,16) (2,11) (2,15) (3,10) (4,13) (4,18) (4,8) (4,12) (5,18) (5,16) (6,20) (6,14) (6,11) (6,15) (7,18) (7,16) (7,22) (8,20) (8,18) (9,21) (11,17) (11,13) (11,19) (11,14) (11,16) (12,13) (12,16) (12,22) (13,19) (13,14) (14,18) (14,22) (15,19) (16,17) (16,20) (17,18) (18,22) (19,20) (20,22)\nIs there a path between node 20 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph840-0_10", + "image": "data/connectivity/graph_visual/medium/graph840.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,3) (0,17) (0,12) (0,18) (0,11) (0,4) (0,16) (0,19) (0,8) (0,24) (0,15) (0,9) (0,1) (0,7) (0,22) (1,10) (1,3) (1,17) (1,12) (1,18) (1,11) (1,4) (1,16) (1,19) (1,8) (1,24) (1,15) (1,9) (1,7) (1,22) (2,23) (2,6) (2,21) (2,14) (2,13) (2,5) (2,20) (3,10) (3,17) (3,12) (3,18) (3,11) (3,4) (3,16) (3,19) (3,8) (3,24) (3,15) (3,9) (3,7) (3,22) (4,10) (4,17) (4,12) (4,18) (4,11) (4,16) (4,19) (4,8) (4,24) (4,15) (4,9) (4,7) (4,22) (5,23) (5,6) (5,21) (5,14) (5,13) (5,20) (6,23) (6,21) (6,14) (6,13) (6,20) (7,10) (7,17) (7,12) (7,18) (7,11) (7,16) (7,19) (7,8) (7,24) (7,15) (7,9) (7,22) (8,10) (8,17) (8,12) (8,18) (8,11) (8,16) (8,19) (8,24) (8,15) (8,9) (8,22) (9,10) (9,17) (9,12) (9,18) (9,11) (9,16) (9,19) (9,24) (9,15) (9,22) (10,17) (10,12) (10,18) (10,11) (10,16) (10,19) (10,24) (10,15) (10,22) (11,17) (11,12) (11,18) (11,16) (11,19) (11,24) (11,15) (11,22) (12,17) (12,18) (12,16) (12,19) (12,24) (12,15) (12,22) (13,23) (13,21) (13,14) (13,20) (14,23) (14,21) (14,20) (15,17) (15,18) (15,16) (15,19) (15,24) (15,22) (16,17) (16,18) (16,19) (16,24) (16,22) (17,18) (17,19) (17,24) (17,22) (18,19) (18,24) (18,22) (19,24) (19,22) (20,23) (20,21) (21,23) (22,24)\nIs there a path between node 0 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph188-12_11", + "image": "data/connectivity/graph_visual/medium/graph188.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,11) (0,1) (0,9) (0,17) (0,3) (0,14) (0,15) (0,4) (0,10) (0,2) (0,6) (1,16) (1,11) (1,9) (1,17) (1,3) (1,14) (1,15) (1,4) (1,10) (1,2) (1,6) (2,16) (2,11) (2,9) (2,17) (2,3) (2,14) (2,15) (2,4) (2,10) (2,6) (3,16) (3,11) (3,9) (3,17) (3,14) (3,15) (3,4) (3,10) (3,6) (4,16) (4,11) (4,9) (4,17) (4,14) (4,15) (4,10) (4,6) (5,8) (5,12) (5,7) (5,13) (6,16) (6,11) (6,9) (6,17) (6,14) (6,15) (6,10) (7,8) (7,12) (7,13) (8,12) (8,13) (9,16) (9,11) (9,17) (9,14) (9,15) (9,10) (10,16) (10,11) (10,17) (10,14) (10,15) (11,16) (11,17) (11,14) (11,15) (12,13) (14,16) (14,17) (14,15) (15,16) (15,17) (16,17)\nIs there a path between node 12 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph64-13_2", + "image": "data/connectivity/graph_visual/medium/graph64.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,8) (0,5) (0,2) (0,3) (0,10) (0,6) (0,1) (0,4) (0,9) (0,7) (0,12) (1,8) (1,5) (1,2) (1,3) (1,10) (1,6) (1,4) (1,9) (1,7) (1,12) (2,8) (2,5) (2,3) (2,10) (2,6) (2,4) (2,9) (2,7) (2,12) (3,8) (3,5) (3,10) (3,6) (3,4) (3,9) (3,7) (3,12) (4,8) (4,5) (4,10) (4,6) (4,9) (4,7) (4,12) (5,8) (5,10) (5,6) (5,9) (5,7) (5,12) (6,8) (6,10) (6,9) (6,7) (6,12) (7,8) (7,10) (7,9) (7,12) (8,10) (8,9) (8,12) (9,10) (9,12) (10,12) (11,13)\nIs there a path between node 13 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph137-2_14", + "image": "data/connectivity/graph_visual/medium/graph137.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,2) (0,13) (1,15) (1,14) (1,13) (2,5) (2,4) (4,15) (4,13) (5,14) (5,9) (5,13) (6,7) (6,12) (9,14) (10,16) (11,16) (12,17)\nIs there a path between node 2 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph686-8_17", + "image": "data/connectivity/graph_visual/medium/graph686.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,18) (1,14) (1,6) (1,16) (1,4) (1,15) (1,19) (1,20) (1,23) (1,7) (1,13) (1,22) (1,9) (1,21) (1,2) (2,14) (2,6) (2,16) (2,4) (2,15) (2,19) (2,20) (2,23) (2,7) (2,13) (2,22) (2,9) (2,21) (3,5) (3,10) (3,12) (3,11) (3,17) (4,14) (4,6) (4,16) (4,15) (4,19) (4,20) (4,23) (4,7) (4,13) (4,22) (4,9) (4,21) (5,10) (5,12) (5,11) (5,17) (6,14) (6,16) (6,15) (6,19) (6,20) (6,23) (6,7) (6,13) (6,22) (6,9) (6,21) (7,14) (7,16) (7,15) (7,19) (7,20) (7,23) (7,13) (7,22) (7,9) (7,21) (8,18) (9,14) (9,16) (9,15) (9,19) (9,20) (9,23) (9,13) (9,22) (9,21) (10,12) (10,11) (10,17) (11,12) (11,17) (12,17) (13,14) (13,16) (13,15) (13,19) (13,20) (13,23) (13,22) (13,21) (14,16) (14,15) (14,19) (14,20) (14,23) (14,22) (14,21) (15,16) (15,19) (15,20) (15,23) (15,22) (15,21) (16,19) (16,20) (16,23) (16,22) (16,21) (19,20) (19,23) (19,22) (19,21) (20,23) (20,22) (20,21) (21,23) (21,22) (22,23)\nIs there a path between node 8 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph374-10_17", + "image": "data/connectivity/graph_visual/medium/graph374.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,4) (0,12) (0,11) (1,14) (1,7) (1,15) (1,3) (1,20) (1,8) (1,5) (2,14) (2,7) (2,19) (2,10) (2,3) (2,20) (2,8) (2,5) (2,13) (2,16) (3,14) (3,7) (3,19) (3,10) (3,8) (3,5) (3,13) (3,16) (4,9) (4,11) (5,14) (5,7) (5,19) (5,10) (5,20) (5,8) (5,13) (7,14) (7,19) (7,8) (7,13) (7,17) (8,14) (8,19) (8,10) (8,15) (8,20) (8,16) (8,17) (9,12) (9,11) (10,19) (10,15) (10,13) (10,16) (11,12) (13,14) (13,15) (13,20) (13,16) (13,17) (14,19) (14,15) (14,20) (14,17) (15,20) (15,16) (15,17) (16,20) (16,17) (17,19) (19,20)\nIs there a path between node 10 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph194-7_16", + "image": "data/connectivity/graph_visual/medium/graph194.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,11) (0,16) (0,13) (0,8) (0,1) (0,15) (0,3) (0,14) (0,9) (1,11) (1,16) (1,13) (1,8) (1,15) (1,3) (1,14) (1,9) (2,7) (2,6) (2,4) (2,5) (2,17) (2,12) (3,11) (3,16) (3,13) (3,8) (3,15) (3,14) (3,9) (4,7) (4,6) (4,5) (4,17) (4,12) (5,7) (5,6) (5,17) (5,12) (6,7) (6,17) (6,12) (7,17) (7,12) (8,11) (8,16) (8,13) (8,15) (8,14) (8,9) (9,11) (9,16) (9,13) (9,15) (9,14) (11,16) (11,13) (11,15) (11,14) (12,17) (13,16) (13,15) (13,14) (14,16) (14,15) (15,16)\nIs there a path between node 7 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph359-2_13", + "image": "data/connectivity/graph_visual/medium/graph359.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,8) (0,7) (0,18) (0,5) (0,2) (0,1) (1,11) (1,17) (2,20) (2,9) (3,11) (3,18) (3,20) (3,12) (4,14) (6,19) (6,16) (6,8) (6,15) (6,12) (6,9) (7,15) (7,12) (7,17) (8,18) (9,17) (11,16) (11,15) (12,19) (12,17) (15,19) (15,20) (16,19) (16,18) (16,17)\nIs there a path between node 2 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph846-6_21", + "image": "data/connectivity/graph_visual/medium/graph846.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,17) (0,7) (0,21) (0,19) (0,6) (0,11) (0,5) (1,15) (1,20) (1,2) (1,4) (1,14) (1,16) (1,3) (1,22) (1,12) (1,24) (1,18) (1,9) (1,13) (1,23) (1,8) (2,15) (2,20) (2,4) (2,14) (2,16) (2,3) (2,22) (2,12) (2,24) (2,18) (2,9) (2,13) (2,23) (2,8) (3,15) (3,20) (3,4) (3,14) (3,16) (3,22) (3,12) (3,24) (3,18) (3,9) (3,13) (3,23) (3,8) (4,15) (4,20) (4,14) (4,16) (4,22) (4,12) (4,24) (4,18) (4,9) (4,13) (4,23) (4,8) (5,10) (5,17) (5,7) (5,21) (5,19) (5,6) (5,11) (6,10) (6,17) (6,7) (6,21) (6,19) (6,11) (7,10) (7,17) (7,21) (7,19) (7,11) (8,15) (8,20) (8,14) (8,16) (8,22) (8,12) (8,24) (8,18) (8,9) (8,13) (8,23) (9,15) (9,20) (9,14) (9,16) (9,22) (9,12) (9,24) (9,18) (9,13) (9,23) (10,17) (10,21) (10,19) (10,11) (11,17) (11,21) (11,19) (12,15) (12,20) (12,14) (12,16) (12,22) (12,24) (12,18) (12,13) (12,23) (13,15) (13,20) (13,14) (13,16) (13,22) (13,24) (13,18) (13,23) (14,15) (14,20) (14,16) (14,22) (14,24) (14,18) (14,23) (15,20) (15,16) (15,22) (15,24) (15,18) (15,23) (16,20) (16,22) (16,24) (16,18) (16,23) (17,21) (17,19) (18,20) (18,22) (18,24) (18,23) (19,21) (20,22) (20,24) (20,23) (22,24) (22,23) (23,24)\nIs there a path between node 6 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph369-13_11", + "image": "data/connectivity/graph_visual/medium/graph369.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (1,2) (1,16) (1,19) (1,10) (1,13) (1,18) (1,14) (1,20) (1,5) (1,4) (1,15) (1,6) (1,8) (1,12) (2,16) (2,19) (2,7) (2,9) (2,18) (2,11) (2,14) (2,20) (2,5) (2,6) (2,12) (3,17) (4,16) (4,19) (4,10) (4,7) (4,9) (4,13) (4,14) (4,15) (4,6) (4,8) (4,12) (5,19) (5,10) (5,7) (5,9) (5,13) (5,18) (5,14) (5,20) (5,15) (5,6) (5,8) (5,12) (6,16) (6,19) (6,10) (6,13) (6,18) (6,15) (6,8) (6,12) (7,16) (7,19) (7,9) (7,13) (7,18) (7,14) (7,20) (7,15) (8,16) (8,19) (8,9) (8,13) (8,18) (8,14) (8,15) (8,12) (9,16) (9,10) (9,13) (9,18) (9,11) (9,20) (10,16) (10,19) (10,13) (10,11) (10,14) (10,20) (10,15) (10,12) (11,13) (11,18) (11,14) (11,20) (11,15) (12,16) (12,14) (12,20) (12,15) (13,16) (13,19) (13,18) (13,14) (13,20) (13,15) (14,19) (14,20) (15,16) (15,19) (15,18) (15,20) (16,19) (16,20) (18,20) (19,20)\nIs there a path between node 13 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph47-8_2", + "image": "data/connectivity/graph_visual/medium/graph47.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,12) (0,7) (0,10) (0,8) (0,9) (0,2) (0,4) (0,3) (1,5) (1,6) (1,11) (2,12) (2,7) (2,10) (2,8) (2,9) (2,4) (2,3) (3,12) (3,7) (3,10) (3,8) (3,9) (3,4) (4,12) (4,7) (4,10) (4,8) (4,9) (5,6) (5,11) (6,11) (7,12) (7,10) (7,8) (7,9) (8,12) (8,10) (8,9) (9,12) (9,10) (10,12)\nIs there a path between node 8 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph668-22_20", + "image": "data/connectivity/graph_visual/medium/graph668.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (0,7) (0,10) (1,21) (1,13) (1,22) (1,11) (1,12) (1,15) (1,6) (2,18) (2,19) (2,13) (2,11) (2,12) (2,15) (3,17) (3,10) (4,23) (4,8) (4,5) (4,20) (5,14) (5,9) (5,20) (6,19) (6,21) (6,13) (6,22) (6,12) (6,15) (7,10) (8,23) (8,14) (9,14) (9,20) (10,17) (11,18) (11,21) (11,13) (11,12) (11,15) (12,18) (12,19) (12,21) (12,13) (12,22) (12,15) (13,18) (13,21) (13,22) (13,15) (14,23) (15,18) (15,19) (15,21) (18,19) (18,22) (19,21) (20,23) (21,22)\nIs there a path between node 22 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph734-9_15", + "image": "data/connectivity/graph_visual/medium/graph734.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,8) (0,14) (0,10) (1,21) (1,22) (1,17) (1,12) (2,23) (2,3) (3,23) (3,10) (3,15) (4,23) (4,10) (4,15) (4,11) (5,16) (5,17) (6,21) (6,13) (6,17) (6,12) (7,9) (7,22) (7,18) (8,20) (8,15) (8,11) (9,24) (9,17) (9,12) (12,19) (12,17) (13,21) (13,22) (15,23) (16,24) (16,22) (16,17) (17,24) (17,21) (17,18) (21,22) (22,24)\nIs there a path between node 9 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph29-0_9", + "image": "data/connectivity/graph_visual/medium/graph29.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,9) (0,11) (1,6) (1,3) (1,4) (1,7) (1,8) (1,10) (1,2) (1,5) (2,6) (2,3) (2,4) (2,7) (2,8) (2,10) (2,5) (3,6) (3,4) (3,7) (3,8) (3,10) (3,5) (4,6) (4,7) (4,8) (4,10) (4,5) (5,6) (5,7) (5,8) (5,10) (6,7) (6,8) (6,10) (7,8) (7,10) (8,10) (9,11)\nIs there a path between node 0 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph559-22_23", + "image": "data/connectivity/graph_visual/medium/graph559.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,23) (0,20) (0,17) (0,3) (0,6) (0,5) (0,9) (0,7) (0,13) (0,4) (0,2) (0,1) (1,8) (1,16) (1,23) (1,20) (1,3) (1,6) (1,5) (1,9) (1,14) (1,7) (1,13) (2,18) (2,8) (2,16) (2,20) (2,3) (2,10) (2,5) (2,9) (2,12) (2,14) (2,4) (3,18) (3,8) (3,16) (3,6) (3,5) (3,9) (3,12) (3,14) (3,13) (4,18) (4,8) (4,16) (4,6) (4,10) (4,5) (4,9) (4,12) (4,7) (4,13) (5,8) (5,17) (5,10) (5,9) (5,12) (5,14) (5,7) (5,13) (6,8) (6,16) (6,20) (6,10) (6,12) (6,14) (6,7) (7,8) (7,16) (7,23) (7,17) (7,10) (7,9) (7,12) (7,13) (8,18) (8,17) (8,10) (8,9) (8,12) (8,14) (8,13) (9,18) (9,16) (9,12) (9,14) (9,13) (10,18) (10,23) (10,20) (10,17) (10,12) (10,13) (11,22) (12,23) (12,20) (12,17) (13,18) (13,16) (13,23) (13,20) (13,14) (14,18) (14,16) (14,23) (14,17) (15,19) (15,21) (15,22) (16,18) (16,23) (16,20) (16,17) (17,18) (17,20) (18,20) (19,21) (20,23) (21,22)\nIs there a path between node 22 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph43-10_8", + "image": "data/connectivity/graph_visual/medium/graph43.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,11) (0,3) (0,10) (1,4) (1,9) (1,6) (2,10) (3,5) (3,10) (4,7) (4,9) (4,6) (4,12) (5,10) (6,7) (6,12) (7,9) (8,9) (8,12) (9,12) (10,11)\nIs there a path between node 10 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph607-0_13", + "image": "data/connectivity/graph_visual/medium/graph607.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,11) (0,8) (0,17) (0,13) (0,6) (0,3) (0,15) (0,7) (1,14) (1,19) (1,9) (1,21) (1,12) (1,22) (1,4) (1,18) (1,5) (1,10) (1,20) (2,16) (3,23) (3,11) (3,8) (3,17) (3,13) (3,6) (3,15) (3,7) (4,14) (4,19) (4,9) (4,21) (4,12) (4,22) (4,18) (4,5) (4,10) (4,20) (5,14) (5,19) (5,9) (5,21) (5,12) (5,22) (5,18) (5,10) (5,20) (6,23) (6,11) (6,8) (6,17) (6,13) (6,15) (6,7) (7,23) (7,11) (7,8) (7,17) (7,13) (7,15) (8,23) (8,11) (8,17) (8,13) (8,15) (9,14) (9,19) (9,21) (9,12) (9,22) (9,18) (9,10) (9,20) (10,14) (10,19) (10,21) (10,12) (10,22) (10,18) (10,20) (11,23) (11,17) (11,13) (11,15) (12,14) (12,19) (12,21) (12,22) (12,18) (12,20) (13,23) (13,17) (13,15) (14,19) (14,21) (14,22) (14,18) (14,20) (15,23) (15,17) (17,23) (18,19) (18,21) (18,22) (18,20) (19,21) (19,22) (19,20) (20,21) (20,22) (21,22)\nIs there a path between node 0 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph854-16_22", + "image": "data/connectivity/graph_visual/medium/graph854.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,13) (0,4) (0,2) (0,9) (0,12) (0,7) (0,8) (0,15) (0,1) (0,24) (1,23) (1,13) (1,4) (1,2) (1,9) (1,12) (1,7) (1,8) (1,15) (1,24) (2,23) (2,13) (2,4) (2,9) (2,12) (2,7) (2,8) (2,15) (2,24) (3,11) (3,17) (3,14) (3,6) (3,10) (3,19) (3,18) (4,23) (4,13) (4,9) (4,12) (4,7) (4,8) (4,15) (4,24) (5,21) (5,16) (5,22) (6,11) (6,17) (6,14) (6,10) (6,19) (6,18) (7,23) (7,13) (7,9) (7,12) (7,8) (7,15) (7,24) (8,23) (8,13) (8,9) (8,12) (8,15) (8,24) (9,23) (9,13) (9,12) (9,15) (9,24) (10,11) (10,17) (10,14) (10,19) (10,18) (11,17) (11,14) (11,19) (11,18) (12,23) (12,13) (12,15) (12,24) (13,23) (13,15) (13,24) (14,17) (14,19) (14,18) (15,23) (15,24) (16,21) (16,22) (17,19) (17,18) (18,19) (21,22) (23,24)\nIs there a path between node 16 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph566-21_8", + "image": "data/connectivity/graph_visual/medium/graph566.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (0,9) (0,15) (0,23) (0,4) (0,22) (0,8) (0,7) (0,16) (0,19) (0,3) (0,21) (0,17) (1,6) (1,10) (1,12) (1,2) (1,18) (1,11) (1,14) (1,20) (1,5) (2,6) (2,10) (2,12) (2,18) (2,11) (2,14) (2,20) (2,5) (3,13) (3,9) (3,15) (3,23) (3,4) (3,22) (3,8) (3,7) (3,16) (3,19) (3,21) (3,17) (4,13) (4,9) (4,15) (4,23) (4,22) (4,8) (4,7) (4,16) (4,19) (4,21) (4,17) (5,6) (5,10) (5,12) (5,18) (5,11) (5,14) (5,20) (6,10) (6,12) (6,18) (6,11) (6,14) (6,20) (7,13) (7,9) (7,15) (7,23) (7,22) (7,8) (7,16) (7,19) (7,21) (7,17) (8,13) (8,9) (8,15) (8,23) (8,22) (8,16) (8,19) (8,21) (8,17) (9,13) (9,15) (9,23) (9,22) (9,16) (9,19) (9,21) (9,17) (10,12) (10,18) (10,11) (10,14) (10,20) (11,12) (11,18) (11,14) (11,20) (12,18) (12,14) (12,20) (13,15) (13,23) (13,22) (13,16) (13,19) (13,21) (13,17) (14,18) (14,20) (15,23) (15,22) (15,16) (15,19) (15,21) (15,17) (16,23) (16,22) (16,19) (16,21) (16,17) (17,23) (17,22) (17,19) (17,21) (18,20) (19,23) (19,22) (19,21) (21,23) (21,22) (22,23)\nIs there a path between node 21 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph215-14_4", + "image": "data/connectivity/graph_visual/medium/graph215.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,18) (0,17) (0,8) (0,14) (0,7) (0,6) (0,16) (0,13) (0,5) (1,2) (1,12) (1,4) (1,10) (1,11) (1,9) (1,3) (2,12) (2,4) (2,10) (2,11) (2,9) (2,3) (3,12) (3,4) (3,10) (3,11) (3,9) (4,12) (4,10) (4,11) (4,9) (5,18) (5,17) (5,8) (5,14) (5,7) (5,6) (5,16) (5,13) (6,18) (6,17) (6,8) (6,14) (6,7) (6,16) (6,13) (7,18) (7,17) (7,8) (7,14) (7,16) (7,13) (8,18) (8,17) (8,14) (8,16) (8,13) (9,12) (9,10) (9,11) (10,12) (10,11) (11,12) (13,18) (13,17) (13,14) (13,16) (14,18) (14,17) (14,16) (16,18) (16,17) (17,18)\nIs there a path between node 14 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph269-2_19", + "image": "data/connectivity/graph_visual/medium/graph269.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,5) (0,8) (0,10) (0,4) (1,9) (1,18) (2,7) (2,16) (2,12) (2,3) (2,15) (2,19) (3,6) (3,16) (4,17) (4,5) (4,8) (4,14) (5,17) (5,14) (6,16) (7,16) (7,12) (7,15) (7,19) (8,14) (9,11) (9,13) (10,17) (10,14) (11,18) (11,13) (12,16) (12,15) (15,16) (15,19) (16,19)\nIs there a path between node 2 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph645-9_20", + "image": "data/connectivity/graph_visual/medium/graph645.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,5) (4,19) (4,5) (6,23) (8,9) (8,20) (8,23) (8,22) (8,13) (8,10) (9,15) (9,20) (9,23) (9,22) (9,13) (9,11) (10,23) (10,22) (10,12) (10,11) (10,14) (11,23) (12,15) (12,20) (12,23) (12,16) (13,15) (13,23) (14,18) (14,16) (15,21) (15,22) (15,16) (16,20) (16,21) (20,22) (21,23) (21,22)\nIs there a path between node 9 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph787-6_16", + "image": "data/connectivity/graph_visual/medium/graph787.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (0,14) (0,16) (0,1) (0,15) (0,13) (1,10) (1,22) (1,17) (1,16) (2,14) (4,24) (4,19) (4,14) (4,16) (4,8) (5,11) (5,19) (6,7) (6,18) (7,18) (7,12) (8,24) (8,21) (10,20) (10,24) (10,19) (10,14) (10,21) (10,17) (10,16) (10,13) (11,20) (11,14) (13,20) (13,24) (13,19) (13,15) (14,22) (14,16) (15,20) (15,24) (15,17) (16,20) (16,17) (17,20) (19,22) (20,22) (21,24) (22,24)\nIs there a path between node 6 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph794-19_16", + "image": "data/connectivity/graph_visual/medium/graph794.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,13) (0,15) (1,17) (1,18) (1,7) (2,14) (2,6) (2,15) (2,10) (4,6) (4,15) (4,5) (5,13) (5,21) (5,23) (5,24) (6,13) (6,21) (6,23) (7,17) (10,23) (11,16) (11,18) (12,21) (13,23) (15,24) (21,24) (23,24)\nIs there a path between node 19 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph264-6_16", + "image": "data/connectivity/graph_visual/medium/graph264.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,7) (0,18) (0,16) (1,4) (1,2) (1,13) (1,11) (1,7) (2,19) (2,15) (2,3) (2,7) (2,18) (3,19) (3,17) (3,13) (3,14) (3,18) (3,16) (4,17) (4,11) (4,5) (5,17) (5,15) (5,13) (5,14) (5,11) (5,7) (5,18) (5,12) (5,16) (6,10) (7,19) (7,8) (7,14) (7,12) (8,17) (8,13) (8,14) (8,12) (11,18) (11,12) (12,13) (13,19) (13,15) (13,14) (13,18) (15,17) (16,19) (16,18) (17,19) (18,19)\nIs there a path between node 6 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph827-24_8", + "image": "data/connectivity/graph_visual/medium/graph827.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,23) (0,22) (1,9) (1,24) (1,11) (1,13) (1,8) (1,20) (1,5) (1,4) (1,21) (1,16) (1,3) (1,19) (1,10) (1,18) (1,2) (2,9) (2,24) (2,11) (2,14) (2,8) (2,20) (2,5) (2,21) (2,6) (2,16) (2,3) (2,19) (2,12) (2,10) (2,18) (3,9) (3,11) (3,14) (3,8) (3,5) (3,21) (3,6) (3,16) (3,19) (3,12) (3,10) (3,18) (4,9) (4,11) (4,13) (4,14) (4,20) (4,5) (4,21) (4,16) (4,19) (4,12) (4,18) (5,9) (5,11) (5,13) (5,8) (5,20) (5,21) (5,6) (5,16) (5,12) (5,10) (5,18) (6,9) (6,24) (6,11) (6,13) (6,14) (6,20) (6,16) (6,19) (6,10) (6,18) (7,23) (7,15) (8,9) (8,24) (8,11) (8,13) (8,14) (8,20) (8,21) (8,16) (8,10) (8,18) (9,24) (9,11) (9,14) (9,20) (9,21) (9,16) (9,19) (9,10) (9,18) (10,24) (10,11) (10,14) (10,20) (10,16) (10,19) (10,12) (10,18) (11,13) (11,14) (11,20) (11,21) (11,16) (11,12) (11,18) (12,24) (12,13) (12,14) (12,20) (12,21) (12,16) (12,19) (12,18) (13,24) (13,14) (13,21) (13,16) (13,18) (14,24) (14,21) (14,19) (14,18) (15,22) (15,17) (16,24) (16,19) (16,18) (17,23) (17,22) (18,24) (18,19) (19,24) (19,21) (20,24) (20,21) (21,24)\nIs there a path between node 24 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph339-0_2", + "image": "data/connectivity/graph_visual/medium/graph339.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (0,12) (0,18) (0,5) (0,16) (0,10) (0,2) (0,11) (1,17) (1,12) (1,18) (1,4) (1,5) (1,16) (1,10) (1,11) (2,17) (2,12) (2,18) (2,4) (2,5) (2,10) (2,11) (3,15) (3,13) (3,6) (3,20) (3,7) (3,19) (3,8) (3,14) (4,17) (4,12) (4,18) (4,10) (5,17) (5,12) (5,16) (5,10) (5,11) (6,15) (6,20) (6,7) (6,14) (6,9) (7,15) (7,13) (7,20) (7,19) (7,8) (8,15) (8,13) (8,19) (8,9) (9,15) (9,13) (9,19) (9,14) (10,17) (10,12) (10,18) (10,11) (11,17) (12,17) (12,18) (13,19) (13,14) (14,20) (14,19) (15,20) (15,19) (16,17) (16,18) (19,20)\nIs there a path between node 0 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph549-10_3", + "image": "data/connectivity/graph_visual/medium/graph549.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (1,10) (2,11) (2,9) (3,21) (4,10) (4,23) (5,7) (5,9) (7,11) (7,9) (8,18) (8,17) (10,22) (13,19) (14,16) (15,19) (16,17) (17,19)\nIs there a path between node 10 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph340-11_0", + "image": "data/connectivity/graph_visual/medium/graph340.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,9) (0,11) (0,6) (0,14) (0,8) (0,19) (0,16) (0,4) (0,13) (0,17) (0,15) (1,9) (1,5) (1,14) (1,8) (1,16) (1,12) (1,13) (1,17) (1,15) (2,9) (2,11) (2,6) (2,20) (2,5) (2,14) (2,16) (2,4) (2,17) (2,15) (3,18) (4,9) (4,11) (4,6) (4,5) (4,14) (4,8) (4,19) (4,16) (4,12) (5,11) (5,6) (5,20) (5,8) (5,17) (5,15) (6,9) (6,20) (6,14) (6,8) (6,19) (6,16) (6,12) (6,13) (6,17) (6,15) (8,11) (8,20) (8,14) (8,19) (8,16) (8,12) (8,13) (8,17) (8,15) (9,11) (9,20) (9,14) (9,19) (9,16) (9,13) (9,17) (9,15) (11,20) (11,16) (11,13) (11,17) (11,15) (12,20) (12,14) (12,19) (12,13) (12,17) (12,15) (13,20) (13,14) (13,19) (13,17) (13,15) (14,19) (14,16) (14,17) (15,20) (15,19) (15,17) (16,19) (16,17) (17,19) (19,20)\nIs there a path between node 11 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph495-7_3", + "image": "data/connectivity/graph_visual/medium/graph495.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,14) (1,21) (1,3) (1,15) (1,7) (3,12) (4,10) (5,10) (6,22) (7,21) (7,15) (9,12) (11,13) (11,21) (14,20) (15,17) (15,21) (16,18) (18,22)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph173-14_15", + "image": "data/connectivity/graph_visual/medium/graph173.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,7) (0,17) (0,11) (0,15) (0,12) (0,4) (0,14) (0,8) (0,16) (0,5) (1,7) (1,11) (1,15) (1,2) (1,9) (1,12) (1,14) (1,13) (1,5) (2,7) (2,11) (2,15) (2,9) (2,12) (2,4) (2,14) (2,13) (2,8) (2,16) (2,5) (4,7) (4,12) (5,17) (5,11) (5,15) (5,12) (5,13) (5,16) (6,10) (7,17) (7,11) (7,12) (7,14) (7,8) (8,11) (8,13) (8,16) (9,17) (9,11) (9,15) (9,12) (9,13) (9,16) (11,15) (11,12) (11,14) (11,13) (11,16) (12,17) (12,15) (12,14) (12,16) (13,17) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 14 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph288-2_0", + "image": "data/connectivity/graph_visual/medium/graph288.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,7) (0,19) (0,16) (1,18) (3,4) (3,14) (3,15) (3,16) (4,15) (4,16) (4,13) (6,19) (6,14) (7,17) (7,12) (8,17) (8,16) (8,13) (9,16) (9,13) (10,19) (10,14) (12,14) (12,13) (13,19) (13,14) (13,15) (14,15) (15,17) (17,19)\nIs there a path between node 2 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph841-12_5", + "image": "data/connectivity/graph_visual/medium/graph841.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,2) (0,7) (0,8) (0,4) (0,13) (1,6) (1,12) (1,14) (1,17) (1,16) (1,10) (1,18) (1,21) (1,15) (1,24) (1,11) (1,22) (1,9) (1,23) (2,20) (2,7) (2,8) (2,4) (2,13) (3,19) (3,5) (4,20) (4,7) (4,8) (4,13) (5,19) (6,12) (6,14) (6,17) (6,16) (6,10) (6,18) (6,21) (6,15) (6,24) (6,11) (6,22) (6,9) (6,23) (7,20) (7,8) (7,13) (8,20) (8,13) (9,12) (9,14) (9,17) (9,16) (9,10) (9,18) (9,21) (9,15) (9,24) (9,11) (9,22) (9,23) (10,12) (10,14) (10,17) (10,16) (10,18) (10,21) (10,15) (10,24) (10,11) (10,22) (10,23) (11,12) (11,14) (11,17) (11,16) (11,18) (11,21) (11,15) (11,24) (11,22) (11,23) (12,14) (12,17) (12,16) (12,18) (12,21) (12,15) (12,24) (12,22) (12,23) (13,20) (14,17) (14,16) (14,18) (14,21) (14,15) (14,24) (14,22) (14,23) (15,17) (15,16) (15,18) (15,21) (15,24) (15,22) (15,23) (16,17) (16,18) (16,21) (16,24) (16,22) (16,23) (17,18) (17,21) (17,24) (17,22) (17,23) (18,21) (18,24) (18,22) (18,23) (21,24) (21,22) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 12 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph682-4_6", + "image": "data/connectivity/graph_visual/medium/graph682.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,21) (0,6) (0,16) (0,3) (0,10) (0,12) (0,22) (0,19) (0,13) (0,18) (0,17) (0,7) (0,2) (0,14) (0,5) (0,23) (1,20) (1,9) (2,8) (2,21) (2,6) (2,16) (2,3) (2,10) (2,12) (2,22) (2,19) (2,13) (2,18) (2,17) (2,7) (2,14) (2,5) (2,23) (3,8) (3,21) (3,6) (3,16) (3,10) (3,12) (3,22) (3,19) (3,13) (3,18) (3,17) (3,7) (3,14) (3,5) (3,23) (4,15) (4,11) (5,8) (5,21) (5,6) (5,16) (5,10) (5,12) (5,22) (5,19) (5,13) (5,18) (5,17) (5,7) (5,14) (5,23) (6,8) (6,21) (6,16) (6,10) (6,12) (6,22) (6,19) (6,13) (6,18) (6,17) (6,7) (6,14) (6,23) (7,8) (7,21) (7,16) (7,10) (7,12) (7,22) (7,19) (7,13) (7,18) (7,17) (7,14) (7,23) (8,21) (8,16) (8,10) (8,12) (8,22) (8,19) (8,13) (8,18) (8,17) (8,14) (8,23) (9,20) (10,21) (10,16) (10,12) (10,22) (10,19) (10,13) (10,18) (10,17) (10,14) (10,23) (11,15) (12,21) (12,16) (12,22) (12,19) (12,13) (12,18) (12,17) (12,14) (12,23) (13,21) (13,16) (13,22) (13,19) (13,18) (13,17) (13,14) (13,23) (14,21) (14,16) (14,22) (14,19) (14,18) (14,17) (14,23) (16,21) (16,22) (16,19) (16,18) (16,17) (16,23) (17,21) (17,22) (17,19) (17,18) (17,23) (18,21) (18,22) (18,19) (18,23) (19,21) (19,22) (19,23) (21,22) (21,23) (22,23)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph683-11_12", + "image": "data/connectivity/graph_visual/medium/graph683.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (1,22) (1,14) (1,5) (1,9) (1,13) (1,16) (1,17) (1,12) (1,19) (1,3) (1,8) (1,10) (1,23) (1,15) (1,18) (1,7) (1,20) (2,21) (2,11) (3,22) (3,14) (3,5) (3,9) (3,13) (3,16) (3,17) (3,12) (3,19) (3,8) (3,10) (3,23) (3,15) (3,18) (3,7) (3,20) (5,22) (5,14) (5,9) (5,13) (5,16) (5,17) (5,12) (5,19) (5,8) (5,10) (5,23) (5,15) (5,18) (5,7) (5,20) (7,22) (7,14) (7,9) (7,13) (7,16) (7,17) (7,12) (7,19) (7,8) (7,10) (7,23) (7,15) (7,18) (7,20) (8,22) (8,14) (8,9) (8,13) (8,16) (8,17) (8,12) (8,19) (8,10) (8,23) (8,15) (8,18) (8,20) (9,22) (9,14) (9,13) (9,16) (9,17) (9,12) (9,19) (9,10) (9,23) (9,15) (9,18) (9,20) (10,22) (10,14) (10,13) (10,16) (10,17) (10,12) (10,19) (10,23) (10,15) (10,18) (10,20) (11,21) (12,22) (12,14) (12,13) (12,16) (12,17) (12,19) (12,23) (12,15) (12,18) (12,20) (13,22) (13,14) (13,16) (13,17) (13,19) (13,23) (13,15) (13,18) (13,20) (14,22) (14,16) (14,17) (14,19) (14,23) (14,15) (14,18) (14,20) (15,22) (15,16) (15,17) (15,19) (15,23) (15,18) (15,20) (16,22) (16,17) (16,19) (16,23) (16,18) (16,20) (17,22) (17,19) (17,23) (17,18) (17,20) (18,22) (18,19) (18,23) (18,20) (19,22) (19,23) (19,20) (20,22) (20,23) (22,23)\nIs there a path between node 11 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph582-4_2", + "image": "data/connectivity/graph_visual/medium/graph582.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,19) (1,7) (1,14) (1,11) (1,2) (1,17) (2,4) (3,7) (3,14) (3,19) (3,4) (4,7) (4,5) (4,8) (4,19) (4,17) (5,11) (7,13) (7,17) (8,11) (8,17) (9,22) (9,21) (9,10) (11,19) (14,19) (15,22) (18,20)\nIs there a path between node 4 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph28-6_0", + "image": "data/connectivity/graph_visual/medium/graph28.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,1) (0,4) (0,3) (0,6) (0,2) (0,8) (0,5) (0,11) (1,4) (1,3) (1,6) (1,2) (1,8) (1,5) (1,11) (2,4) (2,3) (2,6) (2,8) (2,5) (2,11) (3,4) (3,6) (3,8) (3,5) (3,11) (4,6) (4,8) (4,5) (4,11) (5,6) (5,8) (5,11) (6,8) (6,11) (7,9) (7,10) (8,11) (9,10)\nIs there a path between node 6 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph374-6_0", + "image": "data/connectivity/graph_visual/medium/graph374.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,4) (0,12) (0,11) (1,14) (1,7) (1,15) (1,3) (1,20) (1,8) (1,5) (2,14) (2,7) (2,19) (2,10) (2,3) (2,20) (2,8) (2,5) (2,13) (2,16) (3,14) (3,7) (3,19) (3,10) (3,8) (3,5) (3,13) (3,16) (4,9) (4,11) (5,14) (5,7) (5,19) (5,10) (5,20) (5,8) (5,13) (7,14) (7,19) (7,8) (7,13) (7,17) (8,14) (8,19) (8,10) (8,15) (8,20) (8,16) (8,17) (9,12) (9,11) (10,19) (10,15) (10,13) (10,16) (11,12) (13,14) (13,15) (13,20) (13,16) (13,17) (14,19) (14,15) (14,20) (14,17) (15,20) (15,16) (15,17) (16,20) (16,17) (17,19) (19,20)\nIs there a path between node 6 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph146-3_14", + "image": "data/connectivity/graph_visual/medium/graph146.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,2) (0,7) (0,3) (0,14) (0,4) (0,9) (0,5) (0,16) (1,8) (1,10) (2,12) (2,17) (2,14) (2,11) (2,9) (2,16) (3,12) (3,17) (3,14) (3,11) (3,4) (3,9) (3,5) (3,16) (4,7) (4,14) (4,11) (4,9) (5,12) (5,7) (5,14) (5,16) (6,8) (6,10) (7,14) (7,11) (7,9) (7,16) (8,10) (9,12) (9,17) (9,11) (11,16) (12,17) (12,14) (12,16) (13,15) (14,17) (14,16) (16,17)\nIs there a path between node 3 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph118-0_7", + "image": "data/connectivity/graph_visual/medium/graph118.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,4) (1,3) (1,7) (1,13) (1,6) (1,10) (2,12) (2,8) (3,8) (3,11) (3,6) (3,10) (5,12) (5,15) (5,9) (7,16) (7,13) (7,8) (8,15) (8,16) (8,9) (9,15) (9,13) (10,12) (11,14) (11,12) (11,13) (12,15) (13,14) (14,16)\nIs there a path between node 0 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph535-20_7", + "image": "data/connectivity/graph_visual/medium/graph535.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,3) (0,7) (0,4) (0,18) (0,13) (0,2) (0,12) (0,10) (0,11) (0,9) (0,5) (0,20) (0,22) (0,19) (0,6) (0,8) (0,14) (1,17) (1,15) (1,16) (2,21) (2,3) (2,7) (2,4) (2,18) (2,13) (2,12) (2,10) (2,11) (2,9) (2,5) (2,20) (2,22) (2,19) (2,6) (2,8) (2,14) (3,21) (3,7) (3,4) (3,18) (3,13) (3,12) (3,10) (3,11) (3,9) (3,5) (3,20) (3,22) (3,19) (3,6) (3,8) (3,14) (4,21) (4,7) (4,18) (4,13) (4,12) (4,10) (4,11) (4,9) (4,5) (4,20) (4,22) (4,19) (4,6) (4,8) (4,14) (5,21) (5,7) (5,18) (5,13) (5,12) (5,10) (5,11) (5,9) (5,20) (5,22) (5,19) (5,6) (5,8) (5,14) (6,21) (6,7) (6,18) (6,13) (6,12) (6,10) (6,11) (6,9) (6,20) (6,22) (6,19) (6,8) (6,14) (7,21) (7,18) (7,13) (7,12) (7,10) (7,11) (7,9) (7,20) (7,22) (7,19) (7,8) (7,14) (8,21) (8,18) (8,13) (8,12) (8,10) (8,11) (8,9) (8,20) (8,22) (8,19) (8,14) (9,21) (9,18) (9,13) (9,12) (9,10) (9,11) (9,20) (9,22) (9,19) (9,14) (10,21) (10,18) (10,13) (10,12) (10,11) (10,20) (10,22) (10,19) (10,14) (11,21) (11,18) (11,13) (11,12) (11,20) (11,22) (11,19) (11,14) (12,21) (12,18) (12,13) (12,20) (12,22) (12,19) (12,14) (13,21) (13,18) (13,20) (13,22) (13,19) (13,14) (14,21) (14,18) (14,20) (14,22) (14,19) (15,17) (15,16) (16,17) (18,21) (18,20) (18,22) (18,19) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 20 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph648-9_0", + "image": "data/connectivity/graph_visual/medium/graph648.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,18) (0,10) (0,20) (0,19) (1,7) (1,11) (1,20) (1,19) (3,13) (3,7) (3,8) (3,18) (3,10) (3,5) (3,20) (4,13) (4,8) (4,5) (4,19) (5,13) (5,6) (5,8) (5,21) (6,13) (6,14) (7,13) (7,12) (7,14) (9,22) (9,16) (9,17) (10,12) (10,11) (10,14) (12,20) (12,14) (13,14) (15,22) (18,20) (19,20)\nIs there a path between node 9 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph656-8_17", + "image": "data/connectivity/graph_visual/medium/graph656.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,19) (0,4) (0,17) (0,16) (0,22) (0,20) (0,18) (0,10) (0,21) (0,7) (0,8) (0,9) (0,15) (0,14) (1,3) (1,13) (1,6) (1,4) (1,16) (1,22) (1,20) (1,10) (1,21) (1,5) (1,7) (1,9) (1,15) (1,14) (2,11) (3,13) (3,6) (3,19) (3,4) (3,17) (3,16) (3,22) (3,20) (3,18) (3,10) (3,5) (3,7) (3,23) (3,8) (3,14) (4,13) (4,19) (4,17) (4,20) (4,18) (4,10) (4,5) (4,7) (4,23) (4,8) (4,15) (4,14) (5,13) (5,6) (5,19) (5,17) (5,16) (5,22) (5,20) (5,10) (5,23) (5,9) (5,14) (6,13) (6,17) (6,22) (6,18) (6,10) (6,21) (6,7) (6,23) (6,15) (6,14) (7,13) (7,19) (7,17) (7,16) (7,22) (7,20) (7,18) (7,10) (7,21) (7,9) (7,14) (8,19) (8,20) (8,18) (8,10) (8,21) (8,9) (8,15) (9,13) (9,19) (9,17) (9,16) (9,22) (9,21) (9,14) (10,13) (10,17) (10,22) (10,20) (10,18) (10,23) (10,15) (10,14) (13,17) (13,16) (13,22) (13,20) (13,18) (13,21) (13,23) (13,15) (13,14) (14,17) (14,16) (14,20) (14,18) (14,23) (15,19) (15,17) (15,16) (15,22) (15,20) (15,21) (15,23) (16,18) (16,21) (17,19) (17,22) (17,20) (17,23) (18,19) (18,22) (18,20) (18,21) (18,23) (19,22) (19,20) (19,21) (20,22) (21,22) (21,23) (22,23)\nIs there a path between node 8 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph286-1_0", + "image": "data/connectivity/graph_visual/medium/graph286.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (0,9) (1,11) (1,4) (2,6) (2,14) (2,19) (3,15) (4,18) (4,17) (4,9) (4,19) (5,6) (5,11) (5,10) (6,11) (6,18) (8,10) (8,14) (9,18) (9,10) (9,14) (10,18) (10,19) (11,14) (11,19) (12,15) (12,13) (16,19)\nIs there a path between node 1 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph66-0_2", + "image": "data/connectivity/graph_visual/medium/graph66.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (0,1) (0,13) (0,7) (0,4) (0,10) (0,12) (0,5) (0,11) (0,6) (0,9) (0,8) (1,3) (1,13) (1,7) (1,4) (1,10) (1,12) (1,5) (1,11) (1,6) (1,9) (1,8) (3,13) (3,7) (3,4) (3,10) (3,12) (3,5) (3,11) (3,6) (3,9) (3,8) (4,13) (4,7) (4,10) (4,12) (4,5) (4,11) (4,6) (4,9) (4,8) (5,13) (5,7) (5,10) (5,12) (5,11) (5,6) (5,9) (5,8) (6,13) (6,7) (6,10) (6,12) (6,11) (6,9) (6,8) (7,13) (7,10) (7,12) (7,11) (7,9) (7,8) (8,13) (8,10) (8,12) (8,11) (8,9) (9,13) (9,10) (9,12) (9,11) (10,13) (10,12) (10,11) (11,13) (11,12) (12,13)\nIs there a path between node 0 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph572-14_16", + "image": "data/connectivity/graph_visual/medium/graph572.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,19) (0,9) (0,7) (0,15) (0,18) (0,3) (0,2) (0,22) (0,5) (0,13) (0,4) (0,17) (0,20) (0,10) (0,1) (0,23) (0,21) (0,8) (1,12) (1,19) (1,9) (1,7) (1,15) (1,18) (1,3) (1,2) (1,22) (1,5) (1,13) (1,4) (1,17) (1,20) (1,10) (1,23) (1,21) (1,8) (2,12) (2,19) (2,9) (2,7) (2,15) (2,18) (2,3) (2,22) (2,5) (2,13) (2,4) (2,17) (2,20) (2,10) (2,23) (2,21) (2,8) (3,12) (3,19) (3,9) (3,7) (3,15) (3,18) (3,22) (3,5) (3,13) (3,4) (3,17) (3,20) (3,10) (3,23) (3,21) (3,8) (4,12) (4,19) (4,9) (4,7) (4,15) (4,18) (4,22) (4,5) (4,13) (4,17) (4,20) (4,10) (4,23) (4,21) (4,8) (5,12) (5,19) (5,9) (5,7) (5,15) (5,18) (5,22) (5,13) (5,17) (5,20) (5,10) (5,23) (5,21) (5,8) (7,12) (7,19) (7,9) (7,15) (7,18) (7,22) (7,13) (7,17) (7,20) (7,10) (7,23) (7,21) (7,8) (8,12) (8,19) (8,9) (8,15) (8,18) (8,22) (8,13) (8,17) (8,20) (8,10) (8,23) (8,21) (9,12) (9,19) (9,15) (9,18) (9,22) (9,13) (9,17) (9,20) (9,10) (9,23) (9,21) (10,12) (10,19) (10,15) (10,18) (10,22) (10,13) (10,17) (10,20) (10,23) (10,21) (11,16) (12,19) (12,15) (12,18) (12,22) (12,13) (12,17) (12,20) (12,23) (12,21) (13,19) (13,15) (13,18) (13,22) (13,17) (13,20) (13,23) (13,21) (15,19) (15,18) (15,22) (15,17) (15,20) (15,23) (15,21) (17,19) (17,18) (17,22) (17,20) (17,23) (17,21) (18,19) (18,22) (18,20) (18,23) (18,21) (19,22) (19,20) (19,23) (19,21) (20,22) (20,23) (20,21) (21,22) (21,23) (22,23)\nIs there a path between node 14 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph756-13_14", + "image": "data/connectivity/graph_visual/medium/graph756.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,16) (0,15) (0,18) (0,6) (0,1) (0,2) (0,13) (0,24) (0,4) (0,10) (0,22) (0,3) (0,5) (1,21) (1,15) (1,18) (1,13) (1,24) (1,8) (1,17) (1,14) (1,22) (1,23) (1,12) (1,19) (1,20) (1,5) (2,7) (2,15) (2,18) (2,13) (2,24) (2,8) (2,17) (2,10) (2,22) (2,3) (2,12) (2,20) (2,5) (3,7) (3,21) (3,16) (3,6) (3,24) (3,8) (3,17) (3,22) (3,23) (3,12) (3,19) (3,20) (3,5) (4,21) (4,15) (4,6) (4,13) (4,24) (4,14) (4,10) (4,23) (4,12) (4,5) (5,7) (5,21) (5,16) (5,18) (5,6) (5,13) (5,8) (5,17) (5,14) (5,10) (5,22) (5,23) (5,12) (5,19) (5,20) (6,21) (6,15) (6,18) (6,13) (6,24) (6,17) (6,14) (6,22) (6,12) (6,19) (6,20) (7,21) (7,15) (7,18) (7,13) (7,8) (7,17) (7,10) (7,23) (7,19) (7,20) (8,16) (8,15) (8,18) (8,17) (8,14) (8,10) (8,22) (8,23) (8,19) (9,11) (10,16) (10,15) (10,18) (10,13) (10,24) (10,17) (10,14) (10,22) (10,23) (10,12) (10,20) (12,21) (12,16) (12,15) (12,24) (12,17) (12,14) (12,22) (12,19) (13,21) (13,16) (13,15) (13,18) (13,17) (13,14) (13,22) (13,19) (13,20) (14,15) (14,18) (14,24) (14,17) (14,19) (14,20) (15,21) (15,16) (15,18) (15,22) (15,23) (15,19) (15,20) (16,21) (16,24) (16,17) (16,23) (16,19) (16,20) (17,21) (17,18) (17,22) (17,23) (17,20) (18,21) (18,22) (18,23) (18,19) (18,20) (19,24) (19,22) (19,23) (19,20) (20,21) (20,24) (20,22) (20,23) (21,24) (21,22) (22,24) (23,24)\nIs there a path between node 13 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph640-19_23", + "image": "data/connectivity/graph_visual/medium/graph640.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,22) (0,16) (0,23) (1,8) (1,4) (1,22) (1,16) (1,18) (1,3) (2,19) (2,9) (2,17) (2,20) (3,14) (3,13) (3,7) (4,8) (4,12) (4,16) (4,23) (4,18) (5,10) (5,9) (5,20) (6,14) (6,13) (6,22) (6,7) (7,22) (7,18) (8,22) (8,18) (9,19) (9,11) (9,20) (9,21) (10,20) (10,21) (11,20) (12,18) (13,22) (13,16) (13,23) (13,18) (15,19) (15,17) (15,21) (16,23) (16,18) (17,19) (18,22)\nIs there a path between node 19 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph8-5_10", + "image": "data/connectivity/graph_visual/medium/graph8.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,2) (0,8) (1,9) (1,3) (1,4) (1,7) (1,5) (1,10) (3,9) (3,7) (3,5) (3,10) (4,9) (4,6) (4,10) (5,9) (5,6) (6,9) (6,7) (6,10) (7,9) (9,10)\nIs there a path between node 5 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph141-2_14", + "image": "data/connectivity/graph_visual/medium/graph141.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,12) (1,10) (3,14) (4,10) (5,12) (6,11) (6,16) (7,14) (8,14) (9,10) (10,15) (16,17)\nIs there a path between node 2 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph694-19_20", + "image": "data/connectivity/graph_visual/medium/graph694.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,23) (0,1) (0,3) (0,5) (0,12) (0,10) (0,15) (0,11) (0,18) (0,19) (0,13) (0,6) (0,14) (0,17) (0,9) (0,7) (0,16) (0,20) (1,4) (1,23) (1,3) (1,5) (1,12) (1,10) (1,15) (1,11) (1,18) (1,19) (1,13) (1,6) (1,14) (1,17) (1,9) (1,7) (1,16) (1,20) (2,22) (2,21) (2,8) (3,4) (3,23) (3,5) (3,12) (3,10) (3,15) (3,11) (3,18) (3,19) (3,13) (3,6) (3,14) (3,17) (3,9) (3,7) (3,16) (3,20) (4,23) (4,5) (4,12) (4,10) (4,15) (4,11) (4,18) (4,19) (4,13) (4,6) (4,14) (4,17) (4,9) (4,7) (4,16) (4,20) (5,23) (5,12) (5,10) (5,15) (5,11) (5,18) (5,19) (5,13) (5,6) (5,14) (5,17) (5,9) (5,7) (5,16) (5,20) (6,23) (6,12) (6,10) (6,15) (6,11) (6,18) (6,19) (6,13) (6,14) (6,17) (6,9) (6,7) (6,16) (6,20) (7,23) (7,12) (7,10) (7,15) (7,11) (7,18) (7,19) (7,13) (7,14) (7,17) (7,9) (7,16) (7,20) (8,22) (8,21) (9,23) (9,12) (9,10) (9,15) (9,11) (9,18) (9,19) (9,13) (9,14) (9,17) (9,16) (9,20) (10,23) (10,12) (10,15) (10,11) (10,18) (10,19) (10,13) (10,14) (10,17) (10,16) (10,20) (11,23) (11,12) (11,15) (11,18) (11,19) (11,13) (11,14) (11,17) (11,16) (11,20) (12,23) (12,15) (12,18) (12,19) (12,13) (12,14) (12,17) (12,16) (12,20) (13,23) (13,15) (13,18) (13,19) (13,14) (13,17) (13,16) (13,20) (14,23) (14,15) (14,18) (14,19) (14,17) (14,16) (14,20) (15,23) (15,18) (15,19) (15,17) (15,16) (15,20) (16,23) (16,18) (16,19) (16,17) (16,20) (17,23) (17,18) (17,19) (17,20) (18,23) (18,19) (18,20) (19,23) (19,20) (20,23) (21,22)\nIs there a path between node 19 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph671-2_1", + "image": "data/connectivity/graph_visual/medium/graph671.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,15) (0,13) (0,6) (0,20) (2,12) (2,18) (2,22) (2,19) (2,8) (2,4) (3,10) (3,11) (3,13) (3,6) (3,5) (3,21) (3,20) (4,17) (4,16) (4,18) (4,22) (4,23) (4,19) (4,8) (5,10) (5,15) (5,13) (5,21) (5,20) (6,11) (6,15) (6,13) (6,21) (6,20) (7,12) (7,17) (7,18) (7,22) (7,23) (7,8) (8,12) (8,16) (8,18) (8,19) (9,14) (10,11) (10,15) (10,13) (10,20) (11,13) (12,17) (12,16) (12,18) (12,23) (12,19) (13,15) (13,21) (15,21) (15,20) (16,17) (16,18) (16,22) (16,23) (16,19) (17,23) (17,19) (18,23) (18,19) (20,21) (22,23)\nIs there a path between node 2 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph551-0_4", + "image": "data/connectivity/graph_visual/medium/graph551.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,11) (2,20) (3,22) (3,6) (3,14) (3,12) (3,13) (3,4) (4,23) (4,12) (5,23) (5,22) (5,12) (5,10) (5,13) (5,15) (6,10) (6,13) (6,18) (8,11) (9,20) (10,12) (11,17) (11,16) (12,14) (12,15) (12,21) (13,19) (13,18) (14,23) (14,15) (14,18) (15,23) (18,23)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph485-14_17", + "image": "data/connectivity/graph_visual/medium/graph485.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,2) (0,8) (0,7) (0,15) (1,9) (1,14) (1,19) (1,20) (1,5) (1,22) (1,10) (1,6) (1,17) (2,16) (2,8) (2,7) (3,16) (3,8) (3,7) (3,15) (4,14) (4,20) (4,5) (4,22) (4,18) (4,13) (4,10) (4,17) (5,14) (5,19) (5,22) (5,18) (5,13) (5,10) (5,6) (5,17) (6,9) (6,14) (6,19) (6,20) (6,22) (6,18) (6,13) (6,10) (6,17) (7,16) (7,8) (8,16) (8,15) (9,19) (9,20) (9,11) (9,22) (9,18) (9,10) (9,17) (10,19) (10,20) (10,11) (10,13) (10,17) (11,14) (11,19) (11,20) (11,22) (11,18) (11,13) (11,17) (12,21) (13,14) (13,19) (13,22) (13,18) (13,17) (14,20) (14,18) (14,17) (15,16) (17,20) (17,22) (18,19) (18,20) (18,22) (20,22)\nIs there a path between node 14 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph725-19_1", + "image": "data/connectivity/graph_visual/medium/graph725.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,7) (0,2) (0,5) (0,18) (0,9) (0,16) (0,21) (0,13) (0,11) (0,14) (0,22) (0,15) (0,6) (2,20) (2,7) (2,5) (2,18) (2,9) (2,16) (2,21) (2,13) (2,11) (2,14) (2,22) (2,15) (2,6) (3,4) (3,10) (3,8) (3,17) (3,19) (3,23) (3,24) (4,10) (4,8) (4,17) (4,19) (4,23) (4,24) (5,20) (5,7) (5,18) (5,9) (5,16) (5,21) (5,13) (5,11) (5,14) (5,22) (5,15) (5,6) (6,20) (6,7) (6,18) (6,9) (6,16) (6,21) (6,13) (6,11) (6,14) (6,22) (6,15) (7,20) (7,18) (7,9) (7,16) (7,21) (7,13) (7,11) (7,14) (7,22) (7,15) (8,10) (8,17) (8,19) (8,23) (8,24) (9,20) (9,18) (9,16) (9,21) (9,13) (9,11) (9,14) (9,22) (9,15) (10,17) (10,19) (10,23) (10,24) (11,20) (11,18) (11,16) (11,21) (11,13) (11,14) (11,22) (11,15) (13,20) (13,18) (13,16) (13,21) (13,14) (13,22) (13,15) (14,20) (14,18) (14,16) (14,21) (14,22) (14,15) (15,20) (15,18) (15,16) (15,21) (15,22) (16,20) (16,18) (16,21) (16,22) (17,19) (17,23) (17,24) (18,20) (18,21) (18,22) (19,23) (19,24) (20,21) (20,22) (21,22) (23,24)\nIs there a path between node 19 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph456-9_0", + "image": "data/connectivity/graph_visual/medium/graph456.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,17) (0,6) (0,9) (0,15) (0,20) (0,7) (0,18) (0,14) (0,4) (0,19) (0,3) (0,1) (0,11) (0,16) (0,2) (0,12) (1,17) (1,6) (1,9) (1,15) (1,20) (1,7) (1,18) (1,14) (1,4) (1,19) (1,3) (1,11) (1,16) (1,2) (1,12) (2,17) (2,6) (2,9) (2,15) (2,20) (2,7) (2,18) (2,14) (2,4) (2,19) (2,3) (2,11) (2,16) (2,12) (3,17) (3,6) (3,9) (3,15) (3,20) (3,7) (3,18) (3,14) (3,4) (3,19) (3,11) (3,16) (3,12) (4,17) (4,6) (4,9) (4,15) (4,20) (4,7) (4,18) (4,14) (4,19) (4,11) (4,16) (4,12) (5,10) (5,21) (5,13) (6,17) (6,9) (6,15) (6,20) (6,7) (6,18) (6,14) (6,19) (6,11) (6,16) (6,12) (7,17) (7,9) (7,15) (7,20) (7,18) (7,14) (7,19) (7,11) (7,16) (7,12) (9,17) (9,15) (9,20) (9,18) (9,14) (9,19) (9,11) (9,16) (9,12) (10,21) (10,13) (11,17) (11,15) (11,20) (11,18) (11,14) (11,19) (11,16) (11,12) (12,17) (12,15) (12,20) (12,18) (12,14) (12,19) (12,16) (13,21) (14,17) (14,15) (14,20) (14,18) (14,19) (14,16) (15,17) (15,20) (15,18) (15,19) (15,16) (16,17) (16,20) (16,18) (16,19) (17,20) (17,18) (17,19) (18,20) (18,19) (19,20)\nIs there a path between node 9 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph490-3_7", + "image": "data/connectivity/graph_visual/medium/graph490.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (2,17) (2,19) (2,18) (2,8) (2,12) (2,21) (2,7) (2,13) (2,11) (2,10) (2,20) (2,5) (2,22) (3,15) (3,4) (3,16) (3,9) (3,6) (3,14) (4,15) (4,16) (4,9) (4,6) (4,14) (5,17) (5,19) (5,18) (5,8) (5,12) (5,21) (5,7) (5,13) (5,11) (5,10) (5,20) (5,22) (6,15) (6,16) (6,9) (6,14) (7,17) (7,19) (7,18) (7,8) (7,12) (7,21) (7,13) (7,11) (7,10) (7,20) (7,22) (8,17) (8,19) (8,18) (8,12) (8,21) (8,13) (8,11) (8,10) (8,20) (8,22) (9,15) (9,16) (9,14) (10,17) (10,19) (10,18) (10,12) (10,21) (10,13) (10,11) (10,20) (10,22) (11,17) (11,19) (11,18) (11,12) (11,21) (11,13) (11,20) (11,22) (12,17) (12,19) (12,18) (12,21) (12,13) (12,20) (12,22) (13,17) (13,19) (13,18) (13,21) (13,20) (13,22) (14,15) (14,16) (15,16) (17,19) (17,18) (17,21) (17,20) (17,22) (18,19) (18,21) (18,20) (18,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 3 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph783-0_6", + "image": "data/connectivity/graph_visual/medium/graph783.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (0,18) (0,24) (0,2) (0,3) (0,20) (0,22) (0,10) (0,17) (1,9) (1,8) (1,20) (2,23) (2,9) (2,16) (2,11) (2,15) (3,23) (3,21) (3,4) (3,24) (3,17) (4,9) (4,18) (4,20) (4,10) (4,17) (5,14) (6,7) (8,21) (8,16) (8,22) (8,10) (8,17) (9,23) (9,21) (9,11) (9,20) (9,10) (9,17) (10,24) (10,20) (10,22) (10,17) (11,18) (11,12) (12,23) (12,21) (12,19) (12,18) (12,20) (15,23) (15,18) (15,24) (15,22) (15,17) (16,23) (16,19) (16,22) (17,18) (17,20) (18,22) (19,23) (19,20) (19,22) (20,22)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph478-10_20", + "image": "data/connectivity/graph_visual/medium/graph478.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,17) (1,15) (1,10) (1,5) (1,11) (1,3) (1,19) (1,6) (2,13) (2,10) (2,18) (2,21) (2,3) (3,18) (3,11) (4,8) (5,10) (7,16) (7,10) (7,11) (10,16) (11,15) (11,16) (12,22) (12,14) (12,20) (13,21) (14,22) (16,21) (16,19) (18,21) (19,21) (20,22)\nIs there a path between node 10 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph567-4_0", + "image": "data/connectivity/graph_visual/medium/graph567.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,14) (0,6) (0,18) (0,11) (0,5) (0,21) (0,10) (1,22) (1,16) (1,2) (1,9) (1,7) (1,13) (1,20) (1,19) (1,15) (1,23) (1,4) (1,3) (1,12) (1,8) (1,17) (2,22) (2,16) (2,9) (2,7) (2,13) (2,20) (2,19) (2,15) (2,23) (2,4) (2,3) (2,12) (2,8) (2,17) (3,22) (3,16) (3,9) (3,7) (3,13) (3,20) (3,19) (3,15) (3,23) (3,4) (3,12) (3,8) (3,17) (4,22) (4,16) (4,9) (4,7) (4,13) (4,20) (4,19) (4,15) (4,23) (4,12) (4,8) (4,17) (5,14) (5,6) (5,18) (5,11) (5,21) (5,10) (6,14) (6,18) (6,11) (6,21) (6,10) (7,22) (7,16) (7,9) (7,13) (7,20) (7,19) (7,15) (7,23) (7,12) (7,8) (7,17) (8,22) (8,16) (8,9) (8,13) (8,20) (8,19) (8,15) (8,23) (8,12) (8,17) (9,22) (9,16) (9,13) (9,20) (9,19) (9,15) (9,23) (9,12) (9,17) (10,14) (10,18) (10,11) (10,21) (11,14) (11,18) (11,21) (12,22) (12,16) (12,13) (12,20) (12,19) (12,15) (12,23) (12,17) (13,22) (13,16) (13,20) (13,19) (13,15) (13,23) (13,17) (14,18) (14,21) (15,22) (15,16) (15,20) (15,19) (15,23) (15,17) (16,22) (16,20) (16,19) (16,23) (16,17) (17,22) (17,20) (17,19) (17,23) (18,21) (19,22) (19,20) (19,23) (20,22) (20,23) (22,23)\nIs there a path between node 4 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph185-11_3", + "image": "data/connectivity/graph_visual/medium/graph185.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,7) (0,9) (0,6) (0,16) (0,3) (0,13) (0,15) (0,4) (0,8) (1,5) (1,17) (1,12) (1,14) (1,2) (2,5) (2,17) (2,12) (2,14) (3,7) (3,9) (3,6) (3,16) (3,13) (3,15) (3,4) (3,8) (4,7) (4,9) (4,6) (4,16) (4,13) (4,15) (4,8) (5,17) (5,12) (5,14) (6,7) (6,9) (6,16) (6,13) (6,15) (6,8) (7,9) (7,16) (7,13) (7,15) (7,8) (8,9) (8,16) (8,13) (8,15) (9,16) (9,13) (9,15) (10,11) (12,17) (12,14) (13,16) (13,15) (14,17) (15,16)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph652-18_0", + "image": "data/connectivity/graph_visual/medium/graph652.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,4) (0,23) (0,18) (0,16) (0,13) (0,6) (0,3) (0,14) (1,15) (1,19) (1,2) (1,9) (1,22) (1,8) (1,21) (1,12) (1,20) (2,15) (2,19) (2,9) (2,22) (2,21) (2,12) (2,20) (3,5) (3,7) (3,23) (3,18) (3,13) (3,6) (3,11) (3,14) (4,5) (4,18) (4,16) (4,13) (4,10) (4,6) (4,11) (5,7) (5,23) (5,16) (5,13) (5,10) (5,6) (5,11) (5,14) (6,7) (6,23) (6,10) (6,11) (6,14) (7,18) (7,10) (7,11) (7,14) (8,15) (8,9) (8,17) (8,21) (8,12) (9,15) (9,19) (9,17) (9,21) (9,12) (9,20) (10,23) (10,18) (10,16) (10,13) (10,11) (10,14) (11,18) (11,16) (11,13) (12,15) (12,22) (12,21) (12,20) (13,18) (13,16) (14,23) (14,18) (15,19) (15,17) (15,21) (15,20) (16,23) (16,18) (17,22) (17,21) (17,20) (18,23) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 18 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph231-7_0", + "image": "data/connectivity/graph_visual/medium/graph231.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,10) (1,15) (2,16) (3,18) (3,8) (5,15) (5,14) (7,9) (8,18) (8,12) (10,17) (12,13) (12,17) (13,14) (14,18) (14,15) (17,18)\nIs there a path between node 7 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph89-12_0", + "image": "data/connectivity/graph_visual/medium/graph89.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,14) (0,2) (0,7) (0,4) (0,1) (0,3) (0,11) (0,6) (0,9) (0,13) (0,8) (0,5) (0,10) (1,14) (1,2) (1,7) (1,4) (1,3) (1,11) (1,6) (1,9) (1,13) (1,8) (1,5) (1,10) (2,14) (2,7) (2,4) (2,3) (2,11) (2,6) (2,9) (2,13) (2,8) (2,5) (2,10) (3,14) (3,7) (3,4) (3,11) (3,6) (3,9) (3,13) (3,8) (3,5) (3,10) (4,14) (4,7) (4,11) (4,6) (4,9) (4,13) (4,8) (4,5) (4,10) (5,14) (5,7) (5,11) (5,6) (5,9) (5,13) (5,8) (5,10) (6,14) (6,7) (6,11) (6,9) (6,13) (6,8) (6,10) (7,14) (7,11) (7,9) (7,13) (7,8) (7,10) (8,14) (8,11) (8,9) (8,13) (8,10) (9,14) (9,11) (9,13) (9,10) (10,14) (10,11) (10,13) (11,14) (11,13) (13,14)\nIs there a path between node 12 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph820-2_12", + "image": "data/connectivity/graph_visual/medium/graph820.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,6) (1,2) (1,4) (1,12) (1,19) (1,3) (1,18) (1,21) (1,16) (1,22) (1,23) (1,24) (1,20) (1,8) (1,13) (1,9) (2,6) (2,4) (2,14) (2,17) (2,15) (2,19) (2,3) (2,18) (2,21) (2,16) (2,22) (2,23) (2,24) (2,20) (2,11) (2,8) (2,13) (2,9) (3,7) (3,6) (3,4) (3,14) (3,15) (3,12) (3,18) (3,16) (3,22) (3,23) (3,24) (3,20) (3,11) (3,8) (4,6) (4,14) (4,17) (4,15) (4,12) (4,19) (4,21) (4,22) (4,23) (4,11) (4,13) (4,9) (5,10) (6,14) (6,15) (6,19) (6,18) (6,21) (6,22) (6,23) (6,20) (6,11) (6,8) (6,13) (6,9) (7,14) (7,18) (7,16) (7,22) (7,23) (7,20) (7,11) (7,9) (8,14) (8,15) (8,19) (8,21) (8,16) (8,22) (8,23) (8,20) (8,11) (8,13) (8,9) (9,14) (9,15) (9,12) (9,19) (9,18) (9,21) (9,16) (9,22) (9,23) (9,20) (9,13) (11,14) (11,17) (11,15) (11,12) (11,21) (11,22) (11,24) (11,20) (12,17) (12,15) (12,19) (12,18) (12,21) (12,16) (12,23) (12,13) (13,17) (13,15) (13,19) (13,18) (13,21) (13,22) (13,23) (13,24) (14,17) (14,15) (14,19) (14,18) (14,16) (14,20) (15,17) (15,19) (15,16) (15,22) (15,24) (15,20) (16,17) (16,19) (16,18) (16,22) (16,23) (16,24) (16,20) (17,19) (17,21) (17,22) (18,19) (18,21) (18,22) (18,23) (18,24) (19,23) (19,20) (20,21) (20,24) (21,22) (21,24) (22,24)\nIs there a path between node 2 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph77-2_13", + "image": "data/connectivity/graph_visual/medium/graph77.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,11) (0,10) (1,8) (1,9) (2,13) (2,7) (2,12) (3,11) (4,14) (4,5) (6,14) (7,11) (7,12) (8,14)\nIs there a path between node 2 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph414-19_20", + "image": "data/connectivity/graph_visual/medium/graph414.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,1) (0,18) (1,18) (1,14) (1,11) (2,4) (2,21) (2,15) (2,9) (2,12) (2,8) (2,3) (2,10) (3,4) (3,9) (3,12) (3,5) (3,20) (3,8) (3,17) (3,10) (3,19) (4,21) (4,15) (4,12) (4,6) (4,5) (4,17) (4,19) (5,21) (5,9) (5,6) (5,20) (5,8) (5,10) (6,15) (6,9) (6,12) (6,8) (6,10) (6,19) (7,13) (8,21) (8,15) (8,9) (8,12) (8,17) (8,10) (8,19) (9,21) (9,20) (9,19) (10,21) (10,20) (10,17) (11,14) (12,21) (12,15) (12,20) (12,19) (14,16) (15,20) (15,17) (17,21) (17,20) (17,19) (19,21)\nIs there a path between node 19 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph491-3_9", + "image": "data/connectivity/graph_visual/medium/graph491.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,2) (0,22) (0,9) (0,7) (0,21) (0,15) (0,6) (0,18) (0,16) (0,1) (0,17) (0,19) (0,13) (0,4) (0,5) (0,14) (0,20) (1,10) (1,2) (1,22) (1,9) (1,7) (1,21) (1,15) (1,6) (1,18) (1,16) (1,17) (1,19) (1,13) (1,4) (1,5) (1,14) (1,20) (2,10) (2,22) (2,9) (2,7) (2,21) (2,15) (2,6) (2,18) (2,16) (2,17) (2,19) (2,13) (2,4) (2,5) (2,14) (2,20) (3,11) (3,8) (3,12) (4,10) (4,22) (4,9) (4,7) (4,21) (4,15) (4,6) (4,18) (4,16) (4,17) (4,19) (4,13) (4,5) (4,14) (4,20) (5,10) (5,22) (5,9) (5,7) (5,21) (5,15) (5,6) (5,18) (5,16) (5,17) (5,19) (5,13) (5,14) (5,20) (6,10) (6,22) (6,9) (6,7) (6,21) (6,15) (6,18) (6,16) (6,17) (6,19) (6,13) (6,14) (6,20) (7,10) (7,22) (7,9) (7,21) (7,15) (7,18) (7,16) (7,17) (7,19) (7,13) (7,14) (7,20) (8,11) (8,12) (9,10) (9,22) (9,21) (9,15) (9,18) (9,16) (9,17) (9,19) (9,13) (9,14) (9,20) (10,22) (10,21) (10,15) (10,18) (10,16) (10,17) (10,19) (10,13) (10,14) (10,20) (11,12) (13,22) (13,21) (13,15) (13,18) (13,16) (13,17) (13,19) (13,14) (13,20) (14,22) (14,21) (14,15) (14,18) (14,16) (14,17) (14,19) (14,20) (15,22) (15,21) (15,18) (15,16) (15,17) (15,19) (15,20) (16,22) (16,21) (16,18) (16,17) (16,19) (16,20) (17,22) (17,21) (17,18) (17,19) (17,20) (18,22) (18,21) (18,19) (18,20) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 3 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph850-23_24", + "image": "data/connectivity/graph_visual/medium/graph850.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,4) (0,11) (0,16) (0,5) (0,2) (0,22) (0,15) (0,8) (0,21) (0,7) (0,9) (0,23) (0,12) (0,3) (0,14) (0,20) (1,19) (1,18) (1,24) (1,17) (1,13) (1,10) (2,6) (2,4) (2,11) (2,16) (2,5) (2,22) (2,15) (2,8) (2,21) (2,7) (2,9) (2,23) (2,12) (2,3) (2,14) (2,20) (3,6) (3,4) (3,11) (3,16) (3,5) (3,22) (3,15) (3,8) (3,21) (3,7) (3,9) (3,23) (3,12) (3,14) (3,20) (4,6) (4,11) (4,16) (4,5) (4,22) (4,15) (4,8) (4,21) (4,7) (4,9) (4,23) (4,12) (4,14) (4,20) (5,6) (5,11) (5,16) (5,22) (5,15) (5,8) (5,21) (5,7) (5,9) (5,23) (5,12) (5,14) (5,20) (6,11) (6,16) (6,22) (6,15) (6,8) (6,21) (6,7) (6,9) (6,23) (6,12) (6,14) (6,20) (7,11) (7,16) (7,22) (7,15) (7,8) (7,21) (7,9) (7,23) (7,12) (7,14) (7,20) (8,11) (8,16) (8,22) (8,15) (8,21) (8,9) (8,23) (8,12) (8,14) (8,20) (9,11) (9,16) (9,22) (9,15) (9,21) (9,23) (9,12) (9,14) (9,20) (10,19) (10,18) (10,24) (10,17) (10,13) (11,16) (11,22) (11,15) (11,21) (11,23) (11,12) (11,14) (11,20) (12,16) (12,22) (12,15) (12,21) (12,23) (12,14) (12,20) (13,19) (13,18) (13,24) (13,17) (14,16) (14,22) (14,15) (14,21) (14,23) (14,20) (15,16) (15,22) (15,21) (15,23) (15,20) (16,22) (16,21) (16,23) (16,20) (17,19) (17,18) (17,24) (18,19) (18,24) (19,24) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 23 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph688-17_7", + "image": "data/connectivity/graph_visual/medium/graph688.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,6) (0,11) (0,14) (0,2) (1,20) (1,8) (1,7) (1,16) (1,21) (1,9) (1,17) (1,5) (1,23) (1,12) (1,22) (2,4) (2,6) (2,11) (2,14) (3,15) (3,18) (3,13) (3,19) (3,10) (4,6) (4,11) (4,14) (5,20) (5,8) (5,7) (5,16) (5,21) (5,9) (5,17) (5,23) (5,12) (5,22) (6,11) (6,14) (7,20) (7,8) (7,16) (7,21) (7,9) (7,17) (7,23) (7,12) (7,22) (8,20) (8,16) (8,21) (8,9) (8,17) (8,23) (8,12) (8,22) (9,20) (9,16) (9,21) (9,17) (9,23) (9,12) (9,22) (10,15) (10,18) (10,13) (10,19) (11,14) (12,20) (12,16) (12,21) (12,17) (12,23) (12,22) (13,15) (13,18) (13,19) (15,18) (15,19) (16,20) (16,21) (16,17) (16,23) (16,22) (17,20) (17,21) (17,23) (17,22) (18,19) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 17 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph5-0_1", + "image": "data/connectivity/graph_visual/medium/graph5.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,10) (1,8) (1,9) (2,10) (2,3) (3,7) (5,10) (6,8) (7,8) (7,9)\nIs there a path between node 0 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph538-0_19", + "image": "data/connectivity/graph_visual/medium/graph538.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,4) (0,11) (0,17) (0,18) (0,6) (0,10) (0,7) (0,12) (0,5) (0,21) (0,8) (0,13) (0,9) (0,3) (0,15) (0,14) (0,20) (0,2) (1,19) (1,16) (2,22) (2,4) (2,11) (2,17) (2,18) (2,6) (2,10) (2,7) (2,12) (2,5) (2,21) (2,8) (2,13) (2,9) (2,3) (2,15) (2,14) (2,20) (3,22) (3,4) (3,11) (3,17) (3,18) (3,6) (3,10) (3,7) (3,12) (3,5) (3,21) (3,8) (3,13) (3,9) (3,15) (3,14) (3,20) (4,22) (4,11) (4,17) (4,18) (4,6) (4,10) (4,7) (4,12) (4,5) (4,21) (4,8) (4,13) (4,9) (4,15) (4,14) (4,20) (5,22) (5,11) (5,17) (5,18) (5,6) (5,10) (5,7) (5,12) (5,21) (5,8) (5,13) (5,9) (5,15) (5,14) (5,20) (6,22) (6,11) (6,17) (6,18) (6,10) (6,7) (6,12) (6,21) (6,8) (6,13) (6,9) (6,15) (6,14) (6,20) (7,22) (7,11) (7,17) (7,18) (7,10) (7,12) (7,21) (7,8) (7,13) (7,9) (7,15) (7,14) (7,20) (8,22) (8,11) (8,17) (8,18) (8,10) (8,12) (8,21) (8,13) (8,9) (8,15) (8,14) (8,20) (9,22) (9,11) (9,17) (9,18) (9,10) (9,12) (9,21) (9,13) (9,15) (9,14) (9,20) (10,22) (10,11) (10,17) (10,18) (10,12) (10,21) (10,13) (10,15) (10,14) (10,20) (11,22) (11,17) (11,18) (11,12) (11,21) (11,13) (11,15) (11,14) (11,20) (12,22) (12,17) (12,18) (12,21) (12,13) (12,15) (12,14) (12,20) (13,22) (13,17) (13,18) (13,21) (13,15) (13,14) (13,20) (14,22) (14,17) (14,18) (14,21) (14,15) (14,20) (15,22) (15,17) (15,18) (15,21) (15,20) (16,19) (17,22) (17,18) (17,21) (17,20) (18,22) (18,21) (18,20) (20,22) (20,21) (21,22)\nIs there a path between node 0 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph852-16_4", + "image": "data/connectivity/graph_visual/medium/graph852.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,8) (0,5) (0,9) (0,10) (0,17) (0,15) (0,11) (0,12) (0,13) (0,14) (0,23) (0,18) (0,3) (0,6) (0,21) (0,20) (0,1) (0,4) (0,24) (0,22) (1,8) (1,5) (1,9) (1,10) (1,17) (1,15) (1,11) (1,12) (1,13) (1,14) (1,23) (1,18) (1,3) (1,6) (1,21) (1,20) (1,4) (1,24) (1,22) (2,16) (2,7) (2,19) (3,8) (3,5) (3,9) (3,10) (3,17) (3,15) (3,11) (3,12) (3,13) (3,14) (3,23) (3,18) (3,6) (3,21) (3,20) (3,4) (3,24) (3,22) (4,8) (4,5) (4,9) (4,10) (4,17) (4,15) (4,11) (4,12) (4,13) (4,14) (4,23) (4,18) (4,6) (4,21) (4,20) (4,24) (4,22) (5,8) (5,9) (5,10) (5,17) (5,15) (5,11) (5,12) (5,13) (5,14) (5,23) (5,18) (5,6) (5,21) (5,20) (5,24) (5,22) (6,8) (6,9) (6,10) (6,17) (6,15) (6,11) (6,12) (6,13) (6,14) (6,23) (6,18) (6,21) (6,20) (6,24) (6,22) (7,16) (7,19) (8,9) (8,10) (8,17) (8,15) (8,11) (8,12) (8,13) (8,14) (8,23) (8,18) (8,21) (8,20) (8,24) (8,22) (9,10) (9,17) (9,15) (9,11) (9,12) (9,13) (9,14) (9,23) (9,18) (9,21) (9,20) (9,24) (9,22) (10,17) (10,15) (10,11) (10,12) (10,13) (10,14) (10,23) (10,18) (10,21) (10,20) (10,24) (10,22) (11,17) (11,15) (11,12) (11,13) (11,14) (11,23) (11,18) (11,21) (11,20) (11,24) (11,22) (12,17) (12,15) (12,13) (12,14) (12,23) (12,18) (12,21) (12,20) (12,24) (12,22) (13,17) (13,15) (13,14) (13,23) (13,18) (13,21) (13,20) (13,24) (13,22) (14,17) (14,15) (14,23) (14,18) (14,21) (14,20) (14,24) (14,22) (15,17) (15,23) (15,18) (15,21) (15,20) (15,24) (15,22) (16,19) (17,23) (17,18) (17,21) (17,20) (17,24) (17,22) (18,23) (18,21) (18,20) (18,24) (18,22) (20,23) (20,21) (20,24) (20,22) (21,23) (21,24) (21,22) (22,23) (22,24) (23,24)\nIs there a path between node 16 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph448-8_10", + "image": "data/connectivity/graph_visual/medium/graph448.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,17) (0,19) (0,1) (0,6) (0,5) (0,7) (0,2) (0,14) (0,4) (0,10) (1,17) (1,6) (1,5) (1,12) (1,7) (1,13) (1,2) (1,20) (1,14) (1,10) (2,9) (2,17) (2,16) (2,19) (2,6) (2,12) (2,7) (2,18) (2,13) (2,20) (2,14) (2,4) (2,10) (3,21) (3,15) (3,11) (4,9) (4,17) (4,16) (4,19) (4,6) (4,5) (4,12) (4,7) (4,13) (4,10) (5,9) (5,17) (5,16) (5,12) (5,18) (5,13) (5,20) (5,14) (6,17) (6,16) (6,12) (6,7) (6,18) (6,20) (6,10) (7,9) (7,17) (7,16) (7,19) (7,13) (7,20) (7,14) (7,10) (8,21) (8,15) (9,16) (9,19) (9,18) (9,13) (9,20) (9,14) (9,10) (10,17) (10,16) (10,18) (10,13) (10,20) (10,14) (11,21) (12,17) (12,16) (12,19) (13,17) (13,16) (13,19) (14,17) (14,19) (14,20) (15,21) (16,17) (16,18) (16,20) (17,19) (17,20) (18,19) (18,20) (19,20)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph636-2_13", + "image": "data/connectivity/graph_visual/medium/graph636.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (0,8) (0,22) (0,15) (0,18) (1,12) (1,16) (1,8) (1,9) (1,22) (1,15) (1,18) (2,6) (2,21) (3,21) (3,11) (3,10) (4,23) (5,20) (5,17) (6,20) (7,11) (8,16) (8,14) (8,13) (8,15) (9,16) (9,15) (9,19) (10,20) (10,21) (10,17) (13,16) (13,14) (14,19) (15,22) (15,18) (17,20) (17,23) (18,22) (21,23)\nIs there a path between node 2 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph785-5_18", + "image": "data/connectivity/graph_visual/medium/graph785.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,15) (0,24) (0,1) (0,10) (1,3) (1,8) (2,13) (3,15) (3,14) (3,10) (4,17) (5,15) (5,24) (7,13) (8,11) (8,16) (8,10) (9,22) (9,20) (10,14) (11,15) (11,24) (13,19) (14,15) (14,18) (15,24) (16,24) (20,22)\nIs there a path between node 5 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph499-5_3", + "image": "data/connectivity/graph_visual/medium/graph499.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (0,15) (0,5) (1,10) (2,19) (2,14) (2,21) (4,22) (4,13) (4,6) (5,15) (6,22) (6,9) (8,13) (8,19) (8,21) (10,20) (11,20) (12,18) (13,14) (15,18) (17,19) (21,22)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph425-13_21", + "image": "data/connectivity/graph_visual/medium/graph425.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,16) (0,8) (0,11) (0,20) (1,14) (1,19) (2,7) (2,16) (2,4) (2,10) (2,11) (2,3) (3,4) (3,10) (4,12) (4,8) (4,17) (5,8) (5,6) (5,10) (5,11) (5,13) (6,7) (6,15) (6,18) (7,13) (8,16) (8,18) (8,20) (10,12) (10,17) (10,20) (11,15) (11,13) (12,16) (12,18) (15,16) (16,20) (19,21)\nIs there a path between node 13 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph110-5_9", + "image": "data/connectivity/graph_visual/medium/graph110.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,12) (0,14) (0,10) (0,3) (0,2) (0,8) (0,15) (0,4) (0,11) (0,13) (0,5) (1,6) (1,9) (1,7) (2,12) (2,14) (2,10) (2,3) (2,8) (2,15) (2,4) (2,11) (2,13) (2,5) (3,12) (3,14) (3,10) (3,8) (3,15) (3,4) (3,11) (3,13) (3,5) (4,12) (4,14) (4,10) (4,8) (4,15) (4,11) (4,13) (4,5) (5,12) (5,14) (5,10) (5,8) (5,15) (5,11) (5,13) (6,9) (6,7) (7,9) (8,12) (8,14) (8,10) (8,15) (8,11) (8,13) (10,12) (10,14) (10,15) (10,11) (10,13) (11,12) (11,14) (11,15) (11,13) (12,14) (12,15) (12,13) (13,14) (13,15) (14,15)\nIs there a path between node 5 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph320-18_1", + "image": "data/connectivity/graph_visual/medium/graph320.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,1) (0,18) (1,19) (1,18) (2,6) (2,10) (2,7) (2,5) (2,16) (2,11) (2,15) (2,4) (3,8) (3,9) (3,13) (3,12) (3,14) (3,17) (4,6) (4,10) (4,7) (4,5) (4,16) (4,11) (4,15) (5,6) (5,10) (5,7) (5,16) (5,11) (5,15) (6,10) (6,7) (6,16) (6,11) (6,15) (7,10) (7,16) (7,11) (7,15) (8,9) (8,13) (8,12) (8,14) (8,17) (9,13) (9,12) (9,14) (9,17) (10,16) (10,11) (10,15) (11,16) (11,15) (12,13) (12,14) (12,17) (13,14) (13,17) (14,17) (15,16) (18,19)\nIs there a path between node 18 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph112-11_10", + "image": "data/connectivity/graph_visual/medium/graph112.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,4) (0,11) (0,2) (0,7) (0,8) (0,16) (0,15) (1,11) (1,2) (1,7) (1,8) (1,16) (1,15) (1,14) (2,4) (2,11) (2,5) (2,7) (2,12) (2,16) (2,15) (3,13) (3,10) (4,6) (4,5) (4,7) (4,8) (4,12) (4,16) (4,15) (4,14) (5,6) (5,7) (5,8) (5,12) (5,16) (5,14) (6,11) (6,7) (6,8) (6,12) (6,16) (6,15) (6,14) (7,11) (7,8) (7,16) (7,14) (8,11) (8,12) (8,16) (11,12) (11,16) (11,15) (11,14) (12,14) (14,16) (14,15)\nIs there a path between node 11 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph487-12_11", + "image": "data/connectivity/graph_visual/medium/graph487.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,14) (0,6) (0,11) (0,19) (0,20) (0,1) (0,15) (0,12) (0,7) (0,22) (0,5) (0,21) (0,3) (0,4) (0,18) (0,17) (1,14) (1,6) (1,11) (1,19) (1,20) (1,15) (1,12) (1,7) (1,22) (1,5) (1,21) (1,3) (1,4) (1,18) (1,17) (2,13) (2,10) (2,8) (2,16) (2,9) (3,14) (3,6) (3,11) (3,19) (3,20) (3,15) (3,12) (3,7) (3,22) (3,5) (3,21) (3,4) (3,18) (3,17) (4,14) (4,6) (4,11) (4,19) (4,20) (4,15) (4,12) (4,7) (4,22) (4,5) (4,21) (4,18) (4,17) (5,14) (5,6) (5,11) (5,19) (5,20) (5,15) (5,12) (5,7) (5,22) (5,21) (5,18) (5,17) (6,14) (6,11) (6,19) (6,20) (6,15) (6,12) (6,7) (6,22) (6,21) (6,18) (6,17) (7,14) (7,11) (7,19) (7,20) (7,15) (7,12) (7,22) (7,21) (7,18) (7,17) (8,13) (8,10) (8,16) (8,9) (9,13) (9,10) (9,16) (10,13) (10,16) (11,14) (11,19) (11,20) (11,15) (11,12) (11,22) (11,21) (11,18) (11,17) (12,14) (12,19) (12,20) (12,15) (12,22) (12,21) (12,18) (12,17) (13,16) (14,19) (14,20) (14,15) (14,22) (14,21) (14,18) (14,17) (15,19) (15,20) (15,22) (15,21) (15,18) (15,17) (17,19) (17,20) (17,22) (17,21) (17,18) (18,19) (18,20) (18,22) (18,21) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22)\nIs there a path between node 12 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph107-5_13", + "image": "data/connectivity/graph_visual/medium/graph107.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (0,7) (0,14) (0,5) (0,13) (0,10) (1,7) (1,14) (1,5) (1,13) (1,10) (2,6) (2,12) (2,4) (2,8) (2,15) (2,3) (2,9) (2,11) (3,6) (3,12) (3,4) (3,8) (3,15) (3,9) (3,11) (4,6) (4,12) (4,8) (4,15) (4,9) (4,11) (5,7) (5,14) (5,13) (5,10) (6,12) (6,8) (6,15) (6,9) (6,11) (7,14) (7,13) (7,10) (8,12) (8,15) (8,9) (8,11) (9,12) (9,15) (9,11) (10,14) (10,13) (11,12) (11,15) (12,15) (13,14)\nIs there a path between node 5 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph223-4_0", + "image": "data/connectivity/graph_visual/medium/graph223.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,1) (1,12) (2,18) (2,14) (3,17) (4,5) (4,11) (6,11) (6,13) (9,14) (13,17)\nIs there a path between node 4 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph290-17_19", + "image": "data/connectivity/graph_visual/medium/graph290.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,5) (0,4) (1,6) (1,14) (1,2) (3,18) (3,4) (4,5) (4,15) (6,11) (6,16) (6,14) (6,10) (6,19) (6,12) (6,9) (7,8) (9,13) (9,10) (9,17) (9,19) (10,13) (10,12) (11,16) (11,14) (11,13) (12,17) (12,19) (13,16) (13,14) (14,19) (16,17)\nIs there a path between node 17 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph347-19_3", + "image": "data/connectivity/graph_visual/medium/graph347.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,13) (0,3) (0,19) (0,12) (0,15) (0,17) (1,20) (1,6) (1,2) (1,7) (2,20) (2,6) (2,7) (3,10) (3,13) (3,19) (3,12) (3,15) (3,17) (4,11) (4,9) (4,18) (4,16) (4,14) (4,8) (4,5) (5,11) (5,9) (5,18) (5,16) (5,14) (5,8) (6,20) (6,7) (7,20) (8,11) (8,9) (8,18) (8,16) (8,14) (9,11) (9,18) (9,16) (9,14) (10,13) (10,19) (10,12) (10,15) (10,17) (11,18) (11,16) (11,14) (12,13) (12,19) (12,15) (12,17) (13,19) (13,15) (13,17) (14,18) (14,16) (15,19) (15,17) (16,18) (17,19)\nIs there a path between node 19 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph559-22_17", + "image": "data/connectivity/graph_visual/medium/graph559.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,23) (0,20) (0,17) (0,3) (0,6) (0,5) (0,9) (0,7) (0,13) (0,4) (0,2) (0,1) (1,8) (1,16) (1,23) (1,20) (1,3) (1,6) (1,5) (1,9) (1,14) (1,7) (1,13) (2,18) (2,8) (2,16) (2,20) (2,3) (2,10) (2,5) (2,9) (2,12) (2,14) (2,4) (3,18) (3,8) (3,16) (3,6) (3,5) (3,9) (3,12) (3,14) (3,13) (4,18) (4,8) (4,16) (4,6) (4,10) (4,5) (4,9) (4,12) (4,7) (4,13) (5,8) (5,17) (5,10) (5,9) (5,12) (5,14) (5,7) (5,13) (6,8) (6,16) (6,20) (6,10) (6,12) (6,14) (6,7) (7,8) (7,16) (7,23) (7,17) (7,10) (7,9) (7,12) (7,13) (8,18) (8,17) (8,10) (8,9) (8,12) (8,14) (8,13) (9,18) (9,16) (9,12) (9,14) (9,13) (10,18) (10,23) (10,20) (10,17) (10,12) (10,13) (11,22) (12,23) (12,20) (12,17) (13,18) (13,16) (13,23) (13,20) (13,14) (14,18) (14,16) (14,23) (14,17) (15,19) (15,21) (15,22) (16,18) (16,23) (16,20) (16,17) (17,18) (17,20) (18,20) (19,21) (20,23) (21,22)\nIs there a path between node 22 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph341-11_4", + "image": "data/connectivity/graph_visual/medium/graph341.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,20) (0,19) (1,16) (1,7) (1,2) (1,15) (1,17) (2,7) (3,5) (3,11) (3,8) (3,4) (3,13) (3,18) (3,9) (4,11) (4,8) (4,6) (4,18) (4,9) (4,12) (5,8) (5,13) (5,6) (6,13) (6,18) (6,9) (6,12) (7,16) (7,15) (7,17) (8,11) (8,13) (8,18) (8,9) (9,11) (9,12) (10,20) (10,19) (10,14) (11,18) (11,12) (12,13) (13,18) (14,20) (15,17) (19,20)\nIs there a path between node 11 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph28-0_6", + "image": "data/connectivity/graph_visual/medium/graph28.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,1) (0,4) (0,3) (0,6) (0,2) (0,8) (0,5) (0,11) (1,4) (1,3) (1,6) (1,2) (1,8) (1,5) (1,11) (2,4) (2,3) (2,6) (2,8) (2,5) (2,11) (3,4) (3,6) (3,8) (3,5) (3,11) (4,6) (4,8) (4,5) (4,11) (5,6) (5,8) (5,11) (6,8) (6,11) (7,9) (7,10) (8,11) (9,10)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph159-9_14", + "image": "data/connectivity/graph_visual/medium/graph159.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,9) (1,15) (1,3) (1,16) (2,4) (2,12) (2,10) (4,8) (4,11) (5,10) (5,17) (5,6) (6,11) (6,10) (6,17) (7,11) (7,12) (7,10) (7,17) (8,17) (9,13)\nIs there a path between node 9 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph740-18_4", + "image": "data/connectivity/graph_visual/medium/graph740.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,15) (1,2) (2,3) (2,16) (3,21) (3,18) (3,5) (3,13) (3,7) (3,16) (4,10) (5,21) (5,24) (6,11) (6,17) (7,18) (7,22) (7,23) (7,16) (8,14) (9,11) (9,14) (11,17) (12,21) (12,18) (12,22) (12,23) (12,16) (12,24) (13,21) (13,18) (13,22) (13,15) (13,16) (13,24) (15,18) (16,21) (16,18) (17,20) (18,21) (22,24) (23,24)\nIs there a path between node 18 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph624-11_2", + "image": "data/connectivity/graph_visual/medium/graph624.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (0,11) (0,13) (0,3) (0,15) (0,4) (0,2) (1,7) (1,8) (2,14) (2,23) (2,21) (2,6) (2,10) (3,9) (3,17) (3,13) (3,5) (3,19) (3,4) (3,16) (3,10) (4,9) (4,22) (4,6) (5,11) (5,18) (5,23) (6,9) (6,14) (6,17) (6,20) (6,15) (6,21) (7,8) (9,17) (9,15) (9,21) (10,18) (10,12) (10,16) (11,17) (11,15) (11,22) (11,16) (12,15) (12,22) (13,23) (13,16) (14,17) (14,18) (14,20) (14,21) (14,22) (14,16) (15,20) (17,20) (17,19) (17,23) (18,19) (18,23) (19,20) (19,23) (21,23) (21,22)\nIs there a path between node 11 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph31-6_10", + "image": "data/connectivity/graph_visual/medium/graph31.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,6) (0,9) (0,11) (1,7) (1,3) (1,4) (1,5) (1,8) (1,2) (1,10) (2,7) (2,3) (2,4) (2,5) (2,8) (2,10) (3,7) (3,4) (3,5) (3,8) (3,10) (4,7) (4,5) (4,8) (4,10) (5,7) (5,8) (5,10) (6,9) (6,11) (7,8) (7,10) (8,10) (9,11)\nIs there a path between node 6 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph354-12_10", + "image": "data/connectivity/graph_visual/medium/graph354.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,9) (1,15) (1,18) (2,12) (2,10) (2,4) (2,19) (2,5) (2,6) (4,13) (4,11) (4,16) (4,6) (5,7) (5,16) (5,10) (5,19) (6,7) (6,10) (7,8) (7,13) (7,16) (7,10) (8,16) (9,20) (10,11) (10,12) (10,16) (11,16) (11,17) (12,16) (12,17) (14,15) (17,19)\nIs there a path between node 12 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph76-0_8", + "image": "data/connectivity/graph_visual/medium/graph76.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,6) (0,12) (0,8) (1,4) (1,6) (1,12) (1,8) (1,7) (2,4) (2,5) (2,13) (2,10) (4,5) (4,9) (4,8) (4,10) (5,12) (5,10) (5,14) (6,11) (7,9) (7,12) (8,11) (8,13) (8,14) (9,10) (11,12) (11,14) (13,14)\nIs there a path between node 0 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph283-2_17", + "image": "data/connectivity/graph_visual/medium/graph283.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,10) (0,8) (1,12) (1,13) (1,5) (2,7) (3,16) (4,18) (4,7) (4,17) (5,15) (5,14) (6,13) (8,10) (8,17) (11,15) (12,15) (13,14) (14,15) (17,18)\nIs there a path between node 2 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph387-14_19", + "image": "data/connectivity/graph_visual/medium/graph387.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (0,2) (0,10) (0,1) (0,4) (0,9) (0,19) (0,8) (0,18) (0,14) (0,6) (1,3) (1,2) (1,10) (1,4) (1,9) (1,19) (1,8) (1,18) (1,14) (1,6) (2,3) (2,10) (2,4) (2,9) (2,19) (2,8) (2,18) (2,14) (2,6) (3,10) (3,4) (3,9) (3,19) (3,8) (3,18) (3,14) (3,6) (4,10) (4,9) (4,19) (4,8) (4,18) (4,14) (4,6) (5,17) (5,11) (5,16) (6,10) (6,9) (6,19) (6,8) (6,18) (6,14) (7,15) (7,20) (7,13) (7,12) (8,10) (8,9) (8,19) (8,18) (8,14) (9,10) (9,19) (9,18) (9,14) (10,19) (10,18) (10,14) (11,17) (11,16) (12,15) (12,20) (12,13) (13,15) (13,20) (14,19) (14,18) (15,20) (16,17) (18,19)\nIs there a path between node 14 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph223-15_13", + "image": "data/connectivity/graph_visual/medium/graph223.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,1) (1,12) (2,18) (2,14) (3,17) (4,5) (4,11) (6,11) (6,13) (9,14) (13,17)\nIs there a path between node 15 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph600-18_23", + "image": "data/connectivity/graph_visual/medium/graph600.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,17) (0,10) (1,5) (1,12) (1,15) (1,9) (1,14) (1,18) (1,19) (1,4) (1,11) (2,13) (2,21) (2,7) (2,8) (3,12) (3,15) (3,23) (3,18) (3,4) (4,12) (4,23) (4,14) (4,18) (4,19) (4,11) (5,12) (5,15) (5,9) (5,23) (5,18) (5,19) (5,20) (5,16) (5,11) (6,17) (7,13) (7,21) (7,22) (8,13) (8,22) (9,12) (9,23) (9,18) (9,19) (9,20) (9,11) (10,17) (11,15) (11,14) (11,18) (11,19) (12,15) (12,23) (12,14) (12,19) (12,20) (12,16) (13,21) (14,15) (14,23) (14,19) (14,20) (14,16) (15,23) (15,18) (15,16) (16,23) (18,23) (18,19) (18,20) (20,23) (21,22)\nIs there a path between node 18 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph813-16_23", + "image": "data/connectivity/graph_visual/medium/graph813.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (1,9) (1,14) (1,11) (1,19) (1,8) (1,2) (1,15) (1,5) (1,24) (2,14) (2,22) (2,3) (2,8) (2,15) (2,18) (2,5) (2,24) (3,14) (3,11) (3,8) (3,15) (3,5) (4,16) (4,13) (4,17) (4,23) (4,10) (4,7) (5,9) (5,12) (5,22) (5,11) (5,19) (5,8) (5,15) (5,6) (6,9) (6,12) (6,22) (6,11) (6,19) (6,8) (6,15) (6,18) (6,24) (7,21) (7,16) (7,17) (7,10) (8,9) (8,14) (8,12) (8,19) (8,15) (8,18) (8,24) (9,14) (9,12) (9,22) (9,11) (9,19) (9,15) (9,18) (9,24) (10,21) (10,16) (10,13) (10,23) (11,12) (11,19) (11,15) (12,14) (12,22) (12,15) (12,18) (12,24) (13,16) (13,23) (14,22) (14,19) (14,18) (14,24) (15,22) (15,19) (15,18) (15,24) (16,21) (16,17) (17,21) (17,23) (18,22) (18,19) (18,24) (21,23) (22,24)\nIs there a path between node 16 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph234-7_8", + "image": "data/connectivity/graph_visual/medium/graph234.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,1) (0,12) (0,11) (0,6) (1,6) (2,10) (2,16) (2,18) (2,17) (2,3) (2,5) (2,7) (2,8) (3,10) (3,16) (3,18) (3,9) (3,5) (4,15) (4,14) (5,16) (5,18) (5,9) (5,7) (5,8) (6,12) (6,11) (7,10) (7,16) (7,18) (7,17) (7,9) (8,10) (8,16) (8,13) (8,18) (8,17) (8,9) (9,10) (9,16) (9,17) (10,16) (10,13) (10,18) (10,17) (13,16) (13,18) (13,17) (14,15) (16,18) (16,17) (17,18)\nIs there a path between node 7 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph173-11_5", + "image": "data/connectivity/graph_visual/medium/graph173.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,7) (0,17) (0,11) (0,15) (0,12) (0,4) (0,14) (0,8) (0,16) (0,5) (1,7) (1,11) (1,15) (1,2) (1,9) (1,12) (1,14) (1,13) (1,5) (2,7) (2,11) (2,15) (2,9) (2,12) (2,4) (2,14) (2,13) (2,8) (2,16) (2,5) (4,7) (4,12) (5,17) (5,11) (5,15) (5,12) (5,13) (5,16) (6,10) (7,17) (7,11) (7,12) (7,14) (7,8) (8,11) (8,13) (8,16) (9,17) (9,11) (9,15) (9,12) (9,13) (9,16) (11,15) (11,12) (11,14) (11,13) (11,16) (12,17) (12,15) (12,14) (12,16) (13,17) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 11 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph344-17_0", + "image": "data/connectivity/graph_visual/medium/graph344.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,14) (0,8) (0,2) (0,1) (0,18) (0,4) (0,5) (0,16) (0,10) (0,19) (0,6) (0,7) (1,14) (1,8) (1,2) (1,18) (1,4) (1,5) (1,16) (1,10) (1,19) (1,6) (1,7) (2,14) (2,8) (2,18) (2,4) (2,5) (2,16) (2,10) (2,19) (2,6) (2,7) (3,17) (3,11) (3,9) (3,15) (3,20) (3,12) (3,13) (4,14) (4,8) (4,18) (4,5) (4,16) (4,10) (4,19) (4,6) (4,7) (5,14) (5,8) (5,18) (5,16) (5,10) (5,19) (5,6) (5,7) (6,14) (6,8) (6,18) (6,16) (6,10) (6,19) (6,7) (7,14) (7,8) (7,18) (7,16) (7,10) (7,19) (8,14) (8,18) (8,16) (8,10) (8,19) (9,17) (9,11) (9,15) (9,20) (9,12) (9,13) (10,14) (10,18) (10,16) (10,19) (11,17) (11,15) (11,20) (11,12) (11,13) (12,17) (12,15) (12,20) (12,13) (13,17) (13,15) (13,20) (14,18) (14,16) (14,19) (15,17) (15,20) (16,18) (16,19) (17,20) (18,19)\nIs there a path between node 17 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph345-9_7", + "image": "data/connectivity/graph_visual/medium/graph345.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,14) (0,6) (0,12) (0,18) (0,1) (0,2) (0,10) (0,15) (0,5) (0,4) (0,16) (0,3) (0,8) (0,19) (0,17) (0,11) (0,13) (0,9) (1,14) (1,6) (1,12) (1,18) (1,2) (1,10) (1,15) (1,5) (1,4) (1,16) (1,3) (1,8) (1,19) (1,17) (1,11) (1,13) (1,9) (2,14) (2,6) (2,12) (2,18) (2,10) (2,15) (2,5) (2,4) (2,16) (2,3) (2,8) (2,19) (2,17) (2,11) (2,13) (2,9) (3,14) (3,6) (3,12) (3,18) (3,10) (3,15) (3,5) (3,4) (3,16) (3,8) (3,19) (3,17) (3,11) (3,13) (3,9) (4,14) (4,6) (4,12) (4,18) (4,10) (4,15) (4,5) (4,16) (4,8) (4,19) (4,17) (4,11) (4,13) (4,9) (5,14) (5,6) (5,12) (5,18) (5,10) (5,15) (5,16) (5,8) (5,19) (5,17) (5,11) (5,13) (5,9) (6,14) (6,12) (6,18) (6,10) (6,15) (6,16) (6,8) (6,19) (6,17) (6,11) (6,13) (6,9) (7,20) (8,14) (8,12) (8,18) (8,10) (8,15) (8,16) (8,19) (8,17) (8,11) (8,13) (8,9) (9,14) (9,12) (9,18) (9,10) (9,15) (9,16) (9,19) (9,17) (9,11) (9,13) (10,14) (10,12) (10,18) (10,15) (10,16) (10,19) (10,17) (10,11) (10,13) (11,14) (11,12) (11,18) (11,15) (11,16) (11,19) (11,17) (11,13) (12,14) (12,18) (12,15) (12,16) (12,19) (12,17) (12,13) (13,14) (13,18) (13,15) (13,16) (13,19) (13,17) (14,18) (14,15) (14,16) (14,19) (14,17) (15,18) (15,16) (15,19) (15,17) (16,18) (16,19) (16,17) (17,18) (17,19) (18,19)\nIs there a path between node 9 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph276-0_5", + "image": "data/connectivity/graph_visual/medium/graph276.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,10) (1,9) (1,16) (1,4) (1,12) (2,8) (2,19) (2,7) (2,14) (2,17) (2,5) (2,18) (2,6) (2,11) (2,3) (2,13) (2,15) (3,8) (3,19) (3,7) (3,14) (3,17) (3,5) (3,18) (3,6) (3,11) (3,13) (3,15) (4,10) (4,9) (4,16) (4,12) (5,8) (5,19) (5,7) (5,14) (5,17) (5,18) (5,6) (5,11) (5,13) (5,15) (6,8) (6,19) (6,7) (6,14) (6,17) (6,18) (6,11) (6,13) (6,15) (7,8) (7,19) (7,14) (7,17) (7,18) (7,11) (7,13) (7,15) (8,19) (8,14) (8,17) (8,18) (8,11) (8,13) (8,15) (9,10) (9,16) (9,12) (10,16) (10,12) (11,19) (11,14) (11,17) (11,18) (11,13) (11,15) (12,16) (13,19) (13,14) (13,17) (13,18) (13,15) (14,19) (14,17) (14,18) (14,15) (15,19) (15,17) (15,18) (17,19) (17,18) (18,19)\nIs there a path between node 0 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph405-13_17", + "image": "data/connectivity/graph_visual/medium/graph405.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,12) (0,8) (1,21) (1,5) (1,14) (2,17) (3,15) (3,21) (3,9) (3,5) (3,20) (3,19) (4,16) (4,7) (4,18) (5,15) (5,13) (6,9) (6,10) (6,20) (7,12) (9,10) (9,20) (9,14) (9,13) (10,21) (10,11) (11,15) (11,14) (13,14) (14,21) (15,19) (16,18) (20,21)\nIs there a path between node 13 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph30-0_6", + "image": "data/connectivity/graph_visual/medium/graph30.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,5) (0,6) (0,4) (0,9) (0,11) (0,1) (0,7) (1,5) (1,6) (1,4) (1,9) (1,11) (1,7) (2,10) (2,3) (2,8) (3,10) (3,8) (4,5) (4,6) (4,9) (4,11) (4,7) (5,6) (5,9) (5,11) (5,7) (6,9) (6,11) (6,7) (7,9) (7,11) (8,10) (9,11)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph704-0_20", + "image": "data/connectivity/graph_visual/medium/graph704.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,7) (1,9) (1,10) (1,14) (2,3) (2,11) (3,11) (3,12) (4,17) (5,18) (5,17) (6,20) (6,22) (6,17) (6,8) (7,23) (7,18) (7,8) (9,21) (9,16) (9,11) (9,13) (10,14) (11,21) (11,14) (11,13) (12,15) (13,21) (13,15) (13,14) (14,15) (17,18) (17,19) (18,23) (18,24) (19,24) (19,22)\nIs there a path between node 0 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph529-13_1", + "image": "data/connectivity/graph_visual/medium/graph529.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,20) (0,19) (0,14) (0,2) (0,9) (0,13) (0,21) (0,12) (0,18) (0,16) (0,7) (1,17) (1,5) (1,4) (1,22) (1,11) (1,3) (1,8) (1,15) (1,10) (1,6) (2,20) (2,19) (2,14) (2,9) (2,13) (2,21) (2,12) (2,18) (2,16) (2,7) (3,17) (3,5) (3,4) (3,22) (3,11) (3,8) (3,15) (3,10) (3,6) (4,17) (4,5) (4,22) (4,11) (4,8) (4,15) (4,10) (4,6) (5,17) (5,22) (5,11) (5,8) (5,15) (5,10) (5,6) (6,17) (6,22) (6,11) (6,8) (6,15) (6,10) (7,20) (7,19) (7,14) (7,9) (7,13) (7,21) (7,12) (7,18) (7,16) (8,17) (8,22) (8,11) (8,15) (8,10) (9,20) (9,19) (9,14) (9,13) (9,21) (9,12) (9,18) (9,16) (10,17) (10,22) (10,11) (10,15) (11,17) (11,22) (11,15) (12,20) (12,19) (12,14) (12,13) (12,21) (12,18) (12,16) (13,20) (13,19) (13,14) (13,21) (13,18) (13,16) (14,20) (14,19) (14,21) (14,18) (14,16) (15,17) (15,22) (16,20) (16,19) (16,21) (16,18) (17,22) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 13 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph312-10_17", + "image": "data/connectivity/graph_visual/medium/graph312.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (0,12) (0,6) (0,18) (0,16) (1,15) (1,17) (1,2) (1,19) (1,5) (1,14) (1,10) (1,13) (1,4) (1,7) (1,11) (1,9) (2,15) (2,17) (2,19) (2,5) (2,14) (2,10) (2,13) (2,4) (2,7) (2,11) (2,9) (4,15) (4,17) (4,19) (4,5) (4,14) (4,10) (4,13) (4,7) (4,11) (4,9) (5,15) (5,17) (5,19) (5,14) (5,10) (5,13) (5,7) (5,11) (5,9) (6,8) (6,12) (6,18) (6,16) (7,15) (7,17) (7,19) (7,14) (7,10) (7,13) (7,11) (7,9) (8,12) (8,18) (8,16) (9,15) (9,17) (9,19) (9,14) (9,10) (9,13) (9,11) (10,15) (10,17) (10,19) (10,14) (10,13) (10,11) (11,15) (11,17) (11,19) (11,14) (11,13) (12,18) (12,16) (13,15) (13,17) (13,19) (13,14) (14,15) (14,17) (14,19) (15,17) (15,19) (16,18) (17,19)\nIs there a path between node 10 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph484-9_18", + "image": "data/connectivity/graph_visual/medium/graph484.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,11) (0,16) (1,15) (1,12) (1,6) (1,9) (1,10) (1,22) (1,13) (1,4) (1,2) (1,14) (2,15) (2,7) (2,9) (2,19) (2,13) (2,4) (3,21) (3,8) (4,7) (4,12) (4,6) (4,10) (4,19) (4,22) (4,13) (4,5) (4,14) (5,15) (5,7) (5,12) (5,6) (5,22) (5,13) (5,14) (6,15) (6,10) (6,14) (7,15) (7,12) (7,9) (7,10) (7,22) (8,17) (8,21) (8,20) (9,10) (9,13) (9,14) (10,15) (10,19) (10,13) (10,14) (11,16) (12,15) (12,19) (12,22) (12,13) (13,15) (13,19) (13,22) (13,14) (14,15) (15,19) (15,22) (19,22)\nIs there a path between node 9 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph779-11_6", + "image": "data/connectivity/graph_visual/medium/graph779.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,8) (0,19) (0,17) (0,22) (0,12) (0,16) (0,1) (0,10) (0,23) (0,14) (0,15) (0,6) (0,11) (0,21) (0,3) (0,20) (0,18) (0,24) (0,4) (0,2) (1,7) (1,8) (1,19) (1,17) (1,22) (1,12) (1,16) (1,10) (1,23) (1,14) (1,15) (1,6) (1,11) (1,21) (1,3) (1,20) (1,18) (1,24) (1,4) (1,2) (2,7) (2,8) (2,19) (2,17) (2,22) (2,12) (2,16) (2,10) (2,23) (2,14) (2,15) (2,6) (2,11) (2,21) (2,3) (2,20) (2,18) (2,24) (2,4) (3,7) (3,8) (3,19) (3,17) (3,22) (3,12) (3,16) (3,10) (3,23) (3,14) (3,15) (3,6) (3,11) (3,21) (3,20) (3,18) (3,24) (3,4) (4,7) (4,8) (4,19) (4,17) (4,22) (4,12) (4,16) (4,10) (4,23) (4,14) (4,15) (4,6) (4,11) (4,21) (4,20) (4,18) (4,24) (5,13) (5,9) (6,7) (6,8) (6,19) (6,17) (6,22) (6,12) (6,16) (6,10) (6,23) (6,14) (6,15) (6,11) (6,21) (6,20) (6,18) (6,24) (7,8) (7,19) (7,17) (7,22) (7,12) (7,16) (7,10) (7,23) (7,14) (7,15) (7,11) (7,21) (7,20) (7,18) (7,24) (8,19) (8,17) (8,22) (8,12) (8,16) (8,10) (8,23) (8,14) (8,15) (8,11) (8,21) (8,20) (8,18) (8,24) (9,13) (10,19) (10,17) (10,22) (10,12) (10,16) (10,23) (10,14) (10,15) (10,11) (10,21) (10,20) (10,18) (10,24) (11,19) (11,17) (11,22) (11,12) (11,16) (11,23) (11,14) (11,15) (11,21) (11,20) (11,18) (11,24) (12,19) (12,17) (12,22) (12,16) (12,23) (12,14) (12,15) (12,21) (12,20) (12,18) (12,24) (14,19) (14,17) (14,22) (14,16) (14,23) (14,15) (14,21) (14,20) (14,18) (14,24) (15,19) (15,17) (15,22) (15,16) (15,23) (15,21) (15,20) (15,18) (15,24) (16,19) (16,17) (16,22) (16,23) (16,21) (16,20) (16,18) (16,24) (17,19) (17,22) (17,23) (17,21) (17,20) (17,18) (17,24) (18,19) (18,22) (18,23) (18,21) (18,20) (18,24) (19,22) (19,23) (19,21) (19,20) (19,24) (20,22) (20,23) (20,21) (20,24) (21,22) (21,23) (21,24) (22,23) (22,24) (23,24)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph545-4_16", + "image": "data/connectivity/graph_visual/medium/graph545.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,17) (0,23) (0,22) (0,1) (0,9) (0,11) (0,14) (0,19) (0,12) (0,18) (0,8) (0,4) (0,16) (0,15) (0,10) (0,6) (1,20) (1,17) (1,23) (1,22) (1,9) (1,11) (1,14) (1,19) (1,12) (1,18) (1,8) (1,4) (1,16) (1,15) (1,10) (1,6) (2,13) (2,5) (2,3) (2,21) (2,7) (3,13) (3,5) (3,21) (3,7) (4,20) (4,17) (4,23) (4,22) (4,9) (4,11) (4,14) (4,19) (4,12) (4,18) (4,8) (4,16) (4,15) (4,10) (4,6) (5,13) (5,21) (5,7) (6,20) (6,17) (6,23) (6,22) (6,9) (6,11) (6,14) (6,19) (6,12) (6,18) (6,8) (6,16) (6,15) (6,10) (7,13) (7,21) (8,20) (8,17) (8,23) (8,22) (8,9) (8,11) (8,14) (8,19) (8,12) (8,18) (8,16) (8,15) (8,10) (9,20) (9,17) (9,23) (9,22) (9,11) (9,14) (9,19) (9,12) (9,18) (9,16) (9,15) (9,10) (10,20) (10,17) (10,23) (10,22) (10,11) (10,14) (10,19) (10,12) (10,18) (10,16) (10,15) (11,20) (11,17) (11,23) (11,22) (11,14) (11,19) (11,12) (11,18) (11,16) (11,15) (12,20) (12,17) (12,23) (12,22) (12,14) (12,19) (12,18) (12,16) (12,15) (13,21) (14,20) (14,17) (14,23) (14,22) (14,19) (14,18) (14,16) (14,15) (15,20) (15,17) (15,23) (15,22) (15,19) (15,18) (15,16) (16,20) (16,17) (16,23) (16,22) (16,19) (16,18) (17,20) (17,23) (17,22) (17,19) (17,18) (18,20) (18,23) (18,22) (18,19) (19,20) (19,23) (19,22) (20,23) (20,22) (22,23)\nIs there a path between node 4 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph107-5_14", + "image": "data/connectivity/graph_visual/medium/graph107.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (0,7) (0,14) (0,5) (0,13) (0,10) (1,7) (1,14) (1,5) (1,13) (1,10) (2,6) (2,12) (2,4) (2,8) (2,15) (2,3) (2,9) (2,11) (3,6) (3,12) (3,4) (3,8) (3,15) (3,9) (3,11) (4,6) (4,12) (4,8) (4,15) (4,9) (4,11) (5,7) (5,14) (5,13) (5,10) (6,12) (6,8) (6,15) (6,9) (6,11) (7,14) (7,13) (7,10) (8,12) (8,15) (8,9) (8,11) (9,12) (9,15) (9,11) (10,14) (10,13) (11,12) (11,15) (12,15) (13,14)\nIs there a path between node 5 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph650-14_20", + "image": "data/connectivity/graph_visual/medium/graph650.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,22) (0,8) (0,16) (0,23) (0,21) (0,5) (1,14) (1,12) (1,9) (1,18) (1,17) (1,15) (1,10) (1,13) (2,20) (2,19) (2,22) (2,6) (2,8) (2,16) (2,21) (2,5) (2,4) (3,11) (3,14) (3,7) (3,18) (3,15) (3,10) (4,20) (4,22) (4,8) (4,23) (4,5) (5,20) (5,19) (5,22) (5,6) (5,8) (5,16) (5,21) (6,19) (6,22) (6,8) (6,16) (6,23) (6,21) (7,11) (7,12) (7,18) (7,17) (7,15) (7,10) (7,13) (8,20) (8,19) (8,22) (8,16) (8,21) (9,11) (9,14) (9,12) (9,18) (9,17) (9,13) (10,11) (10,12) (10,17) (10,15) (11,14) (11,12) (11,18) (11,17) (11,15) (11,13) (12,14) (12,17) (12,13) (13,14) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (16,20) (16,19) (16,22) (17,18) (19,20) (19,22) (19,23) (19,21) (20,22) (20,21) (21,22) (22,23)\nIs there a path between node 14 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph424-12_4", + "image": "data/connectivity/graph_visual/medium/graph424.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,13) (2,4) (2,11) (2,5) (2,21) (3,6) (3,5) (3,17) (4,12) (4,11) (4,20) (4,21) (5,12) (5,10) (5,7) (6,20) (6,17) (7,12) (7,8) (7,20) (7,10) (7,17) (8,10) (8,21) (10,11) (10,20) (11,12) (12,20) (13,18) (14,19) (16,19)\nIs there a path between node 12 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph283-9_0", + "image": "data/connectivity/graph_visual/medium/graph283.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,10) (0,8) (1,12) (1,13) (1,5) (2,7) (3,16) (4,18) (4,7) (4,17) (5,15) (5,14) (6,13) (8,10) (8,17) (11,15) (12,15) (13,14) (14,15) (17,18)\nIs there a path between node 9 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph21-9_0", + "image": "data/connectivity/graph_visual/medium/graph21.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,9) (0,1) (1,7) (1,9) (2,3) (2,6) (3,10) (4,8) (7,9) (8,9) (10,11)\nIs there a path between node 9 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph404-6_17", + "image": "data/connectivity/graph_visual/medium/graph404.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,19) (2,11) (3,4) (3,6) (3,9) (4,20) (4,5) (4,15) (4,12) (5,6) (6,11) (6,20) (6,19) (6,15) (7,14) (7,18) (7,21) (7,13) (7,12) (8,10) (9,12) (10,18) (10,15) (11,20) (12,18) (13,20) (14,21) (15,18) (15,21) (15,19) (18,21)\nIs there a path between node 6 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph272-16_12", + "image": "data/connectivity/graph_visual/medium/graph272.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,13) (0,9) (0,7) (0,12) (0,4) (0,5) (0,19) (0,6) (0,1) (0,17) (1,14) (1,9) (1,3) (1,7) (1,12) (1,4) (1,5) (1,19) (1,15) (1,17) (2,11) (2,8) (2,10) (3,13) (3,14) (3,9) (3,7) (3,12) (3,4) (3,5) (3,6) (3,18) (3,15) (4,13) (4,9) (4,12) (4,19) (4,6) (4,18) (4,15) (4,17) (5,13) (5,14) (5,7) (5,12) (5,19) (5,15) (5,17) (6,13) (6,9) (6,7) (6,19) (6,15) (6,17) (7,13) (7,14) (7,9) (7,12) (7,19) (7,18) (7,17) (8,11) (8,16) (8,10) (9,14) (9,18) (9,17) (10,11) (11,16) (12,14) (12,19) (12,18) (12,15) (12,17) (13,14) (13,19) (13,18) (13,17) (14,19) (14,18) (14,15) (14,17) (15,17) (17,19) (17,18) (18,19)\nIs there a path between node 16 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph697-14_7", + "image": "data/connectivity/graph_visual/medium/graph697.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,6) (0,21) (0,17) (0,16) (0,20) (0,7) (0,12) (0,14) (0,22) (0,15) (1,18) (1,4) (1,2) (1,10) (1,3) (1,23) (1,19) (1,11) (1,9) (1,13) (1,8) (2,18) (2,4) (2,10) (2,3) (2,23) (2,19) (2,11) (2,9) (2,13) (2,8) (3,18) (3,4) (3,10) (3,23) (3,19) (3,11) (3,9) (3,13) (3,8) (4,18) (4,10) (4,23) (4,19) (4,11) (4,9) (4,13) (4,8) (5,6) (5,21) (5,17) (5,16) (5,20) (5,7) (5,12) (5,14) (5,22) (5,15) (6,21) (6,17) (6,16) (6,20) (6,7) (6,12) (6,14) (6,22) (6,15) (7,21) (7,17) (7,16) (7,20) (7,12) (7,14) (7,22) (7,15) (8,18) (8,10) (8,23) (8,19) (8,11) (8,9) (8,13) (9,18) (9,10) (9,23) (9,19) (9,11) (9,13) (10,18) (10,23) (10,19) (10,11) (10,13) (11,18) (11,23) (11,19) (11,13) (12,21) (12,17) (12,16) (12,20) (12,14) (12,22) (12,15) (13,18) (13,23) (13,19) (14,21) (14,17) (14,16) (14,20) (14,22) (14,15) (15,21) (15,17) (15,16) (15,20) (15,22) (16,21) (16,17) (16,20) (16,22) (17,21) (17,20) (17,22) (18,23) (18,19) (19,23) (20,21) (20,22) (21,22)\nIs there a path between node 14 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph221-10_18", + "image": "data/connectivity/graph_visual/medium/graph221.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,11) (0,15) (1,12) (1,2) (1,8) (1,3) (1,15) (2,13) (2,3) (2,14) (2,15) (3,6) (3,12) (3,13) (3,11) (3,14) (3,9) (3,7) (4,8) (4,11) (4,14) (4,16) (5,6) (5,17) (5,15) (5,7) (6,8) (6,11) (6,17) (6,16) (7,13) (7,16) (8,12) (8,17) (8,14) (9,13) (9,15) (11,15) (12,17) (13,17) (14,16) (15,17) (16,17)\nIs there a path between node 10 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph630-12_22", + "image": "data/connectivity/graph_visual/medium/graph630.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,10) (0,7) (0,11) (1,22) (1,21) (2,10) (2,7) (2,12) (2,3) (2,11) (2,20) (3,14) (3,18) (3,5) (3,7) (3,11) (4,10) (4,12) (5,14) (5,17) (5,11) (5,23) (7,19) (7,18) (7,10) (7,21) (8,13) (9,13) (10,18) (10,15) (10,12) (11,21) (12,14) (12,15) (12,21) (14,20) (15,23) (17,19) (17,18) (17,20) (18,19) (20,23) (22,23)\nIs there a path between node 12 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph309-7_16", + "image": "data/connectivity/graph_visual/medium/graph309.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,2) (0,18) (0,11) (0,9) (0,10) (0,7) (0,8) (0,19) (0,17) (0,15) (0,13) (0,5) (1,4) (1,2) (1,18) (1,9) (1,10) (1,6) (1,16) (1,8) (1,19) (1,17) (1,15) (1,5) (2,18) (2,11) (2,10) (2,7) (2,16) (2,8) (2,19) (2,13) (2,5) (4,18) (4,11) (4,9) (4,10) (4,7) (4,16) (4,8) (4,17) (4,13) (4,5) (5,18) (5,9) (5,10) (5,6) (5,16) (5,8) (5,15) (5,13) (6,18) (6,10) (6,16) (6,8) (6,15) (6,13) (7,18) (7,9) (7,10) (7,16) (7,8) (7,19) (7,17) (7,15) (8,18) (8,9) (8,10) (8,16) (8,19) (8,15) (9,18) (9,11) (9,10) (9,17) (9,15) (9,13) (10,18) (10,11) (10,16) (10,19) (10,15) (10,13) (11,16) (11,19) (11,17) (11,13) (12,14) (13,16) (13,19) (13,17) (13,15) (15,18) (15,19) (15,17) (16,18) (16,19) (16,17) (17,18)\nIs there a path between node 7 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph347-6_11", + "image": "data/connectivity/graph_visual/medium/graph347.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,13) (0,3) (0,19) (0,12) (0,15) (0,17) (1,20) (1,6) (1,2) (1,7) (2,20) (2,6) (2,7) (3,10) (3,13) (3,19) (3,12) (3,15) (3,17) (4,11) (4,9) (4,18) (4,16) (4,14) (4,8) (4,5) (5,11) (5,9) (5,18) (5,16) (5,14) (5,8) (6,20) (6,7) (7,20) (8,11) (8,9) (8,18) (8,16) (8,14) (9,11) (9,18) (9,16) (9,14) (10,13) (10,19) (10,12) (10,15) (10,17) (11,18) (11,16) (11,14) (12,13) (12,19) (12,15) (12,17) (13,19) (13,15) (13,17) (14,18) (14,16) (15,19) (15,17) (16,18) (17,19)\nIs there a path between node 6 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph701-22_3", + "image": "data/connectivity/graph_visual/medium/graph701.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,18) (0,19) (0,20) (0,23) (0,9) (0,10) (0,22) (0,13) (0,1) (0,12) (0,5) (0,7) (0,15) (0,4) (1,11) (1,18) (1,19) (1,20) (1,23) (1,9) (1,10) (1,22) (1,13) (1,12) (1,5) (1,7) (1,15) (1,4) (2,8) (2,6) (2,3) (2,24) (2,16) (2,21) (2,17) (2,14) (3,8) (3,6) (3,24) (3,16) (3,21) (3,17) (3,14) (4,11) (4,18) (4,19) (4,20) (4,23) (4,9) (4,10) (4,22) (4,13) (4,12) (4,5) (4,7) (4,15) (5,11) (5,18) (5,19) (5,20) (5,23) (5,9) (5,10) (5,22) (5,13) (5,12) (5,7) (5,15) (6,8) (6,24) (6,16) (6,21) (6,17) (6,14) (7,11) (7,18) (7,19) (7,20) (7,23) (7,9) (7,10) (7,22) (7,13) (7,12) (7,15) (8,24) (8,16) (8,21) (8,17) (8,14) (9,11) (9,18) (9,19) (9,20) (9,23) (9,10) (9,22) (9,13) (9,12) (9,15) (10,11) (10,18) (10,19) (10,20) (10,23) (10,22) (10,13) (10,12) (10,15) (11,18) (11,19) (11,20) (11,23) (11,22) (11,13) (11,12) (11,15) (12,18) (12,19) (12,20) (12,23) (12,22) (12,13) (12,15) (13,18) (13,19) (13,20) (13,23) (13,22) (13,15) (14,24) (14,16) (14,21) (14,17) (15,18) (15,19) (15,20) (15,23) (15,22) (16,24) (16,21) (16,17) (17,24) (17,21) (18,19) (18,20) (18,23) (18,22) (19,20) (19,23) (19,22) (20,23) (20,22) (21,24) (22,23)\nIs there a path between node 22 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph54-0_10", + "image": "data/connectivity/graph_visual/medium/graph54.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,9) (0,3) (0,5) (1,2) (1,8) (1,7) (2,8) (2,7) (3,11) (3,9) (3,13) (5,11) (5,12) (10,11) (11,12) (12,13)\nIs there a path between node 0 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph554-5_16", + "image": "data/connectivity/graph_visual/medium/graph554.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,8) (0,4) (0,10) (2,13) (3,17) (4,12) (4,14) (4,19) (6,22) (7,18) (7,23) (7,16) (7,17) (7,13) (8,12) (8,20) (9,21) (9,19) (10,14) (11,21) (11,15) (12,20) (13,18) (13,23) (14,15) (16,18) (17,23) (19,20)\nIs there a path between node 5 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph614-23_18", + "image": "data/connectivity/graph_visual/medium/graph614.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,18) (0,1) (0,6) (0,10) (1,8) (1,18) (1,6) (1,10) (2,21) (2,20) (2,19) (2,14) (2,16) (2,13) (2,3) (2,12) (2,4) (2,22) (2,11) (2,9) (2,17) (2,15) (3,21) (3,20) (3,19) (3,14) (3,16) (3,13) (3,12) (3,4) (3,22) (3,11) (3,9) (3,17) (3,15) (4,21) (4,20) (4,19) (4,14) (4,16) (4,13) (4,12) (4,22) (4,11) (4,9) (4,17) (4,15) (5,7) (6,8) (6,18) (6,10) (8,18) (8,10) (9,21) (9,20) (9,19) (9,14) (9,16) (9,13) (9,12) (9,22) (9,11) (9,17) (9,15) (10,18) (11,21) (11,20) (11,19) (11,14) (11,16) (11,13) (11,12) (11,22) (11,17) (11,15) (12,21) (12,20) (12,19) (12,14) (12,16) (12,13) (12,22) (12,17) (12,15) (13,21) (13,20) (13,19) (13,14) (13,16) (13,22) (13,17) (13,15) (14,21) (14,20) (14,19) (14,16) (14,22) (14,17) (14,15) (15,21) (15,20) (15,19) (15,16) (15,22) (15,17) (16,21) (16,20) (16,19) (16,22) (16,17) (17,21) (17,20) (17,19) (17,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 23 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph582-19_18", + "image": "data/connectivity/graph_visual/medium/graph582.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,19) (1,7) (1,14) (1,11) (1,2) (1,17) (2,4) (3,7) (3,14) (3,19) (3,4) (4,7) (4,5) (4,8) (4,19) (4,17) (5,11) (7,13) (7,17) (8,11) (8,17) (9,22) (9,21) (9,10) (11,19) (14,19) (15,22) (18,20)\nIs there a path between node 19 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph613-15_17", + "image": "data/connectivity/graph_visual/medium/graph613.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,17) (0,8) (0,22) (0,21) (0,12) (0,6) (0,3) (0,11) (0,20) (0,7) (0,18) (0,19) (0,13) (0,16) (0,4) (0,14) (0,1) (1,9) (1,17) (1,8) (1,22) (1,21) (1,12) (1,6) (1,3) (1,11) (1,20) (1,7) (1,18) (1,19) (1,13) (1,16) (1,4) (1,14) (2,5) (2,15) (2,10) (2,23) (3,9) (3,17) (3,8) (3,22) (3,21) (3,12) (3,6) (3,11) (3,20) (3,7) (3,18) (3,19) (3,13) (3,16) (3,4) (3,14) (4,9) (4,17) (4,8) (4,22) (4,21) (4,12) (4,6) (4,11) (4,20) (4,7) (4,18) (4,19) (4,13) (4,16) (4,14) (5,15) (5,10) (5,23) (6,9) (6,17) (6,8) (6,22) (6,21) (6,12) (6,11) (6,20) (6,7) (6,18) (6,19) (6,13) (6,16) (6,14) (7,9) (7,17) (7,8) (7,22) (7,21) (7,12) (7,11) (7,20) (7,18) (7,19) (7,13) (7,16) (7,14) (8,9) (8,17) (8,22) (8,21) (8,12) (8,11) (8,20) (8,18) (8,19) (8,13) (8,16) (8,14) (9,17) (9,22) (9,21) (9,12) (9,11) (9,20) (9,18) (9,19) (9,13) (9,16) (9,14) (10,15) (10,23) (11,17) (11,22) (11,21) (11,12) (11,20) (11,18) (11,19) (11,13) (11,16) (11,14) (12,17) (12,22) (12,21) (12,20) (12,18) (12,19) (12,13) (12,16) (12,14) (13,17) (13,22) (13,21) (13,20) (13,18) (13,19) (13,16) (13,14) (14,17) (14,22) (14,21) (14,20) (14,18) (14,19) (14,16) (15,23) (16,17) (16,22) (16,21) (16,20) (16,18) (16,19) (17,22) (17,21) (17,20) (17,18) (17,19) (18,22) (18,21) (18,20) (18,19) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 15 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph656-19_13", + "image": "data/connectivity/graph_visual/medium/graph656.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,19) (0,4) (0,17) (0,16) (0,22) (0,20) (0,18) (0,10) (0,21) (0,7) (0,8) (0,9) (0,15) (0,14) (1,3) (1,13) (1,6) (1,4) (1,16) (1,22) (1,20) (1,10) (1,21) (1,5) (1,7) (1,9) (1,15) (1,14) (2,11) (3,13) (3,6) (3,19) (3,4) (3,17) (3,16) (3,22) (3,20) (3,18) (3,10) (3,5) (3,7) (3,23) (3,8) (3,14) (4,13) (4,19) (4,17) (4,20) (4,18) (4,10) (4,5) (4,7) (4,23) (4,8) (4,15) (4,14) (5,13) (5,6) (5,19) (5,17) (5,16) (5,22) (5,20) (5,10) (5,23) (5,9) (5,14) (6,13) (6,17) (6,22) (6,18) (6,10) (6,21) (6,7) (6,23) (6,15) (6,14) (7,13) (7,19) (7,17) (7,16) (7,22) (7,20) (7,18) (7,10) (7,21) (7,9) (7,14) (8,19) (8,20) (8,18) (8,10) (8,21) (8,9) (8,15) (9,13) (9,19) (9,17) (9,16) (9,22) (9,21) (9,14) (10,13) (10,17) (10,22) (10,20) (10,18) (10,23) (10,15) (10,14) (13,17) (13,16) (13,22) (13,20) (13,18) (13,21) (13,23) (13,15) (13,14) (14,17) (14,16) (14,20) (14,18) (14,23) (15,19) (15,17) (15,16) (15,22) (15,20) (15,21) (15,23) (16,18) (16,21) (17,19) (17,22) (17,20) (17,23) (18,19) (18,22) (18,20) (18,21) (18,23) (19,22) (19,20) (19,21) (20,22) (21,22) (21,23) (22,23)\nIs there a path between node 19 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph513-9_2", + "image": "data/connectivity/graph_visual/medium/graph513.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,3) (0,12) (0,7) (0,14) (0,2) (0,4) (0,19) (0,10) (0,16) (0,8) (0,6) (0,20) (0,1) (1,5) (1,21) (1,3) (1,14) (1,11) (1,2) (1,4) (1,8) (1,6) (1,20) (2,5) (2,21) (2,3) (2,12) (2,14) (2,11) (2,4) (2,19) (2,10) (2,16) (2,6) (3,5) (3,21) (3,7) (3,11) (3,4) (3,19) (3,10) (3,16) (3,8) (3,6) (3,20) (4,21) (4,7) (4,14) (4,11) (4,19) (4,10) (4,16) (4,8) (4,6) (5,21) (5,12) (5,7) (5,14) (5,11) (5,19) (5,10) (5,16) (5,8) (5,6) (5,20) (6,12) (6,7) (6,11) (6,10) (6,16) (6,8) (6,20) (7,21) (7,11) (7,10) (7,8) (7,20) (8,12) (8,14) (8,10) (8,16) (8,20) (9,13) (9,15) (9,18) (10,12) (10,14) (10,11) (10,16) (10,20) (11,12) (11,14) (11,20) (12,19) (12,16) (12,20) (13,15) (14,21) (14,16) (14,20) (16,21) (16,19) (16,20) (19,21) (19,20)\nIs there a path between node 9 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph284-18_8", + "image": "data/connectivity/graph_visual/medium/graph284.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,2) (1,7) (1,15) (2,12) (2,15) (3,17) (3,7) (3,12) (3,15) (4,14) (4,16) (4,15) (5,9) (5,6) (6,18) (6,9) (6,13) (7,12) (8,12) (9,18) (10,19) (14,16) (14,15) (16,17)\nIs there a path between node 18 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph810-13_20", + "image": "data/connectivity/graph_visual/medium/graph810.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,6) (0,1) (0,21) (0,23) (0,16) (1,8) (1,6) (1,24) (1,5) (1,3) (1,15) (1,2) (1,21) (1,23) (1,7) (2,9) (2,24) (2,3) (2,15) (2,21) (2,16) (3,9) (3,8) (3,15) (3,7) (4,11) (4,14) (4,20) (5,9) (5,8) (5,17) (5,6) (5,15) (5,21) (5,23) (5,7) (6,9) (6,17) (6,24) (6,15) (6,21) (6,23) (6,7) (7,9) (7,8) (7,24) (7,15) (7,21) (7,16) (8,24) (8,15) (8,21) (8,23) (8,16) (9,24) (9,15) (9,21) (9,16) (10,19) (10,18) (11,14) (11,20) (12,18) (12,22) (14,20) (15,17) (15,24) (15,21) (15,23) (16,17) (16,24) (16,21) (16,23) (17,24) (17,21) (18,19) (19,22) (21,24) (23,24)\nIs there a path between node 13 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph838-10_18", + "image": "data/connectivity/graph_visual/medium/graph838.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,22) (1,18) (1,7) (1,23) (1,2) (1,24) (1,9) (1,21) (1,14) (1,17) (1,16) (1,3) (1,15) (1,6) (1,19) (2,18) (2,7) (2,23) (2,24) (2,9) (2,21) (2,14) (2,17) (2,16) (2,3) (2,15) (2,6) (2,19) (3,18) (3,7) (3,23) (3,24) (3,9) (3,21) (3,14) (3,17) (3,16) (3,15) (3,6) (3,19) (4,11) (4,20) (4,13) (4,5) (4,8) (4,10) (4,12) (5,11) (5,20) (5,13) (5,8) (5,10) (5,12) (6,18) (6,7) (6,23) (6,24) (6,9) (6,21) (6,14) (6,17) (6,16) (6,15) (6,19) (7,18) (7,23) (7,24) (7,9) (7,21) (7,14) (7,17) (7,16) (7,15) (7,19) (8,11) (8,20) (8,13) (8,10) (8,12) (9,18) (9,23) (9,24) (9,21) (9,14) (9,17) (9,16) (9,15) (9,19) (10,11) (10,20) (10,13) (10,12) (11,20) (11,13) (11,12) (12,20) (12,13) (13,20) (14,18) (14,23) (14,24) (14,21) (14,17) (14,16) (14,15) (14,19) (15,18) (15,23) (15,24) (15,21) (15,17) (15,16) (15,19) (16,18) (16,23) (16,24) (16,21) (16,17) (16,19) (17,18) (17,23) (17,24) (17,21) (17,19) (18,23) (18,24) (18,21) (18,19) (19,23) (19,24) (19,21) (21,23) (21,24) (23,24)\nIs there a path between node 10 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph709-10_3", + "image": "data/connectivity/graph_visual/medium/graph709.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,22) (0,5) (0,1) (1,11) (1,8) (1,3) (2,11) (2,13) (2,16) (2,8) (2,17) (3,11) (3,16) (3,5) (4,21) (4,14) (5,11) (5,22) (5,16) (5,17) (6,18) (6,9) (6,10) (7,22) (7,12) (8,22) (8,16) (8,17) (9,18) (9,15) (9,21) (10,19) (11,22) (11,16) (11,17) (12,13) (12,24) (13,16) (14,18) (14,21) (22,24)\nIs there a path between node 10 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph517-22_13", + "image": "data/connectivity/graph_visual/medium/graph517.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,9) (0,17) (0,20) (1,15) (1,22) (1,14) (1,3) (1,21) (1,5) (1,18) (1,7) (1,6) (1,13) (2,15) (2,3) (2,4) (2,11) (2,21) (2,18) (2,8) (2,13) (3,15) (3,22) (3,12) (3,14) (3,4) (3,11) (3,21) (3,5) (3,7) (3,6) (3,16) (4,15) (4,22) (4,12) (4,14) (4,11) (4,5) (4,7) (4,6) (4,16) (4,8) (4,13) (5,15) (5,22) (5,12) (5,11) (5,21) (5,7) (5,6) (5,8) (5,13) (6,15) (6,12) (6,11) (6,21) (6,18) (6,16) (6,8) (6,13) (7,22) (7,12) (7,14) (7,11) (7,21) (7,16) (7,8) (8,22) (8,14) (8,21) (8,18) (8,16) (8,13) (9,19) (9,10) (9,17) (10,17) (11,22) (11,14) (11,21) (11,18) (11,13) (12,22) (12,14) (12,21) (12,18) (12,16) (12,13) (13,14) (13,18) (13,16) (14,15) (14,21) (14,18) (14,16) (15,21) (16,18) (17,20) (18,22)\nIs there a path between node 22 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph637-21_19", + "image": "data/connectivity/graph_visual/medium/graph637.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,12) (0,2) (1,13) (1,20) (1,6) (1,8) (1,3) (2,22) (3,10) (3,13) (3,20) (3,15) (3,6) (3,12) (3,14) (4,5) (4,23) (5,16) (5,23) (5,11) (6,12) (6,14) (6,21) (7,22) (7,8) (8,18) (8,22) (8,14) (9,16) (9,23) (9,19) (10,18) (10,15) (10,12) (10,22) (11,16) (12,18) (13,18) (13,14) (14,21) (15,21) (16,19) (17,20) (17,18) (20,22) (21,22)\nIs there a path between node 21 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph130-5_14", + "image": "data/connectivity/graph_visual/medium/graph130.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,10) (0,1) (0,5) (0,15) (0,6) (0,4) (0,7) (0,16) (0,13) (0,8) (0,2) (0,12) (0,14) (1,10) (1,5) (1,15) (1,6) (1,4) (1,7) (1,16) (1,13) (1,8) (1,2) (1,12) (1,14) (2,10) (2,5) (2,15) (2,6) (2,4) (2,7) (2,16) (2,13) (2,8) (2,12) (2,14) (3,11) (3,9) (4,10) (4,5) (4,15) (4,6) (4,7) (4,16) (4,13) (4,8) (4,12) (4,14) (5,10) (5,15) (5,6) (5,7) (5,16) (5,13) (5,8) (5,12) (5,14) (6,10) (6,15) (6,7) (6,16) (6,13) (6,8) (6,12) (6,14) (7,10) (7,15) (7,16) (7,13) (7,8) (7,12) (7,14) (8,10) (8,15) (8,16) (8,13) (8,12) (8,14) (9,11) (10,15) (10,16) (10,13) (10,12) (10,14) (12,15) (12,16) (12,13) (12,14) (13,15) (13,16) (13,14) (14,15) (14,16) (15,16)\nIs there a path between node 5 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph10-2_10", + "image": "data/connectivity/graph_visual/medium/graph10.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,1) (0,7) (0,4) (0,9) (0,3) (1,7) (1,2) (1,4) (1,9) (1,3) (2,8) (2,9) (2,3) (3,8) (3,6) (3,4) (3,9) (4,8) (4,6) (5,10) (6,9) (8,9)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph566-17_5", + "image": "data/connectivity/graph_visual/medium/graph566.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (0,9) (0,15) (0,23) (0,4) (0,22) (0,8) (0,7) (0,16) (0,19) (0,3) (0,21) (0,17) (1,6) (1,10) (1,12) (1,2) (1,18) (1,11) (1,14) (1,20) (1,5) (2,6) (2,10) (2,12) (2,18) (2,11) (2,14) (2,20) (2,5) (3,13) (3,9) (3,15) (3,23) (3,4) (3,22) (3,8) (3,7) (3,16) (3,19) (3,21) (3,17) (4,13) (4,9) (4,15) (4,23) (4,22) (4,8) (4,7) (4,16) (4,19) (4,21) (4,17) (5,6) (5,10) (5,12) (5,18) (5,11) (5,14) (5,20) (6,10) (6,12) (6,18) (6,11) (6,14) (6,20) (7,13) (7,9) (7,15) (7,23) (7,22) (7,8) (7,16) (7,19) (7,21) (7,17) (8,13) (8,9) (8,15) (8,23) (8,22) (8,16) (8,19) (8,21) (8,17) (9,13) (9,15) (9,23) (9,22) (9,16) (9,19) (9,21) (9,17) (10,12) (10,18) (10,11) (10,14) (10,20) (11,12) (11,18) (11,14) (11,20) (12,18) (12,14) (12,20) (13,15) (13,23) (13,22) (13,16) (13,19) (13,21) (13,17) (14,18) (14,20) (15,23) (15,22) (15,16) (15,19) (15,21) (15,17) (16,23) (16,22) (16,19) (16,21) (16,17) (17,23) (17,22) (17,19) (17,21) (18,20) (19,23) (19,22) (19,21) (21,23) (21,22) (22,23)\nIs there a path between node 17 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph328-3_14", + "image": "data/connectivity/graph_visual/medium/graph328.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,6) (0,1) (0,19) (1,14) (1,6) (1,2) (1,13) (2,5) (2,12) (2,3) (2,9) (3,8) (3,12) (3,13) (3,17) (3,7) (4,16) (4,10) (5,11) (5,20) (5,6) (5,7) (6,17) (6,7) (7,11) (7,14) (7,13) (7,19) (8,20) (8,19) (9,12) (9,13) (11,14) (11,12) (11,13) (12,14) (12,17) (12,19) (13,20) (13,17) (13,15) (14,19) (14,15) (15,20) (15,18) (17,19) (18,20) (19,20)\nIs there a path between node 3 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph463-12_15", + "image": "data/connectivity/graph_visual/medium/graph463.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,10) (0,20) (0,3) (0,21) (0,2) (0,11) (1,15) (1,12) (1,9) (1,19) (1,7) (1,18) (1,6) (1,13) (1,14) (1,5) (1,17) (1,8) (1,4) (1,16) (2,10) (2,20) (2,3) (2,21) (2,11) (3,10) (3,20) (3,21) (3,11) (4,15) (4,12) (4,9) (4,19) (4,7) (4,18) (4,6) (4,13) (4,14) (4,5) (4,17) (4,8) (4,16) (5,15) (5,12) (5,9) (5,19) (5,7) (5,18) (5,6) (5,13) (5,14) (5,17) (5,8) (5,16) (6,15) (6,12) (6,9) (6,19) (6,7) (6,18) (6,13) (6,14) (6,17) (6,8) (6,16) (7,15) (7,12) (7,9) (7,19) (7,18) (7,13) (7,14) (7,17) (7,8) (7,16) (8,15) (8,12) (8,9) (8,19) (8,18) (8,13) (8,14) (8,17) (8,16) (9,15) (9,12) (9,19) (9,18) (9,13) (9,14) (9,17) (9,16) (10,20) (10,21) (10,11) (11,20) (11,21) (12,15) (12,19) (12,18) (12,13) (12,14) (12,17) (12,16) (13,15) (13,19) (13,18) (13,14) (13,17) (13,16) (14,15) (14,19) (14,18) (14,17) (14,16) (15,19) (15,18) (15,17) (15,16) (16,19) (16,18) (16,17) (17,19) (17,18) (18,19) (20,21)\nIs there a path between node 12 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph468-20_4", + "image": "data/connectivity/graph_visual/medium/graph468.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,14) (0,20) (0,13) (1,2) (1,8) (1,9) (2,9) (4,10) (4,20) (5,21) (5,17) (5,9) (6,10) (6,14) (6,13) (7,21) (7,22) (8,9) (10,19) (10,18) (10,12) (10,13) (11,16) (11,18) (12,16) (12,19) (12,18) (13,19) (14,19) (16,18) (17,22) (18,19)\nIs there a path between node 20 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph400-0_17", + "image": "data/connectivity/graph_visual/medium/graph400.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,3) (0,4) (0,10) (1,18) (1,11) (1,16) (1,21) (1,10) (2,5) (2,20) (2,13) (3,11) (3,16) (3,13) (3,10) (4,20) (4,13) (4,6) (4,10) (5,11) (5,16) (5,13) (6,20) (6,16) (6,13) (6,19) (7,9) (8,17) (8,14) (10,18) (10,11) (10,16) (10,21) (11,20) (11,16) (13,21) (15,17) (16,21) (16,19) (18,20)\nIs there a path between node 0 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph800-19_24", + "image": "data/connectivity/graph_visual/medium/graph800.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,4) (0,22) (1,13) (1,4) (1,6) (1,2) (1,10) (1,3) (2,10) (2,23) (2,5) (3,4) (3,17) (3,23) (3,12) (4,12) (5,18) (5,15) (5,12) (5,22) (6,17) (7,19) (10,17) (10,23) (10,14) (10,15) (11,13) (12,18) (12,14) (13,17) (13,23) (13,22) (14,23) (14,15) (15,23) (16,20) (17,18) (17,23) (18,23) (19,24) (19,21) (20,21)\nIs there a path between node 19 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph799-5_21", + "image": "data/connectivity/graph_visual/medium/graph799.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,2) (0,1) (1,23) (1,24) (1,9) (1,19) (1,12) (1,7) (1,16) (1,11) (1,15) (1,22) (2,4) (2,20) (2,11) (2,22) (3,23) (3,5) (3,9) (3,12) (3,11) (3,6) (4,24) (4,5) (4,12) (4,14) (4,15) (4,13) (4,6) (4,22) (5,20) (5,19) (5,7) (5,11) (5,15) (5,10) (5,6) (6,20) (6,12) (6,16) (6,17) (6,13) (6,10) (7,23) (7,14) (7,11) (7,15) (8,21) (8,18) (9,24) (9,20) (9,10) (10,23) (10,20) (10,19) (11,20) (11,14) (11,15) (12,19) (12,14) (12,17) (12,13) (13,19) (14,23) (14,24) (14,19) (14,16) (14,17) (14,15) (14,22) (15,24) (15,17) (16,23) (16,24) (16,20) (17,23) (17,19) (20,24)\nIs there a path between node 5 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph36-5_10", + "image": "data/connectivity/graph_visual/medium/graph36.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,2) (0,12) (0,11) (0,4) (2,10) (2,8) (2,4) (4,6) (4,11) (5,9) (6,7) (6,10) (6,11) (7,8) (8,10) (8,9) (9,12) (10,11)\nIs there a path between node 5 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph439-10_12", + "image": "data/connectivity/graph_visual/medium/graph439.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,12) (0,20) (0,7) (0,11) (0,4) (1,19) (1,3) (1,8) (1,9) (2,6) (2,5) (2,16) (2,14) (2,17) (2,15) (3,8) (4,12) (4,7) (4,11) (4,10) (5,13) (5,6) (5,18) (5,16) (5,14) (5,17) (5,15) (6,21) (6,18) (6,17) (7,12) (7,20) (7,11) (8,19) (9,19) (10,12) (10,11) (11,12) (11,20) (12,20) (13,21) (13,18) (13,14) (13,17) (13,15) (14,21) (14,15) (15,16) (17,18) (18,21)\nIs there a path between node 10 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph502-4_6", + "image": "data/connectivity/graph_visual/medium/graph502.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,3) (0,7) (0,6) (1,19) (1,12) (1,9) (1,22) (1,21) (1,17) (1,2) (1,11) (2,14) (2,21) (2,4) (2,11) (4,10) (4,20) (4,21) (4,13) (4,17) (5,7) (8,19) (8,21) (8,17) (8,11) (9,16) (9,12) (9,15) (10,14) (11,19) (12,22) (12,21) (12,17) (13,14) (13,19) (13,15) (13,21) (14,20) (14,15) (15,16) (15,20) (15,19) (15,21) (16,22) (17,20) (17,19) (17,22) (20,21) (21,22)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph394-18_15", + "image": "data/connectivity/graph_visual/medium/graph394.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,5) (0,6) (0,14) (0,7) (0,9) (0,19) (0,17) (0,20) (0,15) (0,11) (0,3) (0,1) (0,13) (0,16) (0,18) (0,2) (1,10) (1,5) (1,6) (1,14) (1,7) (1,9) (1,19) (1,17) (1,20) (1,15) (1,11) (1,3) (1,13) (1,16) (1,18) (1,2) (2,10) (2,5) (2,6) (2,14) (2,7) (2,9) (2,19) (2,17) (2,20) (2,15) (2,11) (2,3) (2,13) (2,16) (2,18) (3,10) (3,5) (3,6) (3,14) (3,7) (3,9) (3,19) (3,17) (3,20) (3,15) (3,11) (3,13) (3,16) (3,18) (4,12) (4,8) (5,10) (5,6) (5,14) (5,7) (5,9) (5,19) (5,17) (5,20) (5,15) (5,11) (5,13) (5,16) (5,18) (6,10) (6,14) (6,7) (6,9) (6,19) (6,17) (6,20) (6,15) (6,11) (6,13) (6,16) (6,18) (7,10) (7,14) (7,9) (7,19) (7,17) (7,20) (7,15) (7,11) (7,13) (7,16) (7,18) (8,12) (9,10) (9,14) (9,19) (9,17) (9,20) (9,15) (9,11) (9,13) (9,16) (9,18) (10,14) (10,19) (10,17) (10,20) (10,15) (10,11) (10,13) (10,16) (10,18) (11,14) (11,19) (11,17) (11,20) (11,15) (11,13) (11,16) (11,18) (13,14) (13,19) (13,17) (13,20) (13,15) (13,16) (13,18) (14,19) (14,17) (14,20) (14,15) (14,16) (14,18) (15,19) (15,17) (15,20) (15,16) (15,18) (16,19) (16,17) (16,20) (16,18) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20)\nIs there a path between node 18 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph159-11_10", + "image": "data/connectivity/graph_visual/medium/graph159.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,9) (1,15) (1,3) (1,16) (2,4) (2,12) (2,10) (4,8) (4,11) (5,10) (5,17) (5,6) (6,11) (6,10) (6,17) (7,11) (7,12) (7,10) (7,17) (8,17) (9,13)\nIs there a path between node 11 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph0-9_4", + "image": "data/connectivity/graph_visual/medium/graph0.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (3,8) (3,9) (4,5) (8,9)\nIs there a path between node 9 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph326-4_15", + "image": "data/connectivity/graph_visual/medium/graph326.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,19) (0,17) (0,1) (0,4) (0,15) (0,2) (0,13) (0,10) (0,6) (0,18) (0,11) (0,12) (0,5) (1,19) (1,17) (1,4) (1,15) (1,2) (1,13) (1,10) (1,6) (1,18) (1,11) (1,12) (1,5) (2,19) (2,17) (2,4) (2,15) (2,13) (2,10) (2,6) (2,18) (2,11) (2,12) (2,5) (3,20) (3,16) (3,14) (3,8) (4,19) (4,17) (4,15) (4,13) (4,10) (4,6) (4,18) (4,11) (4,12) (4,5) (5,19) (5,17) (5,15) (5,13) (5,10) (5,6) (5,18) (5,11) (5,12) (6,19) (6,17) (6,15) (6,13) (6,10) (6,18) (6,11) (6,12) (7,9) (8,20) (8,16) (8,14) (10,19) (10,17) (10,15) (10,13) (10,18) (10,11) (10,12) (11,19) (11,17) (11,15) (11,13) (11,18) (11,12) (12,19) (12,17) (12,15) (12,13) (12,18) (13,19) (13,17) (13,15) (13,18) (14,20) (14,16) (15,19) (15,17) (15,18) (16,20) (17,19) (17,18) (18,19)\nIs there a path between node 4 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph411-20_17", + "image": "data/connectivity/graph_visual/medium/graph411.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,10) (0,1) (0,14) (0,2) (0,17) (0,13) (1,20) (1,8) (1,11) (1,10) (1,14) (1,2) (2,8) (2,11) (2,10) (2,14) (2,17) (3,15) (3,12) (3,5) (3,7) (3,6) (3,9) (3,19) (3,18) (4,12) (4,16) (4,21) (4,7) (4,6) (4,9) (4,19) (4,18) (5,15) (5,12) (5,16) (5,21) (5,7) (5,9) (5,19) (5,18) (6,12) (6,16) (6,7) (6,9) (6,19) (6,18) (7,12) (7,16) (7,18) (8,20) (8,14) (8,17) (9,12) (9,16) (9,21) (9,19) (9,18) (10,20) (10,13) (11,17) (11,13) (12,15) (12,16) (12,21) (13,20) (13,14) (13,17) (15,16) (15,21) (16,19) (16,18) (18,21) (18,19) (19,21)\nIs there a path between node 20 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph847-4_3", + "image": "data/connectivity/graph_visual/medium/graph847.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,15) (0,6) (0,11) (0,19) (0,1) (0,12) (1,9) (1,15) (1,6) (1,11) (1,19) (1,12) (2,10) (2,21) (2,17) (2,16) (2,22) (2,14) (2,8) (2,5) (3,7) (3,4) (3,13) (3,23) (4,7) (4,13) (4,23) (5,10) (5,21) (5,17) (5,16) (5,22) (5,14) (5,8) (6,9) (6,15) (6,11) (6,19) (6,12) (7,13) (7,23) (8,10) (8,21) (8,17) (8,16) (8,22) (8,14) (9,15) (9,11) (9,19) (9,12) (10,21) (10,17) (10,16) (10,22) (10,14) (11,15) (11,19) (11,12) (12,15) (12,19) (13,23) (14,21) (14,17) (14,16) (14,22) (15,19) (16,21) (16,17) (16,22) (17,21) (17,22) (18,20) (18,24) (20,24) (21,22)\nIs there a path between node 4 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph41-0_10", + "image": "data/connectivity/graph_visual/medium/graph41.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,11) (0,12) (0,5) (0,6) (0,4) (0,8) (0,2) (0,9) (0,1) (0,7) (1,12) (1,5) (1,6) (1,4) (1,8) (1,2) (1,9) (1,10) (1,7) (2,8) (2,10) (2,7) (4,11) (4,12) (4,5) (4,6) (4,8) (4,9) (4,7) (5,11) (5,6) (5,8) (5,10) (5,7) (6,11) (6,12) (6,8) (6,9) (7,11) (7,12) (7,9) (7,10) (8,12) (8,9) (8,10) (9,11) (9,12) (9,10) (10,11) (10,12) (11,12)\nIs there a path between node 0 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph625-18_8", + "image": "data/connectivity/graph_visual/medium/graph625.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (1,11) (1,7) (1,13) (1,21) (1,19) (1,5) (2,17) (2,20) (2,5) (4,9) (4,22) (5,21) (5,19) (6,23) (7,11) (8,11) (8,13) (8,19) (8,18) (11,23) (11,13) (11,18) (13,20) (13,21) (13,19) (13,18) (14,16) (14,15) (18,20) (19,20) (19,21) (20,23)\nIs there a path between node 18 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph627-9_23", + "image": "data/connectivity/graph_visual/medium/graph627.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (1,15) (1,14) (1,12) (2,15) (2,18) (2,4) (2,12) (3,16) (3,14) (3,8) (4,8) (7,21) (8,16) (8,11) (8,14) (8,12) (8,22) (9,21) (11,12) (12,15) (12,18) (13,16) (13,22) (14,15) (14,18) (15,16) (17,22) (19,23)\nIs there a path between node 9 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph411-5_1", + "image": "data/connectivity/graph_visual/medium/graph411.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,10) (0,1) (0,14) (0,2) (0,17) (0,13) (1,20) (1,8) (1,11) (1,10) (1,14) (1,2) (2,8) (2,11) (2,10) (2,14) (2,17) (3,15) (3,12) (3,5) (3,7) (3,6) (3,9) (3,19) (3,18) (4,12) (4,16) (4,21) (4,7) (4,6) (4,9) (4,19) (4,18) (5,15) (5,12) (5,16) (5,21) (5,7) (5,9) (5,19) (5,18) (6,12) (6,16) (6,7) (6,9) (6,19) (6,18) (7,12) (7,16) (7,18) (8,20) (8,14) (8,17) (9,12) (9,16) (9,21) (9,19) (9,18) (10,20) (10,13) (11,17) (11,13) (12,15) (12,16) (12,21) (13,20) (13,14) (13,17) (15,16) (15,21) (16,19) (16,18) (18,21) (18,19) (19,21)\nIs there a path between node 5 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph411-9_5", + "image": "data/connectivity/graph_visual/medium/graph411.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,10) (0,1) (0,14) (0,2) (0,17) (0,13) (1,20) (1,8) (1,11) (1,10) (1,14) (1,2) (2,8) (2,11) (2,10) (2,14) (2,17) (3,15) (3,12) (3,5) (3,7) (3,6) (3,9) (3,19) (3,18) (4,12) (4,16) (4,21) (4,7) (4,6) (4,9) (4,19) (4,18) (5,15) (5,12) (5,16) (5,21) (5,7) (5,9) (5,19) (5,18) (6,12) (6,16) (6,7) (6,9) (6,19) (6,18) (7,12) (7,16) (7,18) (8,20) (8,14) (8,17) (9,12) (9,16) (9,21) (9,19) (9,18) (10,20) (10,13) (11,17) (11,13) (12,15) (12,16) (12,21) (13,20) (13,14) (13,17) (15,16) (15,21) (16,19) (16,18) (18,21) (18,19) (19,21)\nIs there a path between node 9 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph528-1_18", + "image": "data/connectivity/graph_visual/medium/graph528.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,14) (0,6) (0,20) (0,2) (0,21) (0,17) (0,1) (0,9) (0,22) (1,10) (1,14) (1,6) (1,20) (1,2) (1,21) (1,17) (1,9) (1,22) (2,10) (2,14) (2,6) (2,20) (2,21) (2,17) (2,9) (2,22) (3,7) (3,5) (3,8) (3,16) (3,19) (3,18) (3,13) (3,4) (3,12) (3,15) (3,11) (4,7) (4,5) (4,8) (4,16) (4,19) (4,18) (4,13) (4,12) (4,15) (4,11) (5,7) (5,8) (5,16) (5,19) (5,18) (5,13) (5,12) (5,15) (5,11) (6,10) (6,14) (6,20) (6,21) (6,17) (6,9) (6,22) (7,8) (7,16) (7,19) (7,18) (7,13) (7,12) (7,15) (7,11) (8,16) (8,19) (8,18) (8,13) (8,12) (8,15) (8,11) (9,10) (9,14) (9,20) (9,21) (9,17) (9,22) (10,14) (10,20) (10,21) (10,17) (10,22) (11,16) (11,19) (11,18) (11,13) (11,12) (11,15) (12,16) (12,19) (12,18) (12,13) (12,15) (13,16) (13,19) (13,18) (13,15) (14,20) (14,21) (14,17) (14,22) (15,16) (15,19) (15,18) (16,19) (16,18) (17,20) (17,21) (17,22) (18,19) (20,21) (20,22) (21,22)\nIs there a path between node 1 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph205-13_7", + "image": "data/connectivity/graph_visual/medium/graph205.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,16) (0,3) (0,12) (0,6) (0,11) (1,16) (1,3) (1,12) (1,6) (1,11) (1,14) (1,10) (2,15) (2,7) (2,13) (2,5) (2,9) (2,4) (2,18) (3,17) (3,12) (3,11) (3,14) (4,15) (4,7) (4,5) (4,9) (4,8) (5,15) (5,13) (5,9) (5,8) (5,18) (6,16) (6,17) (6,12) (6,14) (6,10) (7,15) (7,13) (7,9) (7,18) (8,15) (8,9) (8,18) (9,13) (9,18) (10,16) (10,17) (10,12) (10,11) (11,16) (11,17) (11,12) (12,16) (12,17) (12,14) (13,15) (13,18) (14,16) (14,17) (15,18) (16,17)\nIs there a path between node 13 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph691-1_20", + "image": "data/connectivity/graph_visual/medium/graph691.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,23) (0,3) (0,7) (0,9) (0,21) (0,13) (0,16) (0,6) (0,8) (0,12) (1,5) (1,22) (1,15) (1,14) (1,18) (1,17) (1,20) (1,11) (1,2) (2,5) (2,22) (2,15) (2,14) (2,18) (2,17) (2,20) (2,11) (3,10) (3,19) (3,23) (3,7) (3,9) (3,21) (3,13) (3,16) (3,6) (3,8) (3,12) (5,22) (5,15) (5,14) (5,18) (5,17) (5,20) (5,11) (6,10) (6,19) (6,23) (6,7) (6,9) (6,21) (6,13) (6,16) (6,8) (6,12) (7,10) (7,19) (7,23) (7,9) (7,21) (7,13) (7,16) (7,8) (7,12) (8,10) (8,19) (8,23) (8,9) (8,21) (8,13) (8,16) (8,12) (9,10) (9,19) (9,23) (9,21) (9,13) (9,16) (9,12) (10,19) (10,23) (10,21) (10,13) (10,16) (10,12) (11,22) (11,15) (11,14) (11,18) (11,17) (11,20) (12,19) (12,23) (12,21) (12,13) (12,16) (13,19) (13,23) (13,21) (13,16) (14,22) (14,15) (14,18) (14,17) (14,20) (15,22) (15,18) (15,17) (15,20) (16,19) (16,23) (16,21) (17,22) (17,18) (17,20) (18,22) (18,20) (19,23) (19,21) (20,22) (21,23)\nIs there a path between node 1 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph94-5_8", + "image": "data/connectivity/graph_visual/medium/graph94.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,9) (0,6) (0,14) (0,1) (0,5) (0,10) (1,9) (1,6) (1,7) (3,9) (3,6) (3,5) (4,12) (4,7) (4,15) (5,6) (5,11) (5,7) (5,10) (6,15) (7,10) (9,12) (9,15) (9,13) (10,15) (13,15)\nIs there a path between node 5 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph448-0_13", + "image": "data/connectivity/graph_visual/medium/graph448.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,17) (0,19) (0,1) (0,6) (0,5) (0,7) (0,2) (0,14) (0,4) (0,10) (1,17) (1,6) (1,5) (1,12) (1,7) (1,13) (1,2) (1,20) (1,14) (1,10) (2,9) (2,17) (2,16) (2,19) (2,6) (2,12) (2,7) (2,18) (2,13) (2,20) (2,14) (2,4) (2,10) (3,21) (3,15) (3,11) (4,9) (4,17) (4,16) (4,19) (4,6) (4,5) (4,12) (4,7) (4,13) (4,10) (5,9) (5,17) (5,16) (5,12) (5,18) (5,13) (5,20) (5,14) (6,17) (6,16) (6,12) (6,7) (6,18) (6,20) (6,10) (7,9) (7,17) (7,16) (7,19) (7,13) (7,20) (7,14) (7,10) (8,21) (8,15) (9,16) (9,19) (9,18) (9,13) (9,20) (9,14) (9,10) (10,17) (10,16) (10,18) (10,13) (10,20) (10,14) (11,21) (12,17) (12,16) (12,19) (13,17) (13,16) (13,19) (14,17) (14,19) (14,20) (15,21) (16,17) (16,18) (16,20) (17,19) (17,20) (18,19) (18,20) (19,20)\nIs there a path between node 0 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph247-14_18", + "image": "data/connectivity/graph_visual/medium/graph247.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (0,13) (0,5) (0,7) (0,16) (0,12) (0,18) (0,9) (0,8) (0,2) (0,11) (0,10) (0,6) (1,15) (1,14) (1,3) (2,4) (2,13) (2,5) (2,7) (2,16) (2,12) (2,18) (2,9) (2,8) (2,11) (2,10) (2,6) (3,15) (3,14) (4,13) (4,5) (4,7) (4,16) (4,12) (4,18) (4,9) (4,8) (4,11) (4,10) (4,6) (5,13) (5,7) (5,16) (5,12) (5,18) (5,9) (5,8) (5,11) (5,10) (5,6) (6,13) (6,7) (6,16) (6,12) (6,18) (6,9) (6,8) (6,11) (6,10) (7,13) (7,16) (7,12) (7,18) (7,9) (7,8) (7,11) (7,10) (8,13) (8,16) (8,12) (8,18) (8,9) (8,11) (8,10) (9,13) (9,16) (9,12) (9,18) (9,11) (9,10) (10,13) (10,16) (10,12) (10,18) (10,11) (11,13) (11,16) (11,12) (11,18) (12,13) (12,16) (12,18) (13,16) (13,18) (14,15) (16,18)\nIs there a path between node 14 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph615-3_0", + "image": "data/connectivity/graph_visual/medium/graph615.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,16) (0,3) (0,11) (0,19) (0,14) (0,7) (1,20) (1,2) (1,10) (1,21) (1,15) (1,23) (1,13) (1,18) (2,20) (2,10) (2,21) (2,15) (2,23) (2,13) (2,18) (3,22) (3,16) (3,11) (3,19) (3,14) (3,7) (4,17) (5,9) (5,6) (5,8) (5,12) (6,9) (6,8) (6,12) (7,22) (7,16) (7,11) (7,19) (7,14) (8,9) (8,12) (9,12) (10,20) (10,21) (10,15) (10,23) (10,13) (10,18) (11,22) (11,16) (11,19) (11,14) (13,20) (13,21) (13,15) (13,23) (13,18) (14,22) (14,16) (14,19) (15,20) (15,21) (15,23) (15,18) (16,22) (16,19) (18,20) (18,21) (18,23) (19,22) (20,21) (20,23) (21,23)\nIs there a path between node 3 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph202-18_11", + "image": "data/connectivity/graph_visual/medium/graph202.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (0,13) (0,12) (0,3) (1,4) (1,13) (1,3) (2,10) (2,15) (2,18) (3,12) (3,14) (4,6) (4,9) (4,17) (6,14) (6,17) (7,14) (8,13) (10,16) (11,12) (11,14) (12,14) (14,17)\nIs there a path between node 18 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph438-20_14", + "image": "data/connectivity/graph_visual/medium/graph438.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,10) (0,5) (0,20) (0,7) (0,19) (0,1) (0,14) (0,12) (0,15) (0,18) (0,4) (1,10) (1,5) (1,7) (1,2) (1,14) (1,12) (1,3) (1,15) (1,16) (1,4) (2,10) (2,5) (2,20) (2,7) (2,19) (2,14) (2,12) (2,15) (2,16) (2,17) (2,18) (2,4) (3,5) (3,20) (3,7) (3,19) (3,14) (3,16) (3,17) (3,18) (4,10) (4,5) (4,20) (4,7) (4,19) (4,14) (4,12) (4,15) (4,16) (4,17) (5,20) (5,7) (5,19) (5,14) (5,12) (5,16) (5,17) (5,18) (6,11) (6,8) (7,10) (7,19) (7,14) (7,12) (7,15) (7,16) (7,17) (7,18) (8,11) (9,21) (9,13) (10,19) (10,14) (10,12) (10,16) (10,18) (12,20) (12,19) (12,14) (12,15) (12,16) (12,17) (14,20) (14,19) (14,15) (14,16) (14,17) (15,20) (15,19) (15,16) (15,17) (15,18) (16,20) (16,19) (16,17) (16,18) (17,20) (17,19) (17,18) (18,19) (19,20)\nIs there a path between node 20 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph32-8_7", + "image": "data/connectivity/graph_visual/medium/graph32.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (0,5) (0,4) (1,10) (1,8) (1,11) (1,9) (1,7) (1,6) (1,2) (2,10) (2,8) (2,11) (2,9) (2,7) (2,6) (3,5) (3,4) (4,5) (6,10) (6,8) (6,11) (6,9) (6,7) (7,10) (7,8) (7,11) (7,9) (8,10) (8,11) (8,9) (9,10) (9,11) (10,11)\nIs there a path between node 8 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph193-0_3", + "image": "data/connectivity/graph_visual/medium/graph193.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,5) (0,7) (0,14) (0,2) (0,16) (0,13) (0,3) (0,12) (0,4) (1,9) (1,15) (1,6) (1,10) (1,17) (2,5) (2,7) (2,14) (2,16) (2,13) (2,3) (2,12) (2,4) (3,5) (3,7) (3,14) (3,16) (3,13) (3,12) (3,4) (4,5) (4,7) (4,14) (4,16) (4,13) (4,12) (5,7) (5,14) (5,16) (5,13) (5,12) (6,9) (6,15) (6,10) (6,17) (7,14) (7,16) (7,13) (7,12) (8,11) (9,15) (9,10) (9,17) (10,15) (10,17) (12,14) (12,16) (12,13) (13,14) (13,16) (14,16) (15,17)\nIs there a path between node 0 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph376-10_2", + "image": "data/connectivity/graph_visual/medium/graph376.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,9) (0,12) (0,2) (0,8) (0,7) (0,19) (0,17) (0,4) (1,6) (1,14) (1,10) (1,18) (1,16) (2,9) (2,5) (2,12) (2,15) (2,20) (2,19) (2,17) (2,13) (3,6) (3,14) (3,10) (3,16) (4,9) (4,5) (4,12) (4,15) (4,20) (4,7) (4,17) (4,13) (5,9) (5,12) (5,15) (5,20) (5,8) (5,19) (6,10) (6,18) (6,16) (7,9) (7,12) (7,15) (7,20) (7,19) (7,17) (7,13) (8,9) (8,15) (8,20) (8,19) (9,12) (9,15) (9,20) (9,13) (10,14) (10,16) (11,14) (11,18) (12,20) (12,19) (12,17) (12,13) (13,20) (13,19) (13,17) (14,16) (15,20) (15,19) (15,17) (16,18) (17,19) (19,20)\nIs there a path between node 10 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph249-0_9", + "image": "data/connectivity/graph_visual/medium/graph249.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,6) (0,2) (0,17) (0,4) (0,5) (0,15) (0,9) (0,12) (0,11) (0,16) (0,8) (0,10) (0,18) (0,14) (1,7) (2,13) (2,6) (2,17) (2,4) (2,5) (2,15) (2,9) (2,12) (2,11) (2,16) (2,8) (2,10) (2,18) (2,14) (4,13) (4,6) (4,17) (4,5) (4,15) (4,9) (4,12) (4,11) (4,16) (4,8) (4,10) (4,18) (4,14) (5,13) (5,6) (5,17) (5,15) (5,9) (5,12) (5,11) (5,16) (5,8) (5,10) (5,18) (5,14) (6,13) (6,17) (6,15) (6,9) (6,12) (6,11) (6,16) (6,8) (6,10) (6,18) (6,14) (8,13) (8,17) (8,15) (8,9) (8,12) (8,11) (8,16) (8,10) (8,18) (8,14) (9,13) (9,17) (9,15) (9,12) (9,11) (9,16) (9,10) (9,18) (9,14) (10,13) (10,17) (10,15) (10,12) (10,11) (10,16) (10,18) (10,14) (11,13) (11,17) (11,15) (11,12) (11,16) (11,18) (11,14) (12,13) (12,17) (12,15) (12,16) (12,18) (12,14) (13,17) (13,15) (13,16) (13,18) (13,14) (14,17) (14,15) (14,16) (14,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 0 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph17-9_5", + "image": "data/connectivity/graph_visual/medium/graph17.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,4) (0,11) (0,5) (0,9) (0,6) (1,2) (1,7) (1,3) (1,10) (1,8) (2,7) (2,3) (2,10) (2,8) (3,7) (3,10) (3,8) (4,11) (4,5) (4,9) (4,6) (5,11) (5,9) (5,6) (6,11) (6,9) (7,10) (7,8) (8,10) (9,11)\nIs there a path between node 9 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph142-17_12", + "image": "data/connectivity/graph_visual/medium/graph142.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,11) (0,6) (1,5) (1,8) (1,10) (1,15) (1,17) (1,13) (1,16) (2,5) (2,4) (2,8) (2,10) (2,14) (2,17) (2,13) (2,16) (3,9) (3,6) (3,12) (4,8) (4,15) (4,14) (4,17) (4,13) (5,8) (5,15) (5,17) (6,7) (6,9) (7,11) (7,9) (8,15) (8,17) (8,13) (8,16) (9,11) (10,15) (10,14) (10,17) (11,12) (13,15) (13,14) (13,16) (14,15) (14,17) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 17 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph347-11_19", + "image": "data/connectivity/graph_visual/medium/graph347.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,13) (0,3) (0,19) (0,12) (0,15) (0,17) (1,20) (1,6) (1,2) (1,7) (2,20) (2,6) (2,7) (3,10) (3,13) (3,19) (3,12) (3,15) (3,17) (4,11) (4,9) (4,18) (4,16) (4,14) (4,8) (4,5) (5,11) (5,9) (5,18) (5,16) (5,14) (5,8) (6,20) (6,7) (7,20) (8,11) (8,9) (8,18) (8,16) (8,14) (9,11) (9,18) (9,16) (9,14) (10,13) (10,19) (10,12) (10,15) (10,17) (11,18) (11,16) (11,14) (12,13) (12,19) (12,15) (12,17) (13,19) (13,15) (13,17) (14,18) (14,16) (15,19) (15,17) (16,18) (17,19)\nIs there a path between node 11 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph515-7_10", + "image": "data/connectivity/graph_visual/medium/graph515.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,17) (0,11) (0,7) (0,12) (0,6) (0,21) (1,8) (1,19) (1,5) (1,9) (1,2) (1,13) (1,4) (2,20) (2,8) (2,19) (2,9) (2,18) (2,13) (3,22) (3,17) (3,11) (3,10) (3,7) (3,16) (3,12) (3,15) (3,14) (3,6) (4,20) (4,8) (4,19) (4,5) (4,18) (4,13) (5,20) (5,8) (5,9) (5,18) (5,13) (6,22) (6,17) (6,10) (6,16) (6,12) (6,15) (7,22) (7,10) (7,16) (7,12) (7,15) (7,21) (8,19) (8,9) (8,18) (9,20) (9,19) (10,22) (10,17) (10,11) (10,12) (10,14) (11,17) (11,16) (11,15) (11,14) (11,21) (12,22) (12,16) (12,15) (12,14) (12,21) (13,20) (13,19) (14,22) (14,17) (15,22) (15,17) (16,22) (16,17) (17,22) (17,21) (18,20) (18,19) (21,22)\nIs there a path between node 7 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph681-17_8", + "image": "data/connectivity/graph_visual/medium/graph681.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,22) (0,16) (0,2) (0,6) (0,17) (0,20) (0,1) (0,12) (0,8) (0,11) (0,4) (0,18) (0,7) (0,3) (0,23) (0,9) (1,21) (1,22) (1,16) (1,2) (1,6) (1,17) (1,20) (1,12) (1,8) (1,11) (1,4) (1,18) (1,7) (1,3) (1,23) (1,9) (2,21) (2,22) (2,16) (2,6) (2,17) (2,20) (2,12) (2,8) (2,11) (2,4) (2,18) (2,7) (2,3) (2,23) (2,9) (3,21) (3,22) (3,16) (3,6) (3,17) (3,20) (3,12) (3,8) (3,11) (3,4) (3,18) (3,7) (3,23) (3,9) (4,21) (4,22) (4,16) (4,6) (4,17) (4,20) (4,12) (4,8) (4,11) (4,18) (4,7) (4,23) (4,9) (5,13) (6,21) (6,22) (6,16) (6,17) (6,20) (6,12) (6,8) (6,11) (6,18) (6,7) (6,23) (6,9) (7,21) (7,22) (7,16) (7,17) (7,20) (7,12) (7,8) (7,11) (7,18) (7,23) (7,9) (8,21) (8,22) (8,16) (8,17) (8,20) (8,12) (8,11) (8,18) (8,23) (8,9) (9,21) (9,22) (9,16) (9,17) (9,20) (9,12) (9,11) (9,18) (9,23) (10,14) (10,19) (10,15) (11,21) (11,22) (11,16) (11,17) (11,20) (11,12) (11,18) (11,23) (12,21) (12,22) (12,16) (12,17) (12,20) (12,18) (12,23) (14,19) (14,15) (15,19) (16,21) (16,22) (16,17) (16,20) (16,18) (16,23) (17,21) (17,22) (17,20) (17,18) (17,23) (18,21) (18,22) (18,20) (18,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 17 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph694-18_0", + "image": "data/connectivity/graph_visual/medium/graph694.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,23) (0,1) (0,3) (0,5) (0,12) (0,10) (0,15) (0,11) (0,18) (0,19) (0,13) (0,6) (0,14) (0,17) (0,9) (0,7) (0,16) (0,20) (1,4) (1,23) (1,3) (1,5) (1,12) (1,10) (1,15) (1,11) (1,18) (1,19) (1,13) (1,6) (1,14) (1,17) (1,9) (1,7) (1,16) (1,20) (2,22) (2,21) (2,8) (3,4) (3,23) (3,5) (3,12) (3,10) (3,15) (3,11) (3,18) (3,19) (3,13) (3,6) (3,14) (3,17) (3,9) (3,7) (3,16) (3,20) (4,23) (4,5) (4,12) (4,10) (4,15) (4,11) (4,18) (4,19) (4,13) (4,6) (4,14) (4,17) (4,9) (4,7) (4,16) (4,20) (5,23) (5,12) (5,10) (5,15) (5,11) (5,18) (5,19) (5,13) (5,6) (5,14) (5,17) (5,9) (5,7) (5,16) (5,20) (6,23) (6,12) (6,10) (6,15) (6,11) (6,18) (6,19) (6,13) (6,14) (6,17) (6,9) (6,7) (6,16) (6,20) (7,23) (7,12) (7,10) (7,15) (7,11) (7,18) (7,19) (7,13) (7,14) (7,17) (7,9) (7,16) (7,20) (8,22) (8,21) (9,23) (9,12) (9,10) (9,15) (9,11) (9,18) (9,19) (9,13) (9,14) (9,17) (9,16) (9,20) (10,23) (10,12) (10,15) (10,11) (10,18) (10,19) (10,13) (10,14) (10,17) (10,16) (10,20) (11,23) (11,12) (11,15) (11,18) (11,19) (11,13) (11,14) (11,17) (11,16) (11,20) (12,23) (12,15) (12,18) (12,19) (12,13) (12,14) (12,17) (12,16) (12,20) (13,23) (13,15) (13,18) (13,19) (13,14) (13,17) (13,16) (13,20) (14,23) (14,15) (14,18) (14,19) (14,17) (14,16) (14,20) (15,23) (15,18) (15,19) (15,17) (15,16) (15,20) (16,23) (16,18) (16,19) (16,17) (16,20) (17,23) (17,18) (17,19) (17,20) (18,23) (18,19) (18,20) (19,23) (19,20) (20,23) (21,22)\nIs there a path between node 18 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph453-19_9", + "image": "data/connectivity/graph_visual/medium/graph453.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,3) (1,20) (1,21) (1,8) (1,5) (1,16) (1,17) (1,19) (1,6) (1,12) (1,14) (1,9) (1,13) (1,18) (1,7) (1,11) (1,15) (1,2) (1,10) (2,20) (2,21) (2,8) (2,5) (2,16) (2,17) (2,19) (2,6) (2,12) (2,14) (2,9) (2,13) (2,18) (2,7) (2,11) (2,15) (2,10) (3,4) (5,20) (5,21) (5,8) (5,16) (5,17) (5,19) (5,6) (5,12) (5,14) (5,9) (5,13) (5,18) (5,7) (5,11) (5,15) (5,10) (6,20) (6,21) (6,8) (6,16) (6,17) (6,19) (6,12) (6,14) (6,9) (6,13) (6,18) (6,7) (6,11) (6,15) (6,10) (7,20) (7,21) (7,8) (7,16) (7,17) (7,19) (7,12) (7,14) (7,9) (7,13) (7,18) (7,11) (7,15) (7,10) (8,20) (8,21) (8,16) (8,17) (8,19) (8,12) (8,14) (8,9) (8,13) (8,18) (8,11) (8,15) (8,10) (9,20) (9,21) (9,16) (9,17) (9,19) (9,12) (9,14) (9,13) (9,18) (9,11) (9,15) (9,10) (10,20) (10,21) (10,16) (10,17) (10,19) (10,12) (10,14) (10,13) (10,18) (10,11) (10,15) (11,20) (11,21) (11,16) (11,17) (11,19) (11,12) (11,14) (11,13) (11,18) (11,15) (12,20) (12,21) (12,16) (12,17) (12,19) (12,14) (12,13) (12,18) (12,15) (13,20) (13,21) (13,16) (13,17) (13,19) (13,14) (13,18) (13,15) (14,20) (14,21) (14,16) (14,17) (14,19) (14,18) (14,15) (15,20) (15,21) (15,16) (15,17) (15,19) (15,18) (16,20) (16,21) (16,17) (16,19) (16,18) (17,20) (17,21) (17,19) (17,18) (18,20) (18,21) (18,19) (19,20) (19,21) (20,21)\nIs there a path between node 19 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph174-9_8", + "image": "data/connectivity/graph_visual/medium/graph174.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,9) (0,7) (0,10) (1,14) (1,9) (1,7) (1,12) (1,10) (2,5) (2,16) (2,8) (2,4) (3,11) (4,17) (4,6) (4,16) (4,8) (5,6) (5,16) (6,16) (7,9) (7,12) (7,13) (7,10) (8,16) (9,12) (10,14) (10,12) (10,13) (11,15) (12,14) (12,13) (13,14)\nIs there a path between node 9 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph150-13_1", + "image": "data/connectivity/graph_visual/medium/graph150.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,6) (1,10) (1,3) (1,16) (1,14) (1,17) (1,7) (1,12) (1,4) (1,8) (1,9) (1,15) (1,11) (1,13) (1,5) (1,2) (2,10) (2,3) (2,16) (2,14) (2,17) (2,7) (2,12) (2,4) (2,8) (2,9) (2,15) (2,11) (2,13) (2,5) (3,10) (3,16) (3,14) (3,17) (3,7) (3,12) (3,4) (3,8) (3,9) (3,15) (3,11) (3,13) (3,5) (4,10) (4,16) (4,14) (4,17) (4,7) (4,12) (4,8) (4,9) (4,15) (4,11) (4,13) (4,5) (5,10) (5,16) (5,14) (5,17) (5,7) (5,12) (5,8) (5,9) (5,15) (5,11) (5,13) (7,10) (7,16) (7,14) (7,17) (7,12) (7,8) (7,9) (7,15) (7,11) (7,13) (8,10) (8,16) (8,14) (8,17) (8,12) (8,9) (8,15) (8,11) (8,13) (9,10) (9,16) (9,14) (9,17) (9,12) (9,15) (9,11) (9,13) (10,16) (10,14) (10,17) (10,12) (10,15) (10,11) (10,13) (11,16) (11,14) (11,17) (11,12) (11,15) (11,13) (12,16) (12,14) (12,17) (12,15) (12,13) (13,16) (13,14) (13,17) (13,15) (14,16) (14,17) (14,15) (15,16) (15,17) (16,17)\nIs there a path between node 13 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph124-8_3", + "image": "data/connectivity/graph_visual/medium/graph124.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,12) (0,4) (0,7) (0,15) (0,2) (0,5) (0,11) (0,8) (0,14) (0,13) (0,10) (0,1) (1,4) (1,7) (1,15) (1,9) (1,2) (1,5) (1,11) (1,8) (1,14) (1,16) (1,10) (2,7) (2,15) (2,9) (2,6) (2,5) (2,11) (2,8) (2,14) (2,16) (2,13) (2,10) (4,12) (4,7) (4,9) (4,6) (4,5) (4,8) (4,16) (4,13) (4,10) (5,12) (5,7) (5,15) (5,9) (5,6) (5,16) (5,13) (5,10) (6,12) (6,15) (6,9) (6,14) (6,16) (7,12) (7,11) (7,8) (7,16) (7,10) (8,12) (8,9) (8,11) (8,14) (8,16) (8,10) (9,11) (10,12) (10,15) (10,14) (10,16) (10,13) (11,15) (11,14) (11,16) (11,13) (12,15) (12,14) (12,16) (12,13) (13,15) (14,15) (14,16) (15,16)\nIs there a path between node 8 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph452-4_10", + "image": "data/connectivity/graph_visual/medium/graph452.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,5) (0,13) (0,16) (0,4) (0,12) (1,5) (1,13) (1,9) (1,16) (1,4) (1,2) (2,13) (2,14) (2,4) (3,11) (3,19) (3,18) (3,15) (3,20) (3,6) (3,8) (3,10) (3,21) (4,13) (4,14) (4,9) (4,12) (5,13) (5,14) (5,9) (5,16) (6,11) (6,19) (6,18) (6,15) (6,17) (6,10) (6,21) (6,7) (7,11) (7,19) (7,18) (7,15) (7,20) (7,17) (7,8) (7,10) (7,21) (8,11) (8,18) (8,15) (8,20) (8,21) (9,13) (9,14) (9,16) (9,12) (10,11) (10,19) (10,18) (10,20) (10,17) (10,21) (11,18) (11,20) (14,16) (15,19) (15,18) (15,20) (15,17) (15,21) (17,19) (17,18) (17,20) (17,21) (18,19) (18,20) (19,20) (19,21) (20,21)\nIs there a path between node 4 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph60-4_7", + "image": "data/connectivity/graph_visual/medium/graph60.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (0,7) (0,4) (0,5) (1,10) (2,11) (2,6) (2,13) (2,7) (2,12) (2,4) (3,9) (3,8) (3,10) (4,11) (4,7) (4,12) (4,5) (5,11) (5,6) (5,7) (5,12) (6,11) (6,13) (6,7) (6,12) (7,11) (7,13) (7,12) (8,9) (8,10) (9,10)\nIs there a path between node 4 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph559-14_17", + "image": "data/connectivity/graph_visual/medium/graph559.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,23) (0,20) (0,17) (0,3) (0,6) (0,5) (0,9) (0,7) (0,13) (0,4) (0,2) (0,1) (1,8) (1,16) (1,23) (1,20) (1,3) (1,6) (1,5) (1,9) (1,14) (1,7) (1,13) (2,18) (2,8) (2,16) (2,20) (2,3) (2,10) (2,5) (2,9) (2,12) (2,14) (2,4) (3,18) (3,8) (3,16) (3,6) (3,5) (3,9) (3,12) (3,14) (3,13) (4,18) (4,8) (4,16) (4,6) (4,10) (4,5) (4,9) (4,12) (4,7) (4,13) (5,8) (5,17) (5,10) (5,9) (5,12) (5,14) (5,7) (5,13) (6,8) (6,16) (6,20) (6,10) (6,12) (6,14) (6,7) (7,8) (7,16) (7,23) (7,17) (7,10) (7,9) (7,12) (7,13) (8,18) (8,17) (8,10) (8,9) (8,12) (8,14) (8,13) (9,18) (9,16) (9,12) (9,14) (9,13) (10,18) (10,23) (10,20) (10,17) (10,12) (10,13) (11,22) (12,23) (12,20) (12,17) (13,18) (13,16) (13,23) (13,20) (13,14) (14,18) (14,16) (14,23) (14,17) (15,19) (15,21) (15,22) (16,18) (16,23) (16,20) (16,17) (17,18) (17,20) (18,20) (19,21) (20,23) (21,22)\nIs there a path between node 14 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph835-10_24", + "image": "data/connectivity/graph_visual/medium/graph835.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (0,3) (1,24) (1,12) (1,17) (1,9) (1,15) (1,16) (1,2) (1,10) (1,13) (1,4) (1,19) (1,7) (1,14) (2,24) (2,12) (2,17) (2,9) (2,15) (2,16) (2,10) (2,13) (2,4) (2,19) (2,7) (2,14) (3,18) (4,24) (4,12) (4,17) (4,9) (4,15) (4,16) (4,10) (4,13) (4,19) (4,7) (4,14) (5,11) (5,23) (5,20) (5,8) (6,22) (6,21) (7,24) (7,12) (7,17) (7,9) (7,15) (7,16) (7,10) (7,13) (7,19) (7,14) (8,11) (8,23) (8,20) (9,24) (9,12) (9,17) (9,15) (9,16) (9,10) (9,13) (9,19) (9,14) (10,24) (10,12) (10,17) (10,15) (10,16) (10,13) (10,19) (10,14) (11,23) (11,20) (12,24) (12,17) (12,15) (12,16) (12,13) (12,19) (12,14) (13,24) (13,17) (13,15) (13,16) (13,19) (13,14) (14,24) (14,17) (14,15) (14,16) (14,19) (15,24) (15,17) (15,16) (15,19) (16,24) (16,17) (16,19) (17,24) (17,19) (19,24) (20,23) (21,22)\nIs there a path between node 10 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph363-15_12", + "image": "data/connectivity/graph_visual/medium/graph363.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,9) (0,8) (0,17) (0,6) (1,14) (1,7) (2,8) (2,17) (2,3) (2,11) (2,10) (2,6) (3,9) (3,19) (3,10) (3,16) (4,18) (4,14) (5,8) (5,17) (5,10) (6,9) (6,11) (6,16) (7,20) (7,15) (8,9) (8,13) (8,19) (9,13) (10,17) (10,13) (12,16) (13,17) (14,18) (14,20) (15,20) (16,19)\nIs there a path between node 15 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph686-15_17", + "image": "data/connectivity/graph_visual/medium/graph686.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,18) (1,14) (1,6) (1,16) (1,4) (1,15) (1,19) (1,20) (1,23) (1,7) (1,13) (1,22) (1,9) (1,21) (1,2) (2,14) (2,6) (2,16) (2,4) (2,15) (2,19) (2,20) (2,23) (2,7) (2,13) (2,22) (2,9) (2,21) (3,5) (3,10) (3,12) (3,11) (3,17) (4,14) (4,6) (4,16) (4,15) (4,19) (4,20) (4,23) (4,7) (4,13) (4,22) (4,9) (4,21) (5,10) (5,12) (5,11) (5,17) (6,14) (6,16) (6,15) (6,19) (6,20) (6,23) (6,7) (6,13) (6,22) (6,9) (6,21) (7,14) (7,16) (7,15) (7,19) (7,20) (7,23) (7,13) (7,22) (7,9) (7,21) (8,18) (9,14) (9,16) (9,15) (9,19) (9,20) (9,23) (9,13) (9,22) (9,21) (10,12) (10,11) (10,17) (11,12) (11,17) (12,17) (13,14) (13,16) (13,15) (13,19) (13,20) (13,23) (13,22) (13,21) (14,16) (14,15) (14,19) (14,20) (14,23) (14,22) (14,21) (15,16) (15,19) (15,20) (15,23) (15,22) (15,21) (16,19) (16,20) (16,23) (16,22) (16,21) (19,20) (19,23) (19,22) (19,21) (20,23) (20,22) (20,21) (21,23) (21,22) (22,23)\nIs there a path between node 15 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph245-9_3", + "image": "data/connectivity/graph_visual/medium/graph245.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,3) (0,13) (0,2) (0,15) (0,6) (0,17) (0,8) (0,16) (0,18) (0,9) (0,12) (0,11) (1,10) (1,14) (1,7) (1,5) (1,4) (2,3) (2,13) (2,15) (2,6) (2,17) (2,8) (2,16) (2,18) (2,9) (2,12) (2,11) (3,13) (3,15) (3,6) (3,17) (3,8) (3,16) (3,18) (3,9) (3,12) (3,11) (4,10) (4,14) (4,7) (4,5) (5,10) (5,14) (5,7) (6,13) (6,15) (6,17) (6,8) (6,16) (6,18) (6,9) (6,12) (6,11) (7,10) (7,14) (8,13) (8,15) (8,17) (8,16) (8,18) (8,9) (8,12) (8,11) (9,13) (9,15) (9,17) (9,16) (9,18) (9,12) (9,11) (10,14) (11,13) (11,15) (11,17) (11,16) (11,18) (11,12) (12,13) (12,15) (12,17) (12,16) (12,18) (13,15) (13,17) (13,16) (13,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 9 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph45-6_2", + "image": "data/connectivity/graph_visual/medium/graph45.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,6) (0,1) (0,8) (0,12) (0,9) (0,3) (1,8) (1,12) (1,9) (1,3) (1,11) (1,4) (2,7) (3,8) (3,12) (3,9) (4,6) (4,8) (4,11) (5,7) (5,10) (6,8) (6,12) (6,9) (6,11) (7,10) (8,11) (9,12) (9,11) (11,12)\nIs there a path between node 6 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph73-2_5", + "image": "data/connectivity/graph_visual/medium/graph73.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (0,12) (0,5) (1,12) (1,8) (2,3) (2,8) (2,5) (3,9) (3,10) (3,12) (3,8) (5,12) (6,13) (7,10) (7,14) (8,10) (9,10) (12,14)\nIs there a path between node 2 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph848-13_5", + "image": "data/connectivity/graph_visual/medium/graph848.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,20) (0,4) (0,14) (0,8) (0,1) (0,17) (0,15) (0,21) (0,10) (0,11) (0,18) (1,7) (1,20) (1,4) (1,14) (1,8) (1,17) (1,15) (1,21) (1,10) (1,11) (1,18) (2,3) (2,24) (2,5) (2,22) (2,6) (2,13) (2,16) (2,12) (2,23) (2,19) (2,9) (3,24) (3,5) (3,22) (3,6) (3,13) (3,16) (3,12) (3,23) (3,19) (3,9) (4,7) (4,20) (4,14) (4,8) (4,17) (4,15) (4,21) (4,10) (4,11) (4,18) (5,24) (5,22) (5,6) (5,13) (5,16) (5,12) (5,23) (5,19) (5,9) (6,24) (6,22) (6,13) (6,16) (6,12) (6,23) (6,19) (6,9) (7,20) (7,14) (7,8) (7,17) (7,15) (7,21) (7,10) (7,11) (7,18) (8,20) (8,14) (8,17) (8,15) (8,21) (8,10) (8,11) (8,18) (9,24) (9,22) (9,13) (9,16) (9,12) (9,23) (9,19) (10,20) (10,14) (10,17) (10,15) (10,21) (10,11) (10,18) (11,20) (11,14) (11,17) (11,15) (11,21) (11,18) (12,24) (12,22) (12,13) (12,16) (12,23) (12,19) (13,24) (13,22) (13,16) (13,23) (13,19) (14,20) (14,17) (14,15) (14,21) (14,18) (15,20) (15,17) (15,21) (15,18) (16,24) (16,22) (16,23) (16,19) (17,20) (17,21) (17,18) (18,20) (18,21) (19,24) (19,22) (19,23) (20,21) (22,24) (22,23) (23,24)\nIs there a path between node 13 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph93-14_3", + "image": "data/connectivity/graph_visual/medium/graph93.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,2) (0,4) (0,9) (0,5) (0,13) (1,14) (1,15) (1,12) (1,5) (1,7) (2,4) (2,6) (2,9) (2,12) (2,13) (4,11) (4,6) (4,15) (4,7) (4,8) (4,13) (5,11) (5,10) (5,14) (5,6) (5,9) (5,15) (5,12) (5,7) (5,13) (6,14) (7,14) (7,8) (9,13) (10,14) (12,15)\nIs there a path between node 14 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph101-4_8", + "image": "data/connectivity/graph_visual/medium/graph101.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,15) (0,8) (0,6) (0,10) (0,13) (0,2) (0,11) (0,4) (0,14) (0,5) (1,8) (1,10) (1,13) (1,2) (1,9) (1,4) (1,14) (1,5) (2,8) (2,6) (2,10) (2,13) (2,11) (2,7) (2,4) (2,14) (2,5) (3,12) (4,8) (4,6) (4,10) (4,13) (4,7) (5,8) (5,6) (5,10) (5,11) (5,7) (5,14) (6,8) (6,14) (7,15) (7,8) (7,10) (7,9) (7,14) (8,13) (8,11) (8,14) (9,15) (9,10) (9,11) (9,14) (10,13) (10,11) (10,14) (11,15) (11,13) (11,14) (13,15) (14,15)\nIs there a path between node 4 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph11-3_10", + "image": "data/connectivity/graph_visual/medium/graph11.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (0,5) (0,1) (0,9) (0,3) (0,4) (1,6) (1,5) (1,9) (1,3) (1,4) (2,7) (2,8) (2,10) (3,6) (3,5) (3,9) (3,4) (4,6) (4,5) (4,9) (5,6) (5,9) (6,9) (7,8) (7,10) (8,10)\nIs there a path between node 3 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph406-16_14", + "image": "data/connectivity/graph_visual/medium/graph406.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,14) (0,13) (1,20) (1,12) (1,3) (1,15) (1,19) (2,3) (2,15) (3,11) (3,10) (4,20) (4,8) (4,19) (4,10) (5,9) (8,20) (8,15) (8,10) (9,13) (10,20) (11,15) (12,20) (12,15) (13,18) (15,20) (18,21) (19,20)\nIs there a path between node 16 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph584-13_23", + "image": "data/connectivity/graph_visual/medium/graph584.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,22) (0,7) (1,21) (1,15) (1,11) (2,18) (2,3) (2,19) (3,18) (3,7) (4,16) (4,20) (5,21) (5,9) (6,16) (6,23) (7,15) (7,9) (7,22) (7,8) (8,19) (9,21) (9,11) (10,12) (10,23) (11,22) (13,17) (13,15) (13,22) (15,21) (15,19) (17,19) (18,21) (18,19)\nIs there a path between node 13 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph819-12_10", + "image": "data/connectivity/graph_visual/medium/graph819.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,10) (0,5) (0,7) (1,20) (1,4) (1,8) (1,16) (1,9) (1,23) (1,2) (2,20) (2,22) (2,15) (2,4) (2,19) (2,8) (2,16) (2,9) (2,23) (2,14) (2,17) (3,20) (3,4) (3,19) (3,8) (3,23) (3,14) (3,21) (4,20) (4,22) (4,15) (4,8) (4,16) (4,23) (4,14) (4,21) (5,11) (5,10) (5,7) (6,13) (6,12) (6,18) (7,11) (7,10) (8,20) (8,22) (8,15) (8,23) (8,14) (8,21) (9,22) (9,19) (9,16) (9,21) (9,17) (12,18) (13,24) (13,18) (14,20) (14,22) (14,15) (14,19) (14,23) (14,21) (14,17) (15,22) (15,19) (15,16) (15,21) (15,17) (16,20) (16,21) (17,20) (17,19) (17,23) (17,21) (18,24) (19,22) (19,21) (20,22) (20,23) (20,21) (21,22) (21,23) (22,23)\nIs there a path between node 12 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph10-6_8", + "image": "data/connectivity/graph_visual/medium/graph10.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,1) (0,7) (0,4) (0,9) (0,3) (1,7) (1,2) (1,4) (1,9) (1,3) (2,8) (2,9) (2,3) (3,8) (3,6) (3,4) (3,9) (4,8) (4,6) (5,10) (6,9) (8,9)\nIs there a path between node 6 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph804-19_21", + "image": "data/connectivity/graph_visual/medium/graph804.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,4) (1,19) (2,4) (2,10) (2,20) (3,20) (3,19) (4,13) (4,9) (4,7) (4,19) (5,6) (7,12) (7,20) (9,14) (9,13) (9,23) (9,12) (9,10) (10,15) (12,15) (12,20) (13,19) (14,20) (16,17) (18,22) (20,23)\nIs there a path between node 19 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph430-9_19", + "image": "data/connectivity/graph_visual/medium/graph430.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,16) (1,11) (1,2) (1,14) (2,3) (2,10) (2,6) (3,21) (3,9) (3,11) (3,10) (3,6) (4,12) (5,8) (5,13) (6,9) (6,14) (6,10) (6,7) (7,21) (7,9) (7,16) (7,11) (7,18) (7,14) (7,17) (8,12) (8,13) (9,16) (9,11) (11,16) (11,17) (12,13) (15,20) (16,18) (16,17) (17,18) (18,21)\nIs there a path between node 9 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph655-0_6", + "image": "data/connectivity/graph_visual/medium/graph655.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,16) (0,3) (0,21) (0,23) (1,16) (1,7) (1,3) (1,4) (1,11) (1,23) (2,15) (2,18) (2,6) (2,8) (2,12) (2,14) (2,13) (2,5) (3,16) (3,7) (3,4) (3,21) (3,11) (3,23) (4,16) (4,7) (4,21) (4,11) (5,10) (5,15) (5,17) (5,18) (5,8) (5,19) (5,9) (5,14) (5,13) (6,15) (6,17) (6,12) (6,19) (6,9) (7,21) (7,11) (7,23) (8,10) (8,15) (8,9) (8,14) (8,13) (9,15) (9,18) (9,12) (9,19) (9,14) (10,15) (10,12) (10,14) (10,13) (11,16) (11,21) (11,23) (12,15) (12,17) (12,18) (12,19) (12,13) (13,15) (13,17) (13,18) (13,19) (13,14) (14,17) (15,18) (16,23) (17,18) (18,19) (20,22) (21,23)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph40-9_7", + "image": "data/connectivity/graph_visual/medium/graph40.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,1) (0,4) (1,11) (2,3) (2,12) (4,6) (4,7) (5,9) (6,7) (7,9) (7,11) (8,10) (8,12) (9,11)\nIs there a path between node 9 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph225-14_12", + "image": "data/connectivity/graph_visual/medium/graph225.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,1) (1,4) (1,2) (2,12) (2,3) (2,10) (3,10) (3,5) (3,4) (3,18) (4,12) (5,12) (5,11) (5,18) (6,11) (6,9) (9,17) (9,11) (9,18) (10,16) (10,18) (11,16) (11,12) (11,18) (14,15)\nIs there a path between node 14 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph690-20_6", + "image": "data/connectivity/graph_visual/medium/graph690.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,11) (0,1) (0,4) (0,15) (0,10) (0,22) (0,14) (0,8) (1,21) (1,11) (1,4) (1,15) (1,10) (1,22) (1,14) (1,8) (2,3) (2,13) (2,5) (2,7) (3,13) (3,5) (3,7) (4,21) (4,11) (4,15) (4,10) (4,22) (4,14) (4,8) (5,13) (5,7) (6,20) (6,19) (6,16) (6,17) (6,9) (6,18) (6,12) (6,23) (7,13) (8,21) (8,11) (8,15) (8,10) (8,22) (8,14) (9,20) (9,19) (9,16) (9,17) (9,18) (9,12) (9,23) (10,21) (10,11) (10,15) (10,22) (10,14) (11,21) (11,15) (11,22) (11,14) (12,20) (12,19) (12,16) (12,17) (12,18) (12,23) (14,21) (14,15) (14,22) (15,21) (15,22) (16,20) (16,19) (16,17) (16,18) (16,23) (17,20) (17,19) (17,18) (17,23) (18,20) (18,19) (18,23) (19,20) (19,23) (20,23) (21,22)\nIs there a path between node 20 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph474-6_8", + "image": "data/connectivity/graph_visual/medium/graph474.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,12) (0,21) (0,17) (0,16) (0,20) (1,15) (1,14) (1,20) (1,19) (1,9) (1,2) (1,6) (1,3) (2,18) (2,20) (2,19) (2,10) (3,16) (3,13) (4,5) (6,14) (6,18) (6,11) (6,22) (6,7) (6,13) (7,21) (7,15) (7,14) (7,18) (7,19) (7,11) (7,8) (8,12) (8,21) (8,15) (8,14) (8,20) (8,11) (8,9) (8,10) (9,15) (9,11) (9,10) (9,13) (10,18) (10,20) (10,19) (10,11) (10,22) (11,15) (11,16) (11,22) (12,21) (12,17) (12,18) (13,21) (13,17) (13,20) (13,19) (14,20) (15,21) (15,17) (15,18) (16,18) (16,20) (16,19) (17,20) (17,19) (17,22) (18,22)\nIs there a path between node 6 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph3-6_9", + "image": "data/connectivity/graph_visual/medium/graph3.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nIs there a path between node 6 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph87-8_2", + "image": "data/connectivity/graph_visual/medium/graph87.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (0,13) (0,7) (0,3) (0,14) (0,6) (0,10) (0,1) (0,12) (1,9) (1,13) (1,7) (1,3) (1,14) (1,6) (1,10) (1,12) (2,5) (2,11) (2,8) (2,4) (3,9) (3,13) (3,7) (3,14) (3,6) (3,10) (3,12) (4,5) (4,11) (4,8) (5,11) (5,8) (6,9) (6,13) (6,7) (6,14) (6,10) (6,12) (7,9) (7,13) (7,14) (7,10) (7,12) (8,11) (9,13) (9,14) (9,10) (9,12) (10,13) (10,14) (10,12) (12,13) (12,14) (13,14)\nIs there a path between node 8 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph2-5_2", + "image": "data/connectivity/graph_visual/medium/graph2.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,3) (0,7) (0,10) (0,6) (0,2) (0,8) (0,4) (0,1) (1,3) (1,7) (1,10) (1,6) (1,2) (1,8) (1,4) (2,3) (2,7) (2,10) (2,6) (2,8) (2,4) (3,7) (3,10) (3,6) (3,8) (3,4) (4,7) (4,10) (4,6) (4,8) (5,9) (6,7) (6,10) (6,8) (7,10) (7,8) (8,10)\nIs there a path between node 5 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph374-10_11", + "image": "data/connectivity/graph_visual/medium/graph374.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,4) (0,12) (0,11) (1,14) (1,7) (1,15) (1,3) (1,20) (1,8) (1,5) (2,14) (2,7) (2,19) (2,10) (2,3) (2,20) (2,8) (2,5) (2,13) (2,16) (3,14) (3,7) (3,19) (3,10) (3,8) (3,5) (3,13) (3,16) (4,9) (4,11) (5,14) (5,7) (5,19) (5,10) (5,20) (5,8) (5,13) (7,14) (7,19) (7,8) (7,13) (7,17) (8,14) (8,19) (8,10) (8,15) (8,20) (8,16) (8,17) (9,12) (9,11) (10,19) (10,15) (10,13) (10,16) (11,12) (13,14) (13,15) (13,20) (13,16) (13,17) (14,19) (14,15) (14,20) (14,17) (15,20) (15,16) (15,17) (16,20) (16,17) (17,19) (19,20)\nIs there a path between node 10 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph84-7_9", + "image": "data/connectivity/graph_visual/medium/graph84.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,4) (0,13) (0,12) (0,14) (0,8) (0,3) (0,6) (0,2) (0,9) (0,5) (1,10) (1,7) (1,11) (2,4) (2,13) (2,12) (2,14) (2,8) (2,3) (2,6) (2,9) (2,5) (3,4) (3,13) (3,12) (3,14) (3,8) (3,6) (3,9) (3,5) (4,13) (4,12) (4,14) (4,8) (4,6) (4,9) (4,5) (5,13) (5,12) (5,14) (5,8) (5,6) (5,9) (6,13) (6,12) (6,14) (6,8) (6,9) (7,10) (7,11) (8,13) (8,12) (8,14) (8,9) (9,13) (9,12) (9,14) (10,11) (12,13) (12,14) (13,14)\nIs there a path between node 7 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph68-9_1", + "image": "data/connectivity/graph_visual/medium/graph68.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (0,13) (0,8) (0,10) (0,11) (0,6) (0,1) (0,3) (0,12) (1,2) (1,13) (1,8) (1,10) (1,11) (1,6) (1,3) (1,12) (2,13) (2,8) (2,10) (2,11) (2,6) (2,3) (2,12) (3,13) (3,8) (3,10) (3,11) (3,6) (3,12) (4,7) (4,5) (4,9) (5,7) (5,9) (6,13) (6,8) (6,10) (6,11) (6,12) (7,9) (8,13) (8,10) (8,11) (8,12) (10,13) (10,11) (10,12) (11,13) (11,12) (12,13)\nIs there a path between node 9 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph204-1_9", + "image": "data/connectivity/graph_visual/medium/graph204.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,14) (0,16) (0,2) (1,6) (1,17) (1,15) (2,13) (2,8) (2,16) (3,6) (3,4) (4,6) (4,15) (5,8) (5,14) (5,10) (6,15) (8,13) (9,18) (10,13) (13,16)\nIs there a path between node 1 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph720-11_20", + "image": "data/connectivity/graph_visual/medium/graph720.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,21) (0,11) (0,15) (0,4) (0,22) (0,5) (0,3) (0,6) (0,20) (0,13) (0,18) (0,9) (0,1) (0,12) (0,24) (0,16) (0,8) (0,23) (0,2) (1,21) (1,11) (1,15) (1,4) (1,22) (1,5) (1,3) (1,6) (1,20) (1,13) (1,18) (1,9) (1,12) (1,24) (1,16) (1,8) (1,23) (1,2) (2,21) (2,11) (2,15) (2,4) (2,22) (2,5) (2,3) (2,6) (2,20) (2,13) (2,18) (2,9) (2,12) (2,24) (2,16) (2,8) (2,23) (3,21) (3,11) (3,15) (3,4) (3,22) (3,5) (3,6) (3,20) (3,13) (3,18) (3,9) (3,12) (3,24) (3,16) (3,8) (3,23) (4,21) (4,11) (4,15) (4,22) (4,5) (4,6) (4,20) (4,13) (4,18) (4,9) (4,12) (4,24) (4,16) (4,8) (4,23) (5,21) (5,11) (5,15) (5,22) (5,6) (5,20) (5,13) (5,18) (5,9) (5,12) (5,24) (5,16) (5,8) (5,23) (6,21) (6,11) (6,15) (6,22) (6,20) (6,13) (6,18) (6,9) (6,12) (6,24) (6,16) (6,8) (6,23) (7,10) (7,14) (7,17) (7,19) (8,21) (8,11) (8,15) (8,22) (8,20) (8,13) (8,18) (8,9) (8,12) (8,24) (8,16) (8,23) (9,21) (9,11) (9,15) (9,22) (9,20) (9,13) (9,18) (9,12) (9,24) (9,16) (9,23) (10,14) (10,17) (10,19) (11,21) (11,15) (11,22) (11,20) (11,13) (11,18) (11,12) (11,24) (11,16) (11,23) (12,21) (12,15) (12,22) (12,20) (12,13) (12,18) (12,24) (12,16) (12,23) (13,21) (13,15) (13,22) (13,20) (13,18) (13,24) (13,16) (13,23) (14,17) (14,19) (15,21) (15,22) (15,20) (15,18) (15,24) (15,16) (15,23) (16,21) (16,22) (16,20) (16,18) (16,24) (16,23) (17,19) (18,21) (18,22) (18,20) (18,24) (18,23) (20,21) (20,22) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 11 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph734-0_14", + "image": "data/connectivity/graph_visual/medium/graph734.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,8) (0,14) (0,10) (1,21) (1,22) (1,17) (1,12) (2,23) (2,3) (3,23) (3,10) (3,15) (4,23) (4,10) (4,15) (4,11) (5,16) (5,17) (6,21) (6,13) (6,17) (6,12) (7,9) (7,22) (7,18) (8,20) (8,15) (8,11) (9,24) (9,17) (9,12) (12,19) (12,17) (13,21) (13,22) (15,23) (16,24) (16,22) (16,17) (17,24) (17,21) (17,18) (21,22) (22,24)\nIs there a path between node 0 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph564-11_19", + "image": "data/connectivity/graph_visual/medium/graph564.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,12) (0,1) (0,7) (0,16) (0,13) (0,9) (0,2) (0,10) (0,21) (0,19) (0,3) (0,20) (0,8) (0,23) (0,5) (0,4) (0,6) (0,22) (1,15) (1,12) (1,7) (1,16) (1,13) (1,9) (1,2) (1,10) (1,21) (1,19) (1,3) (1,20) (1,8) (1,23) (1,5) (1,4) (1,6) (1,22) (2,15) (2,12) (2,7) (2,16) (2,13) (2,9) (2,10) (2,21) (2,19) (2,3) (2,20) (2,8) (2,23) (2,5) (2,4) (2,6) (2,22) (3,15) (3,12) (3,7) (3,16) (3,13) (3,9) (3,10) (3,21) (3,19) (3,20) (3,8) (3,23) (3,5) (3,4) (3,6) (3,22) (4,15) (4,12) (4,7) (4,16) (4,13) (4,9) (4,10) (4,21) (4,19) (4,20) (4,8) (4,23) (4,5) (4,6) (4,22) (5,15) (5,12) (5,7) (5,16) (5,13) (5,9) (5,10) (5,21) (5,19) (5,20) (5,8) (5,23) (5,6) (5,22) (6,15) (6,12) (6,7) (6,16) (6,13) (6,9) (6,10) (6,21) (6,19) (6,20) (6,8) (6,23) (6,22) (7,15) (7,12) (7,16) (7,13) (7,9) (7,10) (7,21) (7,19) (7,20) (7,8) (7,23) (7,22) (8,15) (8,12) (8,16) (8,13) (8,9) (8,10) (8,21) (8,19) (8,20) (8,23) (8,22) (9,15) (9,12) (9,16) (9,13) (9,10) (9,21) (9,19) (9,20) (9,23) (9,22) (10,15) (10,12) (10,16) (10,13) (10,21) (10,19) (10,20) (10,23) (10,22) (11,17) (11,14) (11,18) (12,15) (12,16) (12,13) (12,21) (12,19) (12,20) (12,23) (12,22) (13,15) (13,16) (13,21) (13,19) (13,20) (13,23) (13,22) (14,17) (14,18) (15,16) (15,21) (15,19) (15,20) (15,23) (15,22) (16,21) (16,19) (16,20) (16,23) (16,22) (17,18) (19,21) (19,20) (19,23) (19,22) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 11 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph629-16_4", + "image": "data/connectivity/graph_visual/medium/graph629.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,14) (2,17) (2,7) (4,16) (4,11) (4,20) (4,12) (5,15) (6,15) (7,10) (7,12) (9,22) (9,18) (10,16) (11,21) (11,16) (12,21) (12,17) (14,23) (14,19) (16,20) (17,21) (20,21)\nIs there a path between node 16 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph129-14_15", + "image": "data/connectivity/graph_visual/medium/graph129.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,12) (0,13) (0,2) (0,16) (0,7) (0,6) (0,9) (0,5) (0,1) (0,8) (1,12) (1,13) (1,2) (1,16) (1,7) (1,6) (1,9) (1,5) (1,8) (2,12) (2,13) (2,16) (2,7) (2,6) (2,9) (2,5) (2,8) (3,10) (3,14) (3,4) (3,11) (3,15) (4,10) (4,14) (4,11) (4,15) (5,12) (5,13) (5,16) (5,7) (5,6) (5,9) (5,8) (6,12) (6,13) (6,16) (6,7) (6,9) (6,8) (7,12) (7,13) (7,16) (7,9) (7,8) (8,12) (8,13) (8,16) (8,9) (9,12) (9,13) (9,16) (10,14) (10,11) (10,15) (11,14) (11,15) (12,13) (12,16) (13,16) (14,15)\nIs there a path between node 14 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph684-14_8", + "image": "data/connectivity/graph_visual/medium/graph684.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,21) (0,12) (0,9) (0,2) (0,6) (0,4) (0,5) (0,14) (0,17) (0,8) (0,20) (0,13) (0,19) (0,22) (0,1) (0,15) (0,10) (0,18) (1,7) (1,21) (1,12) (1,9) (1,2) (1,6) (1,4) (1,5) (1,14) (1,17) (1,8) (1,20) (1,13) (1,19) (1,22) (1,15) (1,10) (1,18) (2,7) (2,21) (2,12) (2,9) (2,6) (2,4) (2,5) (2,14) (2,17) (2,8) (2,20) (2,13) (2,19) (2,22) (2,15) (2,10) (2,18) (3,11) (3,23) (4,7) (4,21) (4,12) (4,9) (4,6) (4,5) (4,14) (4,17) (4,8) (4,20) (4,13) (4,19) (4,22) (4,15) (4,10) (4,18) (5,7) (5,21) (5,12) (5,9) (5,6) (5,14) (5,17) (5,8) (5,20) (5,13) (5,19) (5,22) (5,15) (5,10) (5,18) (6,7) (6,21) (6,12) (6,9) (6,14) (6,17) (6,8) (6,20) (6,13) (6,19) (6,22) (6,15) (6,10) (6,18) (7,21) (7,12) (7,9) (7,14) (7,17) (7,8) (7,20) (7,13) (7,19) (7,22) (7,15) (7,10) (7,18) (8,21) (8,12) (8,9) (8,14) (8,17) (8,20) (8,13) (8,19) (8,22) (8,15) (8,10) (8,18) (9,21) (9,12) (9,14) (9,17) (9,20) (9,13) (9,19) (9,22) (9,15) (9,10) (9,18) (10,21) (10,12) (10,14) (10,17) (10,20) (10,13) (10,19) (10,22) (10,15) (10,18) (11,23) (12,21) (12,14) (12,17) (12,20) (12,13) (12,19) (12,22) (12,15) (12,18) (13,21) (13,14) (13,17) (13,20) (13,19) (13,22) (13,15) (13,18) (14,21) (14,17) (14,20) (14,19) (14,22) (14,15) (14,18) (15,21) (15,17) (15,20) (15,19) (15,22) (15,18) (17,21) (17,20) (17,19) (17,22) (17,18) (18,21) (18,20) (18,19) (18,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 14 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph446-15_0", + "image": "data/connectivity/graph_visual/medium/graph446.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,13) (0,2) (0,5) (0,4) (0,18) (0,9) (0,3) (0,12) (0,21) (0,8) (0,20) (1,16) (1,17) (1,14) (1,19) (2,11) (2,13) (2,5) (2,4) (2,3) (2,21) (2,10) (2,8) (3,11) (3,5) (3,18) (3,12) (3,21) (3,10) (3,8) (3,20) (4,11) (4,13) (4,5) (4,18) (4,9) (4,12) (4,21) (4,10) (4,8) (4,20) (5,11) (5,13) (5,18) (5,12) (5,21) (5,10) (5,8) (5,20) (6,15) (7,15) (8,13) (8,12) (8,10) (9,11) (9,18) (9,12) (9,21) (9,10) (10,11) (10,13) (10,18) (10,21) (10,20) (11,12) (11,20) (12,13) (12,21) (12,20) (13,21) (14,16) (14,17) (14,19) (16,17) (16,19) (18,21) (18,20) (20,21)\nIs there a path between node 15 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph58-10_13", + "image": "data/connectivity/graph_visual/medium/graph58.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (0,1) (1,3) (1,11) (1,2) (1,4) (2,9) (2,12) (3,8) (4,12) (5,11) (5,8) (5,7) (6,13) (10,12)\nIs there a path between node 10 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph521-0_14", + "image": "data/connectivity/graph_visual/medium/graph521.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,10) (0,12) (0,16) (0,9) (0,17) (0,11) (0,5) (0,13) (0,21) (0,4) (1,8) (1,18) (1,7) (3,6) (3,14) (3,10) (3,16) (3,9) (3,11) (3,5) (3,21) (3,4) (3,15) (4,6) (4,10) (4,12) (4,16) (4,9) (4,17) (4,11) (4,13) (4,21) (4,15) (5,6) (5,12) (5,9) (5,19) (5,17) (5,13) (5,21) (5,15) (6,14) (6,10) (6,12) (6,16) (6,19) (6,17) (6,13) (6,21) (6,15) (7,20) (7,8) (7,18) (8,20) (9,14) (9,10) (9,16) (9,19) (9,17) (9,11) (9,13) (9,21) (10,12) (10,19) (10,17) (10,11) (10,15) (11,14) (11,16) (11,19) (11,17) (11,21) (12,14) (12,17) (12,13) (12,21) (13,14) (13,16) (13,17) (13,21) (14,16) (14,21) (15,19) (15,17) (15,21) (16,17) (16,21) (17,19) (17,21) (18,20) (19,21)\nIs there a path between node 0 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph236-15_16", + "image": "data/connectivity/graph_visual/medium/graph236.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,12) (0,7) (0,11) (0,8) (0,9) (0,2) (0,6) (1,18) (1,15) (1,10) (1,17) (1,13) (1,14) (1,4) (1,16) (2,11) (2,8) (2,9) (3,12) (3,7) (3,9) (4,18) (4,17) (4,5) (4,16) (5,18) (5,15) (5,17) (5,13) (5,14) (6,7) (6,11) (7,12) (7,11) (7,8) (7,9) (8,12) (8,11) (8,9) (9,11) (10,18) (10,16) (13,15) (13,17) (13,16) (14,18) (14,15) (14,16) (15,17) (16,17) (17,18)\nIs there a path between node 15 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph296-9_18", + "image": "data/connectivity/graph_visual/medium/graph296.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,1) (0,11) (0,17) (0,3) (0,19) (0,9) (0,16) (0,15) (0,7) (0,12) (0,2) (1,11) (1,10) (1,3) (1,4) (1,8) (1,19) (1,13) (1,9) (1,16) (1,15) (1,7) (1,12) (1,2) (2,17) (2,5) (2,16) (2,15) (3,17) (3,10) (3,5) (3,6) (3,8) (3,13) (3,9) (3,16) (3,15) (3,7) (3,12) (4,11) (4,5) (4,8) (4,19) (4,13) (4,9) (4,7) (4,12) (5,11) (5,10) (5,6) (5,8) (5,19) (5,13) (5,7) (6,11) (6,17) (6,10) (6,8) (6,19) (6,13) (6,16) (6,15) (6,7) (6,12) (7,11) (7,17) (7,10) (7,19) (7,9) (7,16) (7,15) (8,11) (8,17) (8,10) (8,19) (8,13) (8,15) (8,12) (9,11) (9,17) (9,10) (9,13) (9,16) (9,15) (10,11) (10,17) (10,19) (10,13) (10,15) (10,12) (11,19) (11,15) (11,12) (12,17) (12,19) (12,13) (13,19) (13,16) (13,15) (14,18) (15,19) (15,16) (16,17) (17,19)\nIs there a path between node 9 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph284-14_4", + "image": "data/connectivity/graph_visual/medium/graph284.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,2) (1,7) (1,15) (2,12) (2,15) (3,17) (3,7) (3,12) (3,15) (4,14) (4,16) (4,15) (5,9) (5,6) (6,18) (6,9) (6,13) (7,12) (8,12) (9,18) (10,19) (14,16) (14,15) (16,17)\nIs there a path between node 14 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph86-0_14", + "image": "data/connectivity/graph_visual/medium/graph86.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,3) (0,1) (0,14) (0,13) (0,4) (0,10) (0,5) (1,3) (1,14) (1,13) (1,4) (1,10) (1,5) (2,8) (2,11) (2,7) (2,12) (2,6) (2,9) (3,14) (3,13) (3,4) (3,10) (3,5) (4,14) (4,13) (4,10) (4,5) (5,14) (5,13) (5,10) (6,8) (6,11) (6,7) (6,12) (6,9) (7,8) (7,11) (7,12) (7,9) (8,11) (8,12) (8,9) (9,11) (9,12) (10,14) (10,13) (11,12) (13,14)\nIs there a path between node 0 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph850-8_24", + "image": "data/connectivity/graph_visual/medium/graph850.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,4) (0,11) (0,16) (0,5) (0,2) (0,22) (0,15) (0,8) (0,21) (0,7) (0,9) (0,23) (0,12) (0,3) (0,14) (0,20) (1,19) (1,18) (1,24) (1,17) (1,13) (1,10) (2,6) (2,4) (2,11) (2,16) (2,5) (2,22) (2,15) (2,8) (2,21) (2,7) (2,9) (2,23) (2,12) (2,3) (2,14) (2,20) (3,6) (3,4) (3,11) (3,16) (3,5) (3,22) (3,15) (3,8) (3,21) (3,7) (3,9) (3,23) (3,12) (3,14) (3,20) (4,6) (4,11) (4,16) (4,5) (4,22) (4,15) (4,8) (4,21) (4,7) (4,9) (4,23) (4,12) (4,14) (4,20) (5,6) (5,11) (5,16) (5,22) (5,15) (5,8) (5,21) (5,7) (5,9) (5,23) (5,12) (5,14) (5,20) (6,11) (6,16) (6,22) (6,15) (6,8) (6,21) (6,7) (6,9) (6,23) (6,12) (6,14) (6,20) (7,11) (7,16) (7,22) (7,15) (7,8) (7,21) (7,9) (7,23) (7,12) (7,14) (7,20) (8,11) (8,16) (8,22) (8,15) (8,21) (8,9) (8,23) (8,12) (8,14) (8,20) (9,11) (9,16) (9,22) (9,15) (9,21) (9,23) (9,12) (9,14) (9,20) (10,19) (10,18) (10,24) (10,17) (10,13) (11,16) (11,22) (11,15) (11,21) (11,23) (11,12) (11,14) (11,20) (12,16) (12,22) (12,15) (12,21) (12,23) (12,14) (12,20) (13,19) (13,18) (13,24) (13,17) (14,16) (14,22) (14,15) (14,21) (14,23) (14,20) (15,16) (15,22) (15,21) (15,23) (15,20) (16,22) (16,21) (16,23) (16,20) (17,19) (17,18) (17,24) (18,19) (18,24) (19,24) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 8 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph612-17_21", + "image": "data/connectivity/graph_visual/medium/graph612.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,6) (0,12) (0,20) (0,15) (0,9) (0,13) (0,2) (0,14) (0,11) (0,3) (0,23) (0,5) (1,21) (1,7) (1,8) (1,22) (1,4) (1,18) (1,17) (1,16) (2,10) (2,19) (2,6) (2,12) (2,20) (2,15) (2,9) (2,13) (2,14) (2,11) (2,3) (2,23) (2,5) (3,10) (3,19) (3,6) (3,12) (3,20) (3,15) (3,9) (3,13) (3,14) (3,11) (3,23) (3,5) (4,21) (4,7) (4,8) (4,22) (4,18) (4,17) (4,16) (5,10) (5,19) (5,6) (5,12) (5,20) (5,15) (5,9) (5,13) (5,14) (5,11) (5,23) (6,10) (6,19) (6,12) (6,20) (6,15) (6,9) (6,13) (6,14) (6,11) (6,23) (7,21) (7,8) (7,22) (7,18) (7,17) (7,16) (8,21) (8,22) (8,18) (8,17) (8,16) (9,10) (9,19) (9,12) (9,20) (9,15) (9,13) (9,14) (9,11) (9,23) (10,19) (10,12) (10,20) (10,15) (10,13) (10,14) (10,11) (10,23) (11,19) (11,12) (11,20) (11,15) (11,13) (11,14) (11,23) (12,19) (12,20) (12,15) (12,13) (12,14) (12,23) (13,19) (13,20) (13,15) (13,14) (13,23) (14,19) (14,20) (14,15) (14,23) (15,19) (15,20) (15,23) (16,21) (16,22) (16,18) (16,17) (17,21) (17,22) (17,18) (18,21) (18,22) (19,20) (19,23) (20,23) (21,22)\nIs there a path between node 17 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph358-3_17", + "image": "data/connectivity/graph_visual/medium/graph358.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,1) (0,19) (0,18) (0,16) (1,6) (1,15) (2,18) (2,20) (2,11) (3,12) (4,6) (4,16) (4,15) (4,11) (6,9) (6,18) (6,20) (6,11) (9,14) (9,19) (9,18) (9,20) (9,16) (9,11) (10,14) (10,20) (10,16) (11,14) (11,20) (14,19) (14,15) (15,18) (15,16) (16,18) (18,20)\nIs there a path between node 3 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph608-1_2", + "image": "data/connectivity/graph_visual/medium/graph608.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,10) (0,6) (0,9) (0,5) (0,3) (0,17) (0,18) (0,15) (0,21) (1,16) (1,23) (1,12) (1,14) (1,22) (1,4) (1,13) (1,19) (1,2) (1,20) (1,11) (1,7) (2,16) (2,23) (2,12) (2,14) (2,22) (2,4) (2,13) (2,19) (2,20) (2,11) (2,7) (3,8) (3,10) (3,6) (3,9) (3,5) (3,17) (3,18) (3,15) (3,21) (4,16) (4,23) (4,12) (4,14) (4,22) (4,13) (4,19) (4,20) (4,11) (4,7) (5,8) (5,10) (5,6) (5,9) (5,17) (5,18) (5,15) (5,21) (6,8) (6,10) (6,9) (6,17) (6,18) (6,15) (6,21) (7,16) (7,23) (7,12) (7,14) (7,22) (7,13) (7,19) (7,20) (7,11) (8,10) (8,9) (8,17) (8,18) (8,15) (8,21) (9,10) (9,17) (9,18) (9,15) (9,21) (10,17) (10,18) (10,15) (10,21) (11,16) (11,23) (11,12) (11,14) (11,22) (11,13) (11,19) (11,20) (12,16) (12,23) (12,14) (12,22) (12,13) (12,19) (12,20) (13,16) (13,23) (13,14) (13,22) (13,19) (13,20) (14,16) (14,23) (14,22) (14,19) (14,20) (15,17) (15,18) (15,21) (16,23) (16,22) (16,19) (16,20) (17,18) (17,21) (18,21) (19,23) (19,22) (19,20) (20,23) (20,22) (22,23)\nIs there a path between node 1 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph447-6_5", + "image": "data/connectivity/graph_visual/medium/graph447.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,6) (0,3) (0,15) (0,12) (0,20) (0,18) (0,2) (0,13) (0,21) (0,9) (0,14) (0,4) (1,17) (2,16) (2,6) (2,7) (2,12) (2,13) (2,21) (2,5) (3,16) (3,12) (3,18) (3,13) (3,21) (3,9) (3,4) (4,15) (4,7) (4,12) (4,20) (4,13) (4,21) (4,5) (4,9) (5,16) (5,6) (5,15) (5,7) (5,12) (5,18) (5,13) (5,9) (5,14) (6,16) (6,7) (6,12) (6,20) (6,21) (6,14) (7,16) (7,15) (7,12) (7,20) (7,13) (7,9) (8,19) (9,15) (9,20) (9,21) (9,14) (10,19) (11,17) (12,16) (12,20) (12,18) (12,21) (13,20) (13,21) (14,16) (14,15) (14,20) (14,18) (14,21) (15,21) (16,20) (16,18) (18,20) (18,21) (20,21)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph731-22_21", + "image": "data/connectivity/graph_visual/medium/graph731.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,6) (0,8) (1,2) (1,9) (1,24) (1,22) (1,20) (1,3) (1,17) (2,12) (2,19) (2,24) (2,13) (2,10) (3,12) (3,9) (3,24) (3,22) (3,10) (3,18) (4,5) (4,10) (4,17) (5,23) (5,11) (5,16) (5,14) (5,18) (6,7) (7,15) (7,8) (8,15) (9,11) (9,13) (10,21) (10,13) (10,16) (10,17) (11,13) (11,22) (12,21) (12,24) (12,22) (12,16) (12,14) (13,14) (13,17) (14,19) (14,21) (14,16) (16,24) (16,18) (17,19) (17,21) (17,24) (17,22) (17,20) (18,23) (18,19) (18,24) (18,22) (20,23) (20,21) (20,24) (21,22)\nIs there a path between node 22 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph715-19_18", + "image": "data/connectivity/graph_visual/medium/graph715.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,8) (0,13) (0,5) (0,2) (0,19) (0,22) (0,17) (0,16) (0,3) (0,24) (0,20) (0,10) (0,15) (0,7) (0,4) (0,23) (0,6) (0,1) (1,8) (1,13) (1,19) (1,11) (1,22) (1,17) (1,3) (1,24) (1,20) (1,10) (1,15) (1,7) (1,4) (1,23) (1,6) (2,14) (2,8) (2,13) (2,22) (2,17) (2,16) (2,3) (2,24) (2,10) (2,15) (2,7) (2,4) (2,23) (2,6) (3,14) (3,13) (3,19) (3,11) (3,22) (3,17) (3,24) (3,10) (3,15) (3,4) (3,9) (4,13) (4,5) (4,22) (4,17) (4,10) (4,15) (4,7) (4,9) (4,23) (4,6) (5,8) (5,13) (5,19) (5,22) (5,24) (5,20) (5,10) (5,7) (5,23) (6,14) (6,8) (6,13) (6,19) (6,11) (6,22) (6,17) (6,16) (6,20) (6,7) (6,9) (7,14) (7,8) (7,13) (7,19) (7,11) (7,22) (7,20) (7,9) (8,19) (8,11) (8,22) (8,17) (8,20) (8,10) (8,15) (8,9) (9,17) (9,16) (9,24) (9,20) (9,10) (9,15) (9,23) (10,14) (10,13) (10,19) (10,11) (10,22) (10,17) (10,15) (10,23) (11,13) (11,22) (11,16) (12,18) (13,14) (13,19) (13,22) (13,16) (13,24) (13,20) (13,15) (13,23) (14,19) (14,17) (14,16) (14,15) (14,23) (15,19) (15,22) (15,17) (15,24) (15,20) (16,22) (16,17) (16,24) (17,19) (17,24) (17,20) (17,23) (18,21) (19,24) (19,20) (19,23) (20,22) (20,24) (20,23)\nIs there a path between node 19 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph102-1_15", + "image": "data/connectivity/graph_visual/medium/graph102.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,13) (0,3) (0,15) (0,4) (0,12) (0,9) (0,14) (0,2) (0,11) (1,15) (1,4) (1,12) (1,9) (1,14) (1,2) (2,8) (2,13) (2,15) (2,12) (2,6) (2,11) (3,8) (3,13) (3,12) (3,6) (3,10) (3,14) (3,11) (4,8) (4,13) (4,15) (4,10) (4,9) (4,14) (4,11) (5,7) (6,8) (6,13) (6,15) (6,10) (6,9) (6,14) (6,11) (8,15) (8,12) (8,9) (8,14) (9,15) (9,12) (9,10) (9,14) (10,15) (10,12) (10,14) (11,13) (11,15) (11,12) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nIs there a path between node 1 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph176-5_11", + "image": "data/connectivity/graph_visual/medium/graph176.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,7) (0,13) (0,10) (0,9) (1,16) (1,12) (1,17) (1,8) (2,3) (2,14) (2,15) (2,5) (2,11) (3,14) (3,5) (4,7) (4,10) (4,9) (5,15) (5,11) (6,7) (6,10) (7,13) (7,10) (7,9) (8,12) (9,13) (10,13) (11,14) (11,15) (12,16) (12,17) (14,15) (16,17)\nIs there a path between node 5 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph348-2_8", + "image": "data/connectivity/graph_visual/medium/graph348.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,2) (0,7) (0,20) (0,1) (0,18) (0,11) (0,5) (0,15) (0,13) (0,14) (0,3) (0,9) (0,6) (0,4) (0,12) (0,17) (0,16) (1,10) (1,2) (1,7) (1,20) (1,18) (1,11) (1,5) (1,15) (1,13) (1,14) (1,3) (1,9) (1,6) (1,4) (1,12) (1,17) (1,16) (2,10) (2,7) (2,20) (2,18) (2,11) (2,5) (2,15) (2,13) (2,14) (2,3) (2,9) (2,6) (2,4) (2,12) (2,17) (2,16) (3,10) (3,7) (3,20) (3,18) (3,11) (3,5) (3,15) (3,13) (3,14) (3,9) (3,6) (3,4) (3,12) (3,17) (3,16) (4,10) (4,7) (4,20) (4,18) (4,11) (4,5) (4,15) (4,13) (4,14) (4,9) (4,6) (4,12) (4,17) (4,16) (5,10) (5,7) (5,20) (5,18) (5,11) (5,15) (5,13) (5,14) (5,9) (5,6) (5,12) (5,17) (5,16) (6,10) (6,7) (6,20) (6,18) (6,11) (6,15) (6,13) (6,14) (6,9) (6,12) (6,17) (6,16) (7,10) (7,20) (7,18) (7,11) (7,15) (7,13) (7,14) (7,9) (7,12) (7,17) (7,16) (8,19) (9,10) (9,20) (9,18) (9,11) (9,15) (9,13) (9,14) (9,12) (9,17) (9,16) (10,20) (10,18) (10,11) (10,15) (10,13) (10,14) (10,12) (10,17) (10,16) (11,20) (11,18) (11,15) (11,13) (11,14) (11,12) (11,17) (11,16) (12,20) (12,18) (12,15) (12,13) (12,14) (12,17) (12,16) (13,20) (13,18) (13,15) (13,14) (13,17) (13,16) (14,20) (14,18) (14,15) (14,17) (14,16) (15,20) (15,18) (15,17) (15,16) (16,20) (16,18) (16,17) (17,20) (17,18) (18,20)\nIs there a path between node 2 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph406-11_15", + "image": "data/connectivity/graph_visual/medium/graph406.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,14) (0,13) (1,20) (1,12) (1,3) (1,15) (1,19) (2,3) (2,15) (3,11) (3,10) (4,20) (4,8) (4,19) (4,10) (5,9) (8,20) (8,15) (8,10) (9,13) (10,20) (11,15) (12,20) (12,15) (13,18) (15,20) (18,21) (19,20)\nIs there a path between node 11 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph27-7_11", + "image": "data/connectivity/graph_visual/medium/graph27.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,2) (0,9) (0,1) (0,11) (0,4) (0,3) (1,6) (1,2) (1,9) (1,8) (1,11) (2,6) (2,8) (2,11) (2,3) (3,6) (3,9) (3,8) (3,10) (3,11) (3,4) (4,6) (4,8) (4,10) (5,7) (6,9) (6,8) (6,10) (6,11) (8,10) (9,11) (10,11)\nIs there a path between node 7 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph525-1_4", + "image": "data/connectivity/graph_visual/medium/graph525.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,6) (0,18) (0,17) (0,8) (0,15) (0,2) (0,22) (0,16) (0,13) (0,3) (0,12) (0,20) (1,9) (1,21) (1,14) (2,4) (2,10) (2,18) (2,8) (2,15) (2,22) (2,16) (2,13) (2,7) (2,3) (2,12) (2,11) (3,5) (3,10) (3,6) (3,18) (3,8) (3,15) (3,22) (3,16) (3,7) (3,12) (3,11) (3,20) (4,5) (4,10) (4,6) (4,18) (4,8) (4,15) (4,19) (4,22) (4,16) (4,13) (4,12) (4,20) (5,6) (5,18) (5,17) (5,22) (5,16) (5,13) (5,7) (5,20) (6,10) (6,18) (6,17) (6,15) (6,19) (6,22) (6,16) (6,13) (6,12) (6,11) (7,10) (7,18) (7,17) (7,8) (7,19) (7,13) (7,12) (8,10) (8,18) (8,17) (8,15) (8,19) (8,22) (8,16) (8,13) (8,12) (8,11) (8,20) (9,21) (10,17) (10,15) (10,19) (10,16) (10,13) (10,12) (10,20) (11,18) (11,17) (11,15) (11,19) (11,22) (11,16) (11,13) (12,18) (12,17) (12,15) (12,19) (12,22) (12,13) (13,17) (13,15) (13,22) (13,16) (14,21) (15,18) (15,17) (15,16) (15,20) (16,17) (16,19) (16,22) (16,20) (17,18) (17,19) (17,22) (17,20) (18,19) (18,22) (19,22) (20,22)\nIs there a path between node 1 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph404-3_6", + "image": "data/connectivity/graph_visual/medium/graph404.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,19) (2,11) (3,4) (3,6) (3,9) (4,20) (4,5) (4,15) (4,12) (5,6) (6,11) (6,20) (6,19) (6,15) (7,14) (7,18) (7,21) (7,13) (7,12) (8,10) (9,12) (10,18) (10,15) (11,20) (12,18) (13,20) (14,21) (15,18) (15,21) (15,19) (18,21)\nIs there a path between node 3 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph833-8_10", + "image": "data/connectivity/graph_visual/medium/graph833.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,22) (0,18) (0,8) (0,21) (0,5) (0,11) (0,1) (0,24) (0,19) (0,9) (0,15) (0,14) (0,10) (0,4) (0,23) (0,6) (0,17) (0,13) (1,20) (1,22) (1,18) (1,8) (1,21) (1,5) (1,11) (1,24) (1,19) (1,9) (1,15) (1,14) (1,10) (1,4) (1,23) (1,6) (1,17) (1,13) (2,3) (2,7) (2,12) (2,16) (3,7) (3,12) (3,16) (4,20) (4,22) (4,18) (4,8) (4,21) (4,5) (4,11) (4,24) (4,19) (4,9) (4,15) (4,14) (4,10) (4,23) (4,6) (4,17) (4,13) (5,20) (5,22) (5,18) (5,8) (5,21) (5,11) (5,24) (5,19) (5,9) (5,15) (5,14) (5,10) (5,23) (5,6) (5,17) (5,13) (6,20) (6,22) (6,18) (6,8) (6,21) (6,11) (6,24) (6,19) (6,9) (6,15) (6,14) (6,10) (6,23) (6,17) (6,13) (7,12) (7,16) (8,20) (8,22) (8,18) (8,21) (8,11) (8,24) (8,19) (8,9) (8,15) (8,14) (8,10) (8,23) (8,17) (8,13) (9,20) (9,22) (9,18) (9,21) (9,11) (9,24) (9,19) (9,15) (9,14) (9,10) (9,23) (9,17) (9,13) (10,20) (10,22) (10,18) (10,21) (10,11) (10,24) (10,19) (10,15) (10,14) (10,23) (10,17) (10,13) (11,20) (11,22) (11,18) (11,21) (11,24) (11,19) (11,15) (11,14) (11,23) (11,17) (11,13) (12,16) (13,20) (13,22) (13,18) (13,21) (13,24) (13,19) (13,15) (13,14) (13,23) (13,17) (14,20) (14,22) (14,18) (14,21) (14,24) (14,19) (14,15) (14,23) (14,17) (15,20) (15,22) (15,18) (15,21) (15,24) (15,19) (15,23) (15,17) (17,20) (17,22) (17,18) (17,21) (17,24) (17,19) (17,23) (18,20) (18,22) (18,21) (18,24) (18,19) (18,23) (19,20) (19,22) (19,21) (19,24) (19,23) (20,22) (20,21) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph698-22_3", + "image": "data/connectivity/graph_visual/medium/graph698.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,2) (1,22) (1,7) (1,20) (1,13) (1,10) (1,16) (2,11) (3,6) (3,21) (3,18) (3,4) (3,12) (3,9) (3,5) (3,8) (3,19) (3,15) (3,23) (3,17) (3,14) (4,6) (4,21) (4,18) (4,12) (4,9) (4,5) (4,8) (4,19) (4,15) (4,23) (4,17) (4,14) (5,6) (5,21) (5,18) (5,12) (5,9) (5,8) (5,19) (5,15) (5,23) (5,17) (5,14) (6,21) (6,18) (6,12) (6,9) (6,8) (6,19) (6,15) (6,23) (6,17) (6,14) (7,22) (7,20) (7,13) (7,10) (7,16) (8,21) (8,18) (8,12) (8,9) (8,19) (8,15) (8,23) (8,17) (8,14) (9,21) (9,18) (9,12) (9,19) (9,15) (9,23) (9,17) (9,14) (10,22) (10,20) (10,13) (10,16) (12,21) (12,18) (12,19) (12,15) (12,23) (12,17) (12,14) (13,22) (13,20) (13,16) (14,21) (14,18) (14,19) (14,15) (14,23) (14,17) (15,21) (15,18) (15,19) (15,23) (15,17) (16,22) (16,20) (17,21) (17,18) (17,19) (17,23) (18,21) (18,19) (18,23) (19,21) (19,23) (20,22) (21,23)\nIs there a path between node 22 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph373-3_20", + "image": "data/connectivity/graph_visual/medium/graph373.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,6) (0,20) (0,17) (0,8) (0,7) (0,5) (0,11) (1,14) (2,3) (2,10) (2,16) (2,20) (2,9) (2,17) (2,8) (2,4) (2,13) (2,7) (2,5) (2,11) (3,10) (3,6) (3,16) (3,20) (3,9) (3,8) (3,4) (3,13) (3,7) (3,5) (4,10) (4,6) (4,16) (4,9) (4,17) (4,13) (4,7) (5,10) (5,6) (5,20) (5,9) (5,17) (5,7) (5,11) (6,10) (6,20) (6,9) (6,17) (6,13) (6,7) (7,16) (7,20) (7,17) (7,8) (7,13) (7,11) (8,10) (8,16) (8,20) (8,17) (8,13) (8,11) (9,10) (9,16) (9,20) (9,17) (9,13) (9,11) (10,16) (10,17) (10,11) (11,16) (11,20) (11,17) (11,13) (12,19) (13,16) (13,20) (13,17) (15,19) (16,20) (16,17) (17,20) (18,19)\nIs there a path between node 3 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph622-21_13", + "image": "data/connectivity/graph_visual/medium/graph622.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,7) (0,9) (0,23) (0,22) (0,15) (0,6) (0,4) (0,17) (0,10) (0,1) (0,3) (0,2) (1,21) (1,7) (1,9) (1,23) (1,22) (1,15) (1,6) (1,4) (1,17) (1,10) (1,3) (1,2) (2,21) (2,7) (2,9) (2,23) (2,22) (2,15) (2,6) (2,4) (2,17) (2,10) (2,3) (3,21) (3,7) (3,9) (3,23) (3,22) (3,15) (3,6) (3,4) (3,17) (3,10) (4,21) (4,7) (4,9) (4,23) (4,22) (4,15) (4,6) (4,17) (4,10) (5,18) (5,19) (5,14) (5,12) (5,20) (5,13) (5,16) (5,8) (5,11) (6,21) (6,7) (6,9) (6,23) (6,22) (6,15) (6,17) (6,10) (7,21) (7,9) (7,23) (7,22) (7,15) (7,17) (7,10) (8,18) (8,19) (8,14) (8,12) (8,20) (8,13) (8,16) (8,11) (9,21) (9,23) (9,22) (9,15) (9,17) (9,10) (10,21) (10,23) (10,22) (10,15) (10,17) (11,18) (11,19) (11,14) (11,12) (11,20) (11,13) (11,16) (12,18) (12,19) (12,14) (12,20) (12,13) (12,16) (13,18) (13,19) (13,14) (13,20) (13,16) (14,18) (14,19) (14,20) (14,16) (15,21) (15,23) (15,22) (15,17) (16,18) (16,19) (16,20) (17,21) (17,23) (17,22) (18,19) (18,20) (19,20) (21,23) (21,22) (22,23)\nIs there a path between node 21 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph64-8_10", + "image": "data/connectivity/graph_visual/medium/graph64.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,8) (0,5) (0,2) (0,3) (0,10) (0,6) (0,1) (0,4) (0,9) (0,7) (0,12) (1,8) (1,5) (1,2) (1,3) (1,10) (1,6) (1,4) (1,9) (1,7) (1,12) (2,8) (2,5) (2,3) (2,10) (2,6) (2,4) (2,9) (2,7) (2,12) (3,8) (3,5) (3,10) (3,6) (3,4) (3,9) (3,7) (3,12) (4,8) (4,5) (4,10) (4,6) (4,9) (4,7) (4,12) (5,8) (5,10) (5,6) (5,9) (5,7) (5,12) (6,8) (6,10) (6,9) (6,7) (6,12) (7,8) (7,10) (7,9) (7,12) (8,10) (8,9) (8,12) (9,10) (9,12) (10,12) (11,13)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph251-5_13", + "image": "data/connectivity/graph_visual/medium/graph251.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,3) (0,1) (0,15) (0,9) (0,2) (0,6) (0,14) (0,8) (0,11) (0,10) (0,7) (1,13) (1,3) (1,15) (1,9) (1,2) (1,6) (1,14) (1,8) (1,11) (1,10) (1,7) (2,13) (2,3) (2,15) (2,9) (2,6) (2,14) (2,8) (2,11) (2,10) (2,7) (3,13) (3,15) (3,9) (3,6) (3,14) (3,8) (3,11) (3,10) (3,7) (4,12) (5,16) (5,18) (5,17) (6,13) (6,15) (6,9) (6,14) (6,8) (6,11) (6,10) (6,7) (7,13) (7,15) (7,9) (7,14) (7,8) (7,11) (7,10) (8,13) (8,15) (8,9) (8,14) (8,11) (8,10) (9,13) (9,15) (9,14) (9,11) (9,10) (10,13) (10,15) (10,14) (10,11) (11,13) (11,15) (11,14) (13,15) (13,14) (14,15) (16,18) (16,17) (17,18)\nIs there a path between node 5 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph220-8_9", + "image": "data/connectivity/graph_visual/medium/graph220.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,5) (0,16) (0,3) (1,16) (1,2) (1,4) (1,3) (2,8) (4,5) (4,16) (5,16) (6,15) (7,14) (7,9) (7,12) (8,16) (9,15) (10,15) (12,13) (13,17) (14,15) (16,18)\nIs there a path between node 8 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph509-15_11", + "image": "data/connectivity/graph_visual/medium/graph509.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,15) (0,10) (0,1) (0,7) (0,13) (0,3) (0,2) (0,11) (0,12) (1,7) (1,22) (1,12) (2,6) (2,10) (2,18) (2,16) (2,5) (2,7) (2,13) (2,3) (2,11) (3,10) (3,16) (3,5) (4,8) (4,21) (5,18) (5,7) (5,11) (5,12) (6,10) (6,16) (6,17) (6,7) (6,20) (7,20) (7,13) (7,12) (8,21) (9,14) (10,16) (10,11) (11,15) (11,16) (11,17) (12,15) (12,20) (13,17) (13,22) (15,18) (15,16) (15,17) (17,18) (18,20) (19,21) (20,22)\nIs there a path between node 15 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph818-19_23", + "image": "data/connectivity/graph_visual/medium/graph818.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,14) (0,7) (0,8) (0,3) (0,6) (1,14) (1,7) (1,9) (1,8) (1,6) (1,17) (2,13) (3,24) (3,14) (3,8) (3,6) (3,17) (4,11) (4,18) (4,12) (4,20) (4,5) (4,10) (4,19) (4,21) (4,23) (4,22) (5,16) (5,11) (5,18) (5,12) (5,20) (5,10) (5,15) (5,19) (5,21) (5,23) (5,22) (6,24) (6,14) (6,7) (6,8) (6,17) (7,14) (7,8) (7,17) (8,24) (8,14) (8,9) (9,14) (10,16) (10,11) (10,18) (10,12) (10,15) (10,19) (10,21) (10,23) (10,22) (11,16) (11,18) (11,20) (11,21) (11,23) (11,22) (12,16) (12,18) (12,20) (12,15) (12,19) (12,21) (12,23) (12,22) (14,17) (15,16) (15,18) (15,20) (15,19) (15,23) (15,22) (16,20) (16,19) (18,19) (18,21) (18,23) (18,22) (19,20) (19,21) (19,23) (20,23) (20,22) (21,22) (22,23)\nIs there a path between node 19 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph844-18_12", + "image": "data/connectivity/graph_visual/medium/graph844.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,8) (0,10) (0,14) (0,24) (0,2) (0,3) (0,6) (0,7) (0,1) (0,11) (0,16) (0,9) (0,18) (0,23) (0,4) (0,22) (1,8) (1,10) (1,14) (1,24) (1,2) (1,3) (1,6) (1,7) (1,11) (1,16) (1,9) (1,18) (1,23) (1,4) (1,22) (2,8) (2,10) (2,14) (2,24) (2,3) (2,6) (2,7) (2,11) (2,16) (2,9) (2,18) (2,23) (2,4) (2,22) (3,8) (3,10) (3,14) (3,24) (3,6) (3,7) (3,11) (3,16) (3,9) (3,18) (3,23) (3,4) (3,22) (4,8) (4,10) (4,14) (4,24) (4,6) (4,7) (4,11) (4,16) (4,9) (4,18) (4,23) (4,22) (5,15) (5,21) (5,20) (5,17) (6,8) (6,10) (6,14) (6,24) (6,7) (6,11) (6,16) (6,9) (6,18) (6,23) (6,22) (7,8) (7,10) (7,14) (7,24) (7,11) (7,16) (7,9) (7,18) (7,23) (7,22) (8,10) (8,14) (8,24) (8,11) (8,16) (8,9) (8,18) (8,23) (8,22) (9,10) (9,14) (9,24) (9,11) (9,16) (9,18) (9,23) (9,22) (10,14) (10,24) (10,11) (10,16) (10,18) (10,23) (10,22) (11,14) (11,24) (11,16) (11,18) (11,23) (11,22) (12,19) (12,13) (13,19) (14,24) (14,16) (14,18) (14,23) (14,22) (15,21) (15,20) (15,17) (16,24) (16,18) (16,23) (16,22) (17,21) (17,20) (18,24) (18,23) (18,22) (20,21) (22,24) (22,23) (23,24)\nIs there a path between node 18 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph107-7_10", + "image": "data/connectivity/graph_visual/medium/graph107.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (0,7) (0,14) (0,5) (0,13) (0,10) (1,7) (1,14) (1,5) (1,13) (1,10) (2,6) (2,12) (2,4) (2,8) (2,15) (2,3) (2,9) (2,11) (3,6) (3,12) (3,4) (3,8) (3,15) (3,9) (3,11) (4,6) (4,12) (4,8) (4,15) (4,9) (4,11) (5,7) (5,14) (5,13) (5,10) (6,12) (6,8) (6,15) (6,9) (6,11) (7,14) (7,13) (7,10) (8,12) (8,15) (8,9) (8,11) (9,12) (9,15) (9,11) (10,14) (10,13) (11,12) (11,15) (12,15) (13,14)\nIs there a path between node 7 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph268-6_12", + "image": "data/connectivity/graph_visual/medium/graph268.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,6) (0,16) (0,9) (0,3) (0,4) (0,8) (0,17) (1,6) (1,12) (1,13) (1,18) (1,2) (1,4) (1,8) (1,17) (2,6) (2,12) (2,15) (2,9) (2,13) (2,18) (2,4) (2,8) (2,17) (3,6) (3,16) (3,12) (3,9) (3,13) (3,18) (3,8) (3,17) (3,5) (4,6) (4,16) (4,12) (4,9) (4,18) (4,17) (4,5) (5,6) (5,12) (5,15) (5,9) (5,17) (6,12) (6,15) (6,9) (6,13) (6,18) (6,8) (7,10) (7,11) (7,19) (8,16) (8,15) (8,9) (8,18) (9,16) (9,12) (9,15) (9,13) (9,18) (9,17) (10,19) (11,14) (11,19) (12,16) (12,15) (12,13) (12,17) (13,18) (14,19) (15,17) (16,17) (17,18)\nIs there a path between node 6 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph811-19_13", + "image": "data/connectivity/graph_visual/medium/graph811.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,16) (0,23) (0,6) (0,5) (0,4) (0,11) (0,20) (0,7) (0,21) (0,8) (2,3) (2,12) (2,16) (2,23) (2,5) (2,4) (2,11) (2,20) (2,21) (2,8) (3,19) (3,12) (3,16) (3,23) (3,17) (3,4) (3,11) (3,7) (3,21) (4,19) (4,12) (4,16) (4,6) (4,17) (4,11) (4,20) (4,7) (5,12) (5,16) (5,23) (5,17) (5,11) (5,20) (5,7) (5,21) (6,12) (6,16) (6,11) (6,20) (7,19) (7,12) (7,16) (7,23) (7,17) (7,11) (7,20) (7,21) (7,8) (8,19) (8,10) (8,12) (8,16) (8,23) (8,17) (8,20) (9,22) (9,24) (9,15) (9,13) (10,23) (10,17) (10,11) (10,20) (10,21) (11,19) (11,16) (11,23) (11,20) (11,21) (12,19) (12,23) (12,17) (12,21) (13,14) (13,24) (13,15) (15,22) (15,24) (16,19) (16,23) (16,17) (16,20) (16,21) (17,19) (17,23) (17,20) (19,23) (19,21) (20,23) (20,21) (22,24)\nIs there a path between node 19 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph612-23_20", + "image": "data/connectivity/graph_visual/medium/graph612.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,6) (0,12) (0,20) (0,15) (0,9) (0,13) (0,2) (0,14) (0,11) (0,3) (0,23) (0,5) (1,21) (1,7) (1,8) (1,22) (1,4) (1,18) (1,17) (1,16) (2,10) (2,19) (2,6) (2,12) (2,20) (2,15) (2,9) (2,13) (2,14) (2,11) (2,3) (2,23) (2,5) (3,10) (3,19) (3,6) (3,12) (3,20) (3,15) (3,9) (3,13) (3,14) (3,11) (3,23) (3,5) (4,21) (4,7) (4,8) (4,22) (4,18) (4,17) (4,16) (5,10) (5,19) (5,6) (5,12) (5,20) (5,15) (5,9) (5,13) (5,14) (5,11) (5,23) (6,10) (6,19) (6,12) (6,20) (6,15) (6,9) (6,13) (6,14) (6,11) (6,23) (7,21) (7,8) (7,22) (7,18) (7,17) (7,16) (8,21) (8,22) (8,18) (8,17) (8,16) (9,10) (9,19) (9,12) (9,20) (9,15) (9,13) (9,14) (9,11) (9,23) (10,19) (10,12) (10,20) (10,15) (10,13) (10,14) (10,11) (10,23) (11,19) (11,12) (11,20) (11,15) (11,13) (11,14) (11,23) (12,19) (12,20) (12,15) (12,13) (12,14) (12,23) (13,19) (13,20) (13,15) (13,14) (13,23) (14,19) (14,20) (14,15) (14,23) (15,19) (15,20) (15,23) (16,21) (16,22) (16,18) (16,17) (17,21) (17,22) (17,18) (18,21) (18,22) (19,20) (19,23) (20,23) (21,22)\nIs there a path between node 23 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph771-6_9", + "image": "data/connectivity/graph_visual/medium/graph771.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,21) (0,18) (0,10) (0,11) (0,4) (0,24) (0,1) (0,5) (0,12) (0,6) (0,23) (1,7) (1,21) (1,18) (1,10) (1,11) (1,4) (1,24) (1,5) (1,12) (1,6) (1,23) (2,22) (2,17) (2,19) (2,14) (2,3) (2,13) (2,15) (2,9) (2,8) (2,20) (2,16) (3,22) (3,17) (3,19) (3,14) (3,13) (3,15) (3,9) (3,8) (3,20) (3,16) (4,7) (4,21) (4,18) (4,10) (4,11) (4,24) (4,5) (4,12) (4,6) (4,23) (5,7) (5,21) (5,18) (5,10) (5,11) (5,24) (5,12) (5,6) (5,23) (6,7) (6,21) (6,18) (6,10) (6,11) (6,24) (6,12) (6,23) (7,21) (7,18) (7,10) (7,11) (7,24) (7,12) (7,23) (8,22) (8,17) (8,19) (8,14) (8,13) (8,15) (8,9) (8,20) (8,16) (9,22) (9,17) (9,19) (9,14) (9,13) (9,15) (9,20) (9,16) (10,21) (10,18) (10,11) (10,24) (10,12) (10,23) (11,21) (11,18) (11,24) (11,12) (11,23) (12,21) (12,18) (12,24) (12,23) (13,22) (13,17) (13,19) (13,14) (13,15) (13,20) (13,16) (14,22) (14,17) (14,19) (14,15) (14,20) (14,16) (15,22) (15,17) (15,19) (15,20) (15,16) (16,22) (16,17) (16,19) (16,20) (17,22) (17,19) (17,20) (18,21) (18,24) (18,23) (19,22) (19,20) (20,22) (21,24) (21,23) (23,24)\nIs there a path between node 6 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph661-23_3", + "image": "data/connectivity/graph_visual/medium/graph661.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,4) (1,8) (1,17) (1,20) (1,13) (1,18) (1,19) (1,2) (1,23) (1,21) (1,16) (1,7) (2,10) (2,8) (2,6) (2,15) (2,9) (2,17) (2,20) (2,13) (2,18) (2,19) (2,12) (2,21) (2,16) (3,10) (3,8) (3,6) (3,15) (3,9) (3,20) (3,13) (3,18) (3,5) (3,19) (3,12) (3,16) (3,14) (4,11) (5,8) (5,6) (5,15) (5,9) (5,17) (5,20) (5,13) (5,18) (5,19) (5,21) (5,7) (6,10) (6,8) (6,15) (6,17) (6,20) (6,13) (6,18) (6,19) (6,12) (6,21) (6,16) (6,22) (7,15) (7,9) (7,13) (7,18) (7,12) (7,23) (7,14) (7,22) (8,10) (8,20) (8,13) (8,12) (8,21) (8,16) (8,14) (8,22) (9,10) (9,15) (9,20) (9,13) (9,12) (9,16) (9,14) (9,22) (10,15) (10,17) (10,13) (10,18) (10,12) (10,16) (10,14) (10,22) (12,15) (12,17) (12,13) (12,18) (12,23) (12,21) (12,16) (12,14) (12,22) (13,17) (13,20) (13,19) (13,21) (13,14) (13,22) (14,15) (14,17) (14,18) (14,16) (14,22) (15,17) (15,19) (15,16) (15,22) (16,17) (16,20) (16,19) (16,21) (17,19) (17,23) (17,21) (17,22) (18,23) (18,21) (18,22) (19,20) (19,23) (19,21) (19,22) (20,21) (20,22) (21,23) (22,23)\nIs there a path between node 23 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph437-3_7", + "image": "data/connectivity/graph_visual/medium/graph437.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,12) (0,5) (1,21) (1,6) (2,7) (2,3) (4,8) (5,8) (5,12) (6,16) (6,21) (6,20) (6,13) (7,17) (7,11) (9,11) (9,10) (10,17) (13,18) (13,15) (15,19) (15,21) (16,19) (16,20) (20,21)\nIs there a path between node 3 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph722-19_21", + "image": "data/connectivity/graph_visual/medium/graph722.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,1) (0,8) (0,17) (0,3) (0,9) (0,2) (0,12) (1,8) (1,17) (1,3) (1,9) (1,2) (1,12) (2,8) (2,17) (2,3) (2,9) (2,12) (3,8) (3,17) (3,9) (3,12) (4,7) (4,19) (4,22) (4,14) (4,16) (4,24) (4,6) (4,5) (5,7) (5,19) (5,22) (5,14) (5,16) (5,24) (5,6) (6,7) (6,19) (6,22) (6,14) (6,16) (6,24) (7,19) (7,22) (7,14) (7,16) (7,24) (8,17) (8,9) (8,12) (9,17) (9,12) (10,20) (10,13) (10,15) (10,11) (10,23) (10,21) (10,18) (11,20) (11,13) (11,15) (11,23) (11,21) (11,18) (12,17) (13,20) (13,15) (13,23) (13,21) (13,18) (14,19) (14,22) (14,16) (14,24) (15,20) (15,23) (15,21) (15,18) (16,19) (16,22) (16,24) (18,20) (18,23) (18,21) (19,22) (19,24) (20,23) (20,21) (21,23) (22,24)\nIs there a path between node 19 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph677-8_4", + "image": "data/connectivity/graph_visual/medium/graph677.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,4) (0,9) (0,19) (0,14) (0,17) (0,7) (0,6) (0,5) (0,16) (0,13) (0,22) (0,12) (0,15) (0,23) (1,3) (1,2) (1,21) (1,8) (1,20) (2,3) (2,21) (2,8) (2,20) (3,21) (3,8) (3,20) (4,11) (4,9) (4,19) (4,14) (4,17) (4,7) (4,6) (4,5) (4,16) (4,13) (4,22) (4,12) (4,15) (4,23) (5,11) (5,9) (5,19) (5,14) (5,17) (5,7) (5,6) (5,16) (5,13) (5,22) (5,12) (5,15) (5,23) (6,11) (6,9) (6,19) (6,14) (6,17) (6,7) (6,16) (6,13) (6,22) (6,12) (6,15) (6,23) (7,11) (7,9) (7,19) (7,14) (7,17) (7,16) (7,13) (7,22) (7,12) (7,15) (7,23) (8,21) (8,20) (9,11) (9,19) (9,14) (9,17) (9,16) (9,13) (9,22) (9,12) (9,15) (9,23) (11,19) (11,14) (11,17) (11,16) (11,13) (11,22) (11,12) (11,15) (11,23) (12,19) (12,14) (12,17) (12,16) (12,13) (12,22) (12,15) (12,23) (13,19) (13,14) (13,17) (13,16) (13,22) (13,15) (13,23) (14,19) (14,17) (14,16) (14,22) (14,15) (14,23) (15,19) (15,17) (15,16) (15,22) (15,23) (16,19) (16,17) (16,22) (16,23) (17,19) (17,22) (17,23) (19,22) (19,23) (20,21) (22,23)\nIs there a path between node 8 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph33-1_12", + "image": "data/connectivity/graph_visual/medium/graph33.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,3) (0,8) (1,5) (1,10) (1,8) (2,6) (2,7) (3,9) (3,10) (4,11) (4,8) (6,7) (8,9) (8,10) (11,12)\nIs there a path between node 1 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph739-13_6", + "image": "data/connectivity/graph_visual/medium/graph739.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,19) (0,11) (0,13) (0,17) (0,20) (1,4) (2,23) (2,12) (2,22) (2,21) (2,14) (3,19) (3,21) (4,9) (4,24) (4,17) (4,14) (5,6) (5,22) (5,24) (5,11) (5,20) (6,23) (6,22) (6,17) (8,14) (11,23) (11,24) (11,14) (12,22) (13,19) (13,24) (14,19) (14,21) (14,24) (14,20) (17,24) (20,23) (20,21) (21,24) (22,24) (23,24)\nIs there a path between node 13 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph16-10_4", + "image": "data/connectivity/graph_visual/medium/graph16.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,5) (0,11) (0,1) (0,3) (0,10) (0,4) (1,11) (1,3) (1,10) (1,4) (2,7) (3,11) (3,4) (4,5) (4,11) (5,11) (6,9) (6,8) (7,9) (7,8) (8,9) (10,11)\nIs there a path between node 10 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph278-8_1", + "image": "data/connectivity/graph_visual/medium/graph278.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (0,2) (0,3) (0,10) (0,6) (0,4) (0,19) (0,17) (0,13) (0,1) (0,16) (0,18) (0,7) (0,9) (0,15) (1,8) (1,2) (1,3) (1,10) (1,6) (1,4) (1,19) (1,17) (1,13) (1,16) (1,18) (1,7) (1,9) (1,15) (2,8) (2,3) (2,10) (2,6) (2,4) (2,19) (2,17) (2,13) (2,16) (2,18) (2,7) (2,9) (2,15) (3,8) (3,10) (3,6) (3,4) (3,19) (3,17) (3,13) (3,16) (3,18) (3,7) (3,9) (3,15) (4,8) (4,10) (4,6) (4,19) (4,17) (4,13) (4,16) (4,18) (4,7) (4,9) (4,15) (5,11) (5,12) (6,8) (6,10) (6,19) (6,17) (6,13) (6,16) (6,18) (6,7) (6,9) (6,15) (7,8) (7,10) (7,19) (7,17) (7,13) (7,16) (7,18) (7,9) (7,15) (8,10) (8,19) (8,17) (8,13) (8,16) (8,18) (8,9) (8,15) (9,10) (9,19) (9,17) (9,13) (9,16) (9,18) (9,15) (10,19) (10,17) (10,13) (10,16) (10,18) (10,15) (11,12) (13,19) (13,17) (13,16) (13,18) (13,15) (15,19) (15,17) (15,16) (15,18) (16,19) (16,17) (16,18) (17,19) (17,18) (18,19)\nIs there a path between node 8 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph30-1_6", + "image": "data/connectivity/graph_visual/medium/graph30.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,5) (0,6) (0,4) (0,9) (0,11) (0,1) (0,7) (1,5) (1,6) (1,4) (1,9) (1,11) (1,7) (2,10) (2,3) (2,8) (3,10) (3,8) (4,5) (4,6) (4,9) (4,11) (4,7) (5,6) (5,9) (5,11) (5,7) (6,9) (6,11) (6,7) (7,9) (7,11) (8,10) (9,11)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph393-8_14", + "image": "data/connectivity/graph_visual/medium/graph393.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,14) (0,11) (0,17) (0,5) (0,4) (1,20) (1,8) (1,13) (1,2) (1,16) (1,19) (1,7) (1,6) (1,12) (1,9) (2,20) (2,8) (2,13) (2,16) (2,19) (2,7) (2,6) (2,12) (2,9) (3,18) (3,10) (3,15) (4,14) (4,11) (4,17) (4,5) (5,14) (5,11) (5,17) (6,20) (6,8) (6,13) (6,16) (6,19) (6,7) (6,12) (6,9) (7,20) (7,8) (7,13) (7,16) (7,19) (7,12) (7,9) (8,20) (8,13) (8,16) (8,19) (8,12) (8,9) (9,20) (9,13) (9,16) (9,19) (9,12) (10,18) (10,15) (11,14) (11,17) (12,20) (12,13) (12,16) (12,19) (13,20) (13,16) (13,19) (14,17) (15,18) (16,20) (16,19) (19,20)\nIs there a path between node 8 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph358-18_11", + "image": "data/connectivity/graph_visual/medium/graph358.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,1) (0,19) (0,18) (0,16) (1,6) (1,15) (2,18) (2,20) (2,11) (3,12) (4,6) (4,16) (4,15) (4,11) (6,9) (6,18) (6,20) (6,11) (9,14) (9,19) (9,18) (9,20) (9,16) (9,11) (10,14) (10,20) (10,16) (11,14) (11,20) (14,19) (14,15) (15,18) (15,16) (16,18) (18,20)\nIs there a path between node 18 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph368-16_18", + "image": "data/connectivity/graph_visual/medium/graph368.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,11) (0,9) (0,14) (0,7) (0,8) (0,15) (0,16) (0,1) (0,5) (1,9) (1,2) (1,14) (1,7) (1,16) (1,10) (1,17) (1,3) (1,6) (2,11) (2,14) (2,7) (2,8) (2,15) (2,16) (2,3) (2,5) (2,6) (3,11) (3,7) (3,8) (3,16) (3,10) (3,17) (3,6) (4,12) (4,19) (5,14) (5,8) (5,15) (5,16) (5,10) (5,17) (6,9) (6,14) (6,7) (6,8) (6,15) (6,10) (6,17) (7,11) (7,9) (7,14) (7,8) (7,16) (7,10) (8,11) (8,14) (8,15) (8,16) (8,17) (9,11) (9,14) (9,15) (9,16) (9,10) (10,11) (10,14) (10,15) (11,15) (11,16) (11,17) (12,18) (13,18) (14,15) (14,17) (15,16) (15,17) (18,19)\nIs there a path between node 16 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph793-8_24", + "image": "data/connectivity/graph_visual/medium/graph793.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,3) (1,17) (2,12) (2,4) (2,20) (2,9) (2,11) (2,5) (3,13) (3,20) (3,21) (3,10) (4,13) (4,10) (5,21) (6,12) (6,19) (6,9) (6,11) (7,15) (8,17) (9,20) (9,21) (10,13) (10,21) (10,19) (11,13) (11,20) (12,21) (13,21) (14,17) (17,24) (17,22) (20,21)\nIs there a path between node 8 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph492-19_11", + "image": "data/connectivity/graph_visual/medium/graph492.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,6) (0,17) (0,18) (0,8) (0,10) (0,12) (0,14) (0,16) (0,13) (0,9) (0,19) (0,15) (0,4) (0,20) (0,7) (0,5) (0,21) (0,3) (0,2) (1,6) (1,17) (1,18) (1,8) (1,10) (1,12) (1,14) (1,16) (1,13) (1,9) (1,19) (1,15) (1,4) (1,20) (1,7) (1,5) (1,21) (1,3) (1,2) (2,6) (2,17) (2,18) (2,8) (2,10) (2,12) (2,14) (2,16) (2,13) (2,9) (2,19) (2,15) (2,4) (2,20) (2,7) (2,5) (2,21) (2,3) (3,6) (3,17) (3,18) (3,8) (3,10) (3,12) (3,14) (3,16) (3,13) (3,9) (3,19) (3,15) (3,4) (3,20) (3,7) (3,5) (3,21) (4,6) (4,17) (4,18) (4,8) (4,10) (4,12) (4,14) (4,16) (4,13) (4,9) (4,19) (4,15) (4,20) (4,7) (4,5) (4,21) (5,6) (5,17) (5,18) (5,8) (5,10) (5,12) (5,14) (5,16) (5,13) (5,9) (5,19) (5,15) (5,20) (5,7) (5,21) (6,17) (6,18) (6,8) (6,10) (6,12) (6,14) (6,16) (6,13) (6,9) (6,19) (6,15) (6,20) (6,7) (6,21) (7,17) (7,18) (7,8) (7,10) (7,12) (7,14) (7,16) (7,13) (7,9) (7,19) (7,15) (7,20) (7,21) (8,17) (8,18) (8,10) (8,12) (8,14) (8,16) (8,13) (8,9) (8,19) (8,15) (8,20) (8,21) (9,17) (9,18) (9,10) (9,12) (9,14) (9,16) (9,13) (9,19) (9,15) (9,20) (9,21) (10,17) (10,18) (10,12) (10,14) (10,16) (10,13) (10,19) (10,15) (10,20) (10,21) (11,22) (12,17) (12,18) (12,14) (12,16) (12,13) (12,19) (12,15) (12,20) (12,21) (13,17) (13,18) (13,14) (13,16) (13,19) (13,15) (13,20) (13,21) (14,17) (14,18) (14,16) (14,19) (14,15) (14,20) (14,21) (15,17) (15,18) (15,16) (15,19) (15,20) (15,21) (16,17) (16,18) (16,19) (16,20) (16,21) (17,18) (17,19) (17,20) (17,21) (18,19) (18,20) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 19 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph75-3_0", + "image": "data/connectivity/graph_visual/medium/graph75.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,13) (1,6) (1,7) (1,4) (2,6) (2,7) (2,9) (2,10) (2,14) (3,6) (3,9) (3,4) (4,8) (4,9) (4,11) (5,6) (6,8) (6,7) (6,9) (6,10) (7,8) (7,14) (8,13) (9,13) (9,10) (10,13) (10,11)\nIs there a path between node 3 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph465-20_5", + "image": "data/connectivity/graph_visual/medium/graph465.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,14) (0,3) (0,12) (1,21) (1,18) (1,2) (1,17) (1,9) (1,20) (2,21) (2,18) (2,17) (2,9) (2,20) (3,14) (3,12) (4,16) (4,6) (4,5) (4,10) (4,19) (4,7) (4,13) (4,15) (4,11) (4,8) (5,16) (5,6) (5,10) (5,19) (5,7) (5,13) (5,15) (5,11) (5,8) (6,16) (6,10) (6,19) (6,7) (6,13) (6,15) (6,11) (6,8) (7,16) (7,10) (7,19) (7,13) (7,15) (7,11) (7,8) (8,16) (8,10) (8,19) (8,13) (8,15) (8,11) (9,21) (9,18) (9,17) (9,20) (10,16) (10,19) (10,13) (10,15) (10,11) (11,16) (11,19) (11,13) (11,15) (12,14) (13,16) (13,19) (13,15) (15,16) (15,19) (16,19) (17,21) (17,18) (17,20) (18,21) (18,20) (20,21)\nIs there a path between node 20 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph820-0_19", + "image": "data/connectivity/graph_visual/medium/graph820.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,6) (1,2) (1,4) (1,12) (1,19) (1,3) (1,18) (1,21) (1,16) (1,22) (1,23) (1,24) (1,20) (1,8) (1,13) (1,9) (2,6) (2,4) (2,14) (2,17) (2,15) (2,19) (2,3) (2,18) (2,21) (2,16) (2,22) (2,23) (2,24) (2,20) (2,11) (2,8) (2,13) (2,9) (3,7) (3,6) (3,4) (3,14) (3,15) (3,12) (3,18) (3,16) (3,22) (3,23) (3,24) (3,20) (3,11) (3,8) (4,6) (4,14) (4,17) (4,15) (4,12) (4,19) (4,21) (4,22) (4,23) (4,11) (4,13) (4,9) (5,10) (6,14) (6,15) (6,19) (6,18) (6,21) (6,22) (6,23) (6,20) (6,11) (6,8) (6,13) (6,9) (7,14) (7,18) (7,16) (7,22) (7,23) (7,20) (7,11) (7,9) (8,14) (8,15) (8,19) (8,21) (8,16) (8,22) (8,23) (8,20) (8,11) (8,13) (8,9) (9,14) (9,15) (9,12) (9,19) (9,18) (9,21) (9,16) (9,22) (9,23) (9,20) (9,13) (11,14) (11,17) (11,15) (11,12) (11,21) (11,22) (11,24) (11,20) (12,17) (12,15) (12,19) (12,18) (12,21) (12,16) (12,23) (12,13) (13,17) (13,15) (13,19) (13,18) (13,21) (13,22) (13,23) (13,24) (14,17) (14,15) (14,19) (14,18) (14,16) (14,20) (15,17) (15,19) (15,16) (15,22) (15,24) (15,20) (16,17) (16,19) (16,18) (16,22) (16,23) (16,24) (16,20) (17,19) (17,21) (17,22) (18,19) (18,21) (18,22) (18,23) (18,24) (19,23) (19,20) (20,21) (20,24) (21,22) (21,24) (22,24)\nIs there a path between node 0 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph541-7_3", + "image": "data/connectivity/graph_visual/medium/graph541.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,10) (0,11) (0,12) (0,6) (0,14) (0,21) (1,10) (1,11) (1,12) (1,6) (1,14) (1,21) (2,4) (2,20) (2,5) (2,13) (3,15) (3,8) (3,18) (3,17) (3,22) (3,9) (3,16) (3,7) (3,19) (4,20) (4,5) (4,13) (5,20) (5,13) (6,10) (6,11) (6,12) (6,14) (6,21) (7,15) (7,8) (7,18) (7,17) (7,22) (7,9) (7,16) (7,19) (8,15) (8,18) (8,17) (8,22) (8,9) (8,16) (8,19) (9,15) (9,18) (9,17) (9,22) (9,16) (9,19) (10,11) (10,12) (10,14) (10,21) (11,12) (11,14) (11,21) (12,14) (12,21) (13,20) (14,21) (15,18) (15,17) (15,22) (15,16) (15,19) (16,18) (16,17) (16,22) (16,19) (17,18) (17,22) (17,19) (18,22) (18,19) (19,22)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph156-8_7", + "image": "data/connectivity/graph_visual/medium/graph156.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,8) (0,1) (1,12) (1,15) (2,9) (2,6) (3,10) (3,17) (3,15) (5,7) (6,10) (6,9) (6,11) (7,13) (8,17) (8,16) (10,15) (11,12) (15,17)\nIs there a path between node 8 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph279-0_16", + "image": "data/connectivity/graph_visual/medium/graph279.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,2) (0,14) (0,16) (0,7) (0,10) (1,12) (1,11) (1,13) (1,8) (1,17) (1,4) (2,19) (2,14) (2,16) (2,7) (2,10) (3,5) (3,15) (3,18) (3,6) (3,9) (4,12) (4,11) (4,13) (4,8) (4,17) (5,15) (5,18) (5,6) (5,9) (6,15) (6,18) (6,9) (7,19) (7,14) (7,16) (7,10) (8,12) (8,11) (8,13) (8,17) (9,15) (9,18) (10,19) (10,14) (10,16) (11,12) (11,13) (11,17) (12,13) (12,17) (13,17) (14,19) (14,16) (15,18) (16,19)\nIs there a path between node 0 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph101-12_13", + "image": "data/connectivity/graph_visual/medium/graph101.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,15) (0,8) (0,6) (0,10) (0,13) (0,2) (0,11) (0,4) (0,14) (0,5) (1,8) (1,10) (1,13) (1,2) (1,9) (1,4) (1,14) (1,5) (2,8) (2,6) (2,10) (2,13) (2,11) (2,7) (2,4) (2,14) (2,5) (3,12) (4,8) (4,6) (4,10) (4,13) (4,7) (5,8) (5,6) (5,10) (5,11) (5,7) (5,14) (6,8) (6,14) (7,15) (7,8) (7,10) (7,9) (7,14) (8,13) (8,11) (8,14) (9,15) (9,10) (9,11) (9,14) (10,13) (10,11) (10,14) (11,15) (11,13) (11,14) (13,15) (14,15)\nIs there a path between node 12 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph443-15_1", + "image": "data/connectivity/graph_visual/medium/graph443.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,14) (0,16) (0,2) (0,3) (0,18) (0,13) (0,17) (0,15) (0,12) (0,6) (1,10) (1,16) (1,4) (1,2) (1,3) (1,9) (1,18) (1,21) (1,13) (1,15) (1,12) (1,8) (1,6) (2,10) (2,14) (2,16) (2,3) (2,9) (2,7) (2,18) (2,13) (2,17) (2,15) (2,12) (2,8) (2,6) (3,19) (3,10) (3,16) (3,4) (3,7) (3,21) (3,13) (3,12) (3,6) (4,19) (4,10) (4,14) (4,16) (4,21) (4,13) (4,17) (4,15) (4,6) (5,11) (6,19) (6,10) (6,7) (6,18) (6,13) (6,17) (6,15) (7,19) (7,10) (7,14) (7,16) (7,9) (7,18) (7,13) (7,17) (7,15) (7,12) (8,16) (8,9) (8,18) (8,21) (8,17) (8,12) (9,19) (9,18) (9,21) (9,17) (9,15) (9,12) (10,14) (10,16) (10,18) (10,13) (10,17) (10,15) (10,12) (12,14) (12,16) (12,21) (12,13) (12,17) (12,15) (13,16) (13,18) (13,17) (13,15) (14,19) (14,16) (14,18) (14,21) (14,17) (14,15) (15,16) (15,21) (16,19) (16,21) (16,17) (17,19) (17,18) (18,19) (18,21) (19,21)\nIs there a path between node 15 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph380-14_13", + "image": "data/connectivity/graph_visual/medium/graph380.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,11) (0,16) (0,3) (0,20) (0,12) (0,5) (0,17) (0,8) (0,14) (0,18) (0,2) (0,1) (0,6) (1,11) (1,16) (1,3) (1,20) (1,12) (1,5) (1,4) (1,17) (1,14) (1,2) (1,13) (1,6) (2,11) (2,16) (2,3) (2,20) (2,5) (2,8) (2,14) (2,18) (2,13) (2,6) (2,19) (2,9) (3,11) (3,16) (3,20) (3,5) (3,4) (3,17) (3,14) (3,13) (3,6) (3,19) (3,9) (4,11) (4,16) (4,20) (4,12) (4,8) (4,18) (4,13) (4,6) (4,19) (4,9) (5,11) (5,16) (5,20) (5,12) (5,17) (5,8) (5,14) (5,6) (5,19) (5,9) (6,11) (6,16) (6,20) (6,12) (6,17) (6,14) (6,19) (6,9) (8,11) (8,16) (8,20) (8,14) (8,18) (8,19) (8,9) (9,11) (9,12) (9,18) (9,19) (11,20) (11,12) (11,17) (11,14) (11,13) (11,19) (12,16) (12,20) (12,14) (12,18) (12,13) (12,19) (13,16) (13,14) (14,20) (14,18) (14,19) (16,20) (16,18) (17,20) (17,18) (18,20) (19,20)\nIs there a path between node 14 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph759-3_24", + "image": "data/connectivity/graph_visual/medium/graph759.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,4) (0,17) (0,13) (0,21) (0,2) (0,1) (0,24) (0,10) (0,5) (0,14) (0,12) (0,19) (1,4) (1,24) (1,5) (1,18) (1,14) (1,12) (1,19) (1,15) (2,17) (2,13) (2,21) (2,8) (2,14) (2,19) (2,15) (3,11) (3,20) (3,9) (3,6) (3,22) (3,16) (4,17) (4,13) (4,21) (4,24) (4,8) (4,10) (4,5) (4,18) (4,14) (4,12) (4,19) (4,15) (5,17) (5,13) (5,21) (5,8) (5,10) (5,14) (5,12) (5,19) (5,15) (6,11) (6,20) (6,22) (6,7) (6,23) (7,11) (7,9) (7,22) (7,16) (7,23) (8,17) (8,13) (8,18) (8,14) (8,12) (8,19) (8,15) (9,11) (9,20) (9,16) (9,23) (10,13) (10,21) (10,24) (10,18) (10,15) (11,22) (11,16) (12,17) (12,21) (12,24) (12,14) (12,19) (12,15) (13,21) (13,24) (13,18) (13,14) (13,19) (13,15) (14,17) (14,21) (14,24) (14,18) (14,19) (14,15) (15,21) (15,24) (15,18) (15,19) (16,20) (16,23) (17,21) (17,19) (18,21) (18,24) (18,19) (19,21) (19,24) (20,22) (20,23) (22,23)\nIs there a path between node 3 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph771-5_6", + "image": "data/connectivity/graph_visual/medium/graph771.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,21) (0,18) (0,10) (0,11) (0,4) (0,24) (0,1) (0,5) (0,12) (0,6) (0,23) (1,7) (1,21) (1,18) (1,10) (1,11) (1,4) (1,24) (1,5) (1,12) (1,6) (1,23) (2,22) (2,17) (2,19) (2,14) (2,3) (2,13) (2,15) (2,9) (2,8) (2,20) (2,16) (3,22) (3,17) (3,19) (3,14) (3,13) (3,15) (3,9) (3,8) (3,20) (3,16) (4,7) (4,21) (4,18) (4,10) (4,11) (4,24) (4,5) (4,12) (4,6) (4,23) (5,7) (5,21) (5,18) (5,10) (5,11) (5,24) (5,12) (5,6) (5,23) (6,7) (6,21) (6,18) (6,10) (6,11) (6,24) (6,12) (6,23) (7,21) (7,18) (7,10) (7,11) (7,24) (7,12) (7,23) (8,22) (8,17) (8,19) (8,14) (8,13) (8,15) (8,9) (8,20) (8,16) (9,22) (9,17) (9,19) (9,14) (9,13) (9,15) (9,20) (9,16) (10,21) (10,18) (10,11) (10,24) (10,12) (10,23) (11,21) (11,18) (11,24) (11,12) (11,23) (12,21) (12,18) (12,24) (12,23) (13,22) (13,17) (13,19) (13,14) (13,15) (13,20) (13,16) (14,22) (14,17) (14,19) (14,15) (14,20) (14,16) (15,22) (15,17) (15,19) (15,20) (15,16) (16,22) (16,17) (16,19) (16,20) (17,22) (17,19) (17,20) (18,21) (18,24) (18,23) (19,22) (19,20) (20,22) (21,24) (21,23) (23,24)\nIs there a path between node 5 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph506-22_17", + "image": "data/connectivity/graph_visual/medium/graph506.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,12) (2,5) (2,7) (2,19) (3,17) (3,11) (3,9) (3,4) (3,7) (4,10) (4,17) (4,5) (4,11) (4,9) (4,7) (4,19) (5,21) (5,11) (5,9) (5,7) (6,20) (6,18) (7,14) (7,21) (7,11) (7,9) (7,19) (8,15) (9,10) (9,14) (9,19) (10,11) (11,14) (11,17) (11,19) (12,20) (12,18) (13,22) (14,19) (18,22)\nIs there a path between node 22 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph43-8_6", + "image": "data/connectivity/graph_visual/medium/graph43.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,11) (0,3) (0,10) (1,4) (1,9) (1,6) (2,10) (3,5) (3,10) (4,7) (4,9) (4,6) (4,12) (5,10) (6,7) (6,12) (7,9) (8,9) (8,12) (9,12) (10,11)\nIs there a path between node 8 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph58-0_3", + "image": "data/connectivity/graph_visual/medium/graph58.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (0,1) (1,3) (1,11) (1,2) (1,4) (2,9) (2,12) (3,8) (4,12) (5,11) (5,8) (5,7) (6,13) (10,12)\nIs there a path between node 0 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph431-8_11", + "image": "data/connectivity/graph_visual/medium/graph431.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,16) (0,3) (0,5) (0,19) (1,21) (2,21) (2,10) (2,19) (3,4) (3,19) (4,15) (4,10) (4,19) (5,16) (6,8) (8,13) (10,17) (11,13) (14,20) (15,17) (16,17) (17,19)\nIs there a path between node 8 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph222-12_18", + "image": "data/connectivity/graph_visual/medium/graph222.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,2) (0,3) (0,7) (0,10) (0,16) (1,18) (1,17) (1,7) (1,10) (1,16) (1,8) (2,17) (2,10) (2,8) (3,6) (3,15) (3,9) (3,4) (4,12) (4,18) (4,17) (4,9) (4,7) (4,10) (4,13) (6,9) (6,11) (6,16) (7,9) (8,9) (9,15) (9,10) (10,15) (10,18) (10,11) (12,16) (13,16) (15,17) (15,16) (16,18) (16,17) (17,18)\nIs there a path between node 12 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph297-13_1", + "image": "data/connectivity/graph_visual/medium/graph297.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,12) (0,19) (1,2) (1,13) (1,7) (1,6) (1,3) (1,9) (1,16) (1,4) (2,13) (2,7) (2,6) (2,10) (2,9) (2,16) (2,8) (2,15) (3,17) (3,6) (3,5) (3,10) (3,16) (3,4) (4,13) (4,17) (4,6) (4,5) (4,10) (4,9) (4,15) (5,13) (5,7) (5,6) (5,9) (5,16) (5,8) (6,13) (6,7) (6,9) (6,16) (6,8) (6,15) (7,13) (7,10) (7,9) (8,17) (8,10) (8,9) (8,16) (8,15) (9,17) (9,10) (9,16) (9,15) (10,13) (10,17) (10,16) (10,15) (12,19) (12,18) (13,15) (15,17) (15,16) (16,17) (18,19)\nIs there a path between node 13 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph755-19_17", + "image": "data/connectivity/graph_visual/medium/graph755.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (0,18) (0,10) (0,11) (0,2) (0,8) (0,24) (0,9) (0,1) (0,7) (1,18) (1,10) (1,4) (1,8) (1,19) (1,9) (1,7) (2,4) (2,11) (2,6) (2,8) (2,19) (2,9) (2,7) (3,14) (3,20) (3,12) (4,17) (4,18) (4,10) (4,11) (4,19) (4,24) (4,9) (5,14) (5,15) (5,12) (6,17) (6,10) (6,11) (6,8) (6,24) (6,9) (6,7) (7,18) (7,8) (7,19) (7,9) (8,17) (8,19) (9,17) (9,10) (9,11) (9,24) (10,17) (10,11) (10,19) (10,24) (11,17) (11,18) (11,19) (11,24) (12,23) (12,15) (13,16) (13,22) (14,21) (14,20) (15,23) (15,20) (16,22) (17,24) (18,19) (19,24) (20,23) (21,23)\nIs there a path between node 19 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph363-10_4", + "image": "data/connectivity/graph_visual/medium/graph363.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,9) (0,8) (0,17) (0,6) (1,14) (1,7) (2,8) (2,17) (2,3) (2,11) (2,10) (2,6) (3,9) (3,19) (3,10) (3,16) (4,18) (4,14) (5,8) (5,17) (5,10) (6,9) (6,11) (6,16) (7,20) (7,15) (8,9) (8,13) (8,19) (9,13) (10,17) (10,13) (12,16) (13,17) (14,18) (14,20) (15,20) (16,19)\nIs there a path between node 10 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph464-18_12", + "image": "data/connectivity/graph_visual/medium/graph464.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,16) (0,1) (0,9) (0,10) (0,18) (1,4) (1,16) (1,9) (1,10) (1,18) (2,3) (2,7) (2,11) (2,20) (2,8) (2,19) (2,13) (2,12) (2,5) (2,17) (2,6) (2,15) (2,21) (2,14) (3,7) (3,11) (3,20) (3,8) (3,19) (3,13) (3,12) (3,5) (3,17) (3,6) (3,15) (3,21) (3,14) (4,16) (4,9) (4,10) (4,18) (5,7) (5,11) (5,20) (5,8) (5,19) (5,13) (5,12) (5,17) (5,6) (5,15) (5,21) (5,14) (6,7) (6,11) (6,20) (6,8) (6,19) (6,13) (6,12) (6,17) (6,15) (6,21) (6,14) (7,11) (7,20) (7,8) (7,19) (7,13) (7,12) (7,17) (7,15) (7,21) (7,14) (8,11) (8,20) (8,19) (8,13) (8,12) (8,17) (8,15) (8,21) (8,14) (9,16) (9,10) (9,18) (10,16) (10,18) (11,20) (11,19) (11,13) (11,12) (11,17) (11,15) (11,21) (11,14) (12,20) (12,19) (12,13) (12,17) (12,15) (12,21) (12,14) (13,20) (13,19) (13,17) (13,15) (13,21) (13,14) (14,20) (14,19) (14,17) (14,15) (14,21) (15,20) (15,19) (15,17) (15,21) (16,18) (17,20) (17,19) (17,21) (19,20) (19,21) (20,21)\nIs there a path between node 18 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph370-18_13", + "image": "data/connectivity/graph_visual/medium/graph370.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,13) (0,5) (0,16) (0,1) (0,3) (1,13) (1,5) (1,9) (1,20) (1,2) (1,16) (1,3) (2,13) (2,5) (2,12) (2,8) (2,9) (2,20) (2,16) (2,3) (3,8) (3,9) (3,16) (4,7) (4,15) (4,19) (4,6) (4,11) (4,18) (4,10) (4,14) (5,13) (5,12) (5,9) (5,16) (6,7) (6,17) (6,19) (6,11) (6,10) (6,14) (7,15) (7,17) (7,19) (7,11) (7,10) (7,14) (8,13) (8,9) (8,20) (9,13) (9,12) (10,15) (10,19) (10,11) (11,15) (11,17) (11,19) (11,18) (11,14) (12,13) (12,20) (14,15) (14,18) (15,18) (16,20) (17,19) (17,18) (18,19)\nIs there a path between node 18 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph706-7_4", + "image": "data/connectivity/graph_visual/medium/graph706.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (0,2) (0,23) (0,1) (1,16) (1,17) (1,5) (1,15) (1,19) (1,13) (1,4) (2,3) (2,13) (2,4) (2,10) (3,17) (3,15) (3,14) (3,9) (3,20) (3,6) (4,12) (4,18) (5,13) (5,14) (5,9) (6,19) (6,13) (6,23) (6,14) (6,20) (7,21) (9,16) (9,13) (9,23) (9,11) (9,18) (10,16) (10,13) (11,15) (11,23) (12,16) (12,17) (12,23) (13,17) (13,23) (14,16) (14,17) (14,19) (14,18) (15,16) (15,19) (15,23) (15,18) (15,20) (16,17) (17,18) (18,20)\nIs there a path between node 7 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph579-16_18", + "image": "data/connectivity/graph_visual/medium/graph579.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,3) (0,8) (0,10) (0,2) (0,13) (0,19) (1,23) (2,6) (2,20) (2,11) (2,12) (2,8) (2,17) (2,22) (2,5) (2,19) (3,11) (3,12) (3,21) (3,22) (5,16) (5,6) (5,8) (5,17) (5,13) (5,19) (6,20) (6,22) (6,7) (7,8) (7,10) (7,13) (8,11) (8,10) (8,13) (9,20) (9,10) (10,16) (10,11) (11,16) (12,17) (12,22) (12,13) (13,21) (14,23) (14,15) (17,20) (17,21) (21,22)\nIs there a path between node 16 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph297-7_19", + "image": "data/connectivity/graph_visual/medium/graph297.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,12) (0,19) (1,2) (1,13) (1,7) (1,6) (1,3) (1,9) (1,16) (1,4) (2,13) (2,7) (2,6) (2,10) (2,9) (2,16) (2,8) (2,15) (3,17) (3,6) (3,5) (3,10) (3,16) (3,4) (4,13) (4,17) (4,6) (4,5) (4,10) (4,9) (4,15) (5,13) (5,7) (5,6) (5,9) (5,16) (5,8) (6,13) (6,7) (6,9) (6,16) (6,8) (6,15) (7,13) (7,10) (7,9) (8,17) (8,10) (8,9) (8,16) (8,15) (9,17) (9,10) (9,16) (9,15) (10,13) (10,17) (10,16) (10,15) (12,19) (12,18) (13,15) (15,17) (15,16) (16,17) (18,19)\nIs there a path between node 7 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph636-2_5", + "image": "data/connectivity/graph_visual/medium/graph636.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (0,8) (0,22) (0,15) (0,18) (1,12) (1,16) (1,8) (1,9) (1,22) (1,15) (1,18) (2,6) (2,21) (3,21) (3,11) (3,10) (4,23) (5,20) (5,17) (6,20) (7,11) (8,16) (8,14) (8,13) (8,15) (9,16) (9,15) (9,19) (10,20) (10,21) (10,17) (13,16) (13,14) (14,19) (15,22) (15,18) (17,20) (17,23) (18,22) (21,23)\nIs there a path between node 2 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph51-10_8", + "image": "data/connectivity/graph_visual/medium/graph51.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,6) (0,13) (1,6) (1,8) (1,3) (1,4) (2,5) (2,9) (3,12) (3,9) (3,13) (4,6) (4,10) (5,6) (5,9) (6,12) (6,8) (8,9) (9,10) (12,13)\nIs there a path between node 10 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph551-13_22", + "image": "data/connectivity/graph_visual/medium/graph551.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,11) (2,20) (3,22) (3,6) (3,14) (3,12) (3,13) (3,4) (4,23) (4,12) (5,23) (5,22) (5,12) (5,10) (5,13) (5,15) (6,10) (6,13) (6,18) (8,11) (9,20) (10,12) (11,17) (11,16) (12,14) (12,15) (12,21) (13,19) (13,18) (14,23) (14,15) (14,18) (15,23) (18,23)\nIs there a path between node 13 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph426-3_17", + "image": "data/connectivity/graph_visual/medium/graph426.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,8) (0,18) (0,10) (0,2) (0,20) (1,10) (1,17) (1,21) (3,4) (3,18) (4,18) (4,9) (5,16) (7,19) (7,13) (8,18) (8,10) (8,20) (8,21) (9,17) (9,21) (10,17) (12,13) (13,16) (14,15) (17,21) (18,21)\nIs there a path between node 3 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph299-15_8", + "image": "data/connectivity/graph_visual/medium/graph299.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (1,3) (1,2) (1,7) (1,5) (1,18) (1,14) (1,17) (1,12) (1,11) (1,10) (1,19) (1,13) (1,4) (1,9) (2,7) (2,18) (2,16) (2,6) (2,11) (2,10) (2,19) (2,13) (2,4) (2,9) (2,15) (3,7) (3,18) (3,12) (3,6) (3,10) (3,19) (3,13) (3,4) (3,9) (4,7) (4,5) (4,14) (4,17) (4,16) (4,6) (4,11) (4,10) (4,19) (4,9) (5,7) (5,14) (5,17) (5,16) (5,12) (5,6) (5,11) (5,10) (5,13) (5,9) (5,15) (6,14) (6,17) (6,16) (6,12) (6,10) (6,19) (6,9) (7,18) (7,14) (7,17) (7,16) (7,12) (7,10) (7,19) (7,13) (7,9) (7,15) (9,18) (9,14) (9,17) (9,16) (9,12) (9,11) (9,19) (9,13) (9,15) (10,18) (10,14) (10,17) (10,12) (10,11) (10,19) (10,15) (11,18) (11,12) (11,19) (11,15) (12,18) (12,14) (12,17) (12,19) (12,13) (12,15) (13,18) (13,14) (13,17) (14,17) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19)\nIs there a path between node 15 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph704-24_21", + "image": "data/connectivity/graph_visual/medium/graph704.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,7) (1,9) (1,10) (1,14) (2,3) (2,11) (3,11) (3,12) (4,17) (5,18) (5,17) (6,20) (6,22) (6,17) (6,8) (7,23) (7,18) (7,8) (9,21) (9,16) (9,11) (9,13) (10,14) (11,21) (11,14) (11,13) (12,15) (13,21) (13,15) (13,14) (14,15) (17,18) (17,19) (18,23) (18,24) (19,24) (19,22)\nIs there a path between node 24 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph743-3_4", + "image": "data/connectivity/graph_visual/medium/graph743.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (1,22) (1,6) (1,2) (1,14) (2,16) (2,20) (2,5) (2,23) (3,16) (3,20) (3,8) (3,5) (3,6) (4,10) (4,24) (5,17) (5,22) (5,20) (5,7) (6,17) (6,9) (6,23) (7,22) (7,20) (8,16) (8,22) (8,14) (9,16) (9,22) (9,20) (9,12) (9,23) (10,11) (12,22) (12,23) (13,18) (14,16) (14,22) (16,17) (16,22) (16,20) (20,22) (20,23)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph789-20_3", + "image": "data/connectivity/graph_visual/medium/graph789.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,11) (1,12) (1,17) (1,6) (1,20) (1,4) (1,24) (2,3) (2,8) (2,12) (2,17) (2,6) (2,23) (2,24) (2,7) (3,10) (3,5) (3,20) (4,17) (4,6) (4,18) (5,8) (5,24) (5,21) (5,11) (5,19) (6,8) (6,12) (6,24) (6,7) (6,19) (7,12) (7,17) (7,23) (7,19) (8,17) (8,24) (8,21) (8,19) (9,13) (9,22) (10,23) (10,24) (10,11) (11,12) (11,20) (11,23) (11,21) (12,17) (14,22) (14,16) (15,16) (16,22) (17,20) (19,23) (19,21) (20,24) (21,24) (23,24)\nIs there a path between node 20 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph499-9_14", + "image": "data/connectivity/graph_visual/medium/graph499.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (0,15) (0,5) (1,10) (2,19) (2,14) (2,21) (4,22) (4,13) (4,6) (5,15) (6,22) (6,9) (8,13) (8,19) (8,21) (10,20) (11,20) (12,18) (13,14) (15,18) (17,19) (21,22)\nIs there a path between node 9 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph327-10_3", + "image": "data/connectivity/graph_visual/medium/graph327.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,4) (1,13) (2,11) (3,4) (3,6) (3,19) (4,20) (4,12) (4,16) (5,14) (5,9) (6,18) (6,8) (7,13) (7,8) (7,19) (7,15) (8,18) (8,20) (8,15) (11,14) (12,20) (12,13) (12,19) (12,16) (13,18) (13,15) (15,18) (15,19) (18,20) (18,19)\nIs there a path between node 10 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph654-22_6", + "image": "data/connectivity/graph_visual/medium/graph654.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,8) (0,2) (0,17) (0,6) (0,11) (0,23) (0,4) (0,7) (0,14) (0,1) (0,21) (0,12) (0,10) (0,19) (1,20) (1,22) (1,8) (1,2) (1,17) (1,6) (1,9) (1,4) (1,14) (1,21) (1,12) (2,20) (2,22) (2,3) (2,16) (2,17) (2,6) (2,9) (2,11) (2,23) (2,7) (2,21) (2,12) (2,19) (3,20) (3,22) (3,8) (3,16) (3,17) (3,6) (3,11) (3,23) (3,4) (3,7) (3,14) (3,21) (3,12) (3,19) (4,8) (4,17) (4,11) (4,7) (4,12) (4,10) (4,19) (6,20) (6,22) (6,8) (6,16) (6,23) (6,7) (6,21) (6,12) (6,10) (6,19) (7,20) (7,22) (7,16) (7,17) (7,23) (7,21) (7,12) (7,19) (8,20) (8,22) (8,17) (8,9) (8,23) (8,14) (8,21) (8,12) (8,10) (8,19) (9,22) (9,16) (9,17) (9,11) (9,14) (9,21) (9,12) (10,20) (10,22) (10,16) (10,17) (10,11) (10,23) (10,21) (10,19) (11,20) (11,22) (11,23) (11,14) (11,21) (11,12) (11,19) (12,22) (12,16) (12,17) (12,21) (12,19) (13,15) (13,18) (14,20) (14,22) (14,16) (14,17) (14,23) (14,21) (14,19) (15,18) (16,22) (16,21) (17,22) (17,19) (19,20) (19,22) (19,21) (20,22) (20,23) (20,21) (21,22)\nIs there a path between node 22 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph497-8_3", + "image": "data/connectivity/graph_visual/medium/graph497.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,14) (0,13) (0,15) (0,16) (1,19) (1,21) (3,17) (3,15) (4,17) (6,7) (6,15) (7,17) (7,8) (7,13) (7,15) (7,16) (8,16) (9,18) (10,18) (10,19) (12,18) (12,19) (13,15) (14,17) (14,16) (14,20) (15,17) (15,22) (15,16) (15,20) (16,17) (16,22) (17,22) (18,21)\nIs there a path between node 8 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph277-7_14", + "image": "data/connectivity/graph_visual/medium/graph277.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,12) (0,10) (0,16) (1,7) (1,18) (1,3) (1,14) (1,11) (1,5) (1,13) (1,19) (1,15) (1,6) (1,9) (1,8) (1,4) (3,7) (3,18) (3,14) (3,11) (3,5) (3,13) (3,19) (3,15) (3,6) (3,9) (3,8) (3,4) (4,7) (4,18) (4,14) (4,11) (4,5) (4,13) (4,19) (4,15) (4,6) (4,9) (4,8) (5,7) (5,18) (5,14) (5,11) (5,13) (5,19) (5,15) (5,6) (5,9) (5,8) (6,7) (6,18) (6,14) (6,11) (6,13) (6,19) (6,15) (6,9) (6,8) (7,18) (7,14) (7,11) (7,13) (7,19) (7,15) (7,9) (7,8) (8,18) (8,14) (8,11) (8,13) (8,19) (8,15) (8,9) (9,18) (9,14) (9,11) (9,13) (9,19) (9,15) (10,17) (10,12) (10,16) (11,18) (11,14) (11,13) (11,19) (11,15) (12,17) (12,16) (13,18) (13,14) (13,19) (13,15) (14,18) (14,19) (14,15) (15,18) (15,19) (16,17) (18,19)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph330-11_3", + "image": "data/connectivity/graph_visual/medium/graph330.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,5) (1,17) (2,16) (3,18) (3,14) (4,20) (5,17) (6,16) (6,12) (6,8) (8,15) (8,17) (10,13) (10,11) (11,20) (12,15) (12,17) (14,18) (14,19) (16,17)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph440-18_21", + "image": "data/connectivity/graph_visual/medium/graph440.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,5) (0,4) (0,14) (0,8) (0,20) (0,3) (0,12) (0,10) (0,2) (0,9) (1,16) (1,7) (1,21) (1,17) (2,5) (2,11) (2,18) (2,4) (2,8) (2,20) (2,12) (2,9) (3,5) (3,11) (3,18) (3,4) (3,20) (3,13) (3,12) (3,15) (3,9) (4,5) (4,18) (4,14) (4,8) (4,20) (4,13) (4,12) (4,10) (4,15) (4,9) (5,11) (5,18) (5,14) (5,8) (5,12) (5,10) (5,15) (6,11) (6,18) (6,8) (6,20) (6,13) (6,10) (6,15) (7,16) (7,21) (7,19) (7,17) (8,11) (8,18) (8,14) (8,20) (8,12) (8,10) (8,15) (8,9) (9,11) (9,14) (9,20) (9,13) (9,15) (10,11) (10,18) (10,14) (10,20) (10,13) (10,12) (10,15) (11,14) (11,20) (11,13) (11,12) (11,15) (12,18) (12,14) (12,20) (12,13) (13,14) (13,20) (13,15) (14,18) (14,15) (15,20) (16,21) (16,19) (17,21) (17,19) (18,20)\nIs there a path between node 18 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph303-11_7", + "image": "data/connectivity/graph_visual/medium/graph303.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,11) (0,15) (0,17) (1,11) (1,17) (2,10) (2,3) (2,18) (2,14) (2,8) (2,13) (2,4) (2,6) (2,19) (2,9) (3,10) (3,5) (3,7) (3,14) (3,13) (3,12) (3,4) (3,6) (3,19) (3,9) (4,5) (4,18) (4,14) (4,8) (4,13) (4,12) (4,6) (4,19) (4,9) (5,14) (5,8) (5,13) (5,12) (5,19) (6,10) (6,7) (6,18) (6,14) (6,8) (6,13) (6,12) (6,19) (6,9) (7,10) (7,8) (7,19) (8,10) (8,18) (8,14) (8,12) (8,19) (8,9) (9,10) (9,18) (9,14) (9,13) (9,19) (10,18) (10,14) (10,13) (10,19) (11,16) (12,19) (13,18) (14,19) (16,17) (18,19)\nIs there a path between node 11 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph316-5_0", + "image": "data/connectivity/graph_visual/medium/graph316.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,13) (0,18) (1,10) (1,9) (1,11) (1,8) (1,5) (1,17) (1,19) (1,4) (1,6) (1,12) (1,14) (1,7) (1,3) (1,15) (1,2) (1,16) (2,10) (2,9) (2,11) (2,8) (2,5) (2,17) (2,19) (2,4) (2,6) (2,12) (2,14) (2,7) (2,3) (2,15) (2,16) (3,10) (3,9) (3,11) (3,8) (3,5) (3,17) (3,19) (3,4) (3,6) (3,12) (3,14) (3,7) (3,15) (3,16) (4,10) (4,9) (4,11) (4,8) (4,5) (4,17) (4,19) (4,6) (4,12) (4,14) (4,7) (4,15) (4,16) (5,10) (5,9) (5,11) (5,8) (5,17) (5,19) (5,6) (5,12) (5,14) (5,7) (5,15) (5,16) (6,10) (6,9) (6,11) (6,8) (6,17) (6,19) (6,12) (6,14) (6,7) (6,15) (6,16) (7,10) (7,9) (7,11) (7,8) (7,17) (7,19) (7,12) (7,14) (7,15) (7,16) (8,10) (8,9) (8,11) (8,17) (8,19) (8,12) (8,14) (8,15) (8,16) (9,10) (9,11) (9,17) (9,19) (9,12) (9,14) (9,15) (9,16) (10,11) (10,17) (10,19) (10,12) (10,14) (10,15) (10,16) (11,17) (11,19) (11,12) (11,14) (11,15) (11,16) (12,17) (12,19) (12,14) (12,15) (12,16) (13,18) (14,17) (14,19) (14,15) (14,16) (15,17) (15,19) (15,16) (16,17) (16,19) (17,19)\nIs there a path between node 5 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph651-14_2", + "image": "data/connectivity/graph_visual/medium/graph651.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,4) (0,11) (0,18) (0,2) (0,8) (0,19) (0,23) (0,13) (0,7) (0,3) (0,16) (1,21) (1,22) (1,14) (1,17) (2,9) (2,4) (2,11) (2,18) (2,8) (2,19) (2,23) (2,13) (2,7) (2,3) (2,6) (3,9) (3,4) (3,11) (3,18) (3,8) (3,23) (3,13) (3,7) (3,6) (4,9) (4,11) (4,18) (4,23) (5,20) (5,10) (6,9) (6,18) (6,8) (6,13) (6,7) (6,16) (7,9) (7,11) (7,18) (7,8) (7,19) (7,23) (7,13) (7,16) (8,9) (8,11) (8,18) (8,19) (8,23) (8,13) (9,19) (9,23) (9,13) (11,18) (11,19) (11,23) (11,16) (12,21) (12,22) (12,15) (13,19) (13,23) (14,21) (14,22) (14,15) (15,21) (15,22) (16,18) (16,23) (17,21) (18,19) (19,23) (21,22)\nIs there a path between node 14 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph570-3_4", + "image": "data/connectivity/graph_visual/medium/graph570.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,18) (0,12) (0,20) (0,17) (0,14) (0,4) (0,19) (0,15) (0,7) (0,16) (0,21) (1,8) (1,23) (1,2) (1,22) (1,10) (1,5) (2,8) (2,23) (2,22) (2,10) (2,5) (3,13) (3,9) (3,11) (4,6) (4,18) (4,12) (4,20) (4,17) (4,14) (4,19) (4,15) (4,7) (4,16) (4,21) (5,8) (5,23) (5,22) (5,10) (6,18) (6,12) (6,20) (6,17) (6,14) (6,19) (6,15) (6,7) (6,16) (6,21) (7,18) (7,12) (7,20) (7,17) (7,14) (7,19) (7,15) (7,16) (7,21) (8,23) (8,22) (8,10) (9,13) (9,11) (10,23) (10,22) (11,13) (12,18) (12,20) (12,17) (12,14) (12,19) (12,15) (12,16) (12,21) (14,18) (14,20) (14,17) (14,19) (14,15) (14,16) (14,21) (15,18) (15,20) (15,17) (15,19) (15,16) (15,21) (16,18) (16,20) (16,17) (16,19) (16,21) (17,18) (17,20) (17,19) (17,21) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21) (22,23)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph58-0_11", + "image": "data/connectivity/graph_visual/medium/graph58.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (0,1) (1,3) (1,11) (1,2) (1,4) (2,9) (2,12) (3,8) (4,12) (5,11) (5,8) (5,7) (6,13) (10,12)\nIs there a path between node 0 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph575-23_5", + "image": "data/connectivity/graph_visual/medium/graph575.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,14) (0,15) (0,9) (1,8) (2,4) (2,13) (2,8) (3,18) (3,20) (4,18) (4,13) (4,20) (4,10) (5,11) (5,22) (5,19) (5,23) (7,23) (8,16) (8,13) (8,20) (8,10) (9,15) (11,22) (12,17) (12,14) (13,20) (15,22) (17,22) (17,23) (19,22) (19,23)\nIs there a path between node 23 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph136-12_15", + "image": "data/connectivity/graph_visual/medium/graph136.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,17) (1,14) (1,8) (3,14) (4,10) (5,17) (6,15) (7,14) (8,12) (8,15) (9,17) (9,10) (9,16) (12,15) (13,17) (14,15)\nIs there a path between node 12 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph727-16_11", + "image": "data/connectivity/graph_visual/medium/graph727.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,2) (1,12) (1,21) (1,18) (1,15) (1,10) (1,13) (1,19) (1,16) (1,22) (1,7) (1,24) (1,14) (1,9) (1,6) (1,17) (1,3) (1,11) (1,20) (1,5) (1,8) (2,12) (2,21) (2,18) (2,15) (2,10) (2,13) (2,19) (2,16) (2,22) (2,7) (2,24) (2,14) (2,9) (2,6) (2,17) (2,3) (2,11) (2,20) (2,5) (2,8) (3,12) (3,21) (3,18) (3,15) (3,10) (3,13) (3,19) (3,16) (3,22) (3,7) (3,24) (3,14) (3,9) (3,6) (3,17) (3,11) (3,20) (3,5) (3,8) (4,23) (5,12) (5,21) (5,18) (5,15) (5,10) (5,13) (5,19) (5,16) (5,22) (5,7) (5,24) (5,14) (5,9) (5,6) (5,17) (5,11) (5,20) (5,8) (6,12) (6,21) (6,18) (6,15) (6,10) (6,13) (6,19) (6,16) (6,22) (6,7) (6,24) (6,14) (6,9) (6,17) (6,11) (6,20) (6,8) (7,12) (7,21) (7,18) (7,15) (7,10) (7,13) (7,19) (7,16) (7,22) (7,24) (7,14) (7,9) (7,17) (7,11) (7,20) (7,8) (8,12) (8,21) (8,18) (8,15) (8,10) (8,13) (8,19) (8,16) (8,22) (8,24) (8,14) (8,9) (8,17) (8,11) (8,20) (9,12) (9,21) (9,18) (9,15) (9,10) (9,13) (9,19) (9,16) (9,22) (9,24) (9,14) (9,17) (9,11) (9,20) (10,12) (10,21) (10,18) (10,15) (10,13) (10,19) (10,16) (10,22) (10,24) (10,14) (10,17) (10,11) (10,20) (11,12) (11,21) (11,18) (11,15) (11,13) (11,19) (11,16) (11,22) (11,24) (11,14) (11,17) (11,20) (12,21) (12,18) (12,15) (12,13) (12,19) (12,16) (12,22) (12,24) (12,14) (12,17) (12,20) (13,21) (13,18) (13,15) (13,19) (13,16) (13,22) (13,24) (13,14) (13,17) (13,20) (14,21) (14,18) (14,15) (14,19) (14,16) (14,22) (14,24) (14,17) (14,20) (15,21) (15,18) (15,19) (15,16) (15,22) (15,24) (15,17) (15,20) (16,21) (16,18) (16,19) (16,22) (16,24) (16,17) (16,20) (17,21) (17,18) (17,19) (17,22) (17,24) (17,20) (18,21) (18,19) (18,22) (18,24) (18,20) (19,21) (19,22) (19,24) (19,20) (20,21) (20,22) (20,24) (21,22) (21,24) (22,24)\nIs there a path between node 16 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph187-3_16", + "image": "data/connectivity/graph_visual/medium/graph187.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,10) (0,17) (0,1) (0,15) (0,14) (0,4) (0,8) (0,16) (0,13) (0,9) (0,5) (0,11) (1,10) (1,17) (1,15) (1,14) (1,4) (1,8) (1,16) (1,13) (1,9) (1,5) (1,11) (2,3) (2,7) (2,12) (2,6) (3,7) (3,12) (3,6) (4,10) (4,17) (4,15) (4,14) (4,8) (4,16) (4,13) (4,9) (4,5) (4,11) (5,10) (5,17) (5,15) (5,14) (5,8) (5,16) (5,13) (5,9) (5,11) (6,7) (6,12) (7,12) (8,10) (8,17) (8,15) (8,14) (8,16) (8,13) (8,9) (8,11) (9,10) (9,17) (9,15) (9,14) (9,16) (9,13) (9,11) (10,17) (10,15) (10,14) (10,16) (10,13) (10,11) (11,17) (11,15) (11,14) (11,16) (11,13) (13,17) (13,15) (13,14) (13,16) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 3 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph508-4_11", + "image": "data/connectivity/graph_visual/medium/graph508.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (0,1) (0,21) (0,13) (0,10) (1,15) (1,11) (1,17) (1,21) (1,3) (1,16) (1,20) (2,17) (2,21) (3,15) (3,8) (4,18) (4,20) (5,22) (6,17) (6,16) (6,8) (8,18) (8,11) (8,17) (10,15) (10,11) (11,13) (13,18) (13,16) (15,17) (15,20) (16,18) (17,18) (17,21) (19,22)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph213-3_1", + "image": "data/connectivity/graph_visual/medium/graph213.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (0,6) (0,7) (0,1) (1,4) (1,6) (1,7) (2,18) (2,12) (2,5) (2,17) (2,10) (2,8) (2,16) (2,3) (2,14) (2,11) (2,13) (3,18) (3,12) (3,5) (3,17) (3,10) (3,8) (3,16) (3,14) (3,11) (3,13) (4,6) (4,7) (5,18) (5,12) (5,17) (5,10) (5,8) (5,16) (5,14) (5,11) (5,13) (6,7) (8,18) (8,12) (8,17) (8,10) (8,16) (8,14) (8,11) (8,13) (9,15) (10,18) (10,12) (10,17) (10,16) (10,14) (10,11) (10,13) (11,18) (11,12) (11,17) (11,16) (11,14) (11,13) (12,18) (12,17) (12,16) (12,14) (12,13) (13,18) (13,17) (13,16) (13,14) (14,18) (14,17) (14,16) (16,18) (16,17) (17,18)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph478-14_17", + "image": "data/connectivity/graph_visual/medium/graph478.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,17) (1,15) (1,10) (1,5) (1,11) (1,3) (1,19) (1,6) (2,13) (2,10) (2,18) (2,21) (2,3) (3,18) (3,11) (4,8) (5,10) (7,16) (7,10) (7,11) (10,16) (11,15) (11,16) (12,22) (12,14) (12,20) (13,21) (14,22) (16,21) (16,19) (18,21) (19,21) (20,22)\nIs there a path between node 14 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph751-8_7", + "image": "data/connectivity/graph_visual/medium/graph751.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,21) (0,20) (0,18) (0,23) (0,11) (0,14) (0,22) (0,7) (0,10) (0,15) (0,13) (1,4) (1,17) (1,24) (1,12) (1,8) (1,9) (2,3) (2,21) (2,18) (2,23) (2,11) (2,14) (2,22) (2,7) (2,10) (2,15) (2,13) (3,21) (3,20) (3,19) (3,23) (3,11) (3,14) (3,7) (3,10) (3,13) (4,16) (4,5) (4,24) (4,6) (4,8) (5,16) (5,17) (5,24) (5,12) (5,6) (5,8) (5,9) (6,16) (6,17) (6,24) (6,12) (7,21) (7,20) (7,11) (7,22) (7,13) (8,16) (8,24) (8,12) (8,9) (9,16) (9,17) (9,24) (9,12) (10,19) (10,18) (10,23) (10,14) (10,15) (10,13) (11,21) (11,19) (11,23) (11,14) (11,15) (12,16) (12,24) (13,18) (13,23) (13,14) (13,15) (14,21) (14,20) (14,19) (14,18) (14,23) (14,22) (15,21) (15,20) (15,18) (15,23) (15,22) (16,17) (16,24) (17,24) (18,21) (18,20) (18,19) (18,23) (18,22) (19,20) (19,23) (20,21) (20,23) (20,22) (21,23) (22,23)\nIs there a path between node 8 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph644-13_9", + "image": "data/connectivity/graph_visual/medium/graph644.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,9) (1,4) (2,16) (4,18) (4,11) (5,14) (6,8) (7,15) (7,21) (9,15) (9,19) (13,15) (13,16) (15,20) (16,20) (19,21) (19,20)\nIs there a path between node 13 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph612-22_6", + "image": "data/connectivity/graph_visual/medium/graph612.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,6) (0,12) (0,20) (0,15) (0,9) (0,13) (0,2) (0,14) (0,11) (0,3) (0,23) (0,5) (1,21) (1,7) (1,8) (1,22) (1,4) (1,18) (1,17) (1,16) (2,10) (2,19) (2,6) (2,12) (2,20) (2,15) (2,9) (2,13) (2,14) (2,11) (2,3) (2,23) (2,5) (3,10) (3,19) (3,6) (3,12) (3,20) (3,15) (3,9) (3,13) (3,14) (3,11) (3,23) (3,5) (4,21) (4,7) (4,8) (4,22) (4,18) (4,17) (4,16) (5,10) (5,19) (5,6) (5,12) (5,20) (5,15) (5,9) (5,13) (5,14) (5,11) (5,23) (6,10) (6,19) (6,12) (6,20) (6,15) (6,9) (6,13) (6,14) (6,11) (6,23) (7,21) (7,8) (7,22) (7,18) (7,17) (7,16) (8,21) (8,22) (8,18) (8,17) (8,16) (9,10) (9,19) (9,12) (9,20) (9,15) (9,13) (9,14) (9,11) (9,23) (10,19) (10,12) (10,20) (10,15) (10,13) (10,14) (10,11) (10,23) (11,19) (11,12) (11,20) (11,15) (11,13) (11,14) (11,23) (12,19) (12,20) (12,15) (12,13) (12,14) (12,23) (13,19) (13,20) (13,15) (13,14) (13,23) (14,19) (14,20) (14,15) (14,23) (15,19) (15,20) (15,23) (16,21) (16,22) (16,18) (16,17) (17,21) (17,22) (17,18) (18,21) (18,22) (19,20) (19,23) (20,23) (21,22)\nIs there a path between node 22 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph359-10_1", + "image": "data/connectivity/graph_visual/medium/graph359.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,8) (0,7) (0,18) (0,5) (0,2) (0,1) (1,11) (1,17) (2,20) (2,9) (3,11) (3,18) (3,20) (3,12) (4,14) (6,19) (6,16) (6,8) (6,15) (6,12) (6,9) (7,15) (7,12) (7,17) (8,18) (9,17) (11,16) (11,15) (12,19) (12,17) (15,19) (15,20) (16,19) (16,18) (16,17)\nIs there a path between node 10 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph806-15_17", + "image": "data/connectivity/graph_visual/medium/graph806.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,21) (1,17) (1,15) (1,2) (1,4) (1,18) (2,8) (2,13) (2,17) (2,15) (2,23) (2,22) (2,4) (2,18) (2,12) (4,21) (4,8) (4,13) (4,15) (4,23) (4,22) (4,18) (4,12) (5,21) (5,8) (5,13) (5,17) (5,15) (5,22) (5,18) (7,14) (7,16) (7,10) (7,11) (7,19) (8,21) (8,17) (8,23) (8,18) (9,14) (9,24) (10,14) (10,24) (10,19) (11,14) (11,16) (11,24) (12,21) (12,13) (12,17) (12,15) (12,23) (12,22) (12,18) (13,21) (13,17) (13,15) (13,23) (13,22) (14,24) (15,21) (15,17) (15,23) (15,22) (15,18) (16,19) (17,21) (17,18) (18,21) (18,23) (21,22) (22,23)\nIs there a path between node 15 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph454-9_4", + "image": "data/connectivity/graph_visual/medium/graph454.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,21) (0,11) (0,7) (0,1) (0,20) (0,14) (0,16) (0,17) (0,12) (0,9) (0,6) (0,19) (0,2) (0,8) (0,15) (0,10) (1,18) (1,21) (1,11) (1,7) (1,20) (1,14) (1,16) (1,17) (1,12) (1,9) (1,6) (1,19) (1,2) (1,8) (1,15) (1,10) (2,18) (2,21) (2,11) (2,7) (2,20) (2,14) (2,16) (2,17) (2,12) (2,9) (2,6) (2,19) (2,8) (2,15) (2,10) (3,13) (3,4) (3,5) (4,13) (4,5) (5,13) (6,18) (6,21) (6,11) (6,7) (6,20) (6,14) (6,16) (6,17) (6,12) (6,9) (6,19) (6,8) (6,15) (6,10) (7,18) (7,21) (7,11) (7,20) (7,14) (7,16) (7,17) (7,12) (7,9) (7,19) (7,8) (7,15) (7,10) (8,18) (8,21) (8,11) (8,20) (8,14) (8,16) (8,17) (8,12) (8,9) (8,19) (8,15) (8,10) (9,18) (9,21) (9,11) (9,20) (9,14) (9,16) (9,17) (9,12) (9,19) (9,15) (9,10) (10,18) (10,21) (10,11) (10,20) (10,14) (10,16) (10,17) (10,12) (10,19) (10,15) (11,18) (11,21) (11,20) (11,14) (11,16) (11,17) (11,12) (11,19) (11,15) (12,18) (12,21) (12,20) (12,14) (12,16) (12,17) (12,19) (12,15) (14,18) (14,21) (14,20) (14,16) (14,17) (14,19) (14,15) (15,18) (15,21) (15,20) (15,16) (15,17) (15,19) (16,18) (16,21) (16,20) (16,17) (16,19) (17,18) (17,21) (17,20) (17,19) (18,21) (18,20) (18,19) (19,21) (19,20) (20,21)\nIs there a path between node 9 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph737-1_10", + "image": "data/connectivity/graph_visual/medium/graph737.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,3) (0,16) (0,24) (0,7) (1,17) (1,2) (2,9) (2,20) (2,8) (3,22) (3,12) (3,23) (3,21) (4,9) (4,13) (4,18) (5,11) (5,23) (5,21) (6,15) (6,7) (7,11) (7,22) (7,12) (7,16) (7,23) (7,14) (7,21) (8,20) (8,17) (8,18) (10,20) (10,17) (10,18) (11,21) (12,22) (12,14) (14,22) (15,16) (15,24) (16,23) (17,18) (19,21) (21,24) (22,24)\nIs there a path between node 1 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph521-16_13", + "image": "data/connectivity/graph_visual/medium/graph521.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,10) (0,12) (0,16) (0,9) (0,17) (0,11) (0,5) (0,13) (0,21) (0,4) (1,8) (1,18) (1,7) (3,6) (3,14) (3,10) (3,16) (3,9) (3,11) (3,5) (3,21) (3,4) (3,15) (4,6) (4,10) (4,12) (4,16) (4,9) (4,17) (4,11) (4,13) (4,21) (4,15) (5,6) (5,12) (5,9) (5,19) (5,17) (5,13) (5,21) (5,15) (6,14) (6,10) (6,12) (6,16) (6,19) (6,17) (6,13) (6,21) (6,15) (7,20) (7,8) (7,18) (8,20) (9,14) (9,10) (9,16) (9,19) (9,17) (9,11) (9,13) (9,21) (10,12) (10,19) (10,17) (10,11) (10,15) (11,14) (11,16) (11,19) (11,17) (11,21) (12,14) (12,17) (12,13) (12,21) (13,14) (13,16) (13,17) (13,21) (14,16) (14,21) (15,19) (15,17) (15,21) (16,17) (16,21) (17,19) (17,21) (18,20) (19,21)\nIs there a path between node 16 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph307-19_0", + "image": "data/connectivity/graph_visual/medium/graph307.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,11) (0,12) (0,1) (0,6) (0,2) (1,3) (1,11) (1,13) (1,12) (1,6) (1,19) (1,2) (2,3) (2,11) (2,13) (2,12) (2,19) (3,13) (3,12) (3,10) (3,19) (4,18) (5,16) (5,17) (5,9) (5,15) (5,7) (6,13) (6,12) (6,10) (7,14) (8,18) (9,16) (9,14) (9,17) (9,15) (10,11) (10,12) (10,19) (11,13) (11,12) (11,19) (12,13) (12,19) (13,19) (14,15) (15,16) (15,17) (16,17)\nIs there a path between node 19 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph257-9_10", + "image": "data/connectivity/graph_visual/medium/graph257.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,16) (0,18) (0,4) (0,2) (0,13) (0,15) (0,6) (0,14) (0,10) (1,3) (1,5) (1,8) (1,17) (1,11) (1,12) (1,9) (1,7) (2,16) (2,18) (2,4) (2,13) (2,15) (2,6) (2,14) (2,10) (3,5) (3,8) (3,17) (3,11) (3,12) (3,9) (3,7) (4,16) (4,18) (4,13) (4,15) (4,6) (4,14) (4,10) (5,8) (5,17) (5,11) (5,12) (5,9) (5,7) (6,16) (6,18) (6,13) (6,15) (6,14) (6,10) (7,8) (7,17) (7,11) (7,12) (7,9) (8,17) (8,11) (8,12) (8,9) (9,17) (9,11) (9,12) (10,16) (10,18) (10,13) (10,15) (10,14) (11,17) (11,12) (12,17) (13,16) (13,18) (13,15) (13,14) (14,16) (14,18) (14,15) (15,16) (15,18) (16,18)\nIs there a path between node 9 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph36-6_5", + "image": "data/connectivity/graph_visual/medium/graph36.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,2) (0,12) (0,11) (0,4) (2,10) (2,8) (2,4) (4,6) (4,11) (5,9) (6,7) (6,10) (6,11) (7,8) (8,10) (8,9) (9,12) (10,11)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph823-9_21", + "image": "data/connectivity/graph_visual/medium/graph823.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (0,21) (0,3) (0,7) (0,20) (0,17) (0,8) (1,19) (1,21) (1,7) (1,20) (1,8) (1,6) (2,16) (2,23) (3,7) (3,20) (3,17) (3,8) (3,6) (4,5) (4,15) (4,22) (4,24) (4,11) (5,15) (5,22) (5,11) (6,19) (6,13) (6,20) (6,17) (6,8) (7,19) (7,20) (7,17) (7,8) (8,19) (8,21) (8,17) (9,12) (9,18) (9,14) (10,12) (11,15) (11,24) (12,18) (12,14) (13,19) (13,21) (13,20) (13,17) (14,18) (17,19) (17,21) (19,21) (19,20)\nIs there a path between node 9 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph359-18_8", + "image": "data/connectivity/graph_visual/medium/graph359.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,8) (0,7) (0,18) (0,5) (0,2) (0,1) (1,11) (1,17) (2,20) (2,9) (3,11) (3,18) (3,20) (3,12) (4,14) (6,19) (6,16) (6,8) (6,15) (6,12) (6,9) (7,15) (7,12) (7,17) (8,18) (9,17) (11,16) (11,15) (12,19) (12,17) (15,19) (15,20) (16,19) (16,18) (16,17)\nIs there a path between node 18 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph3-4_3", + "image": "data/connectivity/graph_visual/medium/graph3.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nIs there a path between node 4 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph75-2_5", + "image": "data/connectivity/graph_visual/medium/graph75.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,13) (1,6) (1,7) (1,4) (2,6) (2,7) (2,9) (2,10) (2,14) (3,6) (3,9) (3,4) (4,8) (4,9) (4,11) (5,6) (6,8) (6,7) (6,9) (6,10) (7,8) (7,14) (8,13) (9,13) (9,10) (10,13) (10,11)\nIs there a path between node 2 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph276-18_3", + "image": "data/connectivity/graph_visual/medium/graph276.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,10) (1,9) (1,16) (1,4) (1,12) (2,8) (2,19) (2,7) (2,14) (2,17) (2,5) (2,18) (2,6) (2,11) (2,3) (2,13) (2,15) (3,8) (3,19) (3,7) (3,14) (3,17) (3,5) (3,18) (3,6) (3,11) (3,13) (3,15) (4,10) (4,9) (4,16) (4,12) (5,8) (5,19) (5,7) (5,14) (5,17) (5,18) (5,6) (5,11) (5,13) (5,15) (6,8) (6,19) (6,7) (6,14) (6,17) (6,18) (6,11) (6,13) (6,15) (7,8) (7,19) (7,14) (7,17) (7,18) (7,11) (7,13) (7,15) (8,19) (8,14) (8,17) (8,18) (8,11) (8,13) (8,15) (9,10) (9,16) (9,12) (10,16) (10,12) (11,19) (11,14) (11,17) (11,18) (11,13) (11,15) (12,16) (13,19) (13,14) (13,17) (13,18) (13,15) (14,19) (14,17) (14,18) (14,15) (15,19) (15,17) (15,18) (17,19) (17,18) (18,19)\nIs there a path between node 18 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph231-9_4", + "image": "data/connectivity/graph_visual/medium/graph231.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,10) (1,15) (2,16) (3,18) (3,8) (5,15) (5,14) (7,9) (8,18) (8,12) (10,17) (12,13) (12,17) (13,14) (14,18) (14,15) (17,18)\nIs there a path between node 9 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph311-11_1", + "image": "data/connectivity/graph_visual/medium/graph311.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,19) (0,16) (0,18) (0,2) (0,17) (0,7) (0,12) (1,8) (1,3) (1,10) (1,13) (1,6) (1,11) (1,15) (1,5) (1,4) (1,14) (2,9) (2,19) (2,16) (2,18) (2,17) (2,7) (2,12) (3,8) (3,10) (3,13) (3,6) (3,11) (3,15) (3,5) (3,4) (3,14) (4,8) (4,10) (4,13) (4,6) (4,11) (4,15) (4,5) (4,14) (5,8) (5,10) (5,13) (5,6) (5,11) (5,15) (5,14) (6,8) (6,10) (6,13) (6,11) (6,15) (6,14) (7,9) (7,19) (7,16) (7,18) (7,17) (7,12) (8,10) (8,13) (8,11) (8,15) (8,14) (9,19) (9,16) (9,18) (9,17) (9,12) (10,13) (10,11) (10,15) (10,14) (11,13) (11,15) (11,14) (12,19) (12,16) (12,18) (12,17) (13,15) (13,14) (14,15) (16,19) (16,18) (16,17) (17,19) (17,18) (18,19)\nIs there a path between node 11 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph851-12_19", + "image": "data/connectivity/graph_visual/medium/graph851.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,24) (0,15) (0,7) (0,16) (1,3) (1,6) (1,8) (1,14) (1,23) (1,10) (1,11) (2,17) (2,9) (2,21) (2,13) (2,18) (2,4) (2,5) (2,20) (2,22) (2,19) (3,6) (3,8) (3,14) (3,23) (3,10) (3,11) (4,17) (4,9) (4,21) (4,13) (4,18) (4,5) (4,20) (4,22) (4,19) (5,17) (5,9) (5,21) (5,13) (5,18) (5,20) (5,22) (5,19) (6,8) (6,14) (6,23) (6,10) (6,11) (7,12) (7,24) (7,15) (7,16) (8,14) (8,23) (8,10) (8,11) (9,17) (9,21) (9,13) (9,18) (9,20) (9,22) (9,19) (10,14) (10,23) (10,11) (11,14) (11,23) (12,24) (12,15) (12,16) (13,17) (13,21) (13,18) (13,20) (13,22) (13,19) (14,23) (15,24) (15,16) (16,24) (17,21) (17,18) (17,20) (17,22) (17,19) (18,21) (18,20) (18,22) (18,19) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 12 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph663-1_8", + "image": "data/connectivity/graph_visual/medium/graph663.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,8) (0,23) (0,19) (0,9) (0,21) (1,14) (2,7) (2,11) (2,4) (3,5) (3,7) (3,16) (3,17) (3,18) (3,11) (3,4) (4,5) (4,7) (4,10) (4,16) (4,18) (5,7) (5,10) (5,11) (6,22) (6,8) (6,12) (6,19) (7,10) (7,16) (7,17) (7,13) (7,18) (7,11) (8,22) (8,23) (8,15) (8,21) (9,22) (9,23) (9,19) (9,15) (10,18) (11,16) (11,17) (11,13) (12,22) (12,23) (12,15) (12,21) (13,16) (13,17) (13,18) (14,20) (15,23) (15,19) (15,21) (16,18) (17,18) (19,22) (19,21) (21,22) (21,23)\nIs there a path between node 1 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph122-12_10", + "image": "data/connectivity/graph_visual/medium/graph122.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,5) (0,3) (1,13) (1,4) (1,12) (1,16) (1,9) (1,15) (1,11) (1,8) (1,6) (1,7) (1,10) (2,5) (3,14) (4,16) (4,9) (4,11) (4,8) (4,7) (4,10) (6,13) (6,16) (6,11) (6,7) (6,10) (7,13) (7,9) (7,11) (7,8) (7,10) (8,13) (8,12) (8,16) (8,9) (8,15) (8,10) (9,13) (9,16) (9,15) (9,10) (10,16) (10,11) (11,13) (11,16) (11,15) (12,13) (12,15) (13,16) (15,16)\nIs there a path between node 12 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph819-21_7", + "image": "data/connectivity/graph_visual/medium/graph819.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,10) (0,5) (0,7) (1,20) (1,4) (1,8) (1,16) (1,9) (1,23) (1,2) (2,20) (2,22) (2,15) (2,4) (2,19) (2,8) (2,16) (2,9) (2,23) (2,14) (2,17) (3,20) (3,4) (3,19) (3,8) (3,23) (3,14) (3,21) (4,20) (4,22) (4,15) (4,8) (4,16) (4,23) (4,14) (4,21) (5,11) (5,10) (5,7) (6,13) (6,12) (6,18) (7,11) (7,10) (8,20) (8,22) (8,15) (8,23) (8,14) (8,21) (9,22) (9,19) (9,16) (9,21) (9,17) (12,18) (13,24) (13,18) (14,20) (14,22) (14,15) (14,19) (14,23) (14,21) (14,17) (15,22) (15,19) (15,16) (15,21) (15,17) (16,20) (16,21) (17,20) (17,19) (17,23) (17,21) (18,24) (19,22) (19,21) (20,22) (20,23) (20,21) (21,22) (21,23) (22,23)\nIs there a path between node 21 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph342-11_6", + "image": "data/connectivity/graph_visual/medium/graph342.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,2) (0,7) (0,1) (0,6) (0,19) (0,15) (0,8) (0,16) (0,9) (1,2) (1,10) (1,12) (1,14) (1,19) (1,8) (2,10) (2,11) (2,12) (2,14) (2,7) (2,6) (2,15) (2,3) (2,8) (2,9) (3,11) (3,12) (3,14) (3,7) (3,19) (3,8) (3,16) (3,9) (4,20) (4,5) (4,18) (4,17) (5,13) (5,18) (5,17) (6,10) (6,11) (6,14) (6,7) (6,19) (6,8) (6,16) (7,12) (7,14) (7,19) (7,8) (7,16) (7,9) (8,11) (8,12) (8,14) (8,19) (8,16) (8,9) (9,14) (9,19) (9,15) (9,16) (10,11) (10,12) (10,14) (10,19) (10,15) (10,16) (11,14) (11,19) (11,16) (12,14) (12,19) (12,16) (13,18) (13,17) (14,19) (15,19) (15,16) (16,19) (17,20)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph460-4_6", + "image": "data/connectivity/graph_visual/medium/graph460.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,8) (0,1) (0,15) (0,12) (0,6) (0,14) (0,5) (0,2) (0,3) (0,16) (0,17) (0,11) (0,9) (0,7) (0,4) (0,20) (0,13) (0,10) (1,8) (1,15) (1,12) (1,6) (1,14) (1,5) (1,2) (1,3) (1,16) (1,17) (1,11) (1,9) (1,7) (1,4) (1,20) (1,13) (1,10) (2,8) (2,15) (2,12) (2,6) (2,14) (2,5) (2,3) (2,16) (2,17) (2,11) (2,9) (2,7) (2,4) (2,20) (2,13) (2,10) (3,8) (3,15) (3,12) (3,6) (3,14) (3,5) (3,16) (3,17) (3,11) (3,9) (3,7) (3,4) (3,20) (3,13) (3,10) (4,8) (4,15) (4,12) (4,6) (4,14) (4,5) (4,16) (4,17) (4,11) (4,9) (4,7) (4,20) (4,13) (4,10) (5,8) (5,15) (5,12) (5,6) (5,14) (5,16) (5,17) (5,11) (5,9) (5,7) (5,20) (5,13) (5,10) (6,8) (6,15) (6,12) (6,14) (6,16) (6,17) (6,11) (6,9) (6,7) (6,20) (6,13) (6,10) (7,8) (7,15) (7,12) (7,14) (7,16) (7,17) (7,11) (7,9) (7,20) (7,13) (7,10) (8,15) (8,12) (8,14) (8,16) (8,17) (8,11) (8,9) (8,20) (8,13) (8,10) (9,15) (9,12) (9,14) (9,16) (9,17) (9,11) (9,20) (9,13) (9,10) (10,15) (10,12) (10,14) (10,16) (10,17) (10,11) (10,20) (10,13) (11,15) (11,12) (11,14) (11,16) (11,17) (11,20) (11,13) (12,15) (12,14) (12,16) (12,17) (12,20) (12,13) (13,15) (13,14) (13,16) (13,17) (13,20) (14,15) (14,16) (14,17) (14,20) (15,16) (15,17) (15,20) (16,17) (16,20) (17,20) (18,21)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph526-21_19", + "image": "data/connectivity/graph_visual/medium/graph526.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,16) (0,9) (0,20) (0,8) (0,18) (0,4) (0,3) (0,1) (0,12) (0,15) (0,10) (0,14) (1,11) (1,17) (1,5) (1,22) (1,21) (1,9) (1,20) (1,8) (1,18) (1,3) (1,2) (1,10) (2,17) (2,5) (2,22) (2,16) (2,21) (2,20) (2,8) (2,18) (2,3) (2,12) (2,15) (3,11) (3,17) (3,5) (3,22) (3,16) (3,21) (3,9) (3,8) (3,18) (3,4) (3,15) (3,10) (4,17) (4,5) (4,22) (4,16) (4,9) (4,20) (4,8) (4,12) (4,10) (4,14) (5,16) (5,9) (5,20) (5,18) (5,10) (5,14) (7,13) (8,11) (8,17) (8,22) (8,16) (8,21) (8,9) (8,18) (8,12) (8,15) (8,10) (8,14) (9,11) (9,17) (9,16) (9,21) (9,20) (9,18) (9,10) (9,14) (10,11) (10,17) (10,22) (10,16) (10,21) (10,20) (10,18) (10,12) (10,15) (10,14) (11,22) (11,16) (11,21) (11,18) (11,15) (11,14) (12,22) (12,18) (12,14) (14,17) (14,20) (14,18) (14,15) (15,17) (15,22) (15,21) (15,20) (15,18) (16,17) (16,21) (16,20) (16,18) (17,22) (17,20) (17,18) (18,22) (18,21) (20,22) (21,22)\nIs there a path between node 21 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph568-5_0", + "image": "data/connectivity/graph_visual/medium/graph568.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,13) (0,16) (0,1) (1,9) (1,13) (1,16) (2,19) (2,4) (2,18) (2,23) (2,17) (3,5) (3,20) (3,15) (3,6) (3,11) (3,7) (3,10) (3,22) (3,12) (3,14) (3,8) (4,19) (4,18) (4,23) (4,17) (5,20) (5,15) (5,6) (5,11) (5,7) (5,10) (5,22) (5,12) (5,14) (5,8) (6,20) (6,15) (6,11) (6,7) (6,10) (6,22) (6,12) (6,14) (6,8) (7,20) (7,15) (7,11) (7,10) (7,22) (7,12) (7,14) (7,8) (8,20) (8,15) (8,11) (8,10) (8,22) (8,12) (8,14) (9,13) (9,16) (10,20) (10,15) (10,11) (10,22) (10,12) (10,14) (11,20) (11,15) (11,22) (11,12) (11,14) (12,20) (12,15) (12,22) (12,14) (13,16) (14,20) (14,15) (14,22) (15,20) (15,22) (17,19) (17,18) (17,23) (18,19) (18,23) (19,23) (20,22)\nIs there a path between node 5 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph695-1_11", + "image": "data/connectivity/graph_visual/medium/graph695.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,17) (0,16) (0,8) (0,22) (0,18) (0,6) (0,3) (1,12) (1,23) (1,9) (1,19) (1,11) (1,2) (1,14) (2,12) (2,23) (2,9) (2,19) (2,11) (2,14) (3,7) (3,17) (3,16) (3,8) (3,22) (3,18) (3,6) (4,13) (4,15) (4,10) (4,21) (4,5) (4,20) (5,13) (5,15) (5,10) (5,21) (5,20) (6,7) (6,17) (6,16) (6,8) (6,22) (6,18) (7,17) (7,16) (7,8) (7,22) (7,18) (8,17) (8,16) (8,22) (8,18) (9,12) (9,23) (9,19) (9,11) (9,14) (10,13) (10,15) (10,21) (10,20) (11,12) (11,23) (11,19) (11,14) (12,23) (12,19) (12,14) (13,15) (13,21) (13,20) (14,23) (14,19) (15,21) (15,20) (16,17) (16,22) (16,18) (17,22) (17,18) (18,22) (19,23) (20,21)\nIs there a path between node 1 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph406-6_16", + "image": "data/connectivity/graph_visual/medium/graph406.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,14) (0,13) (1,20) (1,12) (1,3) (1,15) (1,19) (2,3) (2,15) (3,11) (3,10) (4,20) (4,8) (4,19) (4,10) (5,9) (8,20) (8,15) (8,10) (9,13) (10,20) (11,15) (12,20) (12,15) (13,18) (15,20) (18,21) (19,20)\nIs there a path between node 6 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph6-4_0", + "image": "data/connectivity/graph_visual/medium/graph6.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (0,1) (1,2) (1,8) (3,7) (5,10) (6,9)\nIs there a path between node 4 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph145-15_12", + "image": "data/connectivity/graph_visual/medium/graph145.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,12) (0,4) (0,11) (0,17) (0,2) (0,5) (0,9) (0,8) (0,16) (0,10) (1,3) (1,12) (1,4) (1,11) (1,17) (1,7) (1,2) (1,5) (1,9) (1,8) (1,10) (2,3) (2,12) (2,4) (2,11) (2,17) (2,7) (2,5) (2,8) (2,16) (3,12) (3,7) (3,9) (3,8) (4,12) (4,11) (4,17) (4,5) (4,9) (4,8) (4,16) (4,10) (5,12) (5,11) (5,17) (5,7) (5,14) (5,9) (5,16) (5,10) (6,15) (6,13) (7,12) (7,11) (7,17) (7,9) (7,16) (7,10) (8,11) (8,14) (8,9) (8,16) (8,10) (9,12) (9,17) (9,10) (10,11) (10,17) (10,14) (10,16) (11,17) (11,16) (14,16) (16,17)\nIs there a path between node 15 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph326-16_6", + "image": "data/connectivity/graph_visual/medium/graph326.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,19) (0,17) (0,1) (0,4) (0,15) (0,2) (0,13) (0,10) (0,6) (0,18) (0,11) (0,12) (0,5) (1,19) (1,17) (1,4) (1,15) (1,2) (1,13) (1,10) (1,6) (1,18) (1,11) (1,12) (1,5) (2,19) (2,17) (2,4) (2,15) (2,13) (2,10) (2,6) (2,18) (2,11) (2,12) (2,5) (3,20) (3,16) (3,14) (3,8) (4,19) (4,17) (4,15) (4,13) (4,10) (4,6) (4,18) (4,11) (4,12) (4,5) (5,19) (5,17) (5,15) (5,13) (5,10) (5,6) (5,18) (5,11) (5,12) (6,19) (6,17) (6,15) (6,13) (6,10) (6,18) (6,11) (6,12) (7,9) (8,20) (8,16) (8,14) (10,19) (10,17) (10,15) (10,13) (10,18) (10,11) (10,12) (11,19) (11,17) (11,15) (11,13) (11,18) (11,12) (12,19) (12,17) (12,15) (12,13) (12,18) (13,19) (13,17) (13,15) (13,18) (14,20) (14,16) (15,19) (15,17) (15,18) (16,20) (17,19) (17,18) (18,19)\nIs there a path between node 16 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph516-14_21", + "image": "data/connectivity/graph_visual/medium/graph516.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,2) (0,11) (0,3) (0,19) (0,9) (0,1) (0,22) (0,13) (0,20) (0,4) (0,7) (0,10) (0,6) (0,14) (1,2) (1,11) (1,19) (1,18) (1,9) (1,21) (1,22) (1,13) (1,4) (1,7) (1,17) (1,14) (2,3) (2,19) (2,9) (2,21) (2,13) (2,12) (2,20) (2,4) (2,10) (2,17) (2,14) (3,11) (3,19) (3,18) (3,9) (3,21) (3,22) (3,13) (3,7) (3,10) (3,17) (3,6) (3,14) (4,19) (4,18) (4,9) (4,13) (4,12) (4,20) (4,7) (4,10) (4,14) (5,8) (5,15) (6,19) (6,18) (6,9) (6,21) (6,22) (6,13) (6,12) (6,20) (6,7) (7,11) (7,18) (7,9) (7,21) (7,22) (7,12) (7,10) (7,17) (7,14) (8,16) (8,15) (9,11) (9,19) (9,18) (9,21) (9,20) (9,10) (9,17) (9,14) (10,11) (10,21) (10,22) (10,13) (10,12) (10,20) (10,17) (10,14) (11,19) (11,18) (11,21) (11,22) (11,13) (11,12) (11,20) (11,17) (11,14) (12,18) (12,21) (12,13) (12,20) (12,17) (13,19) (13,22) (13,14) (14,19) (14,18) (14,21) (14,17) (15,16) (17,19) (17,21) (17,22) (17,20) (18,19) (18,21) (18,22) (18,20) (19,20) (20,21) (20,22) (21,22)\nIs there a path between node 14 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph821-21_22", + "image": "data/connectivity/graph_visual/medium/graph821.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,4) (0,19) (0,23) (0,11) (0,16) (0,5) (0,12) (0,13) (0,3) (0,15) (0,18) (0,10) (0,8) (0,22) (1,2) (3,17) (3,24) (3,4) (3,19) (3,6) (3,11) (3,16) (3,12) (3,13) (3,15) (3,18) (3,22) (4,17) (4,24) (4,14) (4,19) (4,6) (4,23) (4,16) (4,13) (4,18) (4,9) (4,22) (5,14) (5,23) (5,16) (5,12) (5,13) (5,15) (5,18) (5,10) (5,9) (5,8) (5,22) (6,17) (6,24) (6,19) (6,23) (6,16) (6,12) (6,13) (6,15) (6,9) (6,8) (6,22) (7,21) (8,17) (8,24) (8,14) (8,19) (8,12) (8,13) (8,15) (8,9) (8,22) (9,17) (9,14) (9,23) (9,16) (9,12) (9,18) (9,10) (10,17) (10,24) (10,14) (10,11) (10,12) (10,13) (10,15) (10,18) (11,17) (11,24) (11,19) (11,13) (11,15) (11,22) (12,24) (12,14) (12,19) (12,23) (12,16) (12,15) (13,17) (13,24) (13,14) (13,19) (13,23) (13,15) (13,18) (13,22) (14,17) (14,24) (14,16) (14,15) (14,18) (14,22) (15,17) (15,24) (15,23) (16,17) (16,24) (16,19) (16,23) (16,18) (16,22) (17,24) (17,19) (17,18) (17,22) (18,24) (18,23) (19,24) (19,23)\nIs there a path between node 21 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph792-14_0", + "image": "data/connectivity/graph_visual/medium/graph792.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,23) (1,6) (1,7) (1,3) (2,4) (2,22) (3,10) (3,12) (3,9) (4,13) (4,19) (4,5) (4,22) (5,22) (5,11) (6,16) (6,10) (7,24) (9,23) (9,10) (11,13) (11,18) (11,19) (11,22) (12,24) (13,18) (13,14) (16,23) (17,19) (18,20) (19,20)\nIs there a path between node 14 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph196-12_2", + "image": "data/connectivity/graph_visual/medium/graph196.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,2) (0,14) (0,7) (0,13) (1,17) (1,3) (1,10) (1,6) (2,11) (2,12) (2,14) (2,13) (3,17) (3,10) (3,6) (4,9) (4,5) (5,9) (5,16) (6,17) (6,8) (6,10) (7,11) (7,12) (7,14) (7,13) (8,17) (8,15) (9,18) (9,16) (10,17) (12,14) (12,13) (13,14) (15,17)\nIs there a path between node 12 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph251-2_4", + "image": "data/connectivity/graph_visual/medium/graph251.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,3) (0,1) (0,15) (0,9) (0,2) (0,6) (0,14) (0,8) (0,11) (0,10) (0,7) (1,13) (1,3) (1,15) (1,9) (1,2) (1,6) (1,14) (1,8) (1,11) (1,10) (1,7) (2,13) (2,3) (2,15) (2,9) (2,6) (2,14) (2,8) (2,11) (2,10) (2,7) (3,13) (3,15) (3,9) (3,6) (3,14) (3,8) (3,11) (3,10) (3,7) (4,12) (5,16) (5,18) (5,17) (6,13) (6,15) (6,9) (6,14) (6,8) (6,11) (6,10) (6,7) (7,13) (7,15) (7,9) (7,14) (7,8) (7,11) (7,10) (8,13) (8,15) (8,9) (8,14) (8,11) (8,10) (9,13) (9,15) (9,14) (9,11) (9,10) (10,13) (10,15) (10,14) (10,11) (11,13) (11,15) (11,14) (13,15) (13,14) (14,15) (16,18) (16,17) (17,18)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph764-4_1", + "image": "data/connectivity/graph_visual/medium/graph764.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,4) (0,24) (1,22) (1,13) (1,2) (1,18) (1,5) (1,3) (1,19) (1,7) (1,9) (1,21) (1,8) (1,10) (1,23) (1,6) (1,20) (1,14) (1,11) (1,16) (1,17) (1,15) (2,22) (2,13) (2,18) (2,5) (2,3) (2,19) (2,7) (2,9) (2,21) (2,8) (2,10) (2,23) (2,6) (2,20) (2,14) (2,11) (2,16) (2,17) (2,15) (3,22) (3,13) (3,18) (3,5) (3,19) (3,7) (3,9) (3,21) (3,8) (3,10) (3,23) (3,6) (3,20) (3,14) (3,11) (3,16) (3,17) (3,15) (4,12) (4,24) (5,22) (5,13) (5,18) (5,19) (5,7) (5,9) (5,21) (5,8) (5,10) (5,23) (5,6) (5,20) (5,14) (5,11) (5,16) (5,17) (5,15) (6,22) (6,13) (6,18) (6,19) (6,7) (6,9) (6,21) (6,8) (6,10) (6,23) (6,20) (6,14) (6,11) (6,16) (6,17) (6,15) (7,22) (7,13) (7,18) (7,19) (7,9) (7,21) (7,8) (7,10) (7,23) (7,20) (7,14) (7,11) (7,16) (7,17) (7,15) (8,22) (8,13) (8,18) (8,19) (8,9) (8,21) (8,10) (8,23) (8,20) (8,14) (8,11) (8,16) (8,17) (8,15) (9,22) (9,13) (9,18) (9,19) (9,21) (9,10) (9,23) (9,20) (9,14) (9,11) (9,16) (9,17) (9,15) (10,22) (10,13) (10,18) (10,19) (10,21) (10,23) (10,20) (10,14) (10,11) (10,16) (10,17) (10,15) (11,22) (11,13) (11,18) (11,19) (11,21) (11,23) (11,20) (11,14) (11,16) (11,17) (11,15) (12,24) (13,22) (13,18) (13,19) (13,21) (13,23) (13,20) (13,14) (13,16) (13,17) (13,15) (14,22) (14,18) (14,19) (14,21) (14,23) (14,20) (14,16) (14,17) (14,15) (15,22) (15,18) (15,19) (15,21) (15,23) (15,20) (15,16) (15,17) (16,22) (16,18) (16,19) (16,21) (16,23) (16,20) (16,17) (17,22) (17,18) (17,19) (17,21) (17,23) (17,20) (18,22) (18,19) (18,21) (18,23) (18,20) (19,22) (19,21) (19,23) (19,20) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph809-2_14", + "image": "data/connectivity/graph_visual/medium/graph809.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (1,23) (1,15) (1,8) (1,17) (1,19) (1,9) (1,12) (1,20) (1,10) (1,5) (1,22) (1,14) (1,4) (1,18) (1,21) (2,13) (2,3) (2,16) (3,16) (4,23) (4,15) (4,7) (4,17) (4,9) (4,12) (4,20) (4,5) (4,22) (4,14) (4,21) (5,23) (5,15) (5,8) (5,7) (5,19) (5,9) (5,20) (5,22) (5,14) (5,21) (6,24) (6,11) (7,15) (7,8) (7,17) (7,12) (7,20) (7,10) (7,18) (7,21) (8,15) (8,17) (8,19) (8,9) (8,22) (8,14) (8,18) (9,23) (9,15) (9,17) (9,19) (9,20) (9,10) (9,18) (9,21) (10,23) (10,19) (10,22) (10,14) (10,21) (12,23) (12,15) (12,17) (12,19) (12,22) (12,18) (14,15) (14,19) (14,20) (14,22) (14,18) (14,21) (15,19) (15,20) (15,22) (15,18) (17,23) (17,19) (17,20) (17,18) (17,21) (18,23) (18,22) (19,23) (19,20) (19,21) (20,22) (20,21) (21,22)\nIs there a path between node 2 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph72-8_10", + "image": "data/connectivity/graph_visual/medium/graph72.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (0,9) (1,10) (1,3) (2,6) (2,4) (2,7) (3,6) (3,10) (3,9) (3,12) (4,8) (5,9) (5,12) (6,9) (6,12) (6,7) (7,10) (7,9) (7,14) (8,10) (8,9) (8,14) (12,14)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph777-17_19", + "image": "data/connectivity/graph_visual/medium/graph777.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,3) (0,9) (0,12) (0,24) (0,2) (0,17) (0,20) (0,14) (0,13) (0,21) (0,7) (0,8) (0,15) (0,18) (0,5) (0,23) (0,16) (1,4) (1,19) (1,11) (1,22) (1,6) (2,10) (2,3) (2,9) (2,12) (2,24) (2,17) (2,20) (2,14) (2,13) (2,21) (2,7) (2,8) (2,15) (2,18) (2,5) (2,23) (2,16) (3,10) (3,9) (3,12) (3,24) (3,17) (3,20) (3,14) (3,13) (3,21) (3,7) (3,8) (3,15) (3,18) (3,5) (3,23) (3,16) (4,19) (4,11) (4,22) (4,6) (5,10) (5,9) (5,12) (5,24) (5,17) (5,20) (5,14) (5,13) (5,21) (5,7) (5,8) (5,15) (5,18) (5,23) (5,16) (6,19) (6,11) (6,22) (7,10) (7,9) (7,12) (7,24) (7,17) (7,20) (7,14) (7,13) (7,21) (7,8) (7,15) (7,18) (7,23) (7,16) (8,10) (8,9) (8,12) (8,24) (8,17) (8,20) (8,14) (8,13) (8,21) (8,15) (8,18) (8,23) (8,16) (9,10) (9,12) (9,24) (9,17) (9,20) (9,14) (9,13) (9,21) (9,15) (9,18) (9,23) (9,16) (10,12) (10,24) (10,17) (10,20) (10,14) (10,13) (10,21) (10,15) (10,18) (10,23) (10,16) (11,19) (11,22) (12,24) (12,17) (12,20) (12,14) (12,13) (12,21) (12,15) (12,18) (12,23) (12,16) (13,24) (13,17) (13,20) (13,14) (13,21) (13,15) (13,18) (13,23) (13,16) (14,24) (14,17) (14,20) (14,21) (14,15) (14,18) (14,23) (14,16) (15,24) (15,17) (15,20) (15,21) (15,18) (15,23) (15,16) (16,24) (16,17) (16,20) (16,21) (16,18) (16,23) (17,24) (17,20) (17,21) (17,18) (17,23) (18,24) (18,20) (18,21) (18,23) (19,22) (20,24) (20,21) (20,23) (21,24) (21,23) (23,24)\nIs there a path between node 17 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph742-23_13", + "image": "data/connectivity/graph_visual/medium/graph742.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,4) (0,5) (0,10) (0,22) (0,8) (3,9) (3,24) (3,11) (4,21) (4,13) (5,13) (7,9) (8,21) (8,17) (8,18) (9,20) (10,21) (10,22) (13,14) (13,18) (14,18) (15,19) (15,16) (21,22)\nIs there a path between node 23 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph229-14_12", + "image": "data/connectivity/graph_visual/medium/graph229.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,7) (0,4) (1,18) (1,6) (1,13) (2,16) (2,12) (2,6) (3,5) (3,10) (3,17) (3,13) (4,7) (5,18) (5,6) (5,15) (5,10) (5,17) (10,15) (10,14) (11,17) (12,13) (12,14) (14,18) (14,15) (15,17) (16,18)\nIs there a path between node 14 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph218-16_10", + "image": "data/connectivity/graph_visual/medium/graph218.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,14) (0,3) (0,13) (0,18) (0,16) (0,4) (0,10) (0,8) (0,12) (0,15) (0,11) (0,1) (1,14) (1,3) (1,13) (1,18) (1,16) (1,4) (1,10) (1,8) (1,12) (1,15) (1,11) (2,17) (2,6) (2,7) (2,5) (2,9) (3,14) (3,13) (3,18) (3,16) (3,4) (3,10) (3,8) (3,12) (3,15) (3,11) (4,14) (4,13) (4,18) (4,16) (4,10) (4,8) (4,12) (4,15) (4,11) (5,17) (5,6) (5,7) (5,9) (6,17) (6,7) (6,9) (7,17) (7,9) (8,14) (8,13) (8,18) (8,16) (8,10) (8,12) (8,15) (8,11) (9,17) (10,14) (10,13) (10,18) (10,16) (10,12) (10,15) (10,11) (11,14) (11,13) (11,18) (11,16) (11,12) (11,15) (12,14) (12,13) (12,18) (12,16) (12,15) (13,14) (13,18) (13,16) (13,15) (14,18) (14,16) (14,15) (15,18) (15,16) (16,18)\nIs there a path between node 16 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph697-16_23", + "image": "data/connectivity/graph_visual/medium/graph697.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,6) (0,21) (0,17) (0,16) (0,20) (0,7) (0,12) (0,14) (0,22) (0,15) (1,18) (1,4) (1,2) (1,10) (1,3) (1,23) (1,19) (1,11) (1,9) (1,13) (1,8) (2,18) (2,4) (2,10) (2,3) (2,23) (2,19) (2,11) (2,9) (2,13) (2,8) (3,18) (3,4) (3,10) (3,23) (3,19) (3,11) (3,9) (3,13) (3,8) (4,18) (4,10) (4,23) (4,19) (4,11) (4,9) (4,13) (4,8) (5,6) (5,21) (5,17) (5,16) (5,20) (5,7) (5,12) (5,14) (5,22) (5,15) (6,21) (6,17) (6,16) (6,20) (6,7) (6,12) (6,14) (6,22) (6,15) (7,21) (7,17) (7,16) (7,20) (7,12) (7,14) (7,22) (7,15) (8,18) (8,10) (8,23) (8,19) (8,11) (8,9) (8,13) (9,18) (9,10) (9,23) (9,19) (9,11) (9,13) (10,18) (10,23) (10,19) (10,11) (10,13) (11,18) (11,23) (11,19) (11,13) (12,21) (12,17) (12,16) (12,20) (12,14) (12,22) (12,15) (13,18) (13,23) (13,19) (14,21) (14,17) (14,16) (14,20) (14,22) (14,15) (15,21) (15,17) (15,16) (15,20) (15,22) (16,21) (16,17) (16,20) (16,22) (17,21) (17,20) (17,22) (18,23) (18,19) (19,23) (20,21) (20,22) (21,22)\nIs there a path between node 16 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph798-7_14", + "image": "data/connectivity/graph_visual/medium/graph798.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (0,12) (0,11) (0,10) (1,23) (2,24) (2,22) (2,6) (3,21) (3,7) (4,24) (4,12) (4,6) (4,14) (4,15) (4,9) (4,5) (5,18) (5,12) (5,14) (5,11) (6,15) (6,9) (7,17) (7,13) (8,14) (8,9) (9,22) (9,12) (10,19) (10,24) (10,22) (10,14) (10,11) (11,22) (12,24) (13,21) (13,20) (14,19) (14,16) (14,15) (15,19) (17,23) (18,19) (18,24) (19,22)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph677-9_4", + "image": "data/connectivity/graph_visual/medium/graph677.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,4) (0,9) (0,19) (0,14) (0,17) (0,7) (0,6) (0,5) (0,16) (0,13) (0,22) (0,12) (0,15) (0,23) (1,3) (1,2) (1,21) (1,8) (1,20) (2,3) (2,21) (2,8) (2,20) (3,21) (3,8) (3,20) (4,11) (4,9) (4,19) (4,14) (4,17) (4,7) (4,6) (4,5) (4,16) (4,13) (4,22) (4,12) (4,15) (4,23) (5,11) (5,9) (5,19) (5,14) (5,17) (5,7) (5,6) (5,16) (5,13) (5,22) (5,12) (5,15) (5,23) (6,11) (6,9) (6,19) (6,14) (6,17) (6,7) (6,16) (6,13) (6,22) (6,12) (6,15) (6,23) (7,11) (7,9) (7,19) (7,14) (7,17) (7,16) (7,13) (7,22) (7,12) (7,15) (7,23) (8,21) (8,20) (9,11) (9,19) (9,14) (9,17) (9,16) (9,13) (9,22) (9,12) (9,15) (9,23) (11,19) (11,14) (11,17) (11,16) (11,13) (11,22) (11,12) (11,15) (11,23) (12,19) (12,14) (12,17) (12,16) (12,13) (12,22) (12,15) (12,23) (13,19) (13,14) (13,17) (13,16) (13,22) (13,15) (13,23) (14,19) (14,17) (14,16) (14,22) (14,15) (14,23) (15,19) (15,17) (15,16) (15,22) (15,23) (16,19) (16,17) (16,22) (16,23) (17,19) (17,22) (17,23) (19,22) (19,23) (20,21) (22,23)\nIs there a path between node 9 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph691-20_0", + "image": "data/connectivity/graph_visual/medium/graph691.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,23) (0,3) (0,7) (0,9) (0,21) (0,13) (0,16) (0,6) (0,8) (0,12) (1,5) (1,22) (1,15) (1,14) (1,18) (1,17) (1,20) (1,11) (1,2) (2,5) (2,22) (2,15) (2,14) (2,18) (2,17) (2,20) (2,11) (3,10) (3,19) (3,23) (3,7) (3,9) (3,21) (3,13) (3,16) (3,6) (3,8) (3,12) (5,22) (5,15) (5,14) (5,18) (5,17) (5,20) (5,11) (6,10) (6,19) (6,23) (6,7) (6,9) (6,21) (6,13) (6,16) (6,8) (6,12) (7,10) (7,19) (7,23) (7,9) (7,21) (7,13) (7,16) (7,8) (7,12) (8,10) (8,19) (8,23) (8,9) (8,21) (8,13) (8,16) (8,12) (9,10) (9,19) (9,23) (9,21) (9,13) (9,16) (9,12) (10,19) (10,23) (10,21) (10,13) (10,16) (10,12) (11,22) (11,15) (11,14) (11,18) (11,17) (11,20) (12,19) (12,23) (12,21) (12,13) (12,16) (13,19) (13,23) (13,21) (13,16) (14,22) (14,15) (14,18) (14,17) (14,20) (15,22) (15,18) (15,17) (15,20) (16,19) (16,23) (16,21) (17,22) (17,18) (17,20) (18,22) (18,20) (19,23) (19,21) (20,22) (21,23)\nIs there a path between node 20 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph273-13_6", + "image": "data/connectivity/graph_visual/medium/graph273.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,18) (0,5) (0,19) (0,11) (0,8) (0,6) (0,14) (0,10) (1,7) (1,2) (2,7) (2,17) (3,9) (3,18) (3,13) (3,19) (3,11) (3,16) (3,8) (3,6) (3,14) (3,10) (4,9) (4,13) (4,5) (4,15) (4,19) (4,11) (4,16) (4,8) (4,6) (4,10) (5,9) (5,18) (5,13) (5,15) (5,19) (5,11) (5,8) (5,14) (5,10) (6,13) (6,12) (6,15) (6,19) (6,11) (6,16) (6,8) (6,10) (7,17) (8,9) (8,13) (8,12) (8,15) (8,14) (8,10) (9,18) (9,12) (9,19) (9,16) (9,14) (9,10) (10,18) (10,13) (10,12) (10,15) (10,19) (10,16) (10,14) (11,15) (11,19) (11,16) (12,13) (12,19) (13,15) (13,19) (13,16) (14,18) (14,16) (15,18) (15,16) (16,18) (16,19)\nIs there a path between node 13 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph290-5_16", + "image": "data/connectivity/graph_visual/medium/graph290.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,5) (0,4) (1,6) (1,14) (1,2) (3,18) (3,4) (4,5) (4,15) (6,11) (6,16) (6,14) (6,10) (6,19) (6,12) (6,9) (7,8) (9,13) (9,10) (9,17) (9,19) (10,13) (10,12) (11,16) (11,14) (11,13) (12,17) (12,19) (13,16) (13,14) (14,19) (16,17)\nIs there a path between node 5 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph770-11_1", + "image": "data/connectivity/graph_visual/medium/graph770.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,24) (0,6) (0,5) (0,7) (0,17) (0,21) (0,10) (0,18) (0,14) (1,13) (1,19) (1,3) (1,12) (1,4) (1,11) (2,9) (2,8) (2,15) (3,13) (3,19) (3,12) (3,4) (3,11) (4,13) (4,19) (4,12) (4,11) (5,20) (5,24) (5,6) (5,7) (5,17) (5,21) (5,10) (5,18) (5,14) (6,20) (6,24) (6,7) (6,17) (6,21) (6,10) (6,18) (6,14) (7,20) (7,24) (7,17) (7,21) (7,10) (7,18) (7,14) (8,9) (8,15) (9,15) (10,20) (10,24) (10,17) (10,21) (10,18) (10,14) (11,13) (11,19) (11,12) (12,13) (12,19) (13,19) (14,20) (14,24) (14,17) (14,21) (14,18) (16,22) (16,23) (17,20) (17,24) (17,21) (17,18) (18,20) (18,24) (18,21) (20,24) (20,21) (21,24) (22,23)\nIs there a path between node 11 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph426-2_0", + "image": "data/connectivity/graph_visual/medium/graph426.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,8) (0,18) (0,10) (0,2) (0,20) (1,10) (1,17) (1,21) (3,4) (3,18) (4,18) (4,9) (5,16) (7,19) (7,13) (8,18) (8,10) (8,20) (8,21) (9,17) (9,21) (10,17) (12,13) (13,16) (14,15) (17,21) (18,21)\nIs there a path between node 2 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph584-21_9", + "image": "data/connectivity/graph_visual/medium/graph584.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,22) (0,7) (1,21) (1,15) (1,11) (2,18) (2,3) (2,19) (3,18) (3,7) (4,16) (4,20) (5,21) (5,9) (6,16) (6,23) (7,15) (7,9) (7,22) (7,8) (8,19) (9,21) (9,11) (10,12) (10,23) (11,22) (13,17) (13,15) (13,22) (15,21) (15,19) (17,19) (18,21) (18,19)\nIs there a path between node 21 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph58-8_9", + "image": "data/connectivity/graph_visual/medium/graph58.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (0,1) (1,3) (1,11) (1,2) (1,4) (2,9) (2,12) (3,8) (4,12) (5,11) (5,8) (5,7) (6,13) (10,12)\nIs there a path between node 8 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph257-14_9", + "image": "data/connectivity/graph_visual/medium/graph257.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,16) (0,18) (0,4) (0,2) (0,13) (0,15) (0,6) (0,14) (0,10) (1,3) (1,5) (1,8) (1,17) (1,11) (1,12) (1,9) (1,7) (2,16) (2,18) (2,4) (2,13) (2,15) (2,6) (2,14) (2,10) (3,5) (3,8) (3,17) (3,11) (3,12) (3,9) (3,7) (4,16) (4,18) (4,13) (4,15) (4,6) (4,14) (4,10) (5,8) (5,17) (5,11) (5,12) (5,9) (5,7) (6,16) (6,18) (6,13) (6,15) (6,14) (6,10) (7,8) (7,17) (7,11) (7,12) (7,9) (8,17) (8,11) (8,12) (8,9) (9,17) (9,11) (9,12) (10,16) (10,18) (10,13) (10,15) (10,14) (11,17) (11,12) (12,17) (13,16) (13,18) (13,15) (13,14) (14,16) (14,18) (14,15) (15,16) (15,18) (16,18)\nIs there a path between node 14 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph634-10_0", + "image": "data/connectivity/graph_visual/medium/graph634.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,9) (0,18) (0,2) (0,14) (0,20) (0,22) (0,4) (0,1) (0,19) (1,23) (1,2) (1,16) (1,20) (1,22) (1,11) (1,4) (1,12) (2,3) (2,5) (2,7) (2,9) (2,18) (2,16) (2,14) (2,20) (2,8) (2,4) (2,19) (3,15) (3,5) (3,18) (3,16) (3,8) (3,22) (3,11) (4,15) (4,5) (4,18) (4,11) (4,12) (4,19) (5,23) (5,15) (5,16) (5,12) (5,19) (6,17) (7,18) (7,14) (7,20) (8,15) (8,18) (8,21) (12,21) (12,22) (12,19) (14,23) (14,19) (15,19) (16,18) (18,19) (19,23) (19,20) (19,22) (20,23)\nIs there a path between node 10 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph353-0_6", + "image": "data/connectivity/graph_visual/medium/graph353.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,14) (0,17) (0,8) (0,5) (0,3) (0,18) (0,10) (1,4) (2,5) (2,3) (2,9) (2,15) (2,19) (3,8) (3,9) (4,7) (5,14) (5,12) (5,11) (5,18) (6,20) (6,15) (8,13) (8,18) (9,20) (9,13) (9,18) (9,19) (10,16) (10,20) (10,14) (10,19) (11,20) (11,17) (11,15) (13,14) (13,19) (15,16) (15,17) (16,19) (17,20) (17,18) (19,20)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph124-15_6", + "image": "data/connectivity/graph_visual/medium/graph124.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,12) (0,4) (0,7) (0,15) (0,2) (0,5) (0,11) (0,8) (0,14) (0,13) (0,10) (0,1) (1,4) (1,7) (1,15) (1,9) (1,2) (1,5) (1,11) (1,8) (1,14) (1,16) (1,10) (2,7) (2,15) (2,9) (2,6) (2,5) (2,11) (2,8) (2,14) (2,16) (2,13) (2,10) (4,12) (4,7) (4,9) (4,6) (4,5) (4,8) (4,16) (4,13) (4,10) (5,12) (5,7) (5,15) (5,9) (5,6) (5,16) (5,13) (5,10) (6,12) (6,15) (6,9) (6,14) (6,16) (7,12) (7,11) (7,8) (7,16) (7,10) (8,12) (8,9) (8,11) (8,14) (8,16) (8,10) (9,11) (10,12) (10,15) (10,14) (10,16) (10,13) (11,15) (11,14) (11,16) (11,13) (12,15) (12,14) (12,16) (12,13) (13,15) (14,15) (14,16) (15,16)\nIs there a path between node 15 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph764-21_23", + "image": "data/connectivity/graph_visual/medium/graph764.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,4) (0,24) (1,22) (1,13) (1,2) (1,18) (1,5) (1,3) (1,19) (1,7) (1,9) (1,21) (1,8) (1,10) (1,23) (1,6) (1,20) (1,14) (1,11) (1,16) (1,17) (1,15) (2,22) (2,13) (2,18) (2,5) (2,3) (2,19) (2,7) (2,9) (2,21) (2,8) (2,10) (2,23) (2,6) (2,20) (2,14) (2,11) (2,16) (2,17) (2,15) (3,22) (3,13) (3,18) (3,5) (3,19) (3,7) (3,9) (3,21) (3,8) (3,10) (3,23) (3,6) (3,20) (3,14) (3,11) (3,16) (3,17) (3,15) (4,12) (4,24) (5,22) (5,13) (5,18) (5,19) (5,7) (5,9) (5,21) (5,8) (5,10) (5,23) (5,6) (5,20) (5,14) (5,11) (5,16) (5,17) (5,15) (6,22) (6,13) (6,18) (6,19) (6,7) (6,9) (6,21) (6,8) (6,10) (6,23) (6,20) (6,14) (6,11) (6,16) (6,17) (6,15) (7,22) (7,13) (7,18) (7,19) (7,9) (7,21) (7,8) (7,10) (7,23) (7,20) (7,14) (7,11) (7,16) (7,17) (7,15) (8,22) (8,13) (8,18) (8,19) (8,9) (8,21) (8,10) (8,23) (8,20) (8,14) (8,11) (8,16) (8,17) (8,15) (9,22) (9,13) (9,18) (9,19) (9,21) (9,10) (9,23) (9,20) (9,14) (9,11) (9,16) (9,17) (9,15) (10,22) (10,13) (10,18) (10,19) (10,21) (10,23) (10,20) (10,14) (10,11) (10,16) (10,17) (10,15) (11,22) (11,13) (11,18) (11,19) (11,21) (11,23) (11,20) (11,14) (11,16) (11,17) (11,15) (12,24) (13,22) (13,18) (13,19) (13,21) (13,23) (13,20) (13,14) (13,16) (13,17) (13,15) (14,22) (14,18) (14,19) (14,21) (14,23) (14,20) (14,16) (14,17) (14,15) (15,22) (15,18) (15,19) (15,21) (15,23) (15,20) (15,16) (15,17) (16,22) (16,18) (16,19) (16,21) (16,23) (16,20) (16,17) (17,22) (17,18) (17,19) (17,21) (17,23) (17,20) (18,22) (18,19) (18,21) (18,23) (18,20) (19,22) (19,21) (19,23) (19,20) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 21 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph185-7_4", + "image": "data/connectivity/graph_visual/medium/graph185.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,7) (0,9) (0,6) (0,16) (0,3) (0,13) (0,15) (0,4) (0,8) (1,5) (1,17) (1,12) (1,14) (1,2) (2,5) (2,17) (2,12) (2,14) (3,7) (3,9) (3,6) (3,16) (3,13) (3,15) (3,4) (3,8) (4,7) (4,9) (4,6) (4,16) (4,13) (4,15) (4,8) (5,17) (5,12) (5,14) (6,7) (6,9) (6,16) (6,13) (6,15) (6,8) (7,9) (7,16) (7,13) (7,15) (7,8) (8,9) (8,16) (8,13) (8,15) (9,16) (9,13) (9,15) (10,11) (12,17) (12,14) (13,16) (13,15) (14,17) (15,16)\nIs there a path between node 7 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph73-6_0", + "image": "data/connectivity/graph_visual/medium/graph73.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (0,12) (0,5) (1,12) (1,8) (2,3) (2,8) (2,5) (3,9) (3,10) (3,12) (3,8) (5,12) (6,13) (7,10) (7,14) (8,10) (9,10) (12,14)\nIs there a path between node 6 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph652-19_13", + "image": "data/connectivity/graph_visual/medium/graph652.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,4) (0,23) (0,18) (0,16) (0,13) (0,6) (0,3) (0,14) (1,15) (1,19) (1,2) (1,9) (1,22) (1,8) (1,21) (1,12) (1,20) (2,15) (2,19) (2,9) (2,22) (2,21) (2,12) (2,20) (3,5) (3,7) (3,23) (3,18) (3,13) (3,6) (3,11) (3,14) (4,5) (4,18) (4,16) (4,13) (4,10) (4,6) (4,11) (5,7) (5,23) (5,16) (5,13) (5,10) (5,6) (5,11) (5,14) (6,7) (6,23) (6,10) (6,11) (6,14) (7,18) (7,10) (7,11) (7,14) (8,15) (8,9) (8,17) (8,21) (8,12) (9,15) (9,19) (9,17) (9,21) (9,12) (9,20) (10,23) (10,18) (10,16) (10,13) (10,11) (10,14) (11,18) (11,16) (11,13) (12,15) (12,22) (12,21) (12,20) (13,18) (13,16) (14,23) (14,18) (15,19) (15,17) (15,21) (15,20) (16,23) (16,18) (17,22) (17,21) (17,20) (18,23) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 19 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph603-3_7", + "image": "data/connectivity/graph_visual/medium/graph603.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,11) (0,20) (1,4) (1,14) (1,15) (1,16) (1,22) (2,4) (2,14) (2,15) (2,16) (3,4) (3,14) (3,15) (3,16) (4,14) (4,15) (4,16) (5,11) (6,12) (6,19) (6,7) (6,13) (6,9) (6,17) (7,18) (7,21) (7,13) (7,9) (7,17) (8,20) (9,18) (9,19) (9,13) (9,10) (9,17) (10,12) (10,21) (10,13) (12,18) (12,21) (12,19) (12,13) (12,17) (13,18) (13,21) (13,19) (13,17) (14,15) (14,22) (15,22) (17,18) (17,19) (18,21) (18,19) (19,21)\nIs there a path between node 3 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph838-13_8", + "image": "data/connectivity/graph_visual/medium/graph838.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,22) (1,18) (1,7) (1,23) (1,2) (1,24) (1,9) (1,21) (1,14) (1,17) (1,16) (1,3) (1,15) (1,6) (1,19) (2,18) (2,7) (2,23) (2,24) (2,9) (2,21) (2,14) (2,17) (2,16) (2,3) (2,15) (2,6) (2,19) (3,18) (3,7) (3,23) (3,24) (3,9) (3,21) (3,14) (3,17) (3,16) (3,15) (3,6) (3,19) (4,11) (4,20) (4,13) (4,5) (4,8) (4,10) (4,12) (5,11) (5,20) (5,13) (5,8) (5,10) (5,12) (6,18) (6,7) (6,23) (6,24) (6,9) (6,21) (6,14) (6,17) (6,16) (6,15) (6,19) (7,18) (7,23) (7,24) (7,9) (7,21) (7,14) (7,17) (7,16) (7,15) (7,19) (8,11) (8,20) (8,13) (8,10) (8,12) (9,18) (9,23) (9,24) (9,21) (9,14) (9,17) (9,16) (9,15) (9,19) (10,11) (10,20) (10,13) (10,12) (11,20) (11,13) (11,12) (12,20) (12,13) (13,20) (14,18) (14,23) (14,24) (14,21) (14,17) (14,16) (14,15) (14,19) (15,18) (15,23) (15,24) (15,21) (15,17) (15,16) (15,19) (16,18) (16,23) (16,24) (16,21) (16,17) (16,19) (17,18) (17,23) (17,24) (17,21) (17,19) (18,23) (18,24) (18,21) (18,19) (19,23) (19,24) (19,21) (21,23) (21,24) (23,24)\nIs there a path between node 13 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph414-4_16", + "image": "data/connectivity/graph_visual/medium/graph414.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,1) (0,18) (1,18) (1,14) (1,11) (2,4) (2,21) (2,15) (2,9) (2,12) (2,8) (2,3) (2,10) (3,4) (3,9) (3,12) (3,5) (3,20) (3,8) (3,17) (3,10) (3,19) (4,21) (4,15) (4,12) (4,6) (4,5) (4,17) (4,19) (5,21) (5,9) (5,6) (5,20) (5,8) (5,10) (6,15) (6,9) (6,12) (6,8) (6,10) (6,19) (7,13) (8,21) (8,15) (8,9) (8,12) (8,17) (8,10) (8,19) (9,21) (9,20) (9,19) (10,21) (10,20) (10,17) (11,14) (12,21) (12,15) (12,20) (12,19) (14,16) (15,20) (15,17) (17,21) (17,20) (17,19) (19,21)\nIs there a path between node 4 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph533-19_2", + "image": "data/connectivity/graph_visual/medium/graph533.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,2) (0,8) (0,14) (0,18) (0,12) (0,20) (0,1) (0,11) (0,10) (0,3) (0,17) (0,4) (0,9) (0,21) (0,19) (1,2) (1,8) (1,14) (1,18) (1,12) (1,20) (1,11) (1,10) (1,3) (1,17) (1,4) (1,9) (1,21) (1,19) (2,8) (2,14) (2,18) (2,12) (2,20) (2,11) (2,10) (2,3) (2,17) (2,4) (2,9) (2,21) (2,19) (3,8) (3,14) (3,18) (3,12) (3,20) (3,11) (3,10) (3,17) (3,4) (3,9) (3,21) (3,19) (4,8) (4,14) (4,18) (4,12) (4,20) (4,11) (4,10) (4,17) (4,9) (4,21) (4,19) (5,16) (5,6) (5,13) (5,7) (5,15) (5,22) (6,16) (6,13) (6,7) (6,15) (6,22) (7,16) (7,13) (7,15) (7,22) (8,14) (8,18) (8,12) (8,20) (8,11) (8,10) (8,17) (8,9) (8,21) (8,19) (9,14) (9,18) (9,12) (9,20) (9,11) (9,10) (9,17) (9,21) (9,19) (10,14) (10,18) (10,12) (10,20) (10,11) (10,17) (10,21) (10,19) (11,14) (11,18) (11,12) (11,20) (11,17) (11,21) (11,19) (12,14) (12,18) (12,20) (12,17) (12,21) (12,19) (13,16) (13,15) (13,22) (14,18) (14,20) (14,17) (14,21) (14,19) (15,16) (15,22) (16,22) (17,18) (17,20) (17,21) (17,19) (18,20) (18,21) (18,19) (19,20) (19,21) (20,21)\nIs there a path between node 19 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph737-13_21", + "image": "data/connectivity/graph_visual/medium/graph737.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,3) (0,16) (0,24) (0,7) (1,17) (1,2) (2,9) (2,20) (2,8) (3,22) (3,12) (3,23) (3,21) (4,9) (4,13) (4,18) (5,11) (5,23) (5,21) (6,15) (6,7) (7,11) (7,22) (7,12) (7,16) (7,23) (7,14) (7,21) (8,20) (8,17) (8,18) (10,20) (10,17) (10,18) (11,21) (12,22) (12,14) (14,22) (15,16) (15,24) (16,23) (17,18) (19,21) (21,24) (22,24)\nIs there a path between node 13 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph556-12_15", + "image": "data/connectivity/graph_visual/medium/graph556.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,20) (0,7) (0,2) (1,16) (1,18) (1,4) (1,23) (1,15) (1,19) (1,6) (1,5) (1,12) (2,8) (2,10) (2,22) (2,7) (2,13) (3,21) (4,16) (4,18) (4,23) (4,11) (4,17) (4,15) (4,19) (4,6) (4,12) (5,16) (5,18) (5,14) (5,11) (5,17) (5,15) (5,19) (5,6) (5,12) (6,16) (6,18) (6,14) (6,11) (6,17) (6,15) (6,12) (7,8) (7,10) (7,22) (7,20) (7,13) (8,9) (8,10) (8,22) (8,20) (8,13) (9,22) (9,13) (10,22) (10,20) (10,13) (11,16) (11,18) (11,14) (11,23) (11,17) (11,15) (11,19) (11,12) (12,16) (12,18) (12,14) (12,23) (12,17) (12,15) (12,19) (13,22) (13,20) (14,18) (14,23) (14,17) (14,15) (15,16) (15,18) (15,23) (15,17) (15,19) (16,23) (17,18) (17,23) (17,19) (18,23) (18,19) (19,23) (20,22)\nIs there a path between node 12 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph250-7_4", + "image": "data/connectivity/graph_visual/medium/graph250.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,15) (0,1) (0,9) (0,7) (0,18) (0,3) (0,13) (0,14) (0,11) (0,6) (0,17) (0,10) (0,2) (0,12) (1,15) (1,9) (1,7) (1,18) (1,3) (1,13) (1,14) (1,11) (1,6) (1,17) (1,10) (1,2) (1,12) (2,15) (2,9) (2,7) (2,18) (2,3) (2,13) (2,14) (2,11) (2,6) (2,17) (2,10) (2,12) (3,15) (3,9) (3,7) (3,18) (3,13) (3,14) (3,11) (3,6) (3,17) (3,10) (3,12) (4,16) (4,5) (4,8) (5,16) (5,8) (6,15) (6,9) (6,7) (6,18) (6,13) (6,14) (6,11) (6,17) (6,10) (6,12) (7,15) (7,9) (7,18) (7,13) (7,14) (7,11) (7,17) (7,10) (7,12) (8,16) (9,15) (9,18) (9,13) (9,14) (9,11) (9,17) (9,10) (9,12) (10,15) (10,18) (10,13) (10,14) (10,11) (10,17) (10,12) (11,15) (11,18) (11,13) (11,14) (11,17) (11,12) (12,15) (12,18) (12,13) (12,14) (12,17) (13,15) (13,18) (13,14) (13,17) (14,15) (14,18) (14,17) (15,18) (15,17) (17,18)\nIs there a path between node 7 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph3-5_6", + "image": "data/connectivity/graph_visual/medium/graph3.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nIs there a path between node 5 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph613-23_2", + "image": "data/connectivity/graph_visual/medium/graph613.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,17) (0,8) (0,22) (0,21) (0,12) (0,6) (0,3) (0,11) (0,20) (0,7) (0,18) (0,19) (0,13) (0,16) (0,4) (0,14) (0,1) (1,9) (1,17) (1,8) (1,22) (1,21) (1,12) (1,6) (1,3) (1,11) (1,20) (1,7) (1,18) (1,19) (1,13) (1,16) (1,4) (1,14) (2,5) (2,15) (2,10) (2,23) (3,9) (3,17) (3,8) (3,22) (3,21) (3,12) (3,6) (3,11) (3,20) (3,7) (3,18) (3,19) (3,13) (3,16) (3,4) (3,14) (4,9) (4,17) (4,8) (4,22) (4,21) (4,12) (4,6) (4,11) (4,20) (4,7) (4,18) (4,19) (4,13) (4,16) (4,14) (5,15) (5,10) (5,23) (6,9) (6,17) (6,8) (6,22) (6,21) (6,12) (6,11) (6,20) (6,7) (6,18) (6,19) (6,13) (6,16) (6,14) (7,9) (7,17) (7,8) (7,22) (7,21) (7,12) (7,11) (7,20) (7,18) (7,19) (7,13) (7,16) (7,14) (8,9) (8,17) (8,22) (8,21) (8,12) (8,11) (8,20) (8,18) (8,19) (8,13) (8,16) (8,14) (9,17) (9,22) (9,21) (9,12) (9,11) (9,20) (9,18) (9,19) (9,13) (9,16) (9,14) (10,15) (10,23) (11,17) (11,22) (11,21) (11,12) (11,20) (11,18) (11,19) (11,13) (11,16) (11,14) (12,17) (12,22) (12,21) (12,20) (12,18) (12,19) (12,13) (12,16) (12,14) (13,17) (13,22) (13,21) (13,20) (13,18) (13,19) (13,16) (13,14) (14,17) (14,22) (14,21) (14,20) (14,18) (14,19) (14,16) (15,23) (16,17) (16,22) (16,21) (16,20) (16,18) (16,19) (17,22) (17,21) (17,20) (17,18) (17,19) (18,22) (18,21) (18,20) (18,19) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 23 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph735-24_10", + "image": "data/connectivity/graph_visual/medium/graph735.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (0,3) (1,9) (1,17) (1,5) (1,24) (2,9) (2,21) (2,11) (2,15) (2,14) (2,16) (3,19) (3,18) (4,10) (4,13) (4,15) (5,7) (5,17) (5,15) (5,24) (6,23) (7,20) (7,17) (7,24) (8,20) (8,21) (8,10) (8,13) (8,11) (8,24) (9,23) (9,10) (9,13) (9,14) (9,24) (10,12) (10,17) (10,11) (11,20) (11,17) (11,15) (12,21) (12,13) (12,15) (12,14) (13,20) (13,17) (13,14) (13,24) (14,23) (14,15) (15,20) (15,23) (15,16) (16,21) (16,23) (16,17) (16,24) (17,20) (17,21) (18,19) (21,24) (23,24)\nIs there a path between node 24 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph785-23_15", + "image": "data/connectivity/graph_visual/medium/graph785.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,15) (0,24) (0,1) (0,10) (1,3) (1,8) (2,13) (3,15) (3,14) (3,10) (4,17) (5,15) (5,24) (7,13) (8,11) (8,16) (8,10) (9,22) (9,20) (10,14) (11,15) (11,24) (13,19) (14,15) (14,18) (15,24) (16,24) (20,22)\nIs there a path between node 23 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph544-17_3", + "image": "data/connectivity/graph_visual/medium/graph544.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,15) (0,6) (0,17) (0,4) (0,12) (0,16) (0,9) (1,14) (1,23) (1,18) (1,19) (1,3) (1,21) (2,14) (2,5) (2,11) (2,23) (2,22) (2,8) (2,18) (2,19) (2,3) (2,20) (3,14) (3,5) (3,23) (3,22) (3,8) (3,18) (3,19) (3,20) (3,21) (4,7) (4,15) (4,6) (4,17) (4,13) (4,10) (4,16) (5,14) (5,8) (5,18) (5,19) (5,21) (6,13) (6,10) (6,16) (6,9) (7,15) (7,13) (7,9) (8,14) (8,11) (8,23) (8,22) (8,18) (8,19) (8,20) (8,21) (9,15) (9,13) (9,12) (9,16) (10,15) (10,17) (10,13) (10,12) (11,14) (11,23) (11,22) (11,18) (11,19) (12,17) (12,16) (13,17) (13,16) (14,23) (14,19) (15,17) (16,17) (18,23) (18,22) (18,19) (18,21) (19,23) (19,22) (19,20) (20,23) (20,21) (21,23) (22,23)\nIs there a path between node 17 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph258-12_5", + "image": "data/connectivity/graph_visual/medium/graph258.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,2) (1,18) (1,12) (1,15) (1,7) (2,17) (2,3) (3,17) (4,12) (5,17) (5,19) (6,18) (6,10) (6,9) (6,12) (6,16) (7,18) (7,9) (7,13) (7,8) (8,14) (9,18) (9,14) (9,12) (9,13) (10,12) (10,15) (11,17) (12,16) (14,18)\nIs there a path between node 12 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph212-9_15", + "image": "data/connectivity/graph_visual/medium/graph212.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,5) (0,9) (0,14) (0,18) (0,3) (0,1) (0,17) (0,4) (0,8) (0,7) (0,15) (0,11) (0,10) (0,13) (1,5) (1,9) (1,14) (1,18) (1,3) (1,17) (1,4) (1,8) (1,7) (1,15) (1,11) (1,10) (1,13) (3,5) (3,9) (3,14) (3,18) (3,17) (3,4) (3,8) (3,7) (3,15) (3,11) (3,10) (3,13) (4,5) (4,9) (4,14) (4,18) (4,17) (4,8) (4,7) (4,15) (4,11) (4,10) (4,13) (5,9) (5,14) (5,18) (5,17) (5,8) (5,7) (5,15) (5,11) (5,10) (5,13) (6,12) (6,16) (7,9) (7,14) (7,18) (7,17) (7,8) (7,15) (7,11) (7,10) (7,13) (8,9) (8,14) (8,18) (8,17) (8,15) (8,11) (8,10) (8,13) (9,14) (9,18) (9,17) (9,15) (9,11) (9,10) (9,13) (10,14) (10,18) (10,17) (10,15) (10,11) (10,13) (11,14) (11,18) (11,17) (11,15) (11,13) (12,16) (13,14) (13,18) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (15,17) (17,18)\nIs there a path between node 9 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph505-10_21", + "image": "data/connectivity/graph_visual/medium/graph505.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,13) (0,9) (0,10) (1,2) (1,15) (1,7) (1,11) (1,16) (2,3) (2,18) (2,7) (2,11) (2,14) (3,8) (3,4) (4,20) (4,15) (4,22) (4,7) (4,16) (4,14) (5,21) (5,9) (5,10) (7,17) (7,15) (8,20) (8,14) (9,12) (9,21) (9,13) (9,10) (10,12) (10,21) (11,20) (11,15) (11,22) (14,18) (15,16) (16,17) (16,22) (17,22) (18,20)\nIs there a path between node 10 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph701-2_8", + "image": "data/connectivity/graph_visual/medium/graph701.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,18) (0,19) (0,20) (0,23) (0,9) (0,10) (0,22) (0,13) (0,1) (0,12) (0,5) (0,7) (0,15) (0,4) (1,11) (1,18) (1,19) (1,20) (1,23) (1,9) (1,10) (1,22) (1,13) (1,12) (1,5) (1,7) (1,15) (1,4) (2,8) (2,6) (2,3) (2,24) (2,16) (2,21) (2,17) (2,14) (3,8) (3,6) (3,24) (3,16) (3,21) (3,17) (3,14) (4,11) (4,18) (4,19) (4,20) (4,23) (4,9) (4,10) (4,22) (4,13) (4,12) (4,5) (4,7) (4,15) (5,11) (5,18) (5,19) (5,20) (5,23) (5,9) (5,10) (5,22) (5,13) (5,12) (5,7) (5,15) (6,8) (6,24) (6,16) (6,21) (6,17) (6,14) (7,11) (7,18) (7,19) (7,20) (7,23) (7,9) (7,10) (7,22) (7,13) (7,12) (7,15) (8,24) (8,16) (8,21) (8,17) (8,14) (9,11) (9,18) (9,19) (9,20) (9,23) (9,10) (9,22) (9,13) (9,12) (9,15) (10,11) (10,18) (10,19) (10,20) (10,23) (10,22) (10,13) (10,12) (10,15) (11,18) (11,19) (11,20) (11,23) (11,22) (11,13) (11,12) (11,15) (12,18) (12,19) (12,20) (12,23) (12,22) (12,13) (12,15) (13,18) (13,19) (13,20) (13,23) (13,22) (13,15) (14,24) (14,16) (14,21) (14,17) (15,18) (15,19) (15,20) (15,23) (15,22) (16,24) (16,21) (16,17) (17,24) (17,21) (18,19) (18,20) (18,23) (18,22) (19,20) (19,23) (19,22) (20,23) (20,22) (21,24) (22,23)\nIs there a path between node 2 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph767-11_22", + "image": "data/connectivity/graph_visual/medium/graph767.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (0,24) (0,15) (0,2) (0,1) (0,7) (0,8) (0,18) (0,23) (0,5) (0,20) (1,19) (1,24) (1,15) (1,2) (1,7) (1,8) (1,18) (1,23) (1,5) (1,20) (2,19) (2,24) (2,15) (2,7) (2,8) (2,18) (2,23) (2,5) (2,20) (3,12) (3,16) (3,9) (3,14) (3,22) (3,13) (3,4) (3,11) (3,10) (3,17) (3,21) (3,6) (4,12) (4,16) (4,9) (4,14) (4,22) (4,13) (4,11) (4,10) (4,17) (4,21) (4,6) (5,19) (5,24) (5,15) (5,7) (5,8) (5,18) (5,23) (5,20) (6,12) (6,16) (6,9) (6,14) (6,22) (6,13) (6,11) (6,10) (6,17) (6,21) (7,19) (7,24) (7,15) (7,8) (7,18) (7,23) (7,20) (8,19) (8,24) (8,15) (8,18) (8,23) (8,20) (9,12) (9,16) (9,14) (9,22) (9,13) (9,11) (9,10) (9,17) (9,21) (10,12) (10,16) (10,14) (10,22) (10,13) (10,11) (10,17) (10,21) (11,12) (11,16) (11,14) (11,22) (11,13) (11,17) (11,21) (12,16) (12,14) (12,22) (12,13) (12,17) (12,21) (13,16) (13,14) (13,22) (13,17) (13,21) (14,16) (14,22) (14,17) (14,21) (15,19) (15,24) (15,18) (15,23) (15,20) (16,22) (16,17) (16,21) (17,22) (17,21) (18,19) (18,24) (18,23) (18,20) (19,24) (19,23) (19,20) (20,24) (20,23) (21,22) (23,24)\nIs there a path between node 11 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph176-4_11", + "image": "data/connectivity/graph_visual/medium/graph176.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,7) (0,13) (0,10) (0,9) (1,16) (1,12) (1,17) (1,8) (2,3) (2,14) (2,15) (2,5) (2,11) (3,14) (3,5) (4,7) (4,10) (4,9) (5,15) (5,11) (6,7) (6,10) (7,13) (7,10) (7,9) (8,12) (9,13) (10,13) (11,14) (11,15) (12,16) (12,17) (14,15) (16,17)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph417-9_4", + "image": "data/connectivity/graph_visual/medium/graph417.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,14) (0,9) (0,11) (0,4) (0,5) (0,15) (0,18) (0,20) (1,17) (1,16) (1,19) (1,3) (1,21) (1,6) (1,13) (1,8) (1,10) (1,7) (2,14) (2,9) (2,11) (2,4) (2,5) (2,15) (2,18) (2,20) (3,17) (3,16) (3,19) (3,21) (3,6) (3,13) (3,8) (3,10) (3,7) (4,14) (4,9) (4,11) (4,5) (4,15) (4,18) (4,20) (5,14) (5,9) (5,11) (5,15) (5,18) (5,20) (6,17) (6,16) (6,19) (6,21) (6,13) (6,8) (6,10) (6,7) (7,17) (7,16) (7,19) (7,21) (7,13) (7,8) (7,10) (8,17) (8,16) (8,19) (8,21) (8,13) (8,10) (9,14) (9,11) (9,15) (9,18) (9,20) (10,17) (10,16) (10,19) (10,21) (10,13) (11,14) (11,15) (11,18) (11,20) (13,17) (13,16) (13,19) (13,21) (14,15) (14,18) (14,20) (15,18) (15,20) (16,17) (16,19) (16,21) (17,19) (17,21) (18,20) (19,21)\nIs there a path between node 9 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph39-9_3", + "image": "data/connectivity/graph_visual/medium/graph39.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,4) (1,11) (2,8) (2,10) (4,8) (4,11) (5,8) (6,11) (7,8) (7,10) (9,10) (9,11) (11,12)\nIs there a path between node 9 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph295-2_14", + "image": "data/connectivity/graph_visual/medium/graph295.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,7) (1,10) (1,7) (1,12) (1,16) (1,6) (2,15) (3,14) (3,4) (3,5) (3,11) (4,17) (4,19) (4,10) (4,13) (4,12) (4,6) (5,19) (5,16) (6,17) (6,14) (6,9) (6,12) (6,16) (7,14) (7,11) (7,16) (9,14) (9,11) (9,15) (9,13) (9,12) (10,17) (10,14) (10,19) (10,11) (10,12) (11,14) (12,17) (14,17) (16,17) (16,19) (17,19)\nIs there a path between node 2 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph201-4_7", + "image": "data/connectivity/graph_visual/medium/graph201.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,7) (1,4) (3,9) (3,12) (4,15) (5,10) (8,10) (8,16)\nIs there a path between node 4 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph330-16_19", + "image": "data/connectivity/graph_visual/medium/graph330.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,5) (1,17) (2,16) (3,18) (3,14) (4,20) (5,17) (6,16) (6,12) (6,8) (8,15) (8,17) (10,13) (10,11) (11,20) (12,15) (12,17) (14,18) (14,19) (16,17)\nIs there a path between node 16 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph546-11_6", + "image": "data/connectivity/graph_visual/medium/graph546.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,19) (0,17) (0,7) (0,16) (0,21) (1,22) (1,19) (1,20) (1,21) (2,23) (2,6) (3,13) (3,18) (3,4) (3,10) (3,21) (4,19) (4,10) (4,16) (5,14) (5,12) (5,9) (5,11) (6,14) (6,23) (7,15) (7,22) (7,18) (7,8) (7,17) (7,20) (8,13) (8,21) (9,12) (9,11) (10,17) (13,19) (13,17) (13,21) (15,20) (16,18) (16,20) (19,20) (19,21)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph813-22_3", + "image": "data/connectivity/graph_visual/medium/graph813.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (1,9) (1,14) (1,11) (1,19) (1,8) (1,2) (1,15) (1,5) (1,24) (2,14) (2,22) (2,3) (2,8) (2,15) (2,18) (2,5) (2,24) (3,14) (3,11) (3,8) (3,15) (3,5) (4,16) (4,13) (4,17) (4,23) (4,10) (4,7) (5,9) (5,12) (5,22) (5,11) (5,19) (5,8) (5,15) (5,6) (6,9) (6,12) (6,22) (6,11) (6,19) (6,8) (6,15) (6,18) (6,24) (7,21) (7,16) (7,17) (7,10) (8,9) (8,14) (8,12) (8,19) (8,15) (8,18) (8,24) (9,14) (9,12) (9,22) (9,11) (9,19) (9,15) (9,18) (9,24) (10,21) (10,16) (10,13) (10,23) (11,12) (11,19) (11,15) (12,14) (12,22) (12,15) (12,18) (12,24) (13,16) (13,23) (14,22) (14,19) (14,18) (14,24) (15,22) (15,19) (15,18) (15,24) (16,21) (16,17) (17,21) (17,23) (18,22) (18,19) (18,24) (21,23) (22,24)\nIs there a path between node 22 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph8-1_5", + "image": "data/connectivity/graph_visual/medium/graph8.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,2) (0,8) (1,9) (1,3) (1,4) (1,7) (1,5) (1,10) (3,9) (3,7) (3,5) (3,10) (4,9) (4,6) (4,10) (5,9) (5,6) (6,9) (6,7) (6,10) (7,9) (9,10)\nIs there a path between node 1 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph435-5_20", + "image": "data/connectivity/graph_visual/medium/graph435.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,21) (0,10) (0,6) (0,17) (0,11) (1,6) (1,16) (1,4) (1,11) (1,8) (2,3) (4,21) (4,12) (4,17) (4,7) (4,11) (4,13) (5,21) (5,10) (5,16) (5,12) (5,19) (5,14) (5,9) (5,13) (5,8) (6,12) (6,19) (6,14) (6,13) (7,18) (7,12) (7,17) (7,19) (7,9) (8,12) (8,17) (8,19) (8,14) (8,11) (9,21) (9,10) (9,16) (9,17) (9,19) (9,11) (10,18) (10,21) (10,16) (11,18) (11,21) (11,19) (12,17) (13,17) (14,21) (14,19) (16,19)\nIs there a path between node 5 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph639-10_16", + "image": "data/connectivity/graph_visual/medium/graph639.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,12) (1,4) (1,21) (2,19) (2,23) (2,12) (3,16) (3,21) (4,22) (4,16) (5,18) (5,17) (5,8) (5,6) (5,15) (5,19) (5,23) (6,14) (6,23) (7,13) (8,17) (8,15) (8,12) (9,20) (10,20) (10,21) (11,16) (12,17) (12,15) (14,23) (15,18) (15,19) (15,23) (16,21) (17,19) (18,19) (19,23)\nIs there a path between node 10 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph335-1_18", + "image": "data/connectivity/graph_visual/medium/graph335.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,6) (0,19) (0,17) (0,3) (0,10) (0,14) (1,7) (1,8) (1,15) (1,13) (2,9) (2,12) (2,18) (2,4) (3,6) (3,19) (3,17) (3,16) (3,10) (3,14) (4,12) (4,18) (5,9) (5,18) (6,19) (6,17) (6,16) (6,14) (6,20) (7,8) (7,15) (7,13) (9,12) (9,18) (10,16) (10,14) (10,20) (11,15) (12,18) (13,15) (14,19) (14,17) (14,20) (16,19) (16,17) (17,20) (19,20)\nIs there a path between node 1 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph790-3_17", + "image": "data/connectivity/graph_visual/medium/graph790.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,23) (1,9) (2,13) (2,16) (2,24) (3,5) (3,7) (3,11) (4,6) (4,12) (4,5) (4,14) (4,7) (5,6) (5,12) (5,14) (5,11) (6,17) (6,20) (6,7) (10,19) (10,23) (10,16) (10,18) (11,12) (11,20) (11,15) (13,16) (13,22) (13,24) (14,17) (14,20) (15,20) (16,23) (17,20) (18,22) (22,23) (23,24)\nIs there a path between node 3 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph122-14_10", + "image": "data/connectivity/graph_visual/medium/graph122.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,5) (0,3) (1,13) (1,4) (1,12) (1,16) (1,9) (1,15) (1,11) (1,8) (1,6) (1,7) (1,10) (2,5) (3,14) (4,16) (4,9) (4,11) (4,8) (4,7) (4,10) (6,13) (6,16) (6,11) (6,7) (6,10) (7,13) (7,9) (7,11) (7,8) (7,10) (8,13) (8,12) (8,16) (8,9) (8,15) (8,10) (9,13) (9,16) (9,15) (9,10) (10,16) (10,11) (11,13) (11,16) (11,15) (12,13) (12,15) (13,16) (15,16)\nIs there a path between node 14 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph49-11_2", + "image": "data/connectivity/graph_visual/medium/graph49.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,9) (0,7) (0,12) (0,2) (0,8) (0,6) (0,11) (0,4) (1,5) (1,10) (1,3) (2,9) (2,7) (2,12) (2,8) (2,6) (2,11) (2,4) (3,5) (3,10) (4,9) (4,7) (4,12) (4,8) (4,6) (4,11) (5,10) (6,9) (6,7) (6,12) (6,8) (6,11) (7,9) (7,12) (7,8) (7,11) (8,9) (8,12) (8,11) (9,12) (9,11) (11,12)\nIs there a path between node 11 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph534-17_19", + "image": "data/connectivity/graph_visual/medium/graph534.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,19) (0,20) (0,13) (0,2) (0,3) (0,16) (0,15) (0,4) (0,11) (0,22) (0,5) (0,6) (0,7) (0,1) (0,10) (1,21) (1,19) (1,20) (1,13) (1,2) (1,3) (1,16) (1,15) (1,4) (1,11) (1,22) (1,5) (1,6) (1,7) (1,10) (2,21) (2,19) (2,20) (2,13) (2,3) (2,16) (2,15) (2,4) (2,11) (2,22) (2,5) (2,6) (2,7) (2,10) (3,21) (3,19) (3,20) (3,13) (3,16) (3,15) (3,4) (3,11) (3,22) (3,5) (3,6) (3,7) (3,10) (4,21) (4,19) (4,20) (4,13) (4,16) (4,15) (4,11) (4,22) (4,5) (4,6) (4,7) (4,10) (5,21) (5,19) (5,20) (5,13) (5,16) (5,15) (5,11) (5,22) (5,6) (5,7) (5,10) (6,21) (6,19) (6,20) (6,13) (6,16) (6,15) (6,11) (6,22) (6,7) (6,10) (7,21) (7,19) (7,20) (7,13) (7,16) (7,15) (7,11) (7,22) (7,10) (8,12) (8,14) (8,9) (8,18) (9,12) (9,14) (9,18) (10,21) (10,19) (10,20) (10,13) (10,16) (10,15) (10,11) (10,22) (11,21) (11,19) (11,20) (11,13) (11,16) (11,15) (11,22) (12,14) (12,18) (13,21) (13,19) (13,20) (13,16) (13,15) (13,22) (14,18) (15,21) (15,19) (15,20) (15,16) (15,22) (16,21) (16,19) (16,20) (16,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 17 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph366-9_8", + "image": "data/connectivity/graph_visual/medium/graph366.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,7) (0,6) (0,3) (0,18) (0,1) (0,15) (0,12) (0,14) (0,9) (0,16) (0,8) (0,2) (0,11) (0,19) (1,7) (1,6) (1,3) (1,18) (1,15) (1,9) (1,8) (1,2) (1,20) (2,7) (2,3) (2,18) (2,15) (2,12) (2,14) (2,9) (2,16) (2,8) (2,11) (2,19) (2,20) (3,18) (3,15) (3,12) (3,9) (3,16) (3,8) (3,19) (3,20) (4,13) (4,17) (5,17) (6,7) (6,18) (6,15) (6,14) (6,9) (6,16) (6,11) (6,19) (6,20) (7,15) (7,12) (7,14) (7,9) (7,16) (8,18) (8,12) (8,14) (8,9) (8,16) (8,11) (8,19) (8,20) (9,18) (9,15) (9,12) (9,11) (9,19) (9,20) (10,13) (11,18) (11,12) (11,14) (11,16) (11,19) (11,20) (12,18) (12,15) (12,14) (12,19) (12,20) (13,17) (14,19) (16,18) (16,19) (18,20)\nIs there a path between node 9 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph318-2_19", + "image": "data/connectivity/graph_visual/medium/graph318.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,2) (0,15) (1,11) (1,18) (1,19) (1,6) (1,12) (1,3) (1,10) (1,7) (1,14) (1,4) (2,17) (2,15) (3,11) (3,18) (3,19) (3,6) (3,12) (3,10) (3,7) (3,14) (3,4) (4,11) (4,18) (4,19) (4,6) (4,12) (4,10) (4,7) (4,14) (5,9) (5,16) (5,8) (5,13) (6,11) (6,18) (6,19) (6,12) (6,10) (6,7) (6,14) (7,11) (7,18) (7,19) (7,12) (7,10) (7,14) (8,9) (8,16) (8,13) (9,16) (9,13) (10,11) (10,18) (10,19) (10,12) (10,14) (11,18) (11,19) (11,12) (11,14) (12,18) (12,19) (12,14) (13,16) (14,18) (14,19) (15,17) (18,19)\nIs there a path between node 2 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph293-7_4", + "image": "data/connectivity/graph_visual/medium/graph293.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,17) (2,4) (2,3) (2,13) (2,8) (2,16) (3,13) (3,7) (3,19) (3,11) (3,14) (4,11) (5,18) (5,11) (5,14) (6,7) (7,19) (7,16) (7,14) (8,18) (8,13) (10,18) (10,13) (10,11) (10,16) (11,13) (11,19) (11,16) (12,15) (13,16) (16,18) (18,19)\nIs there a path between node 7 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph100-11_10", + "image": "data/connectivity/graph_visual/medium/graph100.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,5) (0,1) (0,2) (0,9) (0,13) (0,4) (0,15) (1,5) (1,2) (1,3) (1,8) (1,7) (1,11) (2,8) (2,9) (2,13) (2,11) (3,5) (3,14) (3,13) (3,4) (3,15) (3,7) (4,5) (4,14) (4,8) (4,9) (4,13) (4,7) (4,11) (5,14) (5,9) (5,13) (5,7) (5,11) (6,10) (6,12) (7,14) (7,8) (7,9) (7,15) (8,9) (8,13) (8,15) (8,11) (9,15) (9,11) (10,12) (11,14) (11,13) (11,15)\nIs there a path between node 11 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph532-1_7", + "image": "data/connectivity/graph_visual/medium/graph532.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,17) (0,19) (0,4) (0,6) (0,18) (0,20) (0,22) (0,16) (0,12) (0,10) (1,13) (1,5) (1,21) (1,7) (2,8) (2,3) (2,9) (2,14) (2,15) (2,11) (3,8) (3,9) (3,14) (3,15) (3,11) (4,17) (4,19) (4,6) (4,18) (4,20) (4,22) (4,16) (4,12) (4,10) (5,13) (5,21) (5,7) (6,17) (6,19) (6,18) (6,20) (6,22) (6,16) (6,12) (6,10) (7,13) (7,21) (8,9) (8,14) (8,15) (8,11) (9,14) (9,15) (9,11) (10,17) (10,19) (10,18) (10,20) (10,22) (10,16) (10,12) (11,14) (11,15) (12,17) (12,19) (12,18) (12,20) (12,22) (12,16) (13,21) (14,15) (16,17) (16,19) (16,18) (16,20) (16,22) (17,19) (17,18) (17,20) (17,22) (18,19) (18,20) (18,22) (19,20) (19,22) (20,22)\nIs there a path between node 1 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph73-11_1", + "image": "data/connectivity/graph_visual/medium/graph73.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (0,12) (0,5) (1,12) (1,8) (2,3) (2,8) (2,5) (3,9) (3,10) (3,12) (3,8) (5,12) (6,13) (7,10) (7,14) (8,10) (9,10) (12,14)\nIs there a path between node 11 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph581-19_6", + "image": "data/connectivity/graph_visual/medium/graph581.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,11) (0,20) (1,22) (1,12) (1,16) (1,6) (1,18) (1,13) (1,17) (1,14) (1,15) (2,11) (2,20) (3,11) (3,7) (4,23) (4,16) (4,18) (4,13) (5,22) (5,23) (5,16) (5,18) (6,12) (6,23) (6,16) (7,20) (8,11) (8,20) (8,9) (9,10) (12,22) (12,21) (12,16) (12,18) (12,13) (12,14) (13,23) (13,16) (13,17) (13,14) (14,19) (14,15) (15,22) (15,19) (16,21) (16,18) (17,22) (17,21) (17,23) (17,19) (19,21) (21,22)\nIs there a path between node 19 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph90-4_1", + "image": "data/connectivity/graph_visual/medium/graph90.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,10) (1,11) (1,9) (1,14) (2,5) (2,6) (3,11) (3,13) (4,11) (4,13) (4,15) (5,7) (5,6) (7,10) (8,11) (8,9) (9,14) (9,12) (11,13) (13,14) (13,15)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph537-0_1", + "image": "data/connectivity/graph_visual/medium/graph537.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (0,16) (1,12) (1,10) (1,7) (1,6) (1,22) (1,13) (1,9) (1,2) (1,19) (1,14) (1,11) (1,21) (1,15) (1,5) (1,20) (1,4) (1,8) (1,17) (1,3) (2,12) (2,10) (2,7) (2,6) (2,22) (2,13) (2,9) (2,19) (2,14) (2,11) (2,21) (2,15) (2,5) (2,20) (2,4) (2,8) (2,17) (2,3) (3,12) (3,10) (3,7) (3,6) (3,22) (3,13) (3,9) (3,19) (3,14) (3,11) (3,21) (3,15) (3,5) (3,20) (3,4) (3,8) (3,17) (4,12) (4,10) (4,7) (4,6) (4,22) (4,13) (4,9) (4,19) (4,14) (4,11) (4,21) (4,15) (4,5) (4,20) (4,8) (4,17) (5,12) (5,10) (5,7) (5,6) (5,22) (5,13) (5,9) (5,19) (5,14) (5,11) (5,21) (5,15) (5,20) (5,8) (5,17) (6,12) (6,10) (6,7) (6,22) (6,13) (6,9) (6,19) (6,14) (6,11) (6,21) (6,15) (6,20) (6,8) (6,17) (7,12) (7,10) (7,22) (7,13) (7,9) (7,19) (7,14) (7,11) (7,21) (7,15) (7,20) (7,8) (7,17) (8,12) (8,10) (8,22) (8,13) (8,9) (8,19) (8,14) (8,11) (8,21) (8,15) (8,20) (8,17) (9,12) (9,10) (9,22) (9,13) (9,19) (9,14) (9,11) (9,21) (9,15) (9,20) (9,17) (10,12) (10,22) (10,13) (10,19) (10,14) (10,11) (10,21) (10,15) (10,20) (10,17) (11,12) (11,22) (11,13) (11,19) (11,14) (11,21) (11,15) (11,20) (11,17) (12,22) (12,13) (12,19) (12,14) (12,21) (12,15) (12,20) (12,17) (13,22) (13,19) (13,14) (13,21) (13,15) (13,20) (13,17) (14,22) (14,19) (14,21) (14,15) (14,20) (14,17) (15,22) (15,19) (15,21) (15,20) (15,17) (16,18) (17,22) (17,19) (17,21) (17,20) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 0 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph660-13_21", + "image": "data/connectivity/graph_visual/medium/graph660.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,11) (0,3) (0,2) (0,9) (0,5) (0,10) (0,23) (1,13) (1,17) (1,20) (1,8) (1,14) (1,4) (2,22) (2,11) (2,9) (2,10) (2,23) (3,21) (3,11) (3,5) (3,15) (3,23) (3,12) (4,18) (4,19) (4,13) (4,8) (4,16) (5,11) (5,9) (5,10) (5,15) (6,18) (6,19) (6,13) (6,20) (6,8) (6,16) (6,14) (7,19) (7,20) (7,8) (7,16) (7,14) (8,18) (8,19) (8,13) (8,17) (8,16) (8,14) (9,22) (9,21) (9,10) (9,15) (9,23) (9,12) (10,22) (10,21) (10,15) (10,12) (11,22) (11,15) (11,23) (11,12) (12,22) (12,15) (12,23) (13,18) (13,19) (13,20) (13,16) (13,14) (14,18) (14,19) (14,17) (14,20) (14,16) (15,22) (15,21) (16,18) (16,19) (16,17) (17,18) (17,19) (17,20) (18,19) (18,20) (19,20) (21,22) (21,23) (22,23)\nIs there a path between node 13 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph281-12_11", + "image": "data/connectivity/graph_visual/medium/graph281.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,16) (0,13) (0,5) (0,1) (0,18) (0,8) (0,10) (0,4) (0,12) (0,14) (0,9) (0,15) (1,16) (1,13) (1,5) (1,18) (1,8) (1,10) (1,4) (1,12) (1,14) (1,9) (1,15) (2,11) (2,19) (2,6) (2,3) (2,7) (2,17) (3,11) (3,19) (3,6) (3,7) (3,17) (4,16) (4,13) (4,5) (4,18) (4,8) (4,10) (4,12) (4,14) (4,9) (4,15) (5,16) (5,13) (5,18) (5,8) (5,10) (5,12) (5,14) (5,9) (5,15) (6,11) (6,19) (6,7) (6,17) (7,11) (7,19) (7,17) (8,16) (8,13) (8,18) (8,10) (8,12) (8,14) (8,9) (8,15) (9,16) (9,13) (9,18) (9,10) (9,12) (9,14) (9,15) (10,16) (10,13) (10,18) (10,12) (10,14) (10,15) (11,19) (11,17) (12,16) (12,13) (12,18) (12,14) (12,15) (13,16) (13,18) (13,14) (13,15) (14,16) (14,18) (14,15) (15,16) (15,18) (16,18) (17,19)\nIs there a path between node 12 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph820-10_20", + "image": "data/connectivity/graph_visual/medium/graph820.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,6) (1,2) (1,4) (1,12) (1,19) (1,3) (1,18) (1,21) (1,16) (1,22) (1,23) (1,24) (1,20) (1,8) (1,13) (1,9) (2,6) (2,4) (2,14) (2,17) (2,15) (2,19) (2,3) (2,18) (2,21) (2,16) (2,22) (2,23) (2,24) (2,20) (2,11) (2,8) (2,13) (2,9) (3,7) (3,6) (3,4) (3,14) (3,15) (3,12) (3,18) (3,16) (3,22) (3,23) (3,24) (3,20) (3,11) (3,8) (4,6) (4,14) (4,17) (4,15) (4,12) (4,19) (4,21) (4,22) (4,23) (4,11) (4,13) (4,9) (5,10) (6,14) (6,15) (6,19) (6,18) (6,21) (6,22) (6,23) (6,20) (6,11) (6,8) (6,13) (6,9) (7,14) (7,18) (7,16) (7,22) (7,23) (7,20) (7,11) (7,9) (8,14) (8,15) (8,19) (8,21) (8,16) (8,22) (8,23) (8,20) (8,11) (8,13) (8,9) (9,14) (9,15) (9,12) (9,19) (9,18) (9,21) (9,16) (9,22) (9,23) (9,20) (9,13) (11,14) (11,17) (11,15) (11,12) (11,21) (11,22) (11,24) (11,20) (12,17) (12,15) (12,19) (12,18) (12,21) (12,16) (12,23) (12,13) (13,17) (13,15) (13,19) (13,18) (13,21) (13,22) (13,23) (13,24) (14,17) (14,15) (14,19) (14,18) (14,16) (14,20) (15,17) (15,19) (15,16) (15,22) (15,24) (15,20) (16,17) (16,19) (16,18) (16,22) (16,23) (16,24) (16,20) (17,19) (17,21) (17,22) (18,19) (18,21) (18,22) (18,23) (18,24) (19,23) (19,20) (20,21) (20,24) (21,22) (21,24) (22,24)\nIs there a path between node 10 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph797-1_13", + "image": "data/connectivity/graph_visual/medium/graph797.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,17) (0,2) (0,10) (0,3) (0,11) (0,12) (2,9) (2,23) (2,18) (2,13) (2,16) (3,4) (4,20) (4,21) (4,24) (5,13) (5,11) (5,16) (6,21) (9,16) (10,18) (10,20) (10,12) (10,21) (11,14) (12,20) (12,14) (12,13) (13,14) (13,19) (14,17) (14,20) (14,16) (14,24) (16,23) (16,17) (16,18) (17,19) (18,23) (18,20) (18,21) (18,24) (19,20) (19,21) (20,23) (22,24)\nIs there a path between node 1 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph839-23_4", + "image": "data/connectivity/graph_visual/medium/graph839.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,8) (0,24) (0,14) (0,4) (0,21) (0,1) (0,15) (0,19) (1,23) (1,8) (1,24) (1,14) (1,4) (1,21) (1,15) (1,19) (2,18) (2,22) (2,16) (2,17) (2,5) (2,10) (2,11) (3,12) (3,13) (3,9) (3,6) (3,20) (3,7) (4,23) (4,8) (4,24) (4,14) (4,21) (4,15) (4,19) (5,18) (5,22) (5,16) (5,17) (5,10) (5,11) (6,12) (6,13) (6,9) (6,20) (6,7) (7,12) (7,13) (7,9) (7,20) (8,23) (8,24) (8,14) (8,21) (8,15) (8,19) (9,12) (9,13) (9,20) (10,18) (10,22) (10,16) (10,17) (10,11) (11,18) (11,22) (11,16) (11,17) (12,13) (12,20) (13,20) (14,23) (14,24) (14,21) (14,15) (14,19) (15,23) (15,24) (15,21) (15,19) (16,18) (16,22) (16,17) (17,18) (17,22) (18,22) (19,23) (19,24) (19,21) (21,23) (21,24) (23,24)\nIs there a path between node 23 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph275-6_13", + "image": "data/connectivity/graph_visual/medium/graph275.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,7) (0,4) (0,9) (0,12) (0,11) (0,5) (1,6) (1,17) (1,8) (1,15) (1,3) (1,2) (1,18) (1,19) (1,13) (1,14) (1,10) (2,6) (2,17) (2,8) (2,15) (2,3) (2,18) (2,19) (2,13) (2,14) (2,10) (3,6) (3,17) (3,8) (3,15) (3,18) (3,19) (3,13) (3,14) (3,10) (4,7) (4,9) (4,12) (4,11) (4,5) (5,7) (5,9) (5,12) (5,11) (6,17) (6,8) (6,15) (6,18) (6,19) (6,13) (6,14) (6,10) (7,9) (7,12) (7,11) (8,17) (8,15) (8,18) (8,19) (8,13) (8,14) (8,10) (9,12) (9,11) (10,17) (10,15) (10,18) (10,19) (10,13) (10,14) (11,12) (13,17) (13,15) (13,18) (13,19) (13,14) (14,17) (14,15) (14,18) (14,19) (15,17) (15,18) (15,19) (17,18) (17,19) (18,19)\nIs there a path between node 6 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph211-17_8", + "image": "data/connectivity/graph_visual/medium/graph211.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,14) (0,1) (0,8) (0,11) (0,7) (1,14) (1,15) (1,17) (1,7) (2,3) (2,6) (2,5) (2,13) (2,16) (2,4) (2,9) (3,6) (3,5) (3,12) (3,13) (3,16) (3,4) (3,9) (4,6) (4,5) (4,12) (4,13) (4,16) (4,9) (5,6) (5,12) (5,13) (5,16) (6,9) (7,14) (7,8) (7,15) (7,17) (7,11) (8,14) (8,17) (8,11) (9,12) (9,13) (10,18) (11,14) (11,15) (11,17) (12,13) (12,16) (13,16) (14,17) (15,17)\nIs there a path between node 17 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph402-5_19", + "image": "data/connectivity/graph_visual/medium/graph402.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,16) (0,1) (0,8) (2,6) (2,17) (2,20) (3,7) (3,13) (5,20) (5,13) (6,17) (6,10) (6,13) (7,10) (7,11) (7,9) (8,19) (8,14) (9,10) (12,17) (12,20) (12,13) (14,21)\nIs there a path between node 5 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph66-2_9", + "image": "data/connectivity/graph_visual/medium/graph66.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (0,1) (0,13) (0,7) (0,4) (0,10) (0,12) (0,5) (0,11) (0,6) (0,9) (0,8) (1,3) (1,13) (1,7) (1,4) (1,10) (1,12) (1,5) (1,11) (1,6) (1,9) (1,8) (3,13) (3,7) (3,4) (3,10) (3,12) (3,5) (3,11) (3,6) (3,9) (3,8) (4,13) (4,7) (4,10) (4,12) (4,5) (4,11) (4,6) (4,9) (4,8) (5,13) (5,7) (5,10) (5,12) (5,11) (5,6) (5,9) (5,8) (6,13) (6,7) (6,10) (6,12) (6,11) (6,9) (6,8) (7,13) (7,10) (7,12) (7,11) (7,9) (7,8) (8,13) (8,10) (8,12) (8,11) (8,9) (9,13) (9,10) (9,12) (9,11) (10,13) (10,12) (10,11) (11,13) (11,12) (12,13)\nIs there a path between node 2 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph202-18_13", + "image": "data/connectivity/graph_visual/medium/graph202.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (0,13) (0,12) (0,3) (1,4) (1,13) (1,3) (2,10) (2,15) (2,18) (3,12) (3,14) (4,6) (4,9) (4,17) (6,14) (6,17) (7,14) (8,13) (10,16) (11,12) (11,14) (12,14) (14,17)\nIs there a path between node 18 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph424-5_8", + "image": "data/connectivity/graph_visual/medium/graph424.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,13) (2,4) (2,11) (2,5) (2,21) (3,6) (3,5) (3,17) (4,12) (4,11) (4,20) (4,21) (5,12) (5,10) (5,7) (6,20) (6,17) (7,12) (7,8) (7,20) (7,10) (7,17) (8,10) (8,21) (10,11) (10,20) (11,12) (12,20) (13,18) (14,19) (16,19)\nIs there a path between node 5 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph644-18_1", + "image": "data/connectivity/graph_visual/medium/graph644.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,9) (1,4) (2,16) (4,18) (4,11) (5,14) (6,8) (7,15) (7,21) (9,15) (9,19) (13,15) (13,16) (15,20) (16,20) (19,21) (19,20)\nIs there a path between node 18 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph448-14_13", + "image": "data/connectivity/graph_visual/medium/graph448.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,17) (0,19) (0,1) (0,6) (0,5) (0,7) (0,2) (0,14) (0,4) (0,10) (1,17) (1,6) (1,5) (1,12) (1,7) (1,13) (1,2) (1,20) (1,14) (1,10) (2,9) (2,17) (2,16) (2,19) (2,6) (2,12) (2,7) (2,18) (2,13) (2,20) (2,14) (2,4) (2,10) (3,21) (3,15) (3,11) (4,9) (4,17) (4,16) (4,19) (4,6) (4,5) (4,12) (4,7) (4,13) (4,10) (5,9) (5,17) (5,16) (5,12) (5,18) (5,13) (5,20) (5,14) (6,17) (6,16) (6,12) (6,7) (6,18) (6,20) (6,10) (7,9) (7,17) (7,16) (7,19) (7,13) (7,20) (7,14) (7,10) (8,21) (8,15) (9,16) (9,19) (9,18) (9,13) (9,20) (9,14) (9,10) (10,17) (10,16) (10,18) (10,13) (10,20) (10,14) (11,21) (12,17) (12,16) (12,19) (13,17) (13,16) (13,19) (14,17) (14,19) (14,20) (15,21) (16,17) (16,18) (16,20) (17,19) (17,20) (18,19) (18,20) (19,20)\nIs there a path between node 14 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph797-23_18", + "image": "data/connectivity/graph_visual/medium/graph797.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,17) (0,2) (0,10) (0,3) (0,11) (0,12) (2,9) (2,23) (2,18) (2,13) (2,16) (3,4) (4,20) (4,21) (4,24) (5,13) (5,11) (5,16) (6,21) (9,16) (10,18) (10,20) (10,12) (10,21) (11,14) (12,20) (12,14) (12,13) (13,14) (13,19) (14,17) (14,20) (14,16) (14,24) (16,23) (16,17) (16,18) (17,19) (18,23) (18,20) (18,21) (18,24) (19,20) (19,21) (20,23) (22,24)\nIs there a path between node 23 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph334-19_2", + "image": "data/connectivity/graph_visual/medium/graph334.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,7) (0,3) (0,20) (1,13) (2,9) (2,12) (2,13) (3,7) (3,20) (5,6) (5,10) (5,11) (5,15) (5,17) (5,12) (6,9) (6,10) (6,11) (8,16) (9,17) (9,13) (10,17) (11,16) (11,18) (12,16) (13,15) (13,17) (13,18) (14,19) (19,20)\nIs there a path between node 19 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph713-20_9", + "image": "data/connectivity/graph_visual/medium/graph713.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (1,6) (1,4) (1,20) (1,18) (1,10) (1,14) (1,21) (1,24) (1,23) (1,15) (1,11) (2,17) (2,19) (2,22) (2,13) (2,9) (4,6) (4,12) (4,10) (4,14) (4,21) (4,23) (4,15) (4,11) (5,17) (5,8) (5,22) (5,13) (5,16) (5,9) (6,20) (6,18) (6,14) (6,21) (6,24) (6,23) (6,15) (8,19) (8,22) (8,13) (8,16) (8,9) (9,17) (9,19) (9,13) (9,16) (10,12) (10,20) (10,21) (10,24) (10,23) (11,12) (11,20) (11,18) (11,14) (11,21) (11,24) (11,23) (12,18) (12,14) (12,21) (12,24) (12,23) (12,15) (13,19) (13,22) (14,18) (14,21) (14,23) (15,20) (15,18) (15,24) (16,17) (16,19) (16,22) (18,20) (18,21) (20,24) (20,23) (21,24) (21,23)\nIs there a path between node 20 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph831-18_0", + "image": "data/connectivity/graph_visual/medium/graph831.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (1,14) (1,20) (2,3) (2,17) (2,18) (2,9) (2,23) (2,6) (2,21) (2,11) (3,24) (3,13) (3,18) (3,9) (3,23) (3,21) (3,16) (3,10) (3,8) (4,12) (4,7) (4,22) (4,20) (4,5) (5,14) (5,12) (5,7) (5,22) (5,20) (6,13) (6,17) (6,15) (6,21) (6,11) (6,10) (6,8) (7,14) (7,12) (7,22) (8,24) (8,13) (8,15) (8,18) (8,23) (8,11) (8,16) (8,10) (9,24) (9,15) (9,23) (9,11) (9,16) (9,10) (10,24) (10,13) (10,17) (10,15) (10,18) (10,23) (10,11) (10,16) (11,24) (11,13) (11,18) (11,23) (11,21) (12,22) (12,20) (13,24) (13,17) (13,18) (13,23) (13,21) (13,16) (14,20) (15,24) (15,17) (15,18) (15,21) (16,24) (16,17) (16,23) (17,24) (17,18) (17,23) (18,24) (20,22) (21,24) (21,23) (23,24)\nIs there a path between node 18 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph650-23_22", + "image": "data/connectivity/graph_visual/medium/graph650.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,22) (0,8) (0,16) (0,23) (0,21) (0,5) (1,14) (1,12) (1,9) (1,18) (1,17) (1,15) (1,10) (1,13) (2,20) (2,19) (2,22) (2,6) (2,8) (2,16) (2,21) (2,5) (2,4) (3,11) (3,14) (3,7) (3,18) (3,15) (3,10) (4,20) (4,22) (4,8) (4,23) (4,5) (5,20) (5,19) (5,22) (5,6) (5,8) (5,16) (5,21) (6,19) (6,22) (6,8) (6,16) (6,23) (6,21) (7,11) (7,12) (7,18) (7,17) (7,15) (7,10) (7,13) (8,20) (8,19) (8,22) (8,16) (8,21) (9,11) (9,14) (9,12) (9,18) (9,17) (9,13) (10,11) (10,12) (10,17) (10,15) (11,14) (11,12) (11,18) (11,17) (11,15) (11,13) (12,14) (12,17) (12,13) (13,14) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (16,20) (16,19) (16,22) (17,18) (19,20) (19,22) (19,23) (19,21) (20,22) (20,21) (21,22) (22,23)\nIs there a path between node 23 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph63-9_2", + "image": "data/connectivity/graph_visual/medium/graph63.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,12) (0,9) (0,6) (1,10) (1,5) (1,2) (1,8) (1,7) (2,5) (2,3) (3,8) (3,11) (3,7) (4,12) (4,6) (4,13) (5,8) (5,11) (6,9) (6,13) (7,10) (7,8) (8,11) (9,13)\nIs there a path between node 9 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph579-18_23", + "image": "data/connectivity/graph_visual/medium/graph579.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,3) (0,8) (0,10) (0,2) (0,13) (0,19) (1,23) (2,6) (2,20) (2,11) (2,12) (2,8) (2,17) (2,22) (2,5) (2,19) (3,11) (3,12) (3,21) (3,22) (5,16) (5,6) (5,8) (5,17) (5,13) (5,19) (6,20) (6,22) (6,7) (7,8) (7,10) (7,13) (8,11) (8,10) (8,13) (9,20) (9,10) (10,16) (10,11) (11,16) (12,17) (12,22) (12,13) (13,21) (14,23) (14,15) (17,20) (17,21) (21,22)\nIs there a path between node 18 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph12-7_9", + "image": "data/connectivity/graph_visual/medium/graph12.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,3) (0,10) (0,7) (0,2) (0,9) (0,1) (0,8) (0,5) (1,3) (1,10) (1,7) (1,2) (1,9) (1,8) (1,5) (2,3) (2,10) (2,7) (2,9) (2,8) (2,5) (3,10) (3,7) (3,9) (3,8) (3,5) (4,6) (5,10) (5,7) (5,9) (5,8) (7,10) (7,9) (7,8) (8,10) (8,9) (9,10)\nIs there a path between node 7 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph459-16_5", + "image": "data/connectivity/graph_visual/medium/graph459.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,9) (0,13) (0,10) (0,12) (0,1) (0,18) (0,8) (0,2) (0,15) (0,6) (0,4) (0,19) (0,21) (0,20) (0,17) (0,5) (1,9) (1,13) (1,10) (1,12) (1,18) (1,8) (1,2) (1,15) (1,6) (1,4) (1,19) (1,21) (1,20) (1,17) (1,5) (2,9) (2,13) (2,10) (2,12) (2,18) (2,8) (2,15) (2,6) (2,4) (2,19) (2,21) (2,20) (2,17) (2,5) (3,16) (3,14) (3,7) (3,11) (4,9) (4,13) (4,10) (4,12) (4,18) (4,8) (4,15) (4,6) (4,19) (4,21) (4,20) (4,17) (4,5) (5,9) (5,13) (5,10) (5,12) (5,18) (5,8) (5,15) (5,6) (5,19) (5,21) (5,20) (5,17) (6,9) (6,13) (6,10) (6,12) (6,18) (6,8) (6,15) (6,19) (6,21) (6,20) (6,17) (7,16) (7,14) (7,11) (8,9) (8,13) (8,10) (8,12) (8,18) (8,15) (8,19) (8,21) (8,20) (8,17) (9,13) (9,10) (9,12) (9,18) (9,15) (9,19) (9,21) (9,20) (9,17) (10,13) (10,12) (10,18) (10,15) (10,19) (10,21) (10,20) (10,17) (11,16) (11,14) (12,13) (12,18) (12,15) (12,19) (12,21) (12,20) (12,17) (13,18) (13,15) (13,19) (13,21) (13,20) (13,17) (14,16) (15,18) (15,19) (15,21) (15,20) (15,17) (17,18) (17,19) (17,21) (17,20) (18,19) (18,21) (18,20) (19,21) (19,20) (20,21)\nIs there a path between node 16 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph670-8_10", + "image": "data/connectivity/graph_visual/medium/graph670.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,21) (0,18) (0,20) (0,16) (1,14) (1,23) (1,7) (1,3) (2,23) (2,7) (2,3) (3,14) (3,23) (3,7) (3,22) (4,11) (5,6) (5,21) (5,20) (5,16) (5,15) (6,21) (6,20) (6,16) (6,15) (7,23) (7,22) (8,12) (8,19) (8,17) (9,13) (9,12) (9,19) (9,10) (10,13) (10,12) (10,19) (10,17) (12,13) (12,19) (12,17) (13,17) (14,23) (15,21) (15,18) (15,16) (16,21) (16,18) (16,20) (17,19) (18,21) (18,20)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph258-11_14", + "image": "data/connectivity/graph_visual/medium/graph258.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,2) (1,18) (1,12) (1,15) (1,7) (2,17) (2,3) (3,17) (4,12) (5,17) (5,19) (6,18) (6,10) (6,9) (6,12) (6,16) (7,18) (7,9) (7,13) (7,8) (8,14) (9,18) (9,14) (9,12) (9,13) (10,12) (10,15) (11,17) (12,16) (14,18)\nIs there a path between node 11 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph695-1_13", + "image": "data/connectivity/graph_visual/medium/graph695.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,17) (0,16) (0,8) (0,22) (0,18) (0,6) (0,3) (1,12) (1,23) (1,9) (1,19) (1,11) (1,2) (1,14) (2,12) (2,23) (2,9) (2,19) (2,11) (2,14) (3,7) (3,17) (3,16) (3,8) (3,22) (3,18) (3,6) (4,13) (4,15) (4,10) (4,21) (4,5) (4,20) (5,13) (5,15) (5,10) (5,21) (5,20) (6,7) (6,17) (6,16) (6,8) (6,22) (6,18) (7,17) (7,16) (7,8) (7,22) (7,18) (8,17) (8,16) (8,22) (8,18) (9,12) (9,23) (9,19) (9,11) (9,14) (10,13) (10,15) (10,21) (10,20) (11,12) (11,23) (11,19) (11,14) (12,23) (12,19) (12,14) (13,15) (13,21) (13,20) (14,23) (14,19) (15,21) (15,20) (16,17) (16,22) (16,18) (17,22) (17,18) (18,22) (19,23) (20,21)\nIs there a path between node 1 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph762-21_7", + "image": "data/connectivity/graph_visual/medium/graph762.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,24) (0,4) (0,17) (0,22) (0,7) (0,23) (0,9) (0,8) (0,3) (0,1) (0,10) (0,19) (0,6) (1,12) (1,24) (1,4) (1,17) (1,5) (1,22) (1,16) (1,23) (1,9) (1,14) (1,3) (1,13) (1,21) (1,10) (1,19) (1,6) (2,15) (2,18) (2,11) (3,12) (3,24) (3,4) (3,17) (3,22) (3,7) (3,16) (3,20) (3,13) (3,21) (4,12) (4,24) (4,5) (4,16) (4,20) (4,23) (4,13) (4,21) (4,10) (4,19) (4,6) (5,12) (5,24) (5,17) (5,22) (5,16) (5,20) (5,23) (5,9) (5,8) (5,13) (5,10) (5,6) (6,12) (6,24) (6,17) (6,22) (6,7) (6,20) (6,23) (6,8) (6,14) (6,13) (6,21) (7,12) (7,24) (7,17) (7,16) (7,23) (7,14) (7,13) (7,21) (7,10) (7,19) (8,12) (8,24) (8,17) (8,22) (8,16) (8,20) (8,23) (8,14) (8,13) (8,21) (8,10) (9,12) (9,24) (9,17) (9,22) (9,20) (9,14) (9,13) (9,21) (9,10) (9,19) (10,17) (10,16) (10,23) (10,14) (10,13) (11,18) (12,17) (12,22) (12,16) (12,23) (12,13) (12,19) (13,24) (13,16) (13,20) (13,21) (13,19) (14,24) (14,17) (14,22) (14,16) (14,21) (16,24) (16,20) (16,23) (16,19) (17,24) (17,22) (17,20) (17,23) (17,21) (17,19) (19,24) (19,22) (19,21) (20,24) (20,22) (20,23) (20,21) (21,24) (21,23) (22,24)\nIs there a path between node 21 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph53-8_0", + "image": "data/connectivity/graph_visual/medium/graph53.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,10) (0,5) (0,7) (0,2) (0,8) (0,4) (0,9) (0,1) (0,12) (0,3) (0,11) (0,13) (1,10) (1,5) (1,7) (1,2) (1,8) (1,4) (1,9) (1,12) (1,3) (1,11) (1,13) (2,10) (2,5) (2,7) (2,8) (2,4) (2,9) (2,12) (2,3) (2,11) (2,13) (3,10) (3,5) (3,7) (3,8) (3,4) (3,9) (3,12) (3,11) (3,13) (4,10) (4,5) (4,7) (4,8) (4,9) (4,12) (4,11) (4,13) (5,10) (5,7) (5,8) (5,9) (5,12) (5,11) (5,13) (7,10) (7,8) (7,9) (7,12) (7,11) (7,13) (8,10) (8,9) (8,12) (8,11) (8,13) (9,10) (9,12) (9,11) (9,13) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nIs there a path between node 8 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph73-4_6", + "image": "data/connectivity/graph_visual/medium/graph73.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (0,12) (0,5) (1,12) (1,8) (2,3) (2,8) (2,5) (3,9) (3,10) (3,12) (3,8) (5,12) (6,13) (7,10) (7,14) (8,10) (9,10) (12,14)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph181-7_2", + "image": "data/connectivity/graph_visual/medium/graph181.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,17) (0,16) (0,5) (0,12) (0,13) (0,14) (0,7) (0,1) (1,5) (1,12) (1,9) (3,11) (3,6) (3,15) (5,17) (5,16) (5,12) (5,14) (5,7) (6,8) (7,16) (7,12) (7,14) (7,10) (7,9) (9,17) (9,16) (9,12) (9,14) (10,17) (10,16) (10,12) (10,13) (10,14) (11,15) (12,17) (12,16) (13,16) (13,14) (14,17) (14,16) (16,17)\nIs there a path between node 7 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph423-10_4", + "image": "data/connectivity/graph_visual/medium/graph423.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,20) (0,15) (1,3) (1,20) (2,11) (3,12) (3,6) (3,16) (3,20) (5,14) (5,7) (6,20) (6,21) (7,13) (7,18) (8,14) (8,13) (9,12) (9,16) (9,21) (10,21) (11,17) (12,16) (14,18) (15,16) (15,21) (16,20) (20,21)\nIs there a path between node 10 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph85-4_1", + "image": "data/connectivity/graph_visual/medium/graph85.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,3) (0,8) (0,6) (0,10) (0,14) (0,2) (0,1) (1,3) (1,8) (1,6) (1,10) (1,14) (1,2) (2,3) (2,8) (2,6) (2,10) (2,14) (3,8) (3,6) (3,10) (3,14) (4,11) (4,5) (4,13) (4,7) (4,9) (4,12) (5,11) (5,13) (5,7) (5,9) (5,12) (6,8) (6,10) (6,14) (7,11) (7,13) (7,9) (7,12) (8,10) (8,14) (9,11) (9,13) (9,12) (10,14) (11,13) (11,12) (12,13)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph498-16_9", + "image": "data/connectivity/graph_visual/medium/graph498.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,8) (0,22) (0,9) (0,19) (0,12) (1,7) (1,15) (1,6) (1,21) (1,9) (1,2) (1,19) (1,12) (1,10) (2,8) (2,3) (2,17) (3,22) (3,6) (3,21) (3,5) (3,10) (4,8) (4,6) (4,21) (4,9) (5,7) (5,8) (5,17) (5,6) (5,9) (5,12) (5,10) (6,7) (6,15) (6,14) (6,17) (7,15) (7,12) (7,10) (9,15) (9,14) (9,22) (10,14) (10,17) (11,16) (12,17) (12,21) (14,18) (15,19) (17,18) (18,21)\nIs there a path between node 16 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph458-5_4", + "image": "data/connectivity/graph_visual/medium/graph458.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,7) (0,5) (0,11) (0,3) (0,10) (0,6) (0,18) (0,15) (0,2) (0,13) (0,16) (0,8) (0,20) (1,12) (1,14) (1,21) (1,9) (1,4) (1,17) (2,19) (2,7) (2,5) (2,11) (2,3) (2,10) (2,6) (2,18) (2,15) (2,13) (2,16) (2,8) (2,20) (3,19) (3,7) (3,5) (3,11) (3,10) (3,6) (3,18) (3,15) (3,13) (3,16) (3,8) (3,20) (4,12) (4,14) (4,21) (4,9) (4,17) (5,19) (5,7) (5,11) (5,10) (5,6) (5,18) (5,15) (5,13) (5,16) (5,8) (5,20) (6,19) (6,7) (6,11) (6,10) (6,18) (6,15) (6,13) (6,16) (6,8) (6,20) (7,19) (7,11) (7,10) (7,18) (7,15) (7,13) (7,16) (7,8) (7,20) (8,19) (8,11) (8,10) (8,18) (8,15) (8,13) (8,16) (8,20) (9,12) (9,14) (9,21) (9,17) (10,19) (10,11) (10,18) (10,15) (10,13) (10,16) (10,20) (11,19) (11,18) (11,15) (11,13) (11,16) (11,20) (12,14) (12,21) (12,17) (13,19) (13,18) (13,15) (13,16) (13,20) (14,21) (14,17) (15,19) (15,18) (15,16) (15,20) (16,19) (16,18) (16,20) (17,21) (18,19) (18,20) (19,20)\nIs there a path between node 5 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph96-10_3", + "image": "data/connectivity/graph_visual/medium/graph96.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,6) (0,12) (0,4) (0,7) (0,15) (1,8) (1,7) (2,3) (4,11) (4,6) (4,10) (4,5) (4,8) (4,7) (5,7) (6,11) (6,12) (6,8) (6,7) (6,15) (7,12) (7,10) (7,15) (7,13) (8,10) (8,14) (9,10) (9,15) (10,11) (10,15) (11,12) (11,15)\nIs there a path between node 10 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph739-1_5", + "image": "data/connectivity/graph_visual/medium/graph739.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,19) (0,11) (0,13) (0,17) (0,20) (1,4) (2,23) (2,12) (2,22) (2,21) (2,14) (3,19) (3,21) (4,9) (4,24) (4,17) (4,14) (5,6) (5,22) (5,24) (5,11) (5,20) (6,23) (6,22) (6,17) (8,14) (11,23) (11,24) (11,14) (12,22) (13,19) (13,24) (14,19) (14,21) (14,24) (14,20) (17,24) (20,23) (20,21) (21,24) (22,24) (23,24)\nIs there a path between node 1 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph507-18_0", + "image": "data/connectivity/graph_visual/medium/graph507.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,13) (0,17) (1,19) (1,22) (1,13) (1,17) (1,10) (1,14) (2,6) (2,16) (2,7) (4,11) (4,21) (4,16) (4,7) (5,15) (5,8) (5,7) (6,11) (6,21) (7,8) (8,15) (8,16) (9,22) (9,14) (10,19) (10,13) (10,18) (12,14) (12,20) (13,17) (13,18) (13,14) (14,18) (14,20) (15,16) (17,22) (18,20) (19,20) (20,22)\nIs there a path between node 18 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph593-16_18", + "image": "data/connectivity/graph_visual/medium/graph593.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,7) (0,14) (0,8) (0,5) (0,4) (0,3) (0,23) (0,12) (0,15) (0,13) (0,17) (0,2) (1,19) (1,7) (1,14) (1,8) (1,3) (1,23) (1,12) (1,15) (1,13) (1,17) (1,6) (2,21) (2,19) (2,7) (2,5) (2,4) (2,3) (2,13) (3,21) (3,19) (3,14) (3,5) (3,4) (3,23) (3,12) (3,15) (4,21) (4,19) (4,14) (4,8) (4,5) (4,23) (4,12) (4,15) (4,6) (5,21) (5,19) (5,7) (5,8) (5,12) (5,17) (6,19) (6,7) (6,23) (6,12) (6,15) (6,13) (6,17) (7,21) (7,14) (7,12) (7,15) (7,13) (7,17) (8,21) (8,19) (8,12) (8,13) (9,11) (9,22) (9,20) (11,22) (11,18) (11,20) (12,14) (12,23) (12,15) (12,13) (12,17) (13,21) (13,23) (14,21) (14,19) (14,23) (14,15) (14,17) (15,21) (15,19) (15,23) (15,17) (16,22) (16,20) (17,19) (17,23) (19,21) (19,23) (20,22)\nIs there a path between node 16 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph112-0_1", + "image": "data/connectivity/graph_visual/medium/graph112.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,4) (0,11) (0,2) (0,7) (0,8) (0,16) (0,15) (1,11) (1,2) (1,7) (1,8) (1,16) (1,15) (1,14) (2,4) (2,11) (2,5) (2,7) (2,12) (2,16) (2,15) (3,13) (3,10) (4,6) (4,5) (4,7) (4,8) (4,12) (4,16) (4,15) (4,14) (5,6) (5,7) (5,8) (5,12) (5,16) (5,14) (6,11) (6,7) (6,8) (6,12) (6,16) (6,15) (6,14) (7,11) (7,8) (7,16) (7,14) (8,11) (8,12) (8,16) (11,12) (11,16) (11,15) (11,14) (12,14) (14,16) (14,15)\nIs there a path between node 0 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph209-14_7", + "image": "data/connectivity/graph_visual/medium/graph209.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,7) (0,6) (0,13) (0,12) (0,9) (0,18) (0,15) (0,17) (1,16) (1,2) (1,3) (2,3) (4,11) (4,8) (4,7) (4,9) (4,18) (4,14) (4,15) (5,8) (5,12) (5,10) (5,15) (6,11) (6,8) (6,7) (6,12) (6,18) (6,10) (6,14) (6,15) (6,17) (7,11) (7,8) (7,13) (7,12) (7,9) (7,10) (7,14) (7,15) (8,13) (8,12) (8,9) (8,18) (8,14) (8,17) (9,11) (9,12) (9,18) (9,10) (9,14) (9,15) (9,17) (10,11) (10,13) (10,18) (10,14) (10,17) (11,13) (11,18) (11,14) (12,18) (12,15) (12,17) (13,18) (13,14) (13,15) (14,18) (14,15) (14,17) (15,18) (15,17) (17,18)\nIs there a path between node 14 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph520-6_17", + "image": "data/connectivity/graph_visual/medium/graph520.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,18) (0,19) (0,3) (0,17) (0,2) (0,21) (0,13) (0,22) (1,19) (1,3) (1,2) (1,13) (2,18) (2,19) (2,5) (2,3) (2,17) (2,13) (2,22) (3,18) (3,5) (3,17) (4,8) (4,9) (4,7) (4,20) (4,12) (5,19) (5,21) (5,13) (6,8) (6,9) (6,20) (6,14) (6,10) (6,15) (6,12) (6,16) (7,9) (7,10) (7,15) (7,12) (7,16) (8,14) (8,16) (9,14) (9,11) (9,15) (9,12) (9,16) (10,20) (10,14) (10,11) (10,16) (11,20) (11,14) (11,12) (11,16) (12,15) (13,18) (13,17) (13,21) (14,20) (14,15) (14,16) (15,20) (15,16) (17,18) (17,21) (17,22) (18,19) (18,22)\nIs there a path between node 6 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph754-0_24", + "image": "data/connectivity/graph_visual/medium/graph754.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,20) (0,13) (0,7) (0,4) (0,11) (0,22) (0,17) (0,23) (1,2) (1,16) (1,21) (1,9) (1,10) (1,8) (1,3) (1,5) (1,24) (1,18) (2,16) (2,21) (2,9) (2,8) (2,3) (2,15) (2,18) (3,16) (3,21) (3,9) (3,10) (3,8) (3,5) (3,15) (4,14) (4,7) (4,12) (4,11) (4,6) (4,23) (5,16) (5,21) (5,9) (5,10) (5,8) (5,15) (5,24) (5,18) (6,14) (6,12) (6,11) (6,17) (6,23) (7,14) (7,20) (7,22) (7,19) (7,23) (8,16) (8,21) (8,9) (8,15) (8,24) (8,18) (9,16) (9,10) (9,24) (10,16) (10,21) (10,15) (10,24) (10,18) (11,14) (11,20) (11,13) (11,12) (11,22) (11,19) (11,17) (11,23) (12,14) (12,20) (12,13) (12,19) (12,17) (12,23) (13,22) (13,19) (13,17) (13,23) (14,20) (14,19) (14,23) (15,16) (15,21) (15,24) (16,21) (16,18) (17,20) (17,22) (18,21) (18,24) (19,22) (20,22) (20,23) (21,24) (22,23)\nIs there a path between node 0 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph184-16_3", + "image": "data/connectivity/graph_visual/medium/graph184.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,4) (0,2) (0,8) (0,1) (0,12) (0,9) (0,6) (0,5) (0,11) (0,13) (0,17) (0,7) (0,14) (0,15) (1,4) (1,2) (1,8) (1,12) (1,9) (1,6) (1,5) (1,11) (1,13) (1,17) (1,7) (1,14) (1,15) (2,4) (2,8) (2,12) (2,9) (2,6) (2,5) (2,11) (2,13) (2,17) (2,7) (2,14) (2,15) (3,10) (4,8) (4,12) (4,9) (4,6) (4,5) (4,11) (4,13) (4,17) (4,7) (4,14) (4,15) (5,8) (5,12) (5,9) (5,6) (5,11) (5,13) (5,17) (5,7) (5,14) (5,15) (6,8) (6,12) (6,9) (6,11) (6,13) (6,17) (6,7) (6,14) (6,15) (7,8) (7,12) (7,9) (7,11) (7,13) (7,17) (7,14) (7,15) (8,12) (8,9) (8,11) (8,13) (8,17) (8,14) (8,15) (9,12) (9,11) (9,13) (9,17) (9,14) (9,15) (11,12) (11,13) (11,17) (11,14) (11,15) (12,13) (12,17) (12,14) (12,15) (13,17) (13,14) (13,15) (14,17) (14,15) (15,17)\nIs there a path between node 16 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph602-1_10", + "image": "data/connectivity/graph_visual/medium/graph602.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,7) (0,1) (0,21) (0,20) (0,9) (1,7) (1,21) (1,20) (1,9) (2,5) (2,11) (2,23) (2,12) (2,22) (2,6) (2,10) (2,19) (3,8) (3,15) (3,17) (4,21) (5,11) (5,12) (5,22) (5,13) (5,18) (5,10) (6,23) (6,22) (6,13) (6,18) (6,10) (6,19) (6,16) (7,21) (7,9) (8,15) (8,17) (9,21) (10,11) (10,12) (10,22) (10,13) (10,19) (11,23) (11,12) (11,22) (11,13) (11,18) (11,19) (11,16) (12,23) (12,22) (12,13) (12,18) (12,19) (12,16) (13,23) (13,22) (13,18) (13,19) (13,16) (14,15) (16,23) (16,22) (16,18) (18,23) (18,22) (18,19) (19,23) (19,22) (20,21) (22,23)\nIs there a path between node 1 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph260-2_0", + "image": "data/connectivity/graph_visual/medium/graph260.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,18) (0,1) (0,8) (0,10) (0,11) (0,7) (0,4) (0,2) (0,6) (0,17) (0,14) (1,19) (1,18) (1,8) (1,10) (1,11) (1,7) (1,4) (1,2) (1,6) (1,17) (1,14) (2,19) (2,18) (2,8) (2,10) (2,11) (2,7) (2,4) (2,6) (2,17) (2,14) (3,13) (3,9) (3,15) (4,19) (4,18) (4,8) (4,10) (4,11) (4,7) (4,6) (4,17) (4,14) (5,12) (5,16) (6,19) (6,18) (6,8) (6,10) (6,11) (6,7) (6,17) (6,14) (7,19) (7,18) (7,8) (7,10) (7,11) (7,17) (7,14) (8,19) (8,18) (8,10) (8,11) (8,17) (8,14) (9,13) (9,15) (10,19) (10,18) (10,11) (10,17) (10,14) (11,19) (11,18) (11,17) (11,14) (12,16) (13,15) (14,19) (14,18) (14,17) (17,19) (17,18) (18,19)\nIs there a path between node 2 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph845-6_13", + "image": "data/connectivity/graph_visual/medium/graph845.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,3) (0,7) (0,16) (0,8) (0,11) (0,12) (0,19) (0,10) (0,1) (0,5) (0,21) (0,2) (0,13) (0,17) (1,24) (1,3) (1,7) (1,16) (1,8) (1,11) (1,12) (1,19) (1,10) (1,5) (1,21) (1,2) (1,13) (1,17) (2,24) (2,3) (2,7) (2,16) (2,8) (2,11) (2,12) (2,19) (2,10) (2,5) (2,21) (2,13) (2,17) (3,24) (3,7) (3,16) (3,8) (3,11) (3,12) (3,19) (3,10) (3,5) (3,21) (3,13) (3,17) (4,22) (4,20) (4,6) (4,18) (4,15) (4,23) (5,24) (5,7) (5,16) (5,8) (5,11) (5,12) (5,19) (5,10) (5,21) (5,13) (5,17) (6,22) (6,20) (6,18) (6,15) (6,23) (7,24) (7,16) (7,8) (7,11) (7,12) (7,19) (7,10) (7,21) (7,13) (7,17) (8,24) (8,16) (8,11) (8,12) (8,19) (8,10) (8,21) (8,13) (8,17) (9,14) (10,24) (10,16) (10,11) (10,12) (10,19) (10,21) (10,13) (10,17) (11,24) (11,16) (11,12) (11,19) (11,21) (11,13) (11,17) (12,24) (12,16) (12,19) (12,21) (12,13) (12,17) (13,24) (13,16) (13,19) (13,21) (13,17) (15,22) (15,20) (15,18) (15,23) (16,24) (16,19) (16,21) (16,17) (17,24) (17,19) (17,21) (18,22) (18,20) (18,23) (19,24) (19,21) (20,22) (20,23) (21,24) (22,23)\nIs there a path between node 6 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph452-21_14", + "image": "data/connectivity/graph_visual/medium/graph452.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,5) (0,13) (0,16) (0,4) (0,12) (1,5) (1,13) (1,9) (1,16) (1,4) (1,2) (2,13) (2,14) (2,4) (3,11) (3,19) (3,18) (3,15) (3,20) (3,6) (3,8) (3,10) (3,21) (4,13) (4,14) (4,9) (4,12) (5,13) (5,14) (5,9) (5,16) (6,11) (6,19) (6,18) (6,15) (6,17) (6,10) (6,21) (6,7) (7,11) (7,19) (7,18) (7,15) (7,20) (7,17) (7,8) (7,10) (7,21) (8,11) (8,18) (8,15) (8,20) (8,21) (9,13) (9,14) (9,16) (9,12) (10,11) (10,19) (10,18) (10,20) (10,17) (10,21) (11,18) (11,20) (14,16) (15,19) (15,18) (15,20) (15,17) (15,21) (17,19) (17,18) (17,20) (17,21) (18,19) (18,20) (19,20) (19,21) (20,21)\nIs there a path between node 21 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph157-0_12", + "image": "data/connectivity/graph_visual/medium/graph157.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,6) (0,16) (0,3) (1,9) (2,10) (2,12) (2,3) (3,10) (3,12) (5,6) (6,8) (7,8) (8,10) (9,15) (9,13) (13,14)\nIs there a path between node 0 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph532-22_5", + "image": "data/connectivity/graph_visual/medium/graph532.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,17) (0,19) (0,4) (0,6) (0,18) (0,20) (0,22) (0,16) (0,12) (0,10) (1,13) (1,5) (1,21) (1,7) (2,8) (2,3) (2,9) (2,14) (2,15) (2,11) (3,8) (3,9) (3,14) (3,15) (3,11) (4,17) (4,19) (4,6) (4,18) (4,20) (4,22) (4,16) (4,12) (4,10) (5,13) (5,21) (5,7) (6,17) (6,19) (6,18) (6,20) (6,22) (6,16) (6,12) (6,10) (7,13) (7,21) (8,9) (8,14) (8,15) (8,11) (9,14) (9,15) (9,11) (10,17) (10,19) (10,18) (10,20) (10,22) (10,16) (10,12) (11,14) (11,15) (12,17) (12,19) (12,18) (12,20) (12,22) (12,16) (13,21) (14,15) (16,17) (16,19) (16,18) (16,20) (16,22) (17,19) (17,18) (17,20) (17,22) (18,19) (18,20) (18,22) (19,20) (19,22) (20,22)\nIs there a path between node 22 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph334-1_14", + "image": "data/connectivity/graph_visual/medium/graph334.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,7) (0,3) (0,20) (1,13) (2,9) (2,12) (2,13) (3,7) (3,20) (5,6) (5,10) (5,11) (5,15) (5,17) (5,12) (6,9) (6,10) (6,11) (8,16) (9,17) (9,13) (10,17) (11,16) (11,18) (12,16) (13,15) (13,17) (13,18) (14,19) (19,20)\nIs there a path between node 1 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph559-10_4", + "image": "data/connectivity/graph_visual/medium/graph559.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,23) (0,20) (0,17) (0,3) (0,6) (0,5) (0,9) (0,7) (0,13) (0,4) (0,2) (0,1) (1,8) (1,16) (1,23) (1,20) (1,3) (1,6) (1,5) (1,9) (1,14) (1,7) (1,13) (2,18) (2,8) (2,16) (2,20) (2,3) (2,10) (2,5) (2,9) (2,12) (2,14) (2,4) (3,18) (3,8) (3,16) (3,6) (3,5) (3,9) (3,12) (3,14) (3,13) (4,18) (4,8) (4,16) (4,6) (4,10) (4,5) (4,9) (4,12) (4,7) (4,13) (5,8) (5,17) (5,10) (5,9) (5,12) (5,14) (5,7) (5,13) (6,8) (6,16) (6,20) (6,10) (6,12) (6,14) (6,7) (7,8) (7,16) (7,23) (7,17) (7,10) (7,9) (7,12) (7,13) (8,18) (8,17) (8,10) (8,9) (8,12) (8,14) (8,13) (9,18) (9,16) (9,12) (9,14) (9,13) (10,18) (10,23) (10,20) (10,17) (10,12) (10,13) (11,22) (12,23) (12,20) (12,17) (13,18) (13,16) (13,23) (13,20) (13,14) (14,18) (14,16) (14,23) (14,17) (15,19) (15,21) (15,22) (16,18) (16,23) (16,20) (16,17) (17,18) (17,20) (18,20) (19,21) (20,23) (21,22)\nIs there a path between node 10 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph569-7_17", + "image": "data/connectivity/graph_visual/medium/graph569.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,19) (0,20) (0,9) (1,13) (1,7) (1,12) (1,5) (1,2) (1,21) (1,18) (1,15) (1,22) (1,17) (2,13) (2,7) (2,12) (2,5) (2,21) (2,18) (2,15) (2,22) (2,17) (3,19) (3,20) (3,9) (4,8) (4,16) (4,6) (4,11) (5,13) (5,7) (5,12) (5,21) (5,18) (5,15) (5,22) (5,17) (6,8) (6,16) (6,11) (7,13) (7,12) (7,21) (7,18) (7,15) (7,22) (7,17) (8,16) (8,11) (9,19) (9,20) (10,14) (10,23) (11,16) (12,13) (12,21) (12,18) (12,15) (12,22) (12,17) (13,21) (13,18) (13,15) (13,22) (13,17) (14,23) (15,21) (15,18) (15,22) (15,17) (17,21) (17,18) (17,22) (18,21) (18,22) (19,20) (21,22)\nIs there a path between node 7 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph831-1_22", + "image": "data/connectivity/graph_visual/medium/graph831.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (1,14) (1,20) (2,3) (2,17) (2,18) (2,9) (2,23) (2,6) (2,21) (2,11) (3,24) (3,13) (3,18) (3,9) (3,23) (3,21) (3,16) (3,10) (3,8) (4,12) (4,7) (4,22) (4,20) (4,5) (5,14) (5,12) (5,7) (5,22) (5,20) (6,13) (6,17) (6,15) (6,21) (6,11) (6,10) (6,8) (7,14) (7,12) (7,22) (8,24) (8,13) (8,15) (8,18) (8,23) (8,11) (8,16) (8,10) (9,24) (9,15) (9,23) (9,11) (9,16) (9,10) (10,24) (10,13) (10,17) (10,15) (10,18) (10,23) (10,11) (10,16) (11,24) (11,13) (11,18) (11,23) (11,21) (12,22) (12,20) (13,24) (13,17) (13,18) (13,23) (13,21) (13,16) (14,20) (15,24) (15,17) (15,18) (15,21) (16,24) (16,17) (16,23) (17,24) (17,18) (17,23) (18,24) (20,22) (21,24) (21,23) (23,24)\nIs there a path between node 1 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph226-6_13", + "image": "data/connectivity/graph_visual/medium/graph226.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,14) (0,18) (0,6) (0,5) (0,10) (1,2) (5,9) (5,7) (5,16) (5,10) (6,7) (6,12) (7,9) (7,17) (7,16) (8,9) (8,11) (8,10) (9,17) (10,11) (10,16) (11,14) (12,17) (12,14) (14,17) (14,18) (14,16) (14,15) (15,17) (15,18) (16,18) (17,18)\nIs there a path between node 6 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph2-6_5", + "image": "data/connectivity/graph_visual/medium/graph2.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,3) (0,7) (0,10) (0,6) (0,2) (0,8) (0,4) (0,1) (1,3) (1,7) (1,10) (1,6) (1,2) (1,8) (1,4) (2,3) (2,7) (2,10) (2,6) (2,8) (2,4) (3,7) (3,10) (3,6) (3,8) (3,4) (4,7) (4,10) (4,6) (4,8) (5,9) (6,7) (6,10) (6,8) (7,10) (7,8) (8,10)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph741-20_5", + "image": "data/connectivity/graph_visual/medium/graph741.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,20) (0,17) (0,15) (3,5) (3,6) (3,8) (4,11) (4,16) (4,24) (5,10) (5,8) (5,14) (11,16) (13,20) (13,16) (13,15) (13,19) (14,18) (15,16) (15,22) (15,24) (17,20) (17,22) (17,21) (19,24) (20,22) (20,21) (21,22)\nIs there a path between node 20 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph238-15_9", + "image": "data/connectivity/graph_visual/medium/graph238.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,2) (0,5) (0,7) (0,18) (0,13) (0,11) (0,17) (1,8) (1,7) (1,18) (1,13) (1,9) (1,15) (1,11) (1,10) (2,8) (2,5) (2,7) (2,15) (3,14) (3,4) (3,12) (4,12) (5,8) (5,18) (5,13) (5,9) (5,11) (5,17) (6,16) (7,18) (7,13) (7,9) (7,11) (7,17) (8,18) (8,13) (8,9) (8,15) (8,11) (8,17) (8,10) (9,18) (9,13) (9,15) (9,17) (10,15) (10,17) (11,18) (11,13) (11,15) (11,17) (12,14) (13,18) (13,15) (15,18) (15,17) (17,18)\nIs there a path between node 15 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph185-15_9", + "image": "data/connectivity/graph_visual/medium/graph185.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,7) (0,9) (0,6) (0,16) (0,3) (0,13) (0,15) (0,4) (0,8) (1,5) (1,17) (1,12) (1,14) (1,2) (2,5) (2,17) (2,12) (2,14) (3,7) (3,9) (3,6) (3,16) (3,13) (3,15) (3,4) (3,8) (4,7) (4,9) (4,6) (4,16) (4,13) (4,15) (4,8) (5,17) (5,12) (5,14) (6,7) (6,9) (6,16) (6,13) (6,15) (6,8) (7,9) (7,16) (7,13) (7,15) (7,8) (8,9) (8,16) (8,13) (8,15) (9,16) (9,13) (9,15) (10,11) (12,17) (12,14) (13,16) (13,15) (14,17) (15,16)\nIs there a path between node 15 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph552-21_3", + "image": "data/connectivity/graph_visual/medium/graph552.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,12) (2,13) (2,22) (3,4) (3,18) (3,10) (3,7) (3,20) (4,21) (4,5) (5,18) (5,23) (5,10) (5,7) (5,20) (5,16) (6,11) (6,10) (6,7) (6,14) (6,16) (6,15) (7,18) (7,9) (7,11) (7,8) (7,16) (8,18) (8,9) (8,10) (8,20) (8,14) (8,16) (8,15) (9,21) (9,23) (10,21) (10,11) (10,15) (11,18) (11,17) (11,16) (12,13) (13,22) (14,18) (14,23) (14,17) (14,16) (14,15) (15,21) (16,18) (16,20) (18,20) (19,22) (20,23)\nIs there a path between node 21 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph236-16_7", + "image": "data/connectivity/graph_visual/medium/graph236.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,12) (0,7) (0,11) (0,8) (0,9) (0,2) (0,6) (1,18) (1,15) (1,10) (1,17) (1,13) (1,14) (1,4) (1,16) (2,11) (2,8) (2,9) (3,12) (3,7) (3,9) (4,18) (4,17) (4,5) (4,16) (5,18) (5,15) (5,17) (5,13) (5,14) (6,7) (6,11) (7,12) (7,11) (7,8) (7,9) (8,12) (8,11) (8,9) (9,11) (10,18) (10,16) (13,15) (13,17) (13,16) (14,18) (14,15) (14,16) (15,17) (16,17) (17,18)\nIs there a path between node 16 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph500-18_21", + "image": "data/connectivity/graph_visual/medium/graph500.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,12) (0,22) (0,14) (0,16) (0,19) (0,4) (0,11) (0,20) (0,13) (0,18) (0,5) (1,22) (1,15) (1,9) (2,7) (3,15) (3,16) (3,9) (3,11) (3,10) (3,5) (4,12) (4,22) (4,14) (4,15) (4,11) (4,13) (4,18) (4,6) (4,17) (5,15) (5,18) (5,6) (6,12) (6,15) (6,11) (6,20) (6,17) (8,22) (8,20) (9,14) (9,15) (9,11) (9,20) (10,19) (11,22) (11,19) (12,14) (12,16) (12,19) (12,17) (13,14) (13,15) (14,22) (14,19) (16,18) (16,17) (18,22) (18,19) (20,22)\nIs there a path between node 18 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph553-4_2", + "image": "data/connectivity/graph_visual/medium/graph553.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,10) (0,9) (0,3) (1,10) (1,4) (1,2) (1,12) (1,14) (1,6) (1,15) (2,7) (2,10) (2,9) (2,17) (2,15) (3,20) (3,14) (3,18) (3,6) (3,15) (4,7) (4,16) (4,13) (4,9) (4,14) (4,21) (4,22) (4,17) (5,23) (5,11) (6,10) (6,16) (6,20) (6,22) (7,16) (7,20) (8,23) (8,19) (9,22) (12,14) (12,17) (13,16) (13,14) (13,17) (14,21) (15,21) (15,18) (16,18) (17,18) (19,23) (20,21)\nIs there a path between node 4 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph274-17_13", + "image": "data/connectivity/graph_visual/medium/graph274.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,4) (0,12) (0,8) (0,3) (1,16) (1,9) (1,14) (1,7) (1,15) (1,6) (2,16) (2,14) (2,15) (2,17) (2,6) (3,5) (3,8) (3,10) (4,13) (4,5) (5,13) (5,12) (6,16) (6,9) (6,14) (6,7) (6,11) (6,15) (6,17) (7,19) (7,14) (7,15) (7,17) (8,12) (8,10) (9,16) (9,19) (9,14) (9,11) (10,13) (11,16) (11,19) (11,14) (11,17) (14,19) (14,15) (14,17) (15,19) (15,17) (16,19) (16,17) (17,19)\nIs there a path between node 17 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph207-5_9", + "image": "data/connectivity/graph_visual/medium/graph207.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,9) (0,12) (1,9) (1,7) (1,12) (2,17) (2,13) (2,18) (2,15) (2,5) (2,16) (2,4) (2,3) (2,6) (2,14) (2,11) (2,10) (2,8) (3,13) (3,18) (3,5) (3,16) (3,4) (3,6) (3,14) (3,11) (3,10) (3,8) (4,13) (4,5) (4,16) (4,6) (4,14) (4,11) (4,10) (4,8) (5,17) (5,13) (5,16) (5,14) (5,10) (5,8) (6,17) (6,13) (6,18) (6,15) (6,14) (6,11) (6,10) (6,8) (7,12) (8,13) (8,18) (8,15) (8,14) (8,10) (10,13) (10,18) (10,16) (10,14) (10,11) (11,17) (11,13) (11,18) (11,15) (11,14) (13,18) (13,15) (13,16) (14,17) (14,15) (14,16) (16,17) (17,18)\nIs there a path between node 5 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph667-15_5", + "image": "data/connectivity/graph_visual/medium/graph667.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,14) (0,6) (0,21) (0,7) (0,12) (0,5) (0,16) (0,15) (0,3) (0,17) (0,22) (1,4) (1,2) (1,11) (2,4) (2,18) (2,11) (3,14) (3,21) (3,7) (3,12) (3,5) (3,19) (3,23) (3,15) (3,22) (3,20) (4,18) (4,11) (5,6) (5,21) (5,12) (5,16) (5,19) (5,15) (5,17) (5,22) (5,20) (6,21) (6,12) (6,16) (6,19) (6,23) (6,15) (6,17) (6,22) (6,20) (7,12) (7,19) (7,23) (7,17) (7,22) (7,20) (8,13) (9,10) (9,13) (10,13) (12,14) (12,21) (12,19) (12,23) (12,15) (12,17) (12,22) (14,21) (14,16) (14,19) (14,23) (14,17) (14,22) (14,20) (15,16) (15,19) (15,23) (15,17) (15,22) (16,21) (16,17) (16,22) (16,20) (17,21) (17,19) (17,22) (17,20) (19,21) (19,23) (19,22) (19,20) (20,23) (20,22) (21,22) (22,23)\nIs there a path between node 15 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph471-22_16", + "image": "data/connectivity/graph_visual/medium/graph471.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,19) (1,12) (1,19) (2,13) (3,20) (3,11) (4,7) (4,16) (4,18) (5,17) (5,7) (6,15) (6,20) (6,11) (7,20) (7,11) (8,12) (8,13) (8,19) (11,17) (11,15) (12,19) (16,17) (16,20) (17,20) (18,20)\nIs there a path between node 22 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph836-1_14", + "image": "data/connectivity/graph_visual/medium/graph836.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,3) (0,8) (0,11) (0,22) (0,24) (0,1) (0,17) (0,14) (0,19) (0,2) (0,20) (1,6) (1,3) (1,8) (1,11) (1,22) (1,24) (1,17) (1,14) (1,19) (1,2) (1,20) (2,6) (2,3) (2,8) (2,11) (2,22) (2,24) (2,17) (2,14) (2,19) (2,20) (3,6) (3,8) (3,11) (3,22) (3,24) (3,17) (3,14) (3,19) (3,20) (4,18) (4,23) (4,15) (4,9) (5,21) (5,13) (5,7) (5,10) (5,16) (5,12) (6,8) (6,11) (6,22) (6,24) (6,17) (6,14) (6,19) (6,20) (7,21) (7,13) (7,10) (7,16) (7,12) (8,11) (8,22) (8,24) (8,17) (8,14) (8,19) (8,20) (9,18) (9,23) (9,15) (10,21) (10,13) (10,16) (10,12) (11,22) (11,24) (11,17) (11,14) (11,19) (11,20) (12,21) (12,13) (12,16) (13,21) (13,16) (14,22) (14,24) (14,17) (14,19) (14,20) (15,18) (15,23) (16,21) (17,22) (17,24) (17,19) (17,20) (18,23) (19,22) (19,24) (19,20) (20,22) (20,24) (22,24)\nIs there a path between node 1 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph289-1_8", + "image": "data/connectivity/graph_visual/medium/graph289.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,13) (0,17) (0,4) (1,14) (2,8) (3,15) (4,11) (4,18) (4,17) (5,19) (7,13) (7,12) (7,10) (8,16) (8,14) (9,12) (9,10) (10,18) (11,18) (11,12) (12,13) (13,18) (13,17) (14,16) (17,18)\nIs there a path between node 1 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph322-2_12", + "image": "data/connectivity/graph_visual/medium/graph322.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,3) (0,1) (0,11) (0,4) (0,16) (0,5) (0,19) (0,6) (0,10) (0,17) (0,12) (1,3) (1,11) (1,4) (1,16) (1,5) (1,19) (1,6) (1,10) (1,17) (1,12) (2,15) (2,14) (2,9) (2,18) (2,7) (3,11) (3,4) (3,16) (3,5) (3,19) (3,6) (3,10) (3,17) (3,12) (4,11) (4,16) (4,5) (4,19) (4,6) (4,10) (4,17) (4,12) (5,11) (5,16) (5,19) (5,6) (5,10) (5,17) (5,12) (6,11) (6,16) (6,19) (6,10) (6,17) (6,12) (7,15) (7,14) (7,9) (7,18) (8,13) (9,15) (9,14) (9,18) (10,11) (10,16) (10,19) (10,17) (10,12) (11,16) (11,19) (11,17) (11,12) (12,16) (12,19) (12,17) (14,15) (14,18) (15,18) (16,19) (16,17) (17,19)\nIs there a path between node 2 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph612-16_5", + "image": "data/connectivity/graph_visual/medium/graph612.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,6) (0,12) (0,20) (0,15) (0,9) (0,13) (0,2) (0,14) (0,11) (0,3) (0,23) (0,5) (1,21) (1,7) (1,8) (1,22) (1,4) (1,18) (1,17) (1,16) (2,10) (2,19) (2,6) (2,12) (2,20) (2,15) (2,9) (2,13) (2,14) (2,11) (2,3) (2,23) (2,5) (3,10) (3,19) (3,6) (3,12) (3,20) (3,15) (3,9) (3,13) (3,14) (3,11) (3,23) (3,5) (4,21) (4,7) (4,8) (4,22) (4,18) (4,17) (4,16) (5,10) (5,19) (5,6) (5,12) (5,20) (5,15) (5,9) (5,13) (5,14) (5,11) (5,23) (6,10) (6,19) (6,12) (6,20) (6,15) (6,9) (6,13) (6,14) (6,11) (6,23) (7,21) (7,8) (7,22) (7,18) (7,17) (7,16) (8,21) (8,22) (8,18) (8,17) (8,16) (9,10) (9,19) (9,12) (9,20) (9,15) (9,13) (9,14) (9,11) (9,23) (10,19) (10,12) (10,20) (10,15) (10,13) (10,14) (10,11) (10,23) (11,19) (11,12) (11,20) (11,15) (11,13) (11,14) (11,23) (12,19) (12,20) (12,15) (12,13) (12,14) (12,23) (13,19) (13,20) (13,15) (13,14) (13,23) (14,19) (14,20) (14,15) (14,23) (15,19) (15,20) (15,23) (16,21) (16,22) (16,18) (16,17) (17,21) (17,22) (17,18) (18,21) (18,22) (19,20) (19,23) (20,23) (21,22)\nIs there a path between node 16 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph258-18_15", + "image": "data/connectivity/graph_visual/medium/graph258.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,2) (1,18) (1,12) (1,15) (1,7) (2,17) (2,3) (3,17) (4,12) (5,17) (5,19) (6,18) (6,10) (6,9) (6,12) (6,16) (7,18) (7,9) (7,13) (7,8) (8,14) (9,18) (9,14) (9,12) (9,13) (10,12) (10,15) (11,17) (12,16) (14,18)\nIs there a path between node 18 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph49-4_5", + "image": "data/connectivity/graph_visual/medium/graph49.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,9) (0,7) (0,12) (0,2) (0,8) (0,6) (0,11) (0,4) (1,5) (1,10) (1,3) (2,9) (2,7) (2,12) (2,8) (2,6) (2,11) (2,4) (3,5) (3,10) (4,9) (4,7) (4,12) (4,8) (4,6) (4,11) (5,10) (6,9) (6,7) (6,12) (6,8) (6,11) (7,9) (7,12) (7,8) (7,11) (8,9) (8,12) (8,11) (9,12) (9,11) (11,12)\nIs there a path between node 4 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph285-4_8", + "image": "data/connectivity/graph_visual/medium/graph285.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,14) (1,9) (1,2) (1,8) (2,18) (2,6) (2,5) (2,8) (2,11) (3,7) (5,13) (5,6) (5,9) (5,8) (6,12) (6,13) (6,18) (6,10) (6,9) (6,8) (6,11) (7,15) (8,16) (8,9) (9,13) (9,10) (10,16) (10,11) (11,12) (11,16) (12,16) (13,16) (14,15)\nIs there a path between node 4 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph38-11_2", + "image": "data/connectivity/graph_visual/medium/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,12) (1,9) (2,10) (2,4) (2,12) (3,7) (4,12) (8,10) (8,11) (10,11)\nIs there a path between node 11 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph42-1_11", + "image": "data/connectivity/graph_visual/medium/graph42.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,6) (0,7) (0,10) (0,8) (0,11) (0,12) (1,3) (1,4) (1,9) (2,6) (2,7) (2,10) (2,8) (2,11) (2,12) (3,4) (3,5) (3,9) (4,5) (4,9) (5,9) (6,7) (6,10) (6,12) (7,10) (7,12) (8,10) (8,11) (8,12) (10,11) (11,12)\nIs there a path between node 1 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph79-2_10", + "image": "data/connectivity/graph_visual/medium/graph79.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (0,6) (0,4) (0,8) (0,14) (0,7) (0,12) (0,11) (0,13) (0,5) (1,6) (1,4) (1,14) (1,7) (1,12) (1,11) (1,13) (2,4) (2,8) (2,12) (2,13) (2,5) (3,10) (4,6) (4,8) (4,7) (4,12) (4,13) (4,5) (5,6) (5,8) (5,7) (5,12) (5,11) (5,13) (6,8) (6,14) (6,7) (6,12) (6,13) (7,8) (7,14) (7,12) (7,11) (7,13) (8,14) (8,12) (8,11) (8,13) (9,10) (11,14) (11,12) (12,14) (12,13) (13,14)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph192-1_15", + "image": "data/connectivity/graph_visual/medium/graph192.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,11) (0,14) (0,5) (0,7) (0,9) (0,1) (0,12) (1,11) (1,14) (1,5) (1,7) (1,9) (1,12) (2,6) (2,10) (2,15) (2,8) (2,17) (2,13) (2,16) (2,3) (2,4) (3,6) (3,10) (3,15) (3,8) (3,17) (3,13) (3,16) (3,4) (4,6) (4,10) (4,15) (4,8) (4,17) (4,13) (4,16) (5,11) (5,14) (5,7) (5,9) (5,12) (6,10) (6,15) (6,8) (6,17) (6,13) (6,16) (7,11) (7,14) (7,9) (7,12) (8,10) (8,15) (8,17) (8,13) (8,16) (9,11) (9,14) (9,12) (10,15) (10,17) (10,13) (10,16) (11,14) (11,12) (12,14) (13,15) (13,17) (13,16) (15,17) (15,16) (16,17)\nIs there a path between node 1 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph24-11_8", + "image": "data/connectivity/graph_visual/medium/graph24.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,1) (0,8) (0,9) (0,3) (1,11) (1,5) (1,4) (1,6) (1,3) (2,10) (3,11) (3,5) (3,8) (3,4) (4,11) (4,6) (4,9) (5,11) (5,8) (5,6) (5,9) (6,11) (7,10) (9,11)\nIs there a path between node 11 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph743-4_8", + "image": "data/connectivity/graph_visual/medium/graph743.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (1,22) (1,6) (1,2) (1,14) (2,16) (2,20) (2,5) (2,23) (3,16) (3,20) (3,8) (3,5) (3,6) (4,10) (4,24) (5,17) (5,22) (5,20) (5,7) (6,17) (6,9) (6,23) (7,22) (7,20) (8,16) (8,22) (8,14) (9,16) (9,22) (9,20) (9,12) (9,23) (10,11) (12,22) (12,23) (13,18) (14,16) (14,22) (16,17) (16,22) (16,20) (20,22) (20,23)\nIs there a path between node 4 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph754-14_23", + "image": "data/connectivity/graph_visual/medium/graph754.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,20) (0,13) (0,7) (0,4) (0,11) (0,22) (0,17) (0,23) (1,2) (1,16) (1,21) (1,9) (1,10) (1,8) (1,3) (1,5) (1,24) (1,18) (2,16) (2,21) (2,9) (2,8) (2,3) (2,15) (2,18) (3,16) (3,21) (3,9) (3,10) (3,8) (3,5) (3,15) (4,14) (4,7) (4,12) (4,11) (4,6) (4,23) (5,16) (5,21) (5,9) (5,10) (5,8) (5,15) (5,24) (5,18) (6,14) (6,12) (6,11) (6,17) (6,23) (7,14) (7,20) (7,22) (7,19) (7,23) (8,16) (8,21) (8,9) (8,15) (8,24) (8,18) (9,16) (9,10) (9,24) (10,16) (10,21) (10,15) (10,24) (10,18) (11,14) (11,20) (11,13) (11,12) (11,22) (11,19) (11,17) (11,23) (12,14) (12,20) (12,13) (12,19) (12,17) (12,23) (13,22) (13,19) (13,17) (13,23) (14,20) (14,19) (14,23) (15,16) (15,21) (15,24) (16,21) (16,18) (17,20) (17,22) (18,21) (18,24) (19,22) (20,22) (20,23) (21,24) (22,23)\nIs there a path between node 14 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph155-5_14", + "image": "data/connectivity/graph_visual/medium/graph155.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,9) (0,1) (0,6) (0,10) (0,3) (0,13) (0,8) (0,14) (0,15) (0,2) (0,7) (0,11) (1,9) (1,6) (1,10) (1,3) (1,13) (1,8) (1,14) (1,15) (1,2) (1,7) (1,11) (2,9) (2,6) (2,10) (2,3) (2,13) (2,8) (2,14) (2,15) (2,7) (2,11) (3,9) (3,6) (3,10) (3,13) (3,8) (3,14) (3,15) (3,7) (3,11) (4,12) (4,5) (4,16) (5,12) (5,16) (6,9) (6,10) (6,13) (6,8) (6,14) (6,15) (6,7) (6,11) (7,9) (7,10) (7,13) (7,8) (7,14) (7,15) (7,11) (8,9) (8,10) (8,13) (8,14) (8,15) (8,11) (9,10) (9,13) (9,14) (9,15) (9,11) (10,13) (10,14) (10,15) (10,11) (11,13) (11,14) (11,15) (12,16) (13,14) (13,15) (14,15)\nIs there a path between node 5 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph729-21_13", + "image": "data/connectivity/graph_visual/medium/graph729.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,16) (1,24) (1,13) (1,7) (2,24) (2,15) (2,18) (2,8) (2,13) (2,7) (3,23) (3,6) (5,20) (5,14) (6,11) (6,23) (7,12) (7,10) (7,21) (7,8) (7,13) (8,10) (8,15) (8,18) (8,22) (8,13) (9,21) (9,13) (10,12) (10,15) (10,13) (12,24) (13,24) (13,22) (14,20) (15,24) (17,24) (19,20) (21,24)\nIs there a path between node 21 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph490-13_1", + "image": "data/connectivity/graph_visual/medium/graph490.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (2,17) (2,19) (2,18) (2,8) (2,12) (2,21) (2,7) (2,13) (2,11) (2,10) (2,20) (2,5) (2,22) (3,15) (3,4) (3,16) (3,9) (3,6) (3,14) (4,15) (4,16) (4,9) (4,6) (4,14) (5,17) (5,19) (5,18) (5,8) (5,12) (5,21) (5,7) (5,13) (5,11) (5,10) (5,20) (5,22) (6,15) (6,16) (6,9) (6,14) (7,17) (7,19) (7,18) (7,8) (7,12) (7,21) (7,13) (7,11) (7,10) (7,20) (7,22) (8,17) (8,19) (8,18) (8,12) (8,21) (8,13) (8,11) (8,10) (8,20) (8,22) (9,15) (9,16) (9,14) (10,17) (10,19) (10,18) (10,12) (10,21) (10,13) (10,11) (10,20) (10,22) (11,17) (11,19) (11,18) (11,12) (11,21) (11,13) (11,20) (11,22) (12,17) (12,19) (12,18) (12,21) (12,13) (12,20) (12,22) (13,17) (13,19) (13,18) (13,21) (13,20) (13,22) (14,15) (14,16) (15,16) (17,19) (17,18) (17,21) (17,20) (17,22) (18,19) (18,21) (18,20) (18,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 13 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph778-2_4", + "image": "data/connectivity/graph_visual/medium/graph778.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,13) (0,16) (0,19) (0,12) (0,15) (0,22) (0,5) (0,4) (0,6) (0,11) (1,18) (1,14) (2,3) (2,8) (2,17) (2,24) (2,23) (2,21) (2,10) (2,20) (3,8) (3,17) (3,24) (3,23) (3,21) (3,10) (3,20) (4,9) (4,13) (4,16) (4,19) (4,12) (4,15) (4,22) (4,5) (4,6) (4,11) (5,9) (5,13) (5,16) (5,19) (5,12) (5,15) (5,22) (5,6) (5,11) (6,9) (6,13) (6,16) (6,19) (6,12) (6,15) (6,22) (6,11) (8,17) (8,24) (8,23) (8,21) (8,10) (8,20) (9,13) (9,16) (9,19) (9,12) (9,15) (9,22) (9,11) (10,17) (10,24) (10,23) (10,21) (10,20) (11,13) (11,16) (11,19) (11,12) (11,15) (11,22) (12,13) (12,16) (12,19) (12,15) (12,22) (13,16) (13,19) (13,15) (13,22) (14,18) (15,16) (15,19) (15,22) (16,19) (16,22) (17,24) (17,23) (17,21) (17,20) (19,22) (20,24) (20,23) (20,21) (21,24) (21,23) (23,24)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph140-9_14", + "image": "data/connectivity/graph_visual/medium/graph140.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,14) (1,9) (2,14) (2,6) (2,5) (3,16) (4,7) (4,9) (4,15) (5,9) (5,15) (6,14) (6,9) (6,12) (7,14) (7,15) (7,12) (8,17) (10,13) (12,14)\nIs there a path between node 9 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph534-16_20", + "image": "data/connectivity/graph_visual/medium/graph534.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,19) (0,20) (0,13) (0,2) (0,3) (0,16) (0,15) (0,4) (0,11) (0,22) (0,5) (0,6) (0,7) (0,1) (0,10) (1,21) (1,19) (1,20) (1,13) (1,2) (1,3) (1,16) (1,15) (1,4) (1,11) (1,22) (1,5) (1,6) (1,7) (1,10) (2,21) (2,19) (2,20) (2,13) (2,3) (2,16) (2,15) (2,4) (2,11) (2,22) (2,5) (2,6) (2,7) (2,10) (3,21) (3,19) (3,20) (3,13) (3,16) (3,15) (3,4) (3,11) (3,22) (3,5) (3,6) (3,7) (3,10) (4,21) (4,19) (4,20) (4,13) (4,16) (4,15) (4,11) (4,22) (4,5) (4,6) (4,7) (4,10) (5,21) (5,19) (5,20) (5,13) (5,16) (5,15) (5,11) (5,22) (5,6) (5,7) (5,10) (6,21) (6,19) (6,20) (6,13) (6,16) (6,15) (6,11) (6,22) (6,7) (6,10) (7,21) (7,19) (7,20) (7,13) (7,16) (7,15) (7,11) (7,22) (7,10) (8,12) (8,14) (8,9) (8,18) (9,12) (9,14) (9,18) (10,21) (10,19) (10,20) (10,13) (10,16) (10,15) (10,11) (10,22) (11,21) (11,19) (11,20) (11,13) (11,16) (11,15) (11,22) (12,14) (12,18) (13,21) (13,19) (13,20) (13,16) (13,15) (13,22) (14,18) (15,21) (15,19) (15,20) (15,16) (15,22) (16,21) (16,19) (16,20) (16,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 16 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph450-12_20", + "image": "data/connectivity/graph_visual/medium/graph450.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,10) (0,20) (0,12) (0,2) (1,13) (1,19) (1,10) (1,9) (1,7) (1,2) (2,13) (2,19) (2,10) (2,20) (2,7) (3,21) (3,8) (3,4) (3,17) (4,21) (4,8) (4,17) (5,11) (5,14) (5,16) (5,15) (6,11) (6,14) (6,16) (6,18) (6,15) (7,13) (7,19) (7,20) (8,17) (9,13) (10,19) (11,18) (12,13) (12,20) (13,19) (13,20) (14,16) (14,18) (14,15) (15,16) (17,21) (19,20)\nIs there a path between node 12 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph226-6_18", + "image": "data/connectivity/graph_visual/medium/graph226.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,14) (0,18) (0,6) (0,5) (0,10) (1,2) (5,9) (5,7) (5,16) (5,10) (6,7) (6,12) (7,9) (7,17) (7,16) (8,9) (8,11) (8,10) (9,17) (10,11) (10,16) (11,14) (12,17) (12,14) (14,17) (14,18) (14,16) (14,15) (15,17) (15,18) (16,18) (17,18)\nIs there a path between node 6 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph689-0_23", + "image": "data/connectivity/graph_visual/medium/graph689.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,8) (0,9) (0,2) (0,10) (0,16) (0,11) (0,17) (0,1) (0,19) (0,13) (0,6) (1,3) (1,8) (1,9) (1,2) (1,10) (1,16) (1,11) (1,17) (1,19) (1,13) (1,6) (2,3) (2,8) (2,9) (2,10) (2,16) (2,11) (2,17) (2,19) (2,13) (2,6) (3,8) (3,9) (3,10) (3,16) (3,11) (3,17) (3,19) (3,13) (3,6) (4,5) (4,21) (4,22) (4,20) (4,18) (4,15) (4,12) (4,23) (4,14) (4,7) (5,21) (5,22) (5,20) (5,18) (5,15) (5,12) (5,23) (5,14) (5,7) (6,8) (6,9) (6,10) (6,16) (6,11) (6,17) (6,19) (6,13) (7,21) (7,22) (7,20) (7,18) (7,15) (7,12) (7,23) (7,14) (8,9) (8,10) (8,16) (8,11) (8,17) (8,19) (8,13) (9,10) (9,16) (9,11) (9,17) (9,19) (9,13) (10,16) (10,11) (10,17) (10,19) (10,13) (11,16) (11,17) (11,19) (11,13) (12,21) (12,22) (12,20) (12,18) (12,15) (12,23) (12,14) (13,16) (13,17) (13,19) (14,21) (14,22) (14,20) (14,18) (14,15) (14,23) (15,21) (15,22) (15,20) (15,18) (15,23) (16,17) (16,19) (17,19) (18,21) (18,22) (18,20) (18,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 0 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph824-18_17", + "image": "data/connectivity/graph_visual/medium/graph824.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,8) (0,12) (0,5) (0,14) (0,15) (0,17) (0,11) (0,16) (0,1) (1,9) (1,8) (1,12) (1,5) (1,14) (1,15) (1,11) (1,16) (1,22) (2,9) (2,8) (2,15) (2,17) (2,11) (2,16) (2,6) (3,20) (3,24) (3,4) (3,13) (3,18) (3,19) (4,24) (4,21) (4,10) (4,18) (4,7) (5,9) (5,12) (5,15) (5,6) (5,22) (6,9) (6,8) (6,12) (6,14) (6,15) (6,17) (6,11) (7,20) (7,24) (7,23) (7,13) (7,21) (7,18) (7,19) (8,12) (8,14) (8,15) (8,11) (8,16) (8,22) (9,12) (9,17) (9,16) (9,22) (10,20) (10,23) (10,13) (10,19) (11,12) (11,14) (11,15) (11,17) (11,16) (12,15) (12,16) (12,22) (13,20) (13,24) (13,21) (13,18) (14,15) (14,17) (14,22) (15,17) (15,22) (16,17) (16,22) (18,20) (18,24) (18,23) (18,21) (18,19) (19,24) (20,24) (20,23) (20,21) (21,24) (21,23) (23,24)\nIs there a path between node 18 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph651-19_7", + "image": "data/connectivity/graph_visual/medium/graph651.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,4) (0,11) (0,18) (0,2) (0,8) (0,19) (0,23) (0,13) (0,7) (0,3) (0,16) (1,21) (1,22) (1,14) (1,17) (2,9) (2,4) (2,11) (2,18) (2,8) (2,19) (2,23) (2,13) (2,7) (2,3) (2,6) (3,9) (3,4) (3,11) (3,18) (3,8) (3,23) (3,13) (3,7) (3,6) (4,9) (4,11) (4,18) (4,23) (5,20) (5,10) (6,9) (6,18) (6,8) (6,13) (6,7) (6,16) (7,9) (7,11) (7,18) (7,8) (7,19) (7,23) (7,13) (7,16) (8,9) (8,11) (8,18) (8,19) (8,23) (8,13) (9,19) (9,23) (9,13) (11,18) (11,19) (11,23) (11,16) (12,21) (12,22) (12,15) (13,19) (13,23) (14,21) (14,22) (14,15) (15,21) (15,22) (16,18) (16,23) (17,21) (18,19) (19,23) (21,22)\nIs there a path between node 19 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph481-3_15", + "image": "data/connectivity/graph_visual/medium/graph481.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,14) (0,2) (0,17) (0,18) (0,9) (0,21) (0,8) (0,13) (0,10) (0,15) (0,12) (1,14) (1,17) (1,22) (1,18) (1,9) (1,21) (1,8) (1,13) (1,7) (1,15) (1,12) (1,19) (2,17) (2,18) (2,9) (2,21) (2,13) (2,7) (2,15) (2,19) (3,16) (5,6) (5,16) (6,16) (7,17) (7,18) (7,9) (7,21) (7,8) (7,10) (7,15) (7,20) (7,12) (7,19) (8,17) (8,22) (8,18) (8,21) (8,13) (8,10) (8,11) (8,20) (8,12) (8,19) (9,14) (9,17) (9,22) (9,18) (9,21) (9,13) (9,10) (9,15) (9,20) (10,14) (10,17) (10,22) (10,13) (10,15) (10,11) (10,20) (10,12) (10,19) (11,14) (11,18) (11,13) (11,15) (11,19) (12,14) (12,22) (12,21) (12,20) (13,17) (13,22) (13,18) (13,21) (13,15) (13,19) (14,17) (14,22) (14,18) (14,21) (14,15) (14,20) (14,19) (15,22) (15,18) (15,19) (17,18) (17,21) (17,19) (18,22) (18,21) (18,20) (18,19) (19,22) (20,22) (20,21) (21,22)\nIs there a path between node 3 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph655-10_5", + "image": "data/connectivity/graph_visual/medium/graph655.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,16) (0,3) (0,21) (0,23) (1,16) (1,7) (1,3) (1,4) (1,11) (1,23) (2,15) (2,18) (2,6) (2,8) (2,12) (2,14) (2,13) (2,5) (3,16) (3,7) (3,4) (3,21) (3,11) (3,23) (4,16) (4,7) (4,21) (4,11) (5,10) (5,15) (5,17) (5,18) (5,8) (5,19) (5,9) (5,14) (5,13) (6,15) (6,17) (6,12) (6,19) (6,9) (7,21) (7,11) (7,23) (8,10) (8,15) (8,9) (8,14) (8,13) (9,15) (9,18) (9,12) (9,19) (9,14) (10,15) (10,12) (10,14) (10,13) (11,16) (11,21) (11,23) (12,15) (12,17) (12,18) (12,19) (12,13) (13,15) (13,17) (13,18) (13,19) (13,14) (14,17) (15,18) (16,23) (17,18) (18,19) (20,22) (21,23)\nIs there a path between node 10 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph345-19_12", + "image": "data/connectivity/graph_visual/medium/graph345.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,14) (0,6) (0,12) (0,18) (0,1) (0,2) (0,10) (0,15) (0,5) (0,4) (0,16) (0,3) (0,8) (0,19) (0,17) (0,11) (0,13) (0,9) (1,14) (1,6) (1,12) (1,18) (1,2) (1,10) (1,15) (1,5) (1,4) (1,16) (1,3) (1,8) (1,19) (1,17) (1,11) (1,13) (1,9) (2,14) (2,6) (2,12) (2,18) (2,10) (2,15) (2,5) (2,4) (2,16) (2,3) (2,8) (2,19) (2,17) (2,11) (2,13) (2,9) (3,14) (3,6) (3,12) (3,18) (3,10) (3,15) (3,5) (3,4) (3,16) (3,8) (3,19) (3,17) (3,11) (3,13) (3,9) (4,14) (4,6) (4,12) (4,18) (4,10) (4,15) (4,5) (4,16) (4,8) (4,19) (4,17) (4,11) (4,13) (4,9) (5,14) (5,6) (5,12) (5,18) (5,10) (5,15) (5,16) (5,8) (5,19) (5,17) (5,11) (5,13) (5,9) (6,14) (6,12) (6,18) (6,10) (6,15) (6,16) (6,8) (6,19) (6,17) (6,11) (6,13) (6,9) (7,20) (8,14) (8,12) (8,18) (8,10) (8,15) (8,16) (8,19) (8,17) (8,11) (8,13) (8,9) (9,14) (9,12) (9,18) (9,10) (9,15) (9,16) (9,19) (9,17) (9,11) (9,13) (10,14) (10,12) (10,18) (10,15) (10,16) (10,19) (10,17) (10,11) (10,13) (11,14) (11,12) (11,18) (11,15) (11,16) (11,19) (11,17) (11,13) (12,14) (12,18) (12,15) (12,16) (12,19) (12,17) (12,13) (13,14) (13,18) (13,15) (13,16) (13,19) (13,17) (14,18) (14,15) (14,16) (14,19) (14,17) (15,18) (15,16) (15,19) (15,17) (16,18) (16,19) (16,17) (17,18) (17,19) (18,19)\nIs there a path between node 19 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph461-18_13", + "image": "data/connectivity/graph_visual/medium/graph461.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,11) (0,17) (0,16) (0,3) (0,9) (0,15) (0,12) (0,1) (0,20) (0,19) (0,6) (0,21) (0,7) (0,8) (0,14) (0,5) (0,2) (1,18) (1,11) (1,17) (1,16) (1,3) (1,9) (1,15) (1,12) (1,20) (1,19) (1,6) (1,21) (1,7) (1,8) (1,14) (1,5) (1,2) (2,18) (2,11) (2,17) (2,16) (2,3) (2,9) (2,15) (2,12) (2,20) (2,19) (2,6) (2,21) (2,7) (2,8) (2,14) (2,5) (3,18) (3,11) (3,17) (3,16) (3,9) (3,15) (3,12) (3,20) (3,19) (3,6) (3,21) (3,7) (3,8) (3,14) (3,5) (5,18) (5,11) (5,17) (5,16) (5,9) (5,15) (5,12) (5,20) (5,19) (5,6) (5,21) (5,7) (5,8) (5,14) (6,18) (6,11) (6,17) (6,16) (6,9) (6,15) (6,12) (6,20) (6,19) (6,21) (6,7) (6,8) (6,14) (7,18) (7,11) (7,17) (7,16) (7,9) (7,15) (7,12) (7,20) (7,19) (7,21) (7,8) (7,14) (8,18) (8,11) (8,17) (8,16) (8,9) (8,15) (8,12) (8,20) (8,19) (8,21) (8,14) (9,18) (9,11) (9,17) (9,16) (9,15) (9,12) (9,20) (9,19) (9,21) (9,14) (10,13) (11,18) (11,17) (11,16) (11,15) (11,12) (11,20) (11,19) (11,21) (11,14) (12,18) (12,17) (12,16) (12,15) (12,20) (12,19) (12,21) (12,14) (14,18) (14,17) (14,16) (14,15) (14,20) (14,19) (14,21) (15,18) (15,17) (15,16) (15,20) (15,19) (15,21) (16,18) (16,17) (16,20) (16,19) (16,21) (17,18) (17,20) (17,19) (17,21) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 18 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph339-12_8", + "image": "data/connectivity/graph_visual/medium/graph339.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (0,12) (0,18) (0,5) (0,16) (0,10) (0,2) (0,11) (1,17) (1,12) (1,18) (1,4) (1,5) (1,16) (1,10) (1,11) (2,17) (2,12) (2,18) (2,4) (2,5) (2,10) (2,11) (3,15) (3,13) (3,6) (3,20) (3,7) (3,19) (3,8) (3,14) (4,17) (4,12) (4,18) (4,10) (5,17) (5,12) (5,16) (5,10) (5,11) (6,15) (6,20) (6,7) (6,14) (6,9) (7,15) (7,13) (7,20) (7,19) (7,8) (8,15) (8,13) (8,19) (8,9) (9,15) (9,13) (9,19) (9,14) (10,17) (10,12) (10,18) (10,11) (11,17) (12,17) (12,18) (13,19) (13,14) (14,20) (14,19) (15,20) (15,19) (16,17) (16,18) (19,20)\nIs there a path between node 12 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph313-14_17", + "image": "data/connectivity/graph_visual/medium/graph313.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,6) (0,5) (1,7) (1,8) (1,19) (1,2) (1,14) (1,11) (1,10) (1,18) (1,13) (1,16) (1,4) (1,12) (1,15) (1,9) (1,17) (1,3) (2,7) (2,8) (2,19) (2,14) (2,11) (2,10) (2,18) (2,13) (2,16) (2,4) (2,12) (2,15) (2,9) (2,17) (2,3) (3,7) (3,8) (3,19) (3,14) (3,11) (3,10) (3,18) (3,13) (3,16) (3,4) (3,12) (3,15) (3,9) (3,17) (4,7) (4,8) (4,19) (4,14) (4,11) (4,10) (4,18) (4,13) (4,16) (4,12) (4,15) (4,9) (4,17) (5,6) (7,8) (7,19) (7,14) (7,11) (7,10) (7,18) (7,13) (7,16) (7,12) (7,15) (7,9) (7,17) (8,19) (8,14) (8,11) (8,10) (8,18) (8,13) (8,16) (8,12) (8,15) (8,9) (8,17) (9,19) (9,14) (9,11) (9,10) (9,18) (9,13) (9,16) (9,12) (9,15) (9,17) (10,19) (10,14) (10,11) (10,18) (10,13) (10,16) (10,12) (10,15) (10,17) (11,19) (11,14) (11,18) (11,13) (11,16) (11,12) (11,15) (11,17) (12,19) (12,14) (12,18) (12,13) (12,16) (12,15) (12,17) (13,19) (13,14) (13,18) (13,16) (13,15) (13,17) (14,19) (14,18) (14,16) (14,15) (14,17) (15,19) (15,18) (15,16) (15,17) (16,19) (16,18) (16,17) (17,19) (17,18) (18,19)\nIs there a path between node 14 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph276-1_14", + "image": "data/connectivity/graph_visual/medium/graph276.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,10) (1,9) (1,16) (1,4) (1,12) (2,8) (2,19) (2,7) (2,14) (2,17) (2,5) (2,18) (2,6) (2,11) (2,3) (2,13) (2,15) (3,8) (3,19) (3,7) (3,14) (3,17) (3,5) (3,18) (3,6) (3,11) (3,13) (3,15) (4,10) (4,9) (4,16) (4,12) (5,8) (5,19) (5,7) (5,14) (5,17) (5,18) (5,6) (5,11) (5,13) (5,15) (6,8) (6,19) (6,7) (6,14) (6,17) (6,18) (6,11) (6,13) (6,15) (7,8) (7,19) (7,14) (7,17) (7,18) (7,11) (7,13) (7,15) (8,19) (8,14) (8,17) (8,18) (8,11) (8,13) (8,15) (9,10) (9,16) (9,12) (10,16) (10,12) (11,19) (11,14) (11,17) (11,18) (11,13) (11,15) (12,16) (13,19) (13,14) (13,17) (13,18) (13,15) (14,19) (14,17) (14,18) (14,15) (15,19) (15,17) (15,18) (17,19) (17,18) (18,19)\nIs there a path between node 1 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph652-11_7", + "image": "data/connectivity/graph_visual/medium/graph652.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,4) (0,23) (0,18) (0,16) (0,13) (0,6) (0,3) (0,14) (1,15) (1,19) (1,2) (1,9) (1,22) (1,8) (1,21) (1,12) (1,20) (2,15) (2,19) (2,9) (2,22) (2,21) (2,12) (2,20) (3,5) (3,7) (3,23) (3,18) (3,13) (3,6) (3,11) (3,14) (4,5) (4,18) (4,16) (4,13) (4,10) (4,6) (4,11) (5,7) (5,23) (5,16) (5,13) (5,10) (5,6) (5,11) (5,14) (6,7) (6,23) (6,10) (6,11) (6,14) (7,18) (7,10) (7,11) (7,14) (8,15) (8,9) (8,17) (8,21) (8,12) (9,15) (9,19) (9,17) (9,21) (9,12) (9,20) (10,23) (10,18) (10,16) (10,13) (10,11) (10,14) (11,18) (11,16) (11,13) (12,15) (12,22) (12,21) (12,20) (13,18) (13,16) (14,23) (14,18) (15,19) (15,17) (15,21) (15,20) (16,23) (16,18) (17,22) (17,21) (17,20) (18,23) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 11 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph809-7_15", + "image": "data/connectivity/graph_visual/medium/graph809.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (1,23) (1,15) (1,8) (1,17) (1,19) (1,9) (1,12) (1,20) (1,10) (1,5) (1,22) (1,14) (1,4) (1,18) (1,21) (2,13) (2,3) (2,16) (3,16) (4,23) (4,15) (4,7) (4,17) (4,9) (4,12) (4,20) (4,5) (4,22) (4,14) (4,21) (5,23) (5,15) (5,8) (5,7) (5,19) (5,9) (5,20) (5,22) (5,14) (5,21) (6,24) (6,11) (7,15) (7,8) (7,17) (7,12) (7,20) (7,10) (7,18) (7,21) (8,15) (8,17) (8,19) (8,9) (8,22) (8,14) (8,18) (9,23) (9,15) (9,17) (9,19) (9,20) (9,10) (9,18) (9,21) (10,23) (10,19) (10,22) (10,14) (10,21) (12,23) (12,15) (12,17) (12,19) (12,22) (12,18) (14,15) (14,19) (14,20) (14,22) (14,18) (14,21) (15,19) (15,20) (15,22) (15,18) (17,23) (17,19) (17,20) (17,18) (17,21) (18,23) (18,22) (19,23) (19,20) (19,21) (20,22) (20,21) (21,22)\nIs there a path between node 7 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph744-7_12", + "image": "data/connectivity/graph_visual/medium/graph744.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,15) (0,16) (0,1) (0,2) (0,12) (0,3) (1,15) (1,21) (1,12) (1,20) (1,23) (2,11) (2,21) (2,7) (2,12) (2,3) (2,23) (3,9) (3,14) (3,16) (3,5) (3,18) (3,12) (3,22) (4,14) (4,15) (4,21) (4,16) (4,18) (4,12) (4,23) (5,7) (5,18) (5,23) (7,8) (7,16) (7,12) (8,9) (8,11) (8,18) (8,12) (8,20) (9,24) (9,18) (9,12) (9,23) (11,21) (12,15) (12,21) (12,16) (12,18) (12,22) (14,24) (14,15) (14,21) (15,24) (15,19) (15,22) (16,22) (16,23) (18,21) (18,19) (19,21) (20,22) (21,23) (22,24)\nIs there a path between node 7 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph653-9_19", + "image": "data/connectivity/graph_visual/medium/graph653.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,13) (0,6) (0,8) (0,11) (0,17) (0,19) (0,22) (1,7) (1,3) (1,5) (1,4) (2,15) (2,13) (2,6) (2,20) (2,14) (2,17) (2,19) (2,23) (2,22) (3,7) (3,18) (3,5) (3,9) (3,21) (3,4) (3,12) (4,10) (4,5) (4,12) (5,16) (5,7) (5,10) (5,18) (5,9) (5,21) (5,12) (6,13) (6,20) (6,8) (6,11) (6,14) (6,17) (6,23) (6,22) (7,16) (7,10) (7,9) (7,21) (7,12) (8,15) (8,13) (8,20) (8,11) (8,19) (8,23) (9,16) (9,18) (9,21) (9,12) (10,16) (10,18) (10,21) (10,12) (11,15) (11,20) (11,14) (11,17) (11,19) (11,22) (13,15) (13,17) (13,23) (13,22) (14,15) (14,20) (15,19) (15,22) (16,21) (17,20) (17,23) (17,22) (18,21) (19,20) (19,23) (19,22) (20,22) (22,23)\nIs there a path between node 9 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph531-12_10", + "image": "data/connectivity/graph_visual/medium/graph531.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,13) (0,7) (0,4) (0,9) (0,21) (0,16) (0,1) (0,18) (0,11) (0,8) (0,6) (0,15) (0,14) (0,12) (0,20) (0,2) (0,22) (1,10) (1,13) (1,7) (1,4) (1,9) (1,21) (1,16) (1,18) (1,11) (1,8) (1,6) (1,15) (1,14) (1,12) (1,20) (1,2) (1,22) (2,10) (2,13) (2,7) (2,4) (2,9) (2,21) (2,16) (2,18) (2,11) (2,8) (2,6) (2,15) (2,14) (2,12) (2,20) (2,22) (3,17) (3,19) (3,5) (4,10) (4,13) (4,7) (4,9) (4,21) (4,16) (4,18) (4,11) (4,8) (4,6) (4,15) (4,14) (4,12) (4,20) (4,22) (5,17) (5,19) (6,10) (6,13) (6,7) (6,9) (6,21) (6,16) (6,18) (6,11) (6,8) (6,15) (6,14) (6,12) (6,20) (6,22) (7,10) (7,13) (7,9) (7,21) (7,16) (7,18) (7,11) (7,8) (7,15) (7,14) (7,12) (7,20) (7,22) (8,10) (8,13) (8,9) (8,21) (8,16) (8,18) (8,11) (8,15) (8,14) (8,12) (8,20) (8,22) (9,10) (9,13) (9,21) (9,16) (9,18) (9,11) (9,15) (9,14) (9,12) (9,20) (9,22) (10,13) (10,21) (10,16) (10,18) (10,11) (10,15) (10,14) (10,12) (10,20) (10,22) (11,13) (11,21) (11,16) (11,18) (11,15) (11,14) (11,12) (11,20) (11,22) (12,13) (12,21) (12,16) (12,18) (12,15) (12,14) (12,20) (12,22) (13,21) (13,16) (13,18) (13,15) (13,14) (13,20) (13,22) (14,21) (14,16) (14,18) (14,15) (14,20) (14,22) (15,21) (15,16) (15,18) (15,20) (15,22) (16,21) (16,18) (16,20) (16,22) (17,19) (18,21) (18,20) (18,22) (20,21) (20,22) (21,22)\nIs there a path between node 12 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph43-4_12", + "image": "data/connectivity/graph_visual/medium/graph43.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,11) (0,3) (0,10) (1,4) (1,9) (1,6) (2,10) (3,5) (3,10) (4,7) (4,9) (4,6) (4,12) (5,10) (6,7) (6,12) (7,9) (8,9) (8,12) (9,12) (10,11)\nIs there a path between node 4 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph601-17_9", + "image": "data/connectivity/graph_visual/medium/graph601.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,17) (0,8) (0,9) (0,2) (0,13) (0,11) (1,6) (1,12) (1,10) (2,15) (2,17) (2,9) (2,14) (2,7) (2,5) (2,11) (3,4) (3,6) (3,12) (3,10) (4,23) (4,6) (4,10) (5,22) (5,9) (5,13) (5,11) (6,23) (6,10) (7,17) (7,22) (7,16) (7,13) (8,15) (8,17) (8,22) (8,13) (9,15) (9,17) (9,22) (9,16) (9,13) (9,11) (10,23) (11,14) (11,13) (12,23) (13,17) (13,16) (14,15) (14,17) (14,22) (14,16) (15,17) (15,22) (16,17) (16,22) (17,22) (19,21) (20,21)\nIs there a path between node 17 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph751-3_8", + "image": "data/connectivity/graph_visual/medium/graph751.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,21) (0,20) (0,18) (0,23) (0,11) (0,14) (0,22) (0,7) (0,10) (0,15) (0,13) (1,4) (1,17) (1,24) (1,12) (1,8) (1,9) (2,3) (2,21) (2,18) (2,23) (2,11) (2,14) (2,22) (2,7) (2,10) (2,15) (2,13) (3,21) (3,20) (3,19) (3,23) (3,11) (3,14) (3,7) (3,10) (3,13) (4,16) (4,5) (4,24) (4,6) (4,8) (5,16) (5,17) (5,24) (5,12) (5,6) (5,8) (5,9) (6,16) (6,17) (6,24) (6,12) (7,21) (7,20) (7,11) (7,22) (7,13) (8,16) (8,24) (8,12) (8,9) (9,16) (9,17) (9,24) (9,12) (10,19) (10,18) (10,23) (10,14) (10,15) (10,13) (11,21) (11,19) (11,23) (11,14) (11,15) (12,16) (12,24) (13,18) (13,23) (13,14) (13,15) (14,21) (14,20) (14,19) (14,18) (14,23) (14,22) (15,21) (15,20) (15,18) (15,23) (15,22) (16,17) (16,24) (17,24) (18,21) (18,20) (18,19) (18,23) (18,22) (19,20) (19,23) (20,21) (20,23) (20,22) (21,23) (22,23)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph396-10_6", + "image": "data/connectivity/graph_visual/medium/graph396.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,12) (0,3) (0,13) (0,15) (0,7) (1,4) (1,6) (2,9) (2,18) (2,13) (3,12) (4,11) (6,8) (6,17) (7,16) (7,12) (7,13) (7,14) (8,11) (8,17) (8,20) (9,18) (9,21) (9,14) (9,15) (10,12) (12,16) (12,15) (13,18) (13,15) (14,16) (14,21) (15,16) (15,18) (16,18)\nIs there a path between node 10 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph196-12_16", + "image": "data/connectivity/graph_visual/medium/graph196.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,2) (0,14) (0,7) (0,13) (1,17) (1,3) (1,10) (1,6) (2,11) (2,12) (2,14) (2,13) (3,17) (3,10) (3,6) (4,9) (4,5) (5,9) (5,16) (6,17) (6,8) (6,10) (7,11) (7,12) (7,14) (7,13) (8,17) (8,15) (9,18) (9,16) (10,17) (12,14) (12,13) (13,14) (15,17)\nIs there a path between node 12 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph247-10_0", + "image": "data/connectivity/graph_visual/medium/graph247.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (0,13) (0,5) (0,7) (0,16) (0,12) (0,18) (0,9) (0,8) (0,2) (0,11) (0,10) (0,6) (1,15) (1,14) (1,3) (2,4) (2,13) (2,5) (2,7) (2,16) (2,12) (2,18) (2,9) (2,8) (2,11) (2,10) (2,6) (3,15) (3,14) (4,13) (4,5) (4,7) (4,16) (4,12) (4,18) (4,9) (4,8) (4,11) (4,10) (4,6) (5,13) (5,7) (5,16) (5,12) (5,18) (5,9) (5,8) (5,11) (5,10) (5,6) (6,13) (6,7) (6,16) (6,12) (6,18) (6,9) (6,8) (6,11) (6,10) (7,13) (7,16) (7,12) (7,18) (7,9) (7,8) (7,11) (7,10) (8,13) (8,16) (8,12) (8,18) (8,9) (8,11) (8,10) (9,13) (9,16) (9,12) (9,18) (9,11) (9,10) (10,13) (10,16) (10,12) (10,18) (10,11) (11,13) (11,16) (11,12) (11,18) (12,13) (12,16) (12,18) (13,16) (13,18) (14,15) (16,18)\nIs there a path between node 10 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph796-19_9", + "image": "data/connectivity/graph_visual/medium/graph796.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,1) (1,16) (1,12) (1,19) (1,21) (4,16) (4,9) (4,17) (4,15) (4,23) (4,21) (6,10) (7,13) (8,23) (8,19) (8,21) (8,18) (8,22) (9,16) (9,24) (9,15) (9,23) (9,12) (9,19) (9,21) (12,15) (15,16) (15,24) (15,23) (15,19) (15,21) (15,18) (16,24) (16,18) (17,23) (18,19) (18,21) (19,23) (21,24) (21,23)\nIs there a path between node 19 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph276-14_15", + "image": "data/connectivity/graph_visual/medium/graph276.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,10) (1,9) (1,16) (1,4) (1,12) (2,8) (2,19) (2,7) (2,14) (2,17) (2,5) (2,18) (2,6) (2,11) (2,3) (2,13) (2,15) (3,8) (3,19) (3,7) (3,14) (3,17) (3,5) (3,18) (3,6) (3,11) (3,13) (3,15) (4,10) (4,9) (4,16) (4,12) (5,8) (5,19) (5,7) (5,14) (5,17) (5,18) (5,6) (5,11) (5,13) (5,15) (6,8) (6,19) (6,7) (6,14) (6,17) (6,18) (6,11) (6,13) (6,15) (7,8) (7,19) (7,14) (7,17) (7,18) (7,11) (7,13) (7,15) (8,19) (8,14) (8,17) (8,18) (8,11) (8,13) (8,15) (9,10) (9,16) (9,12) (10,16) (10,12) (11,19) (11,14) (11,17) (11,18) (11,13) (11,15) (12,16) (13,19) (13,14) (13,17) (13,18) (13,15) (14,19) (14,17) (14,18) (14,15) (15,19) (15,17) (15,18) (17,19) (17,18) (18,19)\nIs there a path between node 14 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph487-22_15", + "image": "data/connectivity/graph_visual/medium/graph487.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,14) (0,6) (0,11) (0,19) (0,20) (0,1) (0,15) (0,12) (0,7) (0,22) (0,5) (0,21) (0,3) (0,4) (0,18) (0,17) (1,14) (1,6) (1,11) (1,19) (1,20) (1,15) (1,12) (1,7) (1,22) (1,5) (1,21) (1,3) (1,4) (1,18) (1,17) (2,13) (2,10) (2,8) (2,16) (2,9) (3,14) (3,6) (3,11) (3,19) (3,20) (3,15) (3,12) (3,7) (3,22) (3,5) (3,21) (3,4) (3,18) (3,17) (4,14) (4,6) (4,11) (4,19) (4,20) (4,15) (4,12) (4,7) (4,22) (4,5) (4,21) (4,18) (4,17) (5,14) (5,6) (5,11) (5,19) (5,20) (5,15) (5,12) (5,7) (5,22) (5,21) (5,18) (5,17) (6,14) (6,11) (6,19) (6,20) (6,15) (6,12) (6,7) (6,22) (6,21) (6,18) (6,17) (7,14) (7,11) (7,19) (7,20) (7,15) (7,12) (7,22) (7,21) (7,18) (7,17) (8,13) (8,10) (8,16) (8,9) (9,13) (9,10) (9,16) (10,13) (10,16) (11,14) (11,19) (11,20) (11,15) (11,12) (11,22) (11,21) (11,18) (11,17) (12,14) (12,19) (12,20) (12,15) (12,22) (12,21) (12,18) (12,17) (13,16) (14,19) (14,20) (14,15) (14,22) (14,21) (14,18) (14,17) (15,19) (15,20) (15,22) (15,21) (15,18) (15,17) (17,19) (17,20) (17,22) (17,21) (17,18) (18,19) (18,20) (18,22) (18,21) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22)\nIs there a path between node 22 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph115-1_7", + "image": "data/connectivity/graph_visual/medium/graph115.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,14) (0,10) (0,16) (0,12) (0,11) (2,7) (3,10) (3,16) (3,13) (3,9) (4,10) (4,16) (5,8) (5,16) (5,13) (5,12) (5,11) (5,9) (6,13) (6,11) (8,10) (8,16) (8,13) (8,15) (9,16) (10,12) (12,14) (13,16) (13,15) (14,15)\nIs there a path between node 1 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph770-6_13", + "image": "data/connectivity/graph_visual/medium/graph770.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,24) (0,6) (0,5) (0,7) (0,17) (0,21) (0,10) (0,18) (0,14) (1,13) (1,19) (1,3) (1,12) (1,4) (1,11) (2,9) (2,8) (2,15) (3,13) (3,19) (3,12) (3,4) (3,11) (4,13) (4,19) (4,12) (4,11) (5,20) (5,24) (5,6) (5,7) (5,17) (5,21) (5,10) (5,18) (5,14) (6,20) (6,24) (6,7) (6,17) (6,21) (6,10) (6,18) (6,14) (7,20) (7,24) (7,17) (7,21) (7,10) (7,18) (7,14) (8,9) (8,15) (9,15) (10,20) (10,24) (10,17) (10,21) (10,18) (10,14) (11,13) (11,19) (11,12) (12,13) (12,19) (13,19) (14,20) (14,24) (14,17) (14,21) (14,18) (16,22) (16,23) (17,20) (17,24) (17,21) (17,18) (18,20) (18,24) (18,21) (20,24) (20,21) (21,24) (22,23)\nIs there a path between node 6 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph305-18_3", + "image": "data/connectivity/graph_visual/medium/graph305.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,1) (0,18) (1,11) (1,18) (2,15) (2,14) (2,7) (2,5) (2,4) (2,3) (2,8) (2,6) (2,16) (3,15) (3,14) (3,5) (3,13) (3,4) (3,9) (3,6) (4,15) (4,7) (4,5) (4,12) (4,8) (4,9) (4,16) (5,14) (5,12) (5,17) (5,9) (5,6) (5,16) (6,15) (6,14) (6,7) (6,17) (6,16) (7,15) (7,14) (7,13) (7,12) (7,9) (7,16) (8,15) (8,14) (8,13) (8,12) (8,17) (8,16) (9,15) (9,14) (9,12) (11,19) (11,18) (12,15) (12,14) (12,13) (12,17) (13,15) (13,14) (14,15) (15,17) (15,16) (16,17) (18,19)\nIs there a path between node 18 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph241-13_6", + "image": "data/connectivity/graph_visual/medium/graph241.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,10) (1,14) (1,18) (1,4) (1,11) (1,15) (1,7) (1,5) (1,3) (2,14) (2,18) (2,16) (2,6) (2,4) (2,9) (2,11) (2,15) (2,7) (2,5) (2,3) (3,14) (3,16) (3,6) (3,4) (3,9) (3,11) (3,15) (3,7) (3,5) (4,14) (4,8) (4,9) (4,11) (4,15) (5,18) (5,16) (5,8) (5,6) (5,9) (5,11) (5,15) (5,7) (6,14) (6,16) (6,12) (6,15) (6,7) (7,14) (7,18) (7,16) (7,12) (7,8) (7,9) (7,15) (8,14) (8,18) (8,16) (8,9) (8,11) (8,15) (9,18) (9,16) (9,11) (11,18) (11,16) (11,12) (11,15) (12,14) (12,18) (12,16) (12,15) (14,18) (14,16) (14,15) (15,16) (16,18)\nIs there a path between node 13 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph514-9_3", + "image": "data/connectivity/graph_visual/medium/graph514.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,14) (0,19) (0,12) (0,1) (1,10) (1,19) (1,12) (1,3) (1,21) (2,9) (2,15) (2,4) (2,11) (2,22) (2,17) (2,7) (2,5) (2,18) (3,10) (3,19) (3,12) (3,21) (4,6) (4,16) (4,9) (4,8) (4,15) (4,11) (4,22) (4,7) (4,13) (4,5) (4,18) (5,6) (5,9) (5,8) (5,11) (5,22) (5,17) (5,7) (5,18) (6,16) (6,9) (6,11) (6,22) (6,17) (6,7) (6,13) (7,9) (7,11) (7,22) (7,17) (7,13) (7,18) (8,16) (8,11) (8,22) (8,13) (8,18) (9,16) (9,15) (9,11) (9,22) (9,17) (9,13) (9,18) (10,14) (10,19) (10,12) (10,21) (11,15) (11,17) (11,13) (12,14) (12,19) (12,21) (13,15) (13,22) (13,18) (14,21) (15,16) (15,22) (15,17) (16,22) (16,17) (16,18) (17,22) (17,18) (18,22) (19,21)\nIs there a path between node 9 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph433-5_6", + "image": "data/connectivity/graph_visual/medium/graph433.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,7) (2,12) (3,18) (3,12) (3,15) (3,9) (5,11) (5,17) (5,20) (6,16) (6,17) (7,21) (7,18) (7,9) (8,21) (8,18) (8,15) (9,21) (9,12) (9,19) (12,21) (14,21) (15,18) (15,19) (16,17) (16,20) (17,20)\nIs there a path between node 5 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph301-13_16", + "image": "data/connectivity/graph_visual/medium/graph301.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,5) (0,14) (0,8) (0,1) (0,17) (0,2) (0,4) (0,10) (0,12) (0,6) (0,7) (0,3) (0,11) (1,5) (1,14) (1,8) (1,17) (1,12) (1,13) (1,3) (2,5) (2,4) (2,10) (2,12) (2,6) (2,7) (2,13) (2,11) (3,14) (3,8) (3,10) (3,12) (3,6) (3,7) (4,14) (4,8) (4,17) (4,10) (4,12) (4,7) (4,11) (5,8) (5,17) (5,12) (5,6) (5,7) (5,13) (5,11) (6,14) (6,10) (6,12) (6,13) (6,11) (7,14) (7,8) (7,17) (7,10) (7,12) (7,13) (7,11) (8,14) (8,17) (8,10) (8,12) (8,11) (9,15) (10,13) (11,14) (11,12) (11,13) (12,17) (12,13) (15,19) (15,18) (15,16) (16,19) (16,18) (18,19)\nIs there a path between node 13 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph665-6_7", + "image": "data/connectivity/graph_visual/medium/graph665.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,10) (0,14) (0,2) (0,8) (1,18) (1,23) (1,5) (1,4) (1,11) (1,9) (1,20) (1,17) (1,7) (2,10) (2,14) (2,16) (2,3) (2,8) (2,22) (3,12) (3,10) (3,14) (3,16) (3,8) (4,18) (4,15) (4,20) (4,17) (4,7) (5,23) (5,15) (5,21) (5,11) (5,9) (5,19) (5,17) (5,7) (7,23) (7,21) (7,11) (7,9) (7,20) (7,17) (8,12) (8,10) (8,14) (8,22) (9,18) (9,23) (9,15) (9,21) (9,11) (9,20) (9,19) (10,16) (10,22) (11,18) (11,15) (11,21) (11,20) (11,19) (11,17) (12,14) (12,16) (14,22) (15,18) (15,20) (17,20) (18,23) (18,19) (19,23) (19,21) (21,23)\nIs there a path between node 6 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph221-13_9", + "image": "data/connectivity/graph_visual/medium/graph221.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,11) (0,15) (1,12) (1,2) (1,8) (1,3) (1,15) (2,13) (2,3) (2,14) (2,15) (3,6) (3,12) (3,13) (3,11) (3,14) (3,9) (3,7) (4,8) (4,11) (4,14) (4,16) (5,6) (5,17) (5,15) (5,7) (6,8) (6,11) (6,17) (6,16) (7,13) (7,16) (8,12) (8,17) (8,14) (9,13) (9,15) (11,15) (12,17) (13,17) (14,16) (15,17) (16,17)\nIs there a path between node 13 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph56-4_6", + "image": "data/connectivity/graph_visual/medium/graph56.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,8) (1,7) (1,11) (2,12) (3,8) (3,4) (4,5) (5,7) (5,6) (5,11) (6,11) (9,12) (10,12) (12,13)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph173-1_6", + "image": "data/connectivity/graph_visual/medium/graph173.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,7) (0,17) (0,11) (0,15) (0,12) (0,4) (0,14) (0,8) (0,16) (0,5) (1,7) (1,11) (1,15) (1,2) (1,9) (1,12) (1,14) (1,13) (1,5) (2,7) (2,11) (2,15) (2,9) (2,12) (2,4) (2,14) (2,13) (2,8) (2,16) (2,5) (4,7) (4,12) (5,17) (5,11) (5,15) (5,12) (5,13) (5,16) (6,10) (7,17) (7,11) (7,12) (7,14) (7,8) (8,11) (8,13) (8,16) (9,17) (9,11) (9,15) (9,12) (9,13) (9,16) (11,15) (11,12) (11,14) (11,13) (11,16) (12,17) (12,15) (12,14) (12,16) (13,17) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph374-7_1", + "image": "data/connectivity/graph_visual/medium/graph374.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,4) (0,12) (0,11) (1,14) (1,7) (1,15) (1,3) (1,20) (1,8) (1,5) (2,14) (2,7) (2,19) (2,10) (2,3) (2,20) (2,8) (2,5) (2,13) (2,16) (3,14) (3,7) (3,19) (3,10) (3,8) (3,5) (3,13) (3,16) (4,9) (4,11) (5,14) (5,7) (5,19) (5,10) (5,20) (5,8) (5,13) (7,14) (7,19) (7,8) (7,13) (7,17) (8,14) (8,19) (8,10) (8,15) (8,20) (8,16) (8,17) (9,12) (9,11) (10,19) (10,15) (10,13) (10,16) (11,12) (13,14) (13,15) (13,20) (13,16) (13,17) (14,19) (14,15) (14,20) (14,17) (15,20) (15,16) (15,17) (16,20) (16,17) (17,19) (19,20)\nIs there a path between node 7 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph817-10_20", + "image": "data/connectivity/graph_visual/medium/graph817.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,22) (0,6) (0,10) (0,2) (0,12) (1,5) (1,20) (1,14) (1,13) (1,15) (1,4) (1,19) (1,24) (1,23) (1,9) (2,17) (2,10) (2,21) (3,22) (3,17) (3,6) (3,10) (3,21) (4,5) (4,14) (4,13) (4,19) (4,23) (4,9) (4,7) (4,16) (5,20) (5,14) (5,15) (5,24) (5,23) (5,7) (5,16) (6,22) (6,17) (6,10) (6,12) (6,21) (7,20) (7,13) (7,15) (7,9) (7,16) (8,22) (8,10) (9,20) (9,14) (9,15) (9,19) (9,24) (10,17) (10,12) (12,17) (12,21) (13,20) (13,14) (13,16) (14,20) (14,19) (15,20) (15,19) (15,24) (15,16) (16,20) (16,19) (16,24) (16,23) (20,24) (21,22) (23,24)\nIs there a path between node 10 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph642-1_22", + "image": "data/connectivity/graph_visual/medium/graph642.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,23) (0,10) (1,8) (1,2) (1,3) (1,6) (1,16) (2,5) (2,21) (2,6) (2,19) (2,10) (3,8) (3,5) (3,4) (4,17) (4,5) (4,9) (4,14) (5,17) (5,22) (5,11) (5,19) (5,13) (5,10) (6,9) (6,11) (6,21) (6,13) (7,12) (7,18) (7,20) (8,15) (8,13) (8,16) (9,17) (10,16) (11,17) (11,14) (11,13) (12,18) (13,17) (13,22) (13,14) (13,21) (14,22) (14,23) (14,19) (14,16) (16,22) (16,23) (17,23)\nIs there a path between node 1 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph581-4_3", + "image": "data/connectivity/graph_visual/medium/graph581.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,11) (0,20) (1,22) (1,12) (1,16) (1,6) (1,18) (1,13) (1,17) (1,14) (1,15) (2,11) (2,20) (3,11) (3,7) (4,23) (4,16) (4,18) (4,13) (5,22) (5,23) (5,16) (5,18) (6,12) (6,23) (6,16) (7,20) (8,11) (8,20) (8,9) (9,10) (12,22) (12,21) (12,16) (12,18) (12,13) (12,14) (13,23) (13,16) (13,17) (13,14) (14,19) (14,15) (15,22) (15,19) (16,21) (16,18) (17,22) (17,21) (17,23) (17,19) (19,21) (21,22)\nIs there a path between node 4 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph590-4_16", + "image": "data/connectivity/graph_visual/medium/graph590.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,16) (0,22) (0,4) (0,15) (0,9) (1,8) (1,17) (1,12) (1,3) (1,5) (1,21) (1,6) (1,13) (1,19) (2,20) (2,16) (2,22) (2,4) (2,9) (3,8) (3,17) (3,14) (3,6) (3,10) (3,19) (4,20) (4,16) (4,22) (4,15) (4,9) (5,8) (5,17) (5,12) (5,14) (5,13) (5,10) (5,19) (6,17) (6,12) (6,14) (6,21) (6,13) (6,10) (6,19) (8,17) (8,12) (8,13) (8,19) (9,20) (9,22) (9,15) (10,17) (10,14) (10,21) (11,18) (11,23) (12,17) (12,21) (12,13) (12,19) (13,17) (13,14) (13,21) (15,20) (16,22) (17,21) (18,23)\nIs there a path between node 4 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph719-16_18", + "image": "data/connectivity/graph_visual/medium/graph719.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,22) (0,21) (0,7) (0,16) (0,14) (1,22) (1,10) (1,16) (2,6) (2,13) (2,24) (2,19) (2,3) (2,9) (2,23) (2,4) (2,15) (2,17) (2,11) (2,5) (3,6) (3,24) (3,19) (3,9) (3,23) (3,4) (3,12) (3,15) (3,17) (3,11) (3,5) (3,8) (4,6) (4,24) (4,9) (4,23) (4,15) (4,17) (4,18) (4,11) (4,5) (5,6) (5,13) (5,24) (5,19) (5,9) (5,23) (5,15) (5,18) (5,8) (6,24) (6,15) (6,17) (6,18) (6,8) (7,20) (7,22) (7,16) (8,24) (8,9) (8,12) (8,15) (8,17) (8,18) (9,13) (9,24) (9,23) (9,12) (9,17) (9,11) (10,20) (10,21) (10,16) (10,14) (11,24) (11,15) (11,17) (11,18) (12,13) (12,19) (12,17) (12,18) (13,24) (13,23) (13,17) (13,18) (14,20) (14,21) (14,16) (15,24) (15,19) (15,23) (15,18) (16,20) (16,21) (17,24) (17,23) (18,19) (19,24) (20,22) (20,21) (21,22)\nIs there a path between node 16 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph603-15_22", + "image": "data/connectivity/graph_visual/medium/graph603.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,11) (0,20) (1,4) (1,14) (1,15) (1,16) (1,22) (2,4) (2,14) (2,15) (2,16) (3,4) (3,14) (3,15) (3,16) (4,14) (4,15) (4,16) (5,11) (6,12) (6,19) (6,7) (6,13) (6,9) (6,17) (7,18) (7,21) (7,13) (7,9) (7,17) (8,20) (9,18) (9,19) (9,13) (9,10) (9,17) (10,12) (10,21) (10,13) (12,18) (12,21) (12,19) (12,13) (12,17) (13,18) (13,21) (13,19) (13,17) (14,15) (14,22) (15,22) (17,18) (17,19) (18,21) (18,19) (19,21)\nIs there a path between node 15 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph752-7_10", + "image": "data/connectivity/graph_visual/medium/graph752.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,20) (0,17) (0,1) (0,21) (1,10) (1,20) (1,21) (3,20) (3,21) (4,5) (4,12) (4,14) (4,16) (4,6) (4,15) (5,7) (5,14) (5,16) (5,19) (5,11) (5,8) (5,15) (6,24) (6,14) (6,16) (6,19) (6,9) (6,13) (6,11) (6,8) (7,24) (7,12) (7,14) (7,19) (7,9) (7,13) (7,11) (7,8) (7,15) (8,24) (8,12) (8,16) (8,19) (8,9) (8,11) (8,15) (9,24) (9,12) (9,14) (9,11) (9,15) (10,20) (10,17) (10,21) (11,24) (11,12) (11,14) (11,16) (11,19) (11,13) (11,15) (12,14) (12,16) (12,19) (12,15) (13,24) (13,14) (13,16) (13,19) (14,24) (14,16) (14,15) (15,24) (15,16) (16,24) (16,19) (17,20) (17,21) (18,23) (19,24) (22,23)\nIs there a path between node 7 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph812-7_9", + "image": "data/connectivity/graph_visual/medium/graph812.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,22) (0,18) (0,21) (0,12) (0,16) (0,14) (0,17) (0,6) (1,3) (2,20) (2,13) (2,4) (2,7) (3,10) (4,20) (4,13) (4,7) (5,19) (5,9) (5,24) (6,15) (6,22) (6,18) (6,21) (6,12) (6,16) (6,17) (7,20) (7,13) (8,15) (8,23) (8,12) (8,16) (8,14) (8,17) (9,19) (9,24) (11,23) (11,18) (11,21) (11,12) (11,16) (11,14) (11,17) (12,23) (12,22) (12,21) (12,16) (12,14) (14,15) (14,22) (14,18) (14,16) (14,17) (15,22) (15,17) (16,23) (16,21) (16,17) (17,23) (17,18) (17,21) (18,23) (18,21) (19,24) (21,23) (21,22) (22,23)\nIs there a path between node 7 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph382-5_13", + "image": "data/connectivity/graph_visual/medium/graph382.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,20) (0,10) (0,13) (0,17) (1,7) (1,5) (1,16) (1,6) (2,14) (2,18) (2,11) (2,9) (2,4) (2,15) (2,19) (2,12) (2,3) (2,8) (3,14) (3,18) (3,11) (3,9) (3,4) (3,15) (3,19) (3,12) (3,8) (4,14) (4,18) (4,11) (4,9) (4,15) (4,19) (4,12) (4,8) (5,7) (5,16) (5,6) (6,7) (6,16) (7,16) (8,14) (8,18) (8,11) (8,9) (8,15) (8,19) (8,12) (9,14) (9,18) (9,11) (9,15) (9,19) (9,12) (10,20) (10,13) (10,17) (11,14) (11,18) (11,15) (11,19) (11,12) (12,14) (12,18) (12,15) (12,19) (13,20) (13,17) (14,18) (14,15) (14,19) (15,18) (15,19) (17,20) (18,19)\nIs there a path between node 5 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph473-10_2", + "image": "data/connectivity/graph_visual/medium/graph473.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,17) (0,11) (2,17) (2,20) (2,11) (3,8) (3,21) (3,18) (3,4) (4,7) (4,12) (6,14) (7,19) (7,21) (7,10) (8,13) (8,19) (8,21) (8,12) (9,19) (9,21) (10,13) (11,14) (12,21) (13,16) (13,18) (14,15) (15,22) (16,19) (16,18) (17,22) (17,20)\nIs there a path between node 10 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph153-4_10", + "image": "data/connectivity/graph_visual/medium/graph153.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,15) (0,4) (0,13) (0,14) (0,8) (0,16) (0,7) (0,1) (0,2) (0,5) (1,3) (1,15) (1,4) (1,13) (1,14) (1,8) (1,16) (1,7) (1,2) (1,5) (2,3) (2,15) (2,4) (2,13) (2,14) (2,8) (2,16) (2,7) (2,5) (3,15) (3,4) (3,13) (3,14) (3,8) (3,16) (3,7) (3,5) (4,15) (4,13) (4,14) (4,8) (4,16) (4,7) (4,5) (5,15) (5,13) (5,14) (5,8) (5,16) (5,7) (6,11) (6,9) (6,10) (6,12) (7,15) (7,13) (7,14) (7,8) (7,16) (8,15) (8,13) (8,14) (8,16) (9,11) (9,10) (9,12) (10,11) (10,12) (11,12) (13,15) (13,14) (13,16) (14,15) (14,16) (15,16)\nIs there a path between node 4 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph416-0_18", + "image": "data/connectivity/graph_visual/medium/graph416.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,4) (0,21) (0,7) (0,11) (0,1) (0,12) (0,10) (0,6) (0,9) (0,17) (0,20) (0,15) (0,13) (1,2) (1,4) (1,21) (1,7) (1,11) (1,12) (1,10) (1,6) (1,9) (1,17) (1,20) (1,15) (1,13) (2,4) (2,21) (2,7) (2,11) (2,12) (2,10) (2,6) (2,9) (2,17) (2,20) (2,15) (2,13) (3,8) (3,16) (3,14) (3,18) (3,5) (3,19) (4,21) (4,7) (4,11) (4,12) (4,10) (4,6) (4,9) (4,17) (4,20) (4,15) (4,13) (5,8) (5,16) (5,14) (5,18) (5,19) (6,21) (6,7) (6,11) (6,12) (6,10) (6,9) (6,17) (6,20) (6,15) (6,13) (7,21) (7,11) (7,12) (7,10) (7,9) (7,17) (7,20) (7,15) (7,13) (8,16) (8,14) (8,18) (8,19) (9,21) (9,11) (9,12) (9,10) (9,17) (9,20) (9,15) (9,13) (10,21) (10,11) (10,12) (10,17) (10,20) (10,15) (10,13) (11,21) (11,12) (11,17) (11,20) (11,15) (11,13) (12,21) (12,17) (12,20) (12,15) (12,13) (13,21) (13,17) (13,20) (13,15) (14,16) (14,18) (14,19) (15,21) (15,17) (15,20) (16,18) (16,19) (17,21) (17,20) (18,19) (20,21)\nIs there a path between node 0 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph745-18_7", + "image": "data/connectivity/graph_visual/medium/graph745.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,1) (0,11) (0,2) (1,6) (1,16) (1,2) (2,6) (2,23) (2,19) (3,13) (3,4) (3,17) (3,7) (3,10) (3,24) (4,17) (4,8) (4,24) (5,9) (5,12) (5,17) (5,18) (5,8) (5,10) (6,22) (6,21) (7,14) (7,12) (7,18) (8,14) (8,13) (8,12) (8,17) (8,18) (8,24) (9,14) (9,12) (9,20) (9,10) (9,24) (10,20) (11,15) (11,16) (13,18) (15,22) (15,19) (16,19) (19,22)\nIs there a path between node 18 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph300-15_13", + "image": "data/connectivity/graph_visual/medium/graph300.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,7) (0,4) (0,11) (0,3) (0,17) (1,10) (1,13) (2,10) (2,13) (2,15) (3,7) (3,4) (3,11) (3,17) (4,5) (4,11) (5,7) (5,11) (5,12) (6,8) (6,14) (6,9) (6,18) (6,19) (7,17) (7,12) (8,14) (8,18) (8,19) (9,18) (9,19) (10,13) (11,17) (11,12) (12,17) (13,16) (13,15) (14,18) (14,19) (15,16) (18,19)\nIs there a path between node 15 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph79-3_1", + "image": "data/connectivity/graph_visual/medium/graph79.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (0,6) (0,4) (0,8) (0,14) (0,7) (0,12) (0,11) (0,13) (0,5) (1,6) (1,4) (1,14) (1,7) (1,12) (1,11) (1,13) (2,4) (2,8) (2,12) (2,13) (2,5) (3,10) (4,6) (4,8) (4,7) (4,12) (4,13) (4,5) (5,6) (5,8) (5,7) (5,12) (5,11) (5,13) (6,8) (6,14) (6,7) (6,12) (6,13) (7,8) (7,14) (7,12) (7,11) (7,13) (8,14) (8,12) (8,11) (8,13) (9,10) (11,14) (11,12) (12,14) (12,13) (13,14)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph691-23_19", + "image": "data/connectivity/graph_visual/medium/graph691.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,23) (0,3) (0,7) (0,9) (0,21) (0,13) (0,16) (0,6) (0,8) (0,12) (1,5) (1,22) (1,15) (1,14) (1,18) (1,17) (1,20) (1,11) (1,2) (2,5) (2,22) (2,15) (2,14) (2,18) (2,17) (2,20) (2,11) (3,10) (3,19) (3,23) (3,7) (3,9) (3,21) (3,13) (3,16) (3,6) (3,8) (3,12) (5,22) (5,15) (5,14) (5,18) (5,17) (5,20) (5,11) (6,10) (6,19) (6,23) (6,7) (6,9) (6,21) (6,13) (6,16) (6,8) (6,12) (7,10) (7,19) (7,23) (7,9) (7,21) (7,13) (7,16) (7,8) (7,12) (8,10) (8,19) (8,23) (8,9) (8,21) (8,13) (8,16) (8,12) (9,10) (9,19) (9,23) (9,21) (9,13) (9,16) (9,12) (10,19) (10,23) (10,21) (10,13) (10,16) (10,12) (11,22) (11,15) (11,14) (11,18) (11,17) (11,20) (12,19) (12,23) (12,21) (12,13) (12,16) (13,19) (13,23) (13,21) (13,16) (14,22) (14,15) (14,18) (14,17) (14,20) (15,22) (15,18) (15,17) (15,20) (16,19) (16,23) (16,21) (17,22) (17,18) (17,20) (18,22) (18,20) (19,23) (19,21) (20,22) (21,23)\nIs there a path between node 23 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph464-7_19", + "image": "data/connectivity/graph_visual/medium/graph464.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,16) (0,1) (0,9) (0,10) (0,18) (1,4) (1,16) (1,9) (1,10) (1,18) (2,3) (2,7) (2,11) (2,20) (2,8) (2,19) (2,13) (2,12) (2,5) (2,17) (2,6) (2,15) (2,21) (2,14) (3,7) (3,11) (3,20) (3,8) (3,19) (3,13) (3,12) (3,5) (3,17) (3,6) (3,15) (3,21) (3,14) (4,16) (4,9) (4,10) (4,18) (5,7) (5,11) (5,20) (5,8) (5,19) (5,13) (5,12) (5,17) (5,6) (5,15) (5,21) (5,14) (6,7) (6,11) (6,20) (6,8) (6,19) (6,13) (6,12) (6,17) (6,15) (6,21) (6,14) (7,11) (7,20) (7,8) (7,19) (7,13) (7,12) (7,17) (7,15) (7,21) (7,14) (8,11) (8,20) (8,19) (8,13) (8,12) (8,17) (8,15) (8,21) (8,14) (9,16) (9,10) (9,18) (10,16) (10,18) (11,20) (11,19) (11,13) (11,12) (11,17) (11,15) (11,21) (11,14) (12,20) (12,19) (12,13) (12,17) (12,15) (12,21) (12,14) (13,20) (13,19) (13,17) (13,15) (13,21) (13,14) (14,20) (14,19) (14,17) (14,15) (14,21) (15,20) (15,19) (15,17) (15,21) (16,18) (17,20) (17,19) (17,21) (19,20) (19,21) (20,21)\nIs there a path between node 7 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph306-3_14", + "image": "data/connectivity/graph_visual/medium/graph306.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,11) (0,17) (0,1) (0,10) (0,9) (0,8) (0,3) (0,2) (0,19) (1,11) (1,17) (1,10) (1,9) (1,8) (1,3) (1,2) (1,4) (2,7) (2,11) (2,17) (2,5) (2,10) (2,3) (3,17) (3,5) (3,9) (3,19) (4,7) (4,17) (4,5) (4,10) (4,9) (4,8) (4,19) (5,11) (5,17) (5,10) (5,9) (5,19) (6,12) (6,16) (6,13) (7,17) (7,10) (7,9) (7,8) (7,19) (8,11) (8,19) (9,11) (10,17) (10,19) (11,19) (12,18) (12,14) (12,13) (13,18) (13,14) (13,16) (14,18) (17,19)\nIs there a path between node 3 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph232-10_11", + "image": "data/connectivity/graph_visual/medium/graph232.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,1) (0,13) (0,15) (0,16) (0,9) (0,14) (0,3) (0,12) (0,17) (0,2) (0,18) (1,11) (1,13) (1,15) (1,16) (1,9) (1,8) (1,14) (1,3) (1,4) (1,17) (1,18) (2,11) (2,13) (2,15) (2,9) (2,8) (2,14) (2,3) (2,12) (2,17) (2,18) (3,11) (3,13) (3,15) (3,16) (3,9) (3,8) (3,14) (3,12) (3,17) (3,18) (4,13) (4,15) (4,16) (4,8) (4,14) (4,12) (4,18) (5,6) (5,7) (5,10) (6,7) (6,10) (7,10) (8,11) (8,15) (8,16) (8,18) (9,11) (9,13) (9,15) (9,16) (9,14) (9,12) (9,17) (9,18) (11,13) (11,16) (11,17) (11,18) (12,15) (12,16) (12,17) (12,18) (13,15) (13,18) (14,15) (14,17) (15,16) (16,17) (16,18) (17,18)\nIs there a path between node 10 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph776-18_17", + "image": "data/connectivity/graph_visual/medium/graph776.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,22) (0,5) (0,12) (0,20) (0,6) (0,19) (0,21) (0,9) (0,17) (0,7) (0,14) (0,15) (1,2) (1,13) (1,3) (1,10) (1,4) (1,18) (1,24) (1,11) (1,16) (1,8) (2,13) (2,3) (2,10) (2,4) (2,18) (2,24) (2,11) (2,16) (2,8) (3,13) (3,10) (3,4) (3,18) (3,24) (3,11) (3,16) (3,8) (4,13) (4,10) (4,18) (4,24) (4,11) (4,16) (4,8) (5,23) (5,22) (5,12) (5,20) (5,6) (5,19) (5,21) (5,9) (5,17) (5,7) (5,14) (5,15) (6,23) (6,22) (6,12) (6,20) (6,19) (6,21) (6,9) (6,17) (6,7) (6,14) (6,15) (7,23) (7,22) (7,12) (7,20) (7,19) (7,21) (7,9) (7,17) (7,14) (7,15) (8,13) (8,10) (8,18) (8,24) (8,11) (8,16) (9,23) (9,22) (9,12) (9,20) (9,19) (9,21) (9,17) (9,14) (9,15) (10,13) (10,18) (10,24) (10,11) (10,16) (11,13) (11,18) (11,24) (11,16) (12,23) (12,22) (12,20) (12,19) (12,21) (12,17) (12,14) (12,15) (13,18) (13,24) (13,16) (14,23) (14,22) (14,20) (14,19) (14,21) (14,17) (14,15) (15,23) (15,22) (15,20) (15,19) (15,21) (15,17) (16,18) (16,24) (17,23) (17,22) (17,20) (17,19) (17,21) (18,24) (19,23) (19,22) (19,20) (19,21) (20,23) (20,22) (20,21) (21,23) (21,22) (22,23)\nIs there a path between node 18 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph298-1_6", + "image": "data/connectivity/graph_visual/medium/graph298.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,19) (0,2) (0,15) (0,7) (0,9) (0,11) (0,1) (1,17) (1,2) (1,9) (1,12) (1,6) (2,17) (2,19) (2,15) (2,3) (2,7) (2,9) (2,12) (3,17) (3,19) (3,15) (3,7) (3,9) (3,12) (3,11) (3,6) (4,18) (4,8) (4,14) (4,13) (4,10) (6,19) (6,15) (6,7) (6,9) (6,12) (6,11) (7,17) (7,19) (7,15) (8,14) (8,13) (8,10) (9,19) (10,14) (10,13) (11,19) (11,15) (11,12) (12,19) (13,18) (14,18) (15,19)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph598-19_13", + "image": "data/connectivity/graph_visual/medium/graph598.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,22) (0,12) (0,10) (0,7) (0,5) (0,14) (0,9) (1,13) (1,6) (1,21) (1,18) (1,20) (1,3) (2,23) (2,22) (2,12) (2,10) (2,17) (2,15) (2,5) (2,14) (2,9) (3,13) (3,21) (3,18) (3,20) (3,4) (4,6) (4,21) (4,18) (4,20) (5,16) (5,22) (5,12) (5,17) (5,8) (5,19) (5,7) (5,15) (6,13) (6,21) (6,18) (7,23) (7,22) (7,12) (7,14) (7,9) (8,23) (8,16) (8,22) (8,12) (8,10) (8,17) (8,19) (8,15) (8,14) (9,16) (9,12) (9,10) (9,17) (9,19) (9,15) (9,14) (10,23) (10,16) (10,22) (10,12) (10,19) (10,14) (12,16) (12,22) (12,17) (12,19) (12,14) (13,21) (13,18) (13,20) (14,23) (14,16) (14,19) (14,15) (15,23) (15,16) (15,22) (15,17) (15,19) (16,23) (16,22) (16,19) (17,23) (17,19) (18,21) (18,20) (19,22) (22,23)\nIs there a path between node 19 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph711-8_20", + "image": "data/connectivity/graph_visual/medium/graph711.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,2) (0,7) (0,15) (0,14) (0,22) (0,10) (0,18) (0,5) (0,9) (0,4) (0,11) (0,8) (0,20) (0,13) (1,2) (1,7) (1,15) (1,14) (1,18) (1,5) (1,16) (1,9) (1,4) (1,11) (1,8) (1,13) (2,24) (2,7) (2,15) (2,14) (2,22) (2,18) (2,16) (2,9) (2,4) (2,11) (2,8) (2,20) (2,23) (3,21) (4,7) (4,14) (4,22) (4,18) (4,16) (4,13) (4,23) (5,24) (5,7) (5,15) (5,14) (5,22) (5,10) (5,18) (5,20) (5,23) (6,12) (7,24) (7,15) (7,14) (7,10) (7,18) (7,16) (7,9) (7,11) (7,8) (7,20) (7,13) (7,23) (8,24) (8,14) (8,10) (8,18) (8,9) (8,13) (8,23) (9,24) (9,15) (9,14) (9,22) (9,10) (9,16) (9,20) (9,23) (10,24) (10,15) (10,14) (10,22) (10,18) (10,16) (10,20) (11,15) (11,14) (11,18) (11,16) (11,20) (11,13) (11,23) (13,24) (13,15) (13,18) (13,16) (13,23) (14,24) (14,15) (14,22) (14,18) (14,16) (14,23) (15,24) (15,22) (15,18) (15,16) (15,20) (15,23) (16,24) (16,20) (16,23) (18,22) (18,20) (18,23) (19,21) (20,22) (22,24) (22,23) (23,24)\nIs there a path between node 8 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph824-11_9", + "image": "data/connectivity/graph_visual/medium/graph824.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,8) (0,12) (0,5) (0,14) (0,15) (0,17) (0,11) (0,16) (0,1) (1,9) (1,8) (1,12) (1,5) (1,14) (1,15) (1,11) (1,16) (1,22) (2,9) (2,8) (2,15) (2,17) (2,11) (2,16) (2,6) (3,20) (3,24) (3,4) (3,13) (3,18) (3,19) (4,24) (4,21) (4,10) (4,18) (4,7) (5,9) (5,12) (5,15) (5,6) (5,22) (6,9) (6,8) (6,12) (6,14) (6,15) (6,17) (6,11) (7,20) (7,24) (7,23) (7,13) (7,21) (7,18) (7,19) (8,12) (8,14) (8,15) (8,11) (8,16) (8,22) (9,12) (9,17) (9,16) (9,22) (10,20) (10,23) (10,13) (10,19) (11,12) (11,14) (11,15) (11,17) (11,16) (12,15) (12,16) (12,22) (13,20) (13,24) (13,21) (13,18) (14,15) (14,17) (14,22) (15,17) (15,22) (16,17) (16,22) (18,20) (18,24) (18,23) (18,21) (18,19) (19,24) (20,24) (20,23) (20,21) (21,24) (21,23) (23,24)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph624-7_13", + "image": "data/connectivity/graph_visual/medium/graph624.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (0,11) (0,13) (0,3) (0,15) (0,4) (0,2) (1,7) (1,8) (2,14) (2,23) (2,21) (2,6) (2,10) (3,9) (3,17) (3,13) (3,5) (3,19) (3,4) (3,16) (3,10) (4,9) (4,22) (4,6) (5,11) (5,18) (5,23) (6,9) (6,14) (6,17) (6,20) (6,15) (6,21) (7,8) (9,17) (9,15) (9,21) (10,18) (10,12) (10,16) (11,17) (11,15) (11,22) (11,16) (12,15) (12,22) (13,23) (13,16) (14,17) (14,18) (14,20) (14,21) (14,22) (14,16) (15,20) (17,20) (17,19) (17,23) (18,19) (18,23) (19,20) (19,23) (21,23) (21,22)\nIs there a path between node 7 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph145-14_8", + "image": "data/connectivity/graph_visual/medium/graph145.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,12) (0,4) (0,11) (0,17) (0,2) (0,5) (0,9) (0,8) (0,16) (0,10) (1,3) (1,12) (1,4) (1,11) (1,17) (1,7) (1,2) (1,5) (1,9) (1,8) (1,10) (2,3) (2,12) (2,4) (2,11) (2,17) (2,7) (2,5) (2,8) (2,16) (3,12) (3,7) (3,9) (3,8) (4,12) (4,11) (4,17) (4,5) (4,9) (4,8) (4,16) (4,10) (5,12) (5,11) (5,17) (5,7) (5,14) (5,9) (5,16) (5,10) (6,15) (6,13) (7,12) (7,11) (7,17) (7,9) (7,16) (7,10) (8,11) (8,14) (8,9) (8,16) (8,10) (9,12) (9,17) (9,10) (10,11) (10,17) (10,14) (10,16) (11,17) (11,16) (14,16) (16,17)\nIs there a path between node 14 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph462-14_9", + "image": "data/connectivity/graph_visual/medium/graph462.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,20) (0,6) (0,10) (0,15) (0,5) (0,1) (0,19) (1,20) (1,6) (1,10) (1,15) (1,5) (1,19) (2,13) (2,8) (2,21) (2,18) (2,7) (3,14) (3,12) (3,4) (3,11) (3,9) (3,16) (3,17) (4,14) (4,12) (4,11) (4,9) (4,16) (4,17) (5,20) (5,6) (5,10) (5,15) (5,19) (6,20) (6,10) (6,15) (6,19) (7,13) (7,8) (7,21) (7,18) (8,13) (8,21) (8,18) (9,14) (9,12) (9,11) (9,16) (9,17) (10,20) (10,15) (10,19) (11,14) (11,12) (11,16) (11,17) (12,14) (12,16) (12,17) (13,21) (13,18) (14,16) (14,17) (15,20) (15,19) (16,17) (18,21) (19,20)\nIs there a path between node 14 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph292-14_2", + "image": "data/connectivity/graph_visual/medium/graph292.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,14) (0,8) (0,12) (1,5) (1,16) (1,6) (1,7) (2,11) (3,16) (3,9) (4,5) (4,9) (5,19) (5,16) (5,6) (5,7) (5,18) (6,16) (6,7) (7,16) (7,18) (8,14) (8,10) (12,15) (13,19) (13,16) (14,15)\nIs there a path between node 14 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph753-13_22", + "image": "data/connectivity/graph_visual/medium/graph753.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,3) (0,23) (0,18) (0,9) (0,5) (0,2) (0,4) (0,8) (0,24) (1,6) (1,3) (1,23) (1,16) (1,10) (1,12) (1,18) (1,9) (1,5) (1,2) (1,4) (1,22) (1,24) (2,6) (2,3) (2,13) (2,23) (2,16) (2,10) (2,12) (2,18) (2,15) (2,19) (2,9) (2,5) (2,11) (2,7) (2,22) (2,8) (2,24) (3,6) (3,13) (3,23) (3,10) (3,12) (3,18) (3,15) (3,9) (3,11) (3,7) (3,4) (3,22) (4,6) (4,13) (4,16) (4,12) (4,15) (4,19) (4,9) (4,5) (4,11) (4,7) (4,22) (4,8) (4,24) (5,6) (5,13) (5,23) (5,16) (5,10) (5,15) (5,19) (5,9) (5,11) (5,22) (6,23) (6,16) (6,10) (6,12) (6,18) (6,19) (6,9) (6,11) (6,7) (6,24) (7,13) (7,23) (7,16) (7,10) (7,12) (7,18) (7,15) (7,19) (7,11) (7,22) (7,24) (8,13) (8,23) (8,10) (8,12) (8,18) (8,15) (8,19) (8,9) (8,11) (8,24) (9,23) (9,16) (9,10) (9,12) (9,18) (9,15) (9,19) (9,22) (10,13) (10,23) (10,16) (10,12) (10,18) (10,15) (10,11) (10,22) (11,13) (11,23) (11,12) (11,18) (11,15) (11,19) (11,22) (11,24) (12,13) (12,23) (12,16) (12,18) (12,19) (13,23) (13,16) (13,18) (13,22) (15,23) (15,16) (15,18) (15,19) (15,24) (16,23) (16,18) (16,19) (16,22) (16,24) (18,23) (18,19) (18,22) (18,24) (19,23) (19,22) (19,24) (22,23) (22,24)\nIs there a path between node 13 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph212-12_11", + "image": "data/connectivity/graph_visual/medium/graph212.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,5) (0,9) (0,14) (0,18) (0,3) (0,1) (0,17) (0,4) (0,8) (0,7) (0,15) (0,11) (0,10) (0,13) (1,5) (1,9) (1,14) (1,18) (1,3) (1,17) (1,4) (1,8) (1,7) (1,15) (1,11) (1,10) (1,13) (3,5) (3,9) (3,14) (3,18) (3,17) (3,4) (3,8) (3,7) (3,15) (3,11) (3,10) (3,13) (4,5) (4,9) (4,14) (4,18) (4,17) (4,8) (4,7) (4,15) (4,11) (4,10) (4,13) (5,9) (5,14) (5,18) (5,17) (5,8) (5,7) (5,15) (5,11) (5,10) (5,13) (6,12) (6,16) (7,9) (7,14) (7,18) (7,17) (7,8) (7,15) (7,11) (7,10) (7,13) (8,9) (8,14) (8,18) (8,17) (8,15) (8,11) (8,10) (8,13) (9,14) (9,18) (9,17) (9,15) (9,11) (9,10) (9,13) (10,14) (10,18) (10,17) (10,15) (10,11) (10,13) (11,14) (11,18) (11,17) (11,15) (11,13) (12,16) (13,14) (13,18) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (15,17) (17,18)\nIs there a path between node 12 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph249-13_3", + "image": "data/connectivity/graph_visual/medium/graph249.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,6) (0,2) (0,17) (0,4) (0,5) (0,15) (0,9) (0,12) (0,11) (0,16) (0,8) (0,10) (0,18) (0,14) (1,7) (2,13) (2,6) (2,17) (2,4) (2,5) (2,15) (2,9) (2,12) (2,11) (2,16) (2,8) (2,10) (2,18) (2,14) (4,13) (4,6) (4,17) (4,5) (4,15) (4,9) (4,12) (4,11) (4,16) (4,8) (4,10) (4,18) (4,14) (5,13) (5,6) (5,17) (5,15) (5,9) (5,12) (5,11) (5,16) (5,8) (5,10) (5,18) (5,14) (6,13) (6,17) (6,15) (6,9) (6,12) (6,11) (6,16) (6,8) (6,10) (6,18) (6,14) (8,13) (8,17) (8,15) (8,9) (8,12) (8,11) (8,16) (8,10) (8,18) (8,14) (9,13) (9,17) (9,15) (9,12) (9,11) (9,16) (9,10) (9,18) (9,14) (10,13) (10,17) (10,15) (10,12) (10,11) (10,16) (10,18) (10,14) (11,13) (11,17) (11,15) (11,12) (11,16) (11,18) (11,14) (12,13) (12,17) (12,15) (12,16) (12,18) (12,14) (13,17) (13,15) (13,16) (13,18) (13,14) (14,17) (14,15) (14,16) (14,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 13 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph640-10_21", + "image": "data/connectivity/graph_visual/medium/graph640.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,22) (0,16) (0,23) (1,8) (1,4) (1,22) (1,16) (1,18) (1,3) (2,19) (2,9) (2,17) (2,20) (3,14) (3,13) (3,7) (4,8) (4,12) (4,16) (4,23) (4,18) (5,10) (5,9) (5,20) (6,14) (6,13) (6,22) (6,7) (7,22) (7,18) (8,22) (8,18) (9,19) (9,11) (9,20) (9,21) (10,20) (10,21) (11,20) (12,18) (13,22) (13,16) (13,23) (13,18) (15,19) (15,17) (15,21) (16,23) (16,18) (17,19) (18,22)\nIs there a path between node 10 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph175-6_10", + "image": "data/connectivity/graph_visual/medium/graph175.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,2) (0,5) (1,13) (1,4) (1,8) (1,17) (1,9) (1,3) (1,6) (1,14) (1,10) (2,7) (2,5) (3,4) (3,8) (3,15) (3,11) (3,6) (3,14) (3,10) (4,13) (4,16) (4,8) (4,17) (4,11) (4,9) (4,6) (4,10) (5,7) (5,12) (6,15) (6,17) (6,11) (6,9) (6,14) (6,10) (8,13) (8,16) (8,15) (8,17) (8,9) (8,14) (8,10) (9,13) (9,15) (9,17) (9,11) (9,14) (9,10) (10,15) (10,17) (10,11) (10,14) (11,13) (11,16) (11,15) (11,14) (13,16) (13,15) (14,16) (14,15) (14,17) (15,16)\nIs there a path between node 6 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph312-10_2", + "image": "data/connectivity/graph_visual/medium/graph312.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (0,12) (0,6) (0,18) (0,16) (1,15) (1,17) (1,2) (1,19) (1,5) (1,14) (1,10) (1,13) (1,4) (1,7) (1,11) (1,9) (2,15) (2,17) (2,19) (2,5) (2,14) (2,10) (2,13) (2,4) (2,7) (2,11) (2,9) (4,15) (4,17) (4,19) (4,5) (4,14) (4,10) (4,13) (4,7) (4,11) (4,9) (5,15) (5,17) (5,19) (5,14) (5,10) (5,13) (5,7) (5,11) (5,9) (6,8) (6,12) (6,18) (6,16) (7,15) (7,17) (7,19) (7,14) (7,10) (7,13) (7,11) (7,9) (8,12) (8,18) (8,16) (9,15) (9,17) (9,19) (9,14) (9,10) (9,13) (9,11) (10,15) (10,17) (10,19) (10,14) (10,13) (10,11) (11,15) (11,17) (11,19) (11,14) (11,13) (12,18) (12,16) (13,15) (13,17) (13,19) (13,14) (14,15) (14,17) (14,19) (15,17) (15,19) (16,18) (17,19)\nIs there a path between node 10 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph184-6_8", + "image": "data/connectivity/graph_visual/medium/graph184.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,4) (0,2) (0,8) (0,1) (0,12) (0,9) (0,6) (0,5) (0,11) (0,13) (0,17) (0,7) (0,14) (0,15) (1,4) (1,2) (1,8) (1,12) (1,9) (1,6) (1,5) (1,11) (1,13) (1,17) (1,7) (1,14) (1,15) (2,4) (2,8) (2,12) (2,9) (2,6) (2,5) (2,11) (2,13) (2,17) (2,7) (2,14) (2,15) (3,10) (4,8) (4,12) (4,9) (4,6) (4,5) (4,11) (4,13) (4,17) (4,7) (4,14) (4,15) (5,8) (5,12) (5,9) (5,6) (5,11) (5,13) (5,17) (5,7) (5,14) (5,15) (6,8) (6,12) (6,9) (6,11) (6,13) (6,17) (6,7) (6,14) (6,15) (7,8) (7,12) (7,9) (7,11) (7,13) (7,17) (7,14) (7,15) (8,12) (8,9) (8,11) (8,13) (8,17) (8,14) (8,15) (9,12) (9,11) (9,13) (9,17) (9,14) (9,15) (11,12) (11,13) (11,17) (11,14) (11,15) (12,13) (12,17) (12,14) (12,15) (13,17) (13,14) (13,15) (14,17) (14,15) (15,17)\nIs there a path between node 6 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph208-18_7", + "image": "data/connectivity/graph_visual/medium/graph208.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,15) (0,13) (0,3) (0,16) (0,10) (1,18) (1,7) (1,2) (1,4) (1,9) (1,12) (1,11) (1,5) (2,18) (2,7) (2,4) (2,9) (2,12) (2,6) (2,11) (2,5) (3,15) (3,17) (4,18) (4,9) (4,12) (4,6) (4,5) (5,18) (5,7) (5,12) (5,6) (5,11) (6,18) (6,7) (6,12) (7,18) (7,12) (9,12) (9,11) (10,15) (10,14) (11,18) (11,12) (13,16) (13,14) (13,17) (14,15) (14,16) (15,16) (16,17)\nIs there a path between node 18 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph558-12_10", + "image": "data/connectivity/graph_visual/medium/graph558.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,6) (0,19) (0,8) (0,17) (0,23) (0,1) (0,18) (0,7) (0,14) (1,15) (1,17) (1,23) (1,18) (1,7) (1,11) (1,14) (2,6) (2,19) (2,17) (2,23) (2,7) (3,15) (3,9) (3,17) (3,23) (3,18) (3,7) (3,11) (3,14) (4,12) (4,21) (5,12) (5,13) (6,15) (6,9) (6,19) (6,8) (6,17) (6,23) (6,10) (6,18) (6,7) (6,11) (6,14) (7,15) (7,9) (7,19) (7,8) (7,17) (7,23) (7,14) (8,19) (8,17) (8,23) (8,18) (8,11) (8,14) (9,19) (9,17) (9,23) (9,10) (9,14) (10,19) (10,17) (10,23) (10,18) (11,15) (11,19) (11,23) (11,18) (11,14) (12,13) (12,21) (13,21) (13,22) (14,19) (14,17) (14,23) (15,19) (15,23) (15,18) (16,20) (17,23) (18,19) (18,23) (19,23) (21,22)\nIs there a path between node 12 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph824-0_18", + "image": "data/connectivity/graph_visual/medium/graph824.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,8) (0,12) (0,5) (0,14) (0,15) (0,17) (0,11) (0,16) (0,1) (1,9) (1,8) (1,12) (1,5) (1,14) (1,15) (1,11) (1,16) (1,22) (2,9) (2,8) (2,15) (2,17) (2,11) (2,16) (2,6) (3,20) (3,24) (3,4) (3,13) (3,18) (3,19) (4,24) (4,21) (4,10) (4,18) (4,7) (5,9) (5,12) (5,15) (5,6) (5,22) (6,9) (6,8) (6,12) (6,14) (6,15) (6,17) (6,11) (7,20) (7,24) (7,23) (7,13) (7,21) (7,18) (7,19) (8,12) (8,14) (8,15) (8,11) (8,16) (8,22) (9,12) (9,17) (9,16) (9,22) (10,20) (10,23) (10,13) (10,19) (11,12) (11,14) (11,15) (11,17) (11,16) (12,15) (12,16) (12,22) (13,20) (13,24) (13,21) (13,18) (14,15) (14,17) (14,22) (15,17) (15,22) (16,17) (16,22) (18,20) (18,24) (18,23) (18,21) (18,19) (19,24) (20,24) (20,23) (20,21) (21,24) (21,23) (23,24)\nIs there a path between node 0 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph75-12_0", + "image": "data/connectivity/graph_visual/medium/graph75.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,13) (1,6) (1,7) (1,4) (2,6) (2,7) (2,9) (2,10) (2,14) (3,6) (3,9) (3,4) (4,8) (4,9) (4,11) (5,6) (6,8) (6,7) (6,9) (6,10) (7,8) (7,14) (8,13) (9,13) (9,10) (10,13) (10,11)\nIs there a path between node 12 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph168-8_14", + "image": "data/connectivity/graph_visual/medium/graph168.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,1) (0,5) (1,11) (1,6) (1,17) (1,10) (2,11) (2,17) (5,6) (5,9) (6,16) (6,8) (6,17) (6,10) (6,14) (8,10) (9,10) (10,11) (10,17) (10,15) (11,15) (14,16) (14,17)\nIs there a path between node 8 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph732-20_18", + "image": "data/connectivity/graph_visual/medium/graph732.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (0,1) (0,11) (0,22) (0,12) (1,18) (1,21) (1,11) (1,4) (1,20) (1,22) (1,12) (2,15) (2,21) (2,4) (2,6) (2,22) (3,19) (4,24) (4,14) (4,8) (4,21) (4,20) (4,7) (4,22) (4,12) (5,23) (5,15) (5,20) (5,9) (5,7) (6,14) (6,8) (6,21) (6,20) (6,10) (7,23) (7,8) (7,11) (7,22) (8,15) (8,21) (9,23) (9,21) (9,20) (9,12) (10,17) (10,14) (10,15) (10,21) (10,20) (10,22) (10,12) (10,16) (11,20) (11,12) (11,16) (12,24) (12,14) (12,23) (14,24) (14,17) (14,15) (14,21) (15,24) (16,24) (16,23) (17,24) (17,18) (17,20) (17,22) (18,24) (18,22) (22,24)\nIs there a path between node 20 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph154-5_4", + "image": "data/connectivity/graph_visual/medium/graph154.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,1) (0,6) (0,13) (0,4) (1,12) (1,6) (1,13) (1,4) (2,16) (2,15) (2,10) (2,11) (2,14) (2,3) (2,17) (2,5) (2,7) (2,8) (2,9) (3,16) (3,15) (3,10) (3,11) (3,14) (3,17) (3,5) (3,7) (3,8) (3,9) (4,12) (4,6) (4,13) (5,16) (5,15) (5,10) (5,11) (5,14) (5,17) (5,7) (5,8) (5,9) (6,12) (6,13) (7,16) (7,15) (7,10) (7,11) (7,14) (7,17) (7,8) (7,9) (8,16) (8,15) (8,10) (8,11) (8,14) (8,17) (8,9) (9,16) (9,15) (9,10) (9,11) (9,14) (9,17) (10,16) (10,15) (10,11) (10,14) (10,17) (11,16) (11,15) (11,14) (11,17) (12,13) (14,16) (14,15) (14,17) (15,16) (15,17) (16,17)\nIs there a path between node 5 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph44-1_6", + "image": "data/connectivity/graph_visual/medium/graph44.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,7) (0,5) (0,4) (0,6) (0,11) (1,10) (1,2) (2,10) (3,9) (3,8) (3,7) (3,5) (3,12) (3,6) (3,11) (4,7) (4,5) (4,12) (4,11) (5,9) (5,8) (5,7) (5,11) (6,9) (6,8) (6,7) (6,12) (7,12) (7,11) (8,9) (8,12) (9,12) (9,11) (11,12)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph739-10_12", + "image": "data/connectivity/graph_visual/medium/graph739.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,19) (0,11) (0,13) (0,17) (0,20) (1,4) (2,23) (2,12) (2,22) (2,21) (2,14) (3,19) (3,21) (4,9) (4,24) (4,17) (4,14) (5,6) (5,22) (5,24) (5,11) (5,20) (6,23) (6,22) (6,17) (8,14) (11,23) (11,24) (11,14) (12,22) (13,19) (13,24) (14,19) (14,21) (14,24) (14,20) (17,24) (20,23) (20,21) (21,24) (22,24) (23,24)\nIs there a path between node 10 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph339-11_9", + "image": "data/connectivity/graph_visual/medium/graph339.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (0,12) (0,18) (0,5) (0,16) (0,10) (0,2) (0,11) (1,17) (1,12) (1,18) (1,4) (1,5) (1,16) (1,10) (1,11) (2,17) (2,12) (2,18) (2,4) (2,5) (2,10) (2,11) (3,15) (3,13) (3,6) (3,20) (3,7) (3,19) (3,8) (3,14) (4,17) (4,12) (4,18) (4,10) (5,17) (5,12) (5,16) (5,10) (5,11) (6,15) (6,20) (6,7) (6,14) (6,9) (7,15) (7,13) (7,20) (7,19) (7,8) (8,15) (8,13) (8,19) (8,9) (9,15) (9,13) (9,19) (9,14) (10,17) (10,12) (10,18) (10,11) (11,17) (12,17) (12,18) (13,19) (13,14) (14,20) (14,19) (15,20) (15,19) (16,17) (16,18) (19,20)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph562-7_21", + "image": "data/connectivity/graph_visual/medium/graph562.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,5) (0,6) (0,13) (0,17) (0,23) (0,9) (0,10) (0,22) (0,2) (0,20) (0,21) (0,12) (1,14) (1,18) (1,3) (1,4) (1,11) (1,16) (1,7) (2,5) (2,13) (2,17) (2,23) (2,9) (2,10) (2,20) (2,21) (2,12) (3,18) (3,4) (3,11) (3,16) (3,7) (4,18) (4,11) (4,16) (4,8) (5,19) (5,13) (5,17) (5,23) (5,9) (5,10) (5,22) (5,15) (5,12) (6,19) (6,13) (6,23) (6,9) (6,22) (6,15) (6,20) (6,12) (7,14) (7,11) (7,16) (8,14) (8,11) (9,19) (9,13) (9,17) (9,23) (9,10) (9,15) (9,20) (9,21) (10,19) (10,13) (10,23) (10,15) (10,20) (11,18) (12,19) (12,23) (12,22) (12,15) (12,20) (12,21) (13,19) (13,23) (13,22) (13,20) (14,18) (15,19) (15,17) (15,22) (15,20) (17,23) (17,22) (17,21) (19,21) (20,23) (20,22) (21,23) (22,23)\nIs there a path between node 7 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph65-11_5", + "image": "data/connectivity/graph_visual/medium/graph65.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (0,4) (0,13) (0,8) (0,6) (0,11) (0,12) (0,10) (0,9) (1,3) (1,5) (1,7) (2,4) (2,13) (2,8) (2,6) (2,11) (2,12) (2,10) (2,9) (3,5) (3,7) (4,13) (4,8) (4,6) (4,11) (4,12) (4,10) (4,9) (5,7) (6,13) (6,8) (6,11) (6,12) (6,10) (6,9) (8,13) (8,11) (8,12) (8,10) (8,9) (9,13) (9,11) (9,12) (9,10) (10,13) (10,11) (10,12) (11,13) (11,12) (12,13)\nIs there a path between node 11 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph284-16_14", + "image": "data/connectivity/graph_visual/medium/graph284.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,2) (1,7) (1,15) (2,12) (2,15) (3,17) (3,7) (3,12) (3,15) (4,14) (4,16) (4,15) (5,9) (5,6) (6,18) (6,9) (6,13) (7,12) (8,12) (9,18) (10,19) (14,16) (14,15) (16,17)\nIs there a path between node 16 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph721-14_16", + "image": "data/connectivity/graph_visual/medium/graph721.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,3) (0,9) (0,20) (0,15) (1,21) (1,11) (1,13) (1,23) (1,19) (1,17) (1,5) (1,4) (1,22) (1,2) (1,16) (1,24) (1,7) (1,18) (1,6) (1,12) (1,8) (1,10) (2,21) (2,11) (2,13) (2,23) (2,19) (2,17) (2,5) (2,4) (2,22) (2,16) (2,24) (2,7) (2,18) (2,6) (2,12) (2,8) (2,10) (3,14) (3,9) (3,20) (3,15) (4,21) (4,11) (4,13) (4,23) (4,19) (4,17) (4,5) (4,22) (4,16) (4,24) (4,7) (4,18) (4,6) (4,12) (4,8) (4,10) (5,21) (5,11) (5,13) (5,23) (5,19) (5,17) (5,22) (5,16) (5,24) (5,7) (5,18) (5,6) (5,12) (5,8) (5,10) (6,21) (6,11) (6,13) (6,23) (6,19) (6,17) (6,22) (6,16) (6,24) (6,7) (6,18) (6,12) (6,8) (6,10) (7,21) (7,11) (7,13) (7,23) (7,19) (7,17) (7,22) (7,16) (7,24) (7,18) (7,12) (7,8) (7,10) (8,21) (8,11) (8,13) (8,23) (8,19) (8,17) (8,22) (8,16) (8,24) (8,18) (8,12) (8,10) (9,14) (9,20) (9,15) (10,21) (10,11) (10,13) (10,23) (10,19) (10,17) (10,22) (10,16) (10,24) (10,18) (10,12) (11,21) (11,13) (11,23) (11,19) (11,17) (11,22) (11,16) (11,24) (11,18) (11,12) (12,21) (12,13) (12,23) (12,19) (12,17) (12,22) (12,16) (12,24) (12,18) (13,21) (13,23) (13,19) (13,17) (13,22) (13,16) (13,24) (13,18) (14,20) (14,15) (15,20) (16,21) (16,23) (16,19) (16,17) (16,22) (16,24) (16,18) (17,21) (17,23) (17,19) (17,22) (17,24) (17,18) (18,21) (18,23) (18,19) (18,22) (18,24) (19,21) (19,23) (19,22) (19,24) (21,23) (21,22) (21,24) (22,23) (22,24) (23,24)\nIs there a path between node 14 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph401-11_9", + "image": "data/connectivity/graph_visual/medium/graph401.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,11) (0,1) (1,11) (2,4) (2,14) (3,21) (3,18) (3,6) (3,12) (3,13) (5,6) (6,21) (6,20) (6,8) (6,12) (6,13) (7,16) (7,12) (8,20) (9,20) (9,13) (10,11) (12,17) (12,16) (13,20) (13,17) (13,19) (15,21) (15,16) (15,19) (16,21) (16,19) (17,19) (18,19) (19,20) (20,21)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph492-11_7", + "image": "data/connectivity/graph_visual/medium/graph492.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,6) (0,17) (0,18) (0,8) (0,10) (0,12) (0,14) (0,16) (0,13) (0,9) (0,19) (0,15) (0,4) (0,20) (0,7) (0,5) (0,21) (0,3) (0,2) (1,6) (1,17) (1,18) (1,8) (1,10) (1,12) (1,14) (1,16) (1,13) (1,9) (1,19) (1,15) (1,4) (1,20) (1,7) (1,5) (1,21) (1,3) (1,2) (2,6) (2,17) (2,18) (2,8) (2,10) (2,12) (2,14) (2,16) (2,13) (2,9) (2,19) (2,15) (2,4) (2,20) (2,7) (2,5) (2,21) (2,3) (3,6) (3,17) (3,18) (3,8) (3,10) (3,12) (3,14) (3,16) (3,13) (3,9) (3,19) (3,15) (3,4) (3,20) (3,7) (3,5) (3,21) (4,6) (4,17) (4,18) (4,8) (4,10) (4,12) (4,14) (4,16) (4,13) (4,9) (4,19) (4,15) (4,20) (4,7) (4,5) (4,21) (5,6) (5,17) (5,18) (5,8) (5,10) (5,12) (5,14) (5,16) (5,13) (5,9) (5,19) (5,15) (5,20) (5,7) (5,21) (6,17) (6,18) (6,8) (6,10) (6,12) (6,14) (6,16) (6,13) (6,9) (6,19) (6,15) (6,20) (6,7) (6,21) (7,17) (7,18) (7,8) (7,10) (7,12) (7,14) (7,16) (7,13) (7,9) (7,19) (7,15) (7,20) (7,21) (8,17) (8,18) (8,10) (8,12) (8,14) (8,16) (8,13) (8,9) (8,19) (8,15) (8,20) (8,21) (9,17) (9,18) (9,10) (9,12) (9,14) (9,16) (9,13) (9,19) (9,15) (9,20) (9,21) (10,17) (10,18) (10,12) (10,14) (10,16) (10,13) (10,19) (10,15) (10,20) (10,21) (11,22) (12,17) (12,18) (12,14) (12,16) (12,13) (12,19) (12,15) (12,20) (12,21) (13,17) (13,18) (13,14) (13,16) (13,19) (13,15) (13,20) (13,21) (14,17) (14,18) (14,16) (14,19) (14,15) (14,20) (14,21) (15,17) (15,18) (15,16) (15,19) (15,20) (15,21) (16,17) (16,18) (16,19) (16,20) (16,21) (17,18) (17,19) (17,20) (17,21) (18,19) (18,20) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 11 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph705-0_14", + "image": "data/connectivity/graph_visual/medium/graph705.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (1,7) (1,2) (1,22) (1,23) (1,16) (1,3) (2,17) (2,21) (2,8) (2,23) (2,12) (3,22) (3,12) (4,17) (4,21) (4,8) (4,7) (4,18) (4,10) (5,14) (5,15) (5,9) (6,18) (6,22) (6,15) (6,23) (6,11) (7,21) (7,8) (7,18) (7,22) (7,12) (7,11) (8,21) (8,18) (8,16) (9,10) (9,11) (10,18) (10,14) (10,16) (10,11) (11,17) (11,22) (11,23) (12,14) (14,21) (15,22) (16,17) (17,21) (18,23) (19,24)\nIs there a path between node 0 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph167-2_3", + "image": "data/connectivity/graph_visual/medium/graph167.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,17) (0,8) (0,6) (0,12) (0,16) (0,3) (1,17) (1,2) (1,8) (1,9) (1,4) (1,12) (1,3) (2,17) (2,11) (2,9) (2,16) (2,14) (2,5) (3,13) (3,9) (3,14) (4,17) (4,7) (4,13) (4,16) (4,5) (5,7) (5,13) (5,9) (5,14) (6,8) (6,11) (6,9) (6,12) (6,16) (6,14) (7,8) (7,13) (8,13) (9,13) (9,12) (11,13) (11,12) (11,14) (13,14)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph825-18_17", + "image": "data/connectivity/graph_visual/medium/graph825.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,1) (0,6) (0,13) (0,16) (0,21) (0,5) (1,12) (1,15) (1,6) (1,5) (2,8) (2,9) (2,19) (2,7) (2,22) (2,4) (2,17) (2,20) (3,11) (3,8) (3,14) (3,9) (3,23) (3,7) (3,22) (3,17) (3,20) (4,11) (4,8) (4,14) (4,19) (4,23) (4,7) (5,10) (5,15) (5,6) (5,13) (5,18) (5,21) (6,12) (6,15) (6,18) (6,21) (7,8) (7,24) (7,14) (7,9) (7,19) (7,22) (7,17) (7,20) (8,11) (8,14) (8,22) (8,17) (8,20) (9,11) (9,24) (9,14) (9,19) (9,17) (10,12) (10,15) (10,16) (10,18) (10,21) (11,24) (11,14) (11,19) (11,23) (11,22) (11,17) (12,15) (12,16) (12,18) (12,21) (13,15) (13,16) (13,18) (14,24) (14,19) (14,23) (14,20) (15,16) (15,18) (16,18) (16,21) (17,24) (17,23) (17,20) (18,21) (19,23) (19,20) (20,24) (20,23) (20,22) (22,24) (22,23)\nIs there a path between node 18 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph232-15_11", + "image": "data/connectivity/graph_visual/medium/graph232.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,1) (0,13) (0,15) (0,16) (0,9) (0,14) (0,3) (0,12) (0,17) (0,2) (0,18) (1,11) (1,13) (1,15) (1,16) (1,9) (1,8) (1,14) (1,3) (1,4) (1,17) (1,18) (2,11) (2,13) (2,15) (2,9) (2,8) (2,14) (2,3) (2,12) (2,17) (2,18) (3,11) (3,13) (3,15) (3,16) (3,9) (3,8) (3,14) (3,12) (3,17) (3,18) (4,13) (4,15) (4,16) (4,8) (4,14) (4,12) (4,18) (5,6) (5,7) (5,10) (6,7) (6,10) (7,10) (8,11) (8,15) (8,16) (8,18) (9,11) (9,13) (9,15) (9,16) (9,14) (9,12) (9,17) (9,18) (11,13) (11,16) (11,17) (11,18) (12,15) (12,16) (12,17) (12,18) (13,15) (13,18) (14,15) (14,17) (15,16) (16,17) (16,18) (17,18)\nIs there a path between node 15 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph843-20_0", + "image": "data/connectivity/graph_visual/medium/graph843.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,21) (0,4) (0,1) (0,23) (0,19) (0,2) (0,18) (0,16) (0,5) (0,12) (0,20) (0,14) (1,15) (1,21) (1,4) (1,23) (1,19) (1,2) (1,18) (1,16) (1,5) (1,12) (1,20) (1,14) (2,15) (2,21) (2,4) (2,23) (2,19) (2,18) (2,16) (2,5) (2,12) (2,20) (2,14) (3,10) (3,8) (3,6) (3,17) (3,13) (3,7) (3,11) (3,22) (3,9) (3,24) (4,15) (4,21) (4,23) (4,19) (4,18) (4,16) (4,5) (4,12) (4,20) (4,14) (5,15) (5,21) (5,23) (5,19) (5,18) (5,16) (5,12) (5,20) (5,14) (6,10) (6,8) (6,17) (6,13) (6,7) (6,11) (6,22) (6,9) (6,24) (7,10) (7,8) (7,17) (7,13) (7,11) (7,22) (7,9) (7,24) (8,10) (8,17) (8,13) (8,11) (8,22) (8,9) (8,24) (9,10) (9,17) (9,13) (9,11) (9,22) (9,24) (10,17) (10,13) (10,11) (10,22) (10,24) (11,17) (11,13) (11,22) (11,24) (12,15) (12,21) (12,23) (12,19) (12,18) (12,16) (12,20) (12,14) (13,17) (13,22) (13,24) (14,15) (14,21) (14,23) (14,19) (14,18) (14,16) (14,20) (15,21) (15,23) (15,19) (15,18) (15,16) (15,20) (16,21) (16,23) (16,19) (16,18) (16,20) (17,22) (17,24) (18,21) (18,23) (18,19) (18,20) (19,21) (19,23) (19,20) (20,21) (20,23) (21,23) (22,24)\nIs there a path between node 20 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph129-14_6", + "image": "data/connectivity/graph_visual/medium/graph129.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,12) (0,13) (0,2) (0,16) (0,7) (0,6) (0,9) (0,5) (0,1) (0,8) (1,12) (1,13) (1,2) (1,16) (1,7) (1,6) (1,9) (1,5) (1,8) (2,12) (2,13) (2,16) (2,7) (2,6) (2,9) (2,5) (2,8) (3,10) (3,14) (3,4) (3,11) (3,15) (4,10) (4,14) (4,11) (4,15) (5,12) (5,13) (5,16) (5,7) (5,6) (5,9) (5,8) (6,12) (6,13) (6,16) (6,7) (6,9) (6,8) (7,12) (7,13) (7,16) (7,9) (7,8) (8,12) (8,13) (8,16) (8,9) (9,12) (9,13) (9,16) (10,14) (10,11) (10,15) (11,14) (11,15) (12,13) (12,16) (13,16) (14,15)\nIs there a path between node 14 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph21-10_4", + "image": "data/connectivity/graph_visual/medium/graph21.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,9) (0,1) (1,7) (1,9) (2,3) (2,6) (3,10) (4,8) (7,9) (8,9) (10,11)\nIs there a path between node 10 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph853-0_10", + "image": "data/connectivity/graph_visual/medium/graph853.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,15) (0,6) (0,16) (0,2) (1,5) (1,21) (1,19) (1,11) (1,18) (1,12) (1,8) (1,14) (1,20) (1,24) (1,9) (1,10) (2,7) (2,15) (2,6) (2,16) (3,22) (3,17) (3,13) (3,4) (3,23) (4,22) (4,17) (4,13) (4,23) (5,21) (5,19) (5,11) (5,18) (5,12) (5,8) (5,14) (5,20) (5,24) (5,9) (5,10) (6,7) (6,15) (6,16) (7,15) (7,16) (8,21) (8,19) (8,11) (8,18) (8,12) (8,14) (8,20) (8,24) (8,9) (8,10) (9,21) (9,19) (9,11) (9,18) (9,12) (9,14) (9,20) (9,24) (9,10) (10,21) (10,19) (10,11) (10,18) (10,12) (10,14) (10,20) (10,24) (11,21) (11,19) (11,18) (11,12) (11,14) (11,20) (11,24) (12,21) (12,19) (12,18) (12,14) (12,20) (12,24) (13,22) (13,17) (13,23) (14,21) (14,19) (14,18) (14,20) (14,24) (15,16) (17,22) (17,23) (18,21) (18,19) (18,20) (18,24) (19,21) (19,20) (19,24) (20,21) (20,24) (21,24) (22,23)\nIs there a path between node 0 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph479-14_15", + "image": "data/connectivity/graph_visual/medium/graph479.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,4) (0,10) (0,12) (0,20) (0,14) (0,8) (0,3) (0,6) (0,5) (0,15) (0,19) (0,7) (0,9) (0,22) (0,2) (0,21) (0,18) (1,4) (1,10) (1,12) (1,20) (1,8) (1,5) (1,15) (1,16) (1,19) (1,7) (1,9) (1,22) (1,2) (1,18) (2,4) (2,10) (2,12) (2,14) (2,3) (2,5) (2,15) (2,19) (2,7) (2,22) (2,21) (2,18) (3,4) (3,12) (3,20) (3,14) (3,6) (3,5) (3,15) (3,16) (3,19) (3,7) (3,9) (3,22) (3,21) (3,18) (4,10) (4,12) (4,8) (4,6) (4,5) (4,15) (4,16) (4,19) (4,7) (4,9) (4,21) (4,18) (5,12) (5,14) (5,8) (5,6) (5,15) (5,16) (5,19) (5,7) (5,9) (5,22) (5,18) (6,10) (6,12) (6,20) (6,14) (6,16) (6,19) (6,7) (6,9) (6,22) (6,21) (6,18) (7,10) (7,12) (7,14) (7,8) (7,16) (7,9) (7,22) (7,21) (7,18) (8,10) (8,12) (8,14) (8,15) (8,16) (8,19) (8,9) (8,21) (9,12) (9,20) (9,15) (9,16) (9,22) (9,21) (9,18) (10,12) (10,20) (10,14) (10,15) (10,16) (10,18) (12,16) (12,19) (13,17) (14,20) (14,16) (15,16) (15,22) (15,21) (16,20) (16,21) (16,18) (18,22) (18,21) (19,20) (19,22) (19,21) (21,22)\nIs there a path between node 14 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph672-4_19", + "image": "data/connectivity/graph_visual/medium/graph672.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,14) (0,10) (0,4) (0,9) (0,20) (1,8) (1,6) (1,16) (1,11) (3,7) (3,22) (3,19) (3,21) (3,15) (3,17) (4,23) (4,14) (4,9) (5,8) (5,13) (5,11) (6,8) (6,13) (6,11) (7,22) (7,19) (7,17) (8,13) (8,16) (8,11) (9,23) (9,12) (9,10) (9,18) (9,20) (10,23) (10,14) (10,18) (11,13) (11,16) (12,23) (12,18) (14,23) (14,18) (14,20) (15,19) (15,21) (15,17) (17,22) (17,19) (17,21) (18,23) (18,20) (19,21) (20,23) (21,22)\nIs there a path between node 4 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph375-16_8", + "image": "data/connectivity/graph_visual/medium/graph375.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,15) (0,5) (0,3) (0,11) (0,9) (0,8) (0,13) (1,15) (1,5) (1,3) (1,11) (1,4) (1,9) (1,10) (1,8) (3,15) (3,4) (3,10) (3,8) (4,15) (4,12) (4,9) (4,10) (4,8) (4,13) (5,15) (5,11) (5,9) (5,10) (6,7) (6,20) (6,17) (6,18) (6,14) (7,19) (7,20) (7,18) (8,12) (8,11) (8,9) (8,10) (8,13) (9,15) (9,12) (9,11) (9,10) (10,15) (10,11) (10,13) (11,12) (12,13) (14,19) (14,20) (14,17) (14,18) (17,19) (17,20) (17,18) (18,19) (18,20)\nIs there a path between node 16 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph317-4_9", + "image": "data/connectivity/graph_visual/medium/graph317.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,1) (0,18) (0,8) (0,7) (1,18) (1,8) (1,7) (2,17) (2,16) (2,11) (2,5) (2,9) (2,19) (2,6) (2,10) (2,14) (2,4) (2,12) (2,3) (2,15) (2,13) (3,17) (3,16) (3,11) (3,5) (3,9) (3,19) (3,6) (3,10) (3,14) (3,4) (3,12) (3,15) (3,13) (4,17) (4,16) (4,11) (4,5) (4,9) (4,19) (4,6) (4,10) (4,14) (4,12) (4,15) (4,13) (5,17) (5,16) (5,11) (5,9) (5,19) (5,6) (5,10) (5,14) (5,12) (5,15) (5,13) (6,17) (6,16) (6,11) (6,9) (6,19) (6,10) (6,14) (6,12) (6,15) (6,13) (7,18) (7,8) (8,18) (9,17) (9,16) (9,11) (9,19) (9,10) (9,14) (9,12) (9,15) (9,13) (10,17) (10,16) (10,11) (10,19) (10,14) (10,12) (10,15) (10,13) (11,17) (11,16) (11,19) (11,14) (11,12) (11,15) (11,13) (12,17) (12,16) (12,19) (12,14) (12,15) (12,13) (13,17) (13,16) (13,19) (13,14) (13,15) (14,17) (14,16) (14,19) (14,15) (15,17) (15,16) (15,19) (16,17) (16,19) (17,19)\nIs there a path between node 4 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph139-5_15", + "image": "data/connectivity/graph_visual/medium/graph139.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,10) (0,17) (1,13) (1,14) (2,11) (3,11) (5,6) (5,13) (6,12) (6,14) (7,16) (8,17) (10,17) (12,13) (12,15) (12,14) (13,15)\nIs there a path between node 5 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph704-8_11", + "image": "data/connectivity/graph_visual/medium/graph704.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,7) (1,9) (1,10) (1,14) (2,3) (2,11) (3,11) (3,12) (4,17) (5,18) (5,17) (6,20) (6,22) (6,17) (6,8) (7,23) (7,18) (7,8) (9,21) (9,16) (9,11) (9,13) (10,14) (11,21) (11,14) (11,13) (12,15) (13,21) (13,15) (13,14) (14,15) (17,18) (17,19) (18,23) (18,24) (19,24) (19,22)\nIs there a path between node 8 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph633-15_21", + "image": "data/connectivity/graph_visual/medium/graph633.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,10) (1,9) (3,17) (3,8) (3,23) (4,17) (4,15) (4,22) (4,8) (4,23) (4,16) (6,11) (6,10) (7,21) (8,17) (8,23) (8,16) (10,18) (10,19) (11,18) (11,14) (15,23) (16,17) (16,23) (19,20) (21,22) (21,23)\nIs there a path between node 15 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph45-8_6", + "image": "data/connectivity/graph_visual/medium/graph45.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,6) (0,1) (0,8) (0,12) (0,9) (0,3) (1,8) (1,12) (1,9) (1,3) (1,11) (1,4) (2,7) (3,8) (3,12) (3,9) (4,6) (4,8) (4,11) (5,7) (5,10) (6,8) (6,12) (6,9) (6,11) (7,10) (8,11) (9,12) (9,11) (11,12)\nIs there a path between node 8 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph3-6_10", + "image": "data/connectivity/graph_visual/medium/graph3.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nIs there a path between node 6 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph401-9_16", + "image": "data/connectivity/graph_visual/medium/graph401.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,11) (0,1) (1,11) (2,4) (2,14) (3,21) (3,18) (3,6) (3,12) (3,13) (5,6) (6,21) (6,20) (6,8) (6,12) (6,13) (7,16) (7,12) (8,20) (9,20) (9,13) (10,11) (12,17) (12,16) (13,20) (13,17) (13,19) (15,21) (15,16) (15,19) (16,21) (16,19) (17,19) (18,19) (19,20) (20,21)\nIs there a path between node 9 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph369-8_12", + "image": "data/connectivity/graph_visual/medium/graph369.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (1,2) (1,16) (1,19) (1,10) (1,13) (1,18) (1,14) (1,20) (1,5) (1,4) (1,15) (1,6) (1,8) (1,12) (2,16) (2,19) (2,7) (2,9) (2,18) (2,11) (2,14) (2,20) (2,5) (2,6) (2,12) (3,17) (4,16) (4,19) (4,10) (4,7) (4,9) (4,13) (4,14) (4,15) (4,6) (4,8) (4,12) (5,19) (5,10) (5,7) (5,9) (5,13) (5,18) (5,14) (5,20) (5,15) (5,6) (5,8) (5,12) (6,16) (6,19) (6,10) (6,13) (6,18) (6,15) (6,8) (6,12) (7,16) (7,19) (7,9) (7,13) (7,18) (7,14) (7,20) (7,15) (8,16) (8,19) (8,9) (8,13) (8,18) (8,14) (8,15) (8,12) (9,16) (9,10) (9,13) (9,18) (9,11) (9,20) (10,16) (10,19) (10,13) (10,11) (10,14) (10,20) (10,15) (10,12) (11,13) (11,18) (11,14) (11,20) (11,15) (12,16) (12,14) (12,20) (12,15) (13,16) (13,19) (13,18) (13,14) (13,20) (13,15) (14,19) (14,20) (15,16) (15,19) (15,18) (15,20) (16,19) (16,20) (18,20) (19,20)\nIs there a path between node 8 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph342-12_13", + "image": "data/connectivity/graph_visual/medium/graph342.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,2) (0,7) (0,1) (0,6) (0,19) (0,15) (0,8) (0,16) (0,9) (1,2) (1,10) (1,12) (1,14) (1,19) (1,8) (2,10) (2,11) (2,12) (2,14) (2,7) (2,6) (2,15) (2,3) (2,8) (2,9) (3,11) (3,12) (3,14) (3,7) (3,19) (3,8) (3,16) (3,9) (4,20) (4,5) (4,18) (4,17) (5,13) (5,18) (5,17) (6,10) (6,11) (6,14) (6,7) (6,19) (6,8) (6,16) (7,12) (7,14) (7,19) (7,8) (7,16) (7,9) (8,11) (8,12) (8,14) (8,19) (8,16) (8,9) (9,14) (9,19) (9,15) (9,16) (10,11) (10,12) (10,14) (10,19) (10,15) (10,16) (11,14) (11,19) (11,16) (12,14) (12,19) (12,16) (13,18) (13,17) (14,19) (15,19) (15,16) (16,19) (17,20)\nIs there a path between node 12 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph408-7_20", + "image": "data/connectivity/graph_visual/medium/graph408.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,17) (0,7) (0,18) (0,14) (0,8) (0,19) (0,15) (0,4) (0,21) (1,3) (1,6) (1,11) (2,7) (2,9) (2,14) (2,8) (2,19) (2,13) (2,15) (2,10) (3,5) (3,20) (3,6) (3,11) (4,17) (4,7) (4,18) (4,9) (4,21) (5,12) (5,6) (5,11) (6,12) (6,20) (7,17) (7,18) (7,9) (7,14) (7,8) (7,13) (7,15) (8,17) (8,18) (8,14) (8,13) (8,15) (8,21) (8,10) (9,17) (9,18) (9,14) (9,13) (9,21) (10,17) (10,18) (10,14) (10,13) (10,15) (11,12) (11,20) (12,20) (12,16) (13,18) (13,14) (13,19) (13,15) (13,21) (14,18) (14,15) (14,21) (15,17) (15,18) (15,19) (15,21) (17,18) (17,19) (18,19) (19,21)\nIs there a path between node 7 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph381-2_12", + "image": "data/connectivity/graph_visual/medium/graph381.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,20) (0,1) (0,15) (0,6) (0,9) (0,4) (0,16) (0,19) (1,20) (1,15) (1,6) (1,9) (1,4) (1,16) (1,19) (2,14) (2,10) (2,3) (2,11) (2,7) (2,18) (2,5) (2,12) (2,17) (2,8) (3,14) (3,10) (3,11) (3,7) (3,18) (3,5) (3,12) (3,17) (3,8) (4,20) (4,15) (4,6) (4,9) (4,16) (4,19) (5,14) (5,10) (5,11) (5,7) (5,18) (5,12) (5,17) (5,8) (6,20) (6,15) (6,9) (6,16) (6,19) (7,14) (7,10) (7,11) (7,18) (7,12) (7,17) (7,8) (8,14) (8,10) (8,11) (8,18) (8,12) (8,17) (9,20) (9,15) (9,16) (9,19) (10,14) (10,11) (10,18) (10,12) (10,17) (11,14) (11,18) (11,12) (11,17) (12,14) (12,18) (12,17) (14,18) (14,17) (15,20) (15,16) (15,19) (16,20) (16,19) (17,18) (19,20)\nIs there a path between node 2 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph19-6_11", + "image": "data/connectivity/graph_visual/medium/graph19.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,8) (0,4) (0,11) (1,3) (3,9) (3,7) (4,8) (5,11) (6,10) (6,9) (6,7) (8,11)\nIs there a path between node 6 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph684-16_14", + "image": "data/connectivity/graph_visual/medium/graph684.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,21) (0,12) (0,9) (0,2) (0,6) (0,4) (0,5) (0,14) (0,17) (0,8) (0,20) (0,13) (0,19) (0,22) (0,1) (0,15) (0,10) (0,18) (1,7) (1,21) (1,12) (1,9) (1,2) (1,6) (1,4) (1,5) (1,14) (1,17) (1,8) (1,20) (1,13) (1,19) (1,22) (1,15) (1,10) (1,18) (2,7) (2,21) (2,12) (2,9) (2,6) (2,4) (2,5) (2,14) (2,17) (2,8) (2,20) (2,13) (2,19) (2,22) (2,15) (2,10) (2,18) (3,11) (3,23) (4,7) (4,21) (4,12) (4,9) (4,6) (4,5) (4,14) (4,17) (4,8) (4,20) (4,13) (4,19) (4,22) (4,15) (4,10) (4,18) (5,7) (5,21) (5,12) (5,9) (5,6) (5,14) (5,17) (5,8) (5,20) (5,13) (5,19) (5,22) (5,15) (5,10) (5,18) (6,7) (6,21) (6,12) (6,9) (6,14) (6,17) (6,8) (6,20) (6,13) (6,19) (6,22) (6,15) (6,10) (6,18) (7,21) (7,12) (7,9) (7,14) (7,17) (7,8) (7,20) (7,13) (7,19) (7,22) (7,15) (7,10) (7,18) (8,21) (8,12) (8,9) (8,14) (8,17) (8,20) (8,13) (8,19) (8,22) (8,15) (8,10) (8,18) (9,21) (9,12) (9,14) (9,17) (9,20) (9,13) (9,19) (9,22) (9,15) (9,10) (9,18) (10,21) (10,12) (10,14) (10,17) (10,20) (10,13) (10,19) (10,22) (10,15) (10,18) (11,23) (12,21) (12,14) (12,17) (12,20) (12,13) (12,19) (12,22) (12,15) (12,18) (13,21) (13,14) (13,17) (13,20) (13,19) (13,22) (13,15) (13,18) (14,21) (14,17) (14,20) (14,19) (14,22) (14,15) (14,18) (15,21) (15,17) (15,20) (15,19) (15,22) (15,18) (17,21) (17,20) (17,19) (17,22) (17,18) (18,21) (18,20) (18,19) (18,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 16 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph550-14_12", + "image": "data/connectivity/graph_visual/medium/graph550.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,10) (0,19) (0,13) (0,20) (1,15) (1,23) (3,5) (3,7) (3,14) (3,22) (4,18) (4,19) (4,20) (5,7) (5,14) (5,15) (5,12) (6,10) (7,11) (7,14) (7,22) (7,8) (8,14) (8,22) (8,21) (10,18) (10,19) (10,13) (10,20) (11,17) (11,14) (11,23) (11,16) (12,23) (13,18) (13,20) (14,22) (14,21) (15,21) (15,16) (17,21) (18,19) (19,20) (21,22)\nIs there a path between node 14 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph122-10_3", + "image": "data/connectivity/graph_visual/medium/graph122.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,5) (0,3) (1,13) (1,4) (1,12) (1,16) (1,9) (1,15) (1,11) (1,8) (1,6) (1,7) (1,10) (2,5) (3,14) (4,16) (4,9) (4,11) (4,8) (4,7) (4,10) (6,13) (6,16) (6,11) (6,7) (6,10) (7,13) (7,9) (7,11) (7,8) (7,10) (8,13) (8,12) (8,16) (8,9) (8,15) (8,10) (9,13) (9,16) (9,15) (9,10) (10,16) (10,11) (11,13) (11,16) (11,15) (12,13) (12,15) (13,16) (15,16)\nIs there a path between node 10 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph36-3_12", + "image": "data/connectivity/graph_visual/medium/graph36.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,2) (0,12) (0,11) (0,4) (2,10) (2,8) (2,4) (4,6) (4,11) (5,9) (6,7) (6,10) (6,11) (7,8) (8,10) (8,9) (9,12) (10,11)\nIs there a path between node 3 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph9-8_4", + "image": "data/connectivity/graph_visual/medium/graph9.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,7) (0,5) (0,9) (0,6) (0,1) (1,2) (1,7) (1,3) (1,6) (2,7) (2,4) (2,9) (2,6) (3,7) (3,5) (4,9) (4,6) (6,7) (6,9) (8,10)\nIs there a path between node 8 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph854-5_21", + "image": "data/connectivity/graph_visual/medium/graph854.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,13) (0,4) (0,2) (0,9) (0,12) (0,7) (0,8) (0,15) (0,1) (0,24) (1,23) (1,13) (1,4) (1,2) (1,9) (1,12) (1,7) (1,8) (1,15) (1,24) (2,23) (2,13) (2,4) (2,9) (2,12) (2,7) (2,8) (2,15) (2,24) (3,11) (3,17) (3,14) (3,6) (3,10) (3,19) (3,18) (4,23) (4,13) (4,9) (4,12) (4,7) (4,8) (4,15) (4,24) (5,21) (5,16) (5,22) (6,11) (6,17) (6,14) (6,10) (6,19) (6,18) (7,23) (7,13) (7,9) (7,12) (7,8) (7,15) (7,24) (8,23) (8,13) (8,9) (8,12) (8,15) (8,24) (9,23) (9,13) (9,12) (9,15) (9,24) (10,11) (10,17) (10,14) (10,19) (10,18) (11,17) (11,14) (11,19) (11,18) (12,23) (12,13) (12,15) (12,24) (13,23) (13,15) (13,24) (14,17) (14,19) (14,18) (15,23) (15,24) (16,21) (16,22) (17,19) (17,18) (18,19) (21,22) (23,24)\nIs there a path between node 5 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph688-11_3", + "image": "data/connectivity/graph_visual/medium/graph688.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,6) (0,11) (0,14) (0,2) (1,20) (1,8) (1,7) (1,16) (1,21) (1,9) (1,17) (1,5) (1,23) (1,12) (1,22) (2,4) (2,6) (2,11) (2,14) (3,15) (3,18) (3,13) (3,19) (3,10) (4,6) (4,11) (4,14) (5,20) (5,8) (5,7) (5,16) (5,21) (5,9) (5,17) (5,23) (5,12) (5,22) (6,11) (6,14) (7,20) (7,8) (7,16) (7,21) (7,9) (7,17) (7,23) (7,12) (7,22) (8,20) (8,16) (8,21) (8,9) (8,17) (8,23) (8,12) (8,22) (9,20) (9,16) (9,21) (9,17) (9,23) (9,12) (9,22) (10,15) (10,18) (10,13) (10,19) (11,14) (12,20) (12,16) (12,21) (12,17) (12,23) (12,22) (13,15) (13,18) (13,19) (15,18) (15,19) (16,20) (16,21) (16,17) (16,23) (16,22) (17,20) (17,21) (17,23) (17,22) (18,19) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph214-4_16", + "image": "data/connectivity/graph_visual/medium/graph214.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,1) (0,6) (0,17) (0,10) (0,16) (0,13) (1,11) (1,6) (1,17) (1,10) (1,16) (1,13) (2,12) (2,8) (2,15) (2,14) (2,3) (2,9) (2,7) (2,4) (2,18) (2,5) (3,12) (3,8) (3,15) (3,14) (3,9) (3,7) (3,4) (3,18) (3,5) (4,12) (4,8) (4,15) (4,14) (4,9) (4,7) (4,18) (4,5) (5,12) (5,8) (5,15) (5,14) (5,9) (5,7) (5,18) (6,11) (6,17) (6,10) (6,16) (6,13) (7,12) (7,8) (7,15) (7,14) (7,9) (7,18) (8,12) (8,15) (8,14) (8,9) (8,18) (9,12) (9,15) (9,14) (9,18) (10,11) (10,17) (10,16) (10,13) (11,17) (11,16) (11,13) (12,15) (12,14) (12,18) (13,17) (13,16) (14,15) (14,18) (15,18) (16,17)\nIs there a path between node 4 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph437-2_15", + "image": "data/connectivity/graph_visual/medium/graph437.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,12) (0,5) (1,21) (1,6) (2,7) (2,3) (4,8) (5,8) (5,12) (6,16) (6,21) (6,20) (6,13) (7,17) (7,11) (9,11) (9,10) (10,17) (13,18) (13,15) (15,19) (15,21) (16,19) (16,20) (20,21)\nIs there a path between node 2 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph672-7_14", + "image": "data/connectivity/graph_visual/medium/graph672.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,14) (0,10) (0,4) (0,9) (0,20) (1,8) (1,6) (1,16) (1,11) (3,7) (3,22) (3,19) (3,21) (3,15) (3,17) (4,23) (4,14) (4,9) (5,8) (5,13) (5,11) (6,8) (6,13) (6,11) (7,22) (7,19) (7,17) (8,13) (8,16) (8,11) (9,23) (9,12) (9,10) (9,18) (9,20) (10,23) (10,14) (10,18) (11,13) (11,16) (12,23) (12,18) (14,23) (14,18) (14,20) (15,19) (15,21) (15,17) (17,22) (17,19) (17,21) (18,23) (18,20) (19,21) (20,23) (21,22)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph780-14_24", + "image": "data/connectivity/graph_visual/medium/graph780.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,18) (0,15) (0,12) (0,5) (1,24) (2,21) (2,23) (2,9) (2,15) (2,19) (3,23) (3,15) (3,8) (3,16) (5,21) (5,22) (5,6) (5,19) (5,8) (5,10) (5,16) (6,14) (6,22) (6,9) (6,12) (6,17) (9,23) (9,22) (9,20) (9,10) (10,22) (10,18) (10,19) (11,24) (12,14) (13,14) (13,21) (13,23) (13,18) (13,15) (14,21) (14,18) (14,15) (14,16) (15,20) (15,17) (17,23) (17,22) (17,18) (17,20) (17,19) (18,19) (19,20) (21,23)\nIs there a path between node 14 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph517-10_13", + "image": "data/connectivity/graph_visual/medium/graph517.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,9) (0,17) (0,20) (1,15) (1,22) (1,14) (1,3) (1,21) (1,5) (1,18) (1,7) (1,6) (1,13) (2,15) (2,3) (2,4) (2,11) (2,21) (2,18) (2,8) (2,13) (3,15) (3,22) (3,12) (3,14) (3,4) (3,11) (3,21) (3,5) (3,7) (3,6) (3,16) (4,15) (4,22) (4,12) (4,14) (4,11) (4,5) (4,7) (4,6) (4,16) (4,8) (4,13) (5,15) (5,22) (5,12) (5,11) (5,21) (5,7) (5,6) (5,8) (5,13) (6,15) (6,12) (6,11) (6,21) (6,18) (6,16) (6,8) (6,13) (7,22) (7,12) (7,14) (7,11) (7,21) (7,16) (7,8) (8,22) (8,14) (8,21) (8,18) (8,16) (8,13) (9,19) (9,10) (9,17) (10,17) (11,22) (11,14) (11,21) (11,18) (11,13) (12,22) (12,14) (12,21) (12,18) (12,16) (12,13) (13,14) (13,18) (13,16) (14,15) (14,21) (14,18) (14,16) (15,21) (16,18) (17,20) (18,22)\nIs there a path between node 10 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph259-16_17", + "image": "data/connectivity/graph_visual/medium/graph259.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,18) (0,13) (0,3) (0,14) (0,15) (0,19) (0,7) (0,9) (0,10) (1,5) (1,18) (1,12) (1,13) (1,14) (1,6) (1,17) (1,16) (1,9) (1,10) (1,11) (2,18) (2,12) (2,13) (2,6) (2,15) (2,19) (2,7) (2,17) (2,16) (2,9) (2,10) (2,11) (3,18) (3,12) (3,13) (3,14) (3,6) (3,19) (3,17) (3,9) (3,10) (3,11) (5,18) (5,12) (5,13) (5,14) (5,6) (5,15) (5,19) (5,7) (5,16) (5,11) (6,18) (6,12) (6,7) (6,17) (6,16) (6,9) (6,10) (7,18) (7,12) (7,13) (7,15) (7,19) (7,17) (7,16) (7,10) (7,11) (9,18) (9,13) (9,15) (9,19) (9,16) (9,10) (10,18) (10,13) (10,14) (10,19) (10,17) (10,11) (11,12) (11,13) (11,14) (11,15) (11,19) (11,17) (11,16) (12,14) (12,19) (12,17) (12,16) (13,18) (13,15) (13,19) (13,17) (14,18) (14,15) (14,19) (14,17) (14,16) (15,18) (15,19) (15,16) (16,18) (17,18) (17,19) (18,19)\nIs there a path between node 16 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph391-8_20", + "image": "data/connectivity/graph_visual/medium/graph391.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,9) (0,20) (0,8) (0,14) (0,2) (0,11) (0,1) (0,10) (0,7) (0,12) (0,4) (0,5) (0,15) (0,16) (1,18) (1,9) (1,20) (1,8) (1,14) (1,2) (1,11) (1,10) (1,7) (1,12) (1,4) (1,5) (1,15) (1,16) (2,18) (2,9) (2,20) (2,8) (2,14) (2,11) (2,10) (2,7) (2,12) (2,4) (2,5) (2,15) (2,16) (3,13) (3,19) (4,18) (4,9) (4,20) (4,8) (4,14) (4,11) (4,10) (4,7) (4,12) (4,5) (4,15) (4,16) (5,18) (5,9) (5,20) (5,8) (5,14) (5,11) (5,10) (5,7) (5,12) (5,15) (5,16) (6,17) (7,18) (7,9) (7,20) (7,8) (7,14) (7,11) (7,10) (7,12) (7,15) (7,16) (8,18) (8,9) (8,20) (8,14) (8,11) (8,10) (8,12) (8,15) (8,16) (9,18) (9,20) (9,14) (9,11) (9,10) (9,12) (9,15) (9,16) (10,18) (10,20) (10,14) (10,11) (10,12) (10,15) (10,16) (11,18) (11,20) (11,14) (11,12) (11,15) (11,16) (12,18) (12,20) (12,14) (12,15) (12,16) (13,19) (14,18) (14,20) (14,15) (14,16) (15,18) (15,20) (15,16) (16,18) (16,20) (18,20)\nIs there a path between node 8 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph278-12_1", + "image": "data/connectivity/graph_visual/medium/graph278.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (0,2) (0,3) (0,10) (0,6) (0,4) (0,19) (0,17) (0,13) (0,1) (0,16) (0,18) (0,7) (0,9) (0,15) (1,8) (1,2) (1,3) (1,10) (1,6) (1,4) (1,19) (1,17) (1,13) (1,16) (1,18) (1,7) (1,9) (1,15) (2,8) (2,3) (2,10) (2,6) (2,4) (2,19) (2,17) (2,13) (2,16) (2,18) (2,7) (2,9) (2,15) (3,8) (3,10) (3,6) (3,4) (3,19) (3,17) (3,13) (3,16) (3,18) (3,7) (3,9) (3,15) (4,8) (4,10) (4,6) (4,19) (4,17) (4,13) (4,16) (4,18) (4,7) (4,9) (4,15) (5,11) (5,12) (6,8) (6,10) (6,19) (6,17) (6,13) (6,16) (6,18) (6,7) (6,9) (6,15) (7,8) (7,10) (7,19) (7,17) (7,13) (7,16) (7,18) (7,9) (7,15) (8,10) (8,19) (8,17) (8,13) (8,16) (8,18) (8,9) (8,15) (9,10) (9,19) (9,17) (9,13) (9,16) (9,18) (9,15) (10,19) (10,17) (10,13) (10,16) (10,18) (10,15) (11,12) (13,19) (13,17) (13,16) (13,18) (13,15) (15,19) (15,17) (15,16) (15,18) (16,19) (16,17) (16,18) (17,19) (17,18) (18,19)\nIs there a path between node 12 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph12-5_4", + "image": "data/connectivity/graph_visual/medium/graph12.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,3) (0,10) (0,7) (0,2) (0,9) (0,1) (0,8) (0,5) (1,3) (1,10) (1,7) (1,2) (1,9) (1,8) (1,5) (2,3) (2,10) (2,7) (2,9) (2,8) (2,5) (3,10) (3,7) (3,9) (3,8) (3,5) (4,6) (5,10) (5,7) (5,9) (5,8) (7,10) (7,9) (7,8) (8,10) (8,9) (9,10)\nIs there a path between node 5 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph3-6_8", + "image": "data/connectivity/graph_visual/medium/graph3.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nIs there a path between node 6 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph830-18_1", + "image": "data/connectivity/graph_visual/medium/graph830.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,18) (1,15) (1,5) (1,23) (1,10) (1,2) (1,20) (1,6) (1,22) (1,13) (1,21) (2,18) (2,14) (2,24) (2,15) (2,5) (2,23) (2,10) (2,20) (2,22) (2,13) (3,19) (4,17) (4,12) (4,7) (5,14) (5,23) (5,10) (5,22) (5,21) (6,18) (6,14) (6,24) (6,15) (6,10) (6,20) (6,22) (6,13) (6,21) (7,16) (7,11) (7,17) (7,12) (7,9) (9,11) (9,17) (9,12) (10,24) (10,23) (10,20) (10,22) (10,13) (10,21) (11,16) (11,17) (11,12) (12,16) (12,17) (13,18) (13,14) (13,24) (13,15) (13,23) (13,20) (13,22) (13,21) (14,18) (14,24) (14,15) (14,23) (14,20) (14,21) (15,23) (15,22) (15,21) (16,17) (18,24) (18,23) (18,22) (18,21) (20,24) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (23,24)\nIs there a path between node 18 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph486-11_22", + "image": "data/connectivity/graph_visual/medium/graph486.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,19) (0,1) (0,11) (0,21) (0,13) (1,11) (1,6) (1,21) (1,22) (2,14) (2,7) (2,8) (2,10) (2,9) (2,4) (3,18) (3,17) (3,20) (3,15) (4,14) (4,16) (4,7) (4,8) (4,9) (4,5) (5,14) (5,8) (5,10) (5,9) (6,19) (6,12) (6,11) (6,21) (6,13) (7,14) (7,16) (7,8) (7,10) (8,14) (8,16) (8,10) (9,10) (10,14) (10,16) (11,12) (11,21) (12,19) (12,21) (12,22) (12,13) (13,21) (13,22) (14,16) (15,18) (15,17) (17,18) (17,20) (19,21) (19,22) (21,22)\nIs there a path between node 11 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph148-10_1", + "image": "data/connectivity/graph_visual/medium/graph148.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,17) (0,10) (0,1) (0,14) (0,13) (0,4) (0,6) (0,8) (0,11) (0,15) (0,2) (0,12) (1,14) (1,13) (1,4) (1,8) (1,15) (1,2) (1,3) (1,12) (2,17) (2,14) (2,4) (2,6) (2,8) (2,11) (2,15) (2,3) (2,12) (3,10) (3,14) (3,13) (3,4) (3,6) (3,8) (3,11) (4,10) (4,14) (4,13) (4,6) (4,8) (4,15) (5,16) (5,9) (6,14) (6,13) (6,15) (6,12) (8,17) (8,10) (8,13) (8,12) (10,17) (10,13) (10,11) (10,15) (10,12) (11,17) (11,13) (11,15) (11,12) (12,17) (12,14) (12,13) (12,15) (13,17) (13,14) (14,17) (14,15) (15,17)\nIs there a path between node 10 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph76-0_2", + "image": "data/connectivity/graph_visual/medium/graph76.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,6) (0,12) (0,8) (1,4) (1,6) (1,12) (1,8) (1,7) (2,4) (2,5) (2,13) (2,10) (4,5) (4,9) (4,8) (4,10) (5,12) (5,10) (5,14) (6,11) (7,9) (7,12) (8,11) (8,13) (8,14) (9,10) (11,12) (11,14) (13,14)\nIs there a path between node 0 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph762-2_12", + "image": "data/connectivity/graph_visual/medium/graph762.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,24) (0,4) (0,17) (0,22) (0,7) (0,23) (0,9) (0,8) (0,3) (0,1) (0,10) (0,19) (0,6) (1,12) (1,24) (1,4) (1,17) (1,5) (1,22) (1,16) (1,23) (1,9) (1,14) (1,3) (1,13) (1,21) (1,10) (1,19) (1,6) (2,15) (2,18) (2,11) (3,12) (3,24) (3,4) (3,17) (3,22) (3,7) (3,16) (3,20) (3,13) (3,21) (4,12) (4,24) (4,5) (4,16) (4,20) (4,23) (4,13) (4,21) (4,10) (4,19) (4,6) (5,12) (5,24) (5,17) (5,22) (5,16) (5,20) (5,23) (5,9) (5,8) (5,13) (5,10) (5,6) (6,12) (6,24) (6,17) (6,22) (6,7) (6,20) (6,23) (6,8) (6,14) (6,13) (6,21) (7,12) (7,24) (7,17) (7,16) (7,23) (7,14) (7,13) (7,21) (7,10) (7,19) (8,12) (8,24) (8,17) (8,22) (8,16) (8,20) (8,23) (8,14) (8,13) (8,21) (8,10) (9,12) (9,24) (9,17) (9,22) (9,20) (9,14) (9,13) (9,21) (9,10) (9,19) (10,17) (10,16) (10,23) (10,14) (10,13) (11,18) (12,17) (12,22) (12,16) (12,23) (12,13) (12,19) (13,24) (13,16) (13,20) (13,21) (13,19) (14,24) (14,17) (14,22) (14,16) (14,21) (16,24) (16,20) (16,23) (16,19) (17,24) (17,22) (17,20) (17,23) (17,21) (17,19) (19,24) (19,22) (19,21) (20,24) (20,22) (20,23) (20,21) (21,24) (21,23) (22,24)\nIs there a path between node 2 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph492-5_11", + "image": "data/connectivity/graph_visual/medium/graph492.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,6) (0,17) (0,18) (0,8) (0,10) (0,12) (0,14) (0,16) (0,13) (0,9) (0,19) (0,15) (0,4) (0,20) (0,7) (0,5) (0,21) (0,3) (0,2) (1,6) (1,17) (1,18) (1,8) (1,10) (1,12) (1,14) (1,16) (1,13) (1,9) (1,19) (1,15) (1,4) (1,20) (1,7) (1,5) (1,21) (1,3) (1,2) (2,6) (2,17) (2,18) (2,8) (2,10) (2,12) (2,14) (2,16) (2,13) (2,9) (2,19) (2,15) (2,4) (2,20) (2,7) (2,5) (2,21) (2,3) (3,6) (3,17) (3,18) (3,8) (3,10) (3,12) (3,14) (3,16) (3,13) (3,9) (3,19) (3,15) (3,4) (3,20) (3,7) (3,5) (3,21) (4,6) (4,17) (4,18) (4,8) (4,10) (4,12) (4,14) (4,16) (4,13) (4,9) (4,19) (4,15) (4,20) (4,7) (4,5) (4,21) (5,6) (5,17) (5,18) (5,8) (5,10) (5,12) (5,14) (5,16) (5,13) (5,9) (5,19) (5,15) (5,20) (5,7) (5,21) (6,17) (6,18) (6,8) (6,10) (6,12) (6,14) (6,16) (6,13) (6,9) (6,19) (6,15) (6,20) (6,7) (6,21) (7,17) (7,18) (7,8) (7,10) (7,12) (7,14) (7,16) (7,13) (7,9) (7,19) (7,15) (7,20) (7,21) (8,17) (8,18) (8,10) (8,12) (8,14) (8,16) (8,13) (8,9) (8,19) (8,15) (8,20) (8,21) (9,17) (9,18) (9,10) (9,12) (9,14) (9,16) (9,13) (9,19) (9,15) (9,20) (9,21) (10,17) (10,18) (10,12) (10,14) (10,16) (10,13) (10,19) (10,15) (10,20) (10,21) (11,22) (12,17) (12,18) (12,14) (12,16) (12,13) (12,19) (12,15) (12,20) (12,21) (13,17) (13,18) (13,14) (13,16) (13,19) (13,15) (13,20) (13,21) (14,17) (14,18) (14,16) (14,19) (14,15) (14,20) (14,21) (15,17) (15,18) (15,16) (15,19) (15,20) (15,21) (16,17) (16,18) (16,19) (16,20) (16,21) (17,18) (17,19) (17,20) (17,21) (18,19) (18,20) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 5 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph836-11_7", + "image": "data/connectivity/graph_visual/medium/graph836.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,3) (0,8) (0,11) (0,22) (0,24) (0,1) (0,17) (0,14) (0,19) (0,2) (0,20) (1,6) (1,3) (1,8) (1,11) (1,22) (1,24) (1,17) (1,14) (1,19) (1,2) (1,20) (2,6) (2,3) (2,8) (2,11) (2,22) (2,24) (2,17) (2,14) (2,19) (2,20) (3,6) (3,8) (3,11) (3,22) (3,24) (3,17) (3,14) (3,19) (3,20) (4,18) (4,23) (4,15) (4,9) (5,21) (5,13) (5,7) (5,10) (5,16) (5,12) (6,8) (6,11) (6,22) (6,24) (6,17) (6,14) (6,19) (6,20) (7,21) (7,13) (7,10) (7,16) (7,12) (8,11) (8,22) (8,24) (8,17) (8,14) (8,19) (8,20) (9,18) (9,23) (9,15) (10,21) (10,13) (10,16) (10,12) (11,22) (11,24) (11,17) (11,14) (11,19) (11,20) (12,21) (12,13) (12,16) (13,21) (13,16) (14,22) (14,24) (14,17) (14,19) (14,20) (15,18) (15,23) (16,21) (17,22) (17,24) (17,19) (17,20) (18,23) (19,22) (19,24) (19,20) (20,22) (20,24) (22,24)\nIs there a path between node 11 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph833-5_22", + "image": "data/connectivity/graph_visual/medium/graph833.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,22) (0,18) (0,8) (0,21) (0,5) (0,11) (0,1) (0,24) (0,19) (0,9) (0,15) (0,14) (0,10) (0,4) (0,23) (0,6) (0,17) (0,13) (1,20) (1,22) (1,18) (1,8) (1,21) (1,5) (1,11) (1,24) (1,19) (1,9) (1,15) (1,14) (1,10) (1,4) (1,23) (1,6) (1,17) (1,13) (2,3) (2,7) (2,12) (2,16) (3,7) (3,12) (3,16) (4,20) (4,22) (4,18) (4,8) (4,21) (4,5) (4,11) (4,24) (4,19) (4,9) (4,15) (4,14) (4,10) (4,23) (4,6) (4,17) (4,13) (5,20) (5,22) (5,18) (5,8) (5,21) (5,11) (5,24) (5,19) (5,9) (5,15) (5,14) (5,10) (5,23) (5,6) (5,17) (5,13) (6,20) (6,22) (6,18) (6,8) (6,21) (6,11) (6,24) (6,19) (6,9) (6,15) (6,14) (6,10) (6,23) (6,17) (6,13) (7,12) (7,16) (8,20) (8,22) (8,18) (8,21) (8,11) (8,24) (8,19) (8,9) (8,15) (8,14) (8,10) (8,23) (8,17) (8,13) (9,20) (9,22) (9,18) (9,21) (9,11) (9,24) (9,19) (9,15) (9,14) (9,10) (9,23) (9,17) (9,13) (10,20) (10,22) (10,18) (10,21) (10,11) (10,24) (10,19) (10,15) (10,14) (10,23) (10,17) (10,13) (11,20) (11,22) (11,18) (11,21) (11,24) (11,19) (11,15) (11,14) (11,23) (11,17) (11,13) (12,16) (13,20) (13,22) (13,18) (13,21) (13,24) (13,19) (13,15) (13,14) (13,23) (13,17) (14,20) (14,22) (14,18) (14,21) (14,24) (14,19) (14,15) (14,23) (14,17) (15,20) (15,22) (15,18) (15,21) (15,24) (15,19) (15,23) (15,17) (17,20) (17,22) (17,18) (17,21) (17,24) (17,19) (17,23) (18,20) (18,22) (18,21) (18,24) (18,19) (18,23) (19,20) (19,22) (19,21) (19,24) (19,23) (20,22) (20,21) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 5 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph364-8_11", + "image": "data/connectivity/graph_visual/medium/graph364.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,2) (1,11) (1,7) (2,11) (2,15) (2,12) (2,3) (3,9) (3,7) (4,19) (4,7) (6,16) (6,13) (6,18) (8,17) (8,15) (8,12) (9,17) (9,19) (9,11) (10,19) (10,11) (11,20) (15,19) (17,20)\nIs there a path between node 8 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph289-4_18", + "image": "data/connectivity/graph_visual/medium/graph289.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (0,13) (0,17) (0,4) (1,14) (2,8) (3,15) (4,11) (4,18) (4,17) (5,19) (7,13) (7,12) (7,10) (8,16) (8,14) (9,12) (9,10) (10,18) (11,18) (11,12) (12,13) (13,18) (13,17) (14,16) (17,18)\nIs there a path between node 4 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph97-10_13", + "image": "data/connectivity/graph_visual/medium/graph97.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (1,15) (1,10) (2,15) (3,14) (3,7) (3,4) (4,7) (4,5) (5,14) (5,7) (5,11) (5,8) (6,12) (6,7) (7,12) (8,12) (8,11) (10,15)\nIs there a path between node 10 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph656-7_8", + "image": "data/connectivity/graph_visual/medium/graph656.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,19) (0,4) (0,17) (0,16) (0,22) (0,20) (0,18) (0,10) (0,21) (0,7) (0,8) (0,9) (0,15) (0,14) (1,3) (1,13) (1,6) (1,4) (1,16) (1,22) (1,20) (1,10) (1,21) (1,5) (1,7) (1,9) (1,15) (1,14) (2,11) (3,13) (3,6) (3,19) (3,4) (3,17) (3,16) (3,22) (3,20) (3,18) (3,10) (3,5) (3,7) (3,23) (3,8) (3,14) (4,13) (4,19) (4,17) (4,20) (4,18) (4,10) (4,5) (4,7) (4,23) (4,8) (4,15) (4,14) (5,13) (5,6) (5,19) (5,17) (5,16) (5,22) (5,20) (5,10) (5,23) (5,9) (5,14) (6,13) (6,17) (6,22) (6,18) (6,10) (6,21) (6,7) (6,23) (6,15) (6,14) (7,13) (7,19) (7,17) (7,16) (7,22) (7,20) (7,18) (7,10) (7,21) (7,9) (7,14) (8,19) (8,20) (8,18) (8,10) (8,21) (8,9) (8,15) (9,13) (9,19) (9,17) (9,16) (9,22) (9,21) (9,14) (10,13) (10,17) (10,22) (10,20) (10,18) (10,23) (10,15) (10,14) (13,17) (13,16) (13,22) (13,20) (13,18) (13,21) (13,23) (13,15) (13,14) (14,17) (14,16) (14,20) (14,18) (14,23) (15,19) (15,17) (15,16) (15,22) (15,20) (15,21) (15,23) (16,18) (16,21) (17,19) (17,22) (17,20) (17,23) (18,19) (18,22) (18,20) (18,21) (18,23) (19,22) (19,20) (19,21) (20,22) (21,22) (21,23) (22,23)\nIs there a path between node 7 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph493-19_0", + "image": "data/connectivity/graph_visual/medium/graph493.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,9) (0,19) (0,7) (0,2) (0,14) (0,12) (0,15) (0,22) (0,20) (1,16) (1,10) (1,3) (1,11) (1,4) (1,17) (1,5) (2,6) (2,9) (2,19) (2,7) (2,14) (2,12) (2,15) (2,22) (2,20) (3,16) (3,10) (3,11) (3,4) (3,17) (3,5) (4,16) (4,10) (4,11) (4,17) (4,5) (5,16) (5,10) (5,11) (5,17) (6,9) (6,19) (6,7) (6,14) (6,12) (6,15) (6,22) (6,20) (7,9) (7,19) (7,14) (7,12) (7,15) (7,22) (7,20) (8,13) (8,21) (8,18) (9,19) (9,14) (9,12) (9,15) (9,22) (9,20) (10,16) (10,11) (10,17) (11,16) (11,17) (12,19) (12,14) (12,15) (12,22) (12,20) (13,21) (13,18) (14,19) (14,15) (14,22) (14,20) (15,19) (15,22) (15,20) (16,17) (18,21) (19,22) (19,20) (20,22)\nIs there a path between node 19 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph10-10_7", + "image": "data/connectivity/graph_visual/medium/graph10.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,1) (0,7) (0,4) (0,9) (0,3) (1,7) (1,2) (1,4) (1,9) (1,3) (2,8) (2,9) (2,3) (3,8) (3,6) (3,4) (3,9) (4,8) (4,6) (5,10) (6,9) (8,9)\nIs there a path between node 10 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph23-3_6", + "image": "data/connectivity/graph_visual/medium/graph23.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (0,5) (0,7) (0,6) (0,2) (0,4) (0,8) (0,9) (1,10) (2,3) (2,5) (2,7) (2,6) (2,4) (2,8) (2,9) (2,11) (3,5) (3,4) (3,8) (3,11) (4,5) (4,6) (4,9) (4,11) (5,6) (5,8) (5,9) (6,7) (6,8) (6,9) (6,11) (7,8) (7,11) (8,9) (9,11)\nIs there a path between node 3 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph95-1_5", + "image": "data/connectivity/graph_visual/medium/graph95.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,6) (0,8) (0,15) (1,10) (2,5) (3,9) (3,10) (4,11) (5,6) (5,7) (5,11) (6,13) (6,11) (7,13) (8,12) (8,13) (11,12) (11,15) (12,15) (13,15)\nIs there a path between node 1 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph581-13_9", + "image": "data/connectivity/graph_visual/medium/graph581.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,11) (0,20) (1,22) (1,12) (1,16) (1,6) (1,18) (1,13) (1,17) (1,14) (1,15) (2,11) (2,20) (3,11) (3,7) (4,23) (4,16) (4,18) (4,13) (5,22) (5,23) (5,16) (5,18) (6,12) (6,23) (6,16) (7,20) (8,11) (8,20) (8,9) (9,10) (12,22) (12,21) (12,16) (12,18) (12,13) (12,14) (13,23) (13,16) (13,17) (13,14) (14,19) (14,15) (15,22) (15,19) (16,21) (16,18) (17,22) (17,21) (17,23) (17,19) (19,21) (21,22)\nIs there a path between node 13 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph423-11_19", + "image": "data/connectivity/graph_visual/medium/graph423.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,20) (0,15) (1,3) (1,20) (2,11) (3,12) (3,6) (3,16) (3,20) (5,14) (5,7) (6,20) (6,21) (7,13) (7,18) (8,14) (8,13) (9,12) (9,16) (9,21) (10,21) (11,17) (12,16) (14,18) (15,16) (15,21) (16,20) (20,21)\nIs there a path between node 11 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph714-10_16", + "image": "data/connectivity/graph_visual/medium/graph714.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,1) (2,23) (2,9) (2,17) (2,4) (2,19) (2,3) (2,24) (2,16) (2,22) (2,18) (2,20) (2,8) (3,23) (3,11) (3,9) (3,17) (3,19) (3,24) (3,21) (3,16) (3,22) (3,20) (3,13) (3,8) (4,11) (4,9) (4,17) (4,19) (4,21) (4,16) (4,8) (5,15) (5,12) (5,10) (8,11) (8,9) (8,17) (8,19) (8,24) (8,21) (8,16) (8,18) (8,20) (8,13) (9,11) (9,17) (9,24) (9,14) (9,21) (9,16) (9,22) (9,18) (10,15) (10,12) (11,23) (11,19) (11,14) (11,21) (11,16) (11,20) (11,13) (12,15) (13,23) (13,17) (13,24) (13,14) (13,21) (13,16) (13,18) (13,20) (14,17) (14,19) (14,21) (14,20) (16,23) (16,17) (16,19) (16,24) (16,21) (16,18) (16,20) (17,23) (17,18) (17,20) (18,19) (18,21) (18,22) (18,20) (19,23) (19,24) (19,21) (19,22) (19,20) (20,23) (20,24) (20,21) (20,22) (21,23) (21,24) (21,22) (22,23) (22,24)\nIs there a path between node 10 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph47-5_12", + "image": "data/connectivity/graph_visual/medium/graph47.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,12) (0,7) (0,10) (0,8) (0,9) (0,2) (0,4) (0,3) (1,5) (1,6) (1,11) (2,12) (2,7) (2,10) (2,8) (2,9) (2,4) (2,3) (3,12) (3,7) (3,10) (3,8) (3,9) (3,4) (4,12) (4,7) (4,10) (4,8) (4,9) (5,6) (5,11) (6,11) (7,12) (7,10) (7,8) (7,9) (8,12) (8,10) (8,9) (9,12) (9,10) (10,12)\nIs there a path between node 5 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph314-5_17", + "image": "data/connectivity/graph_visual/medium/graph314.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,2) (0,18) (0,4) (0,12) (0,1) (0,19) (0,14) (0,16) (0,13) (0,15) (0,11) (0,8) (1,2) (1,18) (1,4) (1,12) (1,19) (1,14) (1,16) (1,13) (1,15) (1,11) (1,8) (2,18) (2,4) (2,12) (2,19) (2,14) (2,16) (2,13) (2,15) (2,11) (2,8) (3,6) (3,9) (3,10) (3,17) (4,18) (4,12) (4,19) (4,14) (4,16) (4,13) (4,15) (4,11) (4,8) (5,7) (6,9) (6,10) (6,17) (8,18) (8,12) (8,19) (8,14) (8,16) (8,13) (8,15) (8,11) (9,10) (9,17) (10,17) (11,18) (11,12) (11,19) (11,14) (11,16) (11,13) (11,15) (12,18) (12,19) (12,14) (12,16) (12,13) (12,15) (13,18) (13,19) (13,14) (13,16) (13,15) (14,18) (14,19) (14,16) (14,15) (15,18) (15,19) (15,16) (16,18) (16,19) (18,19)\nIs there a path between node 5 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph669-22_19", + "image": "data/connectivity/graph_visual/medium/graph669.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,7) (0,2) (0,9) (0,1) (0,17) (0,14) (0,18) (0,4) (0,5) (0,16) (0,15) (0,10) (0,22) (1,12) (1,3) (1,7) (1,14) (1,18) (1,5) (1,15) (1,10) (1,22) (2,3) (2,7) (2,9) (2,17) (2,18) (2,5) (2,16) (2,15) (2,10) (2,22) (3,7) (3,21) (3,9) (3,17) (3,14) (3,18) (3,4) (3,5) (3,15) (3,22) (4,6) (4,12) (4,7) (4,21) (4,9) (4,23) (4,16) (4,15) (4,22) (5,6) (5,12) (5,7) (5,17) (5,23) (5,16) (5,15) (5,10) (6,12) (6,7) (6,21) (6,18) (6,15) (6,10) (6,22) (7,9) (7,14) (7,18) (7,23) (7,16) (7,10) (7,22) (8,19) (8,20) (8,13) (8,11) (9,21) (9,14) (9,23) (9,16) (9,15) (9,10) (9,22) (10,12) (10,21) (10,17) (10,14) (10,23) (10,16) (10,15) (10,22) (11,19) (11,20) (11,13) (12,21) (12,14) (12,23) (12,16) (12,22) (14,17) (14,18) (14,23) (14,15) (14,22) (15,21) (15,17) (15,18) (15,23) (15,16) (16,21) (16,18) (16,23) (17,21) (17,18) (17,23) (17,22) (18,23) (19,20) (21,23) (21,22) (22,23)\nIs there a path between node 22 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph633-7_3", + "image": "data/connectivity/graph_visual/medium/graph633.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,10) (1,9) (3,17) (3,8) (3,23) (4,17) (4,15) (4,22) (4,8) (4,23) (4,16) (6,11) (6,10) (7,21) (8,17) (8,23) (8,16) (10,18) (10,19) (11,18) (11,14) (15,23) (16,17) (16,23) (19,20) (21,22) (21,23)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph548-17_21", + "image": "data/connectivity/graph_visual/medium/graph548.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,9) (0,17) (0,7) (1,18) (1,3) (1,23) (1,19) (2,21) (2,14) (2,9) (2,16) (2,11) (2,5) (3,23) (3,6) (4,9) (4,11) (4,8) (4,20) (5,21) (5,8) (5,13) (6,10) (7,21) (7,17) (7,22) (8,14) (9,11) (9,13) (9,20) (9,22) (10,23) (11,16) (11,12) (12,21) (12,14) (13,21) (13,17) (14,16) (16,20) (19,23)\nIs there a path between node 17 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph247-17_12", + "image": "data/connectivity/graph_visual/medium/graph247.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (0,13) (0,5) (0,7) (0,16) (0,12) (0,18) (0,9) (0,8) (0,2) (0,11) (0,10) (0,6) (1,15) (1,14) (1,3) (2,4) (2,13) (2,5) (2,7) (2,16) (2,12) (2,18) (2,9) (2,8) (2,11) (2,10) (2,6) (3,15) (3,14) (4,13) (4,5) (4,7) (4,16) (4,12) (4,18) (4,9) (4,8) (4,11) (4,10) (4,6) (5,13) (5,7) (5,16) (5,12) (5,18) (5,9) (5,8) (5,11) (5,10) (5,6) (6,13) (6,7) (6,16) (6,12) (6,18) (6,9) (6,8) (6,11) (6,10) (7,13) (7,16) (7,12) (7,18) (7,9) (7,8) (7,11) (7,10) (8,13) (8,16) (8,12) (8,18) (8,9) (8,11) (8,10) (9,13) (9,16) (9,12) (9,18) (9,11) (9,10) (10,13) (10,16) (10,12) (10,18) (10,11) (11,13) (11,16) (11,12) (11,18) (12,13) (12,16) (12,18) (13,16) (13,18) (14,15) (16,18)\nIs there a path between node 17 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph580-8_21", + "image": "data/connectivity/graph_visual/medium/graph580.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,1) (0,16) (0,3) (2,16) (3,8) (3,11) (3,23) (4,13) (5,22) (5,20) (5,10) (5,13) (6,11) (6,21) (6,23) (7,8) (7,16) (7,19) (8,15) (8,14) (8,21) (9,12) (9,18) (10,12) (11,14) (12,22) (13,18) (14,19) (14,21) (16,23)\nIs there a path between node 8 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph712-22_20", + "image": "data/connectivity/graph_visual/medium/graph712.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (0,15) (0,1) (0,11) (0,7) (0,17) (0,12) (0,4) (0,3) (0,5) (0,19) (0,9) (0,6) (0,22) (1,18) (1,15) (1,10) (1,2) (1,7) (1,8) (1,17) (1,12) (1,3) (1,5) (1,6) (1,22) (1,21) (2,18) (2,15) (2,24) (2,8) (2,17) (2,12) (2,4) (2,3) (2,19) (2,9) (2,22) (2,21) (3,24) (3,10) (3,11) (3,7) (3,12) (3,5) (3,9) (3,6) (3,22) (3,20) (3,21) (4,15) (4,10) (4,11) (4,7) (4,8) (4,17) (4,12) (4,5) (4,19) (4,9) (4,22) (5,15) (5,24) (5,7) (5,17) (5,19) (5,6) (5,20) (6,18) (6,15) (6,10) (6,7) (6,8) (6,17) (6,12) (6,19) (6,9) (6,22) (6,21) (7,15) (7,10) (7,11) (7,8) (7,12) (7,19) (7,22) (7,20) (7,21) (8,18) (8,15) (8,24) (8,11) (8,17) (8,9) (8,22) (8,20) (8,21) (9,18) (9,24) (9,11) (9,19) (9,20) (9,21) (10,24) (10,11) (10,17) (10,19) (10,22) (10,21) (11,18) (11,15) (11,24) (11,17) (11,12) (11,19) (11,22) (11,20) (11,21) (12,18) (12,24) (12,17) (12,19) (12,22) (12,20) (13,16) (14,16) (15,17) (15,19) (15,20) (16,23) (17,18) (17,19) (17,22) (17,21) (18,22) (18,20) (18,21) (19,24) (19,20) (19,21) (20,24) (20,21) (22,24)\nIs there a path between node 22 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph203-4_8", + "image": "data/connectivity/graph_visual/medium/graph203.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,3) (0,6) (0,2) (0,9) (0,4) (1,14) (1,3) (1,9) (1,7) (1,18) (2,3) (2,10) (2,8) (2,17) (2,16) (3,12) (3,6) (3,9) (3,7) (4,10) (4,6) (4,9) (4,7) (6,8) (7,14) (7,12) (8,16) (9,17) (9,16) (10,17) (10,16) (10,18) (12,13) (12,17) (14,18) (16,17)\nIs there a path between node 4 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph659-13_23", + "image": "data/connectivity/graph_visual/medium/graph659.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,21) (0,14) (0,23) (0,11) (0,19) (0,17) (0,22) (0,8) (0,9) (0,16) (0,10) (0,4) (1,3) (1,14) (1,11) (1,17) (1,7) (1,16) (2,15) (2,13) (2,5) (3,21) (3,14) (3,11) (3,20) (3,19) (3,17) (3,22) (3,9) (3,16) (3,10) (4,6) (4,21) (4,14) (4,23) (4,20) (4,17) (4,22) (4,7) (4,8) (4,9) (4,10) (5,15) (5,12) (6,21) (6,14) (6,23) (6,11) (6,20) (6,18) (6,19) (6,17) (6,7) (6,9) (6,16) (6,10) (7,21) (7,23) (7,11) (7,20) (7,19) (7,17) (7,22) (7,8) (7,16) (8,14) (8,23) (8,20) (8,18) (8,17) (8,22) (8,9) (8,10) (9,21) (9,14) (9,23) (9,11) (9,18) (9,19) (9,17) (9,22) (9,16) (9,10) (10,21) (10,14) (10,23) (10,11) (10,20) (10,18) (10,19) (10,16) (11,23) (11,20) (11,19) (11,17) (11,16) (12,15) (12,13) (13,15) (14,21) (14,23) (14,20) (14,18) (14,19) (14,17) (16,21) (16,23) (16,20) (16,18) (16,17) (17,21) (17,23) (17,20) (17,18) (18,21) (18,23) (18,19) (18,22) (19,21) (19,23) (19,20) (19,22) (20,21) (20,23) (20,22) (21,23) (22,23)\nIs there a path between node 13 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph337-6_0", + "image": "data/connectivity/graph_visual/medium/graph337.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,11) (0,3) (0,17) (1,13) (1,14) (2,13) (2,14) (2,20) (2,6) (3,5) (3,11) (3,18) (4,10) (4,12) (4,7) (5,19) (5,18) (5,17) (6,14) (6,20) (7,8) (7,12) (8,10) (8,9) (8,12) (8,15) (9,10) (10,12) (10,15) (11,16) (11,18) (12,15) (14,20) (16,19) (16,18) (17,19) (17,18) (18,19)\nIs there a path between node 6 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph788-18_14", + "image": "data/connectivity/graph_visual/medium/graph788.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,2) (0,20) (0,18) (0,19) (0,7) (0,1) (0,9) (0,24) (1,15) (1,10) (1,2) (1,5) (1,7) (1,12) (1,3) (1,9) (1,22) (1,17) (1,11) (2,6) (2,18) (2,16) (2,3) (2,11) (3,15) (3,20) (3,18) (3,5) (3,22) (3,11) (5,18) (5,9) (5,11) (6,15) (6,23) (6,18) (6,8) (6,12) (6,22) (7,10) (7,20) (7,18) (7,16) (7,9) (8,15) (8,20) (8,24) (9,15) (9,17) (9,11) (10,23) (10,18) (10,13) (10,24) (10,11) (11,23) (11,13) (11,12) (11,17) (12,15) (12,23) (12,19) (12,16) (12,17) (13,23) (13,17) (14,21) (15,23) (15,20) (15,19) (15,22) (16,24) (18,23) (18,20) (19,23) (19,20) (20,22) (20,24)\nIs there a path between node 18 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph537-2_14", + "image": "data/connectivity/graph_visual/medium/graph537.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (0,16) (1,12) (1,10) (1,7) (1,6) (1,22) (1,13) (1,9) (1,2) (1,19) (1,14) (1,11) (1,21) (1,15) (1,5) (1,20) (1,4) (1,8) (1,17) (1,3) (2,12) (2,10) (2,7) (2,6) (2,22) (2,13) (2,9) (2,19) (2,14) (2,11) (2,21) (2,15) (2,5) (2,20) (2,4) (2,8) (2,17) (2,3) (3,12) (3,10) (3,7) (3,6) (3,22) (3,13) (3,9) (3,19) (3,14) (3,11) (3,21) (3,15) (3,5) (3,20) (3,4) (3,8) (3,17) (4,12) (4,10) (4,7) (4,6) (4,22) (4,13) (4,9) (4,19) (4,14) (4,11) (4,21) (4,15) (4,5) (4,20) (4,8) (4,17) (5,12) (5,10) (5,7) (5,6) (5,22) (5,13) (5,9) (5,19) (5,14) (5,11) (5,21) (5,15) (5,20) (5,8) (5,17) (6,12) (6,10) (6,7) (6,22) (6,13) (6,9) (6,19) (6,14) (6,11) (6,21) (6,15) (6,20) (6,8) (6,17) (7,12) (7,10) (7,22) (7,13) (7,9) (7,19) (7,14) (7,11) (7,21) (7,15) (7,20) (7,8) (7,17) (8,12) (8,10) (8,22) (8,13) (8,9) (8,19) (8,14) (8,11) (8,21) (8,15) (8,20) (8,17) (9,12) (9,10) (9,22) (9,13) (9,19) (9,14) (9,11) (9,21) (9,15) (9,20) (9,17) (10,12) (10,22) (10,13) (10,19) (10,14) (10,11) (10,21) (10,15) (10,20) (10,17) (11,12) (11,22) (11,13) (11,19) (11,14) (11,21) (11,15) (11,20) (11,17) (12,22) (12,13) (12,19) (12,14) (12,21) (12,15) (12,20) (12,17) (13,22) (13,19) (13,14) (13,21) (13,15) (13,20) (13,17) (14,22) (14,19) (14,21) (14,15) (14,20) (14,17) (15,22) (15,19) (15,21) (15,20) (15,17) (16,18) (17,22) (17,19) (17,21) (17,20) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 2 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph209-2_13", + "image": "data/connectivity/graph_visual/medium/graph209.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,7) (0,6) (0,13) (0,12) (0,9) (0,18) (0,15) (0,17) (1,16) (1,2) (1,3) (2,3) (4,11) (4,8) (4,7) (4,9) (4,18) (4,14) (4,15) (5,8) (5,12) (5,10) (5,15) (6,11) (6,8) (6,7) (6,12) (6,18) (6,10) (6,14) (6,15) (6,17) (7,11) (7,8) (7,13) (7,12) (7,9) (7,10) (7,14) (7,15) (8,13) (8,12) (8,9) (8,18) (8,14) (8,17) (9,11) (9,12) (9,18) (9,10) (9,14) (9,15) (9,17) (10,11) (10,13) (10,18) (10,14) (10,17) (11,13) (11,18) (11,14) (12,18) (12,15) (12,17) (13,18) (13,14) (13,15) (14,18) (14,15) (14,17) (15,18) (15,17) (17,18)\nIs there a path between node 2 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph130-5_0", + "image": "data/connectivity/graph_visual/medium/graph130.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,10) (0,1) (0,5) (0,15) (0,6) (0,4) (0,7) (0,16) (0,13) (0,8) (0,2) (0,12) (0,14) (1,10) (1,5) (1,15) (1,6) (1,4) (1,7) (1,16) (1,13) (1,8) (1,2) (1,12) (1,14) (2,10) (2,5) (2,15) (2,6) (2,4) (2,7) (2,16) (2,13) (2,8) (2,12) (2,14) (3,11) (3,9) (4,10) (4,5) (4,15) (4,6) (4,7) (4,16) (4,13) (4,8) (4,12) (4,14) (5,10) (5,15) (5,6) (5,7) (5,16) (5,13) (5,8) (5,12) (5,14) (6,10) (6,15) (6,7) (6,16) (6,13) (6,8) (6,12) (6,14) (7,10) (7,15) (7,16) (7,13) (7,8) (7,12) (7,14) (8,10) (8,15) (8,16) (8,13) (8,12) (8,14) (9,11) (10,15) (10,16) (10,13) (10,12) (10,14) (12,15) (12,16) (12,13) (12,14) (13,15) (13,16) (13,14) (14,15) (14,16) (15,16)\nIs there a path between node 5 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph594-16_4", + "image": "data/connectivity/graph_visual/medium/graph594.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,13) (0,4) (0,19) (0,9) (0,18) (0,17) (0,21) (0,10) (0,16) (0,2) (0,1) (0,23) (0,14) (0,7) (1,11) (1,13) (1,4) (1,9) (1,6) (1,17) (1,21) (1,10) (1,23) (1,14) (1,7) (2,11) (2,13) (2,19) (2,18) (2,17) (2,21) (2,10) (2,16) (2,23) (2,14) (3,8) (3,12) (3,5) (3,20) (3,22) (4,13) (4,19) (4,9) (4,18) (4,17) (4,21) (4,10) (4,14) (4,7) (5,8) (5,15) (5,20) (5,22) (6,13) (6,19) (6,18) (6,21) (6,10) (6,7) (7,13) (7,9) (7,18) (7,17) (7,10) (7,14) (8,15) (8,12) (8,22) (9,11) (9,19) (9,18) (9,17) (9,21) (9,10) (9,16) (9,23) (9,14) (10,11) (10,13) (10,19) (10,18) (10,17) (10,16) (10,23) (10,14) (11,13) (11,19) (11,17) (11,21) (11,16) (11,23) (11,14) (12,20) (12,22) (13,19) (13,18) (13,17) (13,16) (13,23) (13,14) (14,19) (14,18) (14,17) (14,16) (14,23) (15,22) (16,19) (16,17) (16,21) (16,23) (17,18) (18,23) (19,23) (20,22)\nIs there a path between node 16 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph615-23_1", + "image": "data/connectivity/graph_visual/medium/graph615.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,16) (0,3) (0,11) (0,19) (0,14) (0,7) (1,20) (1,2) (1,10) (1,21) (1,15) (1,23) (1,13) (1,18) (2,20) (2,10) (2,21) (2,15) (2,23) (2,13) (2,18) (3,22) (3,16) (3,11) (3,19) (3,14) (3,7) (4,17) (5,9) (5,6) (5,8) (5,12) (6,9) (6,8) (6,12) (7,22) (7,16) (7,11) (7,19) (7,14) (8,9) (8,12) (9,12) (10,20) (10,21) (10,15) (10,23) (10,13) (10,18) (11,22) (11,16) (11,19) (11,14) (13,20) (13,21) (13,15) (13,23) (13,18) (14,22) (14,16) (14,19) (15,20) (15,21) (15,23) (15,18) (16,22) (16,19) (18,20) (18,21) (18,23) (19,22) (20,21) (20,23) (21,23)\nIs there a path between node 23 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph778-19_20", + "image": "data/connectivity/graph_visual/medium/graph778.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,13) (0,16) (0,19) (0,12) (0,15) (0,22) (0,5) (0,4) (0,6) (0,11) (1,18) (1,14) (2,3) (2,8) (2,17) (2,24) (2,23) (2,21) (2,10) (2,20) (3,8) (3,17) (3,24) (3,23) (3,21) (3,10) (3,20) (4,9) (4,13) (4,16) (4,19) (4,12) (4,15) (4,22) (4,5) (4,6) (4,11) (5,9) (5,13) (5,16) (5,19) (5,12) (5,15) (5,22) (5,6) (5,11) (6,9) (6,13) (6,16) (6,19) (6,12) (6,15) (6,22) (6,11) (8,17) (8,24) (8,23) (8,21) (8,10) (8,20) (9,13) (9,16) (9,19) (9,12) (9,15) (9,22) (9,11) (10,17) (10,24) (10,23) (10,21) (10,20) (11,13) (11,16) (11,19) (11,12) (11,15) (11,22) (12,13) (12,16) (12,19) (12,15) (12,22) (13,16) (13,19) (13,15) (13,22) (14,18) (15,16) (15,19) (15,22) (16,19) (16,22) (17,24) (17,23) (17,21) (17,20) (19,22) (20,24) (20,23) (20,21) (21,24) (21,23) (23,24)\nIs there a path between node 19 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph106-9_14", + "image": "data/connectivity/graph_visual/medium/graph106.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,11) (1,7) (1,15) (1,2) (1,9) (1,14) (1,3) (1,12) (1,8) (1,13) (1,4) (1,5) (1,6) (1,10) (2,7) (2,15) (2,9) (2,14) (2,3) (2,12) (2,8) (2,13) (2,4) (2,5) (2,6) (2,10) (3,7) (3,15) (3,9) (3,14) (3,12) (3,8) (3,13) (3,4) (3,5) (3,6) (3,10) (4,7) (4,15) (4,9) (4,14) (4,12) (4,8) (4,13) (4,5) (4,6) (4,10) (5,7) (5,15) (5,9) (5,14) (5,12) (5,8) (5,13) (5,6) (5,10) (6,7) (6,15) (6,9) (6,14) (6,12) (6,8) (6,13) (6,10) (7,15) (7,9) (7,14) (7,12) (7,8) (7,13) (7,10) (8,15) (8,9) (8,14) (8,12) (8,13) (8,10) (9,15) (9,14) (9,12) (9,13) (9,10) (10,15) (10,14) (10,12) (10,13) (12,15) (12,14) (12,13) (13,15) (13,14) (14,15)\nIs there a path between node 9 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph479-7_14", + "image": "data/connectivity/graph_visual/medium/graph479.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,4) (0,10) (0,12) (0,20) (0,14) (0,8) (0,3) (0,6) (0,5) (0,15) (0,19) (0,7) (0,9) (0,22) (0,2) (0,21) (0,18) (1,4) (1,10) (1,12) (1,20) (1,8) (1,5) (1,15) (1,16) (1,19) (1,7) (1,9) (1,22) (1,2) (1,18) (2,4) (2,10) (2,12) (2,14) (2,3) (2,5) (2,15) (2,19) (2,7) (2,22) (2,21) (2,18) (3,4) (3,12) (3,20) (3,14) (3,6) (3,5) (3,15) (3,16) (3,19) (3,7) (3,9) (3,22) (3,21) (3,18) (4,10) (4,12) (4,8) (4,6) (4,5) (4,15) (4,16) (4,19) (4,7) (4,9) (4,21) (4,18) (5,12) (5,14) (5,8) (5,6) (5,15) (5,16) (5,19) (5,7) (5,9) (5,22) (5,18) (6,10) (6,12) (6,20) (6,14) (6,16) (6,19) (6,7) (6,9) (6,22) (6,21) (6,18) (7,10) (7,12) (7,14) (7,8) (7,16) (7,9) (7,22) (7,21) (7,18) (8,10) (8,12) (8,14) (8,15) (8,16) (8,19) (8,9) (8,21) (9,12) (9,20) (9,15) (9,16) (9,22) (9,21) (9,18) (10,12) (10,20) (10,14) (10,15) (10,16) (10,18) (12,16) (12,19) (13,17) (14,20) (14,16) (15,16) (15,22) (15,21) (16,20) (16,21) (16,18) (18,22) (18,21) (19,20) (19,22) (19,21) (21,22)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph457-13_6", + "image": "data/connectivity/graph_visual/medium/graph457.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,5) (0,4) (0,12) (0,8) (0,14) (1,16) (1,9) (1,11) (1,2) (1,10) (1,21) (1,7) (1,6) (1,15) (1,13) (1,19) (1,3) (1,17) (1,20) (2,16) (2,9) (2,11) (2,10) (2,21) (2,7) (2,6) (2,15) (2,13) (2,19) (2,3) (2,17) (2,20) (3,16) (3,9) (3,11) (3,10) (3,21) (3,7) (3,6) (3,15) (3,13) (3,19) (3,17) (3,20) (4,18) (4,5) (4,12) (4,8) (4,14) (5,18) (5,12) (5,8) (5,14) (6,16) (6,9) (6,11) (6,10) (6,21) (6,7) (6,15) (6,13) (6,19) (6,17) (6,20) (7,16) (7,9) (7,11) (7,10) (7,21) (7,15) (7,13) (7,19) (7,17) (7,20) (8,18) (8,12) (8,14) (9,16) (9,11) (9,10) (9,21) (9,15) (9,13) (9,19) (9,17) (9,20) (10,16) (10,11) (10,21) (10,15) (10,13) (10,19) (10,17) (10,20) (11,16) (11,21) (11,15) (11,13) (11,19) (11,17) (11,20) (12,18) (12,14) (13,16) (13,21) (13,15) (13,19) (13,17) (13,20) (14,18) (15,16) (15,21) (15,19) (15,17) (15,20) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (19,21) (19,20) (20,21)\nIs there a path between node 13 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph275-11_15", + "image": "data/connectivity/graph_visual/medium/graph275.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,7) (0,4) (0,9) (0,12) (0,11) (0,5) (1,6) (1,17) (1,8) (1,15) (1,3) (1,2) (1,18) (1,19) (1,13) (1,14) (1,10) (2,6) (2,17) (2,8) (2,15) (2,3) (2,18) (2,19) (2,13) (2,14) (2,10) (3,6) (3,17) (3,8) (3,15) (3,18) (3,19) (3,13) (3,14) (3,10) (4,7) (4,9) (4,12) (4,11) (4,5) (5,7) (5,9) (5,12) (5,11) (6,17) (6,8) (6,15) (6,18) (6,19) (6,13) (6,14) (6,10) (7,9) (7,12) (7,11) (8,17) (8,15) (8,18) (8,19) (8,13) (8,14) (8,10) (9,12) (9,11) (10,17) (10,15) (10,18) (10,19) (10,13) (10,14) (11,12) (13,17) (13,15) (13,18) (13,19) (13,14) (14,17) (14,15) (14,18) (14,19) (15,17) (15,18) (15,19) (17,18) (17,19) (18,19)\nIs there a path between node 11 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph802-6_16", + "image": "data/connectivity/graph_visual/medium/graph802.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,12) (1,6) (1,18) (4,24) (4,16) (4,15) (4,12) (5,23) (5,6) (6,23) (6,18) (7,9) (7,13) (7,11) (8,14) (9,14) (9,11) (11,17) (11,14) (12,24) (12,22) (12,18) (14,21) (16,22) (16,18) (19,20) (22,23) (23,24)\nIs there a path between node 6 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph836-5_21", + "image": "data/connectivity/graph_visual/medium/graph836.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,3) (0,8) (0,11) (0,22) (0,24) (0,1) (0,17) (0,14) (0,19) (0,2) (0,20) (1,6) (1,3) (1,8) (1,11) (1,22) (1,24) (1,17) (1,14) (1,19) (1,2) (1,20) (2,6) (2,3) (2,8) (2,11) (2,22) (2,24) (2,17) (2,14) (2,19) (2,20) (3,6) (3,8) (3,11) (3,22) (3,24) (3,17) (3,14) (3,19) (3,20) (4,18) (4,23) (4,15) (4,9) (5,21) (5,13) (5,7) (5,10) (5,16) (5,12) (6,8) (6,11) (6,22) (6,24) (6,17) (6,14) (6,19) (6,20) (7,21) (7,13) (7,10) (7,16) (7,12) (8,11) (8,22) (8,24) (8,17) (8,14) (8,19) (8,20) (9,18) (9,23) (9,15) (10,21) (10,13) (10,16) (10,12) (11,22) (11,24) (11,17) (11,14) (11,19) (11,20) (12,21) (12,13) (12,16) (13,21) (13,16) (14,22) (14,24) (14,17) (14,19) (14,20) (15,18) (15,23) (16,21) (17,22) (17,24) (17,19) (17,20) (18,23) (19,22) (19,24) (19,20) (20,22) (20,24) (22,24)\nIs there a path between node 5 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph140-15_10", + "image": "data/connectivity/graph_visual/medium/graph140.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,14) (1,9) (2,14) (2,6) (2,5) (3,16) (4,7) (4,9) (4,15) (5,9) (5,15) (6,14) (6,9) (6,12) (7,14) (7,15) (7,12) (8,17) (10,13) (12,14)\nIs there a path between node 15 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph713-17_22", + "image": "data/connectivity/graph_visual/medium/graph713.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (1,6) (1,4) (1,20) (1,18) (1,10) (1,14) (1,21) (1,24) (1,23) (1,15) (1,11) (2,17) (2,19) (2,22) (2,13) (2,9) (4,6) (4,12) (4,10) (4,14) (4,21) (4,23) (4,15) (4,11) (5,17) (5,8) (5,22) (5,13) (5,16) (5,9) (6,20) (6,18) (6,14) (6,21) (6,24) (6,23) (6,15) (8,19) (8,22) (8,13) (8,16) (8,9) (9,17) (9,19) (9,13) (9,16) (10,12) (10,20) (10,21) (10,24) (10,23) (11,12) (11,20) (11,18) (11,14) (11,21) (11,24) (11,23) (12,18) (12,14) (12,21) (12,24) (12,23) (12,15) (13,19) (13,22) (14,18) (14,21) (14,23) (15,20) (15,18) (15,24) (16,17) (16,19) (16,22) (18,20) (18,21) (20,24) (20,23) (21,24) (21,23)\nIs there a path between node 17 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph51-1_13", + "image": "data/connectivity/graph_visual/medium/graph51.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,6) (0,13) (1,6) (1,8) (1,3) (1,4) (2,5) (2,9) (3,12) (3,9) (3,13) (4,6) (4,10) (5,6) (5,9) (6,12) (6,8) (8,9) (9,10) (12,13)\nIs there a path between node 1 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph24-7_1", + "image": "data/connectivity/graph_visual/medium/graph24.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,1) (0,8) (0,9) (0,3) (1,11) (1,5) (1,4) (1,6) (1,3) (2,10) (3,11) (3,5) (3,8) (3,4) (4,11) (4,6) (4,9) (5,11) (5,8) (5,6) (5,9) (6,11) (7,10) (9,11)\nIs there a path between node 7 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph761-1_13", + "image": "data/connectivity/graph_visual/medium/graph761.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,16) (0,17) (0,9) (1,18) (1,8) (1,22) (1,21) (1,19) (1,6) (1,24) (1,13) (1,3) (1,7) (1,2) (1,15) (1,10) (1,11) (1,23) (2,8) (2,22) (2,21) (2,19) (2,6) (2,24) (2,13) (2,15) (2,14) (2,4) (2,12) (2,23) (3,18) (3,21) (3,24) (3,15) (3,10) (3,11) (3,14) (3,12) (3,23) (4,20) (4,8) (4,21) (4,6) (4,24) (4,13) (4,7) (4,15) (4,10) (4,11) (4,14) (4,12) (4,23) (5,16) (5,9) (6,20) (6,18) (6,8) (6,21) (6,19) (6,24) (6,13) (6,7) (6,15) (6,11) (6,14) (6,12) (6,23) (7,20) (7,18) (7,22) (7,21) (7,24) (7,13) (7,15) (7,11) (7,12) (7,23) (8,20) (8,18) (8,22) (8,21) (8,19) (8,24) (8,13) (8,15) (8,10) (8,11) (8,14) (8,23) (9,16) (9,17) (10,20) (10,18) (10,22) (10,21) (10,19) (10,13) (10,15) (10,14) (10,12) (11,20) (11,18) (11,22) (11,21) (11,19) (11,24) (11,13) (11,14) (11,12) (11,23) (12,18) (12,22) (12,21) (12,19) (12,24) (12,14) (12,23) (13,22) (13,21) (13,24) (13,15) (13,14) (13,23) (14,20) (14,18) (14,22) (14,21) (14,19) (14,23) (15,21) (16,17) (18,20) (18,21) (18,19) (18,23) (19,20) (19,24) (19,23) (20,21) (20,24) (20,23) (21,24) (21,23) (22,24) (22,23)\nIs there a path between node 1 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph583-21_17", + "image": "data/connectivity/graph_visual/medium/graph583.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,17) (0,10) (0,22) (1,23) (1,19) (1,5) (1,18) (2,20) (2,12) (2,5) (2,16) (3,19) (3,5) (3,7) (3,15) (3,18) (4,21) (4,17) (4,22) (5,23) (5,19) (5,12) (5,18) (6,21) (7,23) (7,16) (7,18) (7,14) (8,9) (8,10) (8,22) (9,11) (12,23) (12,16) (12,14) (13,23) (13,16) (13,18) (14,23) (14,19) (14,15) (15,23) (16,23) (17,22) (18,20) (19,20)\nIs there a path between node 21 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph91-15_4", + "image": "data/connectivity/graph_visual/medium/graph91.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,15) (1,14) (1,3) (1,9) (1,10) (1,4) (1,7) (1,6) (1,13) (1,12) (1,11) (2,15) (3,14) (3,8) (3,9) (3,10) (3,4) (3,12) (3,11) (4,8) (4,9) (4,10) (4,7) (4,5) (4,11) (5,9) (5,7) (5,13) (5,12) (5,11) (6,14) (6,8) (6,7) (6,13) (6,11) (7,8) (7,9) (7,10) (7,11) (8,14) (8,10) (8,12) (8,11) (9,14) (9,10) (9,13) (9,12) (10,14) (10,13) (10,12) (11,14) (11,13) (11,12) (12,14)\nIs there a path between node 15 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph378-2_4", + "image": "data/connectivity/graph_visual/medium/graph378.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (0,1) (0,19) (0,11) (0,17) (0,16) (0,6) (1,9) (1,5) (1,4) (1,18) (1,20) (1,11) (1,16) (1,6) (1,12) (2,15) (2,7) (2,13) (3,9) (3,5) (3,4) (3,20) (3,8) (3,11) (3,17) (3,6) (3,12) (4,5) (4,18) (4,19) (4,20) (4,17) (4,16) (4,12) (5,9) (5,18) (5,20) (5,8) (5,11) (6,9) (6,18) (6,19) (6,11) (6,12) (7,15) (7,13) (8,9) (8,18) (8,19) (8,20) (8,17) (8,16) (9,18) (9,19) (9,20) (9,11) (9,16) (9,12) (11,18) (11,17) (11,16) (12,18) (12,20) (12,17) (13,15) (16,18) (16,19) (16,17) (17,19) (17,20) (18,19) (19,20)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph772-0_13", + "image": "data/connectivity/graph_visual/medium/graph772.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,18) (0,22) (0,4) (0,12) (0,21) (0,24) (0,16) (1,3) (1,11) (1,10) (1,5) (1,8) (1,19) (1,9) (1,17) (1,7) (1,2) (1,20) (2,3) (2,11) (2,10) (2,5) (2,8) (2,19) (2,9) (2,17) (2,7) (2,20) (3,11) (3,10) (3,5) (3,8) (3,19) (3,9) (3,17) (3,7) (3,20) (4,15) (4,18) (4,22) (4,12) (4,21) (4,24) (4,16) (5,11) (5,10) (5,8) (5,19) (5,9) (5,17) (5,7) (5,20) (6,23) (6,14) (6,13) (7,11) (7,10) (7,8) (7,19) (7,9) (7,17) (7,20) (8,11) (8,10) (8,19) (8,9) (8,17) (8,20) (9,11) (9,10) (9,19) (9,17) (9,20) (10,11) (10,19) (10,17) (10,20) (11,19) (11,17) (11,20) (12,15) (12,18) (12,22) (12,21) (12,24) (12,16) (13,23) (13,14) (14,23) (15,18) (15,22) (15,21) (15,24) (15,16) (16,18) (16,22) (16,21) (16,24) (17,19) (17,20) (18,22) (18,21) (18,24) (19,20) (21,22) (21,24) (22,24)\nIs there a path between node 0 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph781-9_6", + "image": "data/connectivity/graph_visual/medium/graph781.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,14) (1,7) (1,20) (1,12) (1,10) (2,15) (2,21) (4,13) (4,19) (4,22) (5,14) (5,7) (5,9) (6,23) (6,18) (6,21) (7,11) (7,20) (8,14) (8,12) (9,11) (9,10) (10,17) (10,12) (11,17) (13,19) (15,21) (18,24) (23,24)\nIs there a path between node 9 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph65-4_5", + "image": "data/connectivity/graph_visual/medium/graph65.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (0,4) (0,13) (0,8) (0,6) (0,11) (0,12) (0,10) (0,9) (1,3) (1,5) (1,7) (2,4) (2,13) (2,8) (2,6) (2,11) (2,12) (2,10) (2,9) (3,5) (3,7) (4,13) (4,8) (4,6) (4,11) (4,12) (4,10) (4,9) (5,7) (6,13) (6,8) (6,11) (6,12) (6,10) (6,9) (8,13) (8,11) (8,12) (8,10) (8,9) (9,13) (9,11) (9,12) (9,10) (10,13) (10,11) (10,12) (11,13) (11,12) (12,13)\nIs there a path between node 4 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph355-9_17", + "image": "data/connectivity/graph_visual/medium/graph355.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,13) (1,16) (1,11) (1,15) (1,3) (1,20) (2,12) (2,15) (2,20) (2,8) (2,9) (3,16) (3,11) (3,15) (3,13) (4,16) (4,12) (4,11) (4,15) (5,6) (6,18) (7,17) (7,16) (7,15) (7,9) (8,13) (9,17) (9,20) (10,14) (10,18) (11,17) (17,20)\nIs there a path between node 9 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph609-7_17", + "image": "data/connectivity/graph_visual/medium/graph609.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,4) (0,2) (0,20) (0,6) (0,1) (0,15) (0,17) (0,11) (0,12) (0,21) (0,7) (0,14) (0,9) (0,10) (0,22) (0,23) (1,3) (1,4) (1,2) (1,20) (1,6) (1,15) (1,17) (1,11) (1,12) (1,21) (1,7) (1,14) (1,9) (1,10) (1,22) (1,23) (2,3) (2,4) (2,20) (2,6) (2,15) (2,17) (2,11) (2,12) (2,21) (2,7) (2,14) (2,9) (2,10) (2,22) (2,23) (3,4) (3,20) (3,6) (3,15) (3,17) (3,11) (3,12) (3,21) (3,7) (3,14) (3,9) (3,10) (3,22) (3,23) (4,20) (4,6) (4,15) (4,17) (4,11) (4,12) (4,21) (4,7) (4,14) (4,9) (4,10) (4,22) (4,23) (5,18) (6,20) (6,15) (6,17) (6,11) (6,12) (6,21) (6,7) (6,14) (6,9) (6,10) (6,22) (6,23) (7,20) (7,15) (7,17) (7,11) (7,12) (7,21) (7,14) (7,9) (7,10) (7,22) (7,23) (8,16) (8,19) (8,13) (9,20) (9,15) (9,17) (9,11) (9,12) (9,21) (9,14) (9,10) (9,22) (9,23) (10,20) (10,15) (10,17) (10,11) (10,12) (10,21) (10,14) (10,22) (10,23) (11,20) (11,15) (11,17) (11,12) (11,21) (11,14) (11,22) (11,23) (12,20) (12,15) (12,17) (12,21) (12,14) (12,22) (12,23) (13,16) (13,19) (14,20) (14,15) (14,17) (14,21) (14,22) (14,23) (15,20) (15,17) (15,21) (15,22) (15,23) (16,19) (17,20) (17,21) (17,22) (17,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 7 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph42-11_6", + "image": "data/connectivity/graph_visual/medium/graph42.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,6) (0,7) (0,10) (0,8) (0,11) (0,12) (1,3) (1,4) (1,9) (2,6) (2,7) (2,10) (2,8) (2,11) (2,12) (3,4) (3,5) (3,9) (4,5) (4,9) (5,9) (6,7) (6,10) (6,12) (7,10) (7,12) (8,10) (8,11) (8,12) (10,11) (11,12)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph689-23_8", + "image": "data/connectivity/graph_visual/medium/graph689.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,8) (0,9) (0,2) (0,10) (0,16) (0,11) (0,17) (0,1) (0,19) (0,13) (0,6) (1,3) (1,8) (1,9) (1,2) (1,10) (1,16) (1,11) (1,17) (1,19) (1,13) (1,6) (2,3) (2,8) (2,9) (2,10) (2,16) (2,11) (2,17) (2,19) (2,13) (2,6) (3,8) (3,9) (3,10) (3,16) (3,11) (3,17) (3,19) (3,13) (3,6) (4,5) (4,21) (4,22) (4,20) (4,18) (4,15) (4,12) (4,23) (4,14) (4,7) (5,21) (5,22) (5,20) (5,18) (5,15) (5,12) (5,23) (5,14) (5,7) (6,8) (6,9) (6,10) (6,16) (6,11) (6,17) (6,19) (6,13) (7,21) (7,22) (7,20) (7,18) (7,15) (7,12) (7,23) (7,14) (8,9) (8,10) (8,16) (8,11) (8,17) (8,19) (8,13) (9,10) (9,16) (9,11) (9,17) (9,19) (9,13) (10,16) (10,11) (10,17) (10,19) (10,13) (11,16) (11,17) (11,19) (11,13) (12,21) (12,22) (12,20) (12,18) (12,15) (12,23) (12,14) (13,16) (13,17) (13,19) (14,21) (14,22) (14,20) (14,18) (14,15) (14,23) (15,21) (15,22) (15,20) (15,18) (15,23) (16,17) (16,19) (17,19) (18,21) (18,22) (18,20) (18,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 23 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph516-10_20", + "image": "data/connectivity/graph_visual/medium/graph516.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,2) (0,11) (0,3) (0,19) (0,9) (0,1) (0,22) (0,13) (0,20) (0,4) (0,7) (0,10) (0,6) (0,14) (1,2) (1,11) (1,19) (1,18) (1,9) (1,21) (1,22) (1,13) (1,4) (1,7) (1,17) (1,14) (2,3) (2,19) (2,9) (2,21) (2,13) (2,12) (2,20) (2,4) (2,10) (2,17) (2,14) (3,11) (3,19) (3,18) (3,9) (3,21) (3,22) (3,13) (3,7) (3,10) (3,17) (3,6) (3,14) (4,19) (4,18) (4,9) (4,13) (4,12) (4,20) (4,7) (4,10) (4,14) (5,8) (5,15) (6,19) (6,18) (6,9) (6,21) (6,22) (6,13) (6,12) (6,20) (6,7) (7,11) (7,18) (7,9) (7,21) (7,22) (7,12) (7,10) (7,17) (7,14) (8,16) (8,15) (9,11) (9,19) (9,18) (9,21) (9,20) (9,10) (9,17) (9,14) (10,11) (10,21) (10,22) (10,13) (10,12) (10,20) (10,17) (10,14) (11,19) (11,18) (11,21) (11,22) (11,13) (11,12) (11,20) (11,17) (11,14) (12,18) (12,21) (12,13) (12,20) (12,17) (13,19) (13,22) (13,14) (14,19) (14,18) (14,21) (14,17) (15,16) (17,19) (17,21) (17,22) (17,20) (18,19) (18,21) (18,22) (18,20) (19,20) (20,21) (20,22) (21,22)\nIs there a path between node 10 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph427-7_13", + "image": "data/connectivity/graph_visual/medium/graph427.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,8) (1,11) (1,9) (1,17) (3,21) (3,11) (3,18) (3,6) (3,10) (3,15) (4,8) (5,18) (5,6) (5,9) (5,15) (6,16) (6,21) (6,11) (6,10) (7,14) (7,9) (7,17) (7,15) (8,12) (8,13) (9,21) (9,17) (9,10) (9,19) (11,14) (11,21) (11,19) (13,20) (14,16) (14,18) (14,17) (14,15) (14,19) (15,16) (16,18) (16,17) (18,21)\nIs there a path between node 7 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph457-14_15", + "image": "data/connectivity/graph_visual/medium/graph457.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,5) (0,4) (0,12) (0,8) (0,14) (1,16) (1,9) (1,11) (1,2) (1,10) (1,21) (1,7) (1,6) (1,15) (1,13) (1,19) (1,3) (1,17) (1,20) (2,16) (2,9) (2,11) (2,10) (2,21) (2,7) (2,6) (2,15) (2,13) (2,19) (2,3) (2,17) (2,20) (3,16) (3,9) (3,11) (3,10) (3,21) (3,7) (3,6) (3,15) (3,13) (3,19) (3,17) (3,20) (4,18) (4,5) (4,12) (4,8) (4,14) (5,18) (5,12) (5,8) (5,14) (6,16) (6,9) (6,11) (6,10) (6,21) (6,7) (6,15) (6,13) (6,19) (6,17) (6,20) (7,16) (7,9) (7,11) (7,10) (7,21) (7,15) (7,13) (7,19) (7,17) (7,20) (8,18) (8,12) (8,14) (9,16) (9,11) (9,10) (9,21) (9,15) (9,13) (9,19) (9,17) (9,20) (10,16) (10,11) (10,21) (10,15) (10,13) (10,19) (10,17) (10,20) (11,16) (11,21) (11,15) (11,13) (11,19) (11,17) (11,20) (12,18) (12,14) (13,16) (13,21) (13,15) (13,19) (13,17) (13,20) (14,18) (15,16) (15,21) (15,19) (15,17) (15,20) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (19,21) (19,20) (20,21)\nIs there a path between node 14 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph819-20_1", + "image": "data/connectivity/graph_visual/medium/graph819.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,10) (0,5) (0,7) (1,20) (1,4) (1,8) (1,16) (1,9) (1,23) (1,2) (2,20) (2,22) (2,15) (2,4) (2,19) (2,8) (2,16) (2,9) (2,23) (2,14) (2,17) (3,20) (3,4) (3,19) (3,8) (3,23) (3,14) (3,21) (4,20) (4,22) (4,15) (4,8) (4,16) (4,23) (4,14) (4,21) (5,11) (5,10) (5,7) (6,13) (6,12) (6,18) (7,11) (7,10) (8,20) (8,22) (8,15) (8,23) (8,14) (8,21) (9,22) (9,19) (9,16) (9,21) (9,17) (12,18) (13,24) (13,18) (14,20) (14,22) (14,15) (14,19) (14,23) (14,21) (14,17) (15,22) (15,19) (15,16) (15,21) (15,17) (16,20) (16,21) (17,20) (17,19) (17,23) (17,21) (18,24) (19,22) (19,21) (20,22) (20,23) (20,21) (21,22) (21,23) (22,23)\nIs there a path between node 20 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph593-7_6", + "image": "data/connectivity/graph_visual/medium/graph593.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,7) (0,14) (0,8) (0,5) (0,4) (0,3) (0,23) (0,12) (0,15) (0,13) (0,17) (0,2) (1,19) (1,7) (1,14) (1,8) (1,3) (1,23) (1,12) (1,15) (1,13) (1,17) (1,6) (2,21) (2,19) (2,7) (2,5) (2,4) (2,3) (2,13) (3,21) (3,19) (3,14) (3,5) (3,4) (3,23) (3,12) (3,15) (4,21) (4,19) (4,14) (4,8) (4,5) (4,23) (4,12) (4,15) (4,6) (5,21) (5,19) (5,7) (5,8) (5,12) (5,17) (6,19) (6,7) (6,23) (6,12) (6,15) (6,13) (6,17) (7,21) (7,14) (7,12) (7,15) (7,13) (7,17) (8,21) (8,19) (8,12) (8,13) (9,11) (9,22) (9,20) (11,22) (11,18) (11,20) (12,14) (12,23) (12,15) (12,13) (12,17) (13,21) (13,23) (14,21) (14,19) (14,23) (14,15) (14,17) (15,21) (15,19) (15,23) (15,17) (16,22) (16,20) (17,19) (17,23) (19,21) (19,23) (20,22)\nIs there a path between node 7 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph406-0_12", + "image": "data/connectivity/graph_visual/medium/graph406.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,14) (0,13) (1,20) (1,12) (1,3) (1,15) (1,19) (2,3) (2,15) (3,11) (3,10) (4,20) (4,8) (4,19) (4,10) (5,9) (8,20) (8,15) (8,10) (9,13) (10,20) (11,15) (12,20) (12,15) (13,18) (15,20) (18,21) (19,20)\nIs there a path between node 0 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph718-8_4", + "image": "data/connectivity/graph_visual/medium/graph718.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,22) (0,2) (0,14) (0,11) (0,13) (0,12) (0,5) (0,6) (0,20) (0,16) (0,19) (1,7) (1,21) (1,23) (2,22) (2,14) (2,11) (2,9) (2,13) (2,4) (2,12) (2,24) (2,20) (2,16) (2,3) (2,19) (3,22) (3,14) (3,9) (3,13) (3,4) (3,12) (3,10) (3,5) (3,24) (3,6) (3,20) (3,19) (4,14) (4,11) (4,9) (4,8) (4,12) (4,10) (4,6) (4,16) (4,19) (5,14) (5,9) (5,13) (5,8) (5,12) (5,24) (5,20) (5,16) (6,14) (6,11) (6,9) (6,13) (6,8) (6,12) (6,10) (6,24) (6,16) (6,19) (7,17) (7,21) (8,22) (8,14) (8,11) (8,9) (8,13) (8,12) (8,10) (8,24) (8,20) (8,19) (9,22) (9,11) (9,13) (9,10) (9,24) (9,16) (9,19) (10,22) (10,11) (10,12) (10,24) (10,20) (10,19) (11,22) (11,13) (11,12) (11,24) (11,20) (12,14) (12,24) (12,20) (12,16) (12,19) (13,14) (13,20) (13,19) (14,22) (14,24) (14,20) (15,18) (15,17) (15,21) (16,22) (16,24) (16,20) (17,18) (17,21) (17,23) (19,22) (19,24) (19,20) (20,22) (20,24) (22,24)\nIs there a path between node 8 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph48-0_1", + "image": "data/connectivity/graph_visual/medium/graph48.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,8) (0,5) (0,6) (0,7) (0,12) (0,9) (0,10) (0,11) (0,3) (0,2) (0,4) (2,8) (2,5) (2,6) (2,7) (2,12) (2,9) (2,10) (2,11) (2,3) (2,4) (3,8) (3,5) (3,6) (3,7) (3,12) (3,9) (3,10) (3,11) (3,4) (4,8) (4,5) (4,6) (4,7) (4,12) (4,9) (4,10) (4,11) (5,8) (5,6) (5,7) (5,12) (5,9) (5,10) (5,11) (6,8) (6,7) (6,12) (6,9) (6,10) (6,11) (7,8) (7,12) (7,9) (7,10) (7,11) (8,12) (8,9) (8,10) (8,11) (9,12) (9,10) (9,11) (10,12) (10,11) (11,12)\nIs there a path between node 0 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph810-0_2", + "image": "data/connectivity/graph_visual/medium/graph810.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,6) (0,1) (0,21) (0,23) (0,16) (1,8) (1,6) (1,24) (1,5) (1,3) (1,15) (1,2) (1,21) (1,23) (1,7) (2,9) (2,24) (2,3) (2,15) (2,21) (2,16) (3,9) (3,8) (3,15) (3,7) (4,11) (4,14) (4,20) (5,9) (5,8) (5,17) (5,6) (5,15) (5,21) (5,23) (5,7) (6,9) (6,17) (6,24) (6,15) (6,21) (6,23) (6,7) (7,9) (7,8) (7,24) (7,15) (7,21) (7,16) (8,24) (8,15) (8,21) (8,23) (8,16) (9,24) (9,15) (9,21) (9,16) (10,19) (10,18) (11,14) (11,20) (12,18) (12,22) (14,20) (15,17) (15,24) (15,21) (15,23) (16,17) (16,24) (16,21) (16,23) (17,24) (17,21) (18,19) (19,22) (21,24) (23,24)\nIs there a path between node 0 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph832-24_14", + "image": "data/connectivity/graph_visual/medium/graph832.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,7) (0,13) (0,24) (0,19) (0,5) (0,10) (0,4) (0,2) (0,21) (0,17) (0,23) (0,9) (0,20) (0,15) (0,22) (1,3) (1,18) (1,6) (1,14) (1,8) (1,11) (2,12) (2,7) (2,13) (2,24) (2,19) (2,5) (2,10) (2,4) (2,21) (2,17) (2,23) (2,9) (2,20) (2,15) (2,22) (3,18) (3,6) (3,14) (3,8) (3,11) (4,12) (4,7) (4,13) (4,24) (4,19) (4,5) (4,10) (4,21) (4,17) (4,23) (4,9) (4,20) (4,15) (4,22) (5,12) (5,7) (5,13) (5,24) (5,19) (5,10) (5,21) (5,17) (5,23) (5,9) (5,20) (5,15) (5,22) (6,18) (6,14) (6,8) (6,11) (7,12) (7,13) (7,24) (7,19) (7,10) (7,21) (7,17) (7,23) (7,9) (7,20) (7,15) (7,22) (8,18) (8,14) (8,11) (9,12) (9,13) (9,24) (9,19) (9,10) (9,21) (9,17) (9,23) (9,20) (9,15) (9,22) (10,12) (10,13) (10,24) (10,19) (10,21) (10,17) (10,23) (10,20) (10,15) (10,22) (11,18) (11,14) (12,13) (12,24) (12,19) (12,21) (12,17) (12,23) (12,20) (12,15) (12,22) (13,24) (13,19) (13,21) (13,17) (13,23) (13,20) (13,15) (13,22) (14,18) (15,24) (15,19) (15,21) (15,17) (15,23) (15,20) (15,22) (17,24) (17,19) (17,21) (17,23) (17,20) (17,22) (19,24) (19,21) (19,23) (19,20) (19,22) (20,24) (20,21) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nIs there a path between node 24 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph164-7_10", + "image": "data/connectivity/graph_visual/medium/graph164.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,6) (0,9) (1,10) (1,12) (1,7) (1,17) (2,13) (3,12) (3,7) (3,9) (3,16) (3,11) (4,8) (4,10) (4,5) (4,6) (4,9) (4,11) (5,6) (6,8) (6,12) (6,7) (6,16) (7,8) (7,11) (8,14) (8,9) (9,16) (10,17) (11,12) (12,14) (12,17) (16,17)\nIs there a path between node 7 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph566-4_23", + "image": "data/connectivity/graph_visual/medium/graph566.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (0,9) (0,15) (0,23) (0,4) (0,22) (0,8) (0,7) (0,16) (0,19) (0,3) (0,21) (0,17) (1,6) (1,10) (1,12) (1,2) (1,18) (1,11) (1,14) (1,20) (1,5) (2,6) (2,10) (2,12) (2,18) (2,11) (2,14) (2,20) (2,5) (3,13) (3,9) (3,15) (3,23) (3,4) (3,22) (3,8) (3,7) (3,16) (3,19) (3,21) (3,17) (4,13) (4,9) (4,15) (4,23) (4,22) (4,8) (4,7) (4,16) (4,19) (4,21) (4,17) (5,6) (5,10) (5,12) (5,18) (5,11) (5,14) (5,20) (6,10) (6,12) (6,18) (6,11) (6,14) (6,20) (7,13) (7,9) (7,15) (7,23) (7,22) (7,8) (7,16) (7,19) (7,21) (7,17) (8,13) (8,9) (8,15) (8,23) (8,22) (8,16) (8,19) (8,21) (8,17) (9,13) (9,15) (9,23) (9,22) (9,16) (9,19) (9,21) (9,17) (10,12) (10,18) (10,11) (10,14) (10,20) (11,12) (11,18) (11,14) (11,20) (12,18) (12,14) (12,20) (13,15) (13,23) (13,22) (13,16) (13,19) (13,21) (13,17) (14,18) (14,20) (15,23) (15,22) (15,16) (15,19) (15,21) (15,17) (16,23) (16,22) (16,19) (16,21) (16,17) (17,23) (17,22) (17,19) (17,21) (18,20) (19,23) (19,22) (19,21) (21,23) (21,22) (22,23)\nIs there a path between node 4 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph79-7_3", + "image": "data/connectivity/graph_visual/medium/graph79.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (0,6) (0,4) (0,8) (0,14) (0,7) (0,12) (0,11) (0,13) (0,5) (1,6) (1,4) (1,14) (1,7) (1,12) (1,11) (1,13) (2,4) (2,8) (2,12) (2,13) (2,5) (3,10) (4,6) (4,8) (4,7) (4,12) (4,13) (4,5) (5,6) (5,8) (5,7) (5,12) (5,11) (5,13) (6,8) (6,14) (6,7) (6,12) (6,13) (7,8) (7,14) (7,12) (7,11) (7,13) (8,14) (8,12) (8,11) (8,13) (9,10) (11,14) (11,12) (12,14) (12,13) (13,14)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph501-8_10", + "image": "data/connectivity/graph_visual/medium/graph501.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,19) (0,7) (0,10) (0,3) (0,15) (0,11) (0,1) (1,6) (1,9) (1,10) (1,15) (1,12) (2,7) (2,3) (2,12) (2,14) (2,13) (3,8) (3,19) (3,7) (3,21) (3,11) (3,12) (3,18) (4,16) (5,9) (5,8) (6,7) (6,17) (6,10) (6,15) (6,21) (6,20) (7,17) (7,15) (7,12) (7,14) (7,22) (7,20) (7,13) (8,9) (8,19) (8,17) (8,15) (8,20) (9,17) (9,11) (9,20) (10,19) (10,15) (11,21) (11,12) (11,14) (11,18) (12,19) (12,17) (12,14) (12,13) (13,20) (14,17) (14,22) (14,20) (14,18) (15,20) (15,18) (17,18) (20,21) (20,22)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph537-18_15", + "image": "data/connectivity/graph_visual/medium/graph537.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (0,16) (1,12) (1,10) (1,7) (1,6) (1,22) (1,13) (1,9) (1,2) (1,19) (1,14) (1,11) (1,21) (1,15) (1,5) (1,20) (1,4) (1,8) (1,17) (1,3) (2,12) (2,10) (2,7) (2,6) (2,22) (2,13) (2,9) (2,19) (2,14) (2,11) (2,21) (2,15) (2,5) (2,20) (2,4) (2,8) (2,17) (2,3) (3,12) (3,10) (3,7) (3,6) (3,22) (3,13) (3,9) (3,19) (3,14) (3,11) (3,21) (3,15) (3,5) (3,20) (3,4) (3,8) (3,17) (4,12) (4,10) (4,7) (4,6) (4,22) (4,13) (4,9) (4,19) (4,14) (4,11) (4,21) (4,15) (4,5) (4,20) (4,8) (4,17) (5,12) (5,10) (5,7) (5,6) (5,22) (5,13) (5,9) (5,19) (5,14) (5,11) (5,21) (5,15) (5,20) (5,8) (5,17) (6,12) (6,10) (6,7) (6,22) (6,13) (6,9) (6,19) (6,14) (6,11) (6,21) (6,15) (6,20) (6,8) (6,17) (7,12) (7,10) (7,22) (7,13) (7,9) (7,19) (7,14) (7,11) (7,21) (7,15) (7,20) (7,8) (7,17) (8,12) (8,10) (8,22) (8,13) (8,9) (8,19) (8,14) (8,11) (8,21) (8,15) (8,20) (8,17) (9,12) (9,10) (9,22) (9,13) (9,19) (9,14) (9,11) (9,21) (9,15) (9,20) (9,17) (10,12) (10,22) (10,13) (10,19) (10,14) (10,11) (10,21) (10,15) (10,20) (10,17) (11,12) (11,22) (11,13) (11,19) (11,14) (11,21) (11,15) (11,20) (11,17) (12,22) (12,13) (12,19) (12,14) (12,21) (12,15) (12,20) (12,17) (13,22) (13,19) (13,14) (13,21) (13,15) (13,20) (13,17) (14,22) (14,19) (14,21) (14,15) (14,20) (14,17) (15,22) (15,19) (15,21) (15,20) (15,17) (16,18) (17,22) (17,19) (17,21) (17,20) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 18 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph422-11_4", + "image": "data/connectivity/graph_visual/medium/graph422.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,20) (0,18) (0,4) (0,8) (0,1) (0,17) (0,15) (0,11) (0,21) (0,9) (0,12) (0,14) (0,3) (1,19) (1,20) (1,18) (1,4) (1,8) (1,17) (1,15) (1,11) (1,21) (1,9) (1,12) (1,14) (1,3) (2,5) (2,7) (2,13) (2,6) (2,10) (2,16) (3,19) (3,20) (3,18) (3,4) (3,8) (3,17) (3,15) (3,11) (3,21) (3,9) (3,12) (3,14) (4,19) (4,20) (4,18) (4,8) (4,17) (4,15) (4,11) (4,21) (4,9) (4,12) (4,14) (5,7) (5,13) (5,6) (5,10) (5,16) (6,7) (6,13) (6,10) (6,16) (7,13) (7,10) (7,16) (8,19) (8,20) (8,18) (8,17) (8,15) (8,11) (8,21) (8,9) (8,12) (8,14) (9,19) (9,20) (9,18) (9,17) (9,15) (9,11) (9,21) (9,12) (9,14) (10,13) (10,16) (11,19) (11,20) (11,18) (11,17) (11,15) (11,21) (11,12) (11,14) (12,19) (12,20) (12,18) (12,17) (12,15) (12,21) (12,14) (13,16) (14,19) (14,20) (14,18) (14,17) (14,15) (14,21) (15,19) (15,20) (15,18) (15,17) (15,21) (17,19) (17,20) (17,18) (17,21) (18,19) (18,20) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 11 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph16-9_11", + "image": "data/connectivity/graph_visual/medium/graph16.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,5) (0,11) (0,1) (0,3) (0,10) (0,4) (1,11) (1,3) (1,10) (1,4) (2,7) (3,11) (3,4) (4,5) (4,11) (5,11) (6,9) (6,8) (7,9) (7,8) (8,9) (10,11)\nIs there a path between node 9 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph645-4_5", + "image": "data/connectivity/graph_visual/medium/graph645.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,5) (4,19) (4,5) (6,23) (8,9) (8,20) (8,23) (8,22) (8,13) (8,10) (9,15) (9,20) (9,23) (9,22) (9,13) (9,11) (10,23) (10,22) (10,12) (10,11) (10,14) (11,23) (12,15) (12,20) (12,23) (12,16) (13,15) (13,23) (14,18) (14,16) (15,21) (15,22) (15,16) (16,20) (16,21) (20,22) (21,23) (21,22)\nIs there a path between node 4 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph674-15_3", + "image": "data/connectivity/graph_visual/medium/graph674.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,13) (0,19) (0,11) (0,16) (0,20) (0,8) (0,5) (0,3) (0,2) (0,7) (0,6) (0,17) (0,14) (0,12) (0,1) (0,18) (0,10) (0,23) (0,9) (1,4) (1,13) (1,19) (1,11) (1,16) (1,20) (1,8) (1,5) (1,3) (1,2) (1,7) (1,6) (1,17) (1,14) (1,12) (1,18) (1,10) (1,23) (1,9) (2,4) (2,13) (2,19) (2,11) (2,16) (2,20) (2,8) (2,5) (2,3) (2,7) (2,6) (2,17) (2,14) (2,12) (2,18) (2,10) (2,23) (2,9) (3,4) (3,13) (3,19) (3,11) (3,16) (3,20) (3,8) (3,5) (3,7) (3,6) (3,17) (3,14) (3,12) (3,18) (3,10) (3,23) (3,9) (4,13) (4,19) (4,11) (4,16) (4,20) (4,8) (4,5) (4,7) (4,6) (4,17) (4,14) (4,12) (4,18) (4,10) (4,23) (4,9) (5,13) (5,19) (5,11) (5,16) (5,20) (5,8) (5,7) (5,6) (5,17) (5,14) (5,12) (5,18) (5,10) (5,23) (5,9) (6,13) (6,19) (6,11) (6,16) (6,20) (6,8) (6,7) (6,17) (6,14) (6,12) (6,18) (6,10) (6,23) (6,9) (7,13) (7,19) (7,11) (7,16) (7,20) (7,8) (7,17) (7,14) (7,12) (7,18) (7,10) (7,23) (7,9) (8,13) (8,19) (8,11) (8,16) (8,20) (8,17) (8,14) (8,12) (8,18) (8,10) (8,23) (8,9) (9,13) (9,19) (9,11) (9,16) (9,20) (9,17) (9,14) (9,12) (9,18) (9,10) (9,23) (10,13) (10,19) (10,11) (10,16) (10,20) (10,17) (10,14) (10,12) (10,18) (10,23) (11,13) (11,19) (11,16) (11,20) (11,17) (11,14) (11,12) (11,18) (11,23) (12,13) (12,19) (12,16) (12,20) (12,17) (12,14) (12,18) (12,23) (13,19) (13,16) (13,20) (13,17) (13,14) (13,18) (13,23) (14,19) (14,16) (14,20) (14,17) (14,18) (14,23) (15,21) (15,22) (16,19) (16,20) (16,17) (16,18) (16,23) (17,19) (17,20) (17,18) (17,23) (18,19) (18,20) (18,23) (19,20) (19,23) (20,23) (21,22)\nIs there a path between node 15 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph51-11_9", + "image": "data/connectivity/graph_visual/medium/graph51.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,6) (0,13) (1,6) (1,8) (1,3) (1,4) (2,5) (2,9) (3,12) (3,9) (3,13) (4,6) (4,10) (5,6) (5,9) (6,12) (6,8) (8,9) (9,10) (12,13)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph379-3_19", + "image": "data/connectivity/graph_visual/medium/graph379.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,10) (1,4) (1,12) (1,15) (1,7) (1,17) (1,16) (2,18) (3,19) (3,14) (4,12) (4,13) (4,11) (4,15) (4,7) (4,17) (4,16) (4,20) (5,12) (5,13) (5,11) (5,15) (5,7) (5,9) (5,16) (6,12) (6,13) (6,11) (6,15) (6,7) (6,17) (6,16) (6,20) (7,12) (7,13) (7,11) (7,16) (7,20) (8,19) (9,12) (9,13) (9,15) (9,16) (9,20) (10,18) (11,12) (11,13) (11,17) (11,16) (11,20) (12,17) (12,16) (12,20) (13,15) (13,17) (13,16) (13,20) (14,19) (15,17) (15,16) (16,17) (16,20) (17,20)\nIs there a path between node 3 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph845-11_13", + "image": "data/connectivity/graph_visual/medium/graph845.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,3) (0,7) (0,16) (0,8) (0,11) (0,12) (0,19) (0,10) (0,1) (0,5) (0,21) (0,2) (0,13) (0,17) (1,24) (1,3) (1,7) (1,16) (1,8) (1,11) (1,12) (1,19) (1,10) (1,5) (1,21) (1,2) (1,13) (1,17) (2,24) (2,3) (2,7) (2,16) (2,8) (2,11) (2,12) (2,19) (2,10) (2,5) (2,21) (2,13) (2,17) (3,24) (3,7) (3,16) (3,8) (3,11) (3,12) (3,19) (3,10) (3,5) (3,21) (3,13) (3,17) (4,22) (4,20) (4,6) (4,18) (4,15) (4,23) (5,24) (5,7) (5,16) (5,8) (5,11) (5,12) (5,19) (5,10) (5,21) (5,13) (5,17) (6,22) (6,20) (6,18) (6,15) (6,23) (7,24) (7,16) (7,8) (7,11) (7,12) (7,19) (7,10) (7,21) (7,13) (7,17) (8,24) (8,16) (8,11) (8,12) (8,19) (8,10) (8,21) (8,13) (8,17) (9,14) (10,24) (10,16) (10,11) (10,12) (10,19) (10,21) (10,13) (10,17) (11,24) (11,16) (11,12) (11,19) (11,21) (11,13) (11,17) (12,24) (12,16) (12,19) (12,21) (12,13) (12,17) (13,24) (13,16) (13,19) (13,21) (13,17) (15,22) (15,20) (15,18) (15,23) (16,24) (16,19) (16,21) (16,17) (17,24) (17,19) (17,21) (18,22) (18,20) (18,23) (19,24) (19,21) (20,22) (20,23) (21,24) (22,23)\nIs there a path between node 11 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph104-3_5", + "image": "data/connectivity/graph_visual/medium/graph104.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,15) (0,11) (0,12) (0,14) (0,8) (0,1) (0,5) (0,3) (0,13) (1,15) (1,11) (1,12) (1,7) (1,8) (1,3) (1,13) (2,4) (2,10) (2,9) (3,15) (3,12) (3,7) (3,5) (3,13) (4,6) (5,15) (5,12) (5,14) (5,7) (5,8) (6,10) (7,15) (7,11) (7,14) (7,8) (7,13) (8,15) (8,11) (8,12) (8,14) (8,13) (11,12) (12,15) (12,14) (12,13) (13,15) (13,14) (14,15)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph201-5_10", + "image": "data/connectivity/graph_visual/medium/graph201.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,7) (1,4) (3,9) (3,12) (4,15) (5,10) (8,10) (8,16)\nIs there a path between node 5 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph791-15_12", + "image": "data/connectivity/graph_visual/medium/graph791.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (1,16) (1,5) (1,10) (1,18) (2,7) (2,14) (2,11) (2,15) (3,16) (3,5) (3,12) (3,15) (3,10) (5,20) (5,24) (5,12) (5,7) (5,14) (7,20) (7,24) (7,18) (8,21) (8,23) (9,20) (9,16) (9,24) (10,20) (10,24) (10,15) (10,18) (11,16) (11,22) (12,24) (12,14) (12,15) (13,24) (13,14) (13,22) (15,18) (15,22) (16,24) (16,18) (17,19) (18,20) (19,21) (19,23) (21,23)\nIs there a path between node 15 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph63-12_4", + "image": "data/connectivity/graph_visual/medium/graph63.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,12) (0,9) (0,6) (1,10) (1,5) (1,2) (1,8) (1,7) (2,5) (2,3) (3,8) (3,11) (3,7) (4,12) (4,6) (4,13) (5,8) (5,11) (6,9) (6,13) (7,10) (7,8) (8,11) (9,13)\nIs there a path between node 12 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph612-4_10", + "image": "data/connectivity/graph_visual/medium/graph612.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,6) (0,12) (0,20) (0,15) (0,9) (0,13) (0,2) (0,14) (0,11) (0,3) (0,23) (0,5) (1,21) (1,7) (1,8) (1,22) (1,4) (1,18) (1,17) (1,16) (2,10) (2,19) (2,6) (2,12) (2,20) (2,15) (2,9) (2,13) (2,14) (2,11) (2,3) (2,23) (2,5) (3,10) (3,19) (3,6) (3,12) (3,20) (3,15) (3,9) (3,13) (3,14) (3,11) (3,23) (3,5) (4,21) (4,7) (4,8) (4,22) (4,18) (4,17) (4,16) (5,10) (5,19) (5,6) (5,12) (5,20) (5,15) (5,9) (5,13) (5,14) (5,11) (5,23) (6,10) (6,19) (6,12) (6,20) (6,15) (6,9) (6,13) (6,14) (6,11) (6,23) (7,21) (7,8) (7,22) (7,18) (7,17) (7,16) (8,21) (8,22) (8,18) (8,17) (8,16) (9,10) (9,19) (9,12) (9,20) (9,15) (9,13) (9,14) (9,11) (9,23) (10,19) (10,12) (10,20) (10,15) (10,13) (10,14) (10,11) (10,23) (11,19) (11,12) (11,20) (11,15) (11,13) (11,14) (11,23) (12,19) (12,20) (12,15) (12,13) (12,14) (12,23) (13,19) (13,20) (13,15) (13,14) (13,23) (14,19) (14,20) (14,15) (14,23) (15,19) (15,20) (15,23) (16,21) (16,22) (16,18) (16,17) (17,21) (17,22) (17,18) (18,21) (18,22) (19,20) (19,23) (20,23) (21,22)\nIs there a path between node 4 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph514-4_22", + "image": "data/connectivity/graph_visual/medium/graph514.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,14) (0,19) (0,12) (0,1) (1,10) (1,19) (1,12) (1,3) (1,21) (2,9) (2,15) (2,4) (2,11) (2,22) (2,17) (2,7) (2,5) (2,18) (3,10) (3,19) (3,12) (3,21) (4,6) (4,16) (4,9) (4,8) (4,15) (4,11) (4,22) (4,7) (4,13) (4,5) (4,18) (5,6) (5,9) (5,8) (5,11) (5,22) (5,17) (5,7) (5,18) (6,16) (6,9) (6,11) (6,22) (6,17) (6,7) (6,13) (7,9) (7,11) (7,22) (7,17) (7,13) (7,18) (8,16) (8,11) (8,22) (8,13) (8,18) (9,16) (9,15) (9,11) (9,22) (9,17) (9,13) (9,18) (10,14) (10,19) (10,12) (10,21) (11,15) (11,17) (11,13) (12,14) (12,19) (12,21) (13,15) (13,22) (13,18) (14,21) (15,16) (15,22) (15,17) (16,22) (16,17) (16,18) (17,22) (17,18) (18,22) (19,21)\nIs there a path between node 4 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph489-7_11", + "image": "data/connectivity/graph_visual/medium/graph489.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,12) (0,13) (0,1) (0,5) (0,3) (1,12) (1,13) (1,5) (1,3) (2,19) (2,10) (2,22) (2,9) (2,4) (2,21) (2,16) (2,17) (2,6) (2,20) (2,8) (2,11) (2,15) (2,18) (2,7) (2,14) (3,12) (3,13) (3,5) (4,19) (4,10) (4,22) (4,9) (4,21) (4,16) (4,17) (4,6) (4,20) (4,8) (4,11) (4,15) (4,18) (4,7) (4,14) (5,12) (5,13) (6,19) (6,10) (6,22) (6,9) (6,21) (6,16) (6,17) (6,20) (6,8) (6,11) (6,15) (6,18) (6,7) (6,14) (7,19) (7,10) (7,22) (7,9) (7,21) (7,16) (7,17) (7,20) (7,8) (7,11) (7,15) (7,18) (7,14) (8,19) (8,10) (8,22) (8,9) (8,21) (8,16) (8,17) (8,20) (8,11) (8,15) (8,18) (8,14) (9,19) (9,10) (9,22) (9,21) (9,16) (9,17) (9,20) (9,11) (9,15) (9,18) (9,14) (10,19) (10,22) (10,21) (10,16) (10,17) (10,20) (10,11) (10,15) (10,18) (10,14) (11,19) (11,22) (11,21) (11,16) (11,17) (11,20) (11,15) (11,18) (11,14) (12,13) (14,19) (14,22) (14,21) (14,16) (14,17) (14,20) (14,15) (14,18) (15,19) (15,22) (15,21) (15,16) (15,17) (15,20) (15,18) (16,19) (16,22) (16,21) (16,17) (16,20) (16,18) (17,19) (17,22) (17,21) (17,20) (17,18) (18,19) (18,22) (18,21) (18,20) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 7 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph183-7_2", + "image": "data/connectivity/graph_visual/medium/graph183.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,9) (0,3) (0,12) (0,2) (0,10) (0,13) (0,7) (0,1) (0,11) (1,9) (1,3) (1,12) (1,2) (1,10) (1,13) (1,7) (1,11) (2,9) (2,3) (2,12) (2,10) (2,13) (2,7) (2,11) (3,9) (3,12) (3,10) (3,13) (3,7) (3,11) (4,16) (4,6) (4,14) (5,8) (5,15) (5,17) (6,16) (6,14) (7,9) (7,12) (7,10) (7,13) (7,11) (8,15) (8,17) (9,12) (9,10) (9,13) (9,11) (10,12) (10,13) (10,11) (11,12) (11,13) (12,13) (14,16) (15,17)\nIs there a path between node 7 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph386-14_6", + "image": "data/connectivity/graph_visual/medium/graph386.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,12) (0,20) (0,15) (0,18) (0,2) (0,10) (0,8) (0,3) (0,9) (0,14) (0,4) (0,13) (0,17) (0,19) (0,1) (0,5) (0,7) (1,12) (1,20) (1,15) (1,18) (1,2) (1,10) (1,8) (1,3) (1,9) (1,14) (1,4) (1,13) (1,17) (1,19) (1,5) (1,7) (2,12) (2,20) (2,15) (2,18) (2,10) (2,8) (2,3) (2,9) (2,14) (2,4) (2,13) (2,17) (2,19) (2,5) (2,7) (3,12) (3,20) (3,15) (3,18) (3,10) (3,8) (3,9) (3,14) (3,4) (3,13) (3,17) (3,19) (3,5) (3,7) (4,12) (4,20) (4,15) (4,18) (4,10) (4,8) (4,9) (4,14) (4,13) (4,17) (4,19) (4,5) (4,7) (5,12) (5,20) (5,15) (5,18) (5,10) (5,8) (5,9) (5,14) (5,13) (5,17) (5,19) (5,7) (6,11) (6,16) (7,12) (7,20) (7,15) (7,18) (7,10) (7,8) (7,9) (7,14) (7,13) (7,17) (7,19) (8,12) (8,20) (8,15) (8,18) (8,10) (8,9) (8,14) (8,13) (8,17) (8,19) (9,12) (9,20) (9,15) (9,18) (9,10) (9,14) (9,13) (9,17) (9,19) (10,12) (10,20) (10,15) (10,18) (10,14) (10,13) (10,17) (10,19) (11,16) (12,20) (12,15) (12,18) (12,14) (12,13) (12,17) (12,19) (13,20) (13,15) (13,18) (13,14) (13,17) (13,19) (14,20) (14,15) (14,18) (14,17) (14,19) (15,20) (15,18) (15,17) (15,19) (17,20) (17,18) (17,19) (18,20) (18,19) (19,20)\nIs there a path between node 14 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph306-1_11", + "image": "data/connectivity/graph_visual/medium/graph306.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,11) (0,17) (0,1) (0,10) (0,9) (0,8) (0,3) (0,2) (0,19) (1,11) (1,17) (1,10) (1,9) (1,8) (1,3) (1,2) (1,4) (2,7) (2,11) (2,17) (2,5) (2,10) (2,3) (3,17) (3,5) (3,9) (3,19) (4,7) (4,17) (4,5) (4,10) (4,9) (4,8) (4,19) (5,11) (5,17) (5,10) (5,9) (5,19) (6,12) (6,16) (6,13) (7,17) (7,10) (7,9) (7,8) (7,19) (8,11) (8,19) (9,11) (10,17) (10,19) (11,19) (12,18) (12,14) (12,13) (13,18) (13,14) (13,16) (14,18) (17,19)\nIs there a path between node 1 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph126-3_10", + "image": "data/connectivity/graph_visual/medium/graph126.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,11) (0,3) (0,7) (0,10) (0,13) (0,12) (0,16) (1,14) (1,2) (1,5) (1,9) (1,8) (1,15) (1,4) (1,6) (2,14) (2,5) (2,9) (2,8) (2,15) (2,4) (2,6) (3,11) (3,7) (3,10) (3,13) (3,12) (3,16) (4,14) (4,5) (4,9) (4,8) (4,15) (4,6) (5,14) (5,9) (5,8) (5,15) (5,6) (6,14) (6,9) (6,8) (6,15) (7,11) (7,10) (7,13) (7,12) (7,16) (8,14) (8,9) (8,15) (9,14) (9,15) (10,11) (10,13) (10,12) (10,16) (11,13) (11,12) (11,16) (12,13) (12,16) (13,16) (14,15)\nIs there a path between node 3 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph444-19_4", + "image": "data/connectivity/graph_visual/medium/graph444.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,3) (0,15) (0,21) (0,17) (0,7) (0,12) (0,5) (0,9) (0,2) (0,19) (0,14) (0,20) (1,3) (1,15) (1,16) (1,17) (1,11) (1,7) (1,12) (1,13) (1,8) (1,18) (1,9) (1,2) (1,19) (1,14) (1,20) (2,15) (2,21) (2,17) (2,11) (2,7) (2,12) (2,5) (2,8) (2,19) (2,14) (2,10) (2,20) (3,15) (3,21) (3,16) (3,17) (3,11) (3,13) (3,5) (3,8) (3,18) (3,14) (3,10) (3,20) (5,15) (5,21) (5,16) (5,17) (5,11) (5,7) (5,12) (5,13) (5,9) (5,19) (5,14) (5,10) (5,20) (7,21) (7,17) (7,11) (7,12) (7,8) (7,18) (7,19) (7,10) (7,20) (8,15) (8,21) (8,16) (8,17) (8,9) (8,19) (8,14) (8,10) (8,20) (9,15) (9,21) (9,16) (9,13) (9,18) (9,14) (10,15) (10,21) (10,16) (10,17) (10,11) (10,12) (10,13) (10,18) (10,19) (10,14) (10,20) (11,15) (11,21) (11,16) (11,17) (11,13) (11,18) (11,14) (11,20) (12,16) (12,17) (12,13) (12,18) (12,20) (13,15) (13,21) (13,16) (13,17) (13,18) (13,14) (13,20) (14,16) (14,17) (14,19) (14,20) (15,16) (15,17) (15,19) (16,17) (16,18) (16,19) (16,20) (17,21) (17,18) (18,19) (18,20) (19,21) (20,21)\nIs there a path between node 19 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph94-10_15", + "image": "data/connectivity/graph_visual/medium/graph94.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,9) (0,6) (0,14) (0,1) (0,5) (0,10) (1,9) (1,6) (1,7) (3,9) (3,6) (3,5) (4,12) (4,7) (4,15) (5,6) (5,11) (5,7) (5,10) (6,15) (7,10) (9,12) (9,15) (9,13) (10,15) (13,15)\nIs there a path between node 10 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph159-17_11", + "image": "data/connectivity/graph_visual/medium/graph159.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,9) (1,15) (1,3) (1,16) (2,4) (2,12) (2,10) (4,8) (4,11) (5,10) (5,17) (5,6) (6,11) (6,10) (6,17) (7,11) (7,12) (7,10) (7,17) (8,17) (9,13)\nIs there a path between node 17 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph557-22_14", + "image": "data/connectivity/graph_visual/medium/graph557.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,2) (0,18) (0,23) (0,21) (0,13) (0,16) (0,15) (0,22) (0,6) (0,14) (1,17) (1,11) (1,10) (1,4) (1,19) (1,9) (2,8) (2,18) (2,23) (2,21) (2,22) (2,14) (2,20) (3,17) (3,11) (3,10) (3,4) (3,19) (3,9) (4,7) (4,10) (4,9) (5,8) (5,21) (5,13) (5,16) (5,15) (5,22) (5,6) (5,14) (5,20) (6,8) (6,18) (6,13) (6,15) (6,14) (6,20) (7,17) (7,10) (7,19) (7,9) (8,18) (8,23) (8,21) (8,13) (8,16) (8,14) (8,20) (9,17) (9,10) (9,19) (10,17) (10,19) (11,19) (13,18) (13,23) (13,21) (13,16) (13,22) (13,14) (13,20) (14,18) (14,23) (14,21) (14,16) (14,22) (14,20) (15,18) (15,21) (15,22) (16,23) (16,21) (17,19) (18,22) (20,23) (20,21) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 22 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph161-5_1", + "image": "data/connectivity/graph_visual/medium/graph161.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,5) (0,2) (0,7) (0,16) (0,6) (1,7) (1,10) (1,4) (2,15) (2,10) (4,5) (4,6) (6,7) (8,11) (8,13) (8,12) (8,14) (11,14) (13,17) (14,17)\nIs there a path between node 5 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph688-18_23", + "image": "data/connectivity/graph_visual/medium/graph688.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,6) (0,11) (0,14) (0,2) (1,20) (1,8) (1,7) (1,16) (1,21) (1,9) (1,17) (1,5) (1,23) (1,12) (1,22) (2,4) (2,6) (2,11) (2,14) (3,15) (3,18) (3,13) (3,19) (3,10) (4,6) (4,11) (4,14) (5,20) (5,8) (5,7) (5,16) (5,21) (5,9) (5,17) (5,23) (5,12) (5,22) (6,11) (6,14) (7,20) (7,8) (7,16) (7,21) (7,9) (7,17) (7,23) (7,12) (7,22) (8,20) (8,16) (8,21) (8,9) (8,17) (8,23) (8,12) (8,22) (9,20) (9,16) (9,21) (9,17) (9,23) (9,12) (9,22) (10,15) (10,18) (10,13) (10,19) (11,14) (12,20) (12,16) (12,21) (12,17) (12,23) (12,22) (13,15) (13,18) (13,19) (15,18) (15,19) (16,20) (16,21) (16,17) (16,23) (16,22) (17,20) (17,21) (17,23) (17,22) (18,19) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 18 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph665-12_18", + "image": "data/connectivity/graph_visual/medium/graph665.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,10) (0,14) (0,2) (0,8) (1,18) (1,23) (1,5) (1,4) (1,11) (1,9) (1,20) (1,17) (1,7) (2,10) (2,14) (2,16) (2,3) (2,8) (2,22) (3,12) (3,10) (3,14) (3,16) (3,8) (4,18) (4,15) (4,20) (4,17) (4,7) (5,23) (5,15) (5,21) (5,11) (5,9) (5,19) (5,17) (5,7) (7,23) (7,21) (7,11) (7,9) (7,20) (7,17) (8,12) (8,10) (8,14) (8,22) (9,18) (9,23) (9,15) (9,21) (9,11) (9,20) (9,19) (10,16) (10,22) (11,18) (11,15) (11,21) (11,20) (11,19) (11,17) (12,14) (12,16) (14,22) (15,18) (15,20) (17,20) (18,23) (18,19) (19,23) (19,21) (21,23)\nIs there a path between node 12 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph640-10_19", + "image": "data/connectivity/graph_visual/medium/graph640.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,22) (0,16) (0,23) (1,8) (1,4) (1,22) (1,16) (1,18) (1,3) (2,19) (2,9) (2,17) (2,20) (3,14) (3,13) (3,7) (4,8) (4,12) (4,16) (4,23) (4,18) (5,10) (5,9) (5,20) (6,14) (6,13) (6,22) (6,7) (7,22) (7,18) (8,22) (8,18) (9,19) (9,11) (9,20) (9,21) (10,20) (10,21) (11,20) (12,18) (13,22) (13,16) (13,23) (13,18) (15,19) (15,17) (15,21) (16,23) (16,18) (17,19) (18,22)\nIs there a path between node 10 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph526-3_11", + "image": "data/connectivity/graph_visual/medium/graph526.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,16) (0,9) (0,20) (0,8) (0,18) (0,4) (0,3) (0,1) (0,12) (0,15) (0,10) (0,14) (1,11) (1,17) (1,5) (1,22) (1,21) (1,9) (1,20) (1,8) (1,18) (1,3) (1,2) (1,10) (2,17) (2,5) (2,22) (2,16) (2,21) (2,20) (2,8) (2,18) (2,3) (2,12) (2,15) (3,11) (3,17) (3,5) (3,22) (3,16) (3,21) (3,9) (3,8) (3,18) (3,4) (3,15) (3,10) (4,17) (4,5) (4,22) (4,16) (4,9) (4,20) (4,8) (4,12) (4,10) (4,14) (5,16) (5,9) (5,20) (5,18) (5,10) (5,14) (7,13) (8,11) (8,17) (8,22) (8,16) (8,21) (8,9) (8,18) (8,12) (8,15) (8,10) (8,14) (9,11) (9,17) (9,16) (9,21) (9,20) (9,18) (9,10) (9,14) (10,11) (10,17) (10,22) (10,16) (10,21) (10,20) (10,18) (10,12) (10,15) (10,14) (11,22) (11,16) (11,21) (11,18) (11,15) (11,14) (12,22) (12,18) (12,14) (14,17) (14,20) (14,18) (14,15) (15,17) (15,22) (15,21) (15,20) (15,18) (16,17) (16,21) (16,20) (16,18) (17,22) (17,20) (17,18) (18,22) (18,21) (20,22) (21,22)\nIs there a path between node 3 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph647-2_14", + "image": "data/connectivity/graph_visual/medium/graph647.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,18) (0,6) (0,1) (1,12) (1,6) (1,3) (2,8) (2,18) (2,20) (2,13) (2,11) (3,23) (3,18) (3,13) (4,16) (4,22) (5,7) (6,18) (6,11) (6,15) (7,9) (8,23) (8,14) (8,20) (8,11) (12,14) (13,18) (14,23) (14,18) (15,18) (16,17) (16,21) (18,23) (18,20)\nIs there a path between node 2 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph678-0_14", + "image": "data/connectivity/graph_visual/medium/graph678.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,16) (0,15) (0,3) (0,1) (0,8) (1,23) (1,16) (1,15) (1,3) (1,8) (2,7) (2,4) (2,20) (2,14) (3,23) (3,16) (3,15) (3,8) (4,7) (4,20) (4,14) (5,12) (5,10) (5,18) (5,9) (5,22) (5,13) (5,17) (6,19) (6,11) (6,21) (7,20) (7,14) (8,23) (8,16) (8,15) (9,12) (9,10) (9,18) (9,22) (9,13) (9,17) (10,12) (10,18) (10,22) (10,13) (10,17) (11,19) (11,21) (12,18) (12,22) (12,13) (12,17) (13,18) (13,22) (13,17) (14,20) (15,23) (15,16) (16,23) (17,18) (17,22) (18,22) (19,21)\nIs there a path between node 0 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph620-14_18", + "image": "data/connectivity/graph_visual/medium/graph620.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,14) (0,2) (0,15) (0,4) (0,11) (0,23) (0,12) (0,10) (0,20) (0,9) (0,7) (0,1) (0,16) (0,22) (0,3) (0,13) (0,19) (1,14) (1,2) (1,15) (1,4) (1,11) (1,23) (1,12) (1,10) (1,20) (1,9) (1,7) (1,16) (1,22) (1,3) (1,13) (1,19) (2,14) (2,15) (2,4) (2,11) (2,23) (2,12) (2,10) (2,20) (2,9) (2,7) (2,16) (2,22) (2,3) (2,13) (2,19) (3,14) (3,15) (3,4) (3,11) (3,23) (3,12) (3,10) (3,20) (3,9) (3,7) (3,16) (3,22) (3,13) (3,19) (4,14) (4,15) (4,11) (4,23) (4,12) (4,10) (4,20) (4,9) (4,7) (4,16) (4,22) (4,13) (4,19) (5,8) (5,6) (5,18) (5,21) (6,8) (6,18) (6,21) (7,14) (7,15) (7,11) (7,23) (7,12) (7,10) (7,20) (7,9) (7,16) (7,22) (7,13) (7,19) (8,18) (8,21) (9,14) (9,15) (9,11) (9,23) (9,12) (9,10) (9,20) (9,16) (9,22) (9,13) (9,19) (10,14) (10,15) (10,11) (10,23) (10,12) (10,20) (10,16) (10,22) (10,13) (10,19) (11,14) (11,15) (11,23) (11,12) (11,20) (11,16) (11,22) (11,13) (11,19) (12,14) (12,15) (12,23) (12,20) (12,16) (12,22) (12,13) (12,19) (13,14) (13,15) (13,23) (13,20) (13,16) (13,22) (13,19) (14,15) (14,23) (14,20) (14,16) (14,22) (14,19) (15,23) (15,20) (15,16) (15,22) (15,19) (16,23) (16,20) (16,22) (16,19) (18,21) (19,23) (19,20) (19,22) (20,23) (20,22) (22,23)\nIs there a path between node 14 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph158-11_4", + "image": "data/connectivity/graph_visual/medium/graph158.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,9) (1,14) (1,8) (2,11) (2,16) (2,7) (2,6) (3,17) (3,11) (3,4) (3,13) (3,6) (4,10) (5,15) (5,10) (6,17) (6,15) (7,17) (7,16) (8,9) (10,17) (10,16) (11,17) (11,15) (11,16) (12,17) (12,16) (15,17) (15,16)\nIs there a path between node 11 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph644-16_6", + "image": "data/connectivity/graph_visual/medium/graph644.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,9) (1,4) (2,16) (4,18) (4,11) (5,14) (6,8) (7,15) (7,21) (9,15) (9,19) (13,15) (13,16) (15,20) (16,20) (19,21) (19,20)\nIs there a path between node 16 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph375-16_1", + "image": "data/connectivity/graph_visual/medium/graph375.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,15) (0,5) (0,3) (0,11) (0,9) (0,8) (0,13) (1,15) (1,5) (1,3) (1,11) (1,4) (1,9) (1,10) (1,8) (3,15) (3,4) (3,10) (3,8) (4,15) (4,12) (4,9) (4,10) (4,8) (4,13) (5,15) (5,11) (5,9) (5,10) (6,7) (6,20) (6,17) (6,18) (6,14) (7,19) (7,20) (7,18) (8,12) (8,11) (8,9) (8,10) (8,13) (9,15) (9,12) (9,11) (9,10) (10,15) (10,11) (10,13) (11,12) (12,13) (14,19) (14,20) (14,17) (14,18) (17,19) (17,20) (17,18) (18,19) (18,20)\nIs there a path between node 16 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph705-22_5", + "image": "data/connectivity/graph_visual/medium/graph705.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (1,7) (1,2) (1,22) (1,23) (1,16) (1,3) (2,17) (2,21) (2,8) (2,23) (2,12) (3,22) (3,12) (4,17) (4,21) (4,8) (4,7) (4,18) (4,10) (5,14) (5,15) (5,9) (6,18) (6,22) (6,15) (6,23) (6,11) (7,21) (7,8) (7,18) (7,22) (7,12) (7,11) (8,21) (8,18) (8,16) (9,10) (9,11) (10,18) (10,14) (10,16) (10,11) (11,17) (11,22) (11,23) (12,14) (14,21) (15,22) (16,17) (17,21) (18,23) (19,24)\nIs there a path between node 22 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph418-13_7", + "image": "data/connectivity/graph_visual/medium/graph418.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,13) (0,19) (0,10) (0,6) (0,17) (0,1) (0,7) (0,2) (1,13) (1,19) (1,10) (1,6) (1,17) (1,7) (1,2) (2,13) (2,19) (2,10) (2,6) (2,17) (2,7) (3,20) (3,12) (3,8) (3,11) (3,14) (4,18) (4,15) (4,21) (4,9) (4,5) (4,16) (5,18) (5,15) (5,21) (5,9) (5,16) (6,13) (6,19) (6,10) (6,17) (6,7) (7,13) (7,19) (7,10) (7,17) (8,20) (8,12) (8,11) (8,14) (9,18) (9,15) (9,21) (9,16) (10,13) (10,19) (10,17) (11,20) (11,12) (11,14) (12,20) (12,14) (13,19) (13,17) (14,20) (15,18) (15,21) (15,16) (16,18) (16,21) (17,19) (18,21)\nIs there a path between node 13 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph659-23_5", + "image": "data/connectivity/graph_visual/medium/graph659.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,21) (0,14) (0,23) (0,11) (0,19) (0,17) (0,22) (0,8) (0,9) (0,16) (0,10) (0,4) (1,3) (1,14) (1,11) (1,17) (1,7) (1,16) (2,15) (2,13) (2,5) (3,21) (3,14) (3,11) (3,20) (3,19) (3,17) (3,22) (3,9) (3,16) (3,10) (4,6) (4,21) (4,14) (4,23) (4,20) (4,17) (4,22) (4,7) (4,8) (4,9) (4,10) (5,15) (5,12) (6,21) (6,14) (6,23) (6,11) (6,20) (6,18) (6,19) (6,17) (6,7) (6,9) (6,16) (6,10) (7,21) (7,23) (7,11) (7,20) (7,19) (7,17) (7,22) (7,8) (7,16) (8,14) (8,23) (8,20) (8,18) (8,17) (8,22) (8,9) (8,10) (9,21) (9,14) (9,23) (9,11) (9,18) (9,19) (9,17) (9,22) (9,16) (9,10) (10,21) (10,14) (10,23) (10,11) (10,20) (10,18) (10,19) (10,16) (11,23) (11,20) (11,19) (11,17) (11,16) (12,15) (12,13) (13,15) (14,21) (14,23) (14,20) (14,18) (14,19) (14,17) (16,21) (16,23) (16,20) (16,18) (16,17) (17,21) (17,23) (17,20) (17,18) (18,21) (18,23) (18,19) (18,22) (19,21) (19,23) (19,20) (19,22) (20,21) (20,23) (20,22) (21,23) (22,23)\nIs there a path between node 23 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph107-1_5", + "image": "data/connectivity/graph_visual/medium/graph107.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (0,7) (0,14) (0,5) (0,13) (0,10) (1,7) (1,14) (1,5) (1,13) (1,10) (2,6) (2,12) (2,4) (2,8) (2,15) (2,3) (2,9) (2,11) (3,6) (3,12) (3,4) (3,8) (3,15) (3,9) (3,11) (4,6) (4,12) (4,8) (4,15) (4,9) (4,11) (5,7) (5,14) (5,13) (5,10) (6,12) (6,8) (6,15) (6,9) (6,11) (7,14) (7,13) (7,10) (8,12) (8,15) (8,9) (8,11) (9,12) (9,15) (9,11) (10,14) (10,13) (11,12) (11,15) (12,15) (13,14)\nIs there a path between node 1 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph580-8_14", + "image": "data/connectivity/graph_visual/medium/graph580.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,1) (0,16) (0,3) (2,16) (3,8) (3,11) (3,23) (4,13) (5,22) (5,20) (5,10) (5,13) (6,11) (6,21) (6,23) (7,8) (7,16) (7,19) (8,15) (8,14) (8,21) (9,12) (9,18) (10,12) (11,14) (12,22) (13,18) (14,19) (14,21) (16,23)\nIs there a path between node 8 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph357-14_9", + "image": "data/connectivity/graph_visual/medium/graph357.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,12) (1,6) (1,2) (1,14) (1,3) (1,10) (2,6) (2,4) (2,9) (2,14) (2,10) (3,4) (3,13) (3,14) (4,9) (5,19) (5,15) (6,17) (6,9) (6,20) (6,10) (7,17) (7,9) (8,19) (8,18) (10,17) (10,13) (10,14) (12,16) (13,14) (17,20) (18,19)\nIs there a path between node 14 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph739-15_3", + "image": "data/connectivity/graph_visual/medium/graph739.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,19) (0,11) (0,13) (0,17) (0,20) (1,4) (2,23) (2,12) (2,22) (2,21) (2,14) (3,19) (3,21) (4,9) (4,24) (4,17) (4,14) (5,6) (5,22) (5,24) (5,11) (5,20) (6,23) (6,22) (6,17) (8,14) (11,23) (11,24) (11,14) (12,22) (13,19) (13,24) (14,19) (14,21) (14,24) (14,20) (17,24) (20,23) (20,21) (21,24) (22,24) (23,24)\nIs there a path between node 15 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph840-6_20", + "image": "data/connectivity/graph_visual/medium/graph840.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,3) (0,17) (0,12) (0,18) (0,11) (0,4) (0,16) (0,19) (0,8) (0,24) (0,15) (0,9) (0,1) (0,7) (0,22) (1,10) (1,3) (1,17) (1,12) (1,18) (1,11) (1,4) (1,16) (1,19) (1,8) (1,24) (1,15) (1,9) (1,7) (1,22) (2,23) (2,6) (2,21) (2,14) (2,13) (2,5) (2,20) (3,10) (3,17) (3,12) (3,18) (3,11) (3,4) (3,16) (3,19) (3,8) (3,24) (3,15) (3,9) (3,7) (3,22) (4,10) (4,17) (4,12) (4,18) (4,11) (4,16) (4,19) (4,8) (4,24) (4,15) (4,9) (4,7) (4,22) (5,23) (5,6) (5,21) (5,14) (5,13) (5,20) (6,23) (6,21) (6,14) (6,13) (6,20) (7,10) (7,17) (7,12) (7,18) (7,11) (7,16) (7,19) (7,8) (7,24) (7,15) (7,9) (7,22) (8,10) (8,17) (8,12) (8,18) (8,11) (8,16) (8,19) (8,24) (8,15) (8,9) (8,22) (9,10) (9,17) (9,12) (9,18) (9,11) (9,16) (9,19) (9,24) (9,15) (9,22) (10,17) (10,12) (10,18) (10,11) (10,16) (10,19) (10,24) (10,15) (10,22) (11,17) (11,12) (11,18) (11,16) (11,19) (11,24) (11,15) (11,22) (12,17) (12,18) (12,16) (12,19) (12,24) (12,15) (12,22) (13,23) (13,21) (13,14) (13,20) (14,23) (14,21) (14,20) (15,17) (15,18) (15,16) (15,19) (15,24) (15,22) (16,17) (16,18) (16,19) (16,24) (16,22) (17,18) (17,19) (17,24) (17,22) (18,19) (18,24) (18,22) (19,24) (19,22) (20,23) (20,21) (21,23) (22,24)\nIs there a path between node 6 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph553-4_8", + "image": "data/connectivity/graph_visual/medium/graph553.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,10) (0,9) (0,3) (1,10) (1,4) (1,2) (1,12) (1,14) (1,6) (1,15) (2,7) (2,10) (2,9) (2,17) (2,15) (3,20) (3,14) (3,18) (3,6) (3,15) (4,7) (4,16) (4,13) (4,9) (4,14) (4,21) (4,22) (4,17) (5,23) (5,11) (6,10) (6,16) (6,20) (6,22) (7,16) (7,20) (8,23) (8,19) (9,22) (12,14) (12,17) (13,16) (13,14) (13,17) (14,21) (15,21) (15,18) (16,18) (17,18) (19,23) (20,21)\nIs there a path between node 4 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph491-2_3", + "image": "data/connectivity/graph_visual/medium/graph491.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,2) (0,22) (0,9) (0,7) (0,21) (0,15) (0,6) (0,18) (0,16) (0,1) (0,17) (0,19) (0,13) (0,4) (0,5) (0,14) (0,20) (1,10) (1,2) (1,22) (1,9) (1,7) (1,21) (1,15) (1,6) (1,18) (1,16) (1,17) (1,19) (1,13) (1,4) (1,5) (1,14) (1,20) (2,10) (2,22) (2,9) (2,7) (2,21) (2,15) (2,6) (2,18) (2,16) (2,17) (2,19) (2,13) (2,4) (2,5) (2,14) (2,20) (3,11) (3,8) (3,12) (4,10) (4,22) (4,9) (4,7) (4,21) (4,15) (4,6) (4,18) (4,16) (4,17) (4,19) (4,13) (4,5) (4,14) (4,20) (5,10) (5,22) (5,9) (5,7) (5,21) (5,15) (5,6) (5,18) (5,16) (5,17) (5,19) (5,13) (5,14) (5,20) (6,10) (6,22) (6,9) (6,7) (6,21) (6,15) (6,18) (6,16) (6,17) (6,19) (6,13) (6,14) (6,20) (7,10) (7,22) (7,9) (7,21) (7,15) (7,18) (7,16) (7,17) (7,19) (7,13) (7,14) (7,20) (8,11) (8,12) (9,10) (9,22) (9,21) (9,15) (9,18) (9,16) (9,17) (9,19) (9,13) (9,14) (9,20) (10,22) (10,21) (10,15) (10,18) (10,16) (10,17) (10,19) (10,13) (10,14) (10,20) (11,12) (13,22) (13,21) (13,15) (13,18) (13,16) (13,17) (13,19) (13,14) (13,20) (14,22) (14,21) (14,15) (14,18) (14,16) (14,17) (14,19) (14,20) (15,22) (15,21) (15,18) (15,16) (15,17) (15,19) (15,20) (16,22) (16,21) (16,18) (16,17) (16,19) (16,20) (17,22) (17,21) (17,18) (17,19) (17,20) (18,22) (18,21) (18,19) (18,20) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph822-18_19", + "image": "data/connectivity/graph_visual/medium/graph822.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (0,19) (0,5) (0,22) (0,2) (0,16) (0,10) (0,24) (0,20) (0,8) (0,15) (1,18) (1,19) (1,4) (1,23) (1,2) (1,10) (1,24) (1,21) (1,20) (1,15) (2,18) (2,6) (2,19) (2,23) (2,7) (2,22) (2,12) (2,16) (2,24) (2,21) (2,20) (2,15) (3,17) (3,13) (3,11) (4,18) (4,9) (4,19) (4,23) (4,7) (4,22) (4,16) (4,10) (4,24) (4,21) (4,20) (4,15) (5,18) (5,23) (5,7) (5,22) (5,12) (5,16) (5,10) (5,24) (5,8) (5,15) (6,18) (6,19) (6,7) (6,22) (6,12) (6,16) (6,10) (6,24) (6,21) (6,20) (6,15) (7,9) (7,19) (7,23) (7,12) (7,10) (7,21) (7,20) (7,15) (8,18) (8,9) (8,19) (8,23) (8,22) (8,12) (8,16) (8,10) (8,20) (8,15) (9,18) (9,19) (9,23) (9,12) (9,10) (9,24) (9,21) (9,20) (9,15) (10,18) (10,19) (10,23) (10,22) (10,12) (10,24) (10,21) (10,20) (10,15) (11,17) (12,18) (12,23) (12,22) (12,16) (12,24) (12,20) (13,17) (15,18) (15,19) (15,22) (15,24) (15,20) (16,18) (16,19) (16,23) (16,22) (16,24) (16,20) (18,23) (18,22) (18,21) (19,23) (19,22) (19,24) (19,20) (20,24) (20,21) (21,23) (21,22) (21,24) (22,24) (23,24)\nIs there a path between node 18 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph725-0_19", + "image": "data/connectivity/graph_visual/medium/graph725.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,7) (0,2) (0,5) (0,18) (0,9) (0,16) (0,21) (0,13) (0,11) (0,14) (0,22) (0,15) (0,6) (2,20) (2,7) (2,5) (2,18) (2,9) (2,16) (2,21) (2,13) (2,11) (2,14) (2,22) (2,15) (2,6) (3,4) (3,10) (3,8) (3,17) (3,19) (3,23) (3,24) (4,10) (4,8) (4,17) (4,19) (4,23) (4,24) (5,20) (5,7) (5,18) (5,9) (5,16) (5,21) (5,13) (5,11) (5,14) (5,22) (5,15) (5,6) (6,20) (6,7) (6,18) (6,9) (6,16) (6,21) (6,13) (6,11) (6,14) (6,22) (6,15) (7,20) (7,18) (7,9) (7,16) (7,21) (7,13) (7,11) (7,14) (7,22) (7,15) (8,10) (8,17) (8,19) (8,23) (8,24) (9,20) (9,18) (9,16) (9,21) (9,13) (9,11) (9,14) (9,22) (9,15) (10,17) (10,19) (10,23) (10,24) (11,20) (11,18) (11,16) (11,21) (11,13) (11,14) (11,22) (11,15) (13,20) (13,18) (13,16) (13,21) (13,14) (13,22) (13,15) (14,20) (14,18) (14,16) (14,21) (14,22) (14,15) (15,20) (15,18) (15,16) (15,21) (15,22) (16,20) (16,18) (16,21) (16,22) (17,19) (17,23) (17,24) (18,20) (18,21) (18,22) (19,23) (19,24) (20,21) (20,22) (21,22) (23,24)\nIs there a path between node 0 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph763-9_24", + "image": "data/connectivity/graph_visual/medium/graph763.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,20) (0,13) (0,24) (0,4) (1,21) (1,3) (1,11) (1,10) (1,23) (1,8) (1,2) (1,22) (1,19) (1,18) (2,21) (2,3) (2,11) (2,10) (2,23) (2,8) (2,22) (2,19) (2,18) (3,21) (3,11) (3,10) (3,23) (3,8) (3,22) (3,19) (3,18) (4,14) (4,20) (4,13) (4,24) (5,7) (5,9) (5,12) (5,16) (5,15) (5,17) (5,6) (6,7) (6,9) (6,12) (6,16) (6,15) (6,17) (7,9) (7,12) (7,16) (7,15) (7,17) (8,21) (8,11) (8,10) (8,23) (8,22) (8,19) (8,18) (9,12) (9,16) (9,15) (9,17) (10,21) (10,11) (10,23) (10,22) (10,19) (10,18) (11,21) (11,23) (11,22) (11,19) (11,18) (12,16) (12,15) (12,17) (13,14) (13,20) (13,24) (14,20) (14,24) (15,16) (15,17) (16,17) (18,21) (18,23) (18,22) (18,19) (19,21) (19,23) (19,22) (20,24) (21,23) (21,22) (22,23)\nIs there a path between node 9 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph382-0_11", + "image": "data/connectivity/graph_visual/medium/graph382.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,20) (0,10) (0,13) (0,17) (1,7) (1,5) (1,16) (1,6) (2,14) (2,18) (2,11) (2,9) (2,4) (2,15) (2,19) (2,12) (2,3) (2,8) (3,14) (3,18) (3,11) (3,9) (3,4) (3,15) (3,19) (3,12) (3,8) (4,14) (4,18) (4,11) (4,9) (4,15) (4,19) (4,12) (4,8) (5,7) (5,16) (5,6) (6,7) (6,16) (7,16) (8,14) (8,18) (8,11) (8,9) (8,15) (8,19) (8,12) (9,14) (9,18) (9,11) (9,15) (9,19) (9,12) (10,20) (10,13) (10,17) (11,14) (11,18) (11,15) (11,19) (11,12) (12,14) (12,18) (12,15) (12,19) (13,20) (13,17) (14,18) (14,15) (14,19) (15,18) (15,19) (17,20) (18,19)\nIs there a path between node 0 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph200-8_9", + "image": "data/connectivity/graph_visual/medium/graph200.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,12) (0,18) (0,6) (0,5) (0,7) (0,16) (1,11) (1,14) (2,4) (3,15) (5,12) (5,17) (5,9) (6,17) (6,7) (7,12) (7,18) (7,17) (7,13) (8,11) (9,12) (9,18) (9,17) (10,15) (13,17) (14,15)\nIs there a path between node 8 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph133-11_12", + "image": "data/connectivity/graph_visual/medium/graph133.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,15) (0,8) (0,4) (0,5) (0,13) (0,2) (0,17) (1,15) (1,8) (1,3) (1,4) (1,5) (1,13) (1,17) (2,15) (2,8) (2,3) (2,4) (2,5) (2,13) (3,8) (3,5) (3,17) (4,15) (4,13) (4,17) (5,15) (5,8) (5,17) (6,14) (6,7) (6,10) (6,16) (6,9) (6,12) (7,14) (7,16) (7,9) (8,13) (9,14) (9,10) (9,11) (9,16) (9,12) (10,14) (10,12) (11,14) (11,12) (12,14) (12,16) (13,17) (15,17)\nIs there a path between node 11 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph806-21_9", + "image": "data/connectivity/graph_visual/medium/graph806.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,21) (1,17) (1,15) (1,2) (1,4) (1,18) (2,8) (2,13) (2,17) (2,15) (2,23) (2,22) (2,4) (2,18) (2,12) (4,21) (4,8) (4,13) (4,15) (4,23) (4,22) (4,18) (4,12) (5,21) (5,8) (5,13) (5,17) (5,15) (5,22) (5,18) (7,14) (7,16) (7,10) (7,11) (7,19) (8,21) (8,17) (8,23) (8,18) (9,14) (9,24) (10,14) (10,24) (10,19) (11,14) (11,16) (11,24) (12,21) (12,13) (12,17) (12,15) (12,23) (12,22) (12,18) (13,21) (13,17) (13,15) (13,23) (13,22) (14,24) (15,21) (15,17) (15,23) (15,22) (15,18) (16,19) (17,21) (17,18) (18,21) (18,23) (21,22) (22,23)\nIs there a path between node 21 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph721-17_0", + "image": "data/connectivity/graph_visual/medium/graph721.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,3) (0,9) (0,20) (0,15) (1,21) (1,11) (1,13) (1,23) (1,19) (1,17) (1,5) (1,4) (1,22) (1,2) (1,16) (1,24) (1,7) (1,18) (1,6) (1,12) (1,8) (1,10) (2,21) (2,11) (2,13) (2,23) (2,19) (2,17) (2,5) (2,4) (2,22) (2,16) (2,24) (2,7) (2,18) (2,6) (2,12) (2,8) (2,10) (3,14) (3,9) (3,20) (3,15) (4,21) (4,11) (4,13) (4,23) (4,19) (4,17) (4,5) (4,22) (4,16) (4,24) (4,7) (4,18) (4,6) (4,12) (4,8) (4,10) (5,21) (5,11) (5,13) (5,23) (5,19) (5,17) (5,22) (5,16) (5,24) (5,7) (5,18) (5,6) (5,12) (5,8) (5,10) (6,21) (6,11) (6,13) (6,23) (6,19) (6,17) (6,22) (6,16) (6,24) (6,7) (6,18) (6,12) (6,8) (6,10) (7,21) (7,11) (7,13) (7,23) (7,19) (7,17) (7,22) (7,16) (7,24) (7,18) (7,12) (7,8) (7,10) (8,21) (8,11) (8,13) (8,23) (8,19) (8,17) (8,22) (8,16) (8,24) (8,18) (8,12) (8,10) (9,14) (9,20) (9,15) (10,21) (10,11) (10,13) (10,23) (10,19) (10,17) (10,22) (10,16) (10,24) (10,18) (10,12) (11,21) (11,13) (11,23) (11,19) (11,17) (11,22) (11,16) (11,24) (11,18) (11,12) (12,21) (12,13) (12,23) (12,19) (12,17) (12,22) (12,16) (12,24) (12,18) (13,21) (13,23) (13,19) (13,17) (13,22) (13,16) (13,24) (13,18) (14,20) (14,15) (15,20) (16,21) (16,23) (16,19) (16,17) (16,22) (16,24) (16,18) (17,21) (17,23) (17,19) (17,22) (17,24) (17,18) (18,21) (18,23) (18,19) (18,22) (18,24) (19,21) (19,23) (19,22) (19,24) (21,23) (21,22) (21,24) (22,23) (22,24) (23,24)\nIs there a path between node 17 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph160-10_2", + "image": "data/connectivity/graph_visual/medium/graph160.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,6) (0,13) (0,15) (0,8) (0,14) (0,2) (1,7) (2,10) (2,13) (2,11) (2,14) (2,17) (3,6) (3,12) (3,11) (4,16) (4,5) (4,7) (6,15) (8,13) (8,14) (10,12) (10,13) (10,17) (11,14) (12,13) (12,15) (14,17) (15,17)\nIs there a path between node 10 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph41-3_9", + "image": "data/connectivity/graph_visual/medium/graph41.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,11) (0,12) (0,5) (0,6) (0,4) (0,8) (0,2) (0,9) (0,1) (0,7) (1,12) (1,5) (1,6) (1,4) (1,8) (1,2) (1,9) (1,10) (1,7) (2,8) (2,10) (2,7) (4,11) (4,12) (4,5) (4,6) (4,8) (4,9) (4,7) (5,11) (5,6) (5,8) (5,10) (5,7) (6,11) (6,12) (6,8) (6,9) (7,11) (7,12) (7,9) (7,10) (8,12) (8,9) (8,10) (9,11) (9,12) (9,10) (10,11) (10,12) (11,12)\nIs there a path between node 3 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph373-11_9", + "image": "data/connectivity/graph_visual/medium/graph373.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,6) (0,20) (0,17) (0,8) (0,7) (0,5) (0,11) (1,14) (2,3) (2,10) (2,16) (2,20) (2,9) (2,17) (2,8) (2,4) (2,13) (2,7) (2,5) (2,11) (3,10) (3,6) (3,16) (3,20) (3,9) (3,8) (3,4) (3,13) (3,7) (3,5) (4,10) (4,6) (4,16) (4,9) (4,17) (4,13) (4,7) (5,10) (5,6) (5,20) (5,9) (5,17) (5,7) (5,11) (6,10) (6,20) (6,9) (6,17) (6,13) (6,7) (7,16) (7,20) (7,17) (7,8) (7,13) (7,11) (8,10) (8,16) (8,20) (8,17) (8,13) (8,11) (9,10) (9,16) (9,20) (9,17) (9,13) (9,11) (10,16) (10,17) (10,11) (11,16) (11,20) (11,17) (11,13) (12,19) (13,16) (13,20) (13,17) (15,19) (16,20) (16,17) (17,20) (18,19)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph634-10_4", + "image": "data/connectivity/graph_visual/medium/graph634.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,9) (0,18) (0,2) (0,14) (0,20) (0,22) (0,4) (0,1) (0,19) (1,23) (1,2) (1,16) (1,20) (1,22) (1,11) (1,4) (1,12) (2,3) (2,5) (2,7) (2,9) (2,18) (2,16) (2,14) (2,20) (2,8) (2,4) (2,19) (3,15) (3,5) (3,18) (3,16) (3,8) (3,22) (3,11) (4,15) (4,5) (4,18) (4,11) (4,12) (4,19) (5,23) (5,15) (5,16) (5,12) (5,19) (6,17) (7,18) (7,14) (7,20) (8,15) (8,18) (8,21) (12,21) (12,22) (12,19) (14,23) (14,19) (15,19) (16,18) (18,19) (19,23) (19,20) (19,22) (20,23)\nIs there a path between node 10 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph853-18_7", + "image": "data/connectivity/graph_visual/medium/graph853.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,15) (0,6) (0,16) (0,2) (1,5) (1,21) (1,19) (1,11) (1,18) (1,12) (1,8) (1,14) (1,20) (1,24) (1,9) (1,10) (2,7) (2,15) (2,6) (2,16) (3,22) (3,17) (3,13) (3,4) (3,23) (4,22) (4,17) (4,13) (4,23) (5,21) (5,19) (5,11) (5,18) (5,12) (5,8) (5,14) (5,20) (5,24) (5,9) (5,10) (6,7) (6,15) (6,16) (7,15) (7,16) (8,21) (8,19) (8,11) (8,18) (8,12) (8,14) (8,20) (8,24) (8,9) (8,10) (9,21) (9,19) (9,11) (9,18) (9,12) (9,14) (9,20) (9,24) (9,10) (10,21) (10,19) (10,11) (10,18) (10,12) (10,14) (10,20) (10,24) (11,21) (11,19) (11,18) (11,12) (11,14) (11,20) (11,24) (12,21) (12,19) (12,18) (12,14) (12,20) (12,24) (13,22) (13,17) (13,23) (14,21) (14,19) (14,18) (14,20) (14,24) (15,16) (17,22) (17,23) (18,21) (18,19) (18,20) (18,24) (19,21) (19,20) (19,24) (20,21) (20,24) (21,24) (22,23)\nIs there a path between node 18 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph363-3_5", + "image": "data/connectivity/graph_visual/medium/graph363.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,9) (0,8) (0,17) (0,6) (1,14) (1,7) (2,8) (2,17) (2,3) (2,11) (2,10) (2,6) (3,9) (3,19) (3,10) (3,16) (4,18) (4,14) (5,8) (5,17) (5,10) (6,9) (6,11) (6,16) (7,20) (7,15) (8,9) (8,13) (8,19) (9,13) (10,17) (10,13) (12,16) (13,17) (14,18) (14,20) (15,20) (16,19)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph551-17_7", + "image": "data/connectivity/graph_visual/medium/graph551.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,11) (2,20) (3,22) (3,6) (3,14) (3,12) (3,13) (3,4) (4,23) (4,12) (5,23) (5,22) (5,12) (5,10) (5,13) (5,15) (6,10) (6,13) (6,18) (8,11) (9,20) (10,12) (11,17) (11,16) (12,14) (12,15) (12,21) (13,19) (13,18) (14,23) (14,15) (14,18) (15,23) (18,23)\nIs there a path between node 17 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph561-9_0", + "image": "data/connectivity/graph_visual/medium/graph561.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,3) (0,20) (0,6) (0,11) (0,4) (0,7) (0,23) (0,14) (0,21) (1,5) (1,10) (2,9) (2,3) (2,20) (2,4) (2,23) (2,14) (2,21) (3,8) (3,9) (3,20) (3,6) (3,11) (3,4) (3,22) (4,9) (4,20) (4,6) (4,7) (4,22) (4,23) (4,14) (4,21) (5,10) (6,8) (6,9) (6,20) (6,11) (6,22) (6,23) (6,14) (7,8) (7,9) (7,22) (7,23) (7,21) (8,20) (8,11) (8,22) (8,14) (8,21) (9,20) (9,22) (9,14) (9,21) (11,20) (11,22) (11,23) (11,14) (13,16) (13,18) (13,15) (13,19) (13,17) (14,20) (14,22) (14,23) (15,16) (15,19) (15,17) (16,18) (16,19) (16,17) (17,19) (18,19) (20,22) (20,23) (20,21) (21,22) (21,23) (22,23)\nIs there a path between node 9 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph7-4_1", + "image": "data/connectivity/graph_visual/medium/graph7.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,6) (1,4) (1,3) (1,2) (1,7) (2,10) (2,4) (2,8) (3,10) (3,6) (3,4) (3,8) (3,5) (4,6) (4,8) (4,5) (4,7) (5,10) (5,8) (6,10) (6,8) (7,10)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph731-5_14", + "image": "data/connectivity/graph_visual/medium/graph731.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,6) (0,8) (1,2) (1,9) (1,24) (1,22) (1,20) (1,3) (1,17) (2,12) (2,19) (2,24) (2,13) (2,10) (3,12) (3,9) (3,24) (3,22) (3,10) (3,18) (4,5) (4,10) (4,17) (5,23) (5,11) (5,16) (5,14) (5,18) (6,7) (7,15) (7,8) (8,15) (9,11) (9,13) (10,21) (10,13) (10,16) (10,17) (11,13) (11,22) (12,21) (12,24) (12,22) (12,16) (12,14) (13,14) (13,17) (14,19) (14,21) (14,16) (16,24) (16,18) (17,19) (17,21) (17,24) (17,22) (17,20) (18,23) (18,19) (18,24) (18,22) (20,23) (20,21) (20,24) (21,22)\nIs there a path between node 5 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph291-9_12", + "image": "data/connectivity/graph_visual/medium/graph291.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,12) (1,2) (1,15) (1,17) (1,8) (1,10) (1,18) (2,3) (2,15) (2,18) (3,16) (3,5) (3,8) (3,10) (4,11) (5,16) (5,7) (5,14) (5,10) (5,18) (7,14) (7,8) (8,10) (8,18) (9,16) (10,14) (14,16) (15,17) (16,17)\nIs there a path between node 9 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph5-10_3", + "image": "data/connectivity/graph_visual/medium/graph5.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,10) (1,8) (1,9) (2,10) (2,3) (3,7) (5,10) (6,8) (7,8) (7,9)\nIs there a path between node 10 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph392-8_11", + "image": "data/connectivity/graph_visual/medium/graph392.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,12) (0,2) (0,7) (0,17) (0,10) (0,16) (0,9) (0,3) (0,13) (0,4) (0,11) (0,20) (0,15) (0,14) (0,1) (1,5) (1,12) (1,2) (1,7) (1,17) (1,10) (1,16) (1,9) (1,3) (1,13) (1,4) (1,11) (1,20) (1,15) (1,14) (2,5) (2,12) (2,7) (2,17) (2,10) (2,16) (2,9) (2,3) (2,13) (2,4) (2,11) (2,20) (2,15) (2,14) (3,5) (3,12) (3,7) (3,17) (3,10) (3,16) (3,9) (3,13) (3,4) (3,11) (3,20) (3,15) (3,14) (4,5) (4,12) (4,7) (4,17) (4,10) (4,16) (4,9) (4,13) (4,11) (4,20) (4,15) (4,14) (5,12) (5,7) (5,17) (5,10) (5,16) (5,9) (5,13) (5,11) (5,20) (5,15) (5,14) (6,18) (6,8) (6,19) (7,12) (7,17) (7,10) (7,16) (7,9) (7,13) (7,11) (7,20) (7,15) (7,14) (8,18) (8,19) (9,12) (9,17) (9,10) (9,16) (9,13) (9,11) (9,20) (9,15) (9,14) (10,12) (10,17) (10,16) (10,13) (10,11) (10,20) (10,15) (10,14) (11,12) (11,17) (11,16) (11,13) (11,20) (11,15) (11,14) (12,17) (12,16) (12,13) (12,20) (12,15) (12,14) (13,17) (13,16) (13,20) (13,15) (13,14) (14,17) (14,16) (14,20) (14,15) (15,17) (15,16) (15,20) (16,17) (16,20) (17,20) (18,19)\nIs there a path between node 8 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph197-4_7", + "image": "data/connectivity/graph_visual/medium/graph197.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,3) (0,18) (0,12) (0,2) (0,11) (0,8) (0,13) (1,4) (1,10) (1,17) (1,5) (1,14) (1,7) (1,6) (1,15) (2,3) (2,18) (2,12) (2,11) (2,8) (2,13) (3,18) (3,12) (3,11) (3,8) (3,13) (4,10) (4,17) (4,5) (4,14) (4,7) (4,6) (4,15) (5,10) (5,17) (5,14) (5,7) (5,6) (5,15) (6,10) (6,17) (6,14) (6,7) (6,15) (7,10) (7,17) (7,14) (7,15) (8,18) (8,12) (8,11) (8,13) (9,16) (10,17) (10,14) (10,15) (11,18) (11,12) (11,13) (12,18) (12,13) (13,18) (14,17) (14,15) (15,17)\nIs there a path between node 4 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph103-4_0", + "image": "data/connectivity/graph_visual/medium/graph103.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (0,5) (0,8) (0,4) (0,12) (0,2) (0,7) (0,14) (0,3) (0,6) (1,13) (1,5) (1,8) (1,4) (1,12) (1,2) (1,9) (1,14) (1,3) (2,13) (2,5) (2,10) (2,4) (2,9) (2,14) (3,5) (3,8) (3,10) (3,4) (3,9) (3,14) (3,6) (4,13) (4,5) (4,10) (4,9) (4,6) (5,13) (5,8) (5,10) (5,12) (5,9) (6,8) (6,10) (6,9) (6,7) (6,14) (7,13) (7,8) (7,10) (7,12) (8,10) (8,12) (8,9) (8,14) (9,13) (9,10) (9,12) (9,14) (10,12) (10,14) (11,15) (12,13)\nIs there a path between node 4 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph617-18_10", + "image": "data/connectivity/graph_visual/medium/graph617.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (1,14) (1,20) (1,10) (1,21) (1,12) (1,5) (2,9) (2,16) (2,22) (2,18) (2,7) (2,23) (2,6) (2,17) (2,3) (2,13) (2,8) (2,11) (2,19) (2,4) (3,9) (3,16) (3,22) (3,18) (3,7) (3,23) (3,6) (3,17) (3,13) (3,8) (3,11) (3,19) (3,4) (4,9) (4,16) (4,22) (4,18) (4,7) (4,23) (4,6) (4,17) (4,13) (4,8) (4,11) (4,19) (5,14) (5,20) (5,10) (5,21) (5,12) (6,9) (6,16) (6,22) (6,18) (6,7) (6,23) (6,17) (6,13) (6,8) (6,11) (6,19) (7,9) (7,16) (7,22) (7,18) (7,23) (7,17) (7,13) (7,8) (7,11) (7,19) (8,9) (8,16) (8,22) (8,18) (8,23) (8,17) (8,13) (8,11) (8,19) (9,16) (9,22) (9,18) (9,23) (9,17) (9,13) (9,11) (9,19) (10,14) (10,20) (10,21) (10,12) (11,16) (11,22) (11,18) (11,23) (11,17) (11,13) (11,19) (12,14) (12,20) (12,21) (13,16) (13,22) (13,18) (13,23) (13,17) (13,19) (14,20) (14,21) (16,22) (16,18) (16,23) (16,17) (16,19) (17,22) (17,18) (17,23) (17,19) (18,22) (18,23) (18,19) (19,22) (19,23) (20,21) (22,23)\nIs there a path between node 18 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph369-2_18", + "image": "data/connectivity/graph_visual/medium/graph369.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (1,2) (1,16) (1,19) (1,10) (1,13) (1,18) (1,14) (1,20) (1,5) (1,4) (1,15) (1,6) (1,8) (1,12) (2,16) (2,19) (2,7) (2,9) (2,18) (2,11) (2,14) (2,20) (2,5) (2,6) (2,12) (3,17) (4,16) (4,19) (4,10) (4,7) (4,9) (4,13) (4,14) (4,15) (4,6) (4,8) (4,12) (5,19) (5,10) (5,7) (5,9) (5,13) (5,18) (5,14) (5,20) (5,15) (5,6) (5,8) (5,12) (6,16) (6,19) (6,10) (6,13) (6,18) (6,15) (6,8) (6,12) (7,16) (7,19) (7,9) (7,13) (7,18) (7,14) (7,20) (7,15) (8,16) (8,19) (8,9) (8,13) (8,18) (8,14) (8,15) (8,12) (9,16) (9,10) (9,13) (9,18) (9,11) (9,20) (10,16) (10,19) (10,13) (10,11) (10,14) (10,20) (10,15) (10,12) (11,13) (11,18) (11,14) (11,20) (11,15) (12,16) (12,14) (12,20) (12,15) (13,16) (13,19) (13,18) (13,14) (13,20) (13,15) (14,19) (14,20) (15,16) (15,19) (15,18) (15,20) (16,19) (16,20) (18,20) (19,20)\nIs there a path between node 2 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph74-1_9", + "image": "data/connectivity/graph_visual/medium/graph74.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,11) (1,9) (2,14) (3,11) (4,13) (4,7) (5,11) (5,9) (6,9) (7,10) (7,12) (10,13) (10,12) (12,13)\nIs there a path between node 1 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph542-2_17", + "image": "data/connectivity/graph_visual/medium/graph542.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,14) (0,9) (0,13) (0,4) (0,12) (0,5) (0,3) (0,15) (0,21) (0,2) (0,18) (0,17) (1,14) (1,9) (1,13) (1,4) (1,12) (1,5) (1,3) (1,15) (1,21) (1,2) (1,18) (1,17) (2,14) (2,9) (2,13) (2,4) (2,12) (2,5) (2,3) (2,15) (2,21) (2,18) (2,17) (3,14) (3,9) (3,13) (3,4) (3,12) (3,5) (3,15) (3,21) (3,18) (3,17) (4,14) (4,9) (4,13) (4,12) (4,5) (4,15) (4,21) (4,18) (4,17) (5,14) (5,9) (5,13) (5,12) (5,15) (5,21) (5,18) (5,17) (6,22) (6,8) (6,11) (6,10) (6,19) (6,20) (6,7) (7,22) (7,8) (7,11) (7,10) (7,19) (7,20) (8,22) (8,11) (8,10) (8,19) (8,20) (9,14) (9,13) (9,12) (9,15) (9,21) (9,18) (9,17) (10,22) (10,11) (10,19) (10,20) (11,22) (11,19) (11,20) (12,14) (12,13) (12,15) (12,21) (12,18) (12,17) (13,14) (13,15) (13,21) (13,18) (13,17) (14,15) (14,21) (14,18) (14,17) (15,21) (15,18) (15,17) (17,21) (17,18) (18,21) (19,22) (19,20) (20,22)\nIs there a path between node 2 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph165-1_17", + "image": "data/connectivity/graph_visual/medium/graph165.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,2) (0,13) (0,11) (0,4) (0,17) (1,14) (1,12) (2,13) (2,10) (2,8) (2,4) (3,13) (3,10) (3,4) (4,5) (4,7) (5,10) (7,16) (9,15) (10,16) (10,13) (11,15) (11,17) (13,16) (13,15) (15,16)\nIs there a path between node 1 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph205-2_9", + "image": "data/connectivity/graph_visual/medium/graph205.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,16) (0,3) (0,12) (0,6) (0,11) (1,16) (1,3) (1,12) (1,6) (1,11) (1,14) (1,10) (2,15) (2,7) (2,13) (2,5) (2,9) (2,4) (2,18) (3,17) (3,12) (3,11) (3,14) (4,15) (4,7) (4,5) (4,9) (4,8) (5,15) (5,13) (5,9) (5,8) (5,18) (6,16) (6,17) (6,12) (6,14) (6,10) (7,15) (7,13) (7,9) (7,18) (8,15) (8,9) (8,18) (9,13) (9,18) (10,16) (10,17) (10,12) (10,11) (11,16) (11,17) (11,12) (12,16) (12,17) (12,14) (13,15) (13,18) (14,16) (14,17) (15,18) (16,17)\nIs there a path between node 2 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph743-7_6", + "image": "data/connectivity/graph_visual/medium/graph743.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (1,22) (1,6) (1,2) (1,14) (2,16) (2,20) (2,5) (2,23) (3,16) (3,20) (3,8) (3,5) (3,6) (4,10) (4,24) (5,17) (5,22) (5,20) (5,7) (6,17) (6,9) (6,23) (7,22) (7,20) (8,16) (8,22) (8,14) (9,16) (9,22) (9,20) (9,12) (9,23) (10,11) (12,22) (12,23) (13,18) (14,16) (14,22) (16,17) (16,22) (16,20) (20,22) (20,23)\nIs there a path between node 7 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph326-8_16", + "image": "data/connectivity/graph_visual/medium/graph326.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,19) (0,17) (0,1) (0,4) (0,15) (0,2) (0,13) (0,10) (0,6) (0,18) (0,11) (0,12) (0,5) (1,19) (1,17) (1,4) (1,15) (1,2) (1,13) (1,10) (1,6) (1,18) (1,11) (1,12) (1,5) (2,19) (2,17) (2,4) (2,15) (2,13) (2,10) (2,6) (2,18) (2,11) (2,12) (2,5) (3,20) (3,16) (3,14) (3,8) (4,19) (4,17) (4,15) (4,13) (4,10) (4,6) (4,18) (4,11) (4,12) (4,5) (5,19) (5,17) (5,15) (5,13) (5,10) (5,6) (5,18) (5,11) (5,12) (6,19) (6,17) (6,15) (6,13) (6,10) (6,18) (6,11) (6,12) (7,9) (8,20) (8,16) (8,14) (10,19) (10,17) (10,15) (10,13) (10,18) (10,11) (10,12) (11,19) (11,17) (11,15) (11,13) (11,18) (11,12) (12,19) (12,17) (12,15) (12,13) (12,18) (13,19) (13,17) (13,15) (13,18) (14,20) (14,16) (15,19) (15,17) (15,18) (16,20) (17,19) (17,18) (18,19)\nIs there a path between node 8 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph504-22_7", + "image": "data/connectivity/graph_visual/medium/graph504.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,3) (0,20) (0,18) (0,14) (0,10) (0,11) (1,16) (1,2) (1,18) (1,13) (1,4) (1,8) (2,11) (2,8) (2,12) (3,16) (3,14) (3,9) (3,10) (3,12) (4,20) (4,6) (4,8) (6,20) (6,14) (6,11) (6,12) (7,21) (7,13) (7,12) (8,21) (8,10) (8,11) (9,16) (9,20) (9,10) (10,15) (10,14) (10,17) (10,12) (11,16) (11,20) (11,21) (11,13) (12,14) (14,21) (14,17) (15,20) (15,17) (17,20) (18,21)\nIs there a path between node 22 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph400-8_14", + "image": "data/connectivity/graph_visual/medium/graph400.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,3) (0,4) (0,10) (1,18) (1,11) (1,16) (1,21) (1,10) (2,5) (2,20) (2,13) (3,11) (3,16) (3,13) (3,10) (4,20) (4,13) (4,6) (4,10) (5,11) (5,16) (5,13) (6,20) (6,16) (6,13) (6,19) (7,9) (8,17) (8,14) (10,18) (10,11) (10,16) (10,21) (11,20) (11,16) (13,21) (15,17) (16,21) (16,19) (18,20)\nIs there a path between node 8 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph97-14_0", + "image": "data/connectivity/graph_visual/medium/graph97.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (1,15) (1,10) (2,15) (3,14) (3,7) (3,4) (4,7) (4,5) (5,14) (5,7) (5,11) (5,8) (6,12) (6,7) (7,12) (8,12) (8,11) (10,15)\nIs there a path between node 14 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph356-16_11", + "image": "data/connectivity/graph_visual/medium/graph356.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,11) (1,16) (1,10) (1,12) (2,16) (2,11) (3,8) (3,13) (4,20) (4,8) (4,17) (5,14) (6,15) (7,13) (7,9) (7,18) (7,17) (8,9) (9,15) (10,19) (11,14) (11,12) (12,14) (17,18) (18,20)\nIs there a path between node 16 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph36-0_4", + "image": "data/connectivity/graph_visual/medium/graph36.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,2) (0,12) (0,11) (0,4) (2,10) (2,8) (2,4) (4,6) (4,11) (5,9) (6,7) (6,10) (6,11) (7,8) (8,10) (8,9) (9,12) (10,11)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph555-0_15", + "image": "data/connectivity/graph_visual/medium/graph555.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,14) (0,5) (0,9) (0,8) (0,6) (0,21) (1,4) (1,15) (1,18) (1,11) (1,10) (1,12) (2,20) (2,14) (2,5) (2,9) (2,22) (2,6) (2,16) (3,9) (3,23) (3,22) (3,6) (3,21) (4,15) (4,11) (4,19) (4,13) (5,20) (5,14) (5,9) (5,8) (5,6) (5,21) (6,20) (6,14) (6,9) (6,23) (6,8) (6,16) (7,18) (7,11) (7,10) (7,12) (7,19) (7,13) (8,20) (8,14) (8,23) (8,21) (9,20) (9,23) (9,22) (9,21) (10,15) (10,18) (10,11) (10,12) (10,19) (10,13) (11,15) (11,13) (12,18) (12,19) (13,18) (13,19) (14,23) (14,22) (14,21) (15,19) (16,23) (16,22) (20,21) (22,23)\nIs there a path between node 0 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph393-11_14", + "image": "data/connectivity/graph_visual/medium/graph393.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,14) (0,11) (0,17) (0,5) (0,4) (1,20) (1,8) (1,13) (1,2) (1,16) (1,19) (1,7) (1,6) (1,12) (1,9) (2,20) (2,8) (2,13) (2,16) (2,19) (2,7) (2,6) (2,12) (2,9) (3,18) (3,10) (3,15) (4,14) (4,11) (4,17) (4,5) (5,14) (5,11) (5,17) (6,20) (6,8) (6,13) (6,16) (6,19) (6,7) (6,12) (6,9) (7,20) (7,8) (7,13) (7,16) (7,19) (7,12) (7,9) (8,20) (8,13) (8,16) (8,19) (8,12) (8,9) (9,20) (9,13) (9,16) (9,19) (9,12) (10,18) (10,15) (11,14) (11,17) (12,20) (12,13) (12,16) (12,19) (13,20) (13,16) (13,19) (14,17) (15,18) (16,20) (16,19) (19,20)\nIs there a path between node 11 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph806-19_23", + "image": "data/connectivity/graph_visual/medium/graph806.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,21) (1,17) (1,15) (1,2) (1,4) (1,18) (2,8) (2,13) (2,17) (2,15) (2,23) (2,22) (2,4) (2,18) (2,12) (4,21) (4,8) (4,13) (4,15) (4,23) (4,22) (4,18) (4,12) (5,21) (5,8) (5,13) (5,17) (5,15) (5,22) (5,18) (7,14) (7,16) (7,10) (7,11) (7,19) (8,21) (8,17) (8,23) (8,18) (9,14) (9,24) (10,14) (10,24) (10,19) (11,14) (11,16) (11,24) (12,21) (12,13) (12,17) (12,15) (12,23) (12,22) (12,18) (13,21) (13,17) (13,15) (13,23) (13,22) (14,24) (15,21) (15,17) (15,23) (15,22) (15,18) (16,19) (17,21) (17,18) (18,21) (18,23) (21,22) (22,23)\nIs there a path between node 19 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph746-22_20", + "image": "data/connectivity/graph_visual/medium/graph746.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,21) (0,14) (0,1) (0,22) (0,16) (0,19) (0,5) (0,10) (0,20) (0,11) (0,24) (0,13) (1,21) (1,9) (1,3) (1,14) (1,22) (1,10) (1,20) (1,12) (1,11) (1,24) (1,13) (1,23) (2,8) (2,4) (2,18) (2,15) (3,9) (3,14) (3,16) (3,19) (3,7) (3,6) (3,5) (3,10) (3,11) (4,8) (4,17) (4,18) (4,15) (5,9) (5,14) (5,22) (5,7) (5,6) (5,10) (5,20) (5,12) (5,11) (5,13) (5,23) (6,21) (6,9) (6,22) (6,19) (6,7) (6,20) (6,12) (6,11) (6,13) (6,23) (7,21) (7,9) (7,14) (7,16) (7,19) (7,10) (7,20) (7,12) (7,11) (7,24) (7,13) (7,23) (8,17) (8,18) (8,15) (9,21) (9,16) (9,10) (9,20) (9,12) (9,11) (9,24) (9,13) (9,23) (10,22) (10,19) (10,12) (10,11) (10,13) (10,23) (11,21) (11,22) (11,19) (11,20) (11,12) (11,24) (11,13) (11,23) (12,21) (12,14) (12,22) (12,20) (12,24) (12,13) (12,23) (13,21) (13,14) (13,22) (13,16) (13,20) (13,23) (14,21) (14,16) (14,20) (14,24) (14,23) (15,18) (16,21) (16,22) (16,19) (16,20) (16,24) (16,23) (17,18) (19,21) (19,20) (19,24) (19,23) (20,21) (20,24) (20,23) (21,24) (21,23) (22,23) (23,24)\nIs there a path between node 22 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph653-6_2", + "image": "data/connectivity/graph_visual/medium/graph653.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,13) (0,6) (0,8) (0,11) (0,17) (0,19) (0,22) (1,7) (1,3) (1,5) (1,4) (2,15) (2,13) (2,6) (2,20) (2,14) (2,17) (2,19) (2,23) (2,22) (3,7) (3,18) (3,5) (3,9) (3,21) (3,4) (3,12) (4,10) (4,5) (4,12) (5,16) (5,7) (5,10) (5,18) (5,9) (5,21) (5,12) (6,13) (6,20) (6,8) (6,11) (6,14) (6,17) (6,23) (6,22) (7,16) (7,10) (7,9) (7,21) (7,12) (8,15) (8,13) (8,20) (8,11) (8,19) (8,23) (9,16) (9,18) (9,21) (9,12) (10,16) (10,18) (10,21) (10,12) (11,15) (11,20) (11,14) (11,17) (11,19) (11,22) (13,15) (13,17) (13,23) (13,22) (14,15) (14,20) (15,19) (15,22) (16,21) (17,20) (17,23) (17,22) (18,21) (19,20) (19,23) (19,22) (20,22) (22,23)\nIs there a path between node 6 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph736-7_1", + "image": "data/connectivity/graph_visual/medium/graph736.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,9) (2,24) (2,5) (2,21) (2,19) (2,23) (2,4) (3,17) (3,7) (4,14) (4,5) (4,21) (4,15) (4,23) (5,10) (5,24) (5,6) (5,15) (6,15) (6,23) (7,16) (8,11) (8,13) (10,14) (11,22) (11,12) (13,22) (13,18) (13,20) (14,15) (14,23) (15,24) (15,21) (16,17) (18,20)\nIs there a path between node 7 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph16-5_4", + "image": "data/connectivity/graph_visual/medium/graph16.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,5) (0,11) (0,1) (0,3) (0,10) (0,4) (1,11) (1,3) (1,10) (1,4) (2,7) (3,11) (3,4) (4,5) (4,11) (5,11) (6,9) (6,8) (7,9) (7,8) (8,9) (10,11)\nIs there a path between node 5 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph37-8_11", + "image": "data/connectivity/graph_visual/medium/graph37.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,10) (1,4) (5,8) (7,12) (9,12) (9,11) (11,12)\nIs there a path between node 8 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph137-12_4", + "image": "data/connectivity/graph_visual/medium/graph137.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,2) (0,13) (1,15) (1,14) (1,13) (2,5) (2,4) (4,15) (4,13) (5,14) (5,9) (5,13) (6,7) (6,12) (9,14) (10,16) (11,16) (12,17)\nIs there a path between node 12 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph529-22_18", + "image": "data/connectivity/graph_visual/medium/graph529.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,20) (0,19) (0,14) (0,2) (0,9) (0,13) (0,21) (0,12) (0,18) (0,16) (0,7) (1,17) (1,5) (1,4) (1,22) (1,11) (1,3) (1,8) (1,15) (1,10) (1,6) (2,20) (2,19) (2,14) (2,9) (2,13) (2,21) (2,12) (2,18) (2,16) (2,7) (3,17) (3,5) (3,4) (3,22) (3,11) (3,8) (3,15) (3,10) (3,6) (4,17) (4,5) (4,22) (4,11) (4,8) (4,15) (4,10) (4,6) (5,17) (5,22) (5,11) (5,8) (5,15) (5,10) (5,6) (6,17) (6,22) (6,11) (6,8) (6,15) (6,10) (7,20) (7,19) (7,14) (7,9) (7,13) (7,21) (7,12) (7,18) (7,16) (8,17) (8,22) (8,11) (8,15) (8,10) (9,20) (9,19) (9,14) (9,13) (9,21) (9,12) (9,18) (9,16) (10,17) (10,22) (10,11) (10,15) (11,17) (11,22) (11,15) (12,20) (12,19) (12,14) (12,13) (12,21) (12,18) (12,16) (13,20) (13,19) (13,14) (13,21) (13,18) (13,16) (14,20) (14,19) (14,21) (14,18) (14,16) (15,17) (15,22) (16,20) (16,19) (16,21) (16,18) (17,22) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 22 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph540-3_10", + "image": "data/connectivity/graph_visual/medium/graph540.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,13) (0,22) (0,15) (0,1) (0,9) (0,14) (0,12) (0,20) (0,5) (0,4) (0,19) (0,18) (0,21) (1,13) (1,22) (1,15) (1,9) (1,14) (1,12) (1,20) (1,5) (1,4) (1,19) (1,18) (1,21) (2,6) (2,11) (2,10) (2,17) (2,7) (2,3) (3,6) (3,11) (3,10) (3,17) (3,7) (4,13) (4,22) (4,15) (4,9) (4,14) (4,12) (4,20) (4,5) (4,19) (4,18) (4,21) (5,13) (5,22) (5,15) (5,9) (5,14) (5,12) (5,20) (5,19) (5,18) (5,21) (6,11) (6,10) (6,17) (6,7) (7,11) (7,10) (7,17) (8,16) (9,13) (9,22) (9,15) (9,14) (9,12) (9,20) (9,19) (9,18) (9,21) (10,11) (10,17) (11,17) (12,13) (12,22) (12,15) (12,14) (12,20) (12,19) (12,18) (12,21) (13,22) (13,15) (13,14) (13,20) (13,19) (13,18) (13,21) (14,22) (14,15) (14,20) (14,19) (14,18) (14,21) (15,22) (15,20) (15,19) (15,18) (15,21) (18,22) (18,20) (18,19) (18,21) (19,22) (19,20) (19,21) (20,22) (20,21) (21,22)\nIs there a path between node 3 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph759-17_16", + "image": "data/connectivity/graph_visual/medium/graph759.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,4) (0,17) (0,13) (0,21) (0,2) (0,1) (0,24) (0,10) (0,5) (0,14) (0,12) (0,19) (1,4) (1,24) (1,5) (1,18) (1,14) (1,12) (1,19) (1,15) (2,17) (2,13) (2,21) (2,8) (2,14) (2,19) (2,15) (3,11) (3,20) (3,9) (3,6) (3,22) (3,16) (4,17) (4,13) (4,21) (4,24) (4,8) (4,10) (4,5) (4,18) (4,14) (4,12) (4,19) (4,15) (5,17) (5,13) (5,21) (5,8) (5,10) (5,14) (5,12) (5,19) (5,15) (6,11) (6,20) (6,22) (6,7) (6,23) (7,11) (7,9) (7,22) (7,16) (7,23) (8,17) (8,13) (8,18) (8,14) (8,12) (8,19) (8,15) (9,11) (9,20) (9,16) (9,23) (10,13) (10,21) (10,24) (10,18) (10,15) (11,22) (11,16) (12,17) (12,21) (12,24) (12,14) (12,19) (12,15) (13,21) (13,24) (13,18) (13,14) (13,19) (13,15) (14,17) (14,21) (14,24) (14,18) (14,19) (14,15) (15,21) (15,24) (15,18) (15,19) (16,20) (16,23) (17,21) (17,19) (18,21) (18,24) (18,19) (19,21) (19,24) (20,22) (20,23) (22,23)\nIs there a path between node 17 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph724-11_6", + "image": "data/connectivity/graph_visual/medium/graph724.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,10) (0,23) (0,13) (0,12) (0,18) (0,8) (0,4) (0,11) (0,9) (0,20) (0,5) (0,14) (0,24) (0,21) (0,1) (0,16) (0,2) (0,7) (0,22) (0,19) (1,15) (1,10) (1,23) (1,13) (1,12) (1,18) (1,8) (1,4) (1,11) (1,9) (1,20) (1,5) (1,14) (1,24) (1,21) (1,16) (1,2) (1,7) (1,22) (1,19) (2,15) (2,10) (2,23) (2,13) (2,12) (2,18) (2,8) (2,4) (2,11) (2,9) (2,20) (2,5) (2,14) (2,24) (2,21) (2,16) (2,7) (2,22) (2,19) (3,17) (3,6) (4,15) (4,10) (4,23) (4,13) (4,12) (4,18) (4,8) (4,11) (4,9) (4,20) (4,5) (4,14) (4,24) (4,21) (4,16) (4,7) (4,22) (4,19) (5,15) (5,10) (5,23) (5,13) (5,12) (5,18) (5,8) (5,11) (5,9) (5,20) (5,14) (5,24) (5,21) (5,16) (5,7) (5,22) (5,19) (6,17) (7,15) (7,10) (7,23) (7,13) (7,12) (7,18) (7,8) (7,11) (7,9) (7,20) (7,14) (7,24) (7,21) (7,16) (7,22) (7,19) (8,15) (8,10) (8,23) (8,13) (8,12) (8,18) (8,11) (8,9) (8,20) (8,14) (8,24) (8,21) (8,16) (8,22) (8,19) (9,15) (9,10) (9,23) (9,13) (9,12) (9,18) (9,11) (9,20) (9,14) (9,24) (9,21) (9,16) (9,22) (9,19) (10,15) (10,23) (10,13) (10,12) (10,18) (10,11) (10,20) (10,14) (10,24) (10,21) (10,16) (10,22) (10,19) (11,15) (11,23) (11,13) (11,12) (11,18) (11,20) (11,14) (11,24) (11,21) (11,16) (11,22) (11,19) (12,15) (12,23) (12,13) (12,18) (12,20) (12,14) (12,24) (12,21) (12,16) (12,22) (12,19) (13,15) (13,23) (13,18) (13,20) (13,14) (13,24) (13,21) (13,16) (13,22) (13,19) (14,15) (14,23) (14,18) (14,20) (14,24) (14,21) (14,16) (14,22) (14,19) (15,23) (15,18) (15,20) (15,24) (15,21) (15,16) (15,22) (15,19) (16,23) (16,18) (16,20) (16,24) (16,21) (16,22) (16,19) (18,23) (18,20) (18,24) (18,21) (18,22) (18,19) (19,23) (19,20) (19,24) (19,21) (19,22) (20,23) (20,24) (20,21) (20,22) (21,23) (21,24) (21,22) (22,23) (22,24) (23,24)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph538-19_13", + "image": "data/connectivity/graph_visual/medium/graph538.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,4) (0,11) (0,17) (0,18) (0,6) (0,10) (0,7) (0,12) (0,5) (0,21) (0,8) (0,13) (0,9) (0,3) (0,15) (0,14) (0,20) (0,2) (1,19) (1,16) (2,22) (2,4) (2,11) (2,17) (2,18) (2,6) (2,10) (2,7) (2,12) (2,5) (2,21) (2,8) (2,13) (2,9) (2,3) (2,15) (2,14) (2,20) (3,22) (3,4) (3,11) (3,17) (3,18) (3,6) (3,10) (3,7) (3,12) (3,5) (3,21) (3,8) (3,13) (3,9) (3,15) (3,14) (3,20) (4,22) (4,11) (4,17) (4,18) (4,6) (4,10) (4,7) (4,12) (4,5) (4,21) (4,8) (4,13) (4,9) (4,15) (4,14) (4,20) (5,22) (5,11) (5,17) (5,18) (5,6) (5,10) (5,7) (5,12) (5,21) (5,8) (5,13) (5,9) (5,15) (5,14) (5,20) (6,22) (6,11) (6,17) (6,18) (6,10) (6,7) (6,12) (6,21) (6,8) (6,13) (6,9) (6,15) (6,14) (6,20) (7,22) (7,11) (7,17) (7,18) (7,10) (7,12) (7,21) (7,8) (7,13) (7,9) (7,15) (7,14) (7,20) (8,22) (8,11) (8,17) (8,18) (8,10) (8,12) (8,21) (8,13) (8,9) (8,15) (8,14) (8,20) (9,22) (9,11) (9,17) (9,18) (9,10) (9,12) (9,21) (9,13) (9,15) (9,14) (9,20) (10,22) (10,11) (10,17) (10,18) (10,12) (10,21) (10,13) (10,15) (10,14) (10,20) (11,22) (11,17) (11,18) (11,12) (11,21) (11,13) (11,15) (11,14) (11,20) (12,22) (12,17) (12,18) (12,21) (12,13) (12,15) (12,14) (12,20) (13,22) (13,17) (13,18) (13,21) (13,15) (13,14) (13,20) (14,22) (14,17) (14,18) (14,21) (14,15) (14,20) (15,22) (15,17) (15,18) (15,21) (15,20) (16,19) (17,22) (17,18) (17,21) (17,20) (18,22) (18,21) (18,20) (20,22) (20,21) (21,22)\nIs there a path between node 19 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph279-14_10", + "image": "data/connectivity/graph_visual/medium/graph279.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,2) (0,14) (0,16) (0,7) (0,10) (1,12) (1,11) (1,13) (1,8) (1,17) (1,4) (2,19) (2,14) (2,16) (2,7) (2,10) (3,5) (3,15) (3,18) (3,6) (3,9) (4,12) (4,11) (4,13) (4,8) (4,17) (5,15) (5,18) (5,6) (5,9) (6,15) (6,18) (6,9) (7,19) (7,14) (7,16) (7,10) (8,12) (8,11) (8,13) (8,17) (9,15) (9,18) (10,19) (10,14) (10,16) (11,12) (11,13) (11,17) (12,13) (12,17) (13,17) (14,19) (14,16) (15,18) (16,19)\nIs there a path between node 14 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph385-20_0", + "image": "data/connectivity/graph_visual/medium/graph385.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,14) (0,17) (0,19) (0,9) (0,5) (0,2) (0,4) (0,7) (0,8) (0,13) (0,12) (0,10) (0,1) (0,15) (0,11) (0,16) (0,18) (0,6) (1,14) (1,17) (1,19) (1,9) (1,5) (1,2) (1,4) (1,7) (1,8) (1,13) (1,12) (1,10) (1,15) (1,11) (1,16) (1,18) (1,6) (2,14) (2,17) (2,19) (2,9) (2,5) (2,4) (2,7) (2,8) (2,13) (2,12) (2,10) (2,15) (2,11) (2,16) (2,18) (2,6) (3,20) (4,14) (4,17) (4,19) (4,9) (4,5) (4,7) (4,8) (4,13) (4,12) (4,10) (4,15) (4,11) (4,16) (4,18) (4,6) (5,14) (5,17) (5,19) (5,9) (5,7) (5,8) (5,13) (5,12) (5,10) (5,15) (5,11) (5,16) (5,18) (5,6) (6,14) (6,17) (6,19) (6,9) (6,7) (6,8) (6,13) (6,12) (6,10) (6,15) (6,11) (6,16) (6,18) (7,14) (7,17) (7,19) (7,9) (7,8) (7,13) (7,12) (7,10) (7,15) (7,11) (7,16) (7,18) (8,14) (8,17) (8,19) (8,9) (8,13) (8,12) (8,10) (8,15) (8,11) (8,16) (8,18) (9,14) (9,17) (9,19) (9,13) (9,12) (9,10) (9,15) (9,11) (9,16) (9,18) (10,14) (10,17) (10,19) (10,13) (10,12) (10,15) (10,11) (10,16) (10,18) (11,14) (11,17) (11,19) (11,13) (11,12) (11,15) (11,16) (11,18) (12,14) (12,17) (12,19) (12,13) (12,15) (12,16) (12,18) (13,14) (13,17) (13,19) (13,15) (13,16) (13,18) (14,17) (14,19) (14,15) (14,16) (14,18) (15,17) (15,19) (15,16) (15,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nIs there a path between node 20 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph465-12_19", + "image": "data/connectivity/graph_visual/medium/graph465.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,14) (0,3) (0,12) (1,21) (1,18) (1,2) (1,17) (1,9) (1,20) (2,21) (2,18) (2,17) (2,9) (2,20) (3,14) (3,12) (4,16) (4,6) (4,5) (4,10) (4,19) (4,7) (4,13) (4,15) (4,11) (4,8) (5,16) (5,6) (5,10) (5,19) (5,7) (5,13) (5,15) (5,11) (5,8) (6,16) (6,10) (6,19) (6,7) (6,13) (6,15) (6,11) (6,8) (7,16) (7,10) (7,19) (7,13) (7,15) (7,11) (7,8) (8,16) (8,10) (8,19) (8,13) (8,15) (8,11) (9,21) (9,18) (9,17) (9,20) (10,16) (10,19) (10,13) (10,15) (10,11) (11,16) (11,19) (11,13) (11,15) (12,14) (13,16) (13,19) (13,15) (15,16) (15,19) (16,19) (17,21) (17,18) (17,20) (18,21) (18,20) (20,21)\nIs there a path between node 12 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph13-6_4", + "image": "data/connectivity/graph_visual/medium/graph13.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (0,7) (0,10) (0,2) (1,8) (1,4) (1,9) (1,3) (1,5) (2,6) (2,7) (2,10) (3,8) (3,4) (3,9) (3,5) (4,8) (4,9) (4,5) (5,8) (5,9) (6,7) (6,10) (7,10) (8,9)\nIs there a path between node 6 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph304-13_17", + "image": "data/connectivity/graph_visual/medium/graph304.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,4) (0,6) (0,9) (0,7) (0,18) (0,10) (0,15) (0,16) (0,13) (0,1) (0,11) (0,2) (0,8) (0,19) (1,5) (1,6) (1,12) (1,7) (1,18) (1,10) (1,15) (1,17) (1,13) (1,11) (1,2) (1,8) (1,19) (2,4) (2,5) (2,12) (2,9) (2,7) (2,18) (2,10) (2,15) (2,17) (2,8) (2,19) (3,14) (4,5) (4,6) (4,12) (4,9) (4,7) (4,10) (4,15) (4,17) (4,16) (4,13) (4,8) (4,19) (5,6) (5,12) (5,9) (5,7) (5,10) (5,15) (5,17) (5,16) (5,13) (5,19) (6,12) (6,7) (6,18) (6,10) (6,15) (6,16) (6,11) (6,8) (6,19) (7,9) (7,10) (7,13) (7,8) (7,19) (8,12) (8,9) (8,15) (8,17) (8,16) (8,11) (8,19) (9,12) (9,18) (9,10) (9,15) (9,17) (9,16) (9,13) (9,11) (10,12) (10,18) (10,15) (10,17) (10,16) (10,13) (10,19) (11,12) (11,18) (11,15) (11,17) (12,17) (12,16) (12,13) (13,18) (13,15) (13,17) (13,16) (15,17) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19)\nIs there a path between node 13 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph750-12_2", + "image": "data/connectivity/graph_visual/medium/graph750.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,22) (0,19) (0,13) (0,3) (0,16) (0,24) (0,1) (0,4) (0,7) (0,6) (0,15) (0,9) (1,11) (1,2) (1,22) (1,10) (1,5) (1,14) (1,13) (1,3) (1,16) (1,24) (1,7) (1,6) (1,20) (1,9) (2,11) (2,22) (2,10) (2,5) (2,14) (2,13) (2,3) (2,16) (2,18) (2,24) (2,4) (2,7) (2,6) (2,15) (2,20) (2,9) (3,11) (3,22) (3,19) (3,10) (3,5) (3,13) (3,18) (3,24) (3,7) (3,6) (3,15) (3,20) (3,9) (4,22) (4,19) (4,5) (4,14) (4,13) (4,16) (4,18) (4,20) (4,9) (5,22) (5,19) (5,10) (5,13) (5,16) (5,18) (5,24) (5,6) (5,15) (6,11) (6,22) (6,19) (6,10) (6,16) (6,18) (6,24) (6,7) (6,15) (6,9) (7,11) (7,22) (7,19) (7,10) (7,14) (7,13) (7,18) (7,24) (7,15) (7,20) (7,9) (8,23) (8,17) (9,22) (9,19) (9,10) (9,14) (9,18) (9,24) (9,15) (9,20) (10,11) (10,22) (10,19) (10,14) (10,13) (10,16) (10,18) (10,24) (10,15) (10,20) (11,22) (11,19) (11,14) (11,13) (11,16) (11,24) (11,15) (11,20) (12,23) (12,21) (13,19) (13,16) (13,18) (13,24) (13,15) (13,20) (14,22) (14,16) (14,18) (14,15) (14,20) (15,16) (15,18) (15,24) (16,22) (16,19) (16,18) (16,24) (17,23) (17,21) (18,19) (19,22) (19,24) (19,20) (20,22) (20,24)\nIs there a path between node 12 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph643-1_4", + "image": "data/connectivity/graph_visual/medium/graph643.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,18) (0,5) (2,3) (2,7) (2,15) (2,18) (3,16) (3,7) (3,15) (3,21) (4,8) (5,7) (6,16) (6,22) (6,18) (8,23) (9,11) (10,23) (11,20) (12,13) (15,22) (15,21) (16,22) (17,22) (17,21) (19,23) (20,23)\nIs there a path between node 1 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph31-8_4", + "image": "data/connectivity/graph_visual/medium/graph31.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,6) (0,9) (0,11) (1,7) (1,3) (1,4) (1,5) (1,8) (1,2) (1,10) (2,7) (2,3) (2,4) (2,5) (2,8) (2,10) (3,7) (3,4) (3,5) (3,8) (3,10) (4,7) (4,5) (4,8) (4,10) (5,7) (5,8) (5,10) (6,9) (6,11) (7,8) (7,10) (8,10) (9,11)\nIs there a path between node 8 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph762-21_16", + "image": "data/connectivity/graph_visual/medium/graph762.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,24) (0,4) (0,17) (0,22) (0,7) (0,23) (0,9) (0,8) (0,3) (0,1) (0,10) (0,19) (0,6) (1,12) (1,24) (1,4) (1,17) (1,5) (1,22) (1,16) (1,23) (1,9) (1,14) (1,3) (1,13) (1,21) (1,10) (1,19) (1,6) (2,15) (2,18) (2,11) (3,12) (3,24) (3,4) (3,17) (3,22) (3,7) (3,16) (3,20) (3,13) (3,21) (4,12) (4,24) (4,5) (4,16) (4,20) (4,23) (4,13) (4,21) (4,10) (4,19) (4,6) (5,12) (5,24) (5,17) (5,22) (5,16) (5,20) (5,23) (5,9) (5,8) (5,13) (5,10) (5,6) (6,12) (6,24) (6,17) (6,22) (6,7) (6,20) (6,23) (6,8) (6,14) (6,13) (6,21) (7,12) (7,24) (7,17) (7,16) (7,23) (7,14) (7,13) (7,21) (7,10) (7,19) (8,12) (8,24) (8,17) (8,22) (8,16) (8,20) (8,23) (8,14) (8,13) (8,21) (8,10) (9,12) (9,24) (9,17) (9,22) (9,20) (9,14) (9,13) (9,21) (9,10) (9,19) (10,17) (10,16) (10,23) (10,14) (10,13) (11,18) (12,17) (12,22) (12,16) (12,23) (12,13) (12,19) (13,24) (13,16) (13,20) (13,21) (13,19) (14,24) (14,17) (14,22) (14,16) (14,21) (16,24) (16,20) (16,23) (16,19) (17,24) (17,22) (17,20) (17,23) (17,21) (17,19) (19,24) (19,22) (19,21) (20,24) (20,22) (20,23) (20,21) (21,24) (21,23) (22,24)\nIs there a path between node 21 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph333-12_5", + "image": "data/connectivity/graph_visual/medium/graph333.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,14) (0,7) (0,2) (1,9) (1,13) (2,19) (2,3) (3,16) (3,17) (3,19) (3,6) (4,16) (4,20) (4,17) (4,14) (4,18) (5,12) (5,13) (6,12) (6,19) (6,10) (6,9) (6,7) (6,13) (7,16) (9,16) (9,12) (9,18) (10,12) (10,17) (10,15) (10,14) (10,13) (12,16) (13,17) (13,18) (14,17) (14,18) (15,19) (16,19) (17,20) (17,18)\nIs there a path between node 12 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph736-24_19", + "image": "data/connectivity/graph_visual/medium/graph736.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,9) (2,24) (2,5) (2,21) (2,19) (2,23) (2,4) (3,17) (3,7) (4,14) (4,5) (4,21) (4,15) (4,23) (5,10) (5,24) (5,6) (5,15) (6,15) (6,23) (7,16) (8,11) (8,13) (10,14) (11,22) (11,12) (13,22) (13,18) (13,20) (14,15) (14,23) (15,24) (15,21) (16,17) (18,20)\nIs there a path between node 24 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph424-5_16", + "image": "data/connectivity/graph_visual/medium/graph424.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,13) (2,4) (2,11) (2,5) (2,21) (3,6) (3,5) (3,17) (4,12) (4,11) (4,20) (4,21) (5,12) (5,10) (5,7) (6,20) (6,17) (7,12) (7,8) (7,20) (7,10) (7,17) (8,10) (8,21) (10,11) (10,20) (11,12) (12,20) (13,18) (14,19) (16,19)\nIs there a path between node 5 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph450-13_18", + "image": "data/connectivity/graph_visual/medium/graph450.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,10) (0,20) (0,12) (0,2) (1,13) (1,19) (1,10) (1,9) (1,7) (1,2) (2,13) (2,19) (2,10) (2,20) (2,7) (3,21) (3,8) (3,4) (3,17) (4,21) (4,8) (4,17) (5,11) (5,14) (5,16) (5,15) (6,11) (6,14) (6,16) (6,18) (6,15) (7,13) (7,19) (7,20) (8,17) (9,13) (10,19) (11,18) (12,13) (12,20) (13,19) (13,20) (14,16) (14,18) (14,15) (15,16) (17,21) (19,20)\nIs there a path between node 13 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph422-8_3", + "image": "data/connectivity/graph_visual/medium/graph422.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,20) (0,18) (0,4) (0,8) (0,1) (0,17) (0,15) (0,11) (0,21) (0,9) (0,12) (0,14) (0,3) (1,19) (1,20) (1,18) (1,4) (1,8) (1,17) (1,15) (1,11) (1,21) (1,9) (1,12) (1,14) (1,3) (2,5) (2,7) (2,13) (2,6) (2,10) (2,16) (3,19) (3,20) (3,18) (3,4) (3,8) (3,17) (3,15) (3,11) (3,21) (3,9) (3,12) (3,14) (4,19) (4,20) (4,18) (4,8) (4,17) (4,15) (4,11) (4,21) (4,9) (4,12) (4,14) (5,7) (5,13) (5,6) (5,10) (5,16) (6,7) (6,13) (6,10) (6,16) (7,13) (7,10) (7,16) (8,19) (8,20) (8,18) (8,17) (8,15) (8,11) (8,21) (8,9) (8,12) (8,14) (9,19) (9,20) (9,18) (9,17) (9,15) (9,11) (9,21) (9,12) (9,14) (10,13) (10,16) (11,19) (11,20) (11,18) (11,17) (11,15) (11,21) (11,12) (11,14) (12,19) (12,20) (12,18) (12,17) (12,15) (12,21) (12,14) (13,16) (14,19) (14,20) (14,18) (14,17) (14,15) (14,21) (15,19) (15,20) (15,18) (15,17) (15,21) (17,19) (17,20) (17,18) (17,21) (18,19) (18,20) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 8 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph59-0_7", + "image": "data/connectivity/graph_visual/medium/graph59.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,6) (0,4) (0,1) (0,11) (0,9) (0,12) (1,2) (1,4) (1,11) (1,9) (1,13) (1,8) (1,12) (2,6) (2,3) (2,4) (2,11) (2,9) (2,13) (2,8) (3,6) (3,9) (3,13) (3,8) (3,12) (4,6) (4,11) (4,9) (4,13) (4,8) (4,12) (5,7) (5,10) (6,11) (6,9) (6,8) (6,12) (8,9) (8,12) (9,11) (9,12) (11,13) (12,13)\nIs there a path between node 0 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph679-11_10", + "image": "data/connectivity/graph_visual/medium/graph679.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (0,20) (0,18) (0,16) (0,17) (0,12) (0,19) (0,9) (0,4) (0,14) (0,23) (0,7) (0,2) (0,5) (0,8) (0,1) (0,22) (0,6) (0,21) (0,11) (1,13) (1,20) (1,18) (1,16) (1,17) (1,12) (1,19) (1,9) (1,4) (1,14) (1,23) (1,7) (1,2) (1,5) (1,8) (1,22) (1,6) (1,21) (1,11) (2,13) (2,20) (2,18) (2,16) (2,17) (2,12) (2,19) (2,9) (2,4) (2,14) (2,23) (2,7) (2,5) (2,8) (2,22) (2,6) (2,21) (2,11) (3,15) (4,13) (4,20) (4,18) (4,16) (4,17) (4,12) (4,19) (4,9) (4,14) (4,23) (4,7) (4,5) (4,8) (4,22) (4,6) (4,21) (4,11) (5,13) (5,20) (5,18) (5,16) (5,17) (5,12) (5,19) (5,9) (5,14) (5,23) (5,7) (5,8) (5,22) (5,6) (5,21) (5,11) (6,13) (6,20) (6,18) (6,16) (6,17) (6,12) (6,19) (6,9) (6,14) (6,23) (6,7) (6,8) (6,22) (6,21) (6,11) (7,13) (7,20) (7,18) (7,16) (7,17) (7,12) (7,19) (7,9) (7,14) (7,23) (7,8) (7,22) (7,21) (7,11) (8,13) (8,20) (8,18) (8,16) (8,17) (8,12) (8,19) (8,9) (8,14) (8,23) (8,22) (8,21) (8,11) (9,13) (9,20) (9,18) (9,16) (9,17) (9,12) (9,19) (9,14) (9,23) (9,22) (9,21) (9,11) (11,13) (11,20) (11,18) (11,16) (11,17) (11,12) (11,19) (11,14) (11,23) (11,22) (11,21) (12,13) (12,20) (12,18) (12,16) (12,17) (12,19) (12,14) (12,23) (12,22) (12,21) (13,20) (13,18) (13,16) (13,17) (13,19) (13,14) (13,23) (13,22) (13,21) (14,20) (14,18) (14,16) (14,17) (14,19) (14,23) (14,22) (14,21) (16,20) (16,18) (16,17) (16,19) (16,23) (16,22) (16,21) (17,20) (17,18) (17,19) (17,23) (17,22) (17,21) (18,20) (18,19) (18,23) (18,22) (18,21) (19,20) (19,23) (19,22) (19,21) (20,23) (20,22) (20,21) (21,23) (21,22) (22,23)\nIs there a path between node 11 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph717-7_4", + "image": "data/connectivity/graph_visual/medium/graph717.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,13) (0,6) (0,16) (0,20) (1,21) (1,18) (1,2) (1,23) (1,7) (1,5) (1,11) (1,9) (1,3) (1,19) (1,14) (1,24) (2,4) (2,22) (2,18) (2,23) (2,5) (2,11) (2,19) (3,18) (3,5) (3,11) (3,19) (3,24) (4,21) (4,22) (4,8) (4,18) (4,23) (4,7) (4,5) (4,9) (4,14) (5,8) (5,7) (5,11) (5,9) (5,19) (6,10) (6,13) (6,16) (6,20) (6,12) (6,15) (7,21) (7,8) (7,23) (7,11) (7,9) (7,19) (8,18) (8,11) (8,14) (8,24) (9,21) (9,22) (9,18) (9,19) (9,14) (9,24) (10,13) (10,20) (10,15) (11,21) (11,22) (11,18) (11,23) (11,14) (12,13) (12,16) (12,20) (13,16) (13,15) (14,22) (14,18) (14,19) (14,24) (15,16) (15,20) (16,20) (18,22) (18,23) (18,19) (18,24) (19,22) (19,23) (19,24) (21,22) (22,23) (22,24) (23,24)\nIs there a path between node 7 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph149-8_14", + "image": "data/connectivity/graph_visual/medium/graph149.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,10) (0,17) (0,5) (0,13) (0,15) (0,16) (0,3) (0,7) (0,11) (0,1) (0,4) (0,14) (1,12) (1,10) (1,17) (1,5) (1,13) (1,15) (1,16) (1,3) (1,7) (1,11) (1,4) (1,14) (2,8) (2,6) (3,12) (3,10) (3,17) (3,5) (3,13) (3,15) (3,16) (3,7) (3,11) (3,4) (3,14) (4,12) (4,10) (4,17) (4,5) (4,13) (4,15) (4,16) (4,7) (4,11) (4,14) (5,12) (5,10) (5,17) (5,13) (5,15) (5,16) (5,7) (5,11) (5,14) (6,8) (7,12) (7,10) (7,17) (7,13) (7,15) (7,16) (7,11) (7,14) (10,12) (10,17) (10,13) (10,15) (10,16) (10,11) (10,14) (11,12) (11,17) (11,13) (11,15) (11,16) (11,14) (12,17) (12,13) (12,15) (12,16) (12,14) (13,17) (13,15) (13,16) (13,14) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 8 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph744-10_7", + "image": "data/connectivity/graph_visual/medium/graph744.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,15) (0,16) (0,1) (0,2) (0,12) (0,3) (1,15) (1,21) (1,12) (1,20) (1,23) (2,11) (2,21) (2,7) (2,12) (2,3) (2,23) (3,9) (3,14) (3,16) (3,5) (3,18) (3,12) (3,22) (4,14) (4,15) (4,21) (4,16) (4,18) (4,12) (4,23) (5,7) (5,18) (5,23) (7,8) (7,16) (7,12) (8,9) (8,11) (8,18) (8,12) (8,20) (9,24) (9,18) (9,12) (9,23) (11,21) (12,15) (12,21) (12,16) (12,18) (12,22) (14,24) (14,15) (14,21) (15,24) (15,19) (15,22) (16,22) (16,23) (18,21) (18,19) (19,21) (20,22) (21,23) (22,24)\nIs there a path between node 10 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph616-10_15", + "image": "data/connectivity/graph_visual/medium/graph616.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,9) (0,12) (0,4) (0,11) (0,14) (0,3) (0,17) (0,22) (0,2) (0,19) (0,15) (0,20) (0,1) (0,16) (0,13) (0,7) (1,5) (1,9) (1,12) (1,4) (1,11) (1,14) (1,3) (1,17) (1,22) (1,2) (1,19) (1,15) (1,20) (1,16) (1,13) (1,7) (2,5) (2,9) (2,12) (2,4) (2,11) (2,14) (2,3) (2,17) (2,22) (2,19) (2,15) (2,20) (2,16) (2,13) (2,7) (3,5) (3,9) (3,12) (3,4) (3,11) (3,14) (3,17) (3,22) (3,19) (3,15) (3,20) (3,16) (3,13) (3,7) (4,5) (4,9) (4,12) (4,11) (4,14) (4,17) (4,22) (4,19) (4,15) (4,20) (4,16) (4,13) (4,7) (5,9) (5,12) (5,11) (5,14) (5,17) (5,22) (5,19) (5,15) (5,20) (5,16) (5,13) (5,7) (6,18) (6,21) (6,8) (6,10) (6,23) (7,9) (7,12) (7,11) (7,14) (7,17) (7,22) (7,19) (7,15) (7,20) (7,16) (7,13) (8,18) (8,21) (8,10) (8,23) (9,12) (9,11) (9,14) (9,17) (9,22) (9,19) (9,15) (9,20) (9,16) (9,13) (10,18) (10,21) (10,23) (11,12) (11,14) (11,17) (11,22) (11,19) (11,15) (11,20) (11,16) (11,13) (12,14) (12,17) (12,22) (12,19) (12,15) (12,20) (12,16) (12,13) (13,14) (13,17) (13,22) (13,19) (13,15) (13,20) (13,16) (14,17) (14,22) (14,19) (14,15) (14,20) (14,16) (15,17) (15,22) (15,19) (15,20) (15,16) (16,17) (16,22) (16,19) (16,20) (17,22) (17,19) (17,20) (18,21) (18,23) (19,22) (19,20) (20,22) (21,23)\nIs there a path between node 10 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph588-10_12", + "image": "data/connectivity/graph_visual/medium/graph588.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (1,5) (1,12) (1,3) (1,17) (1,15) (1,16) (2,21) (2,9) (2,11) (2,13) (2,4) (2,14) (3,23) (3,13) (3,15) (3,19) (3,14) (4,5) (4,12) (4,9) (4,17) (4,11) (5,8) (5,12) (5,22) (5,16) (5,14) (6,10) (7,18) (7,10) (8,12) (8,17) (8,23) (8,11) (8,16) (9,22) (9,13) (11,21) (11,15) (12,17) (12,23) (12,16) (12,14) (13,22) (13,23) (13,19) (13,16) (14,20) (14,22) (14,17) (15,20) (15,19) (16,22) (16,17) (16,23) (16,19) (19,23) (20,22) (22,23)\nIs there a path between node 10 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph228-0_8", + "image": "data/connectivity/graph_visual/medium/graph228.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,9) (0,15) (1,14) (1,17) (2,12) (3,14) (3,16) (4,18) (7,13) (8,16) (8,11) (8,10) (9,12) (11,14) (15,18)\nIs there a path between node 0 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph77-6_7", + "image": "data/connectivity/graph_visual/medium/graph77.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,11) (0,10) (1,8) (1,9) (2,13) (2,7) (2,12) (3,11) (4,14) (4,5) (6,14) (7,11) (7,12) (8,14)\nIs there a path between node 6 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph268-5_3", + "image": "data/connectivity/graph_visual/medium/graph268.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,6) (0,16) (0,9) (0,3) (0,4) (0,8) (0,17) (1,6) (1,12) (1,13) (1,18) (1,2) (1,4) (1,8) (1,17) (2,6) (2,12) (2,15) (2,9) (2,13) (2,18) (2,4) (2,8) (2,17) (3,6) (3,16) (3,12) (3,9) (3,13) (3,18) (3,8) (3,17) (3,5) (4,6) (4,16) (4,12) (4,9) (4,18) (4,17) (4,5) (5,6) (5,12) (5,15) (5,9) (5,17) (6,12) (6,15) (6,9) (6,13) (6,18) (6,8) (7,10) (7,11) (7,19) (8,16) (8,15) (8,9) (8,18) (9,16) (9,12) (9,15) (9,13) (9,18) (9,17) (10,19) (11,14) (11,19) (12,16) (12,15) (12,13) (12,17) (13,18) (14,19) (15,17) (16,17) (17,18)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph371-3_7", + "image": "data/connectivity/graph_visual/medium/graph371.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,15) (0,10) (0,19) (0,5) (0,16) (0,3) (0,12) (0,11) (0,8) (1,17) (1,13) (1,14) (1,7) (2,15) (2,10) (2,6) (2,4) (2,9) (2,19) (2,5) (2,3) (2,18) (2,12) (2,8) (3,15) (3,6) (3,4) (3,9) (3,19) (3,5) (3,16) (3,20) (3,18) (3,11) (3,8) (4,15) (4,10) (4,6) (4,20) (4,18) (4,12) (4,8) (5,15) (5,10) (5,6) (5,9) (5,16) (5,20) (5,18) (5,8) (6,15) (6,10) (6,19) (6,16) (6,12) (6,11) (6,8) (7,17) (8,10) (8,19) (8,16) (8,20) (8,18) (8,11) (9,15) (9,10) (9,20) (9,12) (9,11) (10,15) (10,19) (10,20) (10,18) (10,12) (10,11) (11,15) (11,19) (11,20) (11,18) (11,12) (12,19) (12,16) (12,20) (12,18) (13,17) (13,14) (15,19) (15,20) (15,18) (16,19) (16,20) (18,19) (18,20) (19,20)\nIs there a path between node 3 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph696-21_1", + "image": "data/connectivity/graph_visual/medium/graph696.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,17) (0,12) (0,5) (0,7) (0,20) (0,13) (0,14) (0,8) (0,9) (0,19) (0,4) (0,21) (0,1) (1,15) (1,17) (1,12) (1,5) (1,7) (1,20) (1,13) (1,14) (1,8) (1,9) (1,19) (1,4) (1,21) (2,6) (2,18) (2,23) (2,3) (2,16) (2,11) (2,22) (2,10) (3,6) (3,18) (3,23) (3,16) (3,11) (3,22) (3,10) (4,15) (4,17) (4,12) (4,5) (4,7) (4,20) (4,13) (4,14) (4,8) (4,9) (4,19) (4,21) (5,15) (5,17) (5,12) (5,7) (5,20) (5,13) (5,14) (5,8) (5,9) (5,19) (5,21) (6,18) (6,23) (6,16) (6,11) (6,22) (6,10) (7,15) (7,17) (7,12) (7,20) (7,13) (7,14) (7,8) (7,9) (7,19) (7,21) (8,15) (8,17) (8,12) (8,20) (8,13) (8,14) (8,9) (8,19) (8,21) (9,15) (9,17) (9,12) (9,20) (9,13) (9,14) (9,19) (9,21) (10,18) (10,23) (10,16) (10,11) (10,22) (11,18) (11,23) (11,16) (11,22) (12,15) (12,17) (12,20) (12,13) (12,14) (12,19) (12,21) (13,15) (13,17) (13,20) (13,14) (13,19) (13,21) (14,15) (14,17) (14,20) (14,19) (14,21) (15,17) (15,20) (15,19) (15,21) (16,18) (16,23) (16,22) (17,20) (17,19) (17,21) (18,23) (18,22) (19,20) (19,21) (20,21) (22,23)\nIs there a path between node 21 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph110-3_8", + "image": "data/connectivity/graph_visual/medium/graph110.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,12) (0,14) (0,10) (0,3) (0,2) (0,8) (0,15) (0,4) (0,11) (0,13) (0,5) (1,6) (1,9) (1,7) (2,12) (2,14) (2,10) (2,3) (2,8) (2,15) (2,4) (2,11) (2,13) (2,5) (3,12) (3,14) (3,10) (3,8) (3,15) (3,4) (3,11) (3,13) (3,5) (4,12) (4,14) (4,10) (4,8) (4,15) (4,11) (4,13) (4,5) (5,12) (5,14) (5,10) (5,8) (5,15) (5,11) (5,13) (6,9) (6,7) (7,9) (8,12) (8,14) (8,10) (8,15) (8,11) (8,13) (10,12) (10,14) (10,15) (10,11) (10,13) (11,12) (11,14) (11,15) (11,13) (12,14) (12,15) (12,13) (13,14) (13,15) (14,15)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph517-3_18", + "image": "data/connectivity/graph_visual/medium/graph517.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,9) (0,17) (0,20) (1,15) (1,22) (1,14) (1,3) (1,21) (1,5) (1,18) (1,7) (1,6) (1,13) (2,15) (2,3) (2,4) (2,11) (2,21) (2,18) (2,8) (2,13) (3,15) (3,22) (3,12) (3,14) (3,4) (3,11) (3,21) (3,5) (3,7) (3,6) (3,16) (4,15) (4,22) (4,12) (4,14) (4,11) (4,5) (4,7) (4,6) (4,16) (4,8) (4,13) (5,15) (5,22) (5,12) (5,11) (5,21) (5,7) (5,6) (5,8) (5,13) (6,15) (6,12) (6,11) (6,21) (6,18) (6,16) (6,8) (6,13) (7,22) (7,12) (7,14) (7,11) (7,21) (7,16) (7,8) (8,22) (8,14) (8,21) (8,18) (8,16) (8,13) (9,19) (9,10) (9,17) (10,17) (11,22) (11,14) (11,21) (11,18) (11,13) (12,22) (12,14) (12,21) (12,18) (12,16) (12,13) (13,14) (13,18) (13,16) (14,15) (14,21) (14,18) (14,16) (15,21) (16,18) (17,20) (18,22)\nIs there a path between node 3 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph733-11_7", + "image": "data/connectivity/graph_visual/medium/graph733.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,18) (0,19) (0,22) (0,16) (1,10) (1,17) (1,16) (2,14) (2,22) (2,4) (3,9) (3,12) (3,18) (3,19) (3,22) (3,17) (3,20) (3,16) (4,24) (4,18) (4,5) (4,14) (4,20) (5,24) (5,19) (5,20) (6,10) (6,16) (7,9) (7,12) (7,14) (9,18) (9,19) (9,13) (10,17) (12,14) (12,19) (13,24) (13,18) (13,14) (14,18) (14,17) (14,16) (16,24) (16,19) (16,22) (17,24) (17,20)\nIs there a path between node 11 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph174-9_10", + "image": "data/connectivity/graph_visual/medium/graph174.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,9) (0,7) (0,10) (1,14) (1,9) (1,7) (1,12) (1,10) (2,5) (2,16) (2,8) (2,4) (3,11) (4,17) (4,6) (4,16) (4,8) (5,6) (5,16) (6,16) (7,9) (7,12) (7,13) (7,10) (8,16) (9,12) (10,14) (10,12) (10,13) (11,15) (12,14) (12,13) (13,14)\nIs there a path between node 9 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph778-23_10", + "image": "data/connectivity/graph_visual/medium/graph778.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,13) (0,16) (0,19) (0,12) (0,15) (0,22) (0,5) (0,4) (0,6) (0,11) (1,18) (1,14) (2,3) (2,8) (2,17) (2,24) (2,23) (2,21) (2,10) (2,20) (3,8) (3,17) (3,24) (3,23) (3,21) (3,10) (3,20) (4,9) (4,13) (4,16) (4,19) (4,12) (4,15) (4,22) (4,5) (4,6) (4,11) (5,9) (5,13) (5,16) (5,19) (5,12) (5,15) (5,22) (5,6) (5,11) (6,9) (6,13) (6,16) (6,19) (6,12) (6,15) (6,22) (6,11) (8,17) (8,24) (8,23) (8,21) (8,10) (8,20) (9,13) (9,16) (9,19) (9,12) (9,15) (9,22) (9,11) (10,17) (10,24) (10,23) (10,21) (10,20) (11,13) (11,16) (11,19) (11,12) (11,15) (11,22) (12,13) (12,16) (12,19) (12,15) (12,22) (13,16) (13,19) (13,15) (13,22) (14,18) (15,16) (15,19) (15,22) (16,19) (16,22) (17,24) (17,23) (17,21) (17,20) (19,22) (20,24) (20,23) (20,21) (21,24) (21,23) (23,24)\nIs there a path between node 23 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph209-2_12", + "image": "data/connectivity/graph_visual/medium/graph209.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,7) (0,6) (0,13) (0,12) (0,9) (0,18) (0,15) (0,17) (1,16) (1,2) (1,3) (2,3) (4,11) (4,8) (4,7) (4,9) (4,18) (4,14) (4,15) (5,8) (5,12) (5,10) (5,15) (6,11) (6,8) (6,7) (6,12) (6,18) (6,10) (6,14) (6,15) (6,17) (7,11) (7,8) (7,13) (7,12) (7,9) (7,10) (7,14) (7,15) (8,13) (8,12) (8,9) (8,18) (8,14) (8,17) (9,11) (9,12) (9,18) (9,10) (9,14) (9,15) (9,17) (10,11) (10,13) (10,18) (10,14) (10,17) (11,13) (11,18) (11,14) (12,18) (12,15) (12,17) (13,18) (13,14) (13,15) (14,18) (14,15) (14,17) (15,18) (15,17) (17,18)\nIs there a path between node 2 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph651-6_18", + "image": "data/connectivity/graph_visual/medium/graph651.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,4) (0,11) (0,18) (0,2) (0,8) (0,19) (0,23) (0,13) (0,7) (0,3) (0,16) (1,21) (1,22) (1,14) (1,17) (2,9) (2,4) (2,11) (2,18) (2,8) (2,19) (2,23) (2,13) (2,7) (2,3) (2,6) (3,9) (3,4) (3,11) (3,18) (3,8) (3,23) (3,13) (3,7) (3,6) (4,9) (4,11) (4,18) (4,23) (5,20) (5,10) (6,9) (6,18) (6,8) (6,13) (6,7) (6,16) (7,9) (7,11) (7,18) (7,8) (7,19) (7,23) (7,13) (7,16) (8,9) (8,11) (8,18) (8,19) (8,23) (8,13) (9,19) (9,23) (9,13) (11,18) (11,19) (11,23) (11,16) (12,21) (12,22) (12,15) (13,19) (13,23) (14,21) (14,22) (14,15) (15,21) (15,22) (16,18) (16,23) (17,21) (18,19) (19,23) (21,22)\nIs there a path between node 6 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph762-15_4", + "image": "data/connectivity/graph_visual/medium/graph762.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,24) (0,4) (0,17) (0,22) (0,7) (0,23) (0,9) (0,8) (0,3) (0,1) (0,10) (0,19) (0,6) (1,12) (1,24) (1,4) (1,17) (1,5) (1,22) (1,16) (1,23) (1,9) (1,14) (1,3) (1,13) (1,21) (1,10) (1,19) (1,6) (2,15) (2,18) (2,11) (3,12) (3,24) (3,4) (3,17) (3,22) (3,7) (3,16) (3,20) (3,13) (3,21) (4,12) (4,24) (4,5) (4,16) (4,20) (4,23) (4,13) (4,21) (4,10) (4,19) (4,6) (5,12) (5,24) (5,17) (5,22) (5,16) (5,20) (5,23) (5,9) (5,8) (5,13) (5,10) (5,6) (6,12) (6,24) (6,17) (6,22) (6,7) (6,20) (6,23) (6,8) (6,14) (6,13) (6,21) (7,12) (7,24) (7,17) (7,16) (7,23) (7,14) (7,13) (7,21) (7,10) (7,19) (8,12) (8,24) (8,17) (8,22) (8,16) (8,20) (8,23) (8,14) (8,13) (8,21) (8,10) (9,12) (9,24) (9,17) (9,22) (9,20) (9,14) (9,13) (9,21) (9,10) (9,19) (10,17) (10,16) (10,23) (10,14) (10,13) (11,18) (12,17) (12,22) (12,16) (12,23) (12,13) (12,19) (13,24) (13,16) (13,20) (13,21) (13,19) (14,24) (14,17) (14,22) (14,16) (14,21) (16,24) (16,20) (16,23) (16,19) (17,24) (17,22) (17,20) (17,23) (17,21) (17,19) (19,24) (19,22) (19,21) (20,24) (20,22) (20,23) (20,21) (21,24) (21,23) (22,24)\nIs there a path between node 15 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph26-8_3", + "image": "data/connectivity/graph_visual/medium/graph26.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,10) (0,5) (0,8) (0,11) (0,2) (0,6) (0,9) (1,5) (1,8) (1,9) (2,8) (2,3) (2,11) (2,9) (3,5) (3,8) (3,11) (3,6) (3,9) (4,7) (5,10) (5,8) (6,8) (6,9) (8,10) (9,10) (9,11) (10,11)\nIs there a path between node 8 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph23-10_5", + "image": "data/connectivity/graph_visual/medium/graph23.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (0,5) (0,7) (0,6) (0,2) (0,4) (0,8) (0,9) (1,10) (2,3) (2,5) (2,7) (2,6) (2,4) (2,8) (2,9) (2,11) (3,5) (3,4) (3,8) (3,11) (4,5) (4,6) (4,9) (4,11) (5,6) (5,8) (5,9) (6,7) (6,8) (6,9) (6,11) (7,8) (7,11) (8,9) (9,11)\nIs there a path between node 10 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph147-4_15", + "image": "data/connectivity/graph_visual/medium/graph147.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,9) (0,7) (0,10) (0,6) (0,14) (0,8) (0,16) (0,13) (1,3) (1,6) (1,17) (1,8) (1,12) (1,16) (1,15) (2,5) (2,4) (3,10) (3,6) (3,14) (3,12) (3,16) (3,15) (4,5) (4,11) (5,11) (6,9) (6,7) (6,10) (6,17) (6,8) (6,12) (6,16) (6,13) (6,15) (7,10) (7,17) (7,14) (7,12) (7,16) (7,13) (7,15) (8,10) (8,17) (8,14) (8,12) (8,16) (8,13) (9,10) (9,17) (9,13) (9,15) (10,17) (10,14) (10,12) (10,13) (10,15) (12,17) (12,13) (12,15) (13,14) (13,15) (14,16) (15,16)\nIs there a path between node 4 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph388-8_9", + "image": "data/connectivity/graph_visual/medium/graph388.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,13) (0,19) (0,9) (0,10) (0,17) (0,3) (0,6) (0,2) (1,14) (1,11) (1,8) (1,4) (1,12) (1,15) (1,18) (1,20) (1,16) (2,5) (2,13) (2,19) (2,9) (2,10) (2,17) (2,3) (2,6) (3,5) (3,13) (3,19) (3,9) (3,10) (3,17) (3,6) (4,14) (4,11) (4,8) (4,12) (4,15) (4,18) (4,20) (4,16) (5,13) (5,19) (5,9) (5,10) (5,17) (5,6) (6,13) (6,19) (6,9) (6,10) (6,17) (8,14) (8,11) (8,12) (8,15) (8,18) (8,20) (8,16) (9,13) (9,19) (9,10) (9,17) (10,13) (10,19) (10,17) (11,14) (11,12) (11,15) (11,18) (11,20) (11,16) (12,14) (12,15) (12,18) (12,20) (12,16) (13,19) (13,17) (14,15) (14,18) (14,20) (14,16) (15,18) (15,20) (15,16) (16,18) (16,20) (17,19) (18,20)\nIs there a path between node 8 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph803-24_4", + "image": "data/connectivity/graph_visual/medium/graph803.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (0,24) (1,22) (2,15) (3,23) (3,17) (3,22) (4,13) (4,12) (4,9) (4,11) (5,14) (6,14) (6,16) (7,22) (8,18) (9,19) (9,13) (10,19) (10,13) (10,24) (11,24) (12,19) (12,24) (13,19) (13,24) (13,21) (14,16) (17,23) (19,21)\nIs there a path between node 24 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph200-8_2", + "image": "data/connectivity/graph_visual/medium/graph200.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,12) (0,18) (0,6) (0,5) (0,7) (0,16) (1,11) (1,14) (2,4) (3,15) (5,12) (5,17) (5,9) (6,17) (6,7) (7,12) (7,18) (7,17) (7,13) (8,11) (9,12) (9,18) (9,17) (10,15) (13,17) (14,15)\nIs there a path between node 8 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph690-20_11", + "image": "data/connectivity/graph_visual/medium/graph690.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,11) (0,1) (0,4) (0,15) (0,10) (0,22) (0,14) (0,8) (1,21) (1,11) (1,4) (1,15) (1,10) (1,22) (1,14) (1,8) (2,3) (2,13) (2,5) (2,7) (3,13) (3,5) (3,7) (4,21) (4,11) (4,15) (4,10) (4,22) (4,14) (4,8) (5,13) (5,7) (6,20) (6,19) (6,16) (6,17) (6,9) (6,18) (6,12) (6,23) (7,13) (8,21) (8,11) (8,15) (8,10) (8,22) (8,14) (9,20) (9,19) (9,16) (9,17) (9,18) (9,12) (9,23) (10,21) (10,11) (10,15) (10,22) (10,14) (11,21) (11,15) (11,22) (11,14) (12,20) (12,19) (12,16) (12,17) (12,18) (12,23) (14,21) (14,15) (14,22) (15,21) (15,22) (16,20) (16,19) (16,17) (16,18) (16,23) (17,20) (17,19) (17,18) (17,23) (18,20) (18,19) (18,23) (19,20) (19,23) (20,23) (21,22)\nIs there a path between node 20 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph249-6_3", + "image": "data/connectivity/graph_visual/medium/graph249.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,6) (0,2) (0,17) (0,4) (0,5) (0,15) (0,9) (0,12) (0,11) (0,16) (0,8) (0,10) (0,18) (0,14) (1,7) (2,13) (2,6) (2,17) (2,4) (2,5) (2,15) (2,9) (2,12) (2,11) (2,16) (2,8) (2,10) (2,18) (2,14) (4,13) (4,6) (4,17) (4,5) (4,15) (4,9) (4,12) (4,11) (4,16) (4,8) (4,10) (4,18) (4,14) (5,13) (5,6) (5,17) (5,15) (5,9) (5,12) (5,11) (5,16) (5,8) (5,10) (5,18) (5,14) (6,13) (6,17) (6,15) (6,9) (6,12) (6,11) (6,16) (6,8) (6,10) (6,18) (6,14) (8,13) (8,17) (8,15) (8,9) (8,12) (8,11) (8,16) (8,10) (8,18) (8,14) (9,13) (9,17) (9,15) (9,12) (9,11) (9,16) (9,10) (9,18) (9,14) (10,13) (10,17) (10,15) (10,12) (10,11) (10,16) (10,18) (10,14) (11,13) (11,17) (11,15) (11,12) (11,16) (11,18) (11,14) (12,13) (12,17) (12,15) (12,16) (12,18) (12,14) (13,17) (13,15) (13,16) (13,18) (13,14) (14,17) (14,15) (14,16) (14,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 6 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph498-13_9", + "image": "data/connectivity/graph_visual/medium/graph498.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,8) (0,22) (0,9) (0,19) (0,12) (1,7) (1,15) (1,6) (1,21) (1,9) (1,2) (1,19) (1,12) (1,10) (2,8) (2,3) (2,17) (3,22) (3,6) (3,21) (3,5) (3,10) (4,8) (4,6) (4,21) (4,9) (5,7) (5,8) (5,17) (5,6) (5,9) (5,12) (5,10) (6,7) (6,15) (6,14) (6,17) (7,15) (7,12) (7,10) (9,15) (9,14) (9,22) (10,14) (10,17) (11,16) (12,17) (12,21) (14,18) (15,19) (17,18) (18,21)\nIs there a path between node 13 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph304-4_3", + "image": "data/connectivity/graph_visual/medium/graph304.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,4) (0,6) (0,9) (0,7) (0,18) (0,10) (0,15) (0,16) (0,13) (0,1) (0,11) (0,2) (0,8) (0,19) (1,5) (1,6) (1,12) (1,7) (1,18) (1,10) (1,15) (1,17) (1,13) (1,11) (1,2) (1,8) (1,19) (2,4) (2,5) (2,12) (2,9) (2,7) (2,18) (2,10) (2,15) (2,17) (2,8) (2,19) (3,14) (4,5) (4,6) (4,12) (4,9) (4,7) (4,10) (4,15) (4,17) (4,16) (4,13) (4,8) (4,19) (5,6) (5,12) (5,9) (5,7) (5,10) (5,15) (5,17) (5,16) (5,13) (5,19) (6,12) (6,7) (6,18) (6,10) (6,15) (6,16) (6,11) (6,8) (6,19) (7,9) (7,10) (7,13) (7,8) (7,19) (8,12) (8,9) (8,15) (8,17) (8,16) (8,11) (8,19) (9,12) (9,18) (9,10) (9,15) (9,17) (9,16) (9,13) (9,11) (10,12) (10,18) (10,15) (10,17) (10,16) (10,13) (10,19) (11,12) (11,18) (11,15) (11,17) (12,17) (12,16) (12,13) (13,18) (13,15) (13,17) (13,16) (15,17) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19)\nIs there a path between node 4 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph576-21_2", + "image": "data/connectivity/graph_visual/medium/graph576.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,18) (0,11) (0,23) (0,17) (0,7) (0,16) (0,1) (1,18) (1,6) (1,11) (1,21) (1,22) (1,2) (2,8) (2,16) (3,9) (3,13) (5,18) (5,6) (5,21) (5,17) (6,8) (6,11) (6,17) (6,19) (7,20) (7,8) (7,15) (7,19) (8,18) (8,22) (8,15) (11,14) (11,20) (11,22) (11,17) (11,16) (12,13) (14,18) (14,21) (14,23) (14,19) (15,21) (15,23) (16,21) (16,23) (18,20) (18,21) (18,23) (21,22)\nIs there a path between node 21 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph568-7_22", + "image": "data/connectivity/graph_visual/medium/graph568.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,13) (0,16) (0,1) (1,9) (1,13) (1,16) (2,19) (2,4) (2,18) (2,23) (2,17) (3,5) (3,20) (3,15) (3,6) (3,11) (3,7) (3,10) (3,22) (3,12) (3,14) (3,8) (4,19) (4,18) (4,23) (4,17) (5,20) (5,15) (5,6) (5,11) (5,7) (5,10) (5,22) (5,12) (5,14) (5,8) (6,20) (6,15) (6,11) (6,7) (6,10) (6,22) (6,12) (6,14) (6,8) (7,20) (7,15) (7,11) (7,10) (7,22) (7,12) (7,14) (7,8) (8,20) (8,15) (8,11) (8,10) (8,22) (8,12) (8,14) (9,13) (9,16) (10,20) (10,15) (10,11) (10,22) (10,12) (10,14) (11,20) (11,15) (11,22) (11,12) (11,14) (12,20) (12,15) (12,22) (12,14) (13,16) (14,20) (14,15) (14,22) (15,20) (15,22) (17,19) (17,18) (17,23) (18,19) (18,23) (19,23) (20,22)\nIs there a path between node 7 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph703-6_18", + "image": "data/connectivity/graph_visual/medium/graph703.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,13) (0,17) (0,11) (0,16) (0,14) (0,8) (1,3) (1,20) (2,3) (2,20) (2,21) (3,23) (3,20) (3,18) (6,13) (6,22) (6,14) (6,9) (7,17) (7,22) (7,14) (7,24) (7,9) (8,13) (8,17) (8,22) (8,16) (8,14) (8,24) (9,15) (9,17) (9,11) (9,19) (9,10) (9,24) (9,12) (10,15) (10,17) (10,11) (11,15) (11,22) (12,22) (12,24) (13,15) (13,22) (13,16) (13,24) (14,15) (14,19) (15,24) (16,22) (16,24) (18,20) (18,21) (21,23) (22,24)\nIs there a path between node 6 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph230-17_14", + "image": "data/connectivity/graph_visual/medium/graph230.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,9) (1,14) (1,2) (1,17) (1,16) (1,8) (2,4) (2,17) (3,7) (4,12) (4,18) (4,17) (4,10) (5,14) (5,18) (5,17) (5,10) (5,8) (6,18) (6,17) (6,10) (8,12) (8,10) (8,16) (10,12) (10,14) (12,15) (12,17) (12,16) (14,15) (14,17) (15,17) (15,16) (16,18) (17,18)\nIs there a path between node 17 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph497-10_12", + "image": "data/connectivity/graph_visual/medium/graph497.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,14) (0,13) (0,15) (0,16) (1,19) (1,21) (3,17) (3,15) (4,17) (6,7) (6,15) (7,17) (7,8) (7,13) (7,15) (7,16) (8,16) (9,18) (10,18) (10,19) (12,18) (12,19) (13,15) (14,17) (14,16) (14,20) (15,17) (15,22) (15,16) (15,20) (16,17) (16,22) (17,22) (18,21)\nIs there a path between node 10 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph648-4_8", + "image": "data/connectivity/graph_visual/medium/graph648.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,18) (0,10) (0,20) (0,19) (1,7) (1,11) (1,20) (1,19) (3,13) (3,7) (3,8) (3,18) (3,10) (3,5) (3,20) (4,13) (4,8) (4,5) (4,19) (5,13) (5,6) (5,8) (5,21) (6,13) (6,14) (7,13) (7,12) (7,14) (9,22) (9,16) (9,17) (10,12) (10,11) (10,14) (12,20) (12,14) (13,14) (15,22) (18,20) (19,20)\nIs there a path between node 4 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph496-16_21", + "image": "data/connectivity/graph_visual/medium/graph496.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,20) (0,2) (0,16) (0,1) (1,14) (1,7) (1,21) (1,19) (2,14) (2,20) (2,16) (3,5) (4,13) (4,5) (5,6) (6,9) (7,17) (7,20) (7,22) (8,21) (8,22) (9,13) (9,12) (10,12) (11,14) (11,15) (11,22) (12,13) (15,22) (16,18) (16,21) (16,17) (17,19) (18,19) (18,20) (19,21) (19,22) (20,22) (21,22)\nIs there a path between node 16 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph145-13_14", + "image": "data/connectivity/graph_visual/medium/graph145.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,12) (0,4) (0,11) (0,17) (0,2) (0,5) (0,9) (0,8) (0,16) (0,10) (1,3) (1,12) (1,4) (1,11) (1,17) (1,7) (1,2) (1,5) (1,9) (1,8) (1,10) (2,3) (2,12) (2,4) (2,11) (2,17) (2,7) (2,5) (2,8) (2,16) (3,12) (3,7) (3,9) (3,8) (4,12) (4,11) (4,17) (4,5) (4,9) (4,8) (4,16) (4,10) (5,12) (5,11) (5,17) (5,7) (5,14) (5,9) (5,16) (5,10) (6,15) (6,13) (7,12) (7,11) (7,17) (7,9) (7,16) (7,10) (8,11) (8,14) (8,9) (8,16) (8,10) (9,12) (9,17) (9,10) (10,11) (10,17) (10,14) (10,16) (11,17) (11,16) (14,16) (16,17)\nIs there a path between node 13 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph719-11_20", + "image": "data/connectivity/graph_visual/medium/graph719.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,22) (0,21) (0,7) (0,16) (0,14) (1,22) (1,10) (1,16) (2,6) (2,13) (2,24) (2,19) (2,3) (2,9) (2,23) (2,4) (2,15) (2,17) (2,11) (2,5) (3,6) (3,24) (3,19) (3,9) (3,23) (3,4) (3,12) (3,15) (3,17) (3,11) (3,5) (3,8) (4,6) (4,24) (4,9) (4,23) (4,15) (4,17) (4,18) (4,11) (4,5) (5,6) (5,13) (5,24) (5,19) (5,9) (5,23) (5,15) (5,18) (5,8) (6,24) (6,15) (6,17) (6,18) (6,8) (7,20) (7,22) (7,16) (8,24) (8,9) (8,12) (8,15) (8,17) (8,18) (9,13) (9,24) (9,23) (9,12) (9,17) (9,11) (10,20) (10,21) (10,16) (10,14) (11,24) (11,15) (11,17) (11,18) (12,13) (12,19) (12,17) (12,18) (13,24) (13,23) (13,17) (13,18) (14,20) (14,21) (14,16) (15,24) (15,19) (15,23) (15,18) (16,20) (16,21) (17,24) (17,23) (18,19) (19,24) (20,22) (20,21) (21,22)\nIs there a path between node 11 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph664-19_9", + "image": "data/connectivity/graph_visual/medium/graph664.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,4) (0,14) (0,9) (0,19) (0,7) (0,20) (0,17) (0,16) (1,11) (1,12) (1,2) (1,15) (1,3) (1,23) (1,5) (1,21) (2,12) (2,15) (2,3) (2,23) (2,13) (2,10) (3,22) (3,12) (3,15) (3,23) (3,5) (3,21) (3,13) (4,14) (4,18) (4,9) (4,19) (4,16) (5,22) (5,11) (5,12) (5,23) (5,21) (5,10) (6,18) (6,9) (6,7) (6,20) (6,17) (6,16) (7,14) (7,9) (7,19) (7,20) (7,17) (7,8) (8,14) (8,18) (8,9) (8,19) (8,20) (8,17) (8,16) (9,14) (9,19) (10,11) (10,15) (10,23) (10,21) (10,13) (11,22) (11,12) (11,15) (11,13) (12,22) (12,15) (12,23) (12,21) (12,13) (13,15) (13,21) (14,18) (14,19) (14,20) (14,16) (15,22) (16,20) (16,17) (18,19) (18,20) (19,20) (21,22) (22,23)\nIs there a path between node 19 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph385-12_8", + "image": "data/connectivity/graph_visual/medium/graph385.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,14) (0,17) (0,19) (0,9) (0,5) (0,2) (0,4) (0,7) (0,8) (0,13) (0,12) (0,10) (0,1) (0,15) (0,11) (0,16) (0,18) (0,6) (1,14) (1,17) (1,19) (1,9) (1,5) (1,2) (1,4) (1,7) (1,8) (1,13) (1,12) (1,10) (1,15) (1,11) (1,16) (1,18) (1,6) (2,14) (2,17) (2,19) (2,9) (2,5) (2,4) (2,7) (2,8) (2,13) (2,12) (2,10) (2,15) (2,11) (2,16) (2,18) (2,6) (3,20) (4,14) (4,17) (4,19) (4,9) (4,5) (4,7) (4,8) (4,13) (4,12) (4,10) (4,15) (4,11) (4,16) (4,18) (4,6) (5,14) (5,17) (5,19) (5,9) (5,7) (5,8) (5,13) (5,12) (5,10) (5,15) (5,11) (5,16) (5,18) (5,6) (6,14) (6,17) (6,19) (6,9) (6,7) (6,8) (6,13) (6,12) (6,10) (6,15) (6,11) (6,16) (6,18) (7,14) (7,17) (7,19) (7,9) (7,8) (7,13) (7,12) (7,10) (7,15) (7,11) (7,16) (7,18) (8,14) (8,17) (8,19) (8,9) (8,13) (8,12) (8,10) (8,15) (8,11) (8,16) (8,18) (9,14) (9,17) (9,19) (9,13) (9,12) (9,10) (9,15) (9,11) (9,16) (9,18) (10,14) (10,17) (10,19) (10,13) (10,12) (10,15) (10,11) (10,16) (10,18) (11,14) (11,17) (11,19) (11,13) (11,12) (11,15) (11,16) (11,18) (12,14) (12,17) (12,19) (12,13) (12,15) (12,16) (12,18) (13,14) (13,17) (13,19) (13,15) (13,16) (13,18) (14,17) (14,19) (14,15) (14,16) (14,18) (15,17) (15,19) (15,16) (15,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nIs there a path between node 12 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph63-12_3", + "image": "data/connectivity/graph_visual/medium/graph63.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,12) (0,9) (0,6) (1,10) (1,5) (1,2) (1,8) (1,7) (2,5) (2,3) (3,8) (3,11) (3,7) (4,12) (4,6) (4,13) (5,8) (5,11) (6,9) (6,13) (7,10) (7,8) (8,11) (9,13)\nIs there a path between node 12 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph744-12_5", + "image": "data/connectivity/graph_visual/medium/graph744.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,15) (0,16) (0,1) (0,2) (0,12) (0,3) (1,15) (1,21) (1,12) (1,20) (1,23) (2,11) (2,21) (2,7) (2,12) (2,3) (2,23) (3,9) (3,14) (3,16) (3,5) (3,18) (3,12) (3,22) (4,14) (4,15) (4,21) (4,16) (4,18) (4,12) (4,23) (5,7) (5,18) (5,23) (7,8) (7,16) (7,12) (8,9) (8,11) (8,18) (8,12) (8,20) (9,24) (9,18) (9,12) (9,23) (11,21) (12,15) (12,21) (12,16) (12,18) (12,22) (14,24) (14,15) (14,21) (15,24) (15,19) (15,22) (16,22) (16,23) (18,21) (18,19) (19,21) (20,22) (21,23) (22,24)\nIs there a path between node 12 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph461-7_19", + "image": "data/connectivity/graph_visual/medium/graph461.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,11) (0,17) (0,16) (0,3) (0,9) (0,15) (0,12) (0,1) (0,20) (0,19) (0,6) (0,21) (0,7) (0,8) (0,14) (0,5) (0,2) (1,18) (1,11) (1,17) (1,16) (1,3) (1,9) (1,15) (1,12) (1,20) (1,19) (1,6) (1,21) (1,7) (1,8) (1,14) (1,5) (1,2) (2,18) (2,11) (2,17) (2,16) (2,3) (2,9) (2,15) (2,12) (2,20) (2,19) (2,6) (2,21) (2,7) (2,8) (2,14) (2,5) (3,18) (3,11) (3,17) (3,16) (3,9) (3,15) (3,12) (3,20) (3,19) (3,6) (3,21) (3,7) (3,8) (3,14) (3,5) (5,18) (5,11) (5,17) (5,16) (5,9) (5,15) (5,12) (5,20) (5,19) (5,6) (5,21) (5,7) (5,8) (5,14) (6,18) (6,11) (6,17) (6,16) (6,9) (6,15) (6,12) (6,20) (6,19) (6,21) (6,7) (6,8) (6,14) (7,18) (7,11) (7,17) (7,16) (7,9) (7,15) (7,12) (7,20) (7,19) (7,21) (7,8) (7,14) (8,18) (8,11) (8,17) (8,16) (8,9) (8,15) (8,12) (8,20) (8,19) (8,21) (8,14) (9,18) (9,11) (9,17) (9,16) (9,15) (9,12) (9,20) (9,19) (9,21) (9,14) (10,13) (11,18) (11,17) (11,16) (11,15) (11,12) (11,20) (11,19) (11,21) (11,14) (12,18) (12,17) (12,16) (12,15) (12,20) (12,19) (12,21) (12,14) (14,18) (14,17) (14,16) (14,15) (14,20) (14,19) (14,21) (15,18) (15,17) (15,16) (15,20) (15,19) (15,21) (16,18) (16,17) (16,20) (16,19) (16,21) (17,18) (17,20) (17,19) (17,21) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 7 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph155-13_8", + "image": "data/connectivity/graph_visual/medium/graph155.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,9) (0,1) (0,6) (0,10) (0,3) (0,13) (0,8) (0,14) (0,15) (0,2) (0,7) (0,11) (1,9) (1,6) (1,10) (1,3) (1,13) (1,8) (1,14) (1,15) (1,2) (1,7) (1,11) (2,9) (2,6) (2,10) (2,3) (2,13) (2,8) (2,14) (2,15) (2,7) (2,11) (3,9) (3,6) (3,10) (3,13) (3,8) (3,14) (3,15) (3,7) (3,11) (4,12) (4,5) (4,16) (5,12) (5,16) (6,9) (6,10) (6,13) (6,8) (6,14) (6,15) (6,7) (6,11) (7,9) (7,10) (7,13) (7,8) (7,14) (7,15) (7,11) (8,9) (8,10) (8,13) (8,14) (8,15) (8,11) (9,10) (9,13) (9,14) (9,15) (9,11) (10,13) (10,14) (10,15) (10,11) (11,13) (11,14) (11,15) (12,16) (13,14) (13,15) (14,15)\nIs there a path between node 13 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph257-9_2", + "image": "data/connectivity/graph_visual/medium/graph257.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,16) (0,18) (0,4) (0,2) (0,13) (0,15) (0,6) (0,14) (0,10) (1,3) (1,5) (1,8) (1,17) (1,11) (1,12) (1,9) (1,7) (2,16) (2,18) (2,4) (2,13) (2,15) (2,6) (2,14) (2,10) (3,5) (3,8) (3,17) (3,11) (3,12) (3,9) (3,7) (4,16) (4,18) (4,13) (4,15) (4,6) (4,14) (4,10) (5,8) (5,17) (5,11) (5,12) (5,9) (5,7) (6,16) (6,18) (6,13) (6,15) (6,14) (6,10) (7,8) (7,17) (7,11) (7,12) (7,9) (8,17) (8,11) (8,12) (8,9) (9,17) (9,11) (9,12) (10,16) (10,18) (10,13) (10,15) (10,14) (11,17) (11,12) (12,17) (13,16) (13,18) (13,15) (13,14) (14,16) (14,18) (14,15) (15,16) (15,18) (16,18)\nIs there a path between node 9 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph722-21_17", + "image": "data/connectivity/graph_visual/medium/graph722.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,1) (0,8) (0,17) (0,3) (0,9) (0,2) (0,12) (1,8) (1,17) (1,3) (1,9) (1,2) (1,12) (2,8) (2,17) (2,3) (2,9) (2,12) (3,8) (3,17) (3,9) (3,12) (4,7) (4,19) (4,22) (4,14) (4,16) (4,24) (4,6) (4,5) (5,7) (5,19) (5,22) (5,14) (5,16) (5,24) (5,6) (6,7) (6,19) (6,22) (6,14) (6,16) (6,24) (7,19) (7,22) (7,14) (7,16) (7,24) (8,17) (8,9) (8,12) (9,17) (9,12) (10,20) (10,13) (10,15) (10,11) (10,23) (10,21) (10,18) (11,20) (11,13) (11,15) (11,23) (11,21) (11,18) (12,17) (13,20) (13,15) (13,23) (13,21) (13,18) (14,19) (14,22) (14,16) (14,24) (15,20) (15,23) (15,21) (15,18) (16,19) (16,22) (16,24) (18,20) (18,23) (18,21) (19,22) (19,24) (20,23) (20,21) (21,23) (22,24)\nIs there a path between node 21 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph356-4_18", + "image": "data/connectivity/graph_visual/medium/graph356.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,11) (1,16) (1,10) (1,12) (2,16) (2,11) (3,8) (3,13) (4,20) (4,8) (4,17) (5,14) (6,15) (7,13) (7,9) (7,18) (7,17) (8,9) (9,15) (10,19) (11,14) (11,12) (12,14) (17,18) (18,20)\nIs there a path between node 4 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph231-7_1", + "image": "data/connectivity/graph_visual/medium/graph231.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,10) (1,15) (2,16) (3,18) (3,8) (5,15) (5,14) (7,9) (8,18) (8,12) (10,17) (12,13) (12,17) (13,14) (14,18) (14,15) (17,18)\nIs there a path between node 7 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph473-22_2", + "image": "data/connectivity/graph_visual/medium/graph473.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,17) (0,11) (2,17) (2,20) (2,11) (3,8) (3,21) (3,18) (3,4) (4,7) (4,12) (6,14) (7,19) (7,21) (7,10) (8,13) (8,19) (8,21) (8,12) (9,19) (9,21) (10,13) (11,14) (12,21) (13,16) (13,18) (14,15) (15,22) (16,19) (16,18) (17,22) (17,20)\nIs there a path between node 22 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph857-11_22", + "image": "data/connectivity/graph_visual/medium/graph857.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,21) (0,9) (0,1) (0,3) (0,4) (0,16) (0,24) (0,23) (0,22) (0,8) (0,11) (0,6) (0,14) (0,13) (1,2) (1,21) (1,9) (1,3) (1,4) (1,16) (1,24) (1,23) (1,22) (1,8) (1,11) (1,6) (1,14) (1,13) (2,21) (2,9) (2,3) (2,4) (2,16) (2,24) (2,23) (2,22) (2,8) (2,11) (2,6) (2,14) (2,13) (3,21) (3,9) (3,4) (3,16) (3,24) (3,23) (3,22) (3,8) (3,11) (3,6) (3,14) (3,13) (4,21) (4,9) (4,16) (4,24) (4,23) (4,22) (4,8) (4,11) (4,6) (4,14) (4,13) (6,21) (6,9) (6,16) (6,24) (6,23) (6,22) (6,8) (6,11) (6,14) (6,13) (7,19) (7,17) (7,12) (7,20) (7,10) (7,18) (7,15) (8,21) (8,9) (8,16) (8,24) (8,23) (8,22) (8,11) (8,14) (8,13) (9,21) (9,16) (9,24) (9,23) (9,22) (9,11) (9,14) (9,13) (10,19) (10,17) (10,12) (10,20) (10,18) (10,15) (11,21) (11,16) (11,24) (11,23) (11,22) (11,14) (11,13) (12,19) (12,17) (12,20) (12,18) (12,15) (13,21) (13,16) (13,24) (13,23) (13,22) (13,14) (14,21) (14,16) (14,24) (14,23) (14,22) (15,19) (15,17) (15,20) (15,18) (16,21) (16,24) (16,23) (16,22) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nIs there a path between node 11 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph144-3_12", + "image": "data/connectivity/graph_visual/medium/graph144.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,14) (0,8) (0,3) (0,12) (0,17) (0,2) (0,15) (1,13) (1,8) (1,17) (1,16) (1,2) (1,9) (2,3) (2,12) (2,16) (3,6) (3,14) (3,8) (3,17) (3,16) (3,15) (4,7) (4,5) (4,11) (5,11) (6,10) (6,13) (6,14) (6,8) (6,17) (6,9) (7,11) (8,13) (8,14) (8,12) (8,17) (8,16) (8,9) (9,10) (9,13) (9,14) (9,12) (9,17) (9,16) (9,15) (10,12) (10,17) (10,16) (10,15) (12,13) (12,14) (12,17) (12,16) (12,15) (13,17) (13,16) (13,15) (14,17) (14,15) (15,16) (16,17)\nIs there a path between node 3 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph42-4_11", + "image": "data/connectivity/graph_visual/medium/graph42.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,6) (0,7) (0,10) (0,8) (0,11) (0,12) (1,3) (1,4) (1,9) (2,6) (2,7) (2,10) (2,8) (2,11) (2,12) (3,4) (3,5) (3,9) (4,5) (4,9) (5,9) (6,7) (6,10) (6,12) (7,10) (7,12) (8,10) (8,11) (8,12) (10,11) (11,12)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph53-10_7", + "image": "data/connectivity/graph_visual/medium/graph53.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,10) (0,5) (0,7) (0,2) (0,8) (0,4) (0,9) (0,1) (0,12) (0,3) (0,11) (0,13) (1,10) (1,5) (1,7) (1,2) (1,8) (1,4) (1,9) (1,12) (1,3) (1,11) (1,13) (2,10) (2,5) (2,7) (2,8) (2,4) (2,9) (2,12) (2,3) (2,11) (2,13) (3,10) (3,5) (3,7) (3,8) (3,4) (3,9) (3,12) (3,11) (3,13) (4,10) (4,5) (4,7) (4,8) (4,9) (4,12) (4,11) (4,13) (5,10) (5,7) (5,8) (5,9) (5,12) (5,11) (5,13) (7,10) (7,8) (7,9) (7,12) (7,11) (7,13) (8,10) (8,9) (8,12) (8,11) (8,13) (9,10) (9,12) (9,11) (9,13) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nIs there a path between node 10 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph17-4_6", + "image": "data/connectivity/graph_visual/medium/graph17.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,4) (0,11) (0,5) (0,9) (0,6) (1,2) (1,7) (1,3) (1,10) (1,8) (2,7) (2,3) (2,10) (2,8) (3,7) (3,10) (3,8) (4,11) (4,5) (4,9) (4,6) (5,11) (5,9) (5,6) (6,11) (6,9) (7,10) (7,8) (8,10) (9,11)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph723-11_21", + "image": "data/connectivity/graph_visual/medium/graph723.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,22) (0,15) (0,6) (0,7) (0,11) (0,9) (0,1) (0,4) (0,14) (0,23) (0,17) (0,21) (0,20) (0,8) (0,24) (0,18) (1,3) (1,22) (1,15) (1,6) (1,7) (1,11) (1,9) (1,4) (1,14) (1,23) (1,17) (1,21) (1,20) (1,8) (1,24) (1,18) (2,12) (2,10) (2,13) (2,16) (3,22) (3,15) (3,6) (3,7) (3,11) (3,9) (3,4) (3,14) (3,23) (3,17) (3,21) (3,20) (3,8) (3,24) (3,18) (4,22) (4,15) (4,6) (4,7) (4,11) (4,9) (4,14) (4,23) (4,17) (4,21) (4,20) (4,8) (4,24) (4,18) (5,19) (6,22) (6,15) (6,7) (6,11) (6,9) (6,14) (6,23) (6,17) (6,21) (6,20) (6,8) (6,24) (6,18) (7,22) (7,15) (7,11) (7,9) (7,14) (7,23) (7,17) (7,21) (7,20) (7,8) (7,24) (7,18) (8,22) (8,15) (8,11) (8,9) (8,14) (8,23) (8,17) (8,21) (8,20) (8,24) (8,18) (9,22) (9,15) (9,11) (9,14) (9,23) (9,17) (9,21) (9,20) (9,24) (9,18) (10,12) (10,13) (10,16) (11,22) (11,15) (11,14) (11,23) (11,17) (11,21) (11,20) (11,24) (11,18) (12,13) (12,16) (13,16) (14,22) (14,15) (14,23) (14,17) (14,21) (14,20) (14,24) (14,18) (15,22) (15,23) (15,17) (15,21) (15,20) (15,24) (15,18) (17,22) (17,23) (17,21) (17,20) (17,24) (17,18) (18,22) (18,23) (18,21) (18,20) (18,24) (20,22) (20,23) (20,21) (20,24) (21,22) (21,23) (21,24) (22,23) (22,24) (23,24)\nIs there a path between node 11 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph689-6_2", + "image": "data/connectivity/graph_visual/medium/graph689.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,8) (0,9) (0,2) (0,10) (0,16) (0,11) (0,17) (0,1) (0,19) (0,13) (0,6) (1,3) (1,8) (1,9) (1,2) (1,10) (1,16) (1,11) (1,17) (1,19) (1,13) (1,6) (2,3) (2,8) (2,9) (2,10) (2,16) (2,11) (2,17) (2,19) (2,13) (2,6) (3,8) (3,9) (3,10) (3,16) (3,11) (3,17) (3,19) (3,13) (3,6) (4,5) (4,21) (4,22) (4,20) (4,18) (4,15) (4,12) (4,23) (4,14) (4,7) (5,21) (5,22) (5,20) (5,18) (5,15) (5,12) (5,23) (5,14) (5,7) (6,8) (6,9) (6,10) (6,16) (6,11) (6,17) (6,19) (6,13) (7,21) (7,22) (7,20) (7,18) (7,15) (7,12) (7,23) (7,14) (8,9) (8,10) (8,16) (8,11) (8,17) (8,19) (8,13) (9,10) (9,16) (9,11) (9,17) (9,19) (9,13) (10,16) (10,11) (10,17) (10,19) (10,13) (11,16) (11,17) (11,19) (11,13) (12,21) (12,22) (12,20) (12,18) (12,15) (12,23) (12,14) (13,16) (13,17) (13,19) (14,21) (14,22) (14,20) (14,18) (14,15) (14,23) (15,21) (15,22) (15,20) (15,18) (15,23) (16,17) (16,19) (17,19) (18,21) (18,22) (18,20) (18,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 6 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph430-18_6", + "image": "data/connectivity/graph_visual/medium/graph430.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,16) (1,11) (1,2) (1,14) (2,3) (2,10) (2,6) (3,21) (3,9) (3,11) (3,10) (3,6) (4,12) (5,8) (5,13) (6,9) (6,14) (6,10) (6,7) (7,21) (7,9) (7,16) (7,11) (7,18) (7,14) (7,17) (8,12) (8,13) (9,16) (9,11) (11,16) (11,17) (12,13) (15,20) (16,18) (16,17) (17,18) (18,21)\nIs there a path between node 18 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph688-22_23", + "image": "data/connectivity/graph_visual/medium/graph688.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,6) (0,11) (0,14) (0,2) (1,20) (1,8) (1,7) (1,16) (1,21) (1,9) (1,17) (1,5) (1,23) (1,12) (1,22) (2,4) (2,6) (2,11) (2,14) (3,15) (3,18) (3,13) (3,19) (3,10) (4,6) (4,11) (4,14) (5,20) (5,8) (5,7) (5,16) (5,21) (5,9) (5,17) (5,23) (5,12) (5,22) (6,11) (6,14) (7,20) (7,8) (7,16) (7,21) (7,9) (7,17) (7,23) (7,12) (7,22) (8,20) (8,16) (8,21) (8,9) (8,17) (8,23) (8,12) (8,22) (9,20) (9,16) (9,21) (9,17) (9,23) (9,12) (9,22) (10,15) (10,18) (10,13) (10,19) (11,14) (12,20) (12,16) (12,21) (12,17) (12,23) (12,22) (13,15) (13,18) (13,19) (15,18) (15,19) (16,20) (16,21) (16,17) (16,23) (16,22) (17,20) (17,21) (17,23) (17,22) (18,19) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 22 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph339-4_5", + "image": "data/connectivity/graph_visual/medium/graph339.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (0,12) (0,18) (0,5) (0,16) (0,10) (0,2) (0,11) (1,17) (1,12) (1,18) (1,4) (1,5) (1,16) (1,10) (1,11) (2,17) (2,12) (2,18) (2,4) (2,5) (2,10) (2,11) (3,15) (3,13) (3,6) (3,20) (3,7) (3,19) (3,8) (3,14) (4,17) (4,12) (4,18) (4,10) (5,17) (5,12) (5,16) (5,10) (5,11) (6,15) (6,20) (6,7) (6,14) (6,9) (7,15) (7,13) (7,20) (7,19) (7,8) (8,15) (8,13) (8,19) (8,9) (9,15) (9,13) (9,19) (9,14) (10,17) (10,12) (10,18) (10,11) (11,17) (12,17) (12,18) (13,19) (13,14) (14,20) (14,19) (15,20) (15,19) (16,17) (16,18) (19,20)\nIs there a path between node 4 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph846-19_8", + "image": "data/connectivity/graph_visual/medium/graph846.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,17) (0,7) (0,21) (0,19) (0,6) (0,11) (0,5) (1,15) (1,20) (1,2) (1,4) (1,14) (1,16) (1,3) (1,22) (1,12) (1,24) (1,18) (1,9) (1,13) (1,23) (1,8) (2,15) (2,20) (2,4) (2,14) (2,16) (2,3) (2,22) (2,12) (2,24) (2,18) (2,9) (2,13) (2,23) (2,8) (3,15) (3,20) (3,4) (3,14) (3,16) (3,22) (3,12) (3,24) (3,18) (3,9) (3,13) (3,23) (3,8) (4,15) (4,20) (4,14) (4,16) (4,22) (4,12) (4,24) (4,18) (4,9) (4,13) (4,23) (4,8) (5,10) (5,17) (5,7) (5,21) (5,19) (5,6) (5,11) (6,10) (6,17) (6,7) (6,21) (6,19) (6,11) (7,10) (7,17) (7,21) (7,19) (7,11) (8,15) (8,20) (8,14) (8,16) (8,22) (8,12) (8,24) (8,18) (8,9) (8,13) (8,23) (9,15) (9,20) (9,14) (9,16) (9,22) (9,12) (9,24) (9,18) (9,13) (9,23) (10,17) (10,21) (10,19) (10,11) (11,17) (11,21) (11,19) (12,15) (12,20) (12,14) (12,16) (12,22) (12,24) (12,18) (12,13) (12,23) (13,15) (13,20) (13,14) (13,16) (13,22) (13,24) (13,18) (13,23) (14,15) (14,20) (14,16) (14,22) (14,24) (14,18) (14,23) (15,20) (15,16) (15,22) (15,24) (15,18) (15,23) (16,20) (16,22) (16,24) (16,18) (16,23) (17,21) (17,19) (18,20) (18,22) (18,24) (18,23) (19,21) (20,22) (20,24) (20,23) (22,24) (22,23) (23,24)\nIs there a path between node 19 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph171-1_2", + "image": "data/connectivity/graph_visual/medium/graph171.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,10) (0,7) (0,15) (0,17) (0,6) (1,12) (1,3) (1,4) (1,14) (1,16) (2,8) (2,5) (2,4) (2,9) (2,14) (2,16) (3,12) (3,11) (3,8) (3,4) (3,9) (3,14) (3,16) (4,12) (4,11) (4,8) (4,5) (4,14) (4,16) (5,12) (5,8) (5,9) (5,14) (5,16) (6,10) (6,13) (6,7) (6,15) (6,17) (7,10) (7,13) (7,15) (7,17) (8,11) (8,9) (9,14) (9,16) (10,15) (10,17) (11,12) (11,14) (12,14) (12,16) (13,15) (13,17) (15,17)\nIs there a path between node 1 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph169-5_17", + "image": "data/connectivity/graph_visual/medium/graph169.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,17) (0,13) (0,12) (0,4) (0,1) (1,3) (1,17) (1,16) (1,14) (1,4) (2,5) (2,7) (2,9) (2,11) (2,8) (3,15) (3,13) (3,16) (3,12) (3,14) (3,6) (4,15) (4,13) (4,16) (4,12) (4,6) (5,9) (5,11) (5,10) (6,17) (6,13) (6,12) (7,11) (7,10) (7,8) (8,9) (8,11) (9,10) (10,11) (12,15) (12,17) (12,16) (12,14) (13,17) (13,16) (14,15) (14,17) (15,17) (15,16) (16,17)\nIs there a path between node 5 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph401-17_18", + "image": "data/connectivity/graph_visual/medium/graph401.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,11) (0,1) (1,11) (2,4) (2,14) (3,21) (3,18) (3,6) (3,12) (3,13) (5,6) (6,21) (6,20) (6,8) (6,12) (6,13) (7,16) (7,12) (8,20) (9,20) (9,13) (10,11) (12,17) (12,16) (13,20) (13,17) (13,19) (15,21) (15,16) (15,19) (16,21) (16,19) (17,19) (18,19) (19,20) (20,21)\nIs there a path between node 17 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph656-2_22", + "image": "data/connectivity/graph_visual/medium/graph656.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,19) (0,4) (0,17) (0,16) (0,22) (0,20) (0,18) (0,10) (0,21) (0,7) (0,8) (0,9) (0,15) (0,14) (1,3) (1,13) (1,6) (1,4) (1,16) (1,22) (1,20) (1,10) (1,21) (1,5) (1,7) (1,9) (1,15) (1,14) (2,11) (3,13) (3,6) (3,19) (3,4) (3,17) (3,16) (3,22) (3,20) (3,18) (3,10) (3,5) (3,7) (3,23) (3,8) (3,14) (4,13) (4,19) (4,17) (4,20) (4,18) (4,10) (4,5) (4,7) (4,23) (4,8) (4,15) (4,14) (5,13) (5,6) (5,19) (5,17) (5,16) (5,22) (5,20) (5,10) (5,23) (5,9) (5,14) (6,13) (6,17) (6,22) (6,18) (6,10) (6,21) (6,7) (6,23) (6,15) (6,14) (7,13) (7,19) (7,17) (7,16) (7,22) (7,20) (7,18) (7,10) (7,21) (7,9) (7,14) (8,19) (8,20) (8,18) (8,10) (8,21) (8,9) (8,15) (9,13) (9,19) (9,17) (9,16) (9,22) (9,21) (9,14) (10,13) (10,17) (10,22) (10,20) (10,18) (10,23) (10,15) (10,14) (13,17) (13,16) (13,22) (13,20) (13,18) (13,21) (13,23) (13,15) (13,14) (14,17) (14,16) (14,20) (14,18) (14,23) (15,19) (15,17) (15,16) (15,22) (15,20) (15,21) (15,23) (16,18) (16,21) (17,19) (17,22) (17,20) (17,23) (18,19) (18,22) (18,20) (18,21) (18,23) (19,22) (19,20) (19,21) (20,22) (21,22) (21,23) (22,23)\nIs there a path between node 2 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph408-12_17", + "image": "data/connectivity/graph_visual/medium/graph408.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,17) (0,7) (0,18) (0,14) (0,8) (0,19) (0,15) (0,4) (0,21) (1,3) (1,6) (1,11) (2,7) (2,9) (2,14) (2,8) (2,19) (2,13) (2,15) (2,10) (3,5) (3,20) (3,6) (3,11) (4,17) (4,7) (4,18) (4,9) (4,21) (5,12) (5,6) (5,11) (6,12) (6,20) (7,17) (7,18) (7,9) (7,14) (7,8) (7,13) (7,15) (8,17) (8,18) (8,14) (8,13) (8,15) (8,21) (8,10) (9,17) (9,18) (9,14) (9,13) (9,21) (10,17) (10,18) (10,14) (10,13) (10,15) (11,12) (11,20) (12,20) (12,16) (13,18) (13,14) (13,19) (13,15) (13,21) (14,18) (14,15) (14,21) (15,17) (15,18) (15,19) (15,21) (17,18) (17,19) (18,19) (19,21)\nIs there a path between node 12 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph708-6_18", + "image": "data/connectivity/graph_visual/medium/graph708.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,14) (0,4) (1,9) (1,2) (1,15) (1,23) (2,9) (2,10) (2,18) (3,5) (3,8) (3,15) (3,18) (4,24) (4,13) (5,8) (5,15) (5,10) (5,23) (6,15) (6,10) (7,20) (8,15) (9,21) (10,15) (10,21) (10,18) (11,22) (11,13) (11,14) (12,22) (12,24) (12,13) (12,14) (13,17) (13,19) (13,22) (13,24) (14,24) (14,20) (15,18) (17,19) (17,20) (19,20)\nIs there a path between node 6 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph482-17_22", + "image": "data/connectivity/graph_visual/medium/graph482.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,5) (0,15) (0,19) (0,21) (0,13) (0,10) (0,6) (0,17) (0,18) (0,9) (0,7) (0,4) (1,15) (1,19) (1,21) (1,2) (1,13) (1,3) (1,8) (1,12) (1,18) (1,20) (1,9) (1,7) (1,4) (1,11) (2,5) (2,15) (2,19) (2,21) (2,3) (2,10) (2,16) (2,6) (2,8) (2,17) (2,12) (2,20) (2,9) (2,7) (2,4) (2,11) (3,5) (3,15) (3,21) (3,13) (3,10) (3,8) (3,12) (3,18) (3,9) (3,7) (3,11) (4,5) (4,15) (4,19) (4,21) (4,10) (4,16) (4,6) (4,8) (4,12) (4,20) (5,15) (5,19) (5,21) (5,13) (5,10) (5,6) (5,17) (5,12) (5,18) (5,20) (5,9) (5,7) (6,15) (6,13) (6,8) (6,17) (6,12) (6,18) (6,7) (6,11) (7,21) (7,13) (7,10) (7,8) (7,17) (7,12) (7,18) (7,20) (7,11) (8,15) (8,19) (8,21) (8,13) (8,10) (8,16) (8,17) (8,12) (8,18) (8,20) (9,15) (9,19) (9,21) (9,16) (9,17) (9,12) (9,18) (9,20) (10,15) (10,19) (10,21) (10,13) (10,16) (10,17) (10,18) (11,19) (11,21) (11,13) (11,17) (11,20) (12,15) (12,21) (12,13) (12,16) (12,17) (12,18) (12,20) (13,15) (13,19) (13,16) (13,17) (13,18) (13,20) (15,19) (15,21) (15,18) (15,20) (16,19) (16,21) (16,17) (16,18) (16,20) (17,19) (18,19) (18,20) (19,21) (19,20) (20,21)\nIs there a path between node 17 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph663-11_9", + "image": "data/connectivity/graph_visual/medium/graph663.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,8) (0,23) (0,19) (0,9) (0,21) (1,14) (2,7) (2,11) (2,4) (3,5) (3,7) (3,16) (3,17) (3,18) (3,11) (3,4) (4,5) (4,7) (4,10) (4,16) (4,18) (5,7) (5,10) (5,11) (6,22) (6,8) (6,12) (6,19) (7,10) (7,16) (7,17) (7,13) (7,18) (7,11) (8,22) (8,23) (8,15) (8,21) (9,22) (9,23) (9,19) (9,15) (10,18) (11,16) (11,17) (11,13) (12,22) (12,23) (12,15) (12,21) (13,16) (13,17) (13,18) (14,20) (15,23) (15,19) (15,21) (16,18) (17,18) (19,22) (19,21) (21,22) (21,23)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph413-7_13", + "image": "data/connectivity/graph_visual/medium/graph413.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,13) (0,19) (0,21) (0,4) (0,2) (0,16) (0,6) (0,7) (0,8) (0,3) (0,20) (0,14) (1,9) (1,10) (2,13) (2,19) (2,21) (2,12) (2,16) (2,5) (2,8) (2,20) (2,14) (3,13) (3,21) (3,4) (3,12) (3,16) (3,7) (3,8) (3,20) (3,14) (4,21) (4,12) (4,16) (4,6) (4,5) (4,8) (5,13) (5,19) (5,21) (5,12) (5,6) (5,7) (5,8) (5,14) (6,13) (6,19) (6,12) (6,16) (6,7) (6,8) (6,20) (6,14) (7,13) (7,21) (7,12) (7,16) (7,20) (7,14) (8,19) (8,12) (8,20) (8,14) (9,11) (9,10) (9,15) (9,18) (9,17) (10,11) (10,15) (10,17) (11,15) (11,18) (11,17) (12,21) (12,16) (12,20) (13,19) (13,16) (13,20) (13,14) (14,19) (14,21) (14,16) (14,20) (15,18) (15,17) (16,19) (16,21) (17,18) (19,21) (19,20) (20,21)\nIs there a path between node 7 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph315-14_7", + "image": "data/connectivity/graph_visual/medium/graph315.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,16) (0,8) (0,12) (0,9) (0,4) (0,6) (0,11) (1,19) (1,15) (2,7) (2,10) (2,13) (2,3) (2,5) (2,18) (2,17) (2,14) (3,7) (3,10) (3,13) (3,5) (3,18) (3,17) (3,14) (4,16) (4,8) (4,12) (4,9) (4,6) (4,11) (5,7) (5,10) (5,13) (5,18) (5,17) (5,14) (6,16) (6,8) (6,12) (6,9) (6,11) (7,10) (7,13) (7,18) (7,17) (7,14) (8,16) (8,12) (8,9) (8,11) (9,16) (9,12) (9,11) (10,13) (10,18) (10,17) (10,14) (11,16) (11,12) (12,16) (13,18) (13,17) (13,14) (14,18) (14,17) (15,19) (17,18)\nIs there a path between node 14 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph781-21_10", + "image": "data/connectivity/graph_visual/medium/graph781.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,14) (1,7) (1,20) (1,12) (1,10) (2,15) (2,21) (4,13) (4,19) (4,22) (5,14) (5,7) (5,9) (6,23) (6,18) (6,21) (7,11) (7,20) (8,14) (8,12) (9,11) (9,10) (10,17) (10,12) (11,17) (13,19) (15,21) (18,24) (23,24)\nIs there a path between node 21 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph516-9_0", + "image": "data/connectivity/graph_visual/medium/graph516.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,2) (0,11) (0,3) (0,19) (0,9) (0,1) (0,22) (0,13) (0,20) (0,4) (0,7) (0,10) (0,6) (0,14) (1,2) (1,11) (1,19) (1,18) (1,9) (1,21) (1,22) (1,13) (1,4) (1,7) (1,17) (1,14) (2,3) (2,19) (2,9) (2,21) (2,13) (2,12) (2,20) (2,4) (2,10) (2,17) (2,14) (3,11) (3,19) (3,18) (3,9) (3,21) (3,22) (3,13) (3,7) (3,10) (3,17) (3,6) (3,14) (4,19) (4,18) (4,9) (4,13) (4,12) (4,20) (4,7) (4,10) (4,14) (5,8) (5,15) (6,19) (6,18) (6,9) (6,21) (6,22) (6,13) (6,12) (6,20) (6,7) (7,11) (7,18) (7,9) (7,21) (7,22) (7,12) (7,10) (7,17) (7,14) (8,16) (8,15) (9,11) (9,19) (9,18) (9,21) (9,20) (9,10) (9,17) (9,14) (10,11) (10,21) (10,22) (10,13) (10,12) (10,20) (10,17) (10,14) (11,19) (11,18) (11,21) (11,22) (11,13) (11,12) (11,20) (11,17) (11,14) (12,18) (12,21) (12,13) (12,20) (12,17) (13,19) (13,22) (13,14) (14,19) (14,18) (14,21) (14,17) (15,16) (17,19) (17,21) (17,22) (17,20) (18,19) (18,21) (18,22) (18,20) (19,20) (20,21) (20,22) (21,22)\nIs there a path between node 9 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph211-9_16", + "image": "data/connectivity/graph_visual/medium/graph211.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,14) (0,1) (0,8) (0,11) (0,7) (1,14) (1,15) (1,17) (1,7) (2,3) (2,6) (2,5) (2,13) (2,16) (2,4) (2,9) (3,6) (3,5) (3,12) (3,13) (3,16) (3,4) (3,9) (4,6) (4,5) (4,12) (4,13) (4,16) (4,9) (5,6) (5,12) (5,13) (5,16) (6,9) (7,14) (7,8) (7,15) (7,17) (7,11) (8,14) (8,17) (8,11) (9,12) (9,13) (10,18) (11,14) (11,15) (11,17) (12,13) (12,16) (13,16) (14,17) (15,17)\nIs there a path between node 9 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph131-14_5", + "image": "data/connectivity/graph_visual/medium/graph131.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,5) (0,12) (0,10) (0,9) (0,6) (0,7) (0,15) (0,4) (0,2) (0,13) (0,8) (0,16) (1,14) (1,11) (1,3) (2,5) (2,12) (2,10) (2,9) (2,6) (2,7) (2,15) (2,4) (2,13) (2,8) (2,16) (3,14) (3,11) (4,5) (4,12) (4,10) (4,9) (4,6) (4,7) (4,15) (4,13) (4,8) (4,16) (5,12) (5,10) (5,9) (5,6) (5,7) (5,15) (5,13) (5,8) (5,16) (6,12) (6,10) (6,9) (6,7) (6,15) (6,13) (6,8) (6,16) (7,12) (7,10) (7,9) (7,15) (7,13) (7,8) (7,16) (8,12) (8,10) (8,9) (8,15) (8,13) (8,16) (9,12) (9,10) (9,15) (9,13) (9,16) (10,12) (10,15) (10,13) (10,16) (11,14) (12,15) (12,13) (12,16) (13,15) (13,16) (15,16)\nIs there a path between node 14 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph570-22_15", + "image": "data/connectivity/graph_visual/medium/graph570.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,18) (0,12) (0,20) (0,17) (0,14) (0,4) (0,19) (0,15) (0,7) (0,16) (0,21) (1,8) (1,23) (1,2) (1,22) (1,10) (1,5) (2,8) (2,23) (2,22) (2,10) (2,5) (3,13) (3,9) (3,11) (4,6) (4,18) (4,12) (4,20) (4,17) (4,14) (4,19) (4,15) (4,7) (4,16) (4,21) (5,8) (5,23) (5,22) (5,10) (6,18) (6,12) (6,20) (6,17) (6,14) (6,19) (6,15) (6,7) (6,16) (6,21) (7,18) (7,12) (7,20) (7,17) (7,14) (7,19) (7,15) (7,16) (7,21) (8,23) (8,22) (8,10) (9,13) (9,11) (10,23) (10,22) (11,13) (12,18) (12,20) (12,17) (12,14) (12,19) (12,15) (12,16) (12,21) (14,18) (14,20) (14,17) (14,19) (14,15) (14,16) (14,21) (15,18) (15,20) (15,17) (15,19) (15,16) (15,21) (16,18) (16,20) (16,17) (16,19) (16,21) (17,18) (17,20) (17,19) (17,21) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21) (22,23)\nIs there a path between node 22 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph661-8_2", + "image": "data/connectivity/graph_visual/medium/graph661.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,4) (1,8) (1,17) (1,20) (1,13) (1,18) (1,19) (1,2) (1,23) (1,21) (1,16) (1,7) (2,10) (2,8) (2,6) (2,15) (2,9) (2,17) (2,20) (2,13) (2,18) (2,19) (2,12) (2,21) (2,16) (3,10) (3,8) (3,6) (3,15) (3,9) (3,20) (3,13) (3,18) (3,5) (3,19) (3,12) (3,16) (3,14) (4,11) (5,8) (5,6) (5,15) (5,9) (5,17) (5,20) (5,13) (5,18) (5,19) (5,21) (5,7) (6,10) (6,8) (6,15) (6,17) (6,20) (6,13) (6,18) (6,19) (6,12) (6,21) (6,16) (6,22) (7,15) (7,9) (7,13) (7,18) (7,12) (7,23) (7,14) (7,22) (8,10) (8,20) (8,13) (8,12) (8,21) (8,16) (8,14) (8,22) (9,10) (9,15) (9,20) (9,13) (9,12) (9,16) (9,14) (9,22) (10,15) (10,17) (10,13) (10,18) (10,12) (10,16) (10,14) (10,22) (12,15) (12,17) (12,13) (12,18) (12,23) (12,21) (12,16) (12,14) (12,22) (13,17) (13,20) (13,19) (13,21) (13,14) (13,22) (14,15) (14,17) (14,18) (14,16) (14,22) (15,17) (15,19) (15,16) (15,22) (16,17) (16,20) (16,19) (16,21) (17,19) (17,23) (17,21) (17,22) (18,23) (18,21) (18,22) (19,20) (19,23) (19,21) (19,22) (20,21) (20,22) (21,23) (22,23)\nIs there a path between node 8 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph517-13_6", + "image": "data/connectivity/graph_visual/medium/graph517.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,9) (0,17) (0,20) (1,15) (1,22) (1,14) (1,3) (1,21) (1,5) (1,18) (1,7) (1,6) (1,13) (2,15) (2,3) (2,4) (2,11) (2,21) (2,18) (2,8) (2,13) (3,15) (3,22) (3,12) (3,14) (3,4) (3,11) (3,21) (3,5) (3,7) (3,6) (3,16) (4,15) (4,22) (4,12) (4,14) (4,11) (4,5) (4,7) (4,6) (4,16) (4,8) (4,13) (5,15) (5,22) (5,12) (5,11) (5,21) (5,7) (5,6) (5,8) (5,13) (6,15) (6,12) (6,11) (6,21) (6,18) (6,16) (6,8) (6,13) (7,22) (7,12) (7,14) (7,11) (7,21) (7,16) (7,8) (8,22) (8,14) (8,21) (8,18) (8,16) (8,13) (9,19) (9,10) (9,17) (10,17) (11,22) (11,14) (11,21) (11,18) (11,13) (12,22) (12,14) (12,21) (12,18) (12,16) (12,13) (13,14) (13,18) (13,16) (14,15) (14,21) (14,18) (14,16) (15,21) (16,18) (17,20) (18,22)\nIs there a path between node 13 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph27-9_7", + "image": "data/connectivity/graph_visual/medium/graph27.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,2) (0,9) (0,1) (0,11) (0,4) (0,3) (1,6) (1,2) (1,9) (1,8) (1,11) (2,6) (2,8) (2,11) (2,3) (3,6) (3,9) (3,8) (3,10) (3,11) (3,4) (4,6) (4,8) (4,10) (5,7) (6,9) (6,8) (6,10) (6,11) (8,10) (9,11) (10,11)\nIs there a path between node 9 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph749-2_9", + "image": "data/connectivity/graph_visual/medium/graph749.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,24) (0,22) (0,18) (0,2) (0,6) (0,23) (0,12) (0,15) (0,19) (0,16) (0,10) (0,8) (0,20) (1,5) (1,22) (1,23) (1,9) (1,12) (1,15) (1,16) (1,8) (1,20) (2,24) (2,5) (2,22) (2,18) (2,6) (2,23) (2,9) (2,3) (2,15) (2,19) (2,16) (2,10) (2,8) (2,20) (3,24) (3,5) (3,22) (3,18) (3,6) (3,9) (3,15) (3,10) (3,17) (3,20) (4,13) (4,7) (4,14) (5,11) (5,24) (5,23) (5,12) (5,15) (5,19) (5,10) (5,8) (5,17) (6,11) (6,24) (6,22) (6,18) (6,23) (6,9) (6,19) (6,10) (6,8) (6,17) (6,20) (7,13) (8,11) (8,24) (8,22) (8,18) (8,12) (8,15) (8,17) (8,20) (9,11) (9,24) (9,23) (9,15) (9,19) (9,10) (9,17) (9,20) (10,24) (10,22) (10,18) (10,23) (10,19) (10,16) (10,20) (11,24) (11,22) (11,18) (11,12) (11,19) (11,16) (11,17) (11,20) (12,18) (12,23) (12,19) (12,16) (12,20) (13,14) (15,22) (15,16) (15,17) (15,20) (16,24) (16,22) (16,18) (16,23) (16,19) (16,20) (17,24) (17,18) (17,23) (17,20) (18,22) (18,19) (18,20) (19,24) (19,23) (20,22) (20,23) (22,24) (23,24)\nIs there a path between node 2 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph384-11_8", + "image": "data/connectivity/graph_visual/medium/graph384.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,6) (1,7) (1,5) (1,16) (1,15) (1,3) (1,13) (1,10) (1,12) (1,4) (1,17) (1,20) (1,18) (1,8) (1,2) (1,19) (1,9) (1,11) (1,14) (2,7) (2,5) (2,16) (2,15) (2,3) (2,13) (2,10) (2,12) (2,4) (2,17) (2,20) (2,18) (2,8) (2,19) (2,9) (2,11) (2,14) (3,7) (3,5) (3,16) (3,15) (3,13) (3,10) (3,12) (3,4) (3,17) (3,20) (3,18) (3,8) (3,19) (3,9) (3,11) (3,14) (4,7) (4,5) (4,16) (4,15) (4,13) (4,10) (4,12) (4,17) (4,20) (4,18) (4,8) (4,19) (4,9) (4,11) (4,14) (5,7) (5,16) (5,15) (5,13) (5,10) (5,12) (5,17) (5,20) (5,18) (5,8) (5,19) (5,9) (5,11) (5,14) (7,16) (7,15) (7,13) (7,10) (7,12) (7,17) (7,20) (7,18) (7,8) (7,19) (7,9) (7,11) (7,14) (8,16) (8,15) (8,13) (8,10) (8,12) (8,17) (8,20) (8,18) (8,19) (8,9) (8,11) (8,14) (9,16) (9,15) (9,13) (9,10) (9,12) (9,17) (9,20) (9,18) (9,19) (9,11) (9,14) (10,16) (10,15) (10,13) (10,12) (10,17) (10,20) (10,18) (10,19) (10,11) (10,14) (11,16) (11,15) (11,13) (11,12) (11,17) (11,20) (11,18) (11,19) (11,14) (12,16) (12,15) (12,13) (12,17) (12,20) (12,18) (12,19) (12,14) (13,16) (13,15) (13,17) (13,20) (13,18) (13,19) (13,14) (14,16) (14,15) (14,17) (14,20) (14,18) (14,19) (15,16) (15,17) (15,20) (15,18) (15,19) (16,17) (16,20) (16,18) (16,19) (17,20) (17,18) (17,19) (18,20) (18,19) (19,20)\nIs there a path between node 11 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph424-11_17", + "image": "data/connectivity/graph_visual/medium/graph424.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,13) (2,4) (2,11) (2,5) (2,21) (3,6) (3,5) (3,17) (4,12) (4,11) (4,20) (4,21) (5,12) (5,10) (5,7) (6,20) (6,17) (7,12) (7,8) (7,20) (7,10) (7,17) (8,10) (8,21) (10,11) (10,20) (11,12) (12,20) (13,18) (14,19) (16,19)\nIs there a path between node 11 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph709-2_21", + "image": "data/connectivity/graph_visual/medium/graph709.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,22) (0,5) (0,1) (1,11) (1,8) (1,3) (2,11) (2,13) (2,16) (2,8) (2,17) (3,11) (3,16) (3,5) (4,21) (4,14) (5,11) (5,22) (5,16) (5,17) (6,18) (6,9) (6,10) (7,22) (7,12) (8,22) (8,16) (8,17) (9,18) (9,15) (9,21) (10,19) (11,22) (11,16) (11,17) (12,13) (12,24) (13,16) (14,18) (14,21) (22,24)\nIs there a path between node 2 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph458-1_6", + "image": "data/connectivity/graph_visual/medium/graph458.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,7) (0,5) (0,11) (0,3) (0,10) (0,6) (0,18) (0,15) (0,2) (0,13) (0,16) (0,8) (0,20) (1,12) (1,14) (1,21) (1,9) (1,4) (1,17) (2,19) (2,7) (2,5) (2,11) (2,3) (2,10) (2,6) (2,18) (2,15) (2,13) (2,16) (2,8) (2,20) (3,19) (3,7) (3,5) (3,11) (3,10) (3,6) (3,18) (3,15) (3,13) (3,16) (3,8) (3,20) (4,12) (4,14) (4,21) (4,9) (4,17) (5,19) (5,7) (5,11) (5,10) (5,6) (5,18) (5,15) (5,13) (5,16) (5,8) (5,20) (6,19) (6,7) (6,11) (6,10) (6,18) (6,15) (6,13) (6,16) (6,8) (6,20) (7,19) (7,11) (7,10) (7,18) (7,15) (7,13) (7,16) (7,8) (7,20) (8,19) (8,11) (8,10) (8,18) (8,15) (8,13) (8,16) (8,20) (9,12) (9,14) (9,21) (9,17) (10,19) (10,11) (10,18) (10,15) (10,13) (10,16) (10,20) (11,19) (11,18) (11,15) (11,13) (11,16) (11,20) (12,14) (12,21) (12,17) (13,19) (13,18) (13,15) (13,16) (13,20) (14,21) (14,17) (15,19) (15,18) (15,16) (15,20) (16,19) (16,18) (16,20) (17,21) (18,19) (18,20) (19,20)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph466-5_11", + "image": "data/connectivity/graph_visual/medium/graph466.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,10) (0,14) (0,1) (0,11) (0,17) (0,13) (1,2) (1,10) (1,14) (1,11) (1,17) (1,13) (2,10) (2,14) (2,11) (2,17) (2,13) (3,19) (3,9) (3,12) (3,16) (3,5) (3,7) (3,18) (3,21) (4,15) (4,20) (4,6) (4,8) (5,19) (5,9) (5,12) (5,16) (5,7) (5,18) (5,21) (6,15) (6,20) (6,8) (7,19) (7,9) (7,12) (7,16) (7,18) (7,21) (8,15) (8,20) (9,19) (9,12) (9,16) (9,18) (9,21) (10,14) (10,11) (10,17) (10,13) (11,14) (11,17) (11,13) (12,19) (12,16) (12,18) (12,21) (13,14) (13,17) (14,17) (15,20) (16,19) (16,18) (16,21) (18,19) (18,21) (19,21)\nIs there a path between node 5 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph178-8_10", + "image": "data/connectivity/graph_visual/medium/graph178.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,1) (0,7) (0,14) (0,8) (0,5) (0,11) (0,16) (1,7) (1,17) (1,14) (1,8) (1,6) (1,5) (1,9) (1,16) (1,3) (2,12) (2,4) (2,7) (2,8) (2,5) (2,9) (2,11) (2,16) (2,3) (2,13) (3,12) (3,14) (3,8) (3,5) (3,11) (3,16) (3,13) (4,17) (4,8) (4,6) (4,16) (4,13) (5,12) (5,7) (5,17) (5,14) (5,8) (5,11) (5,16) (6,12) (6,17) (6,9) (6,16) (7,17) (7,14) (7,9) (7,11) (7,16) (8,17) (8,14) (9,17) (9,14) (9,11) (9,16) (11,12) (11,17) (11,14) (11,13) (12,14) (13,17) (13,14) (13,16) (14,17) (16,17)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph160-13_1", + "image": "data/connectivity/graph_visual/medium/graph160.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,6) (0,13) (0,15) (0,8) (0,14) (0,2) (1,7) (2,10) (2,13) (2,11) (2,14) (2,17) (3,6) (3,12) (3,11) (4,16) (4,5) (4,7) (6,15) (8,13) (8,14) (10,12) (10,13) (10,17) (11,14) (12,13) (12,15) (14,17) (15,17)\nIs there a path between node 13 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph630-17_13", + "image": "data/connectivity/graph_visual/medium/graph630.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,10) (0,7) (0,11) (1,22) (1,21) (2,10) (2,7) (2,12) (2,3) (2,11) (2,20) (3,14) (3,18) (3,5) (3,7) (3,11) (4,10) (4,12) (5,14) (5,17) (5,11) (5,23) (7,19) (7,18) (7,10) (7,21) (8,13) (9,13) (10,18) (10,15) (10,12) (11,21) (12,14) (12,15) (12,21) (14,20) (15,23) (17,19) (17,18) (17,20) (18,19) (20,23) (22,23)\nIs there a path between node 17 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph429-14_18", + "image": "data/connectivity/graph_visual/medium/graph429.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,10) (0,2) (0,8) (0,13) (1,11) (1,21) (1,7) (2,20) (2,6) (2,10) (2,3) (2,4) (2,12) (2,18) (3,17) (3,6) (3,4) (3,19) (3,18) (4,17) (4,19) (4,13) (6,17) (6,10) (6,19) (7,14) (8,15) (8,20) (9,20) (9,16) (9,18) (10,20) (10,16) (10,19) (12,19) (12,13) (13,17) (13,15) (13,16) (15,17) (15,19) (16,17) (17,20) (18,19) (19,20)\nIs there a path between node 14 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph673-19_14", + "image": "data/connectivity/graph_visual/medium/graph673.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,10) (0,9) (0,11) (0,19) (0,23) (0,20) (0,17) (0,16) (1,2) (1,10) (1,21) (1,9) (1,11) (1,12) (1,16) (1,6) (2,15) (2,21) (2,19) (2,23) (2,20) (2,16) (2,6) (3,8) (4,7) (6,10) (6,21) (6,9) (6,11) (6,19) (6,23) (6,20) (6,17) (6,16) (8,22) (8,18) (9,10) (9,21) (9,11) (9,19) (9,23) (9,12) (9,20) (9,17) (9,16) (10,15) (10,21) (10,11) (10,12) (10,20) (10,16) (11,15) (11,19) (11,20) (11,17) (11,16) (12,15) (12,21) (12,19) (12,23) (12,20) (13,14) (15,21) (15,23) (15,20) (15,16) (16,21) (16,19) (16,17) (17,21) (17,19) (17,20) (19,21) (19,20) (20,21) (20,23) (21,23)\nIs there a path between node 19 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph725-9_1", + "image": "data/connectivity/graph_visual/medium/graph725.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,7) (0,2) (0,5) (0,18) (0,9) (0,16) (0,21) (0,13) (0,11) (0,14) (0,22) (0,15) (0,6) (2,20) (2,7) (2,5) (2,18) (2,9) (2,16) (2,21) (2,13) (2,11) (2,14) (2,22) (2,15) (2,6) (3,4) (3,10) (3,8) (3,17) (3,19) (3,23) (3,24) (4,10) (4,8) (4,17) (4,19) (4,23) (4,24) (5,20) (5,7) (5,18) (5,9) (5,16) (5,21) (5,13) (5,11) (5,14) (5,22) (5,15) (5,6) (6,20) (6,7) (6,18) (6,9) (6,16) (6,21) (6,13) (6,11) (6,14) (6,22) (6,15) (7,20) (7,18) (7,9) (7,16) (7,21) (7,13) (7,11) (7,14) (7,22) (7,15) (8,10) (8,17) (8,19) (8,23) (8,24) (9,20) (9,18) (9,16) (9,21) (9,13) (9,11) (9,14) (9,22) (9,15) (10,17) (10,19) (10,23) (10,24) (11,20) (11,18) (11,16) (11,21) (11,13) (11,14) (11,22) (11,15) (13,20) (13,18) (13,16) (13,21) (13,14) (13,22) (13,15) (14,20) (14,18) (14,16) (14,21) (14,22) (14,15) (15,20) (15,18) (15,16) (15,21) (15,22) (16,20) (16,18) (16,21) (16,22) (17,19) (17,23) (17,24) (18,20) (18,21) (18,22) (19,23) (19,24) (20,21) (20,22) (21,22) (23,24)\nIs there a path between node 9 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph711-0_20", + "image": "data/connectivity/graph_visual/medium/graph711.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,2) (0,7) (0,15) (0,14) (0,22) (0,10) (0,18) (0,5) (0,9) (0,4) (0,11) (0,8) (0,20) (0,13) (1,2) (1,7) (1,15) (1,14) (1,18) (1,5) (1,16) (1,9) (1,4) (1,11) (1,8) (1,13) (2,24) (2,7) (2,15) (2,14) (2,22) (2,18) (2,16) (2,9) (2,4) (2,11) (2,8) (2,20) (2,23) (3,21) (4,7) (4,14) (4,22) (4,18) (4,16) (4,13) (4,23) (5,24) (5,7) (5,15) (5,14) (5,22) (5,10) (5,18) (5,20) (5,23) (6,12) (7,24) (7,15) (7,14) (7,10) (7,18) (7,16) (7,9) (7,11) (7,8) (7,20) (7,13) (7,23) (8,24) (8,14) (8,10) (8,18) (8,9) (8,13) (8,23) (9,24) (9,15) (9,14) (9,22) (9,10) (9,16) (9,20) (9,23) (10,24) (10,15) (10,14) (10,22) (10,18) (10,16) (10,20) (11,15) (11,14) (11,18) (11,16) (11,20) (11,13) (11,23) (13,24) (13,15) (13,18) (13,16) (13,23) (14,24) (14,15) (14,22) (14,18) (14,16) (14,23) (15,24) (15,22) (15,18) (15,16) (15,20) (15,23) (16,24) (16,20) (16,23) (18,22) (18,20) (18,23) (19,21) (20,22) (22,24) (22,23) (23,24)\nIs there a path between node 0 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph287-15_3", + "image": "data/connectivity/graph_visual/medium/graph287.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,14) (0,4) (0,7) (1,17) (1,6) (1,2) (1,18) (2,5) (2,18) (3,10) (3,9) (3,19) (3,12) (3,8) (4,10) (4,15) (4,12) (5,18) (6,11) (6,16) (6,18) (7,10) (7,19) (7,12) (9,15) (10,14) (11,18) (12,13) (12,15) (13,19) (14,15) (15,19) (17,18)\nIs there a path between node 15 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph688-10_15", + "image": "data/connectivity/graph_visual/medium/graph688.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,6) (0,11) (0,14) (0,2) (1,20) (1,8) (1,7) (1,16) (1,21) (1,9) (1,17) (1,5) (1,23) (1,12) (1,22) (2,4) (2,6) (2,11) (2,14) (3,15) (3,18) (3,13) (3,19) (3,10) (4,6) (4,11) (4,14) (5,20) (5,8) (5,7) (5,16) (5,21) (5,9) (5,17) (5,23) (5,12) (5,22) (6,11) (6,14) (7,20) (7,8) (7,16) (7,21) (7,9) (7,17) (7,23) (7,12) (7,22) (8,20) (8,16) (8,21) (8,9) (8,17) (8,23) (8,12) (8,22) (9,20) (9,16) (9,21) (9,17) (9,23) (9,12) (9,22) (10,15) (10,18) (10,13) (10,19) (11,14) (12,20) (12,16) (12,21) (12,17) (12,23) (12,22) (13,15) (13,18) (13,19) (15,18) (15,19) (16,20) (16,21) (16,17) (16,23) (16,22) (17,20) (17,21) (17,23) (17,22) (18,19) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 10 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph302-5_10", + "image": "data/connectivity/graph_visual/medium/graph302.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,5) (0,7) (0,10) (0,2) (0,4) (0,11) (0,12) (0,18) (0,16) (1,9) (1,15) (2,5) (2,7) (2,19) (2,13) (2,14) (2,6) (2,3) (2,11) (2,12) (2,17) (2,18) (3,7) (3,10) (3,13) (3,17) (3,18) (3,16) (4,5) (4,7) (4,10) (4,14) (4,6) (4,11) (4,12) (4,17) (4,18) (4,16) (5,7) (5,19) (5,10) (5,14) (5,6) (5,11) (5,17) (5,18) (5,16) (6,19) (6,10) (6,11) (6,17) (6,18) (7,19) (7,10) (7,13) (7,12) (7,18) (7,16) (8,9) (8,15) (9,15) (10,19) (10,13) (10,14) (10,11) (10,12) (10,18) (10,16) (11,19) (11,13) (11,12) (11,17) (12,13) (12,14) (12,17) (12,18) (12,16) (13,19) (13,17) (14,19) (14,17) (14,18) (14,16) (16,19) (16,17) (16,18) (17,18) (18,19)\nIs there a path between node 5 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph431-20_7", + "image": "data/connectivity/graph_visual/medium/graph431.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,16) (0,3) (0,5) (0,19) (1,21) (2,21) (2,10) (2,19) (3,4) (3,19) (4,15) (4,10) (4,19) (5,16) (6,8) (8,13) (10,17) (11,13) (14,20) (15,17) (16,17) (17,19)\nIs there a path between node 20 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph145-17_15", + "image": "data/connectivity/graph_visual/medium/graph145.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,12) (0,4) (0,11) (0,17) (0,2) (0,5) (0,9) (0,8) (0,16) (0,10) (1,3) (1,12) (1,4) (1,11) (1,17) (1,7) (1,2) (1,5) (1,9) (1,8) (1,10) (2,3) (2,12) (2,4) (2,11) (2,17) (2,7) (2,5) (2,8) (2,16) (3,12) (3,7) (3,9) (3,8) (4,12) (4,11) (4,17) (4,5) (4,9) (4,8) (4,16) (4,10) (5,12) (5,11) (5,17) (5,7) (5,14) (5,9) (5,16) (5,10) (6,15) (6,13) (7,12) (7,11) (7,17) (7,9) (7,16) (7,10) (8,11) (8,14) (8,9) (8,16) (8,10) (9,12) (9,17) (9,10) (10,11) (10,17) (10,14) (10,16) (11,17) (11,16) (14,16) (16,17)\nIs there a path between node 17 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph305-10_6", + "image": "data/connectivity/graph_visual/medium/graph305.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,1) (0,18) (1,11) (1,18) (2,15) (2,14) (2,7) (2,5) (2,4) (2,3) (2,8) (2,6) (2,16) (3,15) (3,14) (3,5) (3,13) (3,4) (3,9) (3,6) (4,15) (4,7) (4,5) (4,12) (4,8) (4,9) (4,16) (5,14) (5,12) (5,17) (5,9) (5,6) (5,16) (6,15) (6,14) (6,7) (6,17) (6,16) (7,15) (7,14) (7,13) (7,12) (7,9) (7,16) (8,15) (8,14) (8,13) (8,12) (8,17) (8,16) (9,15) (9,14) (9,12) (11,19) (11,18) (12,15) (12,14) (12,13) (12,17) (13,15) (13,14) (14,15) (15,17) (15,16) (16,17) (18,19)\nIs there a path between node 10 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph22-4_9", + "image": "data/connectivity/graph_visual/medium/graph22.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,2) (2,9) (7,11) (10,11)\nIs there a path between node 4 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph272-6_18", + "image": "data/connectivity/graph_visual/medium/graph272.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,13) (0,9) (0,7) (0,12) (0,4) (0,5) (0,19) (0,6) (0,1) (0,17) (1,14) (1,9) (1,3) (1,7) (1,12) (1,4) (1,5) (1,19) (1,15) (1,17) (2,11) (2,8) (2,10) (3,13) (3,14) (3,9) (3,7) (3,12) (3,4) (3,5) (3,6) (3,18) (3,15) (4,13) (4,9) (4,12) (4,19) (4,6) (4,18) (4,15) (4,17) (5,13) (5,14) (5,7) (5,12) (5,19) (5,15) (5,17) (6,13) (6,9) (6,7) (6,19) (6,15) (6,17) (7,13) (7,14) (7,9) (7,12) (7,19) (7,18) (7,17) (8,11) (8,16) (8,10) (9,14) (9,18) (9,17) (10,11) (11,16) (12,14) (12,19) (12,18) (12,15) (12,17) (13,14) (13,19) (13,18) (13,17) (14,19) (14,18) (14,15) (14,17) (15,17) (17,19) (17,18) (18,19)\nIs there a path between node 6 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph589-23_5", + "image": "data/connectivity/graph_visual/medium/graph589.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,6) (0,23) (0,19) (1,8) (1,4) (2,20) (2,17) (2,19) (2,15) (3,13) (3,15) (5,23) (5,12) (5,15) (5,18) (7,9) (9,14) (10,11) (12,23) (12,22) (12,15) (13,21) (13,15) (16,23) (16,17) (16,22) (16,18) (17,22) (18,21) (18,20) (18,22) (19,23) (20,23)\nIs there a path between node 23 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph475-3_8", + "image": "data/connectivity/graph_visual/medium/graph475.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,1) (0,4) (0,13) (0,16) (2,20) (2,19) (2,18) (3,21) (3,9) (4,10) (4,9) (5,20) (5,7) (5,14) (6,14) (7,19) (8,10) (8,13) (9,21) (10,21) (11,19) (11,14) (12,17) (12,13) (13,22) (13,16) (14,19) (15,19) (16,22) (16,21) (18,20) (21,22)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph517-0_21", + "image": "data/connectivity/graph_visual/medium/graph517.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,9) (0,17) (0,20) (1,15) (1,22) (1,14) (1,3) (1,21) (1,5) (1,18) (1,7) (1,6) (1,13) (2,15) (2,3) (2,4) (2,11) (2,21) (2,18) (2,8) (2,13) (3,15) (3,22) (3,12) (3,14) (3,4) (3,11) (3,21) (3,5) (3,7) (3,6) (3,16) (4,15) (4,22) (4,12) (4,14) (4,11) (4,5) (4,7) (4,6) (4,16) (4,8) (4,13) (5,15) (5,22) (5,12) (5,11) (5,21) (5,7) (5,6) (5,8) (5,13) (6,15) (6,12) (6,11) (6,21) (6,18) (6,16) (6,8) (6,13) (7,22) (7,12) (7,14) (7,11) (7,21) (7,16) (7,8) (8,22) (8,14) (8,21) (8,18) (8,16) (8,13) (9,19) (9,10) (9,17) (10,17) (11,22) (11,14) (11,21) (11,18) (11,13) (12,22) (12,14) (12,21) (12,18) (12,16) (12,13) (13,14) (13,18) (13,16) (14,15) (14,21) (14,18) (14,16) (15,21) (16,18) (17,20) (18,22)\nIs there a path between node 0 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph647-7_13", + "image": "data/connectivity/graph_visual/medium/graph647.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,18) (0,6) (0,1) (1,12) (1,6) (1,3) (2,8) (2,18) (2,20) (2,13) (2,11) (3,23) (3,18) (3,13) (4,16) (4,22) (5,7) (6,18) (6,11) (6,15) (7,9) (8,23) (8,14) (8,20) (8,11) (12,14) (13,18) (14,23) (14,18) (15,18) (16,17) (16,21) (18,23) (18,20)\nIs there a path between node 7 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph29-5_0", + "image": "data/connectivity/graph_visual/medium/graph29.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,9) (0,11) (1,6) (1,3) (1,4) (1,7) (1,8) (1,10) (1,2) (1,5) (2,6) (2,3) (2,4) (2,7) (2,8) (2,10) (2,5) (3,6) (3,4) (3,7) (3,8) (3,10) (3,5) (4,6) (4,7) (4,8) (4,10) (4,5) (5,6) (5,7) (5,8) (5,10) (6,7) (6,8) (6,10) (7,8) (7,10) (8,10) (9,11)\nIs there a path between node 5 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph433-9_18", + "image": "data/connectivity/graph_visual/medium/graph433.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,7) (2,12) (3,18) (3,12) (3,15) (3,9) (5,11) (5,17) (5,20) (6,16) (6,17) (7,21) (7,18) (7,9) (8,21) (8,18) (8,15) (9,21) (9,12) (9,19) (12,21) (14,21) (15,18) (15,19) (16,17) (16,20) (17,20)\nIs there a path between node 9 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph146-5_1", + "image": "data/connectivity/graph_visual/medium/graph146.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,2) (0,7) (0,3) (0,14) (0,4) (0,9) (0,5) (0,16) (1,8) (1,10) (2,12) (2,17) (2,14) (2,11) (2,9) (2,16) (3,12) (3,17) (3,14) (3,11) (3,4) (3,9) (3,5) (3,16) (4,7) (4,14) (4,11) (4,9) (5,12) (5,7) (5,14) (5,16) (6,8) (6,10) (7,14) (7,11) (7,9) (7,16) (8,10) (9,12) (9,17) (9,11) (11,16) (12,17) (12,14) (12,16) (13,15) (14,17) (14,16) (16,17)\nIs there a path between node 5 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph684-21_15", + "image": "data/connectivity/graph_visual/medium/graph684.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,21) (0,12) (0,9) (0,2) (0,6) (0,4) (0,5) (0,14) (0,17) (0,8) (0,20) (0,13) (0,19) (0,22) (0,1) (0,15) (0,10) (0,18) (1,7) (1,21) (1,12) (1,9) (1,2) (1,6) (1,4) (1,5) (1,14) (1,17) (1,8) (1,20) (1,13) (1,19) (1,22) (1,15) (1,10) (1,18) (2,7) (2,21) (2,12) (2,9) (2,6) (2,4) (2,5) (2,14) (2,17) (2,8) (2,20) (2,13) (2,19) (2,22) (2,15) (2,10) (2,18) (3,11) (3,23) (4,7) (4,21) (4,12) (4,9) (4,6) (4,5) (4,14) (4,17) (4,8) (4,20) (4,13) (4,19) (4,22) (4,15) (4,10) (4,18) (5,7) (5,21) (5,12) (5,9) (5,6) (5,14) (5,17) (5,8) (5,20) (5,13) (5,19) (5,22) (5,15) (5,10) (5,18) (6,7) (6,21) (6,12) (6,9) (6,14) (6,17) (6,8) (6,20) (6,13) (6,19) (6,22) (6,15) (6,10) (6,18) (7,21) (7,12) (7,9) (7,14) (7,17) (7,8) (7,20) (7,13) (7,19) (7,22) (7,15) (7,10) (7,18) (8,21) (8,12) (8,9) (8,14) (8,17) (8,20) (8,13) (8,19) (8,22) (8,15) (8,10) (8,18) (9,21) (9,12) (9,14) (9,17) (9,20) (9,13) (9,19) (9,22) (9,15) (9,10) (9,18) (10,21) (10,12) (10,14) (10,17) (10,20) (10,13) (10,19) (10,22) (10,15) (10,18) (11,23) (12,21) (12,14) (12,17) (12,20) (12,13) (12,19) (12,22) (12,15) (12,18) (13,21) (13,14) (13,17) (13,20) (13,19) (13,22) (13,15) (13,18) (14,21) (14,17) (14,20) (14,19) (14,22) (14,15) (14,18) (15,21) (15,17) (15,20) (15,19) (15,22) (15,18) (17,21) (17,20) (17,19) (17,22) (17,18) (18,21) (18,20) (18,19) (18,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 21 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph52-2_3", + "image": "data/connectivity/graph_visual/medium/graph52.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (0,5) (0,11) (0,8) (0,6) (0,1) (1,10) (1,3) (1,5) (1,9) (1,6) (1,2) (2,10) (2,3) (2,5) (2,9) (2,8) (2,7) (2,6) (2,13) (3,9) (3,11) (3,8) (3,7) (4,12) (5,10) (5,9) (5,8) (5,7) (5,6) (6,10) (6,9) (6,11) (6,8) (7,10) (7,11) (7,8) (7,13) (8,10) (8,11) (8,13) (9,10) (9,11) (9,13) (10,11) (10,13)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph503-8_6", + "image": "data/connectivity/graph_visual/medium/graph503.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,7) (0,9) (0,16) (0,6) (0,13) (0,1) (1,2) (1,10) (1,16) (1,13) (2,16) (2,12) (4,21) (4,6) (4,13) (4,18) (5,22) (5,8) (5,15) (6,10) (6,13) (8,22) (8,15) (9,17) (9,10) (9,21) (9,13) (9,18) (10,19) (10,12) (10,13) (12,17) (12,19) (12,13) (12,18) (13,17) (13,18) (15,22) (15,20) (16,19) (17,19) (17,21) (18,21) (20,22)\nIs there a path between node 8 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph612-10_14", + "image": "data/connectivity/graph_visual/medium/graph612.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,19) (0,6) (0,12) (0,20) (0,15) (0,9) (0,13) (0,2) (0,14) (0,11) (0,3) (0,23) (0,5) (1,21) (1,7) (1,8) (1,22) (1,4) (1,18) (1,17) (1,16) (2,10) (2,19) (2,6) (2,12) (2,20) (2,15) (2,9) (2,13) (2,14) (2,11) (2,3) (2,23) (2,5) (3,10) (3,19) (3,6) (3,12) (3,20) (3,15) (3,9) (3,13) (3,14) (3,11) (3,23) (3,5) (4,21) (4,7) (4,8) (4,22) (4,18) (4,17) (4,16) (5,10) (5,19) (5,6) (5,12) (5,20) (5,15) (5,9) (5,13) (5,14) (5,11) (5,23) (6,10) (6,19) (6,12) (6,20) (6,15) (6,9) (6,13) (6,14) (6,11) (6,23) (7,21) (7,8) (7,22) (7,18) (7,17) (7,16) (8,21) (8,22) (8,18) (8,17) (8,16) (9,10) (9,19) (9,12) (9,20) (9,15) (9,13) (9,14) (9,11) (9,23) (10,19) (10,12) (10,20) (10,15) (10,13) (10,14) (10,11) (10,23) (11,19) (11,12) (11,20) (11,15) (11,13) (11,14) (11,23) (12,19) (12,20) (12,15) (12,13) (12,14) (12,23) (13,19) (13,20) (13,15) (13,14) (13,23) (14,19) (14,20) (14,15) (14,23) (15,19) (15,20) (15,23) (16,21) (16,22) (16,18) (16,17) (17,21) (17,22) (17,18) (18,21) (18,22) (19,20) (19,23) (20,23) (21,22)\nIs there a path between node 10 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph57-12_11", + "image": "data/connectivity/graph_visual/medium/graph57.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,5) (1,6) (1,8) (1,13) (3,9) (5,6) (5,11) (5,13) (5,10) (6,11) (6,12) (6,13) (7,12) (10,12) (11,12)\nIs there a path between node 12 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph853-12_24", + "image": "data/connectivity/graph_visual/medium/graph853.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,15) (0,6) (0,16) (0,2) (1,5) (1,21) (1,19) (1,11) (1,18) (1,12) (1,8) (1,14) (1,20) (1,24) (1,9) (1,10) (2,7) (2,15) (2,6) (2,16) (3,22) (3,17) (3,13) (3,4) (3,23) (4,22) (4,17) (4,13) (4,23) (5,21) (5,19) (5,11) (5,18) (5,12) (5,8) (5,14) (5,20) (5,24) (5,9) (5,10) (6,7) (6,15) (6,16) (7,15) (7,16) (8,21) (8,19) (8,11) (8,18) (8,12) (8,14) (8,20) (8,24) (8,9) (8,10) (9,21) (9,19) (9,11) (9,18) (9,12) (9,14) (9,20) (9,24) (9,10) (10,21) (10,19) (10,11) (10,18) (10,12) (10,14) (10,20) (10,24) (11,21) (11,19) (11,18) (11,12) (11,14) (11,20) (11,24) (12,21) (12,19) (12,18) (12,14) (12,20) (12,24) (13,22) (13,17) (13,23) (14,21) (14,19) (14,18) (14,20) (14,24) (15,16) (17,22) (17,23) (18,21) (18,19) (18,20) (18,24) (19,21) (19,20) (19,24) (20,21) (20,24) (21,24) (22,23)\nIs there a path between node 12 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph776-11_16", + "image": "data/connectivity/graph_visual/medium/graph776.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,22) (0,5) (0,12) (0,20) (0,6) (0,19) (0,21) (0,9) (0,17) (0,7) (0,14) (0,15) (1,2) (1,13) (1,3) (1,10) (1,4) (1,18) (1,24) (1,11) (1,16) (1,8) (2,13) (2,3) (2,10) (2,4) (2,18) (2,24) (2,11) (2,16) (2,8) (3,13) (3,10) (3,4) (3,18) (3,24) (3,11) (3,16) (3,8) (4,13) (4,10) (4,18) (4,24) (4,11) (4,16) (4,8) (5,23) (5,22) (5,12) (5,20) (5,6) (5,19) (5,21) (5,9) (5,17) (5,7) (5,14) (5,15) (6,23) (6,22) (6,12) (6,20) (6,19) (6,21) (6,9) (6,17) (6,7) (6,14) (6,15) (7,23) (7,22) (7,12) (7,20) (7,19) (7,21) (7,9) (7,17) (7,14) (7,15) (8,13) (8,10) (8,18) (8,24) (8,11) (8,16) (9,23) (9,22) (9,12) (9,20) (9,19) (9,21) (9,17) (9,14) (9,15) (10,13) (10,18) (10,24) (10,11) (10,16) (11,13) (11,18) (11,24) (11,16) (12,23) (12,22) (12,20) (12,19) (12,21) (12,17) (12,14) (12,15) (13,18) (13,24) (13,16) (14,23) (14,22) (14,20) (14,19) (14,21) (14,17) (14,15) (15,23) (15,22) (15,20) (15,19) (15,21) (15,17) (16,18) (16,24) (17,23) (17,22) (17,20) (17,19) (17,21) (18,24) (19,23) (19,22) (19,20) (19,21) (20,23) (20,22) (20,21) (21,23) (21,22) (22,23)\nIs there a path between node 11 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph604-22_6", + "image": "data/connectivity/graph_visual/medium/graph604.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,3) (0,23) (0,12) (0,14) (0,16) (1,7) (1,21) (1,20) (1,6) (1,8) (2,11) (2,5) (2,19) (3,4) (3,23) (3,12) (3,9) (3,16) (4,22) (4,23) (4,12) (5,11) (5,19) (6,7) (6,13) (6,15) (6,21) (6,20) (6,10) (6,8) (6,18) (7,13) (7,20) (7,10) (7,8) (7,18) (8,15) (8,10) (8,18) (9,22) (9,23) (9,12) (9,14) (9,16) (10,13) (10,21) (10,20) (11,17) (11,19) (12,22) (12,23) (12,14) (13,21) (13,20) (13,18) (14,22) (15,20) (15,18) (16,22) (17,19) (18,20) (20,21)\nIs there a path between node 22 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph391-7_1", + "image": "data/connectivity/graph_visual/medium/graph391.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,9) (0,20) (0,8) (0,14) (0,2) (0,11) (0,1) (0,10) (0,7) (0,12) (0,4) (0,5) (0,15) (0,16) (1,18) (1,9) (1,20) (1,8) (1,14) (1,2) (1,11) (1,10) (1,7) (1,12) (1,4) (1,5) (1,15) (1,16) (2,18) (2,9) (2,20) (2,8) (2,14) (2,11) (2,10) (2,7) (2,12) (2,4) (2,5) (2,15) (2,16) (3,13) (3,19) (4,18) (4,9) (4,20) (4,8) (4,14) (4,11) (4,10) (4,7) (4,12) (4,5) (4,15) (4,16) (5,18) (5,9) (5,20) (5,8) (5,14) (5,11) (5,10) (5,7) (5,12) (5,15) (5,16) (6,17) (7,18) (7,9) (7,20) (7,8) (7,14) (7,11) (7,10) (7,12) (7,15) (7,16) (8,18) (8,9) (8,20) (8,14) (8,11) (8,10) (8,12) (8,15) (8,16) (9,18) (9,20) (9,14) (9,11) (9,10) (9,12) (9,15) (9,16) (10,18) (10,20) (10,14) (10,11) (10,12) (10,15) (10,16) (11,18) (11,20) (11,14) (11,12) (11,15) (11,16) (12,18) (12,20) (12,14) (12,15) (12,16) (13,19) (14,18) (14,20) (14,15) (14,16) (15,18) (15,20) (15,16) (16,18) (16,20) (18,20)\nIs there a path between node 7 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph71-4_7", + "image": "data/connectivity/graph_visual/medium/graph71.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,2) (0,5) (0,12) (0,11) (0,8) (0,1) (0,13) (0,10) (0,3) (1,2) (1,5) (1,12) (1,11) (1,8) (1,13) (1,10) (1,3) (2,5) (2,12) (2,11) (2,8) (2,13) (2,10) (2,3) (3,5) (3,12) (3,11) (3,8) (3,13) (3,10) (4,9) (4,6) (4,7) (4,14) (5,12) (5,11) (5,8) (5,13) (5,10) (6,9) (6,7) (6,14) (7,9) (7,14) (8,12) (8,11) (8,13) (8,10) (9,14) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nIs there a path between node 4 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph681-19_2", + "image": "data/connectivity/graph_visual/medium/graph681.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,22) (0,16) (0,2) (0,6) (0,17) (0,20) (0,1) (0,12) (0,8) (0,11) (0,4) (0,18) (0,7) (0,3) (0,23) (0,9) (1,21) (1,22) (1,16) (1,2) (1,6) (1,17) (1,20) (1,12) (1,8) (1,11) (1,4) (1,18) (1,7) (1,3) (1,23) (1,9) (2,21) (2,22) (2,16) (2,6) (2,17) (2,20) (2,12) (2,8) (2,11) (2,4) (2,18) (2,7) (2,3) (2,23) (2,9) (3,21) (3,22) (3,16) (3,6) (3,17) (3,20) (3,12) (3,8) (3,11) (3,4) (3,18) (3,7) (3,23) (3,9) (4,21) (4,22) (4,16) (4,6) (4,17) (4,20) (4,12) (4,8) (4,11) (4,18) (4,7) (4,23) (4,9) (5,13) (6,21) (6,22) (6,16) (6,17) (6,20) (6,12) (6,8) (6,11) (6,18) (6,7) (6,23) (6,9) (7,21) (7,22) (7,16) (7,17) (7,20) (7,12) (7,8) (7,11) (7,18) (7,23) (7,9) (8,21) (8,22) (8,16) (8,17) (8,20) (8,12) (8,11) (8,18) (8,23) (8,9) (9,21) (9,22) (9,16) (9,17) (9,20) (9,12) (9,11) (9,18) (9,23) (10,14) (10,19) (10,15) (11,21) (11,22) (11,16) (11,17) (11,20) (11,12) (11,18) (11,23) (12,21) (12,22) (12,16) (12,17) (12,20) (12,18) (12,23) (14,19) (14,15) (15,19) (16,21) (16,22) (16,17) (16,20) (16,18) (16,23) (17,21) (17,22) (17,20) (17,18) (17,23) (18,21) (18,22) (18,20) (18,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 19 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph409-7_14", + "image": "data/connectivity/graph_visual/medium/graph409.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,6) (0,21) (0,10) (0,17) (0,2) (0,11) (0,1) (0,4) (0,3) (0,19) (0,5) (0,9) (1,6) (1,21) (1,15) (1,10) (1,17) (1,2) (1,11) (1,4) (1,7) (2,6) (2,13) (2,15) (2,10) (2,17) (2,4) (2,3) (2,19) (2,9) (3,6) (3,21) (3,13) (3,10) (3,17) (3,11) (3,19) (3,5) (4,21) (4,13) (4,15) (4,10) (4,17) (4,11) (4,19) (4,5) (4,7) (4,18) (4,9) (5,6) (5,21) (5,15) (5,10) (5,17) (5,11) (5,19) (5,7) (5,9) (6,15) (6,10) (6,17) (6,11) (6,19) (6,7) (6,18) (6,9) (7,13) (7,15) (7,10) (7,17) (7,11) (7,19) (7,18) (8,14) (8,16) (9,21) (9,13) (9,15) (9,17) (9,11) (9,19) (9,18) (10,21) (10,13) (10,15) (10,17) (10,11) (10,19) (10,18) (11,21) (11,13) (11,15) (11,17) (11,18) (12,14) (12,16) (12,20) (13,21) (13,17) (13,18) (15,21) (15,17) (15,18) (17,21) (17,19) (17,18) (18,21) (18,19)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph649-13_11", + "image": "data/connectivity/graph_visual/medium/graph649.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (1,5) (1,18) (1,7) (1,22) (1,11) (1,20) (1,4) (1,23) (2,14) (2,10) (2,21) (2,15) (2,16) (2,3) (3,14) (3,10) (3,15) (3,16) (3,6) (3,19) (4,18) (4,7) (4,22) (4,11) (4,20) (4,23) (5,13) (5,7) (5,22) (5,11) (5,20) (5,23) (6,10) (6,21) (6,15) (6,16) (6,9) (6,8) (6,19) (7,13) (7,22) (7,20) (7,23) (8,10) (8,9) (8,19) (9,21) (9,15) (9,19) (10,21) (10,16) (10,19) (11,18) (11,13) (11,22) (11,23) (12,17) (13,22) (13,20) (14,15) (14,16) (14,19) (15,16) (15,19) (16,21) (16,19) (18,20) (18,23) (19,21) (20,22) (20,23) (22,23)\nIs there a path between node 13 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph423-10_18", + "image": "data/connectivity/graph_visual/medium/graph423.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,20) (0,15) (1,3) (1,20) (2,11) (3,12) (3,6) (3,16) (3,20) (5,14) (5,7) (6,20) (6,21) (7,13) (7,18) (8,14) (8,13) (9,12) (9,16) (9,21) (10,21) (11,17) (12,16) (14,18) (15,16) (15,21) (16,20) (20,21)\nIs there a path between node 10 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph56-6_4", + "image": "data/connectivity/graph_visual/medium/graph56.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,8) (1,7) (1,11) (2,12) (3,8) (3,4) (4,5) (5,7) (5,6) (5,11) (6,11) (9,12) (10,12) (12,13)\nIs there a path between node 6 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph396-9_13", + "image": "data/connectivity/graph_visual/medium/graph396.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,12) (0,3) (0,13) (0,15) (0,7) (1,4) (1,6) (2,9) (2,18) (2,13) (3,12) (4,11) (6,8) (6,17) (7,16) (7,12) (7,13) (7,14) (8,11) (8,17) (8,20) (9,18) (9,21) (9,14) (9,15) (10,12) (12,16) (12,15) (13,18) (13,15) (14,16) (14,21) (15,16) (15,18) (16,18)\nIs there a path between node 9 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph815-16_23", + "image": "data/connectivity/graph_visual/medium/graph815.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,16) (0,22) (0,3) (0,20) (0,14) (0,6) (0,19) (0,15) (0,13) (1,18) (1,9) (1,24) (1,2) (1,21) (1,23) (2,9) (2,24) (2,12) (2,10) (2,23) (2,4) (3,11) (3,16) (3,20) (3,14) (3,6) (3,7) (3,8) (3,15) (3,13) (4,9) (4,24) (4,12) (4,10) (4,21) (4,17) (4,23) (5,9) (5,24) (5,12) (5,10) (5,21) (5,17) (6,16) (6,22) (6,20) (6,7) (6,19) (6,8) (6,15) (6,13) (7,11) (7,16) (7,22) (7,20) (7,19) (7,8) (7,13) (8,22) (8,20) (8,19) (8,15) (8,13) (9,18) (9,10) (9,21) (9,23) (10,18) (10,24) (10,12) (10,17) (10,23) (11,16) (11,22) (11,20) (11,14) (11,19) (12,24) (12,21) (12,17) (12,23) (13,16) (13,22) (13,20) (13,19) (13,15) (14,16) (14,22) (14,19) (14,15) (15,16) (15,22) (15,19) (16,22) (16,20) (16,19) (18,24) (18,21) (19,20) (20,22) (21,24)\nIs there a path between node 16 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph770-0_7", + "image": "data/connectivity/graph_visual/medium/graph770.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,24) (0,6) (0,5) (0,7) (0,17) (0,21) (0,10) (0,18) (0,14) (1,13) (1,19) (1,3) (1,12) (1,4) (1,11) (2,9) (2,8) (2,15) (3,13) (3,19) (3,12) (3,4) (3,11) (4,13) (4,19) (4,12) (4,11) (5,20) (5,24) (5,6) (5,7) (5,17) (5,21) (5,10) (5,18) (5,14) (6,20) (6,24) (6,7) (6,17) (6,21) (6,10) (6,18) (6,14) (7,20) (7,24) (7,17) (7,21) (7,10) (7,18) (7,14) (8,9) (8,15) (9,15) (10,20) (10,24) (10,17) (10,21) (10,18) (10,14) (11,13) (11,19) (11,12) (12,13) (12,19) (13,19) (14,20) (14,24) (14,17) (14,21) (14,18) (16,22) (16,23) (17,20) (17,24) (17,21) (17,18) (18,20) (18,24) (18,21) (20,24) (20,21) (21,24) (22,23)\nIs there a path between node 0 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph840-17_3", + "image": "data/connectivity/graph_visual/medium/graph840.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,3) (0,17) (0,12) (0,18) (0,11) (0,4) (0,16) (0,19) (0,8) (0,24) (0,15) (0,9) (0,1) (0,7) (0,22) (1,10) (1,3) (1,17) (1,12) (1,18) (1,11) (1,4) (1,16) (1,19) (1,8) (1,24) (1,15) (1,9) (1,7) (1,22) (2,23) (2,6) (2,21) (2,14) (2,13) (2,5) (2,20) (3,10) (3,17) (3,12) (3,18) (3,11) (3,4) (3,16) (3,19) (3,8) (3,24) (3,15) (3,9) (3,7) (3,22) (4,10) (4,17) (4,12) (4,18) (4,11) (4,16) (4,19) (4,8) (4,24) (4,15) (4,9) (4,7) (4,22) (5,23) (5,6) (5,21) (5,14) (5,13) (5,20) (6,23) (6,21) (6,14) (6,13) (6,20) (7,10) (7,17) (7,12) (7,18) (7,11) (7,16) (7,19) (7,8) (7,24) (7,15) (7,9) (7,22) (8,10) (8,17) (8,12) (8,18) (8,11) (8,16) (8,19) (8,24) (8,15) (8,9) (8,22) (9,10) (9,17) (9,12) (9,18) (9,11) (9,16) (9,19) (9,24) (9,15) (9,22) (10,17) (10,12) (10,18) (10,11) (10,16) (10,19) (10,24) (10,15) (10,22) (11,17) (11,12) (11,18) (11,16) (11,19) (11,24) (11,15) (11,22) (12,17) (12,18) (12,16) (12,19) (12,24) (12,15) (12,22) (13,23) (13,21) (13,14) (13,20) (14,23) (14,21) (14,20) (15,17) (15,18) (15,16) (15,19) (15,24) (15,22) (16,17) (16,18) (16,19) (16,24) (16,22) (17,18) (17,19) (17,24) (17,22) (18,19) (18,24) (18,22) (19,24) (19,22) (20,23) (20,21) (21,23) (22,24)\nIs there a path between node 17 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph84-7_2", + "image": "data/connectivity/graph_visual/medium/graph84.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,4) (0,13) (0,12) (0,14) (0,8) (0,3) (0,6) (0,2) (0,9) (0,5) (1,10) (1,7) (1,11) (2,4) (2,13) (2,12) (2,14) (2,8) (2,3) (2,6) (2,9) (2,5) (3,4) (3,13) (3,12) (3,14) (3,8) (3,6) (3,9) (3,5) (4,13) (4,12) (4,14) (4,8) (4,6) (4,9) (4,5) (5,13) (5,12) (5,14) (5,8) (5,6) (5,9) (6,13) (6,12) (6,14) (6,8) (6,9) (7,10) (7,11) (8,13) (8,12) (8,14) (8,9) (9,13) (9,12) (9,14) (10,11) (12,13) (12,14) (13,14)\nIs there a path between node 7 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph92-3_14", + "image": "data/connectivity/graph_visual/medium/graph92.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,12) (0,13) (0,6) (0,5) (0,15) (0,14) (0,1) (0,10) (0,8) (0,7) (0,2) (0,11) (0,3) (1,12) (1,13) (1,6) (1,5) (1,15) (1,14) (1,10) (1,8) (1,7) (1,2) (1,11) (1,3) (2,12) (2,13) (2,6) (2,5) (2,15) (2,14) (2,10) (2,8) (2,7) (2,11) (2,3) (3,12) (3,13) (3,6) (3,5) (3,15) (3,14) (3,10) (3,8) (3,7) (3,11) (4,9) (5,12) (5,13) (5,6) (5,15) (5,14) (5,10) (5,8) (5,7) (5,11) (6,12) (6,13) (6,15) (6,14) (6,10) (6,8) (6,7) (6,11) (7,12) (7,13) (7,15) (7,14) (7,10) (7,8) (7,11) (8,12) (8,13) (8,15) (8,14) (8,10) (8,11) (10,12) (10,13) (10,15) (10,14) (10,11) (11,12) (11,13) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nIs there a path between node 3 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph460-12_16", + "image": "data/connectivity/graph_visual/medium/graph460.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,8) (0,1) (0,15) (0,12) (0,6) (0,14) (0,5) (0,2) (0,3) (0,16) (0,17) (0,11) (0,9) (0,7) (0,4) (0,20) (0,13) (0,10) (1,8) (1,15) (1,12) (1,6) (1,14) (1,5) (1,2) (1,3) (1,16) (1,17) (1,11) (1,9) (1,7) (1,4) (1,20) (1,13) (1,10) (2,8) (2,15) (2,12) (2,6) (2,14) (2,5) (2,3) (2,16) (2,17) (2,11) (2,9) (2,7) (2,4) (2,20) (2,13) (2,10) (3,8) (3,15) (3,12) (3,6) (3,14) (3,5) (3,16) (3,17) (3,11) (3,9) (3,7) (3,4) (3,20) (3,13) (3,10) (4,8) (4,15) (4,12) (4,6) (4,14) (4,5) (4,16) (4,17) (4,11) (4,9) (4,7) (4,20) (4,13) (4,10) (5,8) (5,15) (5,12) (5,6) (5,14) (5,16) (5,17) (5,11) (5,9) (5,7) (5,20) (5,13) (5,10) (6,8) (6,15) (6,12) (6,14) (6,16) (6,17) (6,11) (6,9) (6,7) (6,20) (6,13) (6,10) (7,8) (7,15) (7,12) (7,14) (7,16) (7,17) (7,11) (7,9) (7,20) (7,13) (7,10) (8,15) (8,12) (8,14) (8,16) (8,17) (8,11) (8,9) (8,20) (8,13) (8,10) (9,15) (9,12) (9,14) (9,16) (9,17) (9,11) (9,20) (9,13) (9,10) (10,15) (10,12) (10,14) (10,16) (10,17) (10,11) (10,20) (10,13) (11,15) (11,12) (11,14) (11,16) (11,17) (11,20) (11,13) (12,15) (12,14) (12,16) (12,17) (12,20) (12,13) (13,15) (13,14) (13,16) (13,17) (13,20) (14,15) (14,16) (14,17) (14,20) (15,16) (15,17) (15,20) (16,17) (16,20) (17,20) (18,21)\nIs there a path between node 12 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph389-1_2", + "image": "data/connectivity/graph_visual/medium/graph389.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,4) (0,20) (0,6) (0,16) (0,13) (0,9) (0,18) (0,7) (0,3) (0,5) (0,19) (0,1) (0,15) (0,8) (0,10) (0,12) (1,4) (1,20) (1,6) (1,16) (1,13) (1,9) (1,18) (1,7) (1,3) (1,5) (1,19) (1,15) (1,8) (1,10) (1,12) (2,11) (3,4) (3,20) (3,6) (3,16) (3,13) (3,9) (3,18) (3,7) (3,5) (3,19) (3,15) (3,8) (3,10) (3,12) (4,20) (4,6) (4,16) (4,13) (4,9) (4,18) (4,7) (4,5) (4,19) (4,15) (4,8) (4,10) (4,12) (5,20) (5,6) (5,16) (5,13) (5,9) (5,18) (5,7) (5,19) (5,15) (5,8) (5,10) (5,12) (6,20) (6,16) (6,13) (6,9) (6,18) (6,7) (6,19) (6,15) (6,8) (6,10) (6,12) (7,20) (7,16) (7,13) (7,9) (7,18) (7,19) (7,15) (7,8) (7,10) (7,12) (8,20) (8,16) (8,13) (8,9) (8,18) (8,19) (8,15) (8,10) (8,12) (9,20) (9,16) (9,13) (9,18) (9,19) (9,15) (9,10) (9,12) (10,20) (10,16) (10,13) (10,18) (10,19) (10,15) (10,12) (12,20) (12,16) (12,13) (12,18) (12,19) (12,15) (13,20) (13,16) (13,18) (13,19) (13,15) (14,17) (15,20) (15,16) (15,18) (15,19) (16,20) (16,18) (16,19) (18,20) (18,19) (19,20)\nIs there a path between node 1 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph507-18_15", + "image": "data/connectivity/graph_visual/medium/graph507.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,13) (0,17) (1,19) (1,22) (1,13) (1,17) (1,10) (1,14) (2,6) (2,16) (2,7) (4,11) (4,21) (4,16) (4,7) (5,15) (5,8) (5,7) (6,11) (6,21) (7,8) (8,15) (8,16) (9,22) (9,14) (10,19) (10,13) (10,18) (12,14) (12,20) (13,17) (13,18) (13,14) (14,18) (14,20) (15,16) (17,22) (18,20) (19,20) (20,22)\nIs there a path between node 18 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph838-9_14", + "image": "data/connectivity/graph_visual/medium/graph838.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,22) (1,18) (1,7) (1,23) (1,2) (1,24) (1,9) (1,21) (1,14) (1,17) (1,16) (1,3) (1,15) (1,6) (1,19) (2,18) (2,7) (2,23) (2,24) (2,9) (2,21) (2,14) (2,17) (2,16) (2,3) (2,15) (2,6) (2,19) (3,18) (3,7) (3,23) (3,24) (3,9) (3,21) (3,14) (3,17) (3,16) (3,15) (3,6) (3,19) (4,11) (4,20) (4,13) (4,5) (4,8) (4,10) (4,12) (5,11) (5,20) (5,13) (5,8) (5,10) (5,12) (6,18) (6,7) (6,23) (6,24) (6,9) (6,21) (6,14) (6,17) (6,16) (6,15) (6,19) (7,18) (7,23) (7,24) (7,9) (7,21) (7,14) (7,17) (7,16) (7,15) (7,19) (8,11) (8,20) (8,13) (8,10) (8,12) (9,18) (9,23) (9,24) (9,21) (9,14) (9,17) (9,16) (9,15) (9,19) (10,11) (10,20) (10,13) (10,12) (11,20) (11,13) (11,12) (12,20) (12,13) (13,20) (14,18) (14,23) (14,24) (14,21) (14,17) (14,16) (14,15) (14,19) (15,18) (15,23) (15,24) (15,21) (15,17) (15,16) (15,19) (16,18) (16,23) (16,24) (16,21) (16,17) (16,19) (17,18) (17,23) (17,24) (17,21) (17,19) (18,23) (18,24) (18,21) (18,19) (19,23) (19,24) (19,21) (21,23) (21,24) (23,24)\nIs there a path between node 9 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph499-0_4", + "image": "data/connectivity/graph_visual/medium/graph499.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (0,15) (0,5) (1,10) (2,19) (2,14) (2,21) (4,22) (4,13) (4,6) (5,15) (6,22) (6,9) (8,13) (8,19) (8,21) (10,20) (11,20) (12,18) (13,14) (15,18) (17,19) (21,22)\nIs there a path between node 0 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph259-11_18", + "image": "data/connectivity/graph_visual/medium/graph259.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,18) (0,13) (0,3) (0,14) (0,15) (0,19) (0,7) (0,9) (0,10) (1,5) (1,18) (1,12) (1,13) (1,14) (1,6) (1,17) (1,16) (1,9) (1,10) (1,11) (2,18) (2,12) (2,13) (2,6) (2,15) (2,19) (2,7) (2,17) (2,16) (2,9) (2,10) (2,11) (3,18) (3,12) (3,13) (3,14) (3,6) (3,19) (3,17) (3,9) (3,10) (3,11) (5,18) (5,12) (5,13) (5,14) (5,6) (5,15) (5,19) (5,7) (5,16) (5,11) (6,18) (6,12) (6,7) (6,17) (6,16) (6,9) (6,10) (7,18) (7,12) (7,13) (7,15) (7,19) (7,17) (7,16) (7,10) (7,11) (9,18) (9,13) (9,15) (9,19) (9,16) (9,10) (10,18) (10,13) (10,14) (10,19) (10,17) (10,11) (11,12) (11,13) (11,14) (11,15) (11,19) (11,17) (11,16) (12,14) (12,19) (12,17) (12,16) (13,18) (13,15) (13,19) (13,17) (14,18) (14,15) (14,19) (14,17) (14,16) (15,18) (15,19) (15,16) (16,18) (17,18) (17,19) (18,19)\nIs there a path between node 11 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph370-16_5", + "image": "data/connectivity/graph_visual/medium/graph370.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,13) (0,5) (0,16) (0,1) (0,3) (1,13) (1,5) (1,9) (1,20) (1,2) (1,16) (1,3) (2,13) (2,5) (2,12) (2,8) (2,9) (2,20) (2,16) (2,3) (3,8) (3,9) (3,16) (4,7) (4,15) (4,19) (4,6) (4,11) (4,18) (4,10) (4,14) (5,13) (5,12) (5,9) (5,16) (6,7) (6,17) (6,19) (6,11) (6,10) (6,14) (7,15) (7,17) (7,19) (7,11) (7,10) (7,14) (8,13) (8,9) (8,20) (9,13) (9,12) (10,15) (10,19) (10,11) (11,15) (11,17) (11,19) (11,18) (11,14) (12,13) (12,20) (14,15) (14,18) (15,18) (16,20) (17,19) (17,18) (18,19)\nIs there a path between node 16 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph182-11_14", + "image": "data/connectivity/graph_visual/medium/graph182.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,15) (0,9) (0,4) (0,14) (0,6) (0,10) (0,12) (0,2) (1,13) (1,11) (1,3) (1,5) (1,7) (1,16) (1,8) (1,17) (2,15) (2,9) (2,4) (2,14) (2,6) (2,10) (2,12) (3,13) (3,11) (3,5) (3,7) (3,16) (3,8) (3,17) (4,15) (4,9) (4,14) (4,6) (4,10) (4,12) (5,13) (5,11) (5,7) (5,16) (5,8) (5,17) (6,15) (6,9) (6,14) (6,10) (6,12) (7,13) (7,11) (7,16) (7,8) (7,17) (8,13) (8,11) (8,16) (8,17) (9,15) (9,14) (9,10) (9,12) (10,15) (10,14) (10,12) (11,13) (11,16) (11,17) (12,15) (12,14) (13,16) (13,17) (14,15) (16,17)\nIs there a path between node 11 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph494-2_13", + "image": "data/connectivity/graph_visual/medium/graph494.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,13) (1,13) (2,14) (2,17) (2,4) (2,18) (2,15) (2,22) (2,5) (2,21) (2,7) (2,20) (2,12) (2,16) (2,10) (2,9) (2,6) (2,11) (2,19) (2,8) (2,3) (3,14) (3,17) (3,4) (3,18) (3,15) (3,22) (3,5) (3,21) (3,7) (3,20) (3,12) (3,16) (3,10) (3,9) (3,6) (3,11) (3,19) (3,8) (4,14) (4,17) (4,18) (4,15) (4,22) (4,5) (4,21) (4,7) (4,20) (4,12) (4,16) (4,10) (4,9) (4,6) (4,11) (4,19) (4,8) (5,14) (5,17) (5,18) (5,15) (5,22) (5,21) (5,7) (5,20) (5,12) (5,16) (5,10) (5,9) (5,6) (5,11) (5,19) (5,8) (6,14) (6,17) (6,18) (6,15) (6,22) (6,21) (6,7) (6,20) (6,12) (6,16) (6,10) (6,9) (6,11) (6,19) (6,8) (7,14) (7,17) (7,18) (7,15) (7,22) (7,21) (7,20) (7,12) (7,16) (7,10) (7,9) (7,11) (7,19) (7,8) (8,14) (8,17) (8,18) (8,15) (8,22) (8,21) (8,20) (8,12) (8,16) (8,10) (8,9) (8,11) (8,19) (9,14) (9,17) (9,18) (9,15) (9,22) (9,21) (9,20) (9,12) (9,16) (9,10) (9,11) (9,19) (10,14) (10,17) (10,18) (10,15) (10,22) (10,21) (10,20) (10,12) (10,16) (10,11) (10,19) (11,14) (11,17) (11,18) (11,15) (11,22) (11,21) (11,20) (11,12) (11,16) (11,19) (12,14) (12,17) (12,18) (12,15) (12,22) (12,21) (12,20) (12,16) (12,19) (14,17) (14,18) (14,15) (14,22) (14,21) (14,20) (14,16) (14,19) (15,17) (15,18) (15,22) (15,21) (15,20) (15,16) (15,19) (16,17) (16,18) (16,22) (16,21) (16,20) (16,19) (17,18) (17,22) (17,21) (17,20) (17,19) (18,22) (18,21) (18,20) (18,19) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 2 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph344-3_10", + "image": "data/connectivity/graph_visual/medium/graph344.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,14) (0,8) (0,2) (0,1) (0,18) (0,4) (0,5) (0,16) (0,10) (0,19) (0,6) (0,7) (1,14) (1,8) (1,2) (1,18) (1,4) (1,5) (1,16) (1,10) (1,19) (1,6) (1,7) (2,14) (2,8) (2,18) (2,4) (2,5) (2,16) (2,10) (2,19) (2,6) (2,7) (3,17) (3,11) (3,9) (3,15) (3,20) (3,12) (3,13) (4,14) (4,8) (4,18) (4,5) (4,16) (4,10) (4,19) (4,6) (4,7) (5,14) (5,8) (5,18) (5,16) (5,10) (5,19) (5,6) (5,7) (6,14) (6,8) (6,18) (6,16) (6,10) (6,19) (6,7) (7,14) (7,8) (7,18) (7,16) (7,10) (7,19) (8,14) (8,18) (8,16) (8,10) (8,19) (9,17) (9,11) (9,15) (9,20) (9,12) (9,13) (10,14) (10,18) (10,16) (10,19) (11,17) (11,15) (11,20) (11,12) (11,13) (12,17) (12,15) (12,20) (12,13) (13,17) (13,15) (13,20) (14,18) (14,16) (14,19) (15,17) (15,20) (16,18) (16,19) (17,20) (18,19)\nIs there a path between node 3 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph359-10_13", + "image": "data/connectivity/graph_visual/medium/graph359.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,8) (0,7) (0,18) (0,5) (0,2) (0,1) (1,11) (1,17) (2,20) (2,9) (3,11) (3,18) (3,20) (3,12) (4,14) (6,19) (6,16) (6,8) (6,15) (6,12) (6,9) (7,15) (7,12) (7,17) (8,18) (9,17) (11,16) (11,15) (12,19) (12,17) (15,19) (15,20) (16,19) (16,18) (16,17)\nIs there a path between node 10 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph617-4_13", + "image": "data/connectivity/graph_visual/medium/graph617.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (1,14) (1,20) (1,10) (1,21) (1,12) (1,5) (2,9) (2,16) (2,22) (2,18) (2,7) (2,23) (2,6) (2,17) (2,3) (2,13) (2,8) (2,11) (2,19) (2,4) (3,9) (3,16) (3,22) (3,18) (3,7) (3,23) (3,6) (3,17) (3,13) (3,8) (3,11) (3,19) (3,4) (4,9) (4,16) (4,22) (4,18) (4,7) (4,23) (4,6) (4,17) (4,13) (4,8) (4,11) (4,19) (5,14) (5,20) (5,10) (5,21) (5,12) (6,9) (6,16) (6,22) (6,18) (6,7) (6,23) (6,17) (6,13) (6,8) (6,11) (6,19) (7,9) (7,16) (7,22) (7,18) (7,23) (7,17) (7,13) (7,8) (7,11) (7,19) (8,9) (8,16) (8,22) (8,18) (8,23) (8,17) (8,13) (8,11) (8,19) (9,16) (9,22) (9,18) (9,23) (9,17) (9,13) (9,11) (9,19) (10,14) (10,20) (10,21) (10,12) (11,16) (11,22) (11,18) (11,23) (11,17) (11,13) (11,19) (12,14) (12,20) (12,21) (13,16) (13,22) (13,18) (13,23) (13,17) (13,19) (14,20) (14,21) (16,22) (16,18) (16,23) (16,17) (16,19) (17,22) (17,18) (17,23) (17,19) (18,22) (18,23) (18,19) (19,22) (19,23) (20,21) (22,23)\nIs there a path between node 4 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph763-24_0", + "image": "data/connectivity/graph_visual/medium/graph763.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,20) (0,13) (0,24) (0,4) (1,21) (1,3) (1,11) (1,10) (1,23) (1,8) (1,2) (1,22) (1,19) (1,18) (2,21) (2,3) (2,11) (2,10) (2,23) (2,8) (2,22) (2,19) (2,18) (3,21) (3,11) (3,10) (3,23) (3,8) (3,22) (3,19) (3,18) (4,14) (4,20) (4,13) (4,24) (5,7) (5,9) (5,12) (5,16) (5,15) (5,17) (5,6) (6,7) (6,9) (6,12) (6,16) (6,15) (6,17) (7,9) (7,12) (7,16) (7,15) (7,17) (8,21) (8,11) (8,10) (8,23) (8,22) (8,19) (8,18) (9,12) (9,16) (9,15) (9,17) (10,21) (10,11) (10,23) (10,22) (10,19) (10,18) (11,21) (11,23) (11,22) (11,19) (11,18) (12,16) (12,15) (12,17) (13,14) (13,20) (13,24) (14,20) (14,24) (15,16) (15,17) (16,17) (18,21) (18,23) (18,22) (18,19) (19,21) (19,23) (19,22) (20,24) (21,23) (21,22) (22,23)\nIs there a path between node 24 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph370-14_4", + "image": "data/connectivity/graph_visual/medium/graph370.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,13) (0,5) (0,16) (0,1) (0,3) (1,13) (1,5) (1,9) (1,20) (1,2) (1,16) (1,3) (2,13) (2,5) (2,12) (2,8) (2,9) (2,20) (2,16) (2,3) (3,8) (3,9) (3,16) (4,7) (4,15) (4,19) (4,6) (4,11) (4,18) (4,10) (4,14) (5,13) (5,12) (5,9) (5,16) (6,7) (6,17) (6,19) (6,11) (6,10) (6,14) (7,15) (7,17) (7,19) (7,11) (7,10) (7,14) (8,13) (8,9) (8,20) (9,13) (9,12) (10,15) (10,19) (10,11) (11,15) (11,17) (11,19) (11,18) (11,14) (12,13) (12,20) (14,15) (14,18) (15,18) (16,20) (17,19) (17,18) (18,19)\nIs there a path between node 14 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph55-6_4", + "image": "data/connectivity/graph_visual/medium/graph55.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (0,13) (1,10) (1,4) (1,12) (3,11) (3,10) (3,7) (3,12) (4,6) (4,9) (4,10) (5,6) (5,12) (6,11) (6,9) (9,10) (10,12)\nIs there a path between node 6 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph536-10_9", + "image": "data/connectivity/graph_visual/medium/graph536.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,4) (0,7) (0,15) (0,8) (0,16) (0,12) (0,14) (1,17) (1,2) (1,22) (1,5) (1,21) (1,3) (2,17) (2,22) (2,5) (2,21) (2,3) (3,17) (3,22) (3,5) (3,21) (4,7) (4,15) (4,8) (4,16) (4,12) (4,14) (5,17) (5,22) (5,21) (6,20) (6,19) (6,11) (6,10) (6,13) (6,18) (6,9) (7,15) (7,8) (7,16) (7,12) (7,14) (8,15) (8,16) (8,12) (8,14) (9,20) (9,19) (9,11) (9,10) (9,13) (9,18) (10,20) (10,19) (10,11) (10,13) (10,18) (11,20) (11,19) (11,13) (11,18) (12,15) (12,16) (12,14) (13,20) (13,19) (13,18) (14,15) (14,16) (15,16) (17,22) (17,21) (18,20) (18,19) (19,20) (21,22)\nIs there a path between node 10 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph111-1_2", + "image": "data/connectivity/graph_visual/medium/graph111.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,9) (0,10) (0,1) (1,8) (1,3) (1,14) (3,5) (3,6) (3,9) (3,12) (4,9) (4,16) (6,7) (6,12) (7,14) (8,16) (8,14) (10,11) (10,14) (10,12) (11,14) (12,14)\nIs there a path between node 1 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph506-4_11", + "image": "data/connectivity/graph_visual/medium/graph506.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,12) (2,5) (2,7) (2,19) (3,17) (3,11) (3,9) (3,4) (3,7) (4,10) (4,17) (4,5) (4,11) (4,9) (4,7) (4,19) (5,21) (5,11) (5,9) (5,7) (6,20) (6,18) (7,14) (7,21) (7,11) (7,9) (7,19) (8,15) (9,10) (9,14) (9,19) (10,11) (11,14) (11,17) (11,19) (12,20) (12,18) (13,22) (14,19) (18,22)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph126-15_0", + "image": "data/connectivity/graph_visual/medium/graph126.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,11) (0,3) (0,7) (0,10) (0,13) (0,12) (0,16) (1,14) (1,2) (1,5) (1,9) (1,8) (1,15) (1,4) (1,6) (2,14) (2,5) (2,9) (2,8) (2,15) (2,4) (2,6) (3,11) (3,7) (3,10) (3,13) (3,12) (3,16) (4,14) (4,5) (4,9) (4,8) (4,15) (4,6) (5,14) (5,9) (5,8) (5,15) (5,6) (6,14) (6,9) (6,8) (6,15) (7,11) (7,10) (7,13) (7,12) (7,16) (8,14) (8,9) (8,15) (9,14) (9,15) (10,11) (10,13) (10,12) (10,16) (11,13) (11,12) (11,16) (12,13) (12,16) (13,16) (14,15)\nIs there a path between node 15 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph134-13_8", + "image": "data/connectivity/graph_visual/medium/graph134.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,11) (0,6) (0,2) (0,5) (1,7) (1,16) (1,14) (1,17) (1,3) (1,9) (1,13) (1,10) (2,11) (2,6) (2,5) (3,7) (3,16) (3,14) (3,17) (3,9) (3,13) (3,10) (4,8) (4,15) (4,12) (5,11) (5,6) (6,11) (7,16) (7,14) (7,17) (7,9) (7,13) (7,10) (8,15) (8,12) (9,16) (9,14) (9,17) (9,13) (9,10) (10,16) (10,14) (10,17) (10,13) (12,15) (13,16) (13,14) (13,17) (14,16) (14,17) (16,17)\nIs there a path between node 13 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph556-15_4", + "image": "data/connectivity/graph_visual/medium/graph556.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,20) (0,7) (0,2) (1,16) (1,18) (1,4) (1,23) (1,15) (1,19) (1,6) (1,5) (1,12) (2,8) (2,10) (2,22) (2,7) (2,13) (3,21) (4,16) (4,18) (4,23) (4,11) (4,17) (4,15) (4,19) (4,6) (4,12) (5,16) (5,18) (5,14) (5,11) (5,17) (5,15) (5,19) (5,6) (5,12) (6,16) (6,18) (6,14) (6,11) (6,17) (6,15) (6,12) (7,8) (7,10) (7,22) (7,20) (7,13) (8,9) (8,10) (8,22) (8,20) (8,13) (9,22) (9,13) (10,22) (10,20) (10,13) (11,16) (11,18) (11,14) (11,23) (11,17) (11,15) (11,19) (11,12) (12,16) (12,18) (12,14) (12,23) (12,17) (12,15) (12,19) (13,22) (13,20) (14,18) (14,23) (14,17) (14,15) (15,16) (15,18) (15,23) (15,17) (15,19) (16,23) (17,18) (17,23) (17,19) (18,23) (18,19) (19,23) (20,22)\nIs there a path between node 15 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph333-17_1", + "image": "data/connectivity/graph_visual/medium/graph333.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,14) (0,7) (0,2) (1,9) (1,13) (2,19) (2,3) (3,16) (3,17) (3,19) (3,6) (4,16) (4,20) (4,17) (4,14) (4,18) (5,12) (5,13) (6,12) (6,19) (6,10) (6,9) (6,7) (6,13) (7,16) (9,16) (9,12) (9,18) (10,12) (10,17) (10,15) (10,14) (10,13) (12,16) (13,17) (13,18) (14,17) (14,18) (15,19) (16,19) (17,20) (17,18)\nIs there a path between node 17 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph38-7_5", + "image": "data/connectivity/graph_visual/medium/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,12) (1,9) (2,10) (2,4) (2,12) (3,7) (4,12) (8,10) (8,11) (10,11)\nIs there a path between node 7 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph603-0_12", + "image": "data/connectivity/graph_visual/medium/graph603.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,11) (0,20) (1,4) (1,14) (1,15) (1,16) (1,22) (2,4) (2,14) (2,15) (2,16) (3,4) (3,14) (3,15) (3,16) (4,14) (4,15) (4,16) (5,11) (6,12) (6,19) (6,7) (6,13) (6,9) (6,17) (7,18) (7,21) (7,13) (7,9) (7,17) (8,20) (9,18) (9,19) (9,13) (9,10) (9,17) (10,12) (10,21) (10,13) (12,18) (12,21) (12,19) (12,13) (12,17) (13,18) (13,21) (13,19) (13,17) (14,15) (14,22) (15,22) (17,18) (17,19) (18,21) (18,19) (19,21)\nIs there a path between node 0 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph742-14_17", + "image": "data/connectivity/graph_visual/medium/graph742.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,4) (0,5) (0,10) (0,22) (0,8) (3,9) (3,24) (3,11) (4,21) (4,13) (5,13) (7,9) (8,21) (8,17) (8,18) (9,20) (10,21) (10,22) (13,14) (13,18) (14,18) (15,19) (15,16) (21,22)\nIs there a path between node 14 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph524-19_14", + "image": "data/connectivity/graph_visual/medium/graph524.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,16) (0,20) (0,21) (0,2) (0,14) (0,18) (0,10) (0,8) (1,16) (1,20) (1,12) (1,14) (1,18) (1,10) (2,16) (2,12) (2,21) (2,14) (2,18) (2,10) (2,8) (3,17) (3,11) (3,9) (3,22) (3,19) (3,5) (3,6) (3,4) (4,17) (4,9) (4,22) (4,5) (4,6) (4,7) (5,17) (5,13) (5,11) (6,11) (6,9) (6,7) (7,17) (7,13) (7,11) (7,9) (8,16) (8,12) (8,14) (8,18) (8,15) (8,10) (9,17) (9,13) (9,11) (9,19) (10,16) (10,20) (10,12) (10,14) (10,18) (11,17) (11,13) (11,22) (11,19) (12,16) (12,20) (12,21) (12,14) (13,17) (13,22) (14,16) (14,21) (14,18) (14,15) (15,16) (15,20) (15,21) (15,18) (16,20) (16,21) (16,18) (17,22) (17,19) (18,20) (18,21) (19,22)\nIs there a path between node 19 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph469-11_1", + "image": "data/connectivity/graph_visual/medium/graph469.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,3) (0,21) (0,8) (0,11) (0,16) (0,13) (0,10) (0,20) (0,6) (0,4) (1,14) (1,17) (1,18) (1,5) (1,19) (1,2) (2,22) (2,14) (2,5) (3,8) (3,11) (3,10) (3,12) (3,6) (4,11) (4,13) (4,20) (4,12) (5,22) (5,14) (5,17) (5,18) (5,9) (5,19) (6,8) (6,11) (6,16) (6,13) (6,10) (6,20) (6,12) (7,15) (8,11) (8,13) (8,10) (8,20) (8,12) (9,22) (9,14) (9,17) (9,18) (9,19) (10,21) (10,13) (11,16) (11,13) (11,20) (11,12) (12,21) (12,16) (12,13) (12,20) (13,21) (13,16) (13,20) (14,22) (14,18) (16,21) (16,20) (17,22) (17,18) (17,19) (18,19) (20,21)\nIs there a path between node 11 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph588-10_8", + "image": "data/connectivity/graph_visual/medium/graph588.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (1,5) (1,12) (1,3) (1,17) (1,15) (1,16) (2,21) (2,9) (2,11) (2,13) (2,4) (2,14) (3,23) (3,13) (3,15) (3,19) (3,14) (4,5) (4,12) (4,9) (4,17) (4,11) (5,8) (5,12) (5,22) (5,16) (5,14) (6,10) (7,18) (7,10) (8,12) (8,17) (8,23) (8,11) (8,16) (9,22) (9,13) (11,21) (11,15) (12,17) (12,23) (12,16) (12,14) (13,22) (13,23) (13,19) (13,16) (14,20) (14,22) (14,17) (15,20) (15,19) (16,22) (16,17) (16,23) (16,19) (19,23) (20,22) (22,23)\nIs there a path between node 10 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph730-9_18", + "image": "data/connectivity/graph_visual/medium/graph730.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,15) (0,4) (0,2) (0,10) (1,23) (1,19) (1,21) (1,8) (1,17) (2,4) (2,17) (3,23) (3,15) (3,19) (3,21) (3,8) (3,17) (4,21) (4,6) (5,20) (5,10) (5,8) (6,15) (6,10) (7,18) (8,21) (8,13) (9,18) (11,16) (11,24) (11,14) (12,14) (14,22) (15,21) (15,17) (17,23) (18,22) (19,20) (19,21) (20,21) (21,23)\nIs there a path between node 9 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph217-11_12", + "image": "data/connectivity/graph_visual/medium/graph217.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,2) (0,11) (0,14) (0,10) (0,5) (0,1) (0,16) (0,12) (0,18) (0,15) (1,2) (1,11) (1,14) (1,10) (1,5) (1,16) (1,12) (1,18) (1,15) (2,11) (2,14) (2,10) (2,5) (2,16) (2,12) (2,18) (2,15) (3,4) (3,7) (3,8) (3,13) (4,7) (4,8) (4,13) (5,11) (5,14) (5,10) (5,16) (5,12) (5,18) (5,15) (6,9) (6,17) (7,8) (7,13) (8,13) (9,17) (10,11) (10,14) (10,16) (10,12) (10,18) (10,15) (11,14) (11,16) (11,12) (11,18) (11,15) (12,14) (12,16) (12,18) (12,15) (14,16) (14,18) (14,15) (15,16) (15,18) (16,18)\nIs there a path between node 11 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph418-2_21", + "image": "data/connectivity/graph_visual/medium/graph418.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,13) (0,19) (0,10) (0,6) (0,17) (0,1) (0,7) (0,2) (1,13) (1,19) (1,10) (1,6) (1,17) (1,7) (1,2) (2,13) (2,19) (2,10) (2,6) (2,17) (2,7) (3,20) (3,12) (3,8) (3,11) (3,14) (4,18) (4,15) (4,21) (4,9) (4,5) (4,16) (5,18) (5,15) (5,21) (5,9) (5,16) (6,13) (6,19) (6,10) (6,17) (6,7) (7,13) (7,19) (7,10) (7,17) (8,20) (8,12) (8,11) (8,14) (9,18) (9,15) (9,21) (9,16) (10,13) (10,19) (10,17) (11,20) (11,12) (11,14) (12,20) (12,14) (13,19) (13,17) (14,20) (15,18) (15,21) (15,16) (16,18) (16,21) (17,19) (18,21)\nIs there a path between node 2 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph161-17_5", + "image": "data/connectivity/graph_visual/medium/graph161.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,5) (0,2) (0,7) (0,16) (0,6) (1,7) (1,10) (1,4) (2,15) (2,10) (4,5) (4,6) (6,7) (8,11) (8,13) (8,12) (8,14) (11,14) (13,17) (14,17)\nIs there a path between node 17 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph73-14_9", + "image": "data/connectivity/graph_visual/medium/graph73.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (0,12) (0,5) (1,12) (1,8) (2,3) (2,8) (2,5) (3,9) (3,10) (3,12) (3,8) (5,12) (6,13) (7,10) (7,14) (8,10) (9,10) (12,14)\nIs there a path between node 14 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph249-10_11", + "image": "data/connectivity/graph_visual/medium/graph249.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,6) (0,2) (0,17) (0,4) (0,5) (0,15) (0,9) (0,12) (0,11) (0,16) (0,8) (0,10) (0,18) (0,14) (1,7) (2,13) (2,6) (2,17) (2,4) (2,5) (2,15) (2,9) (2,12) (2,11) (2,16) (2,8) (2,10) (2,18) (2,14) (4,13) (4,6) (4,17) (4,5) (4,15) (4,9) (4,12) (4,11) (4,16) (4,8) (4,10) (4,18) (4,14) (5,13) (5,6) (5,17) (5,15) (5,9) (5,12) (5,11) (5,16) (5,8) (5,10) (5,18) (5,14) (6,13) (6,17) (6,15) (6,9) (6,12) (6,11) (6,16) (6,8) (6,10) (6,18) (6,14) (8,13) (8,17) (8,15) (8,9) (8,12) (8,11) (8,16) (8,10) (8,18) (8,14) (9,13) (9,17) (9,15) (9,12) (9,11) (9,16) (9,10) (9,18) (9,14) (10,13) (10,17) (10,15) (10,12) (10,11) (10,16) (10,18) (10,14) (11,13) (11,17) (11,15) (11,12) (11,16) (11,18) (11,14) (12,13) (12,17) (12,15) (12,16) (12,18) (12,14) (13,17) (13,15) (13,16) (13,18) (13,14) (14,17) (14,15) (14,16) (14,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 10 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph654-10_6", + "image": "data/connectivity/graph_visual/medium/graph654.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,8) (0,2) (0,17) (0,6) (0,11) (0,23) (0,4) (0,7) (0,14) (0,1) (0,21) (0,12) (0,10) (0,19) (1,20) (1,22) (1,8) (1,2) (1,17) (1,6) (1,9) (1,4) (1,14) (1,21) (1,12) (2,20) (2,22) (2,3) (2,16) (2,17) (2,6) (2,9) (2,11) (2,23) (2,7) (2,21) (2,12) (2,19) (3,20) (3,22) (3,8) (3,16) (3,17) (3,6) (3,11) (3,23) (3,4) (3,7) (3,14) (3,21) (3,12) (3,19) (4,8) (4,17) (4,11) (4,7) (4,12) (4,10) (4,19) (6,20) (6,22) (6,8) (6,16) (6,23) (6,7) (6,21) (6,12) (6,10) (6,19) (7,20) (7,22) (7,16) (7,17) (7,23) (7,21) (7,12) (7,19) (8,20) (8,22) (8,17) (8,9) (8,23) (8,14) (8,21) (8,12) (8,10) (8,19) (9,22) (9,16) (9,17) (9,11) (9,14) (9,21) (9,12) (10,20) (10,22) (10,16) (10,17) (10,11) (10,23) (10,21) (10,19) (11,20) (11,22) (11,23) (11,14) (11,21) (11,12) (11,19) (12,22) (12,16) (12,17) (12,21) (12,19) (13,15) (13,18) (14,20) (14,22) (14,16) (14,17) (14,23) (14,21) (14,19) (15,18) (16,22) (16,21) (17,22) (17,19) (19,20) (19,22) (19,21) (20,22) (20,23) (20,21) (21,22)\nIs there a path between node 10 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph793-20_24", + "image": "data/connectivity/graph_visual/medium/graph793.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,3) (1,17) (2,12) (2,4) (2,20) (2,9) (2,11) (2,5) (3,13) (3,20) (3,21) (3,10) (4,13) (4,10) (5,21) (6,12) (6,19) (6,9) (6,11) (7,15) (8,17) (9,20) (9,21) (10,13) (10,21) (10,19) (11,13) (11,20) (12,21) (13,21) (14,17) (17,24) (17,22) (20,21)\nIs there a path between node 20 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph47-8_11", + "image": "data/connectivity/graph_visual/medium/graph47.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,12) (0,7) (0,10) (0,8) (0,9) (0,2) (0,4) (0,3) (1,5) (1,6) (1,11) (2,12) (2,7) (2,10) (2,8) (2,9) (2,4) (2,3) (3,12) (3,7) (3,10) (3,8) (3,9) (3,4) (4,12) (4,7) (4,10) (4,8) (4,9) (5,6) (5,11) (6,11) (7,12) (7,10) (7,8) (7,9) (8,12) (8,10) (8,9) (9,12) (9,10) (10,12)\nIs there a path between node 8 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph195-13_0", + "image": "data/connectivity/graph_visual/medium/graph195.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,1) (1,2) (3,11) (3,15) (3,8) (5,18) (5,7) (6,17) (6,7) (7,13) (7,8) (7,14) (8,18) (8,12) (9,11) (9,15) (9,13) (9,17) (10,18) (11,13) (11,17) (12,18) (12,17) (12,14) (13,17) (14,17) (17,18)\nIs there a path between node 13 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph630-10_6", + "image": "data/connectivity/graph_visual/medium/graph630.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,10) (0,7) (0,11) (1,22) (1,21) (2,10) (2,7) (2,12) (2,3) (2,11) (2,20) (3,14) (3,18) (3,5) (3,7) (3,11) (4,10) (4,12) (5,14) (5,17) (5,11) (5,23) (7,19) (7,18) (7,10) (7,21) (8,13) (9,13) (10,18) (10,15) (10,12) (11,21) (12,14) (12,15) (12,21) (14,20) (15,23) (17,19) (17,18) (17,20) (18,19) (20,23) (22,23)\nIs there a path between node 10 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph13-8_10", + "image": "data/connectivity/graph_visual/medium/graph13.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (0,7) (0,10) (0,2) (1,8) (1,4) (1,9) (1,3) (1,5) (2,6) (2,7) (2,10) (3,8) (3,4) (3,9) (3,5) (4,8) (4,9) (4,5) (5,8) (5,9) (6,7) (6,10) (7,10) (8,9)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph284-19_6", + "image": "data/connectivity/graph_visual/medium/graph284.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,2) (1,7) (1,15) (2,12) (2,15) (3,17) (3,7) (3,12) (3,15) (4,14) (4,16) (4,15) (5,9) (5,6) (6,18) (6,9) (6,13) (7,12) (8,12) (9,18) (10,19) (14,16) (14,15) (16,17)\nIs there a path between node 19 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph332-3_4", + "image": "data/connectivity/graph_visual/medium/graph332.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,14) (0,7) (0,2) (1,8) (1,4) (1,12) (1,6) (3,8) (3,11) (3,4) (3,9) (3,12) (3,6) (4,11) (4,6) (5,10) (7,18) (9,11) (10,16) (10,13)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph720-19_18", + "image": "data/connectivity/graph_visual/medium/graph720.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,21) (0,11) (0,15) (0,4) (0,22) (0,5) (0,3) (0,6) (0,20) (0,13) (0,18) (0,9) (0,1) (0,12) (0,24) (0,16) (0,8) (0,23) (0,2) (1,21) (1,11) (1,15) (1,4) (1,22) (1,5) (1,3) (1,6) (1,20) (1,13) (1,18) (1,9) (1,12) (1,24) (1,16) (1,8) (1,23) (1,2) (2,21) (2,11) (2,15) (2,4) (2,22) (2,5) (2,3) (2,6) (2,20) (2,13) (2,18) (2,9) (2,12) (2,24) (2,16) (2,8) (2,23) (3,21) (3,11) (3,15) (3,4) (3,22) (3,5) (3,6) (3,20) (3,13) (3,18) (3,9) (3,12) (3,24) (3,16) (3,8) (3,23) (4,21) (4,11) (4,15) (4,22) (4,5) (4,6) (4,20) (4,13) (4,18) (4,9) (4,12) (4,24) (4,16) (4,8) (4,23) (5,21) (5,11) (5,15) (5,22) (5,6) (5,20) (5,13) (5,18) (5,9) (5,12) (5,24) (5,16) (5,8) (5,23) (6,21) (6,11) (6,15) (6,22) (6,20) (6,13) (6,18) (6,9) (6,12) (6,24) (6,16) (6,8) (6,23) (7,10) (7,14) (7,17) (7,19) (8,21) (8,11) (8,15) (8,22) (8,20) (8,13) (8,18) (8,9) (8,12) (8,24) (8,16) (8,23) (9,21) (9,11) (9,15) (9,22) (9,20) (9,13) (9,18) (9,12) (9,24) (9,16) (9,23) (10,14) (10,17) (10,19) (11,21) (11,15) (11,22) (11,20) (11,13) (11,18) (11,12) (11,24) (11,16) (11,23) (12,21) (12,15) (12,22) (12,20) (12,13) (12,18) (12,24) (12,16) (12,23) (13,21) (13,15) (13,22) (13,20) (13,18) (13,24) (13,16) (13,23) (14,17) (14,19) (15,21) (15,22) (15,20) (15,18) (15,24) (15,16) (15,23) (16,21) (16,22) (16,20) (16,18) (16,24) (16,23) (17,19) (18,21) (18,22) (18,20) (18,24) (18,23) (20,21) (20,22) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 19 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph488-9_22", + "image": "data/connectivity/graph_visual/medium/graph488.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,10) (0,17) (0,16) (0,11) (0,4) (0,6) (0,5) (0,3) (0,19) (0,18) (0,9) (0,14) (0,22) (0,2) (0,13) (1,8) (1,12) (1,7) (1,20) (1,15) (2,21) (2,10) (2,17) (2,16) (2,11) (2,4) (2,6) (2,5) (2,3) (2,19) (2,18) (2,9) (2,14) (2,22) (2,13) (3,21) (3,10) (3,17) (3,16) (3,11) (3,4) (3,6) (3,5) (3,19) (3,18) (3,9) (3,14) (3,22) (3,13) (4,21) (4,10) (4,17) (4,16) (4,11) (4,6) (4,5) (4,19) (4,18) (4,9) (4,14) (4,22) (4,13) (5,21) (5,10) (5,17) (5,16) (5,11) (5,6) (5,19) (5,18) (5,9) (5,14) (5,22) (5,13) (6,21) (6,10) (6,17) (6,16) (6,11) (6,19) (6,18) (6,9) (6,14) (6,22) (6,13) (7,8) (7,12) (7,20) (7,15) (8,12) (8,20) (8,15) (9,21) (9,10) (9,17) (9,16) (9,11) (9,19) (9,18) (9,14) (9,22) (9,13) (10,21) (10,17) (10,16) (10,11) (10,19) (10,18) (10,14) (10,22) (10,13) (11,21) (11,17) (11,16) (11,19) (11,18) (11,14) (11,22) (11,13) (12,20) (12,15) (13,21) (13,17) (13,16) (13,19) (13,18) (13,14) (13,22) (14,21) (14,17) (14,16) (14,19) (14,18) (14,22) (15,20) (16,21) (16,17) (16,19) (16,18) (16,22) (17,21) (17,19) (17,18) (17,22) (18,21) (18,19) (18,22) (19,21) (19,22) (21,22)\nIs there a path between node 9 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph284-6_5", + "image": "data/connectivity/graph_visual/medium/graph284.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,2) (1,7) (1,15) (2,12) (2,15) (3,17) (3,7) (3,12) (3,15) (4,14) (4,16) (4,15) (5,9) (5,6) (6,18) (6,9) (6,13) (7,12) (8,12) (9,18) (10,19) (14,16) (14,15) (16,17)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph646-14_8", + "image": "data/connectivity/graph_visual/medium/graph646.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,14) (1,22) (1,12) (2,11) (2,7) (2,18) (2,3) (2,20) (3,11) (3,7) (3,18) (3,16) (4,20) (5,20) (5,10) (6,20) (6,16) (6,10) (7,11) (7,16) (8,17) (8,13) (9,23) (10,18) (10,16) (11,16) (12,19) (13,14) (13,22) (13,19) (14,19) (17,22) (17,19) (19,22)\nIs there a path between node 14 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph697-23_10", + "image": "data/connectivity/graph_visual/medium/graph697.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,6) (0,21) (0,17) (0,16) (0,20) (0,7) (0,12) (0,14) (0,22) (0,15) (1,18) (1,4) (1,2) (1,10) (1,3) (1,23) (1,19) (1,11) (1,9) (1,13) (1,8) (2,18) (2,4) (2,10) (2,3) (2,23) (2,19) (2,11) (2,9) (2,13) (2,8) (3,18) (3,4) (3,10) (3,23) (3,19) (3,11) (3,9) (3,13) (3,8) (4,18) (4,10) (4,23) (4,19) (4,11) (4,9) (4,13) (4,8) (5,6) (5,21) (5,17) (5,16) (5,20) (5,7) (5,12) (5,14) (5,22) (5,15) (6,21) (6,17) (6,16) (6,20) (6,7) (6,12) (6,14) (6,22) (6,15) (7,21) (7,17) (7,16) (7,20) (7,12) (7,14) (7,22) (7,15) (8,18) (8,10) (8,23) (8,19) (8,11) (8,9) (8,13) (9,18) (9,10) (9,23) (9,19) (9,11) (9,13) (10,18) (10,23) (10,19) (10,11) (10,13) (11,18) (11,23) (11,19) (11,13) (12,21) (12,17) (12,16) (12,20) (12,14) (12,22) (12,15) (13,18) (13,23) (13,19) (14,21) (14,17) (14,16) (14,20) (14,22) (14,15) (15,21) (15,17) (15,16) (15,20) (15,22) (16,21) (16,17) (16,20) (16,22) (17,21) (17,20) (17,22) (18,23) (18,19) (19,23) (20,21) (20,22) (21,22)\nIs there a path between node 23 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph655-17_12", + "image": "data/connectivity/graph_visual/medium/graph655.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,16) (0,3) (0,21) (0,23) (1,16) (1,7) (1,3) (1,4) (1,11) (1,23) (2,15) (2,18) (2,6) (2,8) (2,12) (2,14) (2,13) (2,5) (3,16) (3,7) (3,4) (3,21) (3,11) (3,23) (4,16) (4,7) (4,21) (4,11) (5,10) (5,15) (5,17) (5,18) (5,8) (5,19) (5,9) (5,14) (5,13) (6,15) (6,17) (6,12) (6,19) (6,9) (7,21) (7,11) (7,23) (8,10) (8,15) (8,9) (8,14) (8,13) (9,15) (9,18) (9,12) (9,19) (9,14) (10,15) (10,12) (10,14) (10,13) (11,16) (11,21) (11,23) (12,15) (12,17) (12,18) (12,19) (12,13) (13,15) (13,17) (13,18) (13,19) (13,14) (14,17) (15,18) (16,23) (17,18) (18,19) (20,22) (21,23)\nIs there a path between node 17 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph467-6_2", + "image": "data/connectivity/graph_visual/medium/graph467.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,7) (0,1) (0,18) (0,12) (0,2) (0,4) (0,21) (0,16) (0,20) (0,15) (0,10) (0,19) (0,17) (0,13) (1,11) (1,7) (1,18) (1,12) (1,2) (1,4) (1,21) (1,16) (1,20) (1,15) (1,10) (1,19) (1,17) (1,13) (2,11) (2,7) (2,18) (2,12) (2,4) (2,21) (2,16) (2,20) (2,15) (2,10) (2,19) (2,17) (2,13) (3,5) (4,11) (4,7) (4,18) (4,12) (4,21) (4,16) (4,20) (4,15) (4,10) (4,19) (4,17) (4,13) (6,9) (6,8) (6,14) (7,11) (7,18) (7,12) (7,21) (7,16) (7,20) (7,15) (7,10) (7,19) (7,17) (7,13) (8,9) (8,14) (9,14) (10,11) (10,18) (10,12) (10,21) (10,16) (10,20) (10,15) (10,19) (10,17) (10,13) (11,18) (11,12) (11,21) (11,16) (11,20) (11,15) (11,19) (11,17) (11,13) (12,18) (12,21) (12,16) (12,20) (12,15) (12,19) (12,17) (12,13) (13,18) (13,21) (13,16) (13,20) (13,15) (13,19) (13,17) (15,18) (15,21) (15,16) (15,20) (15,19) (15,17) (16,18) (16,21) (16,20) (16,19) (16,17) (17,18) (17,21) (17,20) (17,19) (18,21) (18,20) (18,19) (19,21) (19,20) (20,21)\nIs there a path between node 6 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph794-24_15", + "image": "data/connectivity/graph_visual/medium/graph794.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,13) (0,15) (1,17) (1,18) (1,7) (2,14) (2,6) (2,15) (2,10) (4,6) (4,15) (4,5) (5,13) (5,21) (5,23) (5,24) (6,13) (6,21) (6,23) (7,17) (10,23) (11,16) (11,18) (12,21) (13,23) (15,24) (21,24) (23,24)\nIs there a path between node 24 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph410-19_17", + "image": "data/connectivity/graph_visual/medium/graph410.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,16) (0,10) (0,15) (0,14) (0,21) (0,7) (0,5) (0,4) (0,2) (1,16) (1,14) (1,21) (1,20) (1,5) (2,16) (2,10) (2,15) (2,14) (2,21) (2,7) (2,20) (2,4) (3,13) (3,12) (3,11) (3,9) (4,16) (4,10) (4,15) (4,14) (4,21) (4,7) (4,20) (5,16) (5,15) (5,14) (5,7) (5,20) (5,6) (6,16) (6,10) (6,14) (6,21) (6,20) (7,16) (7,10) (7,15) (7,21) (8,18) (8,19) (8,13) (8,12) (8,9) (8,17) (9,18) (9,19) (9,12) (9,11) (9,17) (10,14) (11,18) (11,19) (11,13) (11,12) (12,19) (12,13) (12,17) (13,17) (14,16) (14,15) (14,21) (14,20) (15,21) (15,20) (16,20) (17,19) (20,21)\nIs there a path between node 19 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph824-1_11", + "image": "data/connectivity/graph_visual/medium/graph824.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,8) (0,12) (0,5) (0,14) (0,15) (0,17) (0,11) (0,16) (0,1) (1,9) (1,8) (1,12) (1,5) (1,14) (1,15) (1,11) (1,16) (1,22) (2,9) (2,8) (2,15) (2,17) (2,11) (2,16) (2,6) (3,20) (3,24) (3,4) (3,13) (3,18) (3,19) (4,24) (4,21) (4,10) (4,18) (4,7) (5,9) (5,12) (5,15) (5,6) (5,22) (6,9) (6,8) (6,12) (6,14) (6,15) (6,17) (6,11) (7,20) (7,24) (7,23) (7,13) (7,21) (7,18) (7,19) (8,12) (8,14) (8,15) (8,11) (8,16) (8,22) (9,12) (9,17) (9,16) (9,22) (10,20) (10,23) (10,13) (10,19) (11,12) (11,14) (11,15) (11,17) (11,16) (12,15) (12,16) (12,22) (13,20) (13,24) (13,21) (13,18) (14,15) (14,17) (14,22) (15,17) (15,22) (16,17) (16,22) (18,20) (18,24) (18,23) (18,21) (18,19) (19,24) (20,24) (20,23) (20,21) (21,24) (21,23) (23,24)\nIs there a path between node 1 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph693-9_18", + "image": "data/connectivity/graph_visual/medium/graph693.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,18) (0,15) (0,19) (0,13) (0,10) (0,6) (0,1) (0,17) (0,22) (1,4) (1,18) (1,15) (1,19) (1,13) (1,10) (1,6) (1,17) (1,22) (2,7) (2,8) (2,5) (2,12) (2,21) (2,3) (2,23) (2,9) (2,11) (2,14) (2,20) (2,16) (3,7) (3,8) (3,5) (3,12) (3,21) (3,23) (3,9) (3,11) (3,14) (3,20) (3,16) (4,18) (4,15) (4,19) (4,13) (4,10) (4,6) (4,17) (4,22) (5,7) (5,8) (5,12) (5,21) (5,23) (5,9) (5,11) (5,14) (5,20) (5,16) (6,18) (6,15) (6,19) (6,13) (6,10) (6,17) (6,22) (7,8) (7,12) (7,21) (7,23) (7,9) (7,11) (7,14) (7,20) (7,16) (8,12) (8,21) (8,23) (8,9) (8,11) (8,14) (8,20) (8,16) (9,12) (9,21) (9,23) (9,11) (9,14) (9,20) (9,16) (10,18) (10,15) (10,19) (10,13) (10,17) (10,22) (11,12) (11,21) (11,23) (11,14) (11,20) (11,16) (12,21) (12,23) (12,14) (12,20) (12,16) (13,18) (13,15) (13,19) (13,17) (13,22) (14,21) (14,23) (14,20) (14,16) (15,18) (15,19) (15,17) (15,22) (16,21) (16,23) (16,20) (17,18) (17,19) (17,22) (18,19) (18,22) (19,22) (20,21) (20,23) (21,23)\nIs there a path between node 9 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph476-3_8", + "image": "data/connectivity/graph_visual/medium/graph476.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,17) (0,1) (0,19) (0,11) (1,18) (1,7) (1,2) (1,12) (2,17) (2,14) (2,7) (2,16) (2,11) (2,15) (3,10) (4,13) (4,18) (4,8) (4,12) (5,18) (5,16) (6,20) (6,14) (6,11) (6,15) (7,18) (7,16) (7,22) (8,20) (8,18) (9,21) (11,17) (11,13) (11,19) (11,14) (11,16) (12,13) (12,16) (12,22) (13,19) (13,14) (14,18) (14,22) (15,19) (16,17) (16,20) (17,18) (18,22) (19,20) (20,22)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph602-5_11", + "image": "data/connectivity/graph_visual/medium/graph602.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,7) (0,1) (0,21) (0,20) (0,9) (1,7) (1,21) (1,20) (1,9) (2,5) (2,11) (2,23) (2,12) (2,22) (2,6) (2,10) (2,19) (3,8) (3,15) (3,17) (4,21) (5,11) (5,12) (5,22) (5,13) (5,18) (5,10) (6,23) (6,22) (6,13) (6,18) (6,10) (6,19) (6,16) (7,21) (7,9) (8,15) (8,17) (9,21) (10,11) (10,12) (10,22) (10,13) (10,19) (11,23) (11,12) (11,22) (11,13) (11,18) (11,19) (11,16) (12,23) (12,22) (12,13) (12,18) (12,19) (12,16) (13,23) (13,22) (13,18) (13,19) (13,16) (14,15) (16,23) (16,22) (16,18) (18,23) (18,22) (18,19) (19,23) (19,22) (20,21) (22,23)\nIs there a path between node 5 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph79-13_1", + "image": "data/connectivity/graph_visual/medium/graph79.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (0,6) (0,4) (0,8) (0,14) (0,7) (0,12) (0,11) (0,13) (0,5) (1,6) (1,4) (1,14) (1,7) (1,12) (1,11) (1,13) (2,4) (2,8) (2,12) (2,13) (2,5) (3,10) (4,6) (4,8) (4,7) (4,12) (4,13) (4,5) (5,6) (5,8) (5,7) (5,12) (5,11) (5,13) (6,8) (6,14) (6,7) (6,12) (6,13) (7,8) (7,14) (7,12) (7,11) (7,13) (8,14) (8,12) (8,11) (8,13) (9,10) (11,14) (11,12) (12,14) (12,13) (13,14)\nIs there a path between node 13 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph298-19_11", + "image": "data/connectivity/graph_visual/medium/graph298.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,19) (0,2) (0,15) (0,7) (0,9) (0,11) (0,1) (1,17) (1,2) (1,9) (1,12) (1,6) (2,17) (2,19) (2,15) (2,3) (2,7) (2,9) (2,12) (3,17) (3,19) (3,15) (3,7) (3,9) (3,12) (3,11) (3,6) (4,18) (4,8) (4,14) (4,13) (4,10) (6,19) (6,15) (6,7) (6,9) (6,12) (6,11) (7,17) (7,19) (7,15) (8,14) (8,13) (8,10) (9,19) (10,14) (10,13) (11,19) (11,15) (11,12) (12,19) (13,18) (14,18) (15,19)\nIs there a path between node 19 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph403-6_13", + "image": "data/connectivity/graph_visual/medium/graph403.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,3) (0,10) (1,13) (1,4) (1,12) (1,9) (2,20) (2,3) (3,6) (4,12) (5,14) (6,10) (6,14) (7,15) (8,18) (8,15) (9,18) (10,20) (10,16) (10,11) (10,21) (11,14) (12,15) (13,18) (14,20) (17,19) (17,18) (18,19)\nIs there a path between node 6 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph548-19_15", + "image": "data/connectivity/graph_visual/medium/graph548.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,9) (0,17) (0,7) (1,18) (1,3) (1,23) (1,19) (2,21) (2,14) (2,9) (2,16) (2,11) (2,5) (3,23) (3,6) (4,9) (4,11) (4,8) (4,20) (5,21) (5,8) (5,13) (6,10) (7,21) (7,17) (7,22) (8,14) (9,11) (9,13) (9,20) (9,22) (10,23) (11,16) (11,12) (12,21) (12,14) (13,21) (13,17) (14,16) (16,20) (19,23)\nIs there a path between node 19 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph841-20_22", + "image": "data/connectivity/graph_visual/medium/graph841.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,2) (0,7) (0,8) (0,4) (0,13) (1,6) (1,12) (1,14) (1,17) (1,16) (1,10) (1,18) (1,21) (1,15) (1,24) (1,11) (1,22) (1,9) (1,23) (2,20) (2,7) (2,8) (2,4) (2,13) (3,19) (3,5) (4,20) (4,7) (4,8) (4,13) (5,19) (6,12) (6,14) (6,17) (6,16) (6,10) (6,18) (6,21) (6,15) (6,24) (6,11) (6,22) (6,9) (6,23) (7,20) (7,8) (7,13) (8,20) (8,13) (9,12) (9,14) (9,17) (9,16) (9,10) (9,18) (9,21) (9,15) (9,24) (9,11) (9,22) (9,23) (10,12) (10,14) (10,17) (10,16) (10,18) (10,21) (10,15) (10,24) (10,11) (10,22) (10,23) (11,12) (11,14) (11,17) (11,16) (11,18) (11,21) (11,15) (11,24) (11,22) (11,23) (12,14) (12,17) (12,16) (12,18) (12,21) (12,15) (12,24) (12,22) (12,23) (13,20) (14,17) (14,16) (14,18) (14,21) (14,15) (14,24) (14,22) (14,23) (15,17) (15,16) (15,18) (15,21) (15,24) (15,22) (15,23) (16,17) (16,18) (16,21) (16,24) (16,22) (16,23) (17,18) (17,21) (17,24) (17,22) (17,23) (18,21) (18,24) (18,22) (18,23) (21,24) (21,22) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 20 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph834-0_20", + "image": "data/connectivity/graph_visual/medium/graph834.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,5) (0,17) (0,4) (0,7) (0,21) (0,8) (0,22) (0,3) (0,16) (0,23) (0,13) (1,24) (1,15) (1,11) (1,20) (1,10) (1,18) (1,12) (1,14) (1,9) (1,19) (1,6) (2,5) (2,17) (2,4) (2,7) (2,21) (2,8) (2,22) (2,3) (2,16) (2,23) (2,13) (3,5) (3,17) (3,4) (3,7) (3,21) (3,8) (3,22) (3,16) (3,23) (3,13) (4,5) (4,17) (4,7) (4,21) (4,8) (4,22) (4,16) (4,23) (4,13) (5,17) (5,7) (5,21) (5,8) (5,22) (5,16) (5,23) (5,13) (6,24) (6,15) (6,11) (6,20) (6,10) (6,18) (6,12) (6,14) (6,9) (6,19) (7,17) (7,21) (7,8) (7,22) (7,16) (7,23) (7,13) (8,17) (8,21) (8,22) (8,16) (8,23) (8,13) (9,24) (9,15) (9,11) (9,20) (9,10) (9,18) (9,12) (9,14) (9,19) (10,24) (10,15) (10,11) (10,20) (10,18) (10,12) (10,14) (10,19) (11,24) (11,15) (11,20) (11,18) (11,12) (11,14) (11,19) (12,24) (12,15) (12,20) (12,18) (12,14) (12,19) (13,17) (13,21) (13,22) (13,16) (13,23) (14,24) (14,15) (14,20) (14,18) (14,19) (15,24) (15,20) (15,18) (15,19) (16,17) (16,21) (16,22) (16,23) (17,21) (17,22) (17,23) (18,24) (18,20) (18,19) (19,24) (19,20) (20,24) (21,22) (21,23) (22,23)\nIs there a path between node 0 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph473-7_17", + "image": "data/connectivity/graph_visual/medium/graph473.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,17) (0,11) (2,17) (2,20) (2,11) (3,8) (3,21) (3,18) (3,4) (4,7) (4,12) (6,14) (7,19) (7,21) (7,10) (8,13) (8,19) (8,21) (8,12) (9,19) (9,21) (10,13) (11,14) (12,21) (13,16) (13,18) (14,15) (15,22) (16,19) (16,18) (17,22) (17,20)\nIs there a path between node 7 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph389-8_9", + "image": "data/connectivity/graph_visual/medium/graph389.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,4) (0,20) (0,6) (0,16) (0,13) (0,9) (0,18) (0,7) (0,3) (0,5) (0,19) (0,1) (0,15) (0,8) (0,10) (0,12) (1,4) (1,20) (1,6) (1,16) (1,13) (1,9) (1,18) (1,7) (1,3) (1,5) (1,19) (1,15) (1,8) (1,10) (1,12) (2,11) (3,4) (3,20) (3,6) (3,16) (3,13) (3,9) (3,18) (3,7) (3,5) (3,19) (3,15) (3,8) (3,10) (3,12) (4,20) (4,6) (4,16) (4,13) (4,9) (4,18) (4,7) (4,5) (4,19) (4,15) (4,8) (4,10) (4,12) (5,20) (5,6) (5,16) (5,13) (5,9) (5,18) (5,7) (5,19) (5,15) (5,8) (5,10) (5,12) (6,20) (6,16) (6,13) (6,9) (6,18) (6,7) (6,19) (6,15) (6,8) (6,10) (6,12) (7,20) (7,16) (7,13) (7,9) (7,18) (7,19) (7,15) (7,8) (7,10) (7,12) (8,20) (8,16) (8,13) (8,9) (8,18) (8,19) (8,15) (8,10) (8,12) (9,20) (9,16) (9,13) (9,18) (9,19) (9,15) (9,10) (9,12) (10,20) (10,16) (10,13) (10,18) (10,19) (10,15) (10,12) (12,20) (12,16) (12,13) (12,18) (12,19) (12,15) (13,20) (13,16) (13,18) (13,19) (13,15) (14,17) (15,20) (15,16) (15,18) (15,19) (16,20) (16,18) (16,19) (18,20) (18,19) (19,20)\nIs there a path between node 8 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph187-13_4", + "image": "data/connectivity/graph_visual/medium/graph187.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,10) (0,17) (0,1) (0,15) (0,14) (0,4) (0,8) (0,16) (0,13) (0,9) (0,5) (0,11) (1,10) (1,17) (1,15) (1,14) (1,4) (1,8) (1,16) (1,13) (1,9) (1,5) (1,11) (2,3) (2,7) (2,12) (2,6) (3,7) (3,12) (3,6) (4,10) (4,17) (4,15) (4,14) (4,8) (4,16) (4,13) (4,9) (4,5) (4,11) (5,10) (5,17) (5,15) (5,14) (5,8) (5,16) (5,13) (5,9) (5,11) (6,7) (6,12) (7,12) (8,10) (8,17) (8,15) (8,14) (8,16) (8,13) (8,9) (8,11) (9,10) (9,17) (9,15) (9,14) (9,16) (9,13) (9,11) (10,17) (10,15) (10,14) (10,16) (10,13) (10,11) (11,17) (11,15) (11,14) (11,16) (11,13) (13,17) (13,15) (13,14) (13,16) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 13 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph851-0_22", + "image": "data/connectivity/graph_visual/medium/graph851.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,24) (0,15) (0,7) (0,16) (1,3) (1,6) (1,8) (1,14) (1,23) (1,10) (1,11) (2,17) (2,9) (2,21) (2,13) (2,18) (2,4) (2,5) (2,20) (2,22) (2,19) (3,6) (3,8) (3,14) (3,23) (3,10) (3,11) (4,17) (4,9) (4,21) (4,13) (4,18) (4,5) (4,20) (4,22) (4,19) (5,17) (5,9) (5,21) (5,13) (5,18) (5,20) (5,22) (5,19) (6,8) (6,14) (6,23) (6,10) (6,11) (7,12) (7,24) (7,15) (7,16) (8,14) (8,23) (8,10) (8,11) (9,17) (9,21) (9,13) (9,18) (9,20) (9,22) (9,19) (10,14) (10,23) (10,11) (11,14) (11,23) (12,24) (12,15) (12,16) (13,17) (13,21) (13,18) (13,20) (13,22) (13,19) (14,23) (15,24) (15,16) (16,24) (17,21) (17,18) (17,20) (17,22) (17,19) (18,21) (18,20) (18,22) (18,19) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 0 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph180-4_5", + "image": "data/connectivity/graph_visual/medium/graph180.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,14) (0,13) (0,3) (0,4) (0,2) (0,9) (0,11) (0,16) (1,5) (2,15) (2,12) (2,6) (2,14) (2,13) (2,8) (2,17) (2,9) (2,11) (3,15) (3,10) (3,12) (3,6) (3,14) (3,7) (3,13) (3,8) (3,17) (3,16) (4,15) (4,10) (4,12) (4,6) (4,14) (4,7) (4,13) (4,8) (4,17) (4,9) (4,11) (6,15) (6,10) (6,12) (6,7) (6,13) (6,8) (6,9) (6,16) (7,15) (7,12) (7,14) (7,13) (7,9) (7,11) (8,15) (8,10) (8,14) (8,13) (8,17) (8,9) (8,16) (9,15) (9,12) (9,14) (9,13) (9,17) (9,16) (10,15) (10,12) (10,14) (10,13) (10,17) (10,16) (11,15) (11,12) (11,17) (12,14) (12,16) (13,17) (13,16) (14,17) (14,16) (16,17)\nIs there a path between node 4 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph158-11_14", + "image": "data/connectivity/graph_visual/medium/graph158.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,9) (1,14) (1,8) (2,11) (2,16) (2,7) (2,6) (3,17) (3,11) (3,4) (3,13) (3,6) (4,10) (5,15) (5,10) (6,17) (6,15) (7,17) (7,16) (8,9) (10,17) (10,16) (11,17) (11,15) (11,16) (12,17) (12,16) (15,17) (15,16)\nIs there a path between node 11 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph247-3_9", + "image": "data/connectivity/graph_visual/medium/graph247.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (0,13) (0,5) (0,7) (0,16) (0,12) (0,18) (0,9) (0,8) (0,2) (0,11) (0,10) (0,6) (1,15) (1,14) (1,3) (2,4) (2,13) (2,5) (2,7) (2,16) (2,12) (2,18) (2,9) (2,8) (2,11) (2,10) (2,6) (3,15) (3,14) (4,13) (4,5) (4,7) (4,16) (4,12) (4,18) (4,9) (4,8) (4,11) (4,10) (4,6) (5,13) (5,7) (5,16) (5,12) (5,18) (5,9) (5,8) (5,11) (5,10) (5,6) (6,13) (6,7) (6,16) (6,12) (6,18) (6,9) (6,8) (6,11) (6,10) (7,13) (7,16) (7,12) (7,18) (7,9) (7,8) (7,11) (7,10) (8,13) (8,16) (8,12) (8,18) (8,9) (8,11) (8,10) (9,13) (9,16) (9,12) (9,18) (9,11) (9,10) (10,13) (10,16) (10,12) (10,18) (10,11) (11,13) (11,16) (11,12) (11,18) (12,13) (12,16) (12,18) (13,16) (13,18) (14,15) (16,18)\nIs there a path between node 3 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph378-15_7", + "image": "data/connectivity/graph_visual/medium/graph378.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (0,1) (0,19) (0,11) (0,17) (0,16) (0,6) (1,9) (1,5) (1,4) (1,18) (1,20) (1,11) (1,16) (1,6) (1,12) (2,15) (2,7) (2,13) (3,9) (3,5) (3,4) (3,20) (3,8) (3,11) (3,17) (3,6) (3,12) (4,5) (4,18) (4,19) (4,20) (4,17) (4,16) (4,12) (5,9) (5,18) (5,20) (5,8) (5,11) (6,9) (6,18) (6,19) (6,11) (6,12) (7,15) (7,13) (8,9) (8,18) (8,19) (8,20) (8,17) (8,16) (9,18) (9,19) (9,20) (9,11) (9,16) (9,12) (11,18) (11,17) (11,16) (12,18) (12,20) (12,17) (13,15) (16,18) (16,19) (16,17) (17,19) (17,20) (18,19) (19,20)\nIs there a path between node 15 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph829-11_10", + "image": "data/connectivity/graph_visual/medium/graph829.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,6) (1,14) (1,9) (1,12) (1,3) (1,2) (1,23) (1,5) (1,24) (1,11) (1,17) (2,9) (2,12) (2,7) (2,3) (2,15) (2,23) (2,5) (3,14) (3,12) (3,7) (3,15) (3,23) (3,24) (3,11) (3,17) (3,8) (4,10) (4,18) (5,6) (5,14) (5,12) (5,23) (5,24) (5,11) (5,13) (6,14) (6,9) (6,12) (6,7) (6,15) (6,23) (6,24) (6,11) (6,17) (6,13) (6,8) (7,14) (7,9) (7,12) (7,15) (7,23) (7,11) (7,13) (7,8) (8,14) (8,9) (8,16) (8,12) (8,15) (8,23) (8,24) (8,11) (8,17) (8,13) (9,14) (9,16) (9,12) (9,15) (9,23) (9,24) (9,11) (10,18) (10,21) (10,19) (11,14) (11,16) (11,23) (11,24) (11,13) (12,14) (12,16) (12,15) (12,24) (12,13) (13,14) (13,23) (13,17) (14,15) (14,23) (14,17) (15,16) (15,23) (15,24) (15,17) (16,23) (16,17) (17,23) (17,24) (18,21) (19,21) (19,22) (21,22)\nIs there a path between node 11 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph351-4_11", + "image": "data/connectivity/graph_visual/medium/graph351.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,10) (2,9) (2,5) (3,12) (3,14) (3,4) (3,8) (3,18) (4,19) (4,16) (4,11) (5,20) (5,12) (5,14) (5,11) (6,18) (6,16) (7,15) (8,20) (8,12) (8,18) (8,16) (9,20) (9,14) (9,19) (9,11) (11,13) (11,12) (11,18) (11,16) (12,18) (13,19) (13,18) (14,19) (16,20) (18,19)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph608-2_21", + "image": "data/connectivity/graph_visual/medium/graph608.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,10) (0,6) (0,9) (0,5) (0,3) (0,17) (0,18) (0,15) (0,21) (1,16) (1,23) (1,12) (1,14) (1,22) (1,4) (1,13) (1,19) (1,2) (1,20) (1,11) (1,7) (2,16) (2,23) (2,12) (2,14) (2,22) (2,4) (2,13) (2,19) (2,20) (2,11) (2,7) (3,8) (3,10) (3,6) (3,9) (3,5) (3,17) (3,18) (3,15) (3,21) (4,16) (4,23) (4,12) (4,14) (4,22) (4,13) (4,19) (4,20) (4,11) (4,7) (5,8) (5,10) (5,6) (5,9) (5,17) (5,18) (5,15) (5,21) (6,8) (6,10) (6,9) (6,17) (6,18) (6,15) (6,21) (7,16) (7,23) (7,12) (7,14) (7,22) (7,13) (7,19) (7,20) (7,11) (8,10) (8,9) (8,17) (8,18) (8,15) (8,21) (9,10) (9,17) (9,18) (9,15) (9,21) (10,17) (10,18) (10,15) (10,21) (11,16) (11,23) (11,12) (11,14) (11,22) (11,13) (11,19) (11,20) (12,16) (12,23) (12,14) (12,22) (12,13) (12,19) (12,20) (13,16) (13,23) (13,14) (13,22) (13,19) (13,20) (14,16) (14,23) (14,22) (14,19) (14,20) (15,17) (15,18) (15,21) (16,23) (16,22) (16,19) (16,20) (17,18) (17,21) (18,21) (19,23) (19,22) (19,20) (20,23) (20,22) (22,23)\nIs there a path between node 2 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph262-7_6", + "image": "data/connectivity/graph_visual/medium/graph262.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (0,13) (0,12) (0,2) (1,8) (1,13) (1,11) (1,12) (1,4) (2,15) (2,19) (2,4) (3,13) (3,11) (4,8) (4,17) (4,19) (4,16) (5,14) (5,6) (5,9) (5,18) (6,10) (7,18) (8,11) (8,17) (8,16) (9,14) (9,10) (10,14) (11,17) (11,19) (11,16) (12,16) (13,17) (16,19)\nIs there a path between node 7 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph649-15_4", + "image": "data/connectivity/graph_visual/medium/graph649.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (1,5) (1,18) (1,7) (1,22) (1,11) (1,20) (1,4) (1,23) (2,14) (2,10) (2,21) (2,15) (2,16) (2,3) (3,14) (3,10) (3,15) (3,16) (3,6) (3,19) (4,18) (4,7) (4,22) (4,11) (4,20) (4,23) (5,13) (5,7) (5,22) (5,11) (5,20) (5,23) (6,10) (6,21) (6,15) (6,16) (6,9) (6,8) (6,19) (7,13) (7,22) (7,20) (7,23) (8,10) (8,9) (8,19) (9,21) (9,15) (9,19) (10,21) (10,16) (10,19) (11,18) (11,13) (11,22) (11,23) (12,17) (13,22) (13,20) (14,15) (14,16) (14,19) (15,16) (15,19) (16,21) (16,19) (18,20) (18,23) (19,21) (20,22) (20,23) (22,23)\nIs there a path between node 15 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph716-10_17", + "image": "data/connectivity/graph_visual/medium/graph716.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,22) (0,23) (0,15) (0,21) (0,8) (0,12) (0,2) (0,1) (1,24) (1,14) (1,11) (1,22) (1,19) (1,15) (1,8) (1,12) (1,2) (1,17) (2,24) (2,11) (2,19) (2,15) (2,8) (2,7) (2,17) (3,16) (3,6) (3,13) (3,4) (4,16) (4,6) (4,10) (4,13) (4,9) (4,18) (5,16) (5,10) (5,13) (5,9) (5,18) (6,10) (6,9) (6,18) (7,24) (7,14) (7,22) (7,19) (7,21) (7,12) (7,20) (7,17) (8,24) (8,14) (8,23) (8,21) (8,20) (9,16) (9,10) (9,13) (9,18) (10,13) (10,18) (11,24) (11,14) (11,22) (11,19) (11,15) (11,21) (11,17) (12,24) (12,14) (12,19) (12,23) (12,21) (12,20) (12,17) (13,16) (13,18) (14,24) (14,22) (14,19) (14,23) (14,15) (14,21) (14,20) (14,17) (15,24) (15,22) (15,19) (15,20) (15,17) (16,18) (17,24) (17,22) (17,19) (17,21) (17,20) (19,24) (19,22) (19,21) (19,20) (20,24) (20,22) (21,24) (21,22) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 10 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph504-2_8", + "image": "data/connectivity/graph_visual/medium/graph504.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,3) (0,20) (0,18) (0,14) (0,10) (0,11) (1,16) (1,2) (1,18) (1,13) (1,4) (1,8) (2,11) (2,8) (2,12) (3,16) (3,14) (3,9) (3,10) (3,12) (4,20) (4,6) (4,8) (6,20) (6,14) (6,11) (6,12) (7,21) (7,13) (7,12) (8,21) (8,10) (8,11) (9,16) (9,20) (9,10) (10,15) (10,14) (10,17) (10,12) (11,16) (11,20) (11,21) (11,13) (12,14) (14,21) (14,17) (15,20) (15,17) (17,20) (18,21)\nIs there a path between node 2 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph622-0_8", + "image": "data/connectivity/graph_visual/medium/graph622.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,7) (0,9) (0,23) (0,22) (0,15) (0,6) (0,4) (0,17) (0,10) (0,1) (0,3) (0,2) (1,21) (1,7) (1,9) (1,23) (1,22) (1,15) (1,6) (1,4) (1,17) (1,10) (1,3) (1,2) (2,21) (2,7) (2,9) (2,23) (2,22) (2,15) (2,6) (2,4) (2,17) (2,10) (2,3) (3,21) (3,7) (3,9) (3,23) (3,22) (3,15) (3,6) (3,4) (3,17) (3,10) (4,21) (4,7) (4,9) (4,23) (4,22) (4,15) (4,6) (4,17) (4,10) (5,18) (5,19) (5,14) (5,12) (5,20) (5,13) (5,16) (5,8) (5,11) (6,21) (6,7) (6,9) (6,23) (6,22) (6,15) (6,17) (6,10) (7,21) (7,9) (7,23) (7,22) (7,15) (7,17) (7,10) (8,18) (8,19) (8,14) (8,12) (8,20) (8,13) (8,16) (8,11) (9,21) (9,23) (9,22) (9,15) (9,17) (9,10) (10,21) (10,23) (10,22) (10,15) (10,17) (11,18) (11,19) (11,14) (11,12) (11,20) (11,13) (11,16) (12,18) (12,19) (12,14) (12,20) (12,13) (12,16) (13,18) (13,19) (13,14) (13,20) (13,16) (14,18) (14,19) (14,20) (14,16) (15,21) (15,23) (15,22) (15,17) (16,18) (16,19) (16,20) (17,21) (17,23) (17,22) (18,19) (18,20) (19,20) (21,23) (21,22) (22,23)\nIs there a path between node 0 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph230-10_2", + "image": "data/connectivity/graph_visual/medium/graph230.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,9) (1,14) (1,2) (1,17) (1,16) (1,8) (2,4) (2,17) (3,7) (4,12) (4,18) (4,17) (4,10) (5,14) (5,18) (5,17) (5,10) (5,8) (6,18) (6,17) (6,10) (8,12) (8,10) (8,16) (10,12) (10,14) (12,15) (12,17) (12,16) (14,15) (14,17) (15,17) (15,16) (16,18) (17,18)\nIs there a path between node 10 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph426-1_7", + "image": "data/connectivity/graph_visual/medium/graph426.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,8) (0,18) (0,10) (0,2) (0,20) (1,10) (1,17) (1,21) (3,4) (3,18) (4,18) (4,9) (5,16) (7,19) (7,13) (8,18) (8,10) (8,20) (8,21) (9,17) (9,21) (10,17) (12,13) (13,16) (14,15) (17,21) (18,21)\nIs there a path between node 1 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph687-12_19", + "image": "data/connectivity/graph_visual/medium/graph687.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,2) (0,4) (0,11) (0,8) (0,3) (0,20) (0,15) (0,13) (0,6) (0,7) (0,12) (0,14) (0,18) (0,23) (0,16) (0,9) (1,2) (1,4) (1,11) (1,8) (1,3) (1,20) (1,15) (1,13) (1,6) (1,7) (1,12) (1,14) (1,18) (1,23) (1,16) (1,9) (2,4) (2,11) (2,8) (2,3) (2,20) (2,15) (2,13) (2,6) (2,7) (2,12) (2,14) (2,18) (2,23) (2,16) (2,9) (3,4) (3,11) (3,8) (3,20) (3,15) (3,13) (3,6) (3,7) (3,12) (3,14) (3,18) (3,23) (3,16) (3,9) (4,11) (4,8) (4,20) (4,15) (4,13) (4,6) (4,7) (4,12) (4,14) (4,18) (4,23) (4,16) (4,9) (5,21) (5,19) (5,17) (5,22) (6,11) (6,8) (6,20) (6,15) (6,13) (6,7) (6,12) (6,14) (6,18) (6,23) (6,16) (6,9) (7,11) (7,8) (7,20) (7,15) (7,13) (7,12) (7,14) (7,18) (7,23) (7,16) (7,9) (8,11) (8,20) (8,15) (8,13) (8,12) (8,14) (8,18) (8,23) (8,16) (8,9) (9,11) (9,20) (9,15) (9,13) (9,12) (9,14) (9,18) (9,23) (9,16) (11,20) (11,15) (11,13) (11,12) (11,14) (11,18) (11,23) (11,16) (12,20) (12,15) (12,13) (12,14) (12,18) (12,23) (12,16) (13,20) (13,15) (13,14) (13,18) (13,23) (13,16) (14,20) (14,15) (14,18) (14,23) (14,16) (15,20) (15,18) (15,23) (15,16) (16,20) (16,18) (16,23) (17,21) (17,19) (17,22) (18,20) (18,23) (19,21) (19,22) (20,23) (21,22)\nIs there a path between node 12 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph797-6_8", + "image": "data/connectivity/graph_visual/medium/graph797.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,17) (0,2) (0,10) (0,3) (0,11) (0,12) (2,9) (2,23) (2,18) (2,13) (2,16) (3,4) (4,20) (4,21) (4,24) (5,13) (5,11) (5,16) (6,21) (9,16) (10,18) (10,20) (10,12) (10,21) (11,14) (12,20) (12,14) (12,13) (13,14) (13,19) (14,17) (14,20) (14,16) (14,24) (16,23) (16,17) (16,18) (17,19) (18,23) (18,20) (18,21) (18,24) (19,20) (19,21) (20,23) (22,24)\nIs there a path between node 6 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph467-16_18", + "image": "data/connectivity/graph_visual/medium/graph467.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,7) (0,1) (0,18) (0,12) (0,2) (0,4) (0,21) (0,16) (0,20) (0,15) (0,10) (0,19) (0,17) (0,13) (1,11) (1,7) (1,18) (1,12) (1,2) (1,4) (1,21) (1,16) (1,20) (1,15) (1,10) (1,19) (1,17) (1,13) (2,11) (2,7) (2,18) (2,12) (2,4) (2,21) (2,16) (2,20) (2,15) (2,10) (2,19) (2,17) (2,13) (3,5) (4,11) (4,7) (4,18) (4,12) (4,21) (4,16) (4,20) (4,15) (4,10) (4,19) (4,17) (4,13) (6,9) (6,8) (6,14) (7,11) (7,18) (7,12) (7,21) (7,16) (7,20) (7,15) (7,10) (7,19) (7,17) (7,13) (8,9) (8,14) (9,14) (10,11) (10,18) (10,12) (10,21) (10,16) (10,20) (10,15) (10,19) (10,17) (10,13) (11,18) (11,12) (11,21) (11,16) (11,20) (11,15) (11,19) (11,17) (11,13) (12,18) (12,21) (12,16) (12,20) (12,15) (12,19) (12,17) (12,13) (13,18) (13,21) (13,16) (13,20) (13,15) (13,19) (13,17) (15,18) (15,21) (15,16) (15,20) (15,19) (15,17) (16,18) (16,21) (16,20) (16,19) (16,17) (17,18) (17,21) (17,20) (17,19) (18,21) (18,20) (18,19) (19,21) (19,20) (20,21)\nIs there a path between node 16 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph67-12_6", + "image": "data/connectivity/graph_visual/medium/graph67.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,10) (1,3) (1,6) (1,12) (1,7) (1,2) (1,4) (1,11) (1,5) (1,13) (1,8) (1,9) (2,10) (2,3) (2,6) (2,12) (2,7) (2,4) (2,11) (2,5) (2,13) (2,8) (2,9) (3,10) (3,6) (3,12) (3,7) (3,4) (3,11) (3,5) (3,13) (3,8) (3,9) (4,10) (4,6) (4,12) (4,7) (4,11) (4,5) (4,13) (4,8) (4,9) (5,10) (5,6) (5,12) (5,7) (5,11) (5,13) (5,8) (5,9) (6,10) (6,12) (6,7) (6,11) (6,13) (6,8) (6,9) (7,10) (7,12) (7,11) (7,13) (7,8) (7,9) (8,10) (8,12) (8,11) (8,13) (8,9) (9,10) (9,12) (9,11) (9,13) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nIs there a path between node 12 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph638-10_15", + "image": "data/connectivity/graph_visual/medium/graph638.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (1,2) (1,16) (2,19) (2,21) (2,10) (2,23) (2,22) (3,15) (3,17) (3,18) (3,8) (5,15) (7,21) (7,10) (7,23) (7,16) (7,12) (8,20) (8,14) (8,17) (10,21) (10,11) (11,16) (11,22) (12,23) (12,16) (12,22) (13,19) (13,21) (13,23) (13,22) (14,17) (14,18) (15,17) (16,19) (16,23) (18,20)\nIs there a path between node 10 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph827-24_12", + "image": "data/connectivity/graph_visual/medium/graph827.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,23) (0,22) (1,9) (1,24) (1,11) (1,13) (1,8) (1,20) (1,5) (1,4) (1,21) (1,16) (1,3) (1,19) (1,10) (1,18) (1,2) (2,9) (2,24) (2,11) (2,14) (2,8) (2,20) (2,5) (2,21) (2,6) (2,16) (2,3) (2,19) (2,12) (2,10) (2,18) (3,9) (3,11) (3,14) (3,8) (3,5) (3,21) (3,6) (3,16) (3,19) (3,12) (3,10) (3,18) (4,9) (4,11) (4,13) (4,14) (4,20) (4,5) (4,21) (4,16) (4,19) (4,12) (4,18) (5,9) (5,11) (5,13) (5,8) (5,20) (5,21) (5,6) (5,16) (5,12) (5,10) (5,18) (6,9) (6,24) (6,11) (6,13) (6,14) (6,20) (6,16) (6,19) (6,10) (6,18) (7,23) (7,15) (8,9) (8,24) (8,11) (8,13) (8,14) (8,20) (8,21) (8,16) (8,10) (8,18) (9,24) (9,11) (9,14) (9,20) (9,21) (9,16) (9,19) (9,10) (9,18) (10,24) (10,11) (10,14) (10,20) (10,16) (10,19) (10,12) (10,18) (11,13) (11,14) (11,20) (11,21) (11,16) (11,12) (11,18) (12,24) (12,13) (12,14) (12,20) (12,21) (12,16) (12,19) (12,18) (13,24) (13,14) (13,21) (13,16) (13,18) (14,24) (14,21) (14,19) (14,18) (15,22) (15,17) (16,24) (16,19) (16,18) (17,23) (17,22) (18,24) (18,19) (19,24) (19,21) (20,24) (20,21) (21,24)\nIs there a path between node 24 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph128-14_2", + "image": "data/connectivity/graph_visual/medium/graph128.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,10) (0,5) (0,16) (0,1) (0,12) (0,15) (0,11) (0,9) (0,7) (0,6) (0,3) (0,2) (0,4) (1,10) (1,5) (1,16) (1,12) (1,15) (1,11) (1,9) (1,7) (1,6) (1,3) (1,2) (1,4) (2,10) (2,5) (2,16) (2,12) (2,15) (2,11) (2,9) (2,7) (2,6) (2,3) (2,4) (3,10) (3,5) (3,16) (3,12) (3,15) (3,11) (3,9) (3,7) (3,6) (3,4) (4,10) (4,5) (4,16) (4,12) (4,15) (4,11) (4,9) (4,7) (4,6) (5,10) (5,16) (5,12) (5,15) (5,11) (5,9) (5,7) (5,6) (6,10) (6,16) (6,12) (6,15) (6,11) (6,9) (6,7) (7,10) (7,16) (7,12) (7,15) (7,11) (7,9) (8,13) (8,14) (9,10) (9,16) (9,12) (9,15) (9,11) (10,16) (10,12) (10,15) (10,11) (11,16) (11,12) (11,15) (12,16) (12,15) (13,14) (15,16)\nIs there a path between node 14 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph512-20_13", + "image": "data/connectivity/graph_visual/medium/graph512.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,19) (0,3) (0,15) (0,6) (1,17) (1,2) (1,11) (1,12) (1,9) (2,11) (2,12) (2,7) (2,10) (2,9) (2,4) (3,19) (3,22) (3,15) (4,11) (4,5) (4,12) (4,7) (4,10) (4,9) (5,17) (5,11) (5,12) (5,10) (5,9) (6,21) (6,19) (6,22) (6,15) (7,11) (7,10) (7,9) (8,13) (8,20) (8,18) (9,17) (9,11) (9,10) (10,11) (10,12) (11,17) (11,12) (12,17) (13,20) (14,20) (15,21) (15,19) (15,22) (15,16) (16,21) (16,19) (18,20) (19,21) (19,22)\nIs there a path between node 20 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph426-11_16", + "image": "data/connectivity/graph_visual/medium/graph426.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,8) (0,18) (0,10) (0,2) (0,20) (1,10) (1,17) (1,21) (3,4) (3,18) (4,18) (4,9) (5,16) (7,19) (7,13) (8,18) (8,10) (8,20) (8,21) (9,17) (9,21) (10,17) (12,13) (13,16) (14,15) (17,21) (18,21)\nIs there a path between node 11 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph590-21_2", + "image": "data/connectivity/graph_visual/medium/graph590.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,16) (0,22) (0,4) (0,15) (0,9) (1,8) (1,17) (1,12) (1,3) (1,5) (1,21) (1,6) (1,13) (1,19) (2,20) (2,16) (2,22) (2,4) (2,9) (3,8) (3,17) (3,14) (3,6) (3,10) (3,19) (4,20) (4,16) (4,22) (4,15) (4,9) (5,8) (5,17) (5,12) (5,14) (5,13) (5,10) (5,19) (6,17) (6,12) (6,14) (6,21) (6,13) (6,10) (6,19) (8,17) (8,12) (8,13) (8,19) (9,20) (9,22) (9,15) (10,17) (10,14) (10,21) (11,18) (11,23) (12,17) (12,21) (12,13) (12,19) (13,17) (13,14) (13,21) (15,20) (16,22) (17,21) (18,23)\nIs there a path between node 21 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph140-5_8", + "image": "data/connectivity/graph_visual/medium/graph140.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,14) (1,9) (2,14) (2,6) (2,5) (3,16) (4,7) (4,9) (4,15) (5,9) (5,15) (6,14) (6,9) (6,12) (7,14) (7,15) (7,12) (8,17) (10,13) (12,14)\nIs there a path between node 5 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph549-5_17", + "image": "data/connectivity/graph_visual/medium/graph549.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (1,10) (2,11) (2,9) (3,21) (4,10) (4,23) (5,7) (5,9) (7,11) (7,9) (8,18) (8,17) (10,22) (13,19) (14,16) (15,19) (16,17) (17,19)\nIs there a path between node 5 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph255-9_3", + "image": "data/connectivity/graph_visual/medium/graph255.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,10) (0,15) (0,5) (0,1) (0,6) (0,9) (0,2) (0,8) (1,10) (1,15) (1,5) (1,6) (1,9) (1,2) (1,8) (2,10) (2,15) (2,5) (2,6) (2,9) (2,8) (3,17) (3,16) (3,12) (3,4) (3,18) (3,11) (3,13) (4,17) (4,16) (4,12) (4,18) (4,11) (4,13) (5,10) (5,15) (5,6) (5,9) (5,8) (6,10) (6,15) (6,9) (6,8) (7,14) (8,10) (8,15) (8,9) (9,10) (9,15) (10,15) (11,17) (11,16) (11,12) (11,18) (11,13) (12,17) (12,16) (12,18) (12,13) (13,17) (13,16) (13,18) (16,17) (16,18) (17,18)\nIs there a path between node 9 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph529-5_6", + "image": "data/connectivity/graph_visual/medium/graph529.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,20) (0,19) (0,14) (0,2) (0,9) (0,13) (0,21) (0,12) (0,18) (0,16) (0,7) (1,17) (1,5) (1,4) (1,22) (1,11) (1,3) (1,8) (1,15) (1,10) (1,6) (2,20) (2,19) (2,14) (2,9) (2,13) (2,21) (2,12) (2,18) (2,16) (2,7) (3,17) (3,5) (3,4) (3,22) (3,11) (3,8) (3,15) (3,10) (3,6) (4,17) (4,5) (4,22) (4,11) (4,8) (4,15) (4,10) (4,6) (5,17) (5,22) (5,11) (5,8) (5,15) (5,10) (5,6) (6,17) (6,22) (6,11) (6,8) (6,15) (6,10) (7,20) (7,19) (7,14) (7,9) (7,13) (7,21) (7,12) (7,18) (7,16) (8,17) (8,22) (8,11) (8,15) (8,10) (9,20) (9,19) (9,14) (9,13) (9,21) (9,12) (9,18) (9,16) (10,17) (10,22) (10,11) (10,15) (11,17) (11,22) (11,15) (12,20) (12,19) (12,14) (12,13) (12,21) (12,18) (12,16) (13,20) (13,19) (13,14) (13,21) (13,18) (13,16) (14,20) (14,19) (14,21) (14,18) (14,16) (15,17) (15,22) (16,20) (16,19) (16,21) (16,18) (17,22) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 5 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph799-14_13", + "image": "data/connectivity/graph_visual/medium/graph799.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,9) (0,2) (0,1) (1,23) (1,24) (1,9) (1,19) (1,12) (1,7) (1,16) (1,11) (1,15) (1,22) (2,4) (2,20) (2,11) (2,22) (3,23) (3,5) (3,9) (3,12) (3,11) (3,6) (4,24) (4,5) (4,12) (4,14) (4,15) (4,13) (4,6) (4,22) (5,20) (5,19) (5,7) (5,11) (5,15) (5,10) (5,6) (6,20) (6,12) (6,16) (6,17) (6,13) (6,10) (7,23) (7,14) (7,11) (7,15) (8,21) (8,18) (9,24) (9,20) (9,10) (10,23) (10,20) (10,19) (11,20) (11,14) (11,15) (12,19) (12,14) (12,17) (12,13) (13,19) (14,23) (14,24) (14,19) (14,16) (14,17) (14,15) (14,22) (15,24) (15,17) (16,23) (16,24) (16,20) (17,23) (17,19) (20,24)\nIs there a path between node 14 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph449-19_16", + "image": "data/connectivity/graph_visual/medium/graph449.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,10) (0,9) (0,12) (0,15) (1,8) (1,11) (1,5) (1,10) (1,17) (1,9) (1,12) (1,20) (1,15) (2,8) (2,11) (2,10) (2,17) (2,12) (3,11) (3,5) (3,17) (3,9) (3,12) (3,15) (5,11) (5,12) (5,20) (5,15) (6,16) (6,14) (6,18) (7,16) (7,13) (7,21) (7,14) (7,19) (7,18) (8,11) (8,17) (8,20) (9,11) (9,10) (9,17) (9,12) (9,20) (9,15) (10,11) (10,17) (10,12) (10,20) (10,15) (11,12) (11,20) (12,17) (12,20) (13,16) (13,21) (13,14) (13,18) (14,19) (14,18) (15,17) (15,20) (16,19) (16,18) (18,21) (18,19)\nIs there a path between node 19 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph596-7_17", + "image": "data/connectivity/graph_visual/medium/graph596.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (0,16) (0,19) (0,21) (0,18) (0,6) (0,2) (0,3) (0,15) (0,4) (0,14) (1,8) (1,9) (1,11) (1,20) (1,7) (2,13) (2,16) (2,19) (2,18) (2,6) (3,13) (3,16) (3,12) (3,19) (3,5) (3,21) (3,15) (4,10) (4,16) (4,12) (4,19) (4,5) (4,21) (4,18) (4,15) (4,14) (5,16) (5,19) (5,18) (5,6) (5,15) (5,14) (6,10) (6,16) (6,19) (6,21) (6,18) (6,15) (6,14) (7,17) (7,9) (7,23) (7,11) (7,22) (8,9) (8,23) (8,22) (9,23) (9,11) (9,20) (10,13) (10,12) (10,19) (10,21) (10,14) (11,17) (11,23) (11,20) (11,22) (12,13) (12,16) (12,19) (12,21) (12,18) (12,15) (13,16) (13,19) (13,21) (13,18) (13,14) (14,16) (14,19) (14,21) (14,18) (14,15) (15,16) (15,21) (15,18) (16,19) (17,20) (17,22) (18,19) (18,21) (19,21) (20,23)\nIs there a path between node 7 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph551-9_21", + "image": "data/connectivity/graph_visual/medium/graph551.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,11) (2,20) (3,22) (3,6) (3,14) (3,12) (3,13) (3,4) (4,23) (4,12) (5,23) (5,22) (5,12) (5,10) (5,13) (5,15) (6,10) (6,13) (6,18) (8,11) (9,20) (10,12) (11,17) (11,16) (12,14) (12,15) (12,21) (13,19) (13,18) (14,23) (14,15) (14,18) (15,23) (18,23)\nIs there a path between node 9 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph499-17_6", + "image": "data/connectivity/graph_visual/medium/graph499.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (0,15) (0,5) (1,10) (2,19) (2,14) (2,21) (4,22) (4,13) (4,6) (5,15) (6,22) (6,9) (8,13) (8,19) (8,21) (10,20) (11,20) (12,18) (13,14) (15,18) (17,19) (21,22)\nIs there a path between node 17 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph818-15_23", + "image": "data/connectivity/graph_visual/medium/graph818.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,14) (0,7) (0,8) (0,3) (0,6) (1,14) (1,7) (1,9) (1,8) (1,6) (1,17) (2,13) (3,24) (3,14) (3,8) (3,6) (3,17) (4,11) (4,18) (4,12) (4,20) (4,5) (4,10) (4,19) (4,21) (4,23) (4,22) (5,16) (5,11) (5,18) (5,12) (5,20) (5,10) (5,15) (5,19) (5,21) (5,23) (5,22) (6,24) (6,14) (6,7) (6,8) (6,17) (7,14) (7,8) (7,17) (8,24) (8,14) (8,9) (9,14) (10,16) (10,11) (10,18) (10,12) (10,15) (10,19) (10,21) (10,23) (10,22) (11,16) (11,18) (11,20) (11,21) (11,23) (11,22) (12,16) (12,18) (12,20) (12,15) (12,19) (12,21) (12,23) (12,22) (14,17) (15,16) (15,18) (15,20) (15,19) (15,23) (15,22) (16,20) (16,19) (18,19) (18,21) (18,23) (18,22) (19,20) (19,21) (19,23) (20,23) (20,22) (21,22) (22,23)\nIs there a path between node 15 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph338-1_8", + "image": "data/connectivity/graph_visual/medium/graph338.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,8) (0,2) (0,7) (0,9) (0,15) (0,18) (1,8) (1,2) (1,9) (1,15) (1,18) (2,8) (2,7) (2,9) (2,18) (3,17) (3,6) (3,5) (3,16) (3,20) (4,13) (4,11) (5,17) (5,14) (5,10) (5,16) (5,20) (6,17) (6,14) (6,20) (7,8) (7,9) (7,15) (7,12) (8,9) (8,15) (8,12) (8,18) (9,15) (9,18) (10,17) (10,14) (10,16) (10,20) (11,13) (12,18) (13,19) (14,17) (15,18) (16,20)\nIs there a path between node 1 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph594-12_13", + "image": "data/connectivity/graph_visual/medium/graph594.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,13) (0,4) (0,19) (0,9) (0,18) (0,17) (0,21) (0,10) (0,16) (0,2) (0,1) (0,23) (0,14) (0,7) (1,11) (1,13) (1,4) (1,9) (1,6) (1,17) (1,21) (1,10) (1,23) (1,14) (1,7) (2,11) (2,13) (2,19) (2,18) (2,17) (2,21) (2,10) (2,16) (2,23) (2,14) (3,8) (3,12) (3,5) (3,20) (3,22) (4,13) (4,19) (4,9) (4,18) (4,17) (4,21) (4,10) (4,14) (4,7) (5,8) (5,15) (5,20) (5,22) (6,13) (6,19) (6,18) (6,21) (6,10) (6,7) (7,13) (7,9) (7,18) (7,17) (7,10) (7,14) (8,15) (8,12) (8,22) (9,11) (9,19) (9,18) (9,17) (9,21) (9,10) (9,16) (9,23) (9,14) (10,11) (10,13) (10,19) (10,18) (10,17) (10,16) (10,23) (10,14) (11,13) (11,19) (11,17) (11,21) (11,16) (11,23) (11,14) (12,20) (12,22) (13,19) (13,18) (13,17) (13,16) (13,23) (13,14) (14,19) (14,18) (14,17) (14,16) (14,23) (15,22) (16,19) (16,17) (16,21) (16,23) (17,18) (18,23) (19,23) (20,22)\nIs there a path between node 12 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph329-15_11", + "image": "data/connectivity/graph_visual/medium/graph329.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,14) (0,11) (0,7) (1,12) (1,9) (1,6) (1,20) (2,12) (2,9) (2,13) (2,14) (2,19) (2,11) (2,7) (4,5) (6,16) (6,20) (6,7) (7,12) (7,18) (7,8) (7,16) (7,10) (7,11) (8,12) (8,18) (8,16) (8,20) (8,10) (8,17) (9,18) (9,16) (9,14) (9,10) (9,19) (9,11) (10,18) (10,19) (10,17) (12,16) (13,16) (13,17) (16,18)\nIs there a path between node 15 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph387-15_13", + "image": "data/connectivity/graph_visual/medium/graph387.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (0,2) (0,10) (0,1) (0,4) (0,9) (0,19) (0,8) (0,18) (0,14) (0,6) (1,3) (1,2) (1,10) (1,4) (1,9) (1,19) (1,8) (1,18) (1,14) (1,6) (2,3) (2,10) (2,4) (2,9) (2,19) (2,8) (2,18) (2,14) (2,6) (3,10) (3,4) (3,9) (3,19) (3,8) (3,18) (3,14) (3,6) (4,10) (4,9) (4,19) (4,8) (4,18) (4,14) (4,6) (5,17) (5,11) (5,16) (6,10) (6,9) (6,19) (6,8) (6,18) (6,14) (7,15) (7,20) (7,13) (7,12) (8,10) (8,9) (8,19) (8,18) (8,14) (9,10) (9,19) (9,18) (9,14) (10,19) (10,18) (10,14) (11,17) (11,16) (12,15) (12,20) (12,13) (13,15) (13,20) (14,19) (14,18) (15,20) (16,17) (18,19)\nIs there a path between node 15 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph433-16_14", + "image": "data/connectivity/graph_visual/medium/graph433.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,7) (2,12) (3,18) (3,12) (3,15) (3,9) (5,11) (5,17) (5,20) (6,16) (6,17) (7,21) (7,18) (7,9) (8,21) (8,18) (8,15) (9,21) (9,12) (9,19) (12,21) (14,21) (15,18) (15,19) (16,17) (16,20) (17,20)\nIs there a path between node 16 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph117-2_1", + "image": "data/connectivity/graph_visual/medium/graph117.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,8) (0,15) (1,6) (1,8) (1,5) (1,14) (1,10) (4,15) (4,11) (4,7) (5,12) (5,11) (6,9) (6,10) (6,7) (7,8) (7,9) (7,11) (8,13) (8,12) (8,14) (8,10) (9,13) (9,11) (9,10) (10,12) (11,15) (12,15) (12,16) (12,14) (13,15) (13,16) (14,15) (15,16)\nIs there a path between node 2 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph609-13_0", + "image": "data/connectivity/graph_visual/medium/graph609.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,4) (0,2) (0,20) (0,6) (0,1) (0,15) (0,17) (0,11) (0,12) (0,21) (0,7) (0,14) (0,9) (0,10) (0,22) (0,23) (1,3) (1,4) (1,2) (1,20) (1,6) (1,15) (1,17) (1,11) (1,12) (1,21) (1,7) (1,14) (1,9) (1,10) (1,22) (1,23) (2,3) (2,4) (2,20) (2,6) (2,15) (2,17) (2,11) (2,12) (2,21) (2,7) (2,14) (2,9) (2,10) (2,22) (2,23) (3,4) (3,20) (3,6) (3,15) (3,17) (3,11) (3,12) (3,21) (3,7) (3,14) (3,9) (3,10) (3,22) (3,23) (4,20) (4,6) (4,15) (4,17) (4,11) (4,12) (4,21) (4,7) (4,14) (4,9) (4,10) (4,22) (4,23) (5,18) (6,20) (6,15) (6,17) (6,11) (6,12) (6,21) (6,7) (6,14) (6,9) (6,10) (6,22) (6,23) (7,20) (7,15) (7,17) (7,11) (7,12) (7,21) (7,14) (7,9) (7,10) (7,22) (7,23) (8,16) (8,19) (8,13) (9,20) (9,15) (9,17) (9,11) (9,12) (9,21) (9,14) (9,10) (9,22) (9,23) (10,20) (10,15) (10,17) (10,11) (10,12) (10,21) (10,14) (10,22) (10,23) (11,20) (11,15) (11,17) (11,12) (11,21) (11,14) (11,22) (11,23) (12,20) (12,15) (12,17) (12,21) (12,14) (12,22) (12,23) (13,16) (13,19) (14,20) (14,15) (14,17) (14,21) (14,22) (14,23) (15,20) (15,17) (15,21) (15,22) (15,23) (16,19) (17,20) (17,21) (17,22) (17,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 13 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph665-3_16", + "image": "data/connectivity/graph_visual/medium/graph665.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,10) (0,14) (0,2) (0,8) (1,18) (1,23) (1,5) (1,4) (1,11) (1,9) (1,20) (1,17) (1,7) (2,10) (2,14) (2,16) (2,3) (2,8) (2,22) (3,12) (3,10) (3,14) (3,16) (3,8) (4,18) (4,15) (4,20) (4,17) (4,7) (5,23) (5,15) (5,21) (5,11) (5,9) (5,19) (5,17) (5,7) (7,23) (7,21) (7,11) (7,9) (7,20) (7,17) (8,12) (8,10) (8,14) (8,22) (9,18) (9,23) (9,15) (9,21) (9,11) (9,20) (9,19) (10,16) (10,22) (11,18) (11,15) (11,21) (11,20) (11,19) (11,17) (12,14) (12,16) (14,22) (15,18) (15,20) (17,20) (18,23) (18,19) (19,23) (19,21) (21,23)\nIs there a path between node 3 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph124-3_10", + "image": "data/connectivity/graph_visual/medium/graph124.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,12) (0,4) (0,7) (0,15) (0,2) (0,5) (0,11) (0,8) (0,14) (0,13) (0,10) (0,1) (1,4) (1,7) (1,15) (1,9) (1,2) (1,5) (1,11) (1,8) (1,14) (1,16) (1,10) (2,7) (2,15) (2,9) (2,6) (2,5) (2,11) (2,8) (2,14) (2,16) (2,13) (2,10) (4,12) (4,7) (4,9) (4,6) (4,5) (4,8) (4,16) (4,13) (4,10) (5,12) (5,7) (5,15) (5,9) (5,6) (5,16) (5,13) (5,10) (6,12) (6,15) (6,9) (6,14) (6,16) (7,12) (7,11) (7,8) (7,16) (7,10) (8,12) (8,9) (8,11) (8,14) (8,16) (8,10) (9,11) (10,12) (10,15) (10,14) (10,16) (10,13) (11,15) (11,14) (11,16) (11,13) (12,15) (12,14) (12,16) (12,13) (13,15) (14,15) (14,16) (15,16)\nIs there a path between node 3 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph834-15_11", + "image": "data/connectivity/graph_visual/medium/graph834.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,5) (0,17) (0,4) (0,7) (0,21) (0,8) (0,22) (0,3) (0,16) (0,23) (0,13) (1,24) (1,15) (1,11) (1,20) (1,10) (1,18) (1,12) (1,14) (1,9) (1,19) (1,6) (2,5) (2,17) (2,4) (2,7) (2,21) (2,8) (2,22) (2,3) (2,16) (2,23) (2,13) (3,5) (3,17) (3,4) (3,7) (3,21) (3,8) (3,22) (3,16) (3,23) (3,13) (4,5) (4,17) (4,7) (4,21) (4,8) (4,22) (4,16) (4,23) (4,13) (5,17) (5,7) (5,21) (5,8) (5,22) (5,16) (5,23) (5,13) (6,24) (6,15) (6,11) (6,20) (6,10) (6,18) (6,12) (6,14) (6,9) (6,19) (7,17) (7,21) (7,8) (7,22) (7,16) (7,23) (7,13) (8,17) (8,21) (8,22) (8,16) (8,23) (8,13) (9,24) (9,15) (9,11) (9,20) (9,10) (9,18) (9,12) (9,14) (9,19) (10,24) (10,15) (10,11) (10,20) (10,18) (10,12) (10,14) (10,19) (11,24) (11,15) (11,20) (11,18) (11,12) (11,14) (11,19) (12,24) (12,15) (12,20) (12,18) (12,14) (12,19) (13,17) (13,21) (13,22) (13,16) (13,23) (14,24) (14,15) (14,20) (14,18) (14,19) (15,24) (15,20) (15,18) (15,19) (16,17) (16,21) (16,22) (16,23) (17,21) (17,22) (17,23) (18,24) (18,20) (18,19) (19,24) (19,20) (20,24) (21,22) (21,23) (22,23)\nIs there a path between node 15 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph517-2_8", + "image": "data/connectivity/graph_visual/medium/graph517.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,9) (0,17) (0,20) (1,15) (1,22) (1,14) (1,3) (1,21) (1,5) (1,18) (1,7) (1,6) (1,13) (2,15) (2,3) (2,4) (2,11) (2,21) (2,18) (2,8) (2,13) (3,15) (3,22) (3,12) (3,14) (3,4) (3,11) (3,21) (3,5) (3,7) (3,6) (3,16) (4,15) (4,22) (4,12) (4,14) (4,11) (4,5) (4,7) (4,6) (4,16) (4,8) (4,13) (5,15) (5,22) (5,12) (5,11) (5,21) (5,7) (5,6) (5,8) (5,13) (6,15) (6,12) (6,11) (6,21) (6,18) (6,16) (6,8) (6,13) (7,22) (7,12) (7,14) (7,11) (7,21) (7,16) (7,8) (8,22) (8,14) (8,21) (8,18) (8,16) (8,13) (9,19) (9,10) (9,17) (10,17) (11,22) (11,14) (11,21) (11,18) (11,13) (12,22) (12,14) (12,21) (12,18) (12,16) (12,13) (13,14) (13,18) (13,16) (14,15) (14,21) (14,18) (14,16) (15,21) (16,18) (17,20) (18,22)\nIs there a path between node 2 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph360-6_5", + "image": "data/connectivity/graph_visual/medium/graph360.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,8) (1,2) (1,10) (1,7) (1,3) (1,12) (1,17) (2,11) (2,12) (2,20) (2,6) (2,17) (3,7) (3,9) (3,17) (4,12) (4,20) (4,6) (6,7) (6,12) (6,9) (10,11) (10,12) (10,20) (13,19) (14,16) (15,16) (16,18)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph477-20_6", + "image": "data/connectivity/graph_visual/medium/graph477.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,15) (0,20) (0,21) (0,14) (1,17) (1,10) (1,7) (2,21) (3,10) (4,8) (4,9) (5,22) (5,13) (5,7) (5,12) (6,19) (7,22) (7,12) (9,11) (10,17) (10,12) (12,13) (14,18) (14,19) (15,18) (16,20)\nIs there a path between node 20 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph101-10_4", + "image": "data/connectivity/graph_visual/medium/graph101.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,15) (0,8) (0,6) (0,10) (0,13) (0,2) (0,11) (0,4) (0,14) (0,5) (1,8) (1,10) (1,13) (1,2) (1,9) (1,4) (1,14) (1,5) (2,8) (2,6) (2,10) (2,13) (2,11) (2,7) (2,4) (2,14) (2,5) (3,12) (4,8) (4,6) (4,10) (4,13) (4,7) (5,8) (5,6) (5,10) (5,11) (5,7) (5,14) (6,8) (6,14) (7,15) (7,8) (7,10) (7,9) (7,14) (8,13) (8,11) (8,14) (9,15) (9,10) (9,11) (9,14) (10,13) (10,11) (10,14) (11,15) (11,13) (11,14) (13,15) (14,15)\nIs there a path between node 10 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph386-4_15", + "image": "data/connectivity/graph_visual/medium/graph386.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,12) (0,20) (0,15) (0,18) (0,2) (0,10) (0,8) (0,3) (0,9) (0,14) (0,4) (0,13) (0,17) (0,19) (0,1) (0,5) (0,7) (1,12) (1,20) (1,15) (1,18) (1,2) (1,10) (1,8) (1,3) (1,9) (1,14) (1,4) (1,13) (1,17) (1,19) (1,5) (1,7) (2,12) (2,20) (2,15) (2,18) (2,10) (2,8) (2,3) (2,9) (2,14) (2,4) (2,13) (2,17) (2,19) (2,5) (2,7) (3,12) (3,20) (3,15) (3,18) (3,10) (3,8) (3,9) (3,14) (3,4) (3,13) (3,17) (3,19) (3,5) (3,7) (4,12) (4,20) (4,15) (4,18) (4,10) (4,8) (4,9) (4,14) (4,13) (4,17) (4,19) (4,5) (4,7) (5,12) (5,20) (5,15) (5,18) (5,10) (5,8) (5,9) (5,14) (5,13) (5,17) (5,19) (5,7) (6,11) (6,16) (7,12) (7,20) (7,15) (7,18) (7,10) (7,8) (7,9) (7,14) (7,13) (7,17) (7,19) (8,12) (8,20) (8,15) (8,18) (8,10) (8,9) (8,14) (8,13) (8,17) (8,19) (9,12) (9,20) (9,15) (9,18) (9,10) (9,14) (9,13) (9,17) (9,19) (10,12) (10,20) (10,15) (10,18) (10,14) (10,13) (10,17) (10,19) (11,16) (12,20) (12,15) (12,18) (12,14) (12,13) (12,17) (12,19) (13,20) (13,15) (13,18) (13,14) (13,17) (13,19) (14,20) (14,15) (14,18) (14,17) (14,19) (15,20) (15,18) (15,17) (15,19) (17,20) (17,18) (17,19) (18,20) (18,19) (19,20)\nIs there a path between node 4 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph442-6_13", + "image": "data/connectivity/graph_visual/medium/graph442.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (1,11) (1,21) (1,5) (1,7) (1,17) (1,8) (2,18) (2,12) (2,19) (2,13) (2,11) (2,21) (2,9) (2,14) (2,17) (2,8) (3,10) (3,6) (5,18) (5,15) (5,12) (5,11) (5,7) (5,9) (5,14) (5,8) (6,20) (6,16) (7,18) (7,15) (7,19) (7,13) (7,9) (7,14) (7,17) (7,8) (8,15) (8,12) (8,19) (8,11) (8,21) (8,9) (8,14) (9,18) (9,15) (9,12) (9,19) (9,11) (9,14) (9,17) (10,16) (11,18) (11,15) (11,12) (11,19) (11,21) (12,18) (12,15) (12,13) (12,21) (12,17) (13,15) (13,19) (13,14) (14,18) (14,19) (14,21) (14,17) (15,18) (15,21) (15,17) (16,20) (17,18) (17,21) (18,19) (18,21) (19,21)\nIs there a path between node 6 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph395-2_6", + "image": "data/connectivity/graph_visual/medium/graph395.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,1) (0,14) (0,3) (0,19) (0,11) (0,12) (0,7) (0,20) (0,6) (0,2) (0,4) (1,5) (1,14) (1,3) (1,19) (1,11) (1,12) (1,7) (1,20) (1,6) (1,2) (1,4) (2,5) (2,14) (2,3) (2,19) (2,11) (2,12) (2,7) (2,20) (2,6) (2,4) (3,5) (3,14) (3,19) (3,11) (3,12) (3,7) (3,20) (3,6) (3,4) (4,5) (4,14) (4,19) (4,11) (4,12) (4,7) (4,20) (4,6) (5,14) (5,19) (5,11) (5,12) (5,7) (5,20) (5,6) (6,14) (6,19) (6,11) (6,12) (6,7) (6,20) (7,14) (7,19) (7,11) (7,12) (7,20) (8,18) (8,17) (8,13) (8,16) (8,15) (9,10) (11,14) (11,19) (11,12) (11,20) (12,14) (12,19) (12,20) (13,18) (13,17) (13,16) (13,15) (14,19) (14,20) (15,18) (15,17) (15,16) (16,18) (16,17) (17,18) (19,20)\nIs there a path between node 2 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph278-1_11", + "image": "data/connectivity/graph_visual/medium/graph278.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (0,2) (0,3) (0,10) (0,6) (0,4) (0,19) (0,17) (0,13) (0,1) (0,16) (0,18) (0,7) (0,9) (0,15) (1,8) (1,2) (1,3) (1,10) (1,6) (1,4) (1,19) (1,17) (1,13) (1,16) (1,18) (1,7) (1,9) (1,15) (2,8) (2,3) (2,10) (2,6) (2,4) (2,19) (2,17) (2,13) (2,16) (2,18) (2,7) (2,9) (2,15) (3,8) (3,10) (3,6) (3,4) (3,19) (3,17) (3,13) (3,16) (3,18) (3,7) (3,9) (3,15) (4,8) (4,10) (4,6) (4,19) (4,17) (4,13) (4,16) (4,18) (4,7) (4,9) (4,15) (5,11) (5,12) (6,8) (6,10) (6,19) (6,17) (6,13) (6,16) (6,18) (6,7) (6,9) (6,15) (7,8) (7,10) (7,19) (7,17) (7,13) (7,16) (7,18) (7,9) (7,15) (8,10) (8,19) (8,17) (8,13) (8,16) (8,18) (8,9) (8,15) (9,10) (9,19) (9,17) (9,13) (9,16) (9,18) (9,15) (10,19) (10,17) (10,13) (10,16) (10,18) (10,15) (11,12) (13,19) (13,17) (13,16) (13,18) (13,15) (15,19) (15,17) (15,16) (15,18) (16,19) (16,17) (16,18) (17,19) (17,18) (18,19)\nIs there a path between node 1 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph409-1_16", + "image": "data/connectivity/graph_visual/medium/graph409.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,6) (0,21) (0,10) (0,17) (0,2) (0,11) (0,1) (0,4) (0,3) (0,19) (0,5) (0,9) (1,6) (1,21) (1,15) (1,10) (1,17) (1,2) (1,11) (1,4) (1,7) (2,6) (2,13) (2,15) (2,10) (2,17) (2,4) (2,3) (2,19) (2,9) (3,6) (3,21) (3,13) (3,10) (3,17) (3,11) (3,19) (3,5) (4,21) (4,13) (4,15) (4,10) (4,17) (4,11) (4,19) (4,5) (4,7) (4,18) (4,9) (5,6) (5,21) (5,15) (5,10) (5,17) (5,11) (5,19) (5,7) (5,9) (6,15) (6,10) (6,17) (6,11) (6,19) (6,7) (6,18) (6,9) (7,13) (7,15) (7,10) (7,17) (7,11) (7,19) (7,18) (8,14) (8,16) (9,21) (9,13) (9,15) (9,17) (9,11) (9,19) (9,18) (10,21) (10,13) (10,15) (10,17) (10,11) (10,19) (10,18) (11,21) (11,13) (11,15) (11,17) (11,18) (12,14) (12,16) (12,20) (13,21) (13,17) (13,18) (15,21) (15,17) (15,18) (17,21) (17,19) (17,18) (18,21) (18,19)\nIs there a path between node 1 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph418-16_12", + "image": "data/connectivity/graph_visual/medium/graph418.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,13) (0,19) (0,10) (0,6) (0,17) (0,1) (0,7) (0,2) (1,13) (1,19) (1,10) (1,6) (1,17) (1,7) (1,2) (2,13) (2,19) (2,10) (2,6) (2,17) (2,7) (3,20) (3,12) (3,8) (3,11) (3,14) (4,18) (4,15) (4,21) (4,9) (4,5) (4,16) (5,18) (5,15) (5,21) (5,9) (5,16) (6,13) (6,19) (6,10) (6,17) (6,7) (7,13) (7,19) (7,10) (7,17) (8,20) (8,12) (8,11) (8,14) (9,18) (9,15) (9,21) (9,16) (10,13) (10,19) (10,17) (11,20) (11,12) (11,14) (12,20) (12,14) (13,19) (13,17) (14,20) (15,18) (15,21) (15,16) (16,18) (16,21) (17,19) (18,21)\nIs there a path between node 16 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph342-20_8", + "image": "data/connectivity/graph_visual/medium/graph342.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,2) (0,7) (0,1) (0,6) (0,19) (0,15) (0,8) (0,16) (0,9) (1,2) (1,10) (1,12) (1,14) (1,19) (1,8) (2,10) (2,11) (2,12) (2,14) (2,7) (2,6) (2,15) (2,3) (2,8) (2,9) (3,11) (3,12) (3,14) (3,7) (3,19) (3,8) (3,16) (3,9) (4,20) (4,5) (4,18) (4,17) (5,13) (5,18) (5,17) (6,10) (6,11) (6,14) (6,7) (6,19) (6,8) (6,16) (7,12) (7,14) (7,19) (7,8) (7,16) (7,9) (8,11) (8,12) (8,14) (8,19) (8,16) (8,9) (9,14) (9,19) (9,15) (9,16) (10,11) (10,12) (10,14) (10,19) (10,15) (10,16) (11,14) (11,19) (11,16) (12,14) (12,19) (12,16) (13,18) (13,17) (14,19) (15,19) (15,16) (16,19) (17,20)\nIs there a path between node 20 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph95-1_0", + "image": "data/connectivity/graph_visual/medium/graph95.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,6) (0,8) (0,15) (1,10) (2,5) (3,9) (3,10) (4,11) (5,6) (5,7) (5,11) (6,13) (6,11) (7,13) (8,12) (8,13) (11,12) (11,15) (12,15) (13,15)\nIs there a path between node 1 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph571-11_4", + "image": "data/connectivity/graph_visual/medium/graph571.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,22) (0,3) (0,15) (0,6) (0,5) (0,7) (0,2) (0,19) (0,4) (0,11) (0,9) (0,14) (0,21) (1,16) (1,12) (1,18) (1,17) (1,20) (1,23) (1,13) (1,10) (2,8) (2,22) (2,3) (2,15) (2,6) (2,5) (2,7) (2,19) (2,4) (2,11) (2,9) (2,14) (2,21) (3,8) (3,22) (3,15) (3,6) (3,5) (3,7) (3,19) (3,4) (3,11) (3,9) (3,14) (3,21) (4,8) (4,22) (4,15) (4,6) (4,5) (4,7) (4,19) (4,11) (4,9) (4,14) (4,21) (5,8) (5,22) (5,15) (5,6) (5,7) (5,19) (5,11) (5,9) (5,14) (5,21) (6,8) (6,22) (6,15) (6,7) (6,19) (6,11) (6,9) (6,14) (6,21) (7,8) (7,22) (7,15) (7,19) (7,11) (7,9) (7,14) (7,21) (8,22) (8,15) (8,19) (8,11) (8,9) (8,14) (8,21) (9,22) (9,15) (9,19) (9,11) (9,14) (9,21) (10,16) (10,12) (10,18) (10,17) (10,20) (10,23) (10,13) (11,22) (11,15) (11,19) (11,14) (11,21) (12,16) (12,18) (12,17) (12,20) (12,23) (12,13) (13,16) (13,18) (13,17) (13,20) (13,23) (14,22) (14,15) (14,19) (14,21) (15,22) (15,19) (15,21) (16,18) (16,17) (16,20) (16,23) (17,18) (17,20) (17,23) (18,20) (18,23) (19,22) (19,21) (20,23) (21,22)\nIs there a path between node 11 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph664-2_19", + "image": "data/connectivity/graph_visual/medium/graph664.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,4) (0,14) (0,9) (0,19) (0,7) (0,20) (0,17) (0,16) (1,11) (1,12) (1,2) (1,15) (1,3) (1,23) (1,5) (1,21) (2,12) (2,15) (2,3) (2,23) (2,13) (2,10) (3,22) (3,12) (3,15) (3,23) (3,5) (3,21) (3,13) (4,14) (4,18) (4,9) (4,19) (4,16) (5,22) (5,11) (5,12) (5,23) (5,21) (5,10) (6,18) (6,9) (6,7) (6,20) (6,17) (6,16) (7,14) (7,9) (7,19) (7,20) (7,17) (7,8) (8,14) (8,18) (8,9) (8,19) (8,20) (8,17) (8,16) (9,14) (9,19) (10,11) (10,15) (10,23) (10,21) (10,13) (11,22) (11,12) (11,15) (11,13) (12,22) (12,15) (12,23) (12,21) (12,13) (13,15) (13,21) (14,18) (14,19) (14,20) (14,16) (15,22) (16,20) (16,17) (18,19) (18,20) (19,20) (21,22) (22,23)\nIs there a path between node 2 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph576-11_3", + "image": "data/connectivity/graph_visual/medium/graph576.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,18) (0,11) (0,23) (0,17) (0,7) (0,16) (0,1) (1,18) (1,6) (1,11) (1,21) (1,22) (1,2) (2,8) (2,16) (3,9) (3,13) (5,18) (5,6) (5,21) (5,17) (6,8) (6,11) (6,17) (6,19) (7,20) (7,8) (7,15) (7,19) (8,18) (8,22) (8,15) (11,14) (11,20) (11,22) (11,17) (11,16) (12,13) (14,18) (14,21) (14,23) (14,19) (15,21) (15,23) (16,21) (16,23) (18,20) (18,21) (18,23) (21,22)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph64-11_9", + "image": "data/connectivity/graph_visual/medium/graph64.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,8) (0,5) (0,2) (0,3) (0,10) (0,6) (0,1) (0,4) (0,9) (0,7) (0,12) (1,8) (1,5) (1,2) (1,3) (1,10) (1,6) (1,4) (1,9) (1,7) (1,12) (2,8) (2,5) (2,3) (2,10) (2,6) (2,4) (2,9) (2,7) (2,12) (3,8) (3,5) (3,10) (3,6) (3,4) (3,9) (3,7) (3,12) (4,8) (4,5) (4,10) (4,6) (4,9) (4,7) (4,12) (5,8) (5,10) (5,6) (5,9) (5,7) (5,12) (6,8) (6,10) (6,9) (6,7) (6,12) (7,8) (7,10) (7,9) (7,12) (8,10) (8,9) (8,12) (9,10) (9,12) (10,12) (11,13)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph428-19_7", + "image": "data/connectivity/graph_visual/medium/graph428.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,13) (0,7) (0,9) (0,19) (0,10) (1,16) (1,14) (1,7) (1,19) (1,3) (2,21) (3,18) (3,13) (3,9) (3,19) (4,21) (5,6) (5,13) (5,7) (5,9) (5,11) (5,12) (5,10) (6,15) (6,10) (7,14) (7,11) (9,15) (9,18) (9,14) (10,12) (11,13) (12,19) (14,16) (17,20) (20,21)\nIs there a path between node 19 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph185-9_6", + "image": "data/connectivity/graph_visual/medium/graph185.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,7) (0,9) (0,6) (0,16) (0,3) (0,13) (0,15) (0,4) (0,8) (1,5) (1,17) (1,12) (1,14) (1,2) (2,5) (2,17) (2,12) (2,14) (3,7) (3,9) (3,6) (3,16) (3,13) (3,15) (3,4) (3,8) (4,7) (4,9) (4,6) (4,16) (4,13) (4,15) (4,8) (5,17) (5,12) (5,14) (6,7) (6,9) (6,16) (6,13) (6,15) (6,8) (7,9) (7,16) (7,13) (7,15) (7,8) (8,9) (8,16) (8,13) (8,15) (9,16) (9,13) (9,15) (10,11) (12,17) (12,14) (13,16) (13,15) (14,17) (15,16)\nIs there a path between node 9 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph294-12_3", + "image": "data/connectivity/graph_visual/medium/graph294.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,1) (0,19) (1,13) (1,19) (1,11) (1,14) (1,2) (2,4) (2,18) (3,10) (4,13) (4,11) (5,6) (5,10) (5,7) (6,12) (6,7) (7,10) (8,18) (9,15) (10,12) (11,19) (12,15) (13,18)\nIs there a path between node 12 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph501-20_16", + "image": "data/connectivity/graph_visual/medium/graph501.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,19) (0,7) (0,10) (0,3) (0,15) (0,11) (0,1) (1,6) (1,9) (1,10) (1,15) (1,12) (2,7) (2,3) (2,12) (2,14) (2,13) (3,8) (3,19) (3,7) (3,21) (3,11) (3,12) (3,18) (4,16) (5,9) (5,8) (6,7) (6,17) (6,10) (6,15) (6,21) (6,20) (7,17) (7,15) (7,12) (7,14) (7,22) (7,20) (7,13) (8,9) (8,19) (8,17) (8,15) (8,20) (9,17) (9,11) (9,20) (10,19) (10,15) (11,21) (11,12) (11,14) (11,18) (12,19) (12,17) (12,14) (12,13) (13,20) (14,17) (14,22) (14,20) (14,18) (15,20) (15,18) (17,18) (20,21) (20,22)\nIs there a path between node 20 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph766-1_16", + "image": "data/connectivity/graph_visual/medium/graph766.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,24) (0,5) (0,14) (0,18) (0,1) (0,22) (0,2) (0,7) (0,13) (0,23) (0,9) (1,20) (1,24) (1,5) (1,14) (1,18) (1,22) (1,2) (1,7) (1,13) (1,23) (1,9) (2,20) (2,24) (2,5) (2,14) (2,18) (2,22) (2,7) (2,13) (2,23) (2,9) (3,16) (3,19) (3,8) (3,10) (3,21) (3,12) (3,11) (3,15) (4,17) (5,20) (5,24) (5,14) (5,18) (5,22) (5,7) (5,13) (5,23) (5,9) (7,20) (7,24) (7,14) (7,18) (7,22) (7,13) (7,23) (7,9) (8,16) (8,19) (8,10) (8,21) (8,12) (8,11) (8,15) (9,20) (9,24) (9,14) (9,18) (9,22) (9,13) (9,23) (10,16) (10,19) (10,21) (10,12) (10,11) (10,15) (11,16) (11,19) (11,21) (11,12) (11,15) (12,16) (12,19) (12,21) (12,15) (13,20) (13,24) (13,14) (13,18) (13,22) (13,23) (14,20) (14,24) (14,18) (14,22) (14,23) (15,16) (15,19) (15,21) (16,19) (16,21) (18,20) (18,24) (18,22) (18,23) (19,21) (20,24) (20,22) (20,23) (22,24) (22,23) (23,24)\nIs there a path between node 1 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph667-21_7", + "image": "data/connectivity/graph_visual/medium/graph667.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,14) (0,6) (0,21) (0,7) (0,12) (0,5) (0,16) (0,15) (0,3) (0,17) (0,22) (1,4) (1,2) (1,11) (2,4) (2,18) (2,11) (3,14) (3,21) (3,7) (3,12) (3,5) (3,19) (3,23) (3,15) (3,22) (3,20) (4,18) (4,11) (5,6) (5,21) (5,12) (5,16) (5,19) (5,15) (5,17) (5,22) (5,20) (6,21) (6,12) (6,16) (6,19) (6,23) (6,15) (6,17) (6,22) (6,20) (7,12) (7,19) (7,23) (7,17) (7,22) (7,20) (8,13) (9,10) (9,13) (10,13) (12,14) (12,21) (12,19) (12,23) (12,15) (12,17) (12,22) (14,21) (14,16) (14,19) (14,23) (14,17) (14,22) (14,20) (15,16) (15,19) (15,23) (15,17) (15,22) (16,21) (16,17) (16,22) (16,20) (17,21) (17,19) (17,22) (17,20) (19,21) (19,23) (19,22) (19,20) (20,23) (20,22) (21,22) (22,23)\nIs there a path between node 21 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph392-18_19", + "image": "data/connectivity/graph_visual/medium/graph392.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,12) (0,2) (0,7) (0,17) (0,10) (0,16) (0,9) (0,3) (0,13) (0,4) (0,11) (0,20) (0,15) (0,14) (0,1) (1,5) (1,12) (1,2) (1,7) (1,17) (1,10) (1,16) (1,9) (1,3) (1,13) (1,4) (1,11) (1,20) (1,15) (1,14) (2,5) (2,12) (2,7) (2,17) (2,10) (2,16) (2,9) (2,3) (2,13) (2,4) (2,11) (2,20) (2,15) (2,14) (3,5) (3,12) (3,7) (3,17) (3,10) (3,16) (3,9) (3,13) (3,4) (3,11) (3,20) (3,15) (3,14) (4,5) (4,12) (4,7) (4,17) (4,10) (4,16) (4,9) (4,13) (4,11) (4,20) (4,15) (4,14) (5,12) (5,7) (5,17) (5,10) (5,16) (5,9) (5,13) (5,11) (5,20) (5,15) (5,14) (6,18) (6,8) (6,19) (7,12) (7,17) (7,10) (7,16) (7,9) (7,13) (7,11) (7,20) (7,15) (7,14) (8,18) (8,19) (9,12) (9,17) (9,10) (9,16) (9,13) (9,11) (9,20) (9,15) (9,14) (10,12) (10,17) (10,16) (10,13) (10,11) (10,20) (10,15) (10,14) (11,12) (11,17) (11,16) (11,13) (11,20) (11,15) (11,14) (12,17) (12,16) (12,13) (12,20) (12,15) (12,14) (13,17) (13,16) (13,20) (13,15) (13,14) (14,17) (14,16) (14,20) (14,15) (15,17) (15,16) (15,20) (16,17) (16,20) (17,20) (18,19)\nIs there a path between node 18 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph660-11_13", + "image": "data/connectivity/graph_visual/medium/graph660.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,11) (0,3) (0,2) (0,9) (0,5) (0,10) (0,23) (1,13) (1,17) (1,20) (1,8) (1,14) (1,4) (2,22) (2,11) (2,9) (2,10) (2,23) (3,21) (3,11) (3,5) (3,15) (3,23) (3,12) (4,18) (4,19) (4,13) (4,8) (4,16) (5,11) (5,9) (5,10) (5,15) (6,18) (6,19) (6,13) (6,20) (6,8) (6,16) (6,14) (7,19) (7,20) (7,8) (7,16) (7,14) (8,18) (8,19) (8,13) (8,17) (8,16) (8,14) (9,22) (9,21) (9,10) (9,15) (9,23) (9,12) (10,22) (10,21) (10,15) (10,12) (11,22) (11,15) (11,23) (11,12) (12,22) (12,15) (12,23) (13,18) (13,19) (13,20) (13,16) (13,14) (14,18) (14,19) (14,17) (14,20) (14,16) (15,22) (15,21) (16,18) (16,19) (16,17) (17,18) (17,19) (17,20) (18,19) (18,20) (19,20) (21,22) (21,23) (22,23)\nIs there a path between node 11 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph704-6_10", + "image": "data/connectivity/graph_visual/medium/graph704.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,7) (1,9) (1,10) (1,14) (2,3) (2,11) (3,11) (3,12) (4,17) (5,18) (5,17) (6,20) (6,22) (6,17) (6,8) (7,23) (7,18) (7,8) (9,21) (9,16) (9,11) (9,13) (10,14) (11,21) (11,14) (11,13) (12,15) (13,21) (13,15) (13,14) (14,15) (17,18) (17,19) (18,23) (18,24) (19,24) (19,22)\nIs there a path between node 6 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph130-1_11", + "image": "data/connectivity/graph_visual/medium/graph130.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,10) (0,1) (0,5) (0,15) (0,6) (0,4) (0,7) (0,16) (0,13) (0,8) (0,2) (0,12) (0,14) (1,10) (1,5) (1,15) (1,6) (1,4) (1,7) (1,16) (1,13) (1,8) (1,2) (1,12) (1,14) (2,10) (2,5) (2,15) (2,6) (2,4) (2,7) (2,16) (2,13) (2,8) (2,12) (2,14) (3,11) (3,9) (4,10) (4,5) (4,15) (4,6) (4,7) (4,16) (4,13) (4,8) (4,12) (4,14) (5,10) (5,15) (5,6) (5,7) (5,16) (5,13) (5,8) (5,12) (5,14) (6,10) (6,15) (6,7) (6,16) (6,13) (6,8) (6,12) (6,14) (7,10) (7,15) (7,16) (7,13) (7,8) (7,12) (7,14) (8,10) (8,15) (8,16) (8,13) (8,12) (8,14) (9,11) (10,15) (10,16) (10,13) (10,12) (10,14) (12,15) (12,16) (12,13) (12,14) (13,15) (13,16) (13,14) (14,15) (14,16) (15,16)\nIs there a path between node 1 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph177-1_11", + "image": "data/connectivity/graph_visual/medium/graph177.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,4) (0,11) (0,16) (0,7) (0,9) (0,6) (1,8) (1,13) (1,3) (1,15) (1,17) (1,10) (1,12) (1,2) (2,13) (2,3) (2,15) (2,17) (3,13) (3,15) (3,17) (3,10) (3,12) (4,7) (4,5) (4,14) (4,9) (4,6) (5,11) (5,16) (5,7) (5,14) (5,9) (5,6) (6,11) (6,16) (6,7) (6,14) (6,9) (7,11) (7,16) (7,14) (7,9) (8,13) (8,15) (8,17) (8,12) (9,16) (9,14) (10,13) (10,15) (10,17) (10,12) (11,16) (11,14) (13,15) (13,17) (15,17)\nIs there a path between node 1 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph413-14_0", + "image": "data/connectivity/graph_visual/medium/graph413.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,13) (0,19) (0,21) (0,4) (0,2) (0,16) (0,6) (0,7) (0,8) (0,3) (0,20) (0,14) (1,9) (1,10) (2,13) (2,19) (2,21) (2,12) (2,16) (2,5) (2,8) (2,20) (2,14) (3,13) (3,21) (3,4) (3,12) (3,16) (3,7) (3,8) (3,20) (3,14) (4,21) (4,12) (4,16) (4,6) (4,5) (4,8) (5,13) (5,19) (5,21) (5,12) (5,6) (5,7) (5,8) (5,14) (6,13) (6,19) (6,12) (6,16) (6,7) (6,8) (6,20) (6,14) (7,13) (7,21) (7,12) (7,16) (7,20) (7,14) (8,19) (8,12) (8,20) (8,14) (9,11) (9,10) (9,15) (9,18) (9,17) (10,11) (10,15) (10,17) (11,15) (11,18) (11,17) (12,21) (12,16) (12,20) (13,19) (13,16) (13,20) (13,14) (14,19) (14,21) (14,16) (14,20) (15,18) (15,17) (16,19) (16,21) (17,18) (19,21) (19,20) (20,21)\nIs there a path between node 14 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph380-3_7", + "image": "data/connectivity/graph_visual/medium/graph380.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,11) (0,16) (0,3) (0,20) (0,12) (0,5) (0,17) (0,8) (0,14) (0,18) (0,2) (0,1) (0,6) (1,11) (1,16) (1,3) (1,20) (1,12) (1,5) (1,4) (1,17) (1,14) (1,2) (1,13) (1,6) (2,11) (2,16) (2,3) (2,20) (2,5) (2,8) (2,14) (2,18) (2,13) (2,6) (2,19) (2,9) (3,11) (3,16) (3,20) (3,5) (3,4) (3,17) (3,14) (3,13) (3,6) (3,19) (3,9) (4,11) (4,16) (4,20) (4,12) (4,8) (4,18) (4,13) (4,6) (4,19) (4,9) (5,11) (5,16) (5,20) (5,12) (5,17) (5,8) (5,14) (5,6) (5,19) (5,9) (6,11) (6,16) (6,20) (6,12) (6,17) (6,14) (6,19) (6,9) (8,11) (8,16) (8,20) (8,14) (8,18) (8,19) (8,9) (9,11) (9,12) (9,18) (9,19) (11,20) (11,12) (11,17) (11,14) (11,13) (11,19) (12,16) (12,20) (12,14) (12,18) (12,13) (12,19) (13,16) (13,14) (14,20) (14,18) (14,19) (16,20) (16,18) (17,20) (17,18) (18,20) (19,20)\nIs there a path between node 3 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph300-14_8", + "image": "data/connectivity/graph_visual/medium/graph300.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,7) (0,4) (0,11) (0,3) (0,17) (1,10) (1,13) (2,10) (2,13) (2,15) (3,7) (3,4) (3,11) (3,17) (4,5) (4,11) (5,7) (5,11) (5,12) (6,8) (6,14) (6,9) (6,18) (6,19) (7,17) (7,12) (8,14) (8,18) (8,19) (9,18) (9,19) (10,13) (11,17) (11,12) (12,17) (13,16) (13,15) (14,18) (14,19) (15,16) (18,19)\nIs there a path between node 14 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph378-15_11", + "image": "data/connectivity/graph_visual/medium/graph378.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (0,1) (0,19) (0,11) (0,17) (0,16) (0,6) (1,9) (1,5) (1,4) (1,18) (1,20) (1,11) (1,16) (1,6) (1,12) (2,15) (2,7) (2,13) (3,9) (3,5) (3,4) (3,20) (3,8) (3,11) (3,17) (3,6) (3,12) (4,5) (4,18) (4,19) (4,20) (4,17) (4,16) (4,12) (5,9) (5,18) (5,20) (5,8) (5,11) (6,9) (6,18) (6,19) (6,11) (6,12) (7,15) (7,13) (8,9) (8,18) (8,19) (8,20) (8,17) (8,16) (9,18) (9,19) (9,20) (9,11) (9,16) (9,12) (11,18) (11,17) (11,16) (12,18) (12,20) (12,17) (13,15) (16,18) (16,19) (16,17) (17,19) (17,20) (18,19) (19,20)\nIs there a path between node 15 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph92-13_9", + "image": "data/connectivity/graph_visual/medium/graph92.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,12) (0,13) (0,6) (0,5) (0,15) (0,14) (0,1) (0,10) (0,8) (0,7) (0,2) (0,11) (0,3) (1,12) (1,13) (1,6) (1,5) (1,15) (1,14) (1,10) (1,8) (1,7) (1,2) (1,11) (1,3) (2,12) (2,13) (2,6) (2,5) (2,15) (2,14) (2,10) (2,8) (2,7) (2,11) (2,3) (3,12) (3,13) (3,6) (3,5) (3,15) (3,14) (3,10) (3,8) (3,7) (3,11) (4,9) (5,12) (5,13) (5,6) (5,15) (5,14) (5,10) (5,8) (5,7) (5,11) (6,12) (6,13) (6,15) (6,14) (6,10) (6,8) (6,7) (6,11) (7,12) (7,13) (7,15) (7,14) (7,10) (7,8) (7,11) (8,12) (8,13) (8,15) (8,14) (8,10) (8,11) (10,12) (10,13) (10,15) (10,14) (10,11) (11,12) (11,13) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nIs there a path between node 13 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph27-8_6", + "image": "data/connectivity/graph_visual/medium/graph27.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,2) (0,9) (0,1) (0,11) (0,4) (0,3) (1,6) (1,2) (1,9) (1,8) (1,11) (2,6) (2,8) (2,11) (2,3) (3,6) (3,9) (3,8) (3,10) (3,11) (3,4) (4,6) (4,8) (4,10) (5,7) (6,9) (6,8) (6,10) (6,11) (8,10) (9,11) (10,11)\nIs there a path between node 8 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph167-12_13", + "image": "data/connectivity/graph_visual/medium/graph167.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,17) (0,8) (0,6) (0,12) (0,16) (0,3) (1,17) (1,2) (1,8) (1,9) (1,4) (1,12) (1,3) (2,17) (2,11) (2,9) (2,16) (2,14) (2,5) (3,13) (3,9) (3,14) (4,17) (4,7) (4,13) (4,16) (4,5) (5,7) (5,13) (5,9) (5,14) (6,8) (6,11) (6,9) (6,12) (6,16) (6,14) (7,8) (7,13) (8,13) (9,13) (9,12) (11,13) (11,12) (11,14) (13,14)\nIs there a path between node 12 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph611-0_15", + "image": "data/connectivity/graph_visual/medium/graph611.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (0,19) (0,1) (0,14) (0,16) (0,4) (1,17) (1,19) (1,14) (1,16) (1,4) (2,11) (2,15) (3,18) (3,7) (3,9) (3,22) (3,23) (3,21) (3,10) (4,17) (4,19) (4,14) (4,16) (5,6) (5,20) (5,13) (5,8) (5,12) (6,20) (6,13) (6,8) (6,12) (7,18) (7,9) (7,22) (7,23) (7,21) (7,10) (8,20) (8,13) (8,12) (9,18) (9,22) (9,23) (9,21) (9,10) (10,18) (10,22) (10,23) (10,21) (11,15) (12,20) (12,13) (13,20) (14,17) (14,19) (14,16) (16,17) (16,19) (17,19) (18,22) (18,23) (18,21) (21,22) (21,23) (22,23)\nIs there a path between node 0 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph367-3_8", + "image": "data/connectivity/graph_visual/medium/graph367.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,8) (0,14) (0,2) (0,17) (1,5) (1,9) (1,3) (1,11) (1,6) (1,19) (1,20) (1,4) (1,18) (1,10) (1,7) (2,16) (2,8) (2,14) (2,15) (2,12) (3,5) (3,13) (3,6) (3,20) (3,4) (3,18) (3,10) (3,7) (4,5) (4,9) (4,11) (4,19) (4,18) (4,10) (4,7) (5,13) (5,9) (5,11) (5,6) (5,19) (5,20) (5,18) (5,10) (6,13) (6,9) (6,11) (6,18) (6,10) (7,9) (7,11) (7,20) (8,12) (9,13) (9,11) (9,19) (9,20) (9,10) (10,13) (10,19) (10,20) (10,18) (11,19) (11,20) (12,16) (12,14) (12,15) (12,17) (13,18) (14,16) (14,15) (16,17) (18,19) (19,20)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph510-10_14", + "image": "data/connectivity/graph_visual/medium/graph510.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,16) (0,13) (0,7) (0,18) (0,8) (0,20) (0,15) (1,22) (1,21) (1,8) (1,20) (1,15) (2,11) (2,20) (3,17) (4,16) (4,11) (4,7) (4,9) (4,8) (4,20) (5,22) (5,7) (5,18) (5,9) (7,22) (7,20) (8,9) (8,20) (9,16) (9,19) (9,20) (10,17) (11,16) (11,13) (11,18) (12,17) (13,16) (13,22) (13,14) (13,21) (14,22) (14,19) (15,16) (16,19) (16,18) (16,21)\nIs there a path between node 10 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph689-2_8", + "image": "data/connectivity/graph_visual/medium/graph689.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,8) (0,9) (0,2) (0,10) (0,16) (0,11) (0,17) (0,1) (0,19) (0,13) (0,6) (1,3) (1,8) (1,9) (1,2) (1,10) (1,16) (1,11) (1,17) (1,19) (1,13) (1,6) (2,3) (2,8) (2,9) (2,10) (2,16) (2,11) (2,17) (2,19) (2,13) (2,6) (3,8) (3,9) (3,10) (3,16) (3,11) (3,17) (3,19) (3,13) (3,6) (4,5) (4,21) (4,22) (4,20) (4,18) (4,15) (4,12) (4,23) (4,14) (4,7) (5,21) (5,22) (5,20) (5,18) (5,15) (5,12) (5,23) (5,14) (5,7) (6,8) (6,9) (6,10) (6,16) (6,11) (6,17) (6,19) (6,13) (7,21) (7,22) (7,20) (7,18) (7,15) (7,12) (7,23) (7,14) (8,9) (8,10) (8,16) (8,11) (8,17) (8,19) (8,13) (9,10) (9,16) (9,11) (9,17) (9,19) (9,13) (10,16) (10,11) (10,17) (10,19) (10,13) (11,16) (11,17) (11,19) (11,13) (12,21) (12,22) (12,20) (12,18) (12,15) (12,23) (12,14) (13,16) (13,17) (13,19) (14,21) (14,22) (14,20) (14,18) (14,15) (14,23) (15,21) (15,22) (15,20) (15,18) (15,23) (16,17) (16,19) (17,19) (18,21) (18,22) (18,20) (18,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 2 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph200-10_0", + "image": "data/connectivity/graph_visual/medium/graph200.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,12) (0,18) (0,6) (0,5) (0,7) (0,16) (1,11) (1,14) (2,4) (3,15) (5,12) (5,17) (5,9) (6,17) (6,7) (7,12) (7,18) (7,17) (7,13) (8,11) (9,12) (9,18) (9,17) (10,15) (13,17) (14,15)\nIs there a path between node 10 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph513-11_12", + "image": "data/connectivity/graph_visual/medium/graph513.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,3) (0,12) (0,7) (0,14) (0,2) (0,4) (0,19) (0,10) (0,16) (0,8) (0,6) (0,20) (0,1) (1,5) (1,21) (1,3) (1,14) (1,11) (1,2) (1,4) (1,8) (1,6) (1,20) (2,5) (2,21) (2,3) (2,12) (2,14) (2,11) (2,4) (2,19) (2,10) (2,16) (2,6) (3,5) (3,21) (3,7) (3,11) (3,4) (3,19) (3,10) (3,16) (3,8) (3,6) (3,20) (4,21) (4,7) (4,14) (4,11) (4,19) (4,10) (4,16) (4,8) (4,6) (5,21) (5,12) (5,7) (5,14) (5,11) (5,19) (5,10) (5,16) (5,8) (5,6) (5,20) (6,12) (6,7) (6,11) (6,10) (6,16) (6,8) (6,20) (7,21) (7,11) (7,10) (7,8) (7,20) (8,12) (8,14) (8,10) (8,16) (8,20) (9,13) (9,15) (9,18) (10,12) (10,14) (10,11) (10,16) (10,20) (11,12) (11,14) (11,20) (12,19) (12,16) (12,20) (13,15) (14,21) (14,16) (14,20) (16,21) (16,19) (16,20) (19,21) (19,20)\nIs there a path between node 11 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph85-8_1", + "image": "data/connectivity/graph_visual/medium/graph85.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,3) (0,8) (0,6) (0,10) (0,14) (0,2) (0,1) (1,3) (1,8) (1,6) (1,10) (1,14) (1,2) (2,3) (2,8) (2,6) (2,10) (2,14) (3,8) (3,6) (3,10) (3,14) (4,11) (4,5) (4,13) (4,7) (4,9) (4,12) (5,11) (5,13) (5,7) (5,9) (5,12) (6,8) (6,10) (6,14) (7,11) (7,13) (7,9) (7,12) (8,10) (8,14) (9,11) (9,13) (9,12) (10,14) (11,13) (11,12) (12,13)\nIs there a path between node 8 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph851-15_19", + "image": "data/connectivity/graph_visual/medium/graph851.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,12) (0,24) (0,15) (0,7) (0,16) (1,3) (1,6) (1,8) (1,14) (1,23) (1,10) (1,11) (2,17) (2,9) (2,21) (2,13) (2,18) (2,4) (2,5) (2,20) (2,22) (2,19) (3,6) (3,8) (3,14) (3,23) (3,10) (3,11) (4,17) (4,9) (4,21) (4,13) (4,18) (4,5) (4,20) (4,22) (4,19) (5,17) (5,9) (5,21) (5,13) (5,18) (5,20) (5,22) (5,19) (6,8) (6,14) (6,23) (6,10) (6,11) (7,12) (7,24) (7,15) (7,16) (8,14) (8,23) (8,10) (8,11) (9,17) (9,21) (9,13) (9,18) (9,20) (9,22) (9,19) (10,14) (10,23) (10,11) (11,14) (11,23) (12,24) (12,15) (12,16) (13,17) (13,21) (13,18) (13,20) (13,22) (13,19) (14,23) (15,24) (15,16) (16,24) (17,21) (17,18) (17,20) (17,22) (17,19) (18,21) (18,20) (18,22) (18,19) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 15 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph570-10_3", + "image": "data/connectivity/graph_visual/medium/graph570.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,18) (0,12) (0,20) (0,17) (0,14) (0,4) (0,19) (0,15) (0,7) (0,16) (0,21) (1,8) (1,23) (1,2) (1,22) (1,10) (1,5) (2,8) (2,23) (2,22) (2,10) (2,5) (3,13) (3,9) (3,11) (4,6) (4,18) (4,12) (4,20) (4,17) (4,14) (4,19) (4,15) (4,7) (4,16) (4,21) (5,8) (5,23) (5,22) (5,10) (6,18) (6,12) (6,20) (6,17) (6,14) (6,19) (6,15) (6,7) (6,16) (6,21) (7,18) (7,12) (7,20) (7,17) (7,14) (7,19) (7,15) (7,16) (7,21) (8,23) (8,22) (8,10) (9,13) (9,11) (10,23) (10,22) (11,13) (12,18) (12,20) (12,17) (12,14) (12,19) (12,15) (12,16) (12,21) (14,18) (14,20) (14,17) (14,19) (14,15) (14,16) (14,21) (15,18) (15,20) (15,17) (15,19) (15,16) (15,21) (16,18) (16,20) (16,17) (16,19) (16,21) (17,18) (17,20) (17,19) (17,21) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21) (22,23)\nIs there a path between node 10 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph471-22_14", + "image": "data/connectivity/graph_visual/medium/graph471.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,19) (1,12) (1,19) (2,13) (3,20) (3,11) (4,7) (4,16) (4,18) (5,17) (5,7) (6,15) (6,20) (6,11) (7,20) (7,11) (8,12) (8,13) (8,19) (11,17) (11,15) (12,19) (16,17) (16,20) (17,20) (18,20)\nIs there a path between node 22 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph124-12_3", + "image": "data/connectivity/graph_visual/medium/graph124.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,12) (0,4) (0,7) (0,15) (0,2) (0,5) (0,11) (0,8) (0,14) (0,13) (0,10) (0,1) (1,4) (1,7) (1,15) (1,9) (1,2) (1,5) (1,11) (1,8) (1,14) (1,16) (1,10) (2,7) (2,15) (2,9) (2,6) (2,5) (2,11) (2,8) (2,14) (2,16) (2,13) (2,10) (4,12) (4,7) (4,9) (4,6) (4,5) (4,8) (4,16) (4,13) (4,10) (5,12) (5,7) (5,15) (5,9) (5,6) (5,16) (5,13) (5,10) (6,12) (6,15) (6,9) (6,14) (6,16) (7,12) (7,11) (7,8) (7,16) (7,10) (8,12) (8,9) (8,11) (8,14) (8,16) (8,10) (9,11) (10,12) (10,15) (10,14) (10,16) (10,13) (11,15) (11,14) (11,16) (11,13) (12,15) (12,14) (12,16) (12,13) (13,15) (14,15) (14,16) (15,16)\nIs there a path between node 12 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph129-14_2", + "image": "data/connectivity/graph_visual/medium/graph129.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,12) (0,13) (0,2) (0,16) (0,7) (0,6) (0,9) (0,5) (0,1) (0,8) (1,12) (1,13) (1,2) (1,16) (1,7) (1,6) (1,9) (1,5) (1,8) (2,12) (2,13) (2,16) (2,7) (2,6) (2,9) (2,5) (2,8) (3,10) (3,14) (3,4) (3,11) (3,15) (4,10) (4,14) (4,11) (4,15) (5,12) (5,13) (5,16) (5,7) (5,6) (5,9) (5,8) (6,12) (6,13) (6,16) (6,7) (6,9) (6,8) (7,12) (7,13) (7,16) (7,9) (7,8) (8,12) (8,13) (8,16) (8,9) (9,12) (9,13) (9,16) (10,14) (10,11) (10,15) (11,14) (11,15) (12,13) (12,16) (13,16) (14,15)\nIs there a path between node 14 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph406-15_2", + "image": "data/connectivity/graph_visual/medium/graph406.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,14) (0,13) (1,20) (1,12) (1,3) (1,15) (1,19) (2,3) (2,15) (3,11) (3,10) (4,20) (4,8) (4,19) (4,10) (5,9) (8,20) (8,15) (8,10) (9,13) (10,20) (11,15) (12,20) (12,15) (13,18) (15,20) (18,21) (19,20)\nIs there a path between node 15 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph380-9_11", + "image": "data/connectivity/graph_visual/medium/graph380.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,11) (0,16) (0,3) (0,20) (0,12) (0,5) (0,17) (0,8) (0,14) (0,18) (0,2) (0,1) (0,6) (1,11) (1,16) (1,3) (1,20) (1,12) (1,5) (1,4) (1,17) (1,14) (1,2) (1,13) (1,6) (2,11) (2,16) (2,3) (2,20) (2,5) (2,8) (2,14) (2,18) (2,13) (2,6) (2,19) (2,9) (3,11) (3,16) (3,20) (3,5) (3,4) (3,17) (3,14) (3,13) (3,6) (3,19) (3,9) (4,11) (4,16) (4,20) (4,12) (4,8) (4,18) (4,13) (4,6) (4,19) (4,9) (5,11) (5,16) (5,20) (5,12) (5,17) (5,8) (5,14) (5,6) (5,19) (5,9) (6,11) (6,16) (6,20) (6,12) (6,17) (6,14) (6,19) (6,9) (8,11) (8,16) (8,20) (8,14) (8,18) (8,19) (8,9) (9,11) (9,12) (9,18) (9,19) (11,20) (11,12) (11,17) (11,14) (11,13) (11,19) (12,16) (12,20) (12,14) (12,18) (12,13) (12,19) (13,16) (13,14) (14,20) (14,18) (14,19) (16,20) (16,18) (17,20) (17,18) (18,20) (19,20)\nIs there a path between node 9 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph474-4_20", + "image": "data/connectivity/graph_visual/medium/graph474.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,12) (0,21) (0,17) (0,16) (0,20) (1,15) (1,14) (1,20) (1,19) (1,9) (1,2) (1,6) (1,3) (2,18) (2,20) (2,19) (2,10) (3,16) (3,13) (4,5) (6,14) (6,18) (6,11) (6,22) (6,7) (6,13) (7,21) (7,15) (7,14) (7,18) (7,19) (7,11) (7,8) (8,12) (8,21) (8,15) (8,14) (8,20) (8,11) (8,9) (8,10) (9,15) (9,11) (9,10) (9,13) (10,18) (10,20) (10,19) (10,11) (10,22) (11,15) (11,16) (11,22) (12,21) (12,17) (12,18) (13,21) (13,17) (13,20) (13,19) (14,20) (15,21) (15,17) (15,18) (16,18) (16,20) (16,19) (17,20) (17,19) (17,22) (18,22)\nIs there a path between node 4 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph285-19_8", + "image": "data/connectivity/graph_visual/medium/graph285.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,14) (1,9) (1,2) (1,8) (2,18) (2,6) (2,5) (2,8) (2,11) (3,7) (5,13) (5,6) (5,9) (5,8) (6,12) (6,13) (6,18) (6,10) (6,9) (6,8) (6,11) (7,15) (8,16) (8,9) (9,13) (9,10) (10,16) (10,11) (11,12) (11,16) (12,16) (13,16) (14,15)\nIs there a path between node 19 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph470-2_15", + "image": "data/connectivity/graph_visual/medium/graph470.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,15) (0,22) (0,18) (1,5) (1,14) (1,21) (1,16) (1,19) (1,3) (1,17) (1,13) (1,11) (1,2) (1,20) (1,8) (1,6) (1,12) (1,9) (1,7) (2,5) (2,14) (2,21) (2,16) (2,19) (2,3) (2,17) (2,13) (2,11) (2,20) (2,8) (2,6) (2,12) (2,9) (2,7) (3,5) (3,14) (3,21) (3,16) (3,19) (3,17) (3,13) (3,11) (3,20) (3,8) (3,6) (3,12) (3,9) (3,7) (5,14) (5,21) (5,16) (5,19) (5,17) (5,13) (5,11) (5,20) (5,8) (5,6) (5,12) (5,9) (5,7) (6,14) (6,21) (6,16) (6,19) (6,17) (6,13) (6,11) (6,20) (6,8) (6,12) (6,9) (6,7) (7,14) (7,21) (7,16) (7,19) (7,17) (7,13) (7,11) (7,20) (7,8) (7,12) (7,9) (8,14) (8,21) (8,16) (8,19) (8,17) (8,13) (8,11) (8,20) (8,12) (8,9) (9,14) (9,21) (9,16) (9,19) (9,17) (9,13) (9,11) (9,20) (9,12) (10,15) (10,22) (10,18) (11,14) (11,21) (11,16) (11,19) (11,17) (11,13) (11,20) (11,12) (12,14) (12,21) (12,16) (12,19) (12,17) (12,13) (12,20) (13,14) (13,21) (13,16) (13,19) (13,17) (13,20) (14,21) (14,16) (14,19) (14,17) (14,20) (15,22) (15,18) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (18,22) (19,21) (19,20) (20,21)\nIs there a path between node 2 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph748-7_14", + "image": "data/connectivity/graph_visual/medium/graph748.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,8) (0,22) (0,20) (0,17) (0,19) (1,6) (1,9) (1,4) (1,23) (1,14) (1,21) (1,2) (1,13) (2,6) (2,9) (2,4) (2,23) (2,14) (2,5) (2,21) (2,13) (3,9) (3,14) (3,5) (3,21) (4,15) (4,6) (4,9) (4,23) (4,5) (4,21) (4,13) (5,15) (5,6) (5,9) (5,23) (5,10) (5,14) (5,21) (6,15) (6,9) (6,23) (6,10) (6,14) (6,21) (7,18) (7,22) (7,20) (7,17) (7,12) (7,19) (8,11) (8,22) (8,17) (8,12) (8,19) (9,23) (9,10) (9,14) (9,21) (9,13) (10,15) (10,21) (10,13) (11,18) (11,22) (11,24) (11,12) (12,18) (12,22) (12,20) (12,24) (12,19) (13,15) (13,23) (13,14) (14,23) (14,21) (15,23) (15,21) (17,20) (18,20) (18,24) (18,19) (19,22) (19,20) (20,22) (20,24) (21,23) (22,24)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph240-8_12", + "image": "data/connectivity/graph_visual/medium/graph240.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,16) (0,6) (0,8) (0,13) (0,7) (0,12) (1,14) (1,15) (1,11) (2,14) (2,11) (3,16) (3,18) (3,13) (4,14) (4,15) (4,11) (5,17) (5,9) (6,16) (6,7) (6,12) (7,18) (7,8) (7,13) (7,12) (8,18) (8,13) (8,12) (9,17) (10,16) (10,18) (10,13) (11,14) (11,15) (12,16) (12,18) (13,18) (14,15) (16,18)\nIs there a path between node 8 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph41-3_12", + "image": "data/connectivity/graph_visual/medium/graph41.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,11) (0,12) (0,5) (0,6) (0,4) (0,8) (0,2) (0,9) (0,1) (0,7) (1,12) (1,5) (1,6) (1,4) (1,8) (1,2) (1,9) (1,10) (1,7) (2,8) (2,10) (2,7) (4,11) (4,12) (4,5) (4,6) (4,8) (4,9) (4,7) (5,11) (5,6) (5,8) (5,10) (5,7) (6,11) (6,12) (6,8) (6,9) (7,11) (7,12) (7,9) (7,10) (8,12) (8,9) (8,10) (9,11) (9,12) (9,10) (10,11) (10,12) (11,12)\nIs there a path between node 3 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph755-23_7", + "image": "data/connectivity/graph_visual/medium/graph755.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (0,18) (0,10) (0,11) (0,2) (0,8) (0,24) (0,9) (0,1) (0,7) (1,18) (1,10) (1,4) (1,8) (1,19) (1,9) (1,7) (2,4) (2,11) (2,6) (2,8) (2,19) (2,9) (2,7) (3,14) (3,20) (3,12) (4,17) (4,18) (4,10) (4,11) (4,19) (4,24) (4,9) (5,14) (5,15) (5,12) (6,17) (6,10) (6,11) (6,8) (6,24) (6,9) (6,7) (7,18) (7,8) (7,19) (7,9) (8,17) (8,19) (9,17) (9,10) (9,11) (9,24) (10,17) (10,11) (10,19) (10,24) (11,17) (11,18) (11,19) (11,24) (12,23) (12,15) (13,16) (13,22) (14,21) (14,20) (15,23) (15,20) (16,22) (17,24) (18,19) (19,24) (20,23) (21,23)\nIs there a path between node 23 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph400-4_20", + "image": "data/connectivity/graph_visual/medium/graph400.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,3) (0,4) (0,10) (1,18) (1,11) (1,16) (1,21) (1,10) (2,5) (2,20) (2,13) (3,11) (3,16) (3,13) (3,10) (4,20) (4,13) (4,6) (4,10) (5,11) (5,16) (5,13) (6,20) (6,16) (6,13) (6,19) (7,9) (8,17) (8,14) (10,18) (10,11) (10,16) (10,21) (11,20) (11,16) (13,21) (15,17) (16,21) (16,19) (18,20)\nIs there a path between node 4 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph619-7_14", + "image": "data/connectivity/graph_visual/medium/graph619.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,18) (0,8) (0,2) (0,12) (0,22) (0,19) (0,10) (0,21) (0,3) (0,14) (0,20) (0,6) (0,15) (0,23) (0,16) (0,4) (0,17) (0,1) (1,18) (1,8) (1,2) (1,12) (1,22) (1,19) (1,10) (1,21) (1,3) (1,14) (1,20) (1,6) (1,15) (1,23) (1,16) (1,4) (1,17) (2,18) (2,8) (2,12) (2,22) (2,19) (2,10) (2,21) (2,3) (2,14) (2,20) (2,6) (2,15) (2,23) (2,16) (2,4) (2,17) (3,18) (3,8) (3,12) (3,22) (3,19) (3,10) (3,21) (3,14) (3,20) (3,6) (3,15) (3,23) (3,16) (3,4) (3,17) (4,18) (4,8) (4,12) (4,22) (4,19) (4,10) (4,21) (4,14) (4,20) (4,6) (4,15) (4,23) (4,16) (4,17) (5,9) (5,11) (5,7) (5,13) (6,18) (6,8) (6,12) (6,22) (6,19) (6,10) (6,21) (6,14) (6,20) (6,15) (6,23) (6,16) (6,17) (7,9) (7,11) (7,13) (8,18) (8,12) (8,22) (8,19) (8,10) (8,21) (8,14) (8,20) (8,15) (8,23) (8,16) (8,17) (9,11) (9,13) (10,18) (10,12) (10,22) (10,19) (10,21) (10,14) (10,20) (10,15) (10,23) (10,16) (10,17) (11,13) (12,18) (12,22) (12,19) (12,21) (12,14) (12,20) (12,15) (12,23) (12,16) (12,17) (14,18) (14,22) (14,19) (14,21) (14,20) (14,15) (14,23) (14,16) (14,17) (15,18) (15,22) (15,19) (15,21) (15,20) (15,23) (15,16) (15,17) (16,18) (16,22) (16,19) (16,21) (16,20) (16,23) (16,17) (17,18) (17,22) (17,19) (17,21) (17,20) (17,23) (18,22) (18,19) (18,21) (18,20) (18,23) (19,22) (19,21) (19,20) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph385-4_3", + "image": "data/connectivity/graph_visual/medium/graph385.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,14) (0,17) (0,19) (0,9) (0,5) (0,2) (0,4) (0,7) (0,8) (0,13) (0,12) (0,10) (0,1) (0,15) (0,11) (0,16) (0,18) (0,6) (1,14) (1,17) (1,19) (1,9) (1,5) (1,2) (1,4) (1,7) (1,8) (1,13) (1,12) (1,10) (1,15) (1,11) (1,16) (1,18) (1,6) (2,14) (2,17) (2,19) (2,9) (2,5) (2,4) (2,7) (2,8) (2,13) (2,12) (2,10) (2,15) (2,11) (2,16) (2,18) (2,6) (3,20) (4,14) (4,17) (4,19) (4,9) (4,5) (4,7) (4,8) (4,13) (4,12) (4,10) (4,15) (4,11) (4,16) (4,18) (4,6) (5,14) (5,17) (5,19) (5,9) (5,7) (5,8) (5,13) (5,12) (5,10) (5,15) (5,11) (5,16) (5,18) (5,6) (6,14) (6,17) (6,19) (6,9) (6,7) (6,8) (6,13) (6,12) (6,10) (6,15) (6,11) (6,16) (6,18) (7,14) (7,17) (7,19) (7,9) (7,8) (7,13) (7,12) (7,10) (7,15) (7,11) (7,16) (7,18) (8,14) (8,17) (8,19) (8,9) (8,13) (8,12) (8,10) (8,15) (8,11) (8,16) (8,18) (9,14) (9,17) (9,19) (9,13) (9,12) (9,10) (9,15) (9,11) (9,16) (9,18) (10,14) (10,17) (10,19) (10,13) (10,12) (10,15) (10,11) (10,16) (10,18) (11,14) (11,17) (11,19) (11,13) (11,12) (11,15) (11,16) (11,18) (12,14) (12,17) (12,19) (12,13) (12,15) (12,16) (12,18) (13,14) (13,17) (13,19) (13,15) (13,16) (13,18) (14,17) (14,19) (14,15) (14,16) (14,18) (15,17) (15,19) (15,16) (15,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nIs there a path between node 4 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph280-2_16", + "image": "data/connectivity/graph_visual/medium/graph280.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,7) (0,14) (0,13) (0,18) (0,6) (0,19) (1,8) (1,11) (1,10) (1,15) (1,2) (1,3) (1,12) (1,5) (2,8) (2,11) (2,10) (2,15) (2,3) (2,12) (2,5) (3,8) (3,11) (3,10) (3,15) (3,12) (3,5) (4,16) (4,9) (5,8) (5,11) (5,10) (5,15) (5,12) (6,17) (6,7) (6,14) (6,13) (6,18) (6,19) (7,17) (7,14) (7,13) (7,18) (7,19) (8,11) (8,10) (8,15) (8,12) (9,16) (10,11) (10,15) (10,12) (11,15) (11,12) (12,15) (13,17) (13,14) (13,18) (13,19) (14,17) (14,18) (14,19) (17,18) (17,19) (18,19)\nIs there a path between node 2 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph300-14_5", + "image": "data/connectivity/graph_visual/medium/graph300.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,7) (0,4) (0,11) (0,3) (0,17) (1,10) (1,13) (2,10) (2,13) (2,15) (3,7) (3,4) (3,11) (3,17) (4,5) (4,11) (5,7) (5,11) (5,12) (6,8) (6,14) (6,9) (6,18) (6,19) (7,17) (7,12) (8,14) (8,18) (8,19) (9,18) (9,19) (10,13) (11,17) (11,12) (12,17) (13,16) (13,15) (14,18) (14,19) (15,16) (18,19)\nIs there a path between node 14 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph324-1_7", + "image": "data/connectivity/graph_visual/medium/graph324.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (0,8) (0,18) (0,6) (0,1) (0,12) (0,3) (0,7) (0,14) (0,10) (0,19) (0,16) (0,13) (1,17) (1,8) (1,18) (1,2) (1,19) (2,8) (2,6) (2,20) (2,14) (3,17) (3,18) (3,6) (3,14) (3,10) (3,19) (4,17) (4,18) (4,6) (4,19) (4,13) (5,15) (6,17) (6,8) (6,18) (6,13) (7,17) (7,14) (7,10) (8,20) (9,15) (9,11) (10,17) (10,18) (11,15) (12,17) (12,18) (12,14) (12,19) (13,17) (13,18) (13,20) (14,17) (14,18) (14,20) (18,20) (19,20)\nIs there a path between node 1 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph695-23_11", + "image": "data/connectivity/graph_visual/medium/graph695.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,17) (0,16) (0,8) (0,22) (0,18) (0,6) (0,3) (1,12) (1,23) (1,9) (1,19) (1,11) (1,2) (1,14) (2,12) (2,23) (2,9) (2,19) (2,11) (2,14) (3,7) (3,17) (3,16) (3,8) (3,22) (3,18) (3,6) (4,13) (4,15) (4,10) (4,21) (4,5) (4,20) (5,13) (5,15) (5,10) (5,21) (5,20) (6,7) (6,17) (6,16) (6,8) (6,22) (6,18) (7,17) (7,16) (7,8) (7,22) (7,18) (8,17) (8,16) (8,22) (8,18) (9,12) (9,23) (9,19) (9,11) (9,14) (10,13) (10,15) (10,21) (10,20) (11,12) (11,23) (11,19) (11,14) (12,23) (12,19) (12,14) (13,15) (13,21) (13,20) (14,23) (14,19) (15,21) (15,20) (16,17) (16,22) (16,18) (17,22) (17,18) (18,22) (19,23) (20,21)\nIs there a path between node 23 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph740-12_20", + "image": "data/connectivity/graph_visual/medium/graph740.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,15) (1,2) (2,3) (2,16) (3,21) (3,18) (3,5) (3,13) (3,7) (3,16) (4,10) (5,21) (5,24) (6,11) (6,17) (7,18) (7,22) (7,23) (7,16) (8,14) (9,11) (9,14) (11,17) (12,21) (12,18) (12,22) (12,23) (12,16) (12,24) (13,21) (13,18) (13,22) (13,15) (13,16) (13,24) (15,18) (16,21) (16,18) (17,20) (18,21) (22,24) (23,24)\nIs there a path between node 12 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph219-4_15", + "image": "data/connectivity/graph_visual/medium/graph219.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,5) (0,1) (0,12) (0,4) (1,13) (1,3) (1,6) (1,9) (2,15) (2,14) (2,11) (4,7) (5,16) (5,6) (5,9) (6,13) (6,8) (10,13) (10,12) (11,15) (11,14)\nIs there a path between node 4 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph628-21_9", + "image": "data/connectivity/graph_visual/medium/graph628.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,12) (1,13) (1,2) (1,17) (2,10) (2,23) (3,14) (3,9) (3,4) (3,19) (4,5) (4,9) (4,21) (5,14) (6,11) (7,20) (7,8) (9,14) (9,21) (10,13) (10,17) (10,12) (11,18) (11,20) (12,22) (12,23) (12,15) (12,17) (13,15) (14,21) (16,18) (17,23)\nIs there a path between node 21 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph501-1_7", + "image": "data/connectivity/graph_visual/medium/graph501.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,6) (0,19) (0,7) (0,10) (0,3) (0,15) (0,11) (0,1) (1,6) (1,9) (1,10) (1,15) (1,12) (2,7) (2,3) (2,12) (2,14) (2,13) (3,8) (3,19) (3,7) (3,21) (3,11) (3,12) (3,18) (4,16) (5,9) (5,8) (6,7) (6,17) (6,10) (6,15) (6,21) (6,20) (7,17) (7,15) (7,12) (7,14) (7,22) (7,20) (7,13) (8,9) (8,19) (8,17) (8,15) (8,20) (9,17) (9,11) (9,20) (10,19) (10,15) (11,21) (11,12) (11,14) (11,18) (12,19) (12,17) (12,14) (12,13) (13,20) (14,17) (14,22) (14,20) (14,18) (15,20) (15,18) (17,18) (20,21) (20,22)\nIs there a path between node 1 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph239-3_1", + "image": "data/connectivity/graph_visual/medium/graph239.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (0,10) (0,14) (0,8) (0,11) (0,12) (0,9) (0,3) (1,7) (1,2) (2,5) (3,15) (3,17) (3,4) (3,10) (3,14) (3,13) (3,11) (3,12) (3,6) (3,9) (3,18) (4,15) (4,17) (4,10) (4,14) (4,13) (4,8) (4,11) (4,12) (4,6) (4,9) (6,15) (6,17) (6,10) (6,14) (6,13) (6,12) (6,18) (8,15) (8,10) (8,14) (8,13) (8,11) (8,12) (8,9) (9,15) (9,17) (9,13) (10,15) (10,17) (10,14) (10,11) (10,12) (10,18) (11,17) (11,12) (11,18) (12,18) (13,17) (13,14) (13,18) (14,15) (14,17) (15,17) (15,18) (17,18)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph724-24_3", + "image": "data/connectivity/graph_visual/medium/graph724.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,10) (0,23) (0,13) (0,12) (0,18) (0,8) (0,4) (0,11) (0,9) (0,20) (0,5) (0,14) (0,24) (0,21) (0,1) (0,16) (0,2) (0,7) (0,22) (0,19) (1,15) (1,10) (1,23) (1,13) (1,12) (1,18) (1,8) (1,4) (1,11) (1,9) (1,20) (1,5) (1,14) (1,24) (1,21) (1,16) (1,2) (1,7) (1,22) (1,19) (2,15) (2,10) (2,23) (2,13) (2,12) (2,18) (2,8) (2,4) (2,11) (2,9) (2,20) (2,5) (2,14) (2,24) (2,21) (2,16) (2,7) (2,22) (2,19) (3,17) (3,6) (4,15) (4,10) (4,23) (4,13) (4,12) (4,18) (4,8) (4,11) (4,9) (4,20) (4,5) (4,14) (4,24) (4,21) (4,16) (4,7) (4,22) (4,19) (5,15) (5,10) (5,23) (5,13) (5,12) (5,18) (5,8) (5,11) (5,9) (5,20) (5,14) (5,24) (5,21) (5,16) (5,7) (5,22) (5,19) (6,17) (7,15) (7,10) (7,23) (7,13) (7,12) (7,18) (7,8) (7,11) (7,9) (7,20) (7,14) (7,24) (7,21) (7,16) (7,22) (7,19) (8,15) (8,10) (8,23) (8,13) (8,12) (8,18) (8,11) (8,9) (8,20) (8,14) (8,24) (8,21) (8,16) (8,22) (8,19) (9,15) (9,10) (9,23) (9,13) (9,12) (9,18) (9,11) (9,20) (9,14) (9,24) (9,21) (9,16) (9,22) (9,19) (10,15) (10,23) (10,13) (10,12) (10,18) (10,11) (10,20) (10,14) (10,24) (10,21) (10,16) (10,22) (10,19) (11,15) (11,23) (11,13) (11,12) (11,18) (11,20) (11,14) (11,24) (11,21) (11,16) (11,22) (11,19) (12,15) (12,23) (12,13) (12,18) (12,20) (12,14) (12,24) (12,21) (12,16) (12,22) (12,19) (13,15) (13,23) (13,18) (13,20) (13,14) (13,24) (13,21) (13,16) (13,22) (13,19) (14,15) (14,23) (14,18) (14,20) (14,24) (14,21) (14,16) (14,22) (14,19) (15,23) (15,18) (15,20) (15,24) (15,21) (15,16) (15,22) (15,19) (16,23) (16,18) (16,20) (16,24) (16,21) (16,22) (16,19) (18,23) (18,20) (18,24) (18,21) (18,22) (18,19) (19,23) (19,20) (19,24) (19,21) (19,22) (20,23) (20,24) (20,21) (20,22) (21,23) (21,24) (21,22) (22,23) (22,24) (23,24)\nIs there a path between node 24 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph282-1_6", + "image": "data/connectivity/graph_visual/medium/graph282.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,6) (1,15) (1,16) (2,18) (2,17) (2,7) (3,14) (3,7) (5,11) (6,13) (7,17) (8,15) (8,13) (9,17) (10,17) (13,15) (13,16) (16,19)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph640-10_18", + "image": "data/connectivity/graph_visual/medium/graph640.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (0,22) (0,16) (0,23) (1,8) (1,4) (1,22) (1,16) (1,18) (1,3) (2,19) (2,9) (2,17) (2,20) (3,14) (3,13) (3,7) (4,8) (4,12) (4,16) (4,23) (4,18) (5,10) (5,9) (5,20) (6,14) (6,13) (6,22) (6,7) (7,22) (7,18) (8,22) (8,18) (9,19) (9,11) (9,20) (9,21) (10,20) (10,21) (11,20) (12,18) (13,22) (13,16) (13,23) (13,18) (15,19) (15,17) (15,21) (16,23) (16,18) (17,19) (18,22)\nIs there a path between node 10 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph704-0_19", + "image": "data/connectivity/graph_visual/medium/graph704.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,7) (1,9) (1,10) (1,14) (2,3) (2,11) (3,11) (3,12) (4,17) (5,18) (5,17) (6,20) (6,22) (6,17) (6,8) (7,23) (7,18) (7,8) (9,21) (9,16) (9,11) (9,13) (10,14) (11,21) (11,14) (11,13) (12,15) (13,21) (13,15) (13,14) (14,15) (17,18) (17,19) (18,23) (18,24) (19,24) (19,22)\nIs there a path between node 0 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph364-0_18", + "image": "data/connectivity/graph_visual/medium/graph364.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,2) (1,11) (1,7) (2,11) (2,15) (2,12) (2,3) (3,9) (3,7) (4,19) (4,7) (6,16) (6,13) (6,18) (8,17) (8,15) (8,12) (9,17) (9,19) (9,11) (10,19) (10,11) (11,20) (15,19) (17,20)\nIs there a path between node 0 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph834-18_17", + "image": "data/connectivity/graph_visual/medium/graph834.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,5) (0,17) (0,4) (0,7) (0,21) (0,8) (0,22) (0,3) (0,16) (0,23) (0,13) (1,24) (1,15) (1,11) (1,20) (1,10) (1,18) (1,12) (1,14) (1,9) (1,19) (1,6) (2,5) (2,17) (2,4) (2,7) (2,21) (2,8) (2,22) (2,3) (2,16) (2,23) (2,13) (3,5) (3,17) (3,4) (3,7) (3,21) (3,8) (3,22) (3,16) (3,23) (3,13) (4,5) (4,17) (4,7) (4,21) (4,8) (4,22) (4,16) (4,23) (4,13) (5,17) (5,7) (5,21) (5,8) (5,22) (5,16) (5,23) (5,13) (6,24) (6,15) (6,11) (6,20) (6,10) (6,18) (6,12) (6,14) (6,9) (6,19) (7,17) (7,21) (7,8) (7,22) (7,16) (7,23) (7,13) (8,17) (8,21) (8,22) (8,16) (8,23) (8,13) (9,24) (9,15) (9,11) (9,20) (9,10) (9,18) (9,12) (9,14) (9,19) (10,24) (10,15) (10,11) (10,20) (10,18) (10,12) (10,14) (10,19) (11,24) (11,15) (11,20) (11,18) (11,12) (11,14) (11,19) (12,24) (12,15) (12,20) (12,18) (12,14) (12,19) (13,17) (13,21) (13,22) (13,16) (13,23) (14,24) (14,15) (14,20) (14,18) (14,19) (15,24) (15,20) (15,18) (15,19) (16,17) (16,21) (16,22) (16,23) (17,21) (17,22) (17,23) (18,24) (18,20) (18,19) (19,24) (19,20) (20,24) (21,22) (21,23) (22,23)\nIs there a path between node 18 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph412-8_3", + "image": "data/connectivity/graph_visual/medium/graph412.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,14) (0,15) (0,1) (0,7) (0,4) (0,8) (0,13) (0,12) (0,2) (0,16) (0,20) (0,18) (0,11) (0,21) (1,19) (1,14) (1,15) (1,7) (1,8) (1,6) (1,13) (1,12) (1,2) (1,16) (1,20) (1,18) (1,11) (1,21) (1,17) (2,19) (2,14) (2,15) (2,7) (2,4) (2,13) (2,12) (2,18) (2,21) (2,17) (2,5) (3,9) (3,10) (4,19) (4,15) (4,7) (4,8) (4,6) (4,12) (4,16) (4,11) (4,21) (4,17) (4,5) (5,14) (5,15) (5,7) (5,8) (5,13) (5,12) (5,20) (5,11) (5,21) (6,19) (6,14) (6,15) (6,13) (6,16) (6,20) (6,18) (6,11) (6,21) (6,17) (7,19) (7,14) (7,15) (7,8) (7,12) (7,16) (7,20) (7,18) (7,11) (7,21) (8,19) (8,14) (8,15) (8,13) (8,20) (8,11) (8,21) (9,10) (11,19) (11,14) (11,15) (11,13) (11,12) (11,16) (11,20) (11,18) (11,21) (12,14) (12,20) (12,21) (13,19) (13,14) (13,15) (13,16) (13,18) (13,21) (13,17) (14,19) (14,15) (14,21) (15,19) (15,20) (15,18) (16,19) (16,18) (16,21) (16,17) (17,19) (17,20) (17,18) (18,19) (19,20) (19,21)\nIs there a path between node 8 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph184-13_8", + "image": "data/connectivity/graph_visual/medium/graph184.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,4) (0,2) (0,8) (0,1) (0,12) (0,9) (0,6) (0,5) (0,11) (0,13) (0,17) (0,7) (0,14) (0,15) (1,4) (1,2) (1,8) (1,12) (1,9) (1,6) (1,5) (1,11) (1,13) (1,17) (1,7) (1,14) (1,15) (2,4) (2,8) (2,12) (2,9) (2,6) (2,5) (2,11) (2,13) (2,17) (2,7) (2,14) (2,15) (3,10) (4,8) (4,12) (4,9) (4,6) (4,5) (4,11) (4,13) (4,17) (4,7) (4,14) (4,15) (5,8) (5,12) (5,9) (5,6) (5,11) (5,13) (5,17) (5,7) (5,14) (5,15) (6,8) (6,12) (6,9) (6,11) (6,13) (6,17) (6,7) (6,14) (6,15) (7,8) (7,12) (7,9) (7,11) (7,13) (7,17) (7,14) (7,15) (8,12) (8,9) (8,11) (8,13) (8,17) (8,14) (8,15) (9,12) (9,11) (9,13) (9,17) (9,14) (9,15) (11,12) (11,13) (11,17) (11,14) (11,15) (12,13) (12,17) (12,14) (12,15) (13,17) (13,14) (13,15) (14,17) (14,15) (15,17)\nIs there a path between node 13 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph833-7_6", + "image": "data/connectivity/graph_visual/medium/graph833.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,22) (0,18) (0,8) (0,21) (0,5) (0,11) (0,1) (0,24) (0,19) (0,9) (0,15) (0,14) (0,10) (0,4) (0,23) (0,6) (0,17) (0,13) (1,20) (1,22) (1,18) (1,8) (1,21) (1,5) (1,11) (1,24) (1,19) (1,9) (1,15) (1,14) (1,10) (1,4) (1,23) (1,6) (1,17) (1,13) (2,3) (2,7) (2,12) (2,16) (3,7) (3,12) (3,16) (4,20) (4,22) (4,18) (4,8) (4,21) (4,5) (4,11) (4,24) (4,19) (4,9) (4,15) (4,14) (4,10) (4,23) (4,6) (4,17) (4,13) (5,20) (5,22) (5,18) (5,8) (5,21) (5,11) (5,24) (5,19) (5,9) (5,15) (5,14) (5,10) (5,23) (5,6) (5,17) (5,13) (6,20) (6,22) (6,18) (6,8) (6,21) (6,11) (6,24) (6,19) (6,9) (6,15) (6,14) (6,10) (6,23) (6,17) (6,13) (7,12) (7,16) (8,20) (8,22) (8,18) (8,21) (8,11) (8,24) (8,19) (8,9) (8,15) (8,14) (8,10) (8,23) (8,17) (8,13) (9,20) (9,22) (9,18) (9,21) (9,11) (9,24) (9,19) (9,15) (9,14) (9,10) (9,23) (9,17) (9,13) (10,20) (10,22) (10,18) (10,21) (10,11) (10,24) (10,19) (10,15) (10,14) (10,23) (10,17) (10,13) (11,20) (11,22) (11,18) (11,21) (11,24) (11,19) (11,15) (11,14) (11,23) (11,17) (11,13) (12,16) (13,20) (13,22) (13,18) (13,21) (13,24) (13,19) (13,15) (13,14) (13,23) (13,17) (14,20) (14,22) (14,18) (14,21) (14,24) (14,19) (14,15) (14,23) (14,17) (15,20) (15,22) (15,18) (15,21) (15,24) (15,19) (15,23) (15,17) (17,20) (17,22) (17,18) (17,21) (17,24) (17,19) (17,23) (18,20) (18,22) (18,21) (18,24) (18,19) (18,23) (19,20) (19,22) (19,21) (19,24) (19,23) (20,22) (20,21) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 7 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph848-14_10", + "image": "data/connectivity/graph_visual/medium/graph848.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,20) (0,4) (0,14) (0,8) (0,1) (0,17) (0,15) (0,21) (0,10) (0,11) (0,18) (1,7) (1,20) (1,4) (1,14) (1,8) (1,17) (1,15) (1,21) (1,10) (1,11) (1,18) (2,3) (2,24) (2,5) (2,22) (2,6) (2,13) (2,16) (2,12) (2,23) (2,19) (2,9) (3,24) (3,5) (3,22) (3,6) (3,13) (3,16) (3,12) (3,23) (3,19) (3,9) (4,7) (4,20) (4,14) (4,8) (4,17) (4,15) (4,21) (4,10) (4,11) (4,18) (5,24) (5,22) (5,6) (5,13) (5,16) (5,12) (5,23) (5,19) (5,9) (6,24) (6,22) (6,13) (6,16) (6,12) (6,23) (6,19) (6,9) (7,20) (7,14) (7,8) (7,17) (7,15) (7,21) (7,10) (7,11) (7,18) (8,20) (8,14) (8,17) (8,15) (8,21) (8,10) (8,11) (8,18) (9,24) (9,22) (9,13) (9,16) (9,12) (9,23) (9,19) (10,20) (10,14) (10,17) (10,15) (10,21) (10,11) (10,18) (11,20) (11,14) (11,17) (11,15) (11,21) (11,18) (12,24) (12,22) (12,13) (12,16) (12,23) (12,19) (13,24) (13,22) (13,16) (13,23) (13,19) (14,20) (14,17) (14,15) (14,21) (14,18) (15,20) (15,17) (15,21) (15,18) (16,24) (16,22) (16,23) (16,19) (17,20) (17,21) (17,18) (18,20) (18,21) (19,24) (19,22) (19,23) (20,21) (22,24) (22,23) (23,24)\nIs there a path between node 14 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph62-11_1", + "image": "data/connectivity/graph_visual/medium/graph62.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,12) (0,11) (0,13) (0,5) (1,12) (1,11) (1,7) (1,13) (1,5) (2,6) (2,8) (2,9) (2,10) (3,4) (3,8) (3,9) (3,10) (4,6) (4,8) (4,9) (5,11) (5,7) (6,8) (6,9) (6,10) (7,12) (7,11) (8,10) (9,10) (12,13)\nIs there a path between node 11 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph853-1_13", + "image": "data/connectivity/graph_visual/medium/graph853.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,15) (0,6) (0,16) (0,2) (1,5) (1,21) (1,19) (1,11) (1,18) (1,12) (1,8) (1,14) (1,20) (1,24) (1,9) (1,10) (2,7) (2,15) (2,6) (2,16) (3,22) (3,17) (3,13) (3,4) (3,23) (4,22) (4,17) (4,13) (4,23) (5,21) (5,19) (5,11) (5,18) (5,12) (5,8) (5,14) (5,20) (5,24) (5,9) (5,10) (6,7) (6,15) (6,16) (7,15) (7,16) (8,21) (8,19) (8,11) (8,18) (8,12) (8,14) (8,20) (8,24) (8,9) (8,10) (9,21) (9,19) (9,11) (9,18) (9,12) (9,14) (9,20) (9,24) (9,10) (10,21) (10,19) (10,11) (10,18) (10,12) (10,14) (10,20) (10,24) (11,21) (11,19) (11,18) (11,12) (11,14) (11,20) (11,24) (12,21) (12,19) (12,18) (12,14) (12,20) (12,24) (13,22) (13,17) (13,23) (14,21) (14,19) (14,18) (14,20) (14,24) (15,16) (17,22) (17,23) (18,21) (18,19) (18,20) (18,24) (19,21) (19,20) (19,24) (20,21) (20,24) (21,24) (22,23)\nIs there a path between node 1 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph605-19_4", + "image": "data/connectivity/graph_visual/medium/graph605.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,18) (0,8) (0,17) (0,9) (0,16) (0,12) (0,10) (0,2) (0,5) (0,3) (1,23) (1,18) (1,22) (1,8) (1,20) (1,10) (1,5) (1,3) (1,6) (2,23) (2,22) (2,8) (2,17) (2,9) (2,20) (2,15) (2,16) (2,12) (2,10) (2,5) (2,3) (3,23) (3,18) (3,8) (3,9) (3,15) (3,16) (3,12) (3,19) (3,5) (3,6) (4,13) (4,11) (4,21) (5,23) (5,18) (5,22) (5,15) (5,16) (5,10) (5,6) (6,22) (6,17) (6,9) (6,15) (6,16) (6,12) (6,19) (6,10) (7,14) (8,23) (8,18) (8,22) (8,17) (8,15) (8,16) (8,12) (9,23) (9,18) (9,17) (9,20) (9,15) (9,12) (9,19) (9,10) (10,23) (10,18) (10,22) (10,20) (10,15) (10,16) (10,12) (10,19) (11,21) (12,18) (12,22) (12,17) (12,15) (12,16) (13,21) (15,23) (15,22) (15,17) (15,20) (15,16) (15,19) (16,23) (16,18) (16,22) (16,17) (16,19) (17,18) (17,22) (17,20) (17,19) (18,23) (18,22) (18,20) (18,19) (19,23) (19,22) (20,23) (20,22) (22,23)\nIs there a path between node 19 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph299-3_19", + "image": "data/connectivity/graph_visual/medium/graph299.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (1,3) (1,2) (1,7) (1,5) (1,18) (1,14) (1,17) (1,12) (1,11) (1,10) (1,19) (1,13) (1,4) (1,9) (2,7) (2,18) (2,16) (2,6) (2,11) (2,10) (2,19) (2,13) (2,4) (2,9) (2,15) (3,7) (3,18) (3,12) (3,6) (3,10) (3,19) (3,13) (3,4) (3,9) (4,7) (4,5) (4,14) (4,17) (4,16) (4,6) (4,11) (4,10) (4,19) (4,9) (5,7) (5,14) (5,17) (5,16) (5,12) (5,6) (5,11) (5,10) (5,13) (5,9) (5,15) (6,14) (6,17) (6,16) (6,12) (6,10) (6,19) (6,9) (7,18) (7,14) (7,17) (7,16) (7,12) (7,10) (7,19) (7,13) (7,9) (7,15) (9,18) (9,14) (9,17) (9,16) (9,12) (9,11) (9,19) (9,13) (9,15) (10,18) (10,14) (10,17) (10,12) (10,11) (10,19) (10,15) (11,18) (11,12) (11,19) (11,15) (12,18) (12,14) (12,17) (12,19) (12,13) (12,15) (13,18) (13,14) (13,17) (14,17) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19)\nIs there a path between node 3 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph133-16_9", + "image": "data/connectivity/graph_visual/medium/graph133.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,15) (0,8) (0,4) (0,5) (0,13) (0,2) (0,17) (1,15) (1,8) (1,3) (1,4) (1,5) (1,13) (1,17) (2,15) (2,8) (2,3) (2,4) (2,5) (2,13) (3,8) (3,5) (3,17) (4,15) (4,13) (4,17) (5,15) (5,8) (5,17) (6,14) (6,7) (6,10) (6,16) (6,9) (6,12) (7,14) (7,16) (7,9) (8,13) (9,14) (9,10) (9,11) (9,16) (9,12) (10,14) (10,12) (11,14) (11,12) (12,14) (12,16) (13,17) (15,17)\nIs there a path between node 16 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph728-3_10", + "image": "data/connectivity/graph_visual/medium/graph728.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,17) (0,10) (0,7) (0,19) (0,22) (0,13) (0,12) (0,5) (0,4) (0,24) (0,16) (0,1) (0,3) (0,11) (1,2) (1,17) (1,10) (1,7) (1,19) (1,22) (1,13) (1,12) (1,5) (1,4) (1,24) (1,16) (1,3) (1,11) (2,17) (2,10) (2,7) (2,19) (2,22) (2,13) (2,12) (2,5) (2,4) (2,24) (2,16) (2,3) (2,11) (3,17) (3,10) (3,7) (3,19) (3,22) (3,13) (3,12) (3,5) (3,4) (3,24) (3,16) (3,11) (4,17) (4,10) (4,7) (4,19) (4,22) (4,13) (4,12) (4,5) (4,24) (4,16) (4,11) (5,17) (5,10) (5,7) (5,19) (5,22) (5,13) (5,12) (5,24) (5,16) (5,11) (6,8) (6,14) (6,9) (6,23) (7,17) (7,10) (7,19) (7,22) (7,13) (7,12) (7,24) (7,16) (7,11) (8,14) (8,9) (8,23) (9,14) (9,23) (10,17) (10,19) (10,22) (10,13) (10,12) (10,24) (10,16) (10,11) (11,17) (11,19) (11,22) (11,13) (11,12) (11,24) (11,16) (12,17) (12,19) (12,22) (12,13) (12,24) (12,16) (13,17) (13,19) (13,22) (13,24) (13,16) (14,23) (15,20) (15,18) (15,21) (16,17) (16,19) (16,22) (16,24) (17,19) (17,22) (17,24) (18,20) (18,21) (19,22) (19,24) (20,21) (22,24)\nIs there a path between node 3 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph534-5_18", + "image": "data/connectivity/graph_visual/medium/graph534.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,19) (0,20) (0,13) (0,2) (0,3) (0,16) (0,15) (0,4) (0,11) (0,22) (0,5) (0,6) (0,7) (0,1) (0,10) (1,21) (1,19) (1,20) (1,13) (1,2) (1,3) (1,16) (1,15) (1,4) (1,11) (1,22) (1,5) (1,6) (1,7) (1,10) (2,21) (2,19) (2,20) (2,13) (2,3) (2,16) (2,15) (2,4) (2,11) (2,22) (2,5) (2,6) (2,7) (2,10) (3,21) (3,19) (3,20) (3,13) (3,16) (3,15) (3,4) (3,11) (3,22) (3,5) (3,6) (3,7) (3,10) (4,21) (4,19) (4,20) (4,13) (4,16) (4,15) (4,11) (4,22) (4,5) (4,6) (4,7) (4,10) (5,21) (5,19) (5,20) (5,13) (5,16) (5,15) (5,11) (5,22) (5,6) (5,7) (5,10) (6,21) (6,19) (6,20) (6,13) (6,16) (6,15) (6,11) (6,22) (6,7) (6,10) (7,21) (7,19) (7,20) (7,13) (7,16) (7,15) (7,11) (7,22) (7,10) (8,12) (8,14) (8,9) (8,18) (9,12) (9,14) (9,18) (10,21) (10,19) (10,20) (10,13) (10,16) (10,15) (10,11) (10,22) (11,21) (11,19) (11,20) (11,13) (11,16) (11,15) (11,22) (12,14) (12,18) (13,21) (13,19) (13,20) (13,16) (13,15) (13,22) (14,18) (15,21) (15,19) (15,20) (15,16) (15,22) (16,21) (16,19) (16,20) (16,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 5 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph740-6_4", + "image": "data/connectivity/graph_visual/medium/graph740.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,15) (1,2) (2,3) (2,16) (3,21) (3,18) (3,5) (3,13) (3,7) (3,16) (4,10) (5,21) (5,24) (6,11) (6,17) (7,18) (7,22) (7,23) (7,16) (8,14) (9,11) (9,14) (11,17) (12,21) (12,18) (12,22) (12,23) (12,16) (12,24) (13,21) (13,18) (13,22) (13,15) (13,16) (13,24) (15,18) (16,21) (16,18) (17,20) (18,21) (22,24) (23,24)\nIs there a path between node 6 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph143-4_5", + "image": "data/connectivity/graph_visual/medium/graph143.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,17) (0,6) (0,3) (0,1) (1,7) (1,15) (1,17) (1,6) (1,3) (2,16) (2,12) (2,5) (2,4) (3,15) (3,17) (3,6) (4,9) (4,10) (4,8) (4,14) (4,16) (5,9) (5,10) (5,11) (5,14) (5,13) (5,16) (5,12) (6,7) (6,17) (7,17) (8,10) (8,14) (8,13) (8,12) (9,10) (9,11) (9,14) (9,13) (9,16) (9,12) (10,14) (10,16) (10,12) (11,14) (11,13) (11,16) (11,12) (12,14) (12,13) (12,16) (13,14) (14,16) (15,17)\nIs there a path between node 4 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph609-14_17", + "image": "data/connectivity/graph_visual/medium/graph609.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,4) (0,2) (0,20) (0,6) (0,1) (0,15) (0,17) (0,11) (0,12) (0,21) (0,7) (0,14) (0,9) (0,10) (0,22) (0,23) (1,3) (1,4) (1,2) (1,20) (1,6) (1,15) (1,17) (1,11) (1,12) (1,21) (1,7) (1,14) (1,9) (1,10) (1,22) (1,23) (2,3) (2,4) (2,20) (2,6) (2,15) (2,17) (2,11) (2,12) (2,21) (2,7) (2,14) (2,9) (2,10) (2,22) (2,23) (3,4) (3,20) (3,6) (3,15) (3,17) (3,11) (3,12) (3,21) (3,7) (3,14) (3,9) (3,10) (3,22) (3,23) (4,20) (4,6) (4,15) (4,17) (4,11) (4,12) (4,21) (4,7) (4,14) (4,9) (4,10) (4,22) (4,23) (5,18) (6,20) (6,15) (6,17) (6,11) (6,12) (6,21) (6,7) (6,14) (6,9) (6,10) (6,22) (6,23) (7,20) (7,15) (7,17) (7,11) (7,12) (7,21) (7,14) (7,9) (7,10) (7,22) (7,23) (8,16) (8,19) (8,13) (9,20) (9,15) (9,17) (9,11) (9,12) (9,21) (9,14) (9,10) (9,22) (9,23) (10,20) (10,15) (10,17) (10,11) (10,12) (10,21) (10,14) (10,22) (10,23) (11,20) (11,15) (11,17) (11,12) (11,21) (11,14) (11,22) (11,23) (12,20) (12,15) (12,17) (12,21) (12,14) (12,22) (12,23) (13,16) (13,19) (14,20) (14,15) (14,17) (14,21) (14,22) (14,23) (15,20) (15,17) (15,21) (15,22) (15,23) (16,19) (17,20) (17,21) (17,22) (17,23) (20,21) (20,22) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 14 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph716-12_0", + "image": "data/connectivity/graph_visual/medium/graph716.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,24) (0,22) (0,23) (0,15) (0,21) (0,8) (0,12) (0,2) (0,1) (1,24) (1,14) (1,11) (1,22) (1,19) (1,15) (1,8) (1,12) (1,2) (1,17) (2,24) (2,11) (2,19) (2,15) (2,8) (2,7) (2,17) (3,16) (3,6) (3,13) (3,4) (4,16) (4,6) (4,10) (4,13) (4,9) (4,18) (5,16) (5,10) (5,13) (5,9) (5,18) (6,10) (6,9) (6,18) (7,24) (7,14) (7,22) (7,19) (7,21) (7,12) (7,20) (7,17) (8,24) (8,14) (8,23) (8,21) (8,20) (9,16) (9,10) (9,13) (9,18) (10,13) (10,18) (11,24) (11,14) (11,22) (11,19) (11,15) (11,21) (11,17) (12,24) (12,14) (12,19) (12,23) (12,21) (12,20) (12,17) (13,16) (13,18) (14,24) (14,22) (14,19) (14,23) (14,15) (14,21) (14,20) (14,17) (15,24) (15,22) (15,19) (15,20) (15,17) (16,18) (17,24) (17,22) (17,19) (17,21) (17,20) (19,24) (19,22) (19,21) (19,20) (20,24) (20,22) (21,24) (21,22) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 12 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph359-10_18", + "image": "data/connectivity/graph_visual/medium/graph359.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,8) (0,7) (0,18) (0,5) (0,2) (0,1) (1,11) (1,17) (2,20) (2,9) (3,11) (3,18) (3,20) (3,12) (4,14) (6,19) (6,16) (6,8) (6,15) (6,12) (6,9) (7,15) (7,12) (7,17) (8,18) (9,17) (11,16) (11,15) (12,19) (12,17) (15,19) (15,20) (16,19) (16,18) (16,17)\nIs there a path between node 10 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph801-10_18", + "image": "data/connectivity/graph_visual/medium/graph801.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,1) (0,15) (1,8) (1,15) (1,11) (2,9) (2,6) (3,8) (3,4) (3,24) (3,19) (3,11) (4,24) (4,13) (5,21) (5,23) (5,7) (5,17) (5,20) (6,9) (6,23) (7,12) (7,17) (8,22) (8,14) (8,13) (9,21) (9,12) (10,15) (10,19) (10,11) (10,13) (11,14) (12,18) (12,20) (13,22) (13,14) (13,24) (15,22) (16,17) (16,20) (18,21) (18,20)\nIs there a path between node 10 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph18-3_4", + "image": "data/connectivity/graph_visual/medium/graph18.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (0,2) (1,5) (1,2) (2,5) (2,10) (3,10) (3,4) (3,8) (4,5) (5,10) (5,8) (7,11) (8,10) (9,11)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph630-12_4", + "image": "data/connectivity/graph_visual/medium/graph630.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,5) (0,10) (0,7) (0,11) (1,22) (1,21) (2,10) (2,7) (2,12) (2,3) (2,11) (2,20) (3,14) (3,18) (3,5) (3,7) (3,11) (4,10) (4,12) (5,14) (5,17) (5,11) (5,23) (7,19) (7,18) (7,10) (7,21) (8,13) (9,13) (10,18) (10,15) (10,12) (11,21) (12,14) (12,15) (12,21) (14,20) (15,23) (17,19) (17,18) (17,20) (18,19) (20,23) (22,23)\nIs there a path between node 12 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph533-17_20", + "image": "data/connectivity/graph_visual/medium/graph533.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,2) (0,8) (0,14) (0,18) (0,12) (0,20) (0,1) (0,11) (0,10) (0,3) (0,17) (0,4) (0,9) (0,21) (0,19) (1,2) (1,8) (1,14) (1,18) (1,12) (1,20) (1,11) (1,10) (1,3) (1,17) (1,4) (1,9) (1,21) (1,19) (2,8) (2,14) (2,18) (2,12) (2,20) (2,11) (2,10) (2,3) (2,17) (2,4) (2,9) (2,21) (2,19) (3,8) (3,14) (3,18) (3,12) (3,20) (3,11) (3,10) (3,17) (3,4) (3,9) (3,21) (3,19) (4,8) (4,14) (4,18) (4,12) (4,20) (4,11) (4,10) (4,17) (4,9) (4,21) (4,19) (5,16) (5,6) (5,13) (5,7) (5,15) (5,22) (6,16) (6,13) (6,7) (6,15) (6,22) (7,16) (7,13) (7,15) (7,22) (8,14) (8,18) (8,12) (8,20) (8,11) (8,10) (8,17) (8,9) (8,21) (8,19) (9,14) (9,18) (9,12) (9,20) (9,11) (9,10) (9,17) (9,21) (9,19) (10,14) (10,18) (10,12) (10,20) (10,11) (10,17) (10,21) (10,19) (11,14) (11,18) (11,12) (11,20) (11,17) (11,21) (11,19) (12,14) (12,18) (12,20) (12,17) (12,21) (12,19) (13,16) (13,15) (13,22) (14,18) (14,20) (14,17) (14,21) (14,19) (15,16) (15,22) (16,22) (17,18) (17,20) (17,21) (17,19) (18,20) (18,21) (18,19) (19,20) (19,21) (20,21)\nIs there a path between node 17 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph573-14_21", + "image": "data/connectivity/graph_visual/medium/graph573.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (1,17) (2,9) (3,16) (5,18) (5,11) (5,21) (6,21) (6,15) (7,19) (7,21) (8,10) (8,12) (8,16) (10,16) (14,23) (15,21) (16,19) (17,20) (18,19) (20,23)\nIs there a path between node 14 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph735-2_14", + "image": "data/connectivity/graph_visual/medium/graph735.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,19) (0,3) (1,9) (1,17) (1,5) (1,24) (2,9) (2,21) (2,11) (2,15) (2,14) (2,16) (3,19) (3,18) (4,10) (4,13) (4,15) (5,7) (5,17) (5,15) (5,24) (6,23) (7,20) (7,17) (7,24) (8,20) (8,21) (8,10) (8,13) (8,11) (8,24) (9,23) (9,10) (9,13) (9,14) (9,24) (10,12) (10,17) (10,11) (11,20) (11,17) (11,15) (12,21) (12,13) (12,15) (12,14) (13,20) (13,17) (13,14) (13,24) (14,23) (14,15) (15,20) (15,23) (15,16) (16,21) (16,23) (16,17) (16,24) (17,20) (17,21) (18,19) (21,24) (23,24)\nIs there a path between node 2 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph682-16_18", + "image": "data/connectivity/graph_visual/medium/graph682.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,21) (0,6) (0,16) (0,3) (0,10) (0,12) (0,22) (0,19) (0,13) (0,18) (0,17) (0,7) (0,2) (0,14) (0,5) (0,23) (1,20) (1,9) (2,8) (2,21) (2,6) (2,16) (2,3) (2,10) (2,12) (2,22) (2,19) (2,13) (2,18) (2,17) (2,7) (2,14) (2,5) (2,23) (3,8) (3,21) (3,6) (3,16) (3,10) (3,12) (3,22) (3,19) (3,13) (3,18) (3,17) (3,7) (3,14) (3,5) (3,23) (4,15) (4,11) (5,8) (5,21) (5,6) (5,16) (5,10) (5,12) (5,22) (5,19) (5,13) (5,18) (5,17) (5,7) (5,14) (5,23) (6,8) (6,21) (6,16) (6,10) (6,12) (6,22) (6,19) (6,13) (6,18) (6,17) (6,7) (6,14) (6,23) (7,8) (7,21) (7,16) (7,10) (7,12) (7,22) (7,19) (7,13) (7,18) (7,17) (7,14) (7,23) (8,21) (8,16) (8,10) (8,12) (8,22) (8,19) (8,13) (8,18) (8,17) (8,14) (8,23) (9,20) (10,21) (10,16) (10,12) (10,22) (10,19) (10,13) (10,18) (10,17) (10,14) (10,23) (11,15) (12,21) (12,16) (12,22) (12,19) (12,13) (12,18) (12,17) (12,14) (12,23) (13,21) (13,16) (13,22) (13,19) (13,18) (13,17) (13,14) (13,23) (14,21) (14,16) (14,22) (14,19) (14,18) (14,17) (14,23) (16,21) (16,22) (16,19) (16,18) (16,17) (16,23) (17,21) (17,22) (17,19) (17,18) (17,23) (18,21) (18,22) (18,19) (18,23) (19,21) (19,22) (19,23) (21,22) (21,23) (22,23)\nIs there a path between node 16 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph698-2_21", + "image": "data/connectivity/graph_visual/medium/graph698.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,2) (1,22) (1,7) (1,20) (1,13) (1,10) (1,16) (2,11) (3,6) (3,21) (3,18) (3,4) (3,12) (3,9) (3,5) (3,8) (3,19) (3,15) (3,23) (3,17) (3,14) (4,6) (4,21) (4,18) (4,12) (4,9) (4,5) (4,8) (4,19) (4,15) (4,23) (4,17) (4,14) (5,6) (5,21) (5,18) (5,12) (5,9) (5,8) (5,19) (5,15) (5,23) (5,17) (5,14) (6,21) (6,18) (6,12) (6,9) (6,8) (6,19) (6,15) (6,23) (6,17) (6,14) (7,22) (7,20) (7,13) (7,10) (7,16) (8,21) (8,18) (8,12) (8,9) (8,19) (8,15) (8,23) (8,17) (8,14) (9,21) (9,18) (9,12) (9,19) (9,15) (9,23) (9,17) (9,14) (10,22) (10,20) (10,13) (10,16) (12,21) (12,18) (12,19) (12,15) (12,23) (12,17) (12,14) (13,22) (13,20) (13,16) (14,21) (14,18) (14,19) (14,15) (14,23) (14,17) (15,21) (15,18) (15,19) (15,23) (15,17) (16,22) (16,20) (17,21) (17,18) (17,19) (17,23) (18,21) (18,19) (18,23) (19,21) (19,23) (20,22) (21,23)\nIs there a path between node 2 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph774-4_9", + "image": "data/connectivity/graph_visual/medium/graph774.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,7) (0,1) (0,9) (0,13) (0,24) (0,8) (0,11) (1,14) (1,7) (1,9) (1,13) (1,24) (1,8) (1,11) (2,19) (2,18) (2,12) (2,16) (2,4) (2,17) (2,3) (2,21) (2,20) (2,23) (2,22) (2,10) (2,6) (2,5) (2,15) (3,19) (3,18) (3,12) (3,16) (3,4) (3,17) (3,21) (3,20) (3,23) (3,22) (3,10) (3,6) (3,5) (3,15) (4,19) (4,18) (4,12) (4,16) (4,17) (4,21) (4,20) (4,23) (4,22) (4,10) (4,6) (4,5) (4,15) (5,19) (5,18) (5,12) (5,16) (5,17) (5,21) (5,20) (5,23) (5,22) (5,10) (5,6) (5,15) (6,19) (6,18) (6,12) (6,16) (6,17) (6,21) (6,20) (6,23) (6,22) (6,10) (6,15) (7,14) (7,9) (7,13) (7,24) (7,8) (7,11) (8,14) (8,9) (8,13) (8,24) (8,11) (9,14) (9,13) (9,24) (9,11) (10,19) (10,18) (10,12) (10,16) (10,17) (10,21) (10,20) (10,23) (10,22) (10,15) (11,14) (11,13) (11,24) (12,19) (12,18) (12,16) (12,17) (12,21) (12,20) (12,23) (12,22) (12,15) (13,14) (13,24) (14,24) (15,19) (15,18) (15,16) (15,17) (15,21) (15,20) (15,23) (15,22) (16,19) (16,18) (16,17) (16,21) (16,20) (16,23) (16,22) (17,19) (17,18) (17,21) (17,20) (17,23) (17,22) (18,19) (18,21) (18,20) (18,23) (18,22) (19,21) (19,20) (19,23) (19,22) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 4 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph308-14_5", + "image": "data/connectivity/graph_visual/medium/graph308.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,12) (0,8) (0,19) (1,15) (1,13) (1,10) (1,6) (1,11) (1,4) (1,14) (1,18) (1,3) (1,9) (1,2) (2,16) (2,13) (2,7) (2,10) (2,11) (2,4) (2,14) (2,18) (2,3) (2,9) (3,16) (3,13) (3,10) (3,6) (3,4) (3,14) (3,18) (3,5) (4,15) (4,13) (4,7) (4,10) (4,6) (4,11) (4,14) (4,18) (4,9) (4,5) (5,15) (5,16) (5,13) (5,7) (5,10) (5,6) (5,14) (5,9) (6,13) (6,7) (6,14) (6,18) (6,9) (7,15) (7,16) (7,10) (7,11) (7,14) (7,18) (8,17) (8,12) (9,15) (9,13) (9,11) (9,18) (10,15) (10,13) (10,14) (10,18) (11,15) (11,13) (11,18) (12,17) (12,19) (13,15) (13,16) (13,14) (13,18) (14,15) (14,16) (15,16) (16,18) (17,19)\nIs there a path between node 14 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph676-16_22", + "image": "data/connectivity/graph_visual/medium/graph676.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,1) (0,3) (0,20) (0,21) (0,6) (0,11) (0,23) (0,8) (0,9) (0,14) (0,19) (1,10) (1,3) (1,20) (1,21) (1,6) (1,11) (1,23) (1,8) (1,9) (1,14) (1,19) (2,15) (2,18) (2,7) (2,22) (2,13) (2,17) (2,16) (2,12) (2,4) (2,5) (3,10) (3,20) (3,21) (3,6) (3,11) (3,23) (3,8) (3,9) (3,14) (3,19) (4,15) (4,18) (4,7) (4,22) (4,13) (4,17) (4,16) (4,12) (4,5) (5,15) (5,18) (5,7) (5,22) (5,13) (5,17) (5,16) (5,12) (6,10) (6,20) (6,21) (6,11) (6,23) (6,8) (6,9) (6,14) (6,19) (7,15) (7,18) (7,22) (7,13) (7,17) (7,16) (7,12) (8,10) (8,20) (8,21) (8,11) (8,23) (8,9) (8,14) (8,19) (9,10) (9,20) (9,21) (9,11) (9,23) (9,14) (9,19) (10,20) (10,21) (10,11) (10,23) (10,14) (10,19) (11,20) (11,21) (11,23) (11,14) (11,19) (12,15) (12,18) (12,22) (12,13) (12,17) (12,16) (13,15) (13,18) (13,22) (13,17) (13,16) (14,20) (14,21) (14,23) (14,19) (15,18) (15,22) (15,17) (15,16) (16,18) (16,22) (16,17) (17,18) (17,22) (18,22) (19,20) (19,21) (19,23) (20,21) (20,23) (21,23)\nIs there a path between node 16 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph419-16_9", + "image": "data/connectivity/graph_visual/medium/graph419.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,13) (0,1) (0,18) (0,4) (0,2) (0,9) (0,3) (1,13) (1,18) (1,4) (1,2) (1,9) (1,3) (2,13) (2,18) (2,4) (2,9) (2,3) (3,13) (3,18) (3,4) (3,9) (4,13) (4,18) (4,9) (5,10) (5,12) (5,14) (5,21) (5,20) (5,19) (5,17) (5,8) (5,16) (5,7) (5,15) (5,6) (5,11) (6,10) (6,12) (6,14) (6,21) (6,20) (6,19) (6,17) (6,8) (6,16) (6,7) (6,15) (6,11) (7,10) (7,12) (7,14) (7,21) (7,20) (7,19) (7,17) (7,8) (7,16) (7,15) (7,11) (8,10) (8,12) (8,14) (8,21) (8,20) (8,19) (8,17) (8,16) (8,15) (8,11) (9,13) (9,18) (10,12) (10,14) (10,21) (10,20) (10,19) (10,17) (10,16) (10,15) (10,11) (11,12) (11,14) (11,21) (11,20) (11,19) (11,17) (11,16) (11,15) (12,14) (12,21) (12,20) (12,19) (12,17) (12,16) (12,15) (13,18) (14,21) (14,20) (14,19) (14,17) (14,16) (14,15) (15,21) (15,20) (15,19) (15,17) (15,16) (16,21) (16,20) (16,19) (16,17) (17,21) (17,20) (17,19) (19,21) (19,20) (20,21)\nIs there a path between node 16 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph197-5_17", + "image": "data/connectivity/graph_visual/medium/graph197.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,3) (0,18) (0,12) (0,2) (0,11) (0,8) (0,13) (1,4) (1,10) (1,17) (1,5) (1,14) (1,7) (1,6) (1,15) (2,3) (2,18) (2,12) (2,11) (2,8) (2,13) (3,18) (3,12) (3,11) (3,8) (3,13) (4,10) (4,17) (4,5) (4,14) (4,7) (4,6) (4,15) (5,10) (5,17) (5,14) (5,7) (5,6) (5,15) (6,10) (6,17) (6,14) (6,7) (6,15) (7,10) (7,17) (7,14) (7,15) (8,18) (8,12) (8,11) (8,13) (9,16) (10,17) (10,14) (10,15) (11,18) (11,12) (11,13) (12,18) (12,13) (13,18) (14,17) (14,15) (15,17)\nIs there a path between node 5 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph628-17_18", + "image": "data/connectivity/graph_visual/medium/graph628.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,12) (1,13) (1,2) (1,17) (2,10) (2,23) (3,14) (3,9) (3,4) (3,19) (4,5) (4,9) (4,21) (5,14) (6,11) (7,20) (7,8) (9,14) (9,21) (10,13) (10,17) (10,12) (11,18) (11,20) (12,22) (12,23) (12,15) (12,17) (13,15) (14,21) (16,18) (17,23)\nIs there a path between node 17 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph739-4_16", + "image": "data/connectivity/graph_visual/medium/graph739.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (0,19) (0,11) (0,13) (0,17) (0,20) (1,4) (2,23) (2,12) (2,22) (2,21) (2,14) (3,19) (3,21) (4,9) (4,24) (4,17) (4,14) (5,6) (5,22) (5,24) (5,11) (5,20) (6,23) (6,22) (6,17) (8,14) (11,23) (11,24) (11,14) (12,22) (13,19) (13,24) (14,19) (14,21) (14,24) (14,20) (17,24) (20,23) (20,21) (21,24) (22,24) (23,24)\nIs there a path between node 4 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph794-21_0", + "image": "data/connectivity/graph_visual/medium/graph794.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,13) (0,15) (1,17) (1,18) (1,7) (2,14) (2,6) (2,15) (2,10) (4,6) (4,15) (4,5) (5,13) (5,21) (5,23) (5,24) (6,13) (6,21) (6,23) (7,17) (10,23) (11,16) (11,18) (12,21) (13,23) (15,24) (21,24) (23,24)\nIs there a path between node 21 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph178-16_2", + "image": "data/connectivity/graph_visual/medium/graph178.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,1) (0,7) (0,14) (0,8) (0,5) (0,11) (0,16) (1,7) (1,17) (1,14) (1,8) (1,6) (1,5) (1,9) (1,16) (1,3) (2,12) (2,4) (2,7) (2,8) (2,5) (2,9) (2,11) (2,16) (2,3) (2,13) (3,12) (3,14) (3,8) (3,5) (3,11) (3,16) (3,13) (4,17) (4,8) (4,6) (4,16) (4,13) (5,12) (5,7) (5,17) (5,14) (5,8) (5,11) (5,16) (6,12) (6,17) (6,9) (6,16) (7,17) (7,14) (7,9) (7,11) (7,16) (8,17) (8,14) (9,17) (9,14) (9,11) (9,16) (11,12) (11,17) (11,14) (11,13) (12,14) (13,17) (13,14) (13,16) (14,17) (16,17)\nIs there a path between node 16 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph719-18_15", + "image": "data/connectivity/graph_visual/medium/graph719.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,22) (0,21) (0,7) (0,16) (0,14) (1,22) (1,10) (1,16) (2,6) (2,13) (2,24) (2,19) (2,3) (2,9) (2,23) (2,4) (2,15) (2,17) (2,11) (2,5) (3,6) (3,24) (3,19) (3,9) (3,23) (3,4) (3,12) (3,15) (3,17) (3,11) (3,5) (3,8) (4,6) (4,24) (4,9) (4,23) (4,15) (4,17) (4,18) (4,11) (4,5) (5,6) (5,13) (5,24) (5,19) (5,9) (5,23) (5,15) (5,18) (5,8) (6,24) (6,15) (6,17) (6,18) (6,8) (7,20) (7,22) (7,16) (8,24) (8,9) (8,12) (8,15) (8,17) (8,18) (9,13) (9,24) (9,23) (9,12) (9,17) (9,11) (10,20) (10,21) (10,16) (10,14) (11,24) (11,15) (11,17) (11,18) (12,13) (12,19) (12,17) (12,18) (13,24) (13,23) (13,17) (13,18) (14,20) (14,21) (14,16) (15,24) (15,19) (15,23) (15,18) (16,20) (16,21) (17,24) (17,23) (18,19) (19,24) (20,22) (20,21) (21,22)\nIs there a path between node 18 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph295-18_19", + "image": "data/connectivity/graph_visual/medium/graph295.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,7) (1,10) (1,7) (1,12) (1,16) (1,6) (2,15) (3,14) (3,4) (3,5) (3,11) (4,17) (4,19) (4,10) (4,13) (4,12) (4,6) (5,19) (5,16) (6,17) (6,14) (6,9) (6,12) (6,16) (7,14) (7,11) (7,16) (9,14) (9,11) (9,15) (9,13) (9,12) (10,17) (10,14) (10,19) (10,11) (10,12) (11,14) (12,17) (14,17) (16,17) (16,19) (17,19)\nIs there a path between node 18 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph651-11_2", + "image": "data/connectivity/graph_visual/medium/graph651.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,4) (0,11) (0,18) (0,2) (0,8) (0,19) (0,23) (0,13) (0,7) (0,3) (0,16) (1,21) (1,22) (1,14) (1,17) (2,9) (2,4) (2,11) (2,18) (2,8) (2,19) (2,23) (2,13) (2,7) (2,3) (2,6) (3,9) (3,4) (3,11) (3,18) (3,8) (3,23) (3,13) (3,7) (3,6) (4,9) (4,11) (4,18) (4,23) (5,20) (5,10) (6,9) (6,18) (6,8) (6,13) (6,7) (6,16) (7,9) (7,11) (7,18) (7,8) (7,19) (7,23) (7,13) (7,16) (8,9) (8,11) (8,18) (8,19) (8,23) (8,13) (9,19) (9,23) (9,13) (11,18) (11,19) (11,23) (11,16) (12,21) (12,22) (12,15) (13,19) (13,23) (14,21) (14,22) (14,15) (15,21) (15,22) (16,18) (16,23) (17,21) (18,19) (19,23) (21,22)\nIs there a path between node 11 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph105-5_2", + "image": "data/connectivity/graph_visual/medium/graph105.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,11) (0,7) (0,4) (0,10) (0,5) (0,13) (0,12) (0,1) (0,2) (0,3) (0,15) (0,6) (0,8) (0,14) (1,11) (1,7) (1,4) (1,10) (1,5) (1,13) (1,12) (1,2) (1,3) (1,15) (1,6) (1,8) (1,14) (2,11) (2,7) (2,4) (2,10) (2,5) (2,13) (2,12) (2,3) (2,15) (2,6) (2,8) (2,14) (3,11) (3,7) (3,4) (3,10) (3,5) (3,13) (3,12) (3,15) (3,6) (3,8) (3,14) (4,11) (4,7) (4,10) (4,5) (4,13) (4,12) (4,15) (4,6) (4,8) (4,14) (5,11) (5,7) (5,10) (5,13) (5,12) (5,15) (5,6) (5,8) (5,14) (6,11) (6,7) (6,10) (6,13) (6,12) (6,15) (6,8) (6,14) (7,11) (7,10) (7,13) (7,12) (7,15) (7,8) (7,14) (8,11) (8,10) (8,13) (8,12) (8,15) (8,14) (10,11) (10,13) (10,12) (10,15) (10,14) (11,13) (11,12) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nIs there a path between node 5 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph194-12_14", + "image": "data/connectivity/graph_visual/medium/graph194.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,11) (0,16) (0,13) (0,8) (0,1) (0,15) (0,3) (0,14) (0,9) (1,11) (1,16) (1,13) (1,8) (1,15) (1,3) (1,14) (1,9) (2,7) (2,6) (2,4) (2,5) (2,17) (2,12) (3,11) (3,16) (3,13) (3,8) (3,15) (3,14) (3,9) (4,7) (4,6) (4,5) (4,17) (4,12) (5,7) (5,6) (5,17) (5,12) (6,7) (6,17) (6,12) (7,17) (7,12) (8,11) (8,16) (8,13) (8,15) (8,14) (8,9) (9,11) (9,16) (9,13) (9,15) (9,14) (11,16) (11,13) (11,15) (11,14) (12,17) (13,16) (13,15) (13,14) (14,16) (14,15) (15,16)\nIs there a path between node 12 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph556-12_2", + "image": "data/connectivity/graph_visual/medium/graph556.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,20) (0,7) (0,2) (1,16) (1,18) (1,4) (1,23) (1,15) (1,19) (1,6) (1,5) (1,12) (2,8) (2,10) (2,22) (2,7) (2,13) (3,21) (4,16) (4,18) (4,23) (4,11) (4,17) (4,15) (4,19) (4,6) (4,12) (5,16) (5,18) (5,14) (5,11) (5,17) (5,15) (5,19) (5,6) (5,12) (6,16) (6,18) (6,14) (6,11) (6,17) (6,15) (6,12) (7,8) (7,10) (7,22) (7,20) (7,13) (8,9) (8,10) (8,22) (8,20) (8,13) (9,22) (9,13) (10,22) (10,20) (10,13) (11,16) (11,18) (11,14) (11,23) (11,17) (11,15) (11,19) (11,12) (12,16) (12,18) (12,14) (12,23) (12,17) (12,15) (12,19) (13,22) (13,20) (14,18) (14,23) (14,17) (14,15) (15,16) (15,18) (15,23) (15,17) (15,19) (16,23) (17,18) (17,23) (17,19) (18,23) (18,19) (19,23) (20,22)\nIs there a path between node 12 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph531-20_5", + "image": "data/connectivity/graph_visual/medium/graph531.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,13) (0,7) (0,4) (0,9) (0,21) (0,16) (0,1) (0,18) (0,11) (0,8) (0,6) (0,15) (0,14) (0,12) (0,20) (0,2) (0,22) (1,10) (1,13) (1,7) (1,4) (1,9) (1,21) (1,16) (1,18) (1,11) (1,8) (1,6) (1,15) (1,14) (1,12) (1,20) (1,2) (1,22) (2,10) (2,13) (2,7) (2,4) (2,9) (2,21) (2,16) (2,18) (2,11) (2,8) (2,6) (2,15) (2,14) (2,12) (2,20) (2,22) (3,17) (3,19) (3,5) (4,10) (4,13) (4,7) (4,9) (4,21) (4,16) (4,18) (4,11) (4,8) (4,6) (4,15) (4,14) (4,12) (4,20) (4,22) (5,17) (5,19) (6,10) (6,13) (6,7) (6,9) (6,21) (6,16) (6,18) (6,11) (6,8) (6,15) (6,14) (6,12) (6,20) (6,22) (7,10) (7,13) (7,9) (7,21) (7,16) (7,18) (7,11) (7,8) (7,15) (7,14) (7,12) (7,20) (7,22) (8,10) (8,13) (8,9) (8,21) (8,16) (8,18) (8,11) (8,15) (8,14) (8,12) (8,20) (8,22) (9,10) (9,13) (9,21) (9,16) (9,18) (9,11) (9,15) (9,14) (9,12) (9,20) (9,22) (10,13) (10,21) (10,16) (10,18) (10,11) (10,15) (10,14) (10,12) (10,20) (10,22) (11,13) (11,21) (11,16) (11,18) (11,15) (11,14) (11,12) (11,20) (11,22) (12,13) (12,21) (12,16) (12,18) (12,15) (12,14) (12,20) (12,22) (13,21) (13,16) (13,18) (13,15) (13,14) (13,20) (13,22) (14,21) (14,16) (14,18) (14,15) (14,20) (14,22) (15,21) (15,16) (15,18) (15,20) (15,22) (16,21) (16,18) (16,20) (16,22) (17,19) (18,21) (18,20) (18,22) (20,21) (20,22) (21,22)\nIs there a path between node 20 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph139-13_9", + "image": "data/connectivity/graph_visual/medium/graph139.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,10) (0,17) (1,13) (1,14) (2,11) (3,11) (5,6) (5,13) (6,12) (6,14) (7,16) (8,17) (10,17) (12,13) (12,15) (12,14) (13,15)\nIs there a path between node 13 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph2-6_1", + "image": "data/connectivity/graph_visual/medium/graph2.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,3) (0,7) (0,10) (0,6) (0,2) (0,8) (0,4) (0,1) (1,3) (1,7) (1,10) (1,6) (1,2) (1,8) (1,4) (2,3) (2,7) (2,10) (2,6) (2,8) (2,4) (3,7) (3,10) (3,6) (3,8) (3,4) (4,7) (4,10) (4,6) (4,8) (5,9) (6,7) (6,10) (6,8) (7,10) (7,8) (8,10)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph602-21_5", + "image": "data/connectivity/graph_visual/medium/graph602.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,7) (0,1) (0,21) (0,20) (0,9) (1,7) (1,21) (1,20) (1,9) (2,5) (2,11) (2,23) (2,12) (2,22) (2,6) (2,10) (2,19) (3,8) (3,15) (3,17) (4,21) (5,11) (5,12) (5,22) (5,13) (5,18) (5,10) (6,23) (6,22) (6,13) (6,18) (6,10) (6,19) (6,16) (7,21) (7,9) (8,15) (8,17) (9,21) (10,11) (10,12) (10,22) (10,13) (10,19) (11,23) (11,12) (11,22) (11,13) (11,18) (11,19) (11,16) (12,23) (12,22) (12,13) (12,18) (12,19) (12,16) (13,23) (13,22) (13,18) (13,19) (13,16) (14,15) (16,23) (16,22) (16,18) (18,23) (18,22) (18,19) (19,23) (19,22) (20,21) (22,23)\nIs there a path between node 21 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph660-7_17", + "image": "data/connectivity/graph_visual/medium/graph660.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,11) (0,3) (0,2) (0,9) (0,5) (0,10) (0,23) (1,13) (1,17) (1,20) (1,8) (1,14) (1,4) (2,22) (2,11) (2,9) (2,10) (2,23) (3,21) (3,11) (3,5) (3,15) (3,23) (3,12) (4,18) (4,19) (4,13) (4,8) (4,16) (5,11) (5,9) (5,10) (5,15) (6,18) (6,19) (6,13) (6,20) (6,8) (6,16) (6,14) (7,19) (7,20) (7,8) (7,16) (7,14) (8,18) (8,19) (8,13) (8,17) (8,16) (8,14) (9,22) (9,21) (9,10) (9,15) (9,23) (9,12) (10,22) (10,21) (10,15) (10,12) (11,22) (11,15) (11,23) (11,12) (12,22) (12,15) (12,23) (13,18) (13,19) (13,20) (13,16) (13,14) (14,18) (14,19) (14,17) (14,20) (14,16) (15,22) (15,21) (16,18) (16,19) (16,17) (17,18) (17,19) (17,20) (18,19) (18,20) (19,20) (21,22) (21,23) (22,23)\nIs there a path between node 7 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph431-15_19", + "image": "data/connectivity/graph_visual/medium/graph431.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,16) (0,3) (0,5) (0,19) (1,21) (2,21) (2,10) (2,19) (3,4) (3,19) (4,15) (4,10) (4,19) (5,16) (6,8) (8,13) (10,17) (11,13) (14,20) (15,17) (16,17) (17,19)\nIs there a path between node 15 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph245-10_14", + "image": "data/connectivity/graph_visual/medium/graph245.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,3) (0,13) (0,2) (0,15) (0,6) (0,17) (0,8) (0,16) (0,18) (0,9) (0,12) (0,11) (1,10) (1,14) (1,7) (1,5) (1,4) (2,3) (2,13) (2,15) (2,6) (2,17) (2,8) (2,16) (2,18) (2,9) (2,12) (2,11) (3,13) (3,15) (3,6) (3,17) (3,8) (3,16) (3,18) (3,9) (3,12) (3,11) (4,10) (4,14) (4,7) (4,5) (5,10) (5,14) (5,7) (6,13) (6,15) (6,17) (6,8) (6,16) (6,18) (6,9) (6,12) (6,11) (7,10) (7,14) (8,13) (8,15) (8,17) (8,16) (8,18) (8,9) (8,12) (8,11) (9,13) (9,15) (9,17) (9,16) (9,18) (9,12) (9,11) (10,14) (11,13) (11,15) (11,17) (11,16) (11,18) (11,12) (12,13) (12,15) (12,17) (12,16) (12,18) (13,15) (13,17) (13,16) (13,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 10 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph448-4_21", + "image": "data/connectivity/graph_visual/medium/graph448.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,17) (0,19) (0,1) (0,6) (0,5) (0,7) (0,2) (0,14) (0,4) (0,10) (1,17) (1,6) (1,5) (1,12) (1,7) (1,13) (1,2) (1,20) (1,14) (1,10) (2,9) (2,17) (2,16) (2,19) (2,6) (2,12) (2,7) (2,18) (2,13) (2,20) (2,14) (2,4) (2,10) (3,21) (3,15) (3,11) (4,9) (4,17) (4,16) (4,19) (4,6) (4,5) (4,12) (4,7) (4,13) (4,10) (5,9) (5,17) (5,16) (5,12) (5,18) (5,13) (5,20) (5,14) (6,17) (6,16) (6,12) (6,7) (6,18) (6,20) (6,10) (7,9) (7,17) (7,16) (7,19) (7,13) (7,20) (7,14) (7,10) (8,21) (8,15) (9,16) (9,19) (9,18) (9,13) (9,20) (9,14) (9,10) (10,17) (10,16) (10,18) (10,13) (10,20) (10,14) (11,21) (12,17) (12,16) (12,19) (13,17) (13,16) (13,19) (14,17) (14,19) (14,20) (15,21) (16,17) (16,18) (16,20) (17,19) (17,20) (18,19) (18,20) (19,20)\nIs there a path between node 4 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph504-2_19", + "image": "data/connectivity/graph_visual/medium/graph504.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,3) (0,20) (0,18) (0,14) (0,10) (0,11) (1,16) (1,2) (1,18) (1,13) (1,4) (1,8) (2,11) (2,8) (2,12) (3,16) (3,14) (3,9) (3,10) (3,12) (4,20) (4,6) (4,8) (6,20) (6,14) (6,11) (6,12) (7,21) (7,13) (7,12) (8,21) (8,10) (8,11) (9,16) (9,20) (9,10) (10,15) (10,14) (10,17) (10,12) (11,16) (11,20) (11,21) (11,13) (12,14) (14,21) (14,17) (15,20) (15,17) (17,20) (18,21)\nIs there a path between node 2 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph486-15_18", + "image": "data/connectivity/graph_visual/medium/graph486.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,19) (0,1) (0,11) (0,21) (0,13) (1,11) (1,6) (1,21) (1,22) (2,14) (2,7) (2,8) (2,10) (2,9) (2,4) (3,18) (3,17) (3,20) (3,15) (4,14) (4,16) (4,7) (4,8) (4,9) (4,5) (5,14) (5,8) (5,10) (5,9) (6,19) (6,12) (6,11) (6,21) (6,13) (7,14) (7,16) (7,8) (7,10) (8,14) (8,16) (8,10) (9,10) (10,14) (10,16) (11,12) (11,21) (12,19) (12,21) (12,22) (12,13) (13,21) (13,22) (14,16) (15,18) (15,17) (17,18) (17,20) (19,21) (19,22) (21,22)\nIs there a path between node 15 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph494-3_21", + "image": "data/connectivity/graph_visual/medium/graph494.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,13) (1,13) (2,14) (2,17) (2,4) (2,18) (2,15) (2,22) (2,5) (2,21) (2,7) (2,20) (2,12) (2,16) (2,10) (2,9) (2,6) (2,11) (2,19) (2,8) (2,3) (3,14) (3,17) (3,4) (3,18) (3,15) (3,22) (3,5) (3,21) (3,7) (3,20) (3,12) (3,16) (3,10) (3,9) (3,6) (3,11) (3,19) (3,8) (4,14) (4,17) (4,18) (4,15) (4,22) (4,5) (4,21) (4,7) (4,20) (4,12) (4,16) (4,10) (4,9) (4,6) (4,11) (4,19) (4,8) (5,14) (5,17) (5,18) (5,15) (5,22) (5,21) (5,7) (5,20) (5,12) (5,16) (5,10) (5,9) (5,6) (5,11) (5,19) (5,8) (6,14) (6,17) (6,18) (6,15) (6,22) (6,21) (6,7) (6,20) (6,12) (6,16) (6,10) (6,9) (6,11) (6,19) (6,8) (7,14) (7,17) (7,18) (7,15) (7,22) (7,21) (7,20) (7,12) (7,16) (7,10) (7,9) (7,11) (7,19) (7,8) (8,14) (8,17) (8,18) (8,15) (8,22) (8,21) (8,20) (8,12) (8,16) (8,10) (8,9) (8,11) (8,19) (9,14) (9,17) (9,18) (9,15) (9,22) (9,21) (9,20) (9,12) (9,16) (9,10) (9,11) (9,19) (10,14) (10,17) (10,18) (10,15) (10,22) (10,21) (10,20) (10,12) (10,16) (10,11) (10,19) (11,14) (11,17) (11,18) (11,15) (11,22) (11,21) (11,20) (11,12) (11,16) (11,19) (12,14) (12,17) (12,18) (12,15) (12,22) (12,21) (12,20) (12,16) (12,19) (14,17) (14,18) (14,15) (14,22) (14,21) (14,20) (14,16) (14,19) (15,17) (15,18) (15,22) (15,21) (15,20) (15,16) (15,19) (16,17) (16,18) (16,22) (16,21) (16,20) (16,19) (17,18) (17,22) (17,21) (17,20) (17,19) (18,22) (18,21) (18,20) (18,19) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 3 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph451-17_21", + "image": "data/connectivity/graph_visual/medium/graph451.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,19) (0,3) (0,1) (0,16) (0,2) (1,4) (1,19) (1,20) (1,16) (1,12) (2,15) (2,3) (2,20) (2,16) (2,18) (3,4) (3,20) (3,16) (3,18) (4,15) (4,20) (4,16) (5,11) (5,9) (5,17) (5,21) (5,7) (5,14) (5,6) (6,8) (6,17) (6,21) (6,7) (6,13) (7,11) (7,10) (7,9) (7,8) (7,21) (7,13) (7,14) (8,11) (8,9) (8,17) (8,21) (8,13) (8,14) (9,10) (9,17) (9,14) (10,21) (11,21) (11,13) (11,14) (12,19) (12,16) (12,18) (13,17) (13,21) (14,17) (15,19) (15,20) (15,16) (15,18) (16,19) (16,18) (18,19) (18,20) (19,20)\nIs there a path between node 17 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph420-6_12", + "image": "data/connectivity/graph_visual/medium/graph420.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,20) (0,15) (0,1) (0,17) (0,16) (0,19) (0,2) (0,7) (0,5) (0,8) (0,14) (0,6) (0,18) (0,9) (0,3) (0,12) (1,4) (1,20) (1,15) (1,17) (1,16) (1,19) (1,2) (1,7) (1,5) (1,8) (1,14) (1,6) (1,18) (1,9) (1,3) (1,12) (2,4) (2,20) (2,15) (2,17) (2,16) (2,19) (2,7) (2,5) (2,8) (2,14) (2,6) (2,18) (2,9) (2,3) (2,12) (3,4) (3,20) (3,15) (3,17) (3,16) (3,19) (3,7) (3,5) (3,8) (3,14) (3,6) (3,18) (3,9) (3,12) (4,20) (4,15) (4,17) (4,16) (4,19) (4,7) (4,5) (4,8) (4,14) (4,6) (4,18) (4,9) (4,12) (5,20) (5,15) (5,17) (5,16) (5,19) (5,7) (5,8) (5,14) (5,6) (5,18) (5,9) (5,12) (6,20) (6,15) (6,17) (6,16) (6,19) (6,7) (6,8) (6,14) (6,18) (6,9) (6,12) (7,20) (7,15) (7,17) (7,16) (7,19) (7,8) (7,14) (7,18) (7,9) (7,12) (8,20) (8,15) (8,17) (8,16) (8,19) (8,14) (8,18) (8,9) (8,12) (9,20) (9,15) (9,17) (9,16) (9,19) (9,14) (9,18) (9,12) (10,13) (10,11) (11,13) (12,20) (12,15) (12,17) (12,16) (12,19) (12,14) (12,18) (14,20) (14,15) (14,17) (14,16) (14,19) (14,18) (15,20) (15,17) (15,16) (15,19) (15,18) (16,20) (16,17) (16,19) (16,18) (17,20) (17,19) (17,18) (18,20) (18,19) (19,20)\nIs there a path between node 6 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph299-7_9", + "image": "data/connectivity/graph_visual/medium/graph299.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (1,3) (1,2) (1,7) (1,5) (1,18) (1,14) (1,17) (1,12) (1,11) (1,10) (1,19) (1,13) (1,4) (1,9) (2,7) (2,18) (2,16) (2,6) (2,11) (2,10) (2,19) (2,13) (2,4) (2,9) (2,15) (3,7) (3,18) (3,12) (3,6) (3,10) (3,19) (3,13) (3,4) (3,9) (4,7) (4,5) (4,14) (4,17) (4,16) (4,6) (4,11) (4,10) (4,19) (4,9) (5,7) (5,14) (5,17) (5,16) (5,12) (5,6) (5,11) (5,10) (5,13) (5,9) (5,15) (6,14) (6,17) (6,16) (6,12) (6,10) (6,19) (6,9) (7,18) (7,14) (7,17) (7,16) (7,12) (7,10) (7,19) (7,13) (7,9) (7,15) (9,18) (9,14) (9,17) (9,16) (9,12) (9,11) (9,19) (9,13) (9,15) (10,18) (10,14) (10,17) (10,12) (10,11) (10,19) (10,15) (11,18) (11,12) (11,19) (11,15) (12,18) (12,14) (12,17) (12,19) (12,13) (12,15) (13,18) (13,14) (13,17) (14,17) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19)\nIs there a path between node 7 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph474-8_5", + "image": "data/connectivity/graph_visual/medium/graph474.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,12) (0,21) (0,17) (0,16) (0,20) (1,15) (1,14) (1,20) (1,19) (1,9) (1,2) (1,6) (1,3) (2,18) (2,20) (2,19) (2,10) (3,16) (3,13) (4,5) (6,14) (6,18) (6,11) (6,22) (6,7) (6,13) (7,21) (7,15) (7,14) (7,18) (7,19) (7,11) (7,8) (8,12) (8,21) (8,15) (8,14) (8,20) (8,11) (8,9) (8,10) (9,15) (9,11) (9,10) (9,13) (10,18) (10,20) (10,19) (10,11) (10,22) (11,15) (11,16) (11,22) (12,21) (12,17) (12,18) (13,21) (13,17) (13,20) (13,19) (14,20) (15,21) (15,17) (15,18) (16,18) (16,20) (16,19) (17,20) (17,19) (17,22) (18,22)\nIs there a path between node 8 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph800-9_19", + "image": "data/connectivity/graph_visual/medium/graph800.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,4) (0,22) (1,13) (1,4) (1,6) (1,2) (1,10) (1,3) (2,10) (2,23) (2,5) (3,4) (3,17) (3,23) (3,12) (4,12) (5,18) (5,15) (5,12) (5,22) (6,17) (7,19) (10,17) (10,23) (10,14) (10,15) (11,13) (12,18) (12,14) (13,17) (13,23) (13,22) (14,23) (14,15) (15,23) (16,20) (17,18) (17,23) (18,23) (19,24) (19,21) (20,21)\nIs there a path between node 9 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph619-23_11", + "image": "data/connectivity/graph_visual/medium/graph619.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,18) (0,8) (0,2) (0,12) (0,22) (0,19) (0,10) (0,21) (0,3) (0,14) (0,20) (0,6) (0,15) (0,23) (0,16) (0,4) (0,17) (0,1) (1,18) (1,8) (1,2) (1,12) (1,22) (1,19) (1,10) (1,21) (1,3) (1,14) (1,20) (1,6) (1,15) (1,23) (1,16) (1,4) (1,17) (2,18) (2,8) (2,12) (2,22) (2,19) (2,10) (2,21) (2,3) (2,14) (2,20) (2,6) (2,15) (2,23) (2,16) (2,4) (2,17) (3,18) (3,8) (3,12) (3,22) (3,19) (3,10) (3,21) (3,14) (3,20) (3,6) (3,15) (3,23) (3,16) (3,4) (3,17) (4,18) (4,8) (4,12) (4,22) (4,19) (4,10) (4,21) (4,14) (4,20) (4,6) (4,15) (4,23) (4,16) (4,17) (5,9) (5,11) (5,7) (5,13) (6,18) (6,8) (6,12) (6,22) (6,19) (6,10) (6,21) (6,14) (6,20) (6,15) (6,23) (6,16) (6,17) (7,9) (7,11) (7,13) (8,18) (8,12) (8,22) (8,19) (8,10) (8,21) (8,14) (8,20) (8,15) (8,23) (8,16) (8,17) (9,11) (9,13) (10,18) (10,12) (10,22) (10,19) (10,21) (10,14) (10,20) (10,15) (10,23) (10,16) (10,17) (11,13) (12,18) (12,22) (12,19) (12,21) (12,14) (12,20) (12,15) (12,23) (12,16) (12,17) (14,18) (14,22) (14,19) (14,21) (14,20) (14,15) (14,23) (14,16) (14,17) (15,18) (15,22) (15,19) (15,21) (15,20) (15,23) (15,16) (15,17) (16,18) (16,22) (16,19) (16,21) (16,20) (16,23) (16,17) (17,18) (17,22) (17,19) (17,21) (17,20) (17,23) (18,22) (18,19) (18,21) (18,20) (18,23) (19,22) (19,21) (19,20) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 23 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph284-1_18", + "image": "data/connectivity/graph_visual/medium/graph284.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,2) (1,7) (1,15) (2,12) (2,15) (3,17) (3,7) (3,12) (3,15) (4,14) (4,16) (4,15) (5,9) (5,6) (6,18) (6,9) (6,13) (7,12) (8,12) (9,18) (10,19) (14,16) (14,15) (16,17)\nIs there a path between node 1 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph670-9_1", + "image": "data/connectivity/graph_visual/medium/graph670.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,6) (0,21) (0,18) (0,20) (0,16) (1,14) (1,23) (1,7) (1,3) (2,23) (2,7) (2,3) (3,14) (3,23) (3,7) (3,22) (4,11) (5,6) (5,21) (5,20) (5,16) (5,15) (6,21) (6,20) (6,16) (6,15) (7,23) (7,22) (8,12) (8,19) (8,17) (9,13) (9,12) (9,19) (9,10) (10,13) (10,12) (10,19) (10,17) (12,13) (12,19) (12,17) (13,17) (14,23) (15,21) (15,18) (15,16) (16,21) (16,18) (16,20) (17,19) (18,21) (18,20)\nIs there a path between node 9 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph65-3_5", + "image": "data/connectivity/graph_visual/medium/graph65.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (0,4) (0,13) (0,8) (0,6) (0,11) (0,12) (0,10) (0,9) (1,3) (1,5) (1,7) (2,4) (2,13) (2,8) (2,6) (2,11) (2,12) (2,10) (2,9) (3,5) (3,7) (4,13) (4,8) (4,6) (4,11) (4,12) (4,10) (4,9) (5,7) (6,13) (6,8) (6,11) (6,12) (6,10) (6,9) (8,13) (8,11) (8,12) (8,10) (8,9) (9,13) (9,11) (9,12) (9,10) (10,13) (10,11) (10,12) (11,13) (11,12) (12,13)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph229-1_8", + "image": "data/connectivity/graph_visual/medium/graph229.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,7) (0,4) (1,18) (1,6) (1,13) (2,16) (2,12) (2,6) (3,5) (3,10) (3,17) (3,13) (4,7) (5,18) (5,6) (5,15) (5,10) (5,17) (10,15) (10,14) (11,17) (12,13) (12,14) (14,18) (14,15) (15,17) (16,18)\nIs there a path between node 1 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph470-8_11", + "image": "data/connectivity/graph_visual/medium/graph470.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,15) (0,22) (0,18) (1,5) (1,14) (1,21) (1,16) (1,19) (1,3) (1,17) (1,13) (1,11) (1,2) (1,20) (1,8) (1,6) (1,12) (1,9) (1,7) (2,5) (2,14) (2,21) (2,16) (2,19) (2,3) (2,17) (2,13) (2,11) (2,20) (2,8) (2,6) (2,12) (2,9) (2,7) (3,5) (3,14) (3,21) (3,16) (3,19) (3,17) (3,13) (3,11) (3,20) (3,8) (3,6) (3,12) (3,9) (3,7) (5,14) (5,21) (5,16) (5,19) (5,17) (5,13) (5,11) (5,20) (5,8) (5,6) (5,12) (5,9) (5,7) (6,14) (6,21) (6,16) (6,19) (6,17) (6,13) (6,11) (6,20) (6,8) (6,12) (6,9) (6,7) (7,14) (7,21) (7,16) (7,19) (7,17) (7,13) (7,11) (7,20) (7,8) (7,12) (7,9) (8,14) (8,21) (8,16) (8,19) (8,17) (8,13) (8,11) (8,20) (8,12) (8,9) (9,14) (9,21) (9,16) (9,19) (9,17) (9,13) (9,11) (9,20) (9,12) (10,15) (10,22) (10,18) (11,14) (11,21) (11,16) (11,19) (11,17) (11,13) (11,20) (11,12) (12,14) (12,21) (12,16) (12,19) (12,17) (12,13) (12,20) (13,14) (13,21) (13,16) (13,19) (13,17) (13,20) (14,21) (14,16) (14,19) (14,17) (14,20) (15,22) (15,18) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (18,22) (19,21) (19,20) (20,21)\nIs there a path between node 8 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph191-16_6", + "image": "data/connectivity/graph_visual/medium/graph191.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,5) (0,10) (0,11) (0,6) (0,2) (0,15) (0,4) (0,8) (0,7) (0,17) (0,16) (0,12) (0,9) (0,3) (0,14) (1,13) (2,5) (2,10) (2,11) (2,6) (2,15) (2,4) (2,8) (2,7) (2,17) (2,16) (2,12) (2,9) (2,3) (2,14) (3,5) (3,10) (3,11) (3,6) (3,15) (3,4) (3,8) (3,7) (3,17) (3,16) (3,12) (3,9) (3,14) (4,5) (4,10) (4,11) (4,6) (4,15) (4,8) (4,7) (4,17) (4,16) (4,12) (4,9) (4,14) (5,10) (5,11) (5,6) (5,15) (5,8) (5,7) (5,17) (5,16) (5,12) (5,9) (5,14) (6,10) (6,11) (6,15) (6,8) (6,7) (6,17) (6,16) (6,12) (6,9) (6,14) (7,10) (7,11) (7,15) (7,8) (7,17) (7,16) (7,12) (7,9) (7,14) (8,10) (8,11) (8,15) (8,17) (8,16) (8,12) (8,9) (8,14) (9,10) (9,11) (9,15) (9,17) (9,16) (9,12) (9,14) (10,11) (10,15) (10,17) (10,16) (10,12) (10,14) (11,15) (11,17) (11,16) (11,12) (11,14) (12,15) (12,17) (12,16) (12,14) (14,15) (14,17) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 16 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph312-6_13", + "image": "data/connectivity/graph_visual/medium/graph312.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (0,12) (0,6) (0,18) (0,16) (1,15) (1,17) (1,2) (1,19) (1,5) (1,14) (1,10) (1,13) (1,4) (1,7) (1,11) (1,9) (2,15) (2,17) (2,19) (2,5) (2,14) (2,10) (2,13) (2,4) (2,7) (2,11) (2,9) (4,15) (4,17) (4,19) (4,5) (4,14) (4,10) (4,13) (4,7) (4,11) (4,9) (5,15) (5,17) (5,19) (5,14) (5,10) (5,13) (5,7) (5,11) (5,9) (6,8) (6,12) (6,18) (6,16) (7,15) (7,17) (7,19) (7,14) (7,10) (7,13) (7,11) (7,9) (8,12) (8,18) (8,16) (9,15) (9,17) (9,19) (9,14) (9,10) (9,13) (9,11) (10,15) (10,17) (10,19) (10,14) (10,13) (10,11) (11,15) (11,17) (11,19) (11,14) (11,13) (12,18) (12,16) (13,15) (13,17) (13,19) (13,14) (14,15) (14,17) (14,19) (15,17) (15,19) (16,18) (17,19)\nIs there a path between node 6 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph841-12_19", + "image": "data/connectivity/graph_visual/medium/graph841.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,2) (0,7) (0,8) (0,4) (0,13) (1,6) (1,12) (1,14) (1,17) (1,16) (1,10) (1,18) (1,21) (1,15) (1,24) (1,11) (1,22) (1,9) (1,23) (2,20) (2,7) (2,8) (2,4) (2,13) (3,19) (3,5) (4,20) (4,7) (4,8) (4,13) (5,19) (6,12) (6,14) (6,17) (6,16) (6,10) (6,18) (6,21) (6,15) (6,24) (6,11) (6,22) (6,9) (6,23) (7,20) (7,8) (7,13) (8,20) (8,13) (9,12) (9,14) (9,17) (9,16) (9,10) (9,18) (9,21) (9,15) (9,24) (9,11) (9,22) (9,23) (10,12) (10,14) (10,17) (10,16) (10,18) (10,21) (10,15) (10,24) (10,11) (10,22) (10,23) (11,12) (11,14) (11,17) (11,16) (11,18) (11,21) (11,15) (11,24) (11,22) (11,23) (12,14) (12,17) (12,16) (12,18) (12,21) (12,15) (12,24) (12,22) (12,23) (13,20) (14,17) (14,16) (14,18) (14,21) (14,15) (14,24) (14,22) (14,23) (15,17) (15,16) (15,18) (15,21) (15,24) (15,22) (15,23) (16,17) (16,18) (16,21) (16,24) (16,22) (16,23) (17,18) (17,21) (17,24) (17,22) (17,23) (18,21) (18,24) (18,22) (18,23) (21,24) (21,22) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 12 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph723-9_23", + "image": "data/connectivity/graph_visual/medium/graph723.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,22) (0,15) (0,6) (0,7) (0,11) (0,9) (0,1) (0,4) (0,14) (0,23) (0,17) (0,21) (0,20) (0,8) (0,24) (0,18) (1,3) (1,22) (1,15) (1,6) (1,7) (1,11) (1,9) (1,4) (1,14) (1,23) (1,17) (1,21) (1,20) (1,8) (1,24) (1,18) (2,12) (2,10) (2,13) (2,16) (3,22) (3,15) (3,6) (3,7) (3,11) (3,9) (3,4) (3,14) (3,23) (3,17) (3,21) (3,20) (3,8) (3,24) (3,18) (4,22) (4,15) (4,6) (4,7) (4,11) (4,9) (4,14) (4,23) (4,17) (4,21) (4,20) (4,8) (4,24) (4,18) (5,19) (6,22) (6,15) (6,7) (6,11) (6,9) (6,14) (6,23) (6,17) (6,21) (6,20) (6,8) (6,24) (6,18) (7,22) (7,15) (7,11) (7,9) (7,14) (7,23) (7,17) (7,21) (7,20) (7,8) (7,24) (7,18) (8,22) (8,15) (8,11) (8,9) (8,14) (8,23) (8,17) (8,21) (8,20) (8,24) (8,18) (9,22) (9,15) (9,11) (9,14) (9,23) (9,17) (9,21) (9,20) (9,24) (9,18) (10,12) (10,13) (10,16) (11,22) (11,15) (11,14) (11,23) (11,17) (11,21) (11,20) (11,24) (11,18) (12,13) (12,16) (13,16) (14,22) (14,15) (14,23) (14,17) (14,21) (14,20) (14,24) (14,18) (15,22) (15,23) (15,17) (15,21) (15,20) (15,24) (15,18) (17,22) (17,23) (17,21) (17,20) (17,24) (17,18) (18,22) (18,23) (18,21) (18,20) (18,24) (20,22) (20,23) (20,21) (20,24) (21,22) (21,23) (21,24) (22,23) (22,24) (23,24)\nIs there a path between node 9 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph177-4_11", + "image": "data/connectivity/graph_visual/medium/graph177.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,4) (0,11) (0,16) (0,7) (0,9) (0,6) (1,8) (1,13) (1,3) (1,15) (1,17) (1,10) (1,12) (1,2) (2,13) (2,3) (2,15) (2,17) (3,13) (3,15) (3,17) (3,10) (3,12) (4,7) (4,5) (4,14) (4,9) (4,6) (5,11) (5,16) (5,7) (5,14) (5,9) (5,6) (6,11) (6,16) (6,7) (6,14) (6,9) (7,11) (7,16) (7,14) (7,9) (8,13) (8,15) (8,17) (8,12) (9,16) (9,14) (10,13) (10,15) (10,17) (10,12) (11,16) (11,14) (13,15) (13,17) (15,17)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph553-7_9", + "image": "data/connectivity/graph_visual/medium/graph553.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,10) (0,9) (0,3) (1,10) (1,4) (1,2) (1,12) (1,14) (1,6) (1,15) (2,7) (2,10) (2,9) (2,17) (2,15) (3,20) (3,14) (3,18) (3,6) (3,15) (4,7) (4,16) (4,13) (4,9) (4,14) (4,21) (4,22) (4,17) (5,23) (5,11) (6,10) (6,16) (6,20) (6,22) (7,16) (7,20) (8,23) (8,19) (9,22) (12,14) (12,17) (13,16) (13,14) (13,17) (14,21) (15,21) (15,18) (16,18) (17,18) (19,23) (20,21)\nIs there a path between node 7 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph673-10_16", + "image": "data/connectivity/graph_visual/medium/graph673.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,15) (0,10) (0,9) (0,11) (0,19) (0,23) (0,20) (0,17) (0,16) (1,2) (1,10) (1,21) (1,9) (1,11) (1,12) (1,16) (1,6) (2,15) (2,21) (2,19) (2,23) (2,20) (2,16) (2,6) (3,8) (4,7) (6,10) (6,21) (6,9) (6,11) (6,19) (6,23) (6,20) (6,17) (6,16) (8,22) (8,18) (9,10) (9,21) (9,11) (9,19) (9,23) (9,12) (9,20) (9,17) (9,16) (10,15) (10,21) (10,11) (10,12) (10,20) (10,16) (11,15) (11,19) (11,20) (11,17) (11,16) (12,15) (12,21) (12,19) (12,23) (12,20) (13,14) (15,21) (15,23) (15,20) (15,16) (16,21) (16,19) (16,17) (17,21) (17,19) (17,20) (19,21) (19,20) (20,21) (20,23) (21,23)\nIs there a path between node 10 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph481-11_2", + "image": "data/connectivity/graph_visual/medium/graph481.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,14) (0,2) (0,17) (0,18) (0,9) (0,21) (0,8) (0,13) (0,10) (0,15) (0,12) (1,14) (1,17) (1,22) (1,18) (1,9) (1,21) (1,8) (1,13) (1,7) (1,15) (1,12) (1,19) (2,17) (2,18) (2,9) (2,21) (2,13) (2,7) (2,15) (2,19) (3,16) (5,6) (5,16) (6,16) (7,17) (7,18) (7,9) (7,21) (7,8) (7,10) (7,15) (7,20) (7,12) (7,19) (8,17) (8,22) (8,18) (8,21) (8,13) (8,10) (8,11) (8,20) (8,12) (8,19) (9,14) (9,17) (9,22) (9,18) (9,21) (9,13) (9,10) (9,15) (9,20) (10,14) (10,17) (10,22) (10,13) (10,15) (10,11) (10,20) (10,12) (10,19) (11,14) (11,18) (11,13) (11,15) (11,19) (12,14) (12,22) (12,21) (12,20) (13,17) (13,22) (13,18) (13,21) (13,15) (13,19) (14,17) (14,22) (14,18) (14,21) (14,15) (14,20) (14,19) (15,22) (15,18) (15,19) (17,18) (17,21) (17,19) (18,22) (18,21) (18,20) (18,19) (19,22) (20,22) (20,21) (21,22)\nIs there a path between node 11 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph451-15_16", + "image": "data/connectivity/graph_visual/medium/graph451.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,19) (0,3) (0,1) (0,16) (0,2) (1,4) (1,19) (1,20) (1,16) (1,12) (2,15) (2,3) (2,20) (2,16) (2,18) (3,4) (3,20) (3,16) (3,18) (4,15) (4,20) (4,16) (5,11) (5,9) (5,17) (5,21) (5,7) (5,14) (5,6) (6,8) (6,17) (6,21) (6,7) (6,13) (7,11) (7,10) (7,9) (7,8) (7,21) (7,13) (7,14) (8,11) (8,9) (8,17) (8,21) (8,13) (8,14) (9,10) (9,17) (9,14) (10,21) (11,21) (11,13) (11,14) (12,19) (12,16) (12,18) (13,17) (13,21) (14,17) (15,19) (15,20) (15,16) (15,18) (16,19) (16,18) (18,19) (18,20) (19,20)\nIs there a path between node 15 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph119-16_5", + "image": "data/connectivity/graph_visual/medium/graph119.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,6) (0,1) (0,3) (0,4) (0,15) (0,10) (1,5) (2,9) (2,8) (2,12) (2,7) (3,14) (3,9) (3,15) (3,5) (4,14) (4,9) (4,15) (4,5) (4,12) (5,14) (5,7) (6,15) (6,11) (6,12) (7,11) (7,12) (8,16) (9,11) (9,16) (11,12) (12,14)\nIs there a path between node 16 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph610-0_23", + "image": "data/connectivity/graph_visual/medium/graph610.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,21) (0,7) (0,14) (0,2) (0,19) (0,1) (0,18) (0,10) (0,13) (0,16) (1,23) (1,21) (1,7) (1,14) (1,2) (1,19) (1,18) (1,10) (1,13) (1,16) (2,23) (2,21) (2,7) (2,14) (2,19) (2,18) (2,10) (2,13) (2,16) (3,9) (3,12) (3,6) (3,15) (3,20) (3,5) (3,17) (3,22) (3,4) (3,8) (3,11) (4,9) (4,12) (4,6) (4,15) (4,20) (4,5) (4,17) (4,22) (4,8) (4,11) (5,9) (5,12) (5,6) (5,15) (5,20) (5,17) (5,22) (5,8) (5,11) (6,9) (6,12) (6,15) (6,20) (6,17) (6,22) (6,8) (6,11) (7,23) (7,21) (7,14) (7,19) (7,18) (7,10) (7,13) (7,16) (8,9) (8,12) (8,15) (8,20) (8,17) (8,22) (8,11) (9,12) (9,15) (9,20) (9,17) (9,22) (9,11) (10,23) (10,21) (10,14) (10,19) (10,18) (10,13) (10,16) (11,12) (11,15) (11,20) (11,17) (11,22) (12,15) (12,20) (12,17) (12,22) (13,23) (13,21) (13,14) (13,19) (13,18) (13,16) (14,23) (14,21) (14,19) (14,18) (14,16) (15,20) (15,17) (15,22) (16,23) (16,21) (16,19) (16,18) (17,20) (17,22) (18,23) (18,21) (18,19) (19,23) (19,21) (20,22) (21,23)\nIs there a path between node 0 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph658-22_20", + "image": "data/connectivity/graph_visual/medium/graph658.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,5) (0,18) (0,14) (0,15) (0,22) (0,3) (0,2) (0,13) (0,8) (1,23) (1,6) (1,10) (2,5) (2,9) (2,18) (2,4) (2,12) (2,15) (2,22) (2,19) (2,3) (2,13) (3,7) (3,5) (3,12) (3,14) (3,20) (3,15) (3,22) (3,16) (3,8) (4,17) (4,7) (4,9) (4,18) (4,12) (4,20) (4,22) (4,19) (4,13) (4,8) (5,17) (5,7) (5,9) (5,18) (5,12) (5,14) (5,20) (5,22) (5,19) (5,16) (5,13) (6,11) (6,23) (6,21) (6,10) (7,17) (7,9) (7,18) (7,12) (7,14) (7,22) (7,13) (7,8) (8,17) (8,9) (8,18) (8,12) (8,14) (8,20) (8,15) (8,22) (8,19) (8,16) (8,13) (9,12) (9,14) (9,20) (9,15) (9,22) (9,16) (10,11) (10,23) (10,21) (11,23) (11,21) (12,18) (12,14) (12,20) (12,15) (12,22) (12,19) (12,16) (13,17) (13,18) (13,14) (13,20) (13,15) (13,19) (14,17) (14,18) (14,20) (14,15) (14,22) (14,19) (14,16) (15,17) (15,20) (15,22) (16,17) (16,18) (16,20) (16,22) (16,19) (17,18) (17,20) (17,22) (17,19) (18,20) (18,19) (19,20) (20,22) (21,23)\nIs there a path between node 22 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph156-16_14", + "image": "data/connectivity/graph_visual/medium/graph156.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,8) (0,1) (1,12) (1,15) (2,9) (2,6) (3,10) (3,17) (3,15) (5,7) (6,10) (6,9) (6,11) (7,13) (8,17) (8,16) (10,15) (11,12) (15,17)\nIs there a path between node 16 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph720-14_0", + "image": "data/connectivity/graph_visual/medium/graph720.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,21) (0,11) (0,15) (0,4) (0,22) (0,5) (0,3) (0,6) (0,20) (0,13) (0,18) (0,9) (0,1) (0,12) (0,24) (0,16) (0,8) (0,23) (0,2) (1,21) (1,11) (1,15) (1,4) (1,22) (1,5) (1,3) (1,6) (1,20) (1,13) (1,18) (1,9) (1,12) (1,24) (1,16) (1,8) (1,23) (1,2) (2,21) (2,11) (2,15) (2,4) (2,22) (2,5) (2,3) (2,6) (2,20) (2,13) (2,18) (2,9) (2,12) (2,24) (2,16) (2,8) (2,23) (3,21) (3,11) (3,15) (3,4) (3,22) (3,5) (3,6) (3,20) (3,13) (3,18) (3,9) (3,12) (3,24) (3,16) (3,8) (3,23) (4,21) (4,11) (4,15) (4,22) (4,5) (4,6) (4,20) (4,13) (4,18) (4,9) (4,12) (4,24) (4,16) (4,8) (4,23) (5,21) (5,11) (5,15) (5,22) (5,6) (5,20) (5,13) (5,18) (5,9) (5,12) (5,24) (5,16) (5,8) (5,23) (6,21) (6,11) (6,15) (6,22) (6,20) (6,13) (6,18) (6,9) (6,12) (6,24) (6,16) (6,8) (6,23) (7,10) (7,14) (7,17) (7,19) (8,21) (8,11) (8,15) (8,22) (8,20) (8,13) (8,18) (8,9) (8,12) (8,24) (8,16) (8,23) (9,21) (9,11) (9,15) (9,22) (9,20) (9,13) (9,18) (9,12) (9,24) (9,16) (9,23) (10,14) (10,17) (10,19) (11,21) (11,15) (11,22) (11,20) (11,13) (11,18) (11,12) (11,24) (11,16) (11,23) (12,21) (12,15) (12,22) (12,20) (12,13) (12,18) (12,24) (12,16) (12,23) (13,21) (13,15) (13,22) (13,20) (13,18) (13,24) (13,16) (13,23) (14,17) (14,19) (15,21) (15,22) (15,20) (15,18) (15,24) (15,16) (15,23) (16,21) (16,22) (16,20) (16,18) (16,24) (16,23) (17,19) (18,21) (18,22) (18,20) (18,24) (18,23) (20,21) (20,22) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nIs there a path between node 14 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph718-11_8", + "image": "data/connectivity/graph_visual/medium/graph718.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,22) (0,2) (0,14) (0,11) (0,13) (0,12) (0,5) (0,6) (0,20) (0,16) (0,19) (1,7) (1,21) (1,23) (2,22) (2,14) (2,11) (2,9) (2,13) (2,4) (2,12) (2,24) (2,20) (2,16) (2,3) (2,19) (3,22) (3,14) (3,9) (3,13) (3,4) (3,12) (3,10) (3,5) (3,24) (3,6) (3,20) (3,19) (4,14) (4,11) (4,9) (4,8) (4,12) (4,10) (4,6) (4,16) (4,19) (5,14) (5,9) (5,13) (5,8) (5,12) (5,24) (5,20) (5,16) (6,14) (6,11) (6,9) (6,13) (6,8) (6,12) (6,10) (6,24) (6,16) (6,19) (7,17) (7,21) (8,22) (8,14) (8,11) (8,9) (8,13) (8,12) (8,10) (8,24) (8,20) (8,19) (9,22) (9,11) (9,13) (9,10) (9,24) (9,16) (9,19) (10,22) (10,11) (10,12) (10,24) (10,20) (10,19) (11,22) (11,13) (11,12) (11,24) (11,20) (12,14) (12,24) (12,20) (12,16) (12,19) (13,14) (13,20) (13,19) (14,22) (14,24) (14,20) (15,18) (15,17) (15,21) (16,22) (16,24) (16,20) (17,18) (17,21) (17,23) (19,22) (19,24) (19,20) (20,22) (20,24) (22,24)\nIs there a path between node 11 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph18-3_8", + "image": "data/connectivity/graph_visual/medium/graph18.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (0,2) (1,5) (1,2) (2,5) (2,10) (3,10) (3,4) (3,8) (4,5) (5,10) (5,8) (7,11) (8,10) (9,11)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph405-6_7", + "image": "data/connectivity/graph_visual/medium/graph405.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,18) (0,12) (0,8) (1,21) (1,5) (1,14) (2,17) (3,15) (3,21) (3,9) (3,5) (3,20) (3,19) (4,16) (4,7) (4,18) (5,15) (5,13) (6,9) (6,10) (6,20) (7,12) (9,10) (9,20) (9,14) (9,13) (10,21) (10,11) (11,15) (11,14) (13,14) (14,21) (15,19) (16,18) (20,21)\nIs there a path between node 6 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph715-5_7", + "image": "data/connectivity/graph_visual/medium/graph715.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,8) (0,13) (0,5) (0,2) (0,19) (0,22) (0,17) (0,16) (0,3) (0,24) (0,20) (0,10) (0,15) (0,7) (0,4) (0,23) (0,6) (0,1) (1,8) (1,13) (1,19) (1,11) (1,22) (1,17) (1,3) (1,24) (1,20) (1,10) (1,15) (1,7) (1,4) (1,23) (1,6) (2,14) (2,8) (2,13) (2,22) (2,17) (2,16) (2,3) (2,24) (2,10) (2,15) (2,7) (2,4) (2,23) (2,6) (3,14) (3,13) (3,19) (3,11) (3,22) (3,17) (3,24) (3,10) (3,15) (3,4) (3,9) (4,13) (4,5) (4,22) (4,17) (4,10) (4,15) (4,7) (4,9) (4,23) (4,6) (5,8) (5,13) (5,19) (5,22) (5,24) (5,20) (5,10) (5,7) (5,23) (6,14) (6,8) (6,13) (6,19) (6,11) (6,22) (6,17) (6,16) (6,20) (6,7) (6,9) (7,14) (7,8) (7,13) (7,19) (7,11) (7,22) (7,20) (7,9) (8,19) (8,11) (8,22) (8,17) (8,20) (8,10) (8,15) (8,9) (9,17) (9,16) (9,24) (9,20) (9,10) (9,15) (9,23) (10,14) (10,13) (10,19) (10,11) (10,22) (10,17) (10,15) (10,23) (11,13) (11,22) (11,16) (12,18) (13,14) (13,19) (13,22) (13,16) (13,24) (13,20) (13,15) (13,23) (14,19) (14,17) (14,16) (14,15) (14,23) (15,19) (15,22) (15,17) (15,24) (15,20) (16,22) (16,17) (16,24) (17,19) (17,24) (17,20) (17,23) (18,21) (19,24) (19,20) (19,23) (20,22) (20,24) (20,23)\nIs there a path between node 5 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph706-0_21", + "image": "data/connectivity/graph_visual/medium/graph706.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (0,2) (0,23) (0,1) (1,16) (1,17) (1,5) (1,15) (1,19) (1,13) (1,4) (2,3) (2,13) (2,4) (2,10) (3,17) (3,15) (3,14) (3,9) (3,20) (3,6) (4,12) (4,18) (5,13) (5,14) (5,9) (6,19) (6,13) (6,23) (6,14) (6,20) (7,21) (9,16) (9,13) (9,23) (9,11) (9,18) (10,16) (10,13) (11,15) (11,23) (12,16) (12,17) (12,23) (13,17) (13,23) (14,16) (14,17) (14,19) (14,18) (15,16) (15,19) (15,23) (15,18) (15,20) (16,17) (17,18) (18,20)\nIs there a path between node 0 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph252-12_13", + "image": "data/connectivity/graph_visual/medium/graph252.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,5) (0,16) (0,1) (0,14) (0,4) (0,15) (0,3) (0,9) (0,10) (0,6) (0,17) (0,18) (0,11) (1,8) (1,5) (1,16) (1,14) (1,4) (1,15) (1,3) (1,9) (1,10) (1,6) (1,17) (1,18) (1,11) (3,8) (3,5) (3,16) (3,14) (3,4) (3,15) (3,9) (3,10) (3,6) (3,17) (3,18) (3,11) (4,8) (4,5) (4,16) (4,14) (4,15) (4,9) (4,10) (4,6) (4,17) (4,18) (4,11) (5,8) (5,16) (5,14) (5,15) (5,9) (5,10) (5,6) (5,17) (5,18) (5,11) (6,8) (6,16) (6,14) (6,15) (6,9) (6,10) (6,17) (6,18) (6,11) (7,12) (7,13) (8,16) (8,14) (8,15) (8,9) (8,10) (8,17) (8,18) (8,11) (9,16) (9,14) (9,15) (9,10) (9,17) (9,18) (9,11) (10,16) (10,14) (10,15) (10,17) (10,18) (10,11) (11,16) (11,14) (11,15) (11,17) (11,18) (12,13) (14,16) (14,15) (14,17) (14,18) (15,16) (15,17) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 12 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph111-1_8", + "image": "data/connectivity/graph_visual/medium/graph111.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,9) (0,10) (0,1) (1,8) (1,3) (1,14) (3,5) (3,6) (3,9) (3,12) (4,9) (4,16) (6,7) (6,12) (7,14) (8,16) (8,14) (10,11) (10,14) (10,12) (11,14) (12,14)\nIs there a path between node 1 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph660-9_15", + "image": "data/connectivity/graph_visual/medium/graph660.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,11) (0,3) (0,2) (0,9) (0,5) (0,10) (0,23) (1,13) (1,17) (1,20) (1,8) (1,14) (1,4) (2,22) (2,11) (2,9) (2,10) (2,23) (3,21) (3,11) (3,5) (3,15) (3,23) (3,12) (4,18) (4,19) (4,13) (4,8) (4,16) (5,11) (5,9) (5,10) (5,15) (6,18) (6,19) (6,13) (6,20) (6,8) (6,16) (6,14) (7,19) (7,20) (7,8) (7,16) (7,14) (8,18) (8,19) (8,13) (8,17) (8,16) (8,14) (9,22) (9,21) (9,10) (9,15) (9,23) (9,12) (10,22) (10,21) (10,15) (10,12) (11,22) (11,15) (11,23) (11,12) (12,22) (12,15) (12,23) (13,18) (13,19) (13,20) (13,16) (13,14) (14,18) (14,19) (14,17) (14,20) (14,16) (15,22) (15,21) (16,18) (16,19) (16,17) (17,18) (17,19) (17,20) (18,19) (18,20) (19,20) (21,22) (21,23) (22,23)\nIs there a path between node 9 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph752-21_4", + "image": "data/connectivity/graph_visual/medium/graph752.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,20) (0,17) (0,1) (0,21) (1,10) (1,20) (1,21) (3,20) (3,21) (4,5) (4,12) (4,14) (4,16) (4,6) (4,15) (5,7) (5,14) (5,16) (5,19) (5,11) (5,8) (5,15) (6,24) (6,14) (6,16) (6,19) (6,9) (6,13) (6,11) (6,8) (7,24) (7,12) (7,14) (7,19) (7,9) (7,13) (7,11) (7,8) (7,15) (8,24) (8,12) (8,16) (8,19) (8,9) (8,11) (8,15) (9,24) (9,12) (9,14) (9,11) (9,15) (10,20) (10,17) (10,21) (11,24) (11,12) (11,14) (11,16) (11,19) (11,13) (11,15) (12,14) (12,16) (12,19) (12,15) (13,24) (13,14) (13,16) (13,19) (14,24) (14,16) (14,15) (15,24) (15,16) (16,24) (16,19) (17,20) (17,21) (18,23) (19,24) (22,23)\nIs there a path between node 21 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph231-14_12", + "image": "data/connectivity/graph_visual/medium/graph231.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,10) (1,15) (2,16) (3,18) (3,8) (5,15) (5,14) (7,9) (8,18) (8,12) (10,17) (12,13) (12,17) (13,14) (14,18) (14,15) (17,18)\nIs there a path between node 14 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph690-20_16", + "image": "data/connectivity/graph_visual/medium/graph690.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,21) (0,11) (0,1) (0,4) (0,15) (0,10) (0,22) (0,14) (0,8) (1,21) (1,11) (1,4) (1,15) (1,10) (1,22) (1,14) (1,8) (2,3) (2,13) (2,5) (2,7) (3,13) (3,5) (3,7) (4,21) (4,11) (4,15) (4,10) (4,22) (4,14) (4,8) (5,13) (5,7) (6,20) (6,19) (6,16) (6,17) (6,9) (6,18) (6,12) (6,23) (7,13) (8,21) (8,11) (8,15) (8,10) (8,22) (8,14) (9,20) (9,19) (9,16) (9,17) (9,18) (9,12) (9,23) (10,21) (10,11) (10,15) (10,22) (10,14) (11,21) (11,15) (11,22) (11,14) (12,20) (12,19) (12,16) (12,17) (12,18) (12,23) (14,21) (14,15) (14,22) (15,21) (15,22) (16,20) (16,19) (16,17) (16,18) (16,23) (17,20) (17,19) (17,18) (17,23) (18,20) (18,19) (18,23) (19,20) (19,23) (20,23) (21,22)\nIs there a path between node 20 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph380-9_19", + "image": "data/connectivity/graph_visual/medium/graph380.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,11) (0,16) (0,3) (0,20) (0,12) (0,5) (0,17) (0,8) (0,14) (0,18) (0,2) (0,1) (0,6) (1,11) (1,16) (1,3) (1,20) (1,12) (1,5) (1,4) (1,17) (1,14) (1,2) (1,13) (1,6) (2,11) (2,16) (2,3) (2,20) (2,5) (2,8) (2,14) (2,18) (2,13) (2,6) (2,19) (2,9) (3,11) (3,16) (3,20) (3,5) (3,4) (3,17) (3,14) (3,13) (3,6) (3,19) (3,9) (4,11) (4,16) (4,20) (4,12) (4,8) (4,18) (4,13) (4,6) (4,19) (4,9) (5,11) (5,16) (5,20) (5,12) (5,17) (5,8) (5,14) (5,6) (5,19) (5,9) (6,11) (6,16) (6,20) (6,12) (6,17) (6,14) (6,19) (6,9) (8,11) (8,16) (8,20) (8,14) (8,18) (8,19) (8,9) (9,11) (9,12) (9,18) (9,19) (11,20) (11,12) (11,17) (11,14) (11,13) (11,19) (12,16) (12,20) (12,14) (12,18) (12,13) (12,19) (13,16) (13,14) (14,20) (14,18) (14,19) (16,20) (16,18) (17,20) (17,18) (18,20) (19,20)\nIs there a path between node 9 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph299-3_6", + "image": "data/connectivity/graph_visual/medium/graph299.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,8) (1,3) (1,2) (1,7) (1,5) (1,18) (1,14) (1,17) (1,12) (1,11) (1,10) (1,19) (1,13) (1,4) (1,9) (2,7) (2,18) (2,16) (2,6) (2,11) (2,10) (2,19) (2,13) (2,4) (2,9) (2,15) (3,7) (3,18) (3,12) (3,6) (3,10) (3,19) (3,13) (3,4) (3,9) (4,7) (4,5) (4,14) (4,17) (4,16) (4,6) (4,11) (4,10) (4,19) (4,9) (5,7) (5,14) (5,17) (5,16) (5,12) (5,6) (5,11) (5,10) (5,13) (5,9) (5,15) (6,14) (6,17) (6,16) (6,12) (6,10) (6,19) (6,9) (7,18) (7,14) (7,17) (7,16) (7,12) (7,10) (7,19) (7,13) (7,9) (7,15) (9,18) (9,14) (9,17) (9,16) (9,12) (9,11) (9,19) (9,13) (9,15) (10,18) (10,14) (10,17) (10,12) (10,11) (10,19) (10,15) (11,18) (11,12) (11,19) (11,15) (12,18) (12,14) (12,17) (12,19) (12,13) (12,15) (13,18) (13,14) (13,17) (14,17) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19)\nIs there a path between node 3 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph550-23_4", + "image": "data/connectivity/graph_visual/medium/graph550.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,10) (0,19) (0,13) (0,20) (1,15) (1,23) (3,5) (3,7) (3,14) (3,22) (4,18) (4,19) (4,20) (5,7) (5,14) (5,15) (5,12) (6,10) (7,11) (7,14) (7,22) (7,8) (8,14) (8,22) (8,21) (10,18) (10,19) (10,13) (10,20) (11,17) (11,14) (11,23) (11,16) (12,23) (13,18) (13,20) (14,22) (14,21) (15,21) (15,16) (17,21) (18,19) (19,20) (21,22)\nIs there a path between node 23 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph434-9_19", + "image": "data/connectivity/graph_visual/medium/graph434.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,1) (0,17) (0,2) (0,3) (1,2) (2,20) (3,17) (3,7) (4,18) (4,11) (4,9) (5,12) (6,18) (6,11) (6,9) (7,19) (8,17) (8,14) (9,10) (9,18) (9,11) (11,15) (11,18) (11,21) (14,19) (14,17) (16,17) (17,19) (19,20)\nIs there a path between node 9 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph363-3_19", + "image": "data/connectivity/graph_visual/medium/graph363.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,5) (0,9) (0,8) (0,17) (0,6) (1,14) (1,7) (2,8) (2,17) (2,3) (2,11) (2,10) (2,6) (3,9) (3,19) (3,10) (3,16) (4,18) (4,14) (5,8) (5,17) (5,10) (6,9) (6,11) (6,16) (7,20) (7,15) (8,9) (8,13) (8,19) (9,13) (10,17) (10,13) (12,16) (13,17) (14,18) (14,20) (15,20) (16,19)\nIs there a path between node 3 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph69-5_12", + "image": "data/connectivity/graph_visual/medium/graph69.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,5) (0,9) (1,8) (1,4) (2,8) (2,4) (2,3) (3,7) (3,6) (3,10) (3,12) (3,11) (4,10) (4,12) (6,14) (6,8) (6,10) (7,14) (7,11) (8,14) (8,12) (10,14) (11,14) (12,14)\nIs there a path between node 5 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph464-18_2", + "image": "data/connectivity/graph_visual/medium/graph464.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,16) (0,1) (0,9) (0,10) (0,18) (1,4) (1,16) (1,9) (1,10) (1,18) (2,3) (2,7) (2,11) (2,20) (2,8) (2,19) (2,13) (2,12) (2,5) (2,17) (2,6) (2,15) (2,21) (2,14) (3,7) (3,11) (3,20) (3,8) (3,19) (3,13) (3,12) (3,5) (3,17) (3,6) (3,15) (3,21) (3,14) (4,16) (4,9) (4,10) (4,18) (5,7) (5,11) (5,20) (5,8) (5,19) (5,13) (5,12) (5,17) (5,6) (5,15) (5,21) (5,14) (6,7) (6,11) (6,20) (6,8) (6,19) (6,13) (6,12) (6,17) (6,15) (6,21) (6,14) (7,11) (7,20) (7,8) (7,19) (7,13) (7,12) (7,17) (7,15) (7,21) (7,14) (8,11) (8,20) (8,19) (8,13) (8,12) (8,17) (8,15) (8,21) (8,14) (9,16) (9,10) (9,18) (10,16) (10,18) (11,20) (11,19) (11,13) (11,12) (11,17) (11,15) (11,21) (11,14) (12,20) (12,19) (12,13) (12,17) (12,15) (12,21) (12,14) (13,20) (13,19) (13,17) (13,15) (13,21) (13,14) (14,20) (14,19) (14,17) (14,15) (14,21) (15,20) (15,19) (15,17) (15,21) (16,18) (17,20) (17,19) (17,21) (19,20) (19,21) (20,21)\nIs there a path between node 18 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph30-2_8", + "image": "data/connectivity/graph_visual/medium/graph30.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,5) (0,6) (0,4) (0,9) (0,11) (0,1) (0,7) (1,5) (1,6) (1,4) (1,9) (1,11) (1,7) (2,10) (2,3) (2,8) (3,10) (3,8) (4,5) (4,6) (4,9) (4,11) (4,7) (5,6) (5,9) (5,11) (5,7) (6,9) (6,11) (6,7) (7,9) (7,11) (8,10) (9,11)\nIs there a path between node 2 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph677-15_19", + "image": "data/connectivity/graph_visual/medium/graph677.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,4) (0,9) (0,19) (0,14) (0,17) (0,7) (0,6) (0,5) (0,16) (0,13) (0,22) (0,12) (0,15) (0,23) (1,3) (1,2) (1,21) (1,8) (1,20) (2,3) (2,21) (2,8) (2,20) (3,21) (3,8) (3,20) (4,11) (4,9) (4,19) (4,14) (4,17) (4,7) (4,6) (4,5) (4,16) (4,13) (4,22) (4,12) (4,15) (4,23) (5,11) (5,9) (5,19) (5,14) (5,17) (5,7) (5,6) (5,16) (5,13) (5,22) (5,12) (5,15) (5,23) (6,11) (6,9) (6,19) (6,14) (6,17) (6,7) (6,16) (6,13) (6,22) (6,12) (6,15) (6,23) (7,11) (7,9) (7,19) (7,14) (7,17) (7,16) (7,13) (7,22) (7,12) (7,15) (7,23) (8,21) (8,20) (9,11) (9,19) (9,14) (9,17) (9,16) (9,13) (9,22) (9,12) (9,15) (9,23) (11,19) (11,14) (11,17) (11,16) (11,13) (11,22) (11,12) (11,15) (11,23) (12,19) (12,14) (12,17) (12,16) (12,13) (12,22) (12,15) (12,23) (13,19) (13,14) (13,17) (13,16) (13,22) (13,15) (13,23) (14,19) (14,17) (14,16) (14,22) (14,15) (14,23) (15,19) (15,17) (15,16) (15,22) (15,23) (16,19) (16,17) (16,22) (16,23) (17,19) (17,22) (17,23) (19,22) (19,23) (20,21) (22,23)\nIs there a path between node 15 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph701-3_12", + "image": "data/connectivity/graph_visual/medium/graph701.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,18) (0,19) (0,20) (0,23) (0,9) (0,10) (0,22) (0,13) (0,1) (0,12) (0,5) (0,7) (0,15) (0,4) (1,11) (1,18) (1,19) (1,20) (1,23) (1,9) (1,10) (1,22) (1,13) (1,12) (1,5) (1,7) (1,15) (1,4) (2,8) (2,6) (2,3) (2,24) (2,16) (2,21) (2,17) (2,14) (3,8) (3,6) (3,24) (3,16) (3,21) (3,17) (3,14) (4,11) (4,18) (4,19) (4,20) (4,23) (4,9) (4,10) (4,22) (4,13) (4,12) (4,5) (4,7) (4,15) (5,11) (5,18) (5,19) (5,20) (5,23) (5,9) (5,10) (5,22) (5,13) (5,12) (5,7) (5,15) (6,8) (6,24) (6,16) (6,21) (6,17) (6,14) (7,11) (7,18) (7,19) (7,20) (7,23) (7,9) (7,10) (7,22) (7,13) (7,12) (7,15) (8,24) (8,16) (8,21) (8,17) (8,14) (9,11) (9,18) (9,19) (9,20) (9,23) (9,10) (9,22) (9,13) (9,12) (9,15) (10,11) (10,18) (10,19) (10,20) (10,23) (10,22) (10,13) (10,12) (10,15) (11,18) (11,19) (11,20) (11,23) (11,22) (11,13) (11,12) (11,15) (12,18) (12,19) (12,20) (12,23) (12,22) (12,13) (12,15) (13,18) (13,19) (13,20) (13,23) (13,22) (13,15) (14,24) (14,16) (14,21) (14,17) (15,18) (15,19) (15,20) (15,23) (15,22) (16,24) (16,21) (16,17) (17,24) (17,21) (18,19) (18,20) (18,23) (18,22) (19,20) (19,23) (19,22) (20,23) (20,22) (21,24) (22,23)\nIs there a path between node 3 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph800-14_19", + "image": "data/connectivity/graph_visual/medium/graph800.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,4) (0,22) (1,13) (1,4) (1,6) (1,2) (1,10) (1,3) (2,10) (2,23) (2,5) (3,4) (3,17) (3,23) (3,12) (4,12) (5,18) (5,15) (5,12) (5,22) (6,17) (7,19) (10,17) (10,23) (10,14) (10,15) (11,13) (12,18) (12,14) (13,17) (13,23) (13,22) (14,23) (14,15) (15,23) (16,20) (17,18) (17,23) (18,23) (19,24) (19,21) (20,21)\nIs there a path between node 14 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph239-10_8", + "image": "data/connectivity/graph_visual/medium/graph239.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (0,10) (0,14) (0,8) (0,11) (0,12) (0,9) (0,3) (1,7) (1,2) (2,5) (3,15) (3,17) (3,4) (3,10) (3,14) (3,13) (3,11) (3,12) (3,6) (3,9) (3,18) (4,15) (4,17) (4,10) (4,14) (4,13) (4,8) (4,11) (4,12) (4,6) (4,9) (6,15) (6,17) (6,10) (6,14) (6,13) (6,12) (6,18) (8,15) (8,10) (8,14) (8,13) (8,11) (8,12) (8,9) (9,15) (9,17) (9,13) (10,15) (10,17) (10,14) (10,11) (10,12) (10,18) (11,17) (11,12) (11,18) (12,18) (13,17) (13,14) (13,18) (14,15) (14,17) (15,17) (15,18) (17,18)\nIs there a path between node 10 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph27-10_7", + "image": "data/connectivity/graph_visual/medium/graph27.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,2) (0,9) (0,1) (0,11) (0,4) (0,3) (1,6) (1,2) (1,9) (1,8) (1,11) (2,6) (2,8) (2,11) (2,3) (3,6) (3,9) (3,8) (3,10) (3,11) (3,4) (4,6) (4,8) (4,10) (5,7) (6,9) (6,8) (6,10) (6,11) (8,10) (9,11) (10,11)\nIs there a path between node 10 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph801-0_5", + "image": "data/connectivity/graph_visual/medium/graph801.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,14) (0,1) (0,15) (1,8) (1,15) (1,11) (2,9) (2,6) (3,8) (3,4) (3,24) (3,19) (3,11) (4,24) (4,13) (5,21) (5,23) (5,7) (5,17) (5,20) (6,9) (6,23) (7,12) (7,17) (8,22) (8,14) (8,13) (9,21) (9,12) (10,15) (10,19) (10,11) (10,13) (11,14) (12,18) (12,20) (13,22) (13,14) (13,24) (15,22) (16,17) (16,20) (18,21) (18,20)\nIs there a path between node 0 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph191-12_13", + "image": "data/connectivity/graph_visual/medium/graph191.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,5) (0,10) (0,11) (0,6) (0,2) (0,15) (0,4) (0,8) (0,7) (0,17) (0,16) (0,12) (0,9) (0,3) (0,14) (1,13) (2,5) (2,10) (2,11) (2,6) (2,15) (2,4) (2,8) (2,7) (2,17) (2,16) (2,12) (2,9) (2,3) (2,14) (3,5) (3,10) (3,11) (3,6) (3,15) (3,4) (3,8) (3,7) (3,17) (3,16) (3,12) (3,9) (3,14) (4,5) (4,10) (4,11) (4,6) (4,15) (4,8) (4,7) (4,17) (4,16) (4,12) (4,9) (4,14) (5,10) (5,11) (5,6) (5,15) (5,8) (5,7) (5,17) (5,16) (5,12) (5,9) (5,14) (6,10) (6,11) (6,15) (6,8) (6,7) (6,17) (6,16) (6,12) (6,9) (6,14) (7,10) (7,11) (7,15) (7,8) (7,17) (7,16) (7,12) (7,9) (7,14) (8,10) (8,11) (8,15) (8,17) (8,16) (8,12) (8,9) (8,14) (9,10) (9,11) (9,15) (9,17) (9,16) (9,12) (9,14) (10,11) (10,15) (10,17) (10,16) (10,12) (10,14) (11,15) (11,17) (11,16) (11,12) (11,14) (12,15) (12,17) (12,16) (12,14) (14,15) (14,17) (14,16) (15,17) (15,16) (16,17)\nIs there a path between node 12 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph825-15_16", + "image": "data/connectivity/graph_visual/medium/graph825.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,1) (0,6) (0,13) (0,16) (0,21) (0,5) (1,12) (1,15) (1,6) (1,5) (2,8) (2,9) (2,19) (2,7) (2,22) (2,4) (2,17) (2,20) (3,11) (3,8) (3,14) (3,9) (3,23) (3,7) (3,22) (3,17) (3,20) (4,11) (4,8) (4,14) (4,19) (4,23) (4,7) (5,10) (5,15) (5,6) (5,13) (5,18) (5,21) (6,12) (6,15) (6,18) (6,21) (7,8) (7,24) (7,14) (7,9) (7,19) (7,22) (7,17) (7,20) (8,11) (8,14) (8,22) (8,17) (8,20) (9,11) (9,24) (9,14) (9,19) (9,17) (10,12) (10,15) (10,16) (10,18) (10,21) (11,24) (11,14) (11,19) (11,23) (11,22) (11,17) (12,15) (12,16) (12,18) (12,21) (13,15) (13,16) (13,18) (14,24) (14,19) (14,23) (14,20) (15,16) (15,18) (16,18) (16,21) (17,24) (17,23) (17,20) (18,21) (19,23) (19,20) (20,24) (20,23) (20,22) (22,24) (22,23)\nIs there a path between node 15 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph512-11_2", + "image": "data/connectivity/graph_visual/medium/graph512.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,21) (0,19) (0,3) (0,15) (0,6) (1,17) (1,2) (1,11) (1,12) (1,9) (2,11) (2,12) (2,7) (2,10) (2,9) (2,4) (3,19) (3,22) (3,15) (4,11) (4,5) (4,12) (4,7) (4,10) (4,9) (5,17) (5,11) (5,12) (5,10) (5,9) (6,21) (6,19) (6,22) (6,15) (7,11) (7,10) (7,9) (8,13) (8,20) (8,18) (9,17) (9,11) (9,10) (10,11) (10,12) (11,17) (11,12) (12,17) (13,20) (14,20) (15,21) (15,19) (15,22) (15,16) (16,21) (16,19) (18,20) (19,21) (19,22)\nIs there a path between node 11 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph646-12_15", + "image": "data/connectivity/graph_visual/medium/graph646.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,14) (1,22) (1,12) (2,11) (2,7) (2,18) (2,3) (2,20) (3,11) (3,7) (3,18) (3,16) (4,20) (5,20) (5,10) (6,20) (6,16) (6,10) (7,11) (7,16) (8,17) (8,13) (9,23) (10,18) (10,16) (11,16) (12,19) (13,14) (13,22) (13,19) (14,19) (17,22) (17,19) (19,22)\nIs there a path between node 12 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph188-6_16", + "image": "data/connectivity/graph_visual/medium/graph188.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,11) (0,1) (0,9) (0,17) (0,3) (0,14) (0,15) (0,4) (0,10) (0,2) (0,6) (1,16) (1,11) (1,9) (1,17) (1,3) (1,14) (1,15) (1,4) (1,10) (1,2) (1,6) (2,16) (2,11) (2,9) (2,17) (2,3) (2,14) (2,15) (2,4) (2,10) (2,6) (3,16) (3,11) (3,9) (3,17) (3,14) (3,15) (3,4) (3,10) (3,6) (4,16) (4,11) (4,9) (4,17) (4,14) (4,15) (4,10) (4,6) (5,8) (5,12) (5,7) (5,13) (6,16) (6,11) (6,9) (6,17) (6,14) (6,15) (6,10) (7,8) (7,12) (7,13) (8,12) (8,13) (9,16) (9,11) (9,17) (9,14) (9,15) (9,10) (10,16) (10,11) (10,17) (10,14) (10,15) (11,16) (11,17) (11,14) (11,15) (12,13) (14,16) (14,17) (14,15) (15,16) (15,17) (16,17)\nIs there a path between node 6 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph236-14_17", + "image": "data/connectivity/graph_visual/medium/graph236.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,12) (0,7) (0,11) (0,8) (0,9) (0,2) (0,6) (1,18) (1,15) (1,10) (1,17) (1,13) (1,14) (1,4) (1,16) (2,11) (2,8) (2,9) (3,12) (3,7) (3,9) (4,18) (4,17) (4,5) (4,16) (5,18) (5,15) (5,17) (5,13) (5,14) (6,7) (6,11) (7,12) (7,11) (7,8) (7,9) (8,12) (8,11) (8,9) (9,11) (10,18) (10,16) (13,15) (13,17) (13,16) (14,18) (14,15) (14,16) (15,17) (16,17) (17,18)\nIs there a path between node 14 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph542-11_9", + "image": "data/connectivity/graph_visual/medium/graph542.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,14) (0,9) (0,13) (0,4) (0,12) (0,5) (0,3) (0,15) (0,21) (0,2) (0,18) (0,17) (1,14) (1,9) (1,13) (1,4) (1,12) (1,5) (1,3) (1,15) (1,21) (1,2) (1,18) (1,17) (2,14) (2,9) (2,13) (2,4) (2,12) (2,5) (2,3) (2,15) (2,21) (2,18) (2,17) (3,14) (3,9) (3,13) (3,4) (3,12) (3,5) (3,15) (3,21) (3,18) (3,17) (4,14) (4,9) (4,13) (4,12) (4,5) (4,15) (4,21) (4,18) (4,17) (5,14) (5,9) (5,13) (5,12) (5,15) (5,21) (5,18) (5,17) (6,22) (6,8) (6,11) (6,10) (6,19) (6,20) (6,7) (7,22) (7,8) (7,11) (7,10) (7,19) (7,20) (8,22) (8,11) (8,10) (8,19) (8,20) (9,14) (9,13) (9,12) (9,15) (9,21) (9,18) (9,17) (10,22) (10,11) (10,19) (10,20) (11,22) (11,19) (11,20) (12,14) (12,13) (12,15) (12,21) (12,18) (12,17) (13,14) (13,15) (13,21) (13,18) (13,17) (14,15) (14,21) (14,18) (14,17) (15,21) (15,18) (15,17) (17,21) (17,18) (18,21) (19,22) (19,20) (20,22)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph411-9_19", + "image": "data/connectivity/graph_visual/medium/graph411.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,10) (0,1) (0,14) (0,2) (0,17) (0,13) (1,20) (1,8) (1,11) (1,10) (1,14) (1,2) (2,8) (2,11) (2,10) (2,14) (2,17) (3,15) (3,12) (3,5) (3,7) (3,6) (3,9) (3,19) (3,18) (4,12) (4,16) (4,21) (4,7) (4,6) (4,9) (4,19) (4,18) (5,15) (5,12) (5,16) (5,21) (5,7) (5,9) (5,19) (5,18) (6,12) (6,16) (6,7) (6,9) (6,19) (6,18) (7,12) (7,16) (7,18) (8,20) (8,14) (8,17) (9,12) (9,16) (9,21) (9,19) (9,18) (10,20) (10,13) (11,17) (11,13) (12,15) (12,16) (12,21) (13,20) (13,14) (13,17) (15,16) (15,21) (16,19) (16,18) (18,21) (18,19) (19,21)\nIs there a path between node 9 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph582-0_11", + "image": "data/connectivity/graph_visual/medium/graph582.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (0,19) (1,7) (1,14) (1,11) (1,2) (1,17) (2,4) (3,7) (3,14) (3,19) (3,4) (4,7) (4,5) (4,8) (4,19) (4,17) (5,11) (7,13) (7,17) (8,11) (8,17) (9,22) (9,21) (9,10) (11,19) (14,19) (15,22) (18,20)\nIs there a path between node 0 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph233-3_9", + "image": "data/connectivity/graph_visual/medium/graph233.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,7) (0,4) (0,1) (0,2) (0,14) (0,15) (0,8) (0,11) (0,9) (0,16) (1,17) (1,2) (1,15) (1,8) (1,9) (1,18) (2,7) (2,4) (2,14) (2,15) (2,12) (2,8) (2,18) (3,5) (3,13) (4,17) (4,15) (4,12) (4,6) (4,11) (4,16) (4,18) (6,17) (6,7) (6,14) (6,12) (6,11) (6,9) (6,16) (6,18) (7,17) (7,14) (7,15) (7,11) (7,9) (7,16) (8,17) (8,15) (8,18) (9,17) (9,14) (9,15) (9,12) (9,11) (9,18) (10,13) (11,17) (11,14) (11,15) (11,12) (11,16) (11,18) (12,17) (12,14) (12,16) (12,18) (14,17) (14,15) (14,16) (15,16) (15,18) (17,18)\nIs there a path between node 3 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph792-17_3", + "image": "data/connectivity/graph_visual/medium/graph792.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,23) (1,6) (1,7) (1,3) (2,4) (2,22) (3,10) (3,12) (3,9) (4,13) (4,19) (4,5) (4,22) (5,22) (5,11) (6,16) (6,10) (7,24) (9,23) (9,10) (11,13) (11,18) (11,19) (11,22) (12,24) (13,18) (13,14) (16,23) (17,19) (18,20) (19,20)\nIs there a path between node 17 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph746-21_22", + "image": "data/connectivity/graph_visual/medium/graph746.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,21) (0,14) (0,1) (0,22) (0,16) (0,19) (0,5) (0,10) (0,20) (0,11) (0,24) (0,13) (1,21) (1,9) (1,3) (1,14) (1,22) (1,10) (1,20) (1,12) (1,11) (1,24) (1,13) (1,23) (2,8) (2,4) (2,18) (2,15) (3,9) (3,14) (3,16) (3,19) (3,7) (3,6) (3,5) (3,10) (3,11) (4,8) (4,17) (4,18) (4,15) (5,9) (5,14) (5,22) (5,7) (5,6) (5,10) (5,20) (5,12) (5,11) (5,13) (5,23) (6,21) (6,9) (6,22) (6,19) (6,7) (6,20) (6,12) (6,11) (6,13) (6,23) (7,21) (7,9) (7,14) (7,16) (7,19) (7,10) (7,20) (7,12) (7,11) (7,24) (7,13) (7,23) (8,17) (8,18) (8,15) (9,21) (9,16) (9,10) (9,20) (9,12) (9,11) (9,24) (9,13) (9,23) (10,22) (10,19) (10,12) (10,11) (10,13) (10,23) (11,21) (11,22) (11,19) (11,20) (11,12) (11,24) (11,13) (11,23) (12,21) (12,14) (12,22) (12,20) (12,24) (12,13) (12,23) (13,21) (13,14) (13,22) (13,16) (13,20) (13,23) (14,21) (14,16) (14,20) (14,24) (14,23) (15,18) (16,21) (16,22) (16,19) (16,20) (16,24) (16,23) (17,18) (19,21) (19,20) (19,24) (19,23) (20,21) (20,24) (20,23) (21,24) (21,23) (22,23) (23,24)\nIs there a path between node 21 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph152-9_10", + "image": "data/connectivity/graph_visual/medium/graph152.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (0,11) (1,13) (1,16) (1,8) (1,5) (1,4) (1,9) (1,3) (1,15) (1,17) (1,7) (1,6) (1,14) (1,2) (2,13) (2,16) (2,8) (2,5) (2,4) (2,9) (2,3) (2,15) (2,17) (2,7) (2,6) (2,14) (3,13) (3,16) (3,8) (3,5) (3,4) (3,9) (3,15) (3,17) (3,7) (3,6) (3,14) (4,13) (4,16) (4,8) (4,5) (4,9) (4,15) (4,17) (4,7) (4,6) (4,14) (5,13) (5,16) (5,8) (5,9) (5,15) (5,17) (5,7) (5,6) (5,14) (6,13) (6,16) (6,8) (6,9) (6,15) (6,17) (6,7) (6,14) (7,13) (7,16) (7,8) (7,9) (7,15) (7,17) (7,14) (8,13) (8,16) (8,9) (8,15) (8,17) (8,14) (9,13) (9,16) (9,15) (9,17) (9,14) (11,12) (13,16) (13,15) (13,17) (13,14) (14,16) (14,15) (14,17) (15,16) (15,17) (16,17)\nIs there a path between node 9 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph842-7_5", + "image": "data/connectivity/graph_visual/medium/graph842.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,16) (0,23) (0,22) (0,13) (0,7) (0,2) (0,8) (0,9) (0,12) (0,10) (0,4) (0,20) (0,11) (0,18) (0,1) (0,15) (0,19) (1,6) (1,16) (1,23) (1,22) (1,13) (1,7) (1,2) (1,8) (1,9) (1,12) (1,10) (1,4) (1,20) (1,11) (1,18) (1,15) (1,19) (2,6) (2,16) (2,23) (2,22) (2,13) (2,7) (2,8) (2,9) (2,12) (2,10) (2,4) (2,20) (2,11) (2,18) (2,15) (2,19) (3,24) (3,5) (3,14) (4,6) (4,16) (4,23) (4,22) (4,13) (4,7) (4,8) (4,9) (4,12) (4,10) (4,20) (4,11) (4,18) (4,15) (4,19) (5,24) (5,14) (6,16) (6,23) (6,22) (6,13) (6,7) (6,8) (6,9) (6,12) (6,10) (6,20) (6,11) (6,18) (6,15) (6,19) (7,16) (7,23) (7,22) (7,13) (7,8) (7,9) (7,12) (7,10) (7,20) (7,11) (7,18) (7,15) (7,19) (8,16) (8,23) (8,22) (8,13) (8,9) (8,12) (8,10) (8,20) (8,11) (8,18) (8,15) (8,19) (9,16) (9,23) (9,22) (9,13) (9,12) (9,10) (9,20) (9,11) (9,18) (9,15) (9,19) (10,16) (10,23) (10,22) (10,13) (10,12) (10,20) (10,11) (10,18) (10,15) (10,19) (11,16) (11,23) (11,22) (11,13) (11,12) (11,20) (11,18) (11,15) (11,19) (12,16) (12,23) (12,22) (12,13) (12,20) (12,18) (12,15) (12,19) (13,16) (13,23) (13,22) (13,20) (13,18) (13,15) (13,19) (14,24) (15,16) (15,23) (15,22) (15,20) (15,18) (15,19) (16,23) (16,22) (16,20) (16,18) (16,19) (17,21) (18,23) (18,22) (18,20) (18,19) (19,23) (19,22) (19,20) (20,23) (20,22) (22,23)\nIs there a path between node 7 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph14-10_5", + "image": "data/connectivity/graph_visual/medium/graph14.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,1) (0,2) (0,9) (0,5) (1,2) (1,9) (1,5) (2,9) (2,5) (3,10) (3,4) (3,7) (3,6) (3,8) (4,10) (4,7) (4,6) (4,8) (5,9) (6,10) (6,7) (6,8) (7,10) (7,8) (8,10)\nIs there a path between node 10 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph530-6_13", + "image": "data/connectivity/graph_visual/medium/graph530.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,5) (0,1) (0,18) (0,20) (0,19) (0,4) (0,10) (0,16) (0,12) (0,8) (0,21) (0,3) (0,9) (0,6) (0,11) (0,13) (1,5) (1,18) (1,20) (1,19) (1,4) (1,10) (1,16) (1,12) (1,8) (1,21) (1,3) (1,9) (1,6) (1,11) (1,13) (2,15) (2,22) (3,5) (3,18) (3,20) (3,19) (3,4) (3,10) (3,16) (3,12) (3,8) (3,21) (3,9) (3,6) (3,11) (3,13) (4,5) (4,18) (4,20) (4,19) (4,10) (4,16) (4,12) (4,8) (4,21) (4,9) (4,6) (4,11) (4,13) (5,18) (5,20) (5,19) (5,10) (5,16) (5,12) (5,8) (5,21) (5,9) (5,6) (5,11) (5,13) (6,18) (6,20) (6,19) (6,10) (6,16) (6,12) (6,8) (6,21) (6,9) (6,11) (6,13) (7,14) (7,17) (8,18) (8,20) (8,19) (8,10) (8,16) (8,12) (8,21) (8,9) (8,11) (8,13) (9,18) (9,20) (9,19) (9,10) (9,16) (9,12) (9,21) (9,11) (9,13) (10,18) (10,20) (10,19) (10,16) (10,12) (10,21) (10,11) (10,13) (11,18) (11,20) (11,19) (11,16) (11,12) (11,21) (11,13) (12,18) (12,20) (12,19) (12,16) (12,21) (12,13) (13,18) (13,20) (13,19) (13,16) (13,21) (14,17) (15,22) (16,18) (16,20) (16,19) (16,21) (18,20) (18,19) (18,21) (19,20) (19,21) (20,21)\nIs there a path between node 6 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph827-12_0", + "image": "data/connectivity/graph_visual/medium/graph827.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,7) (0,23) (0,22) (1,9) (1,24) (1,11) (1,13) (1,8) (1,20) (1,5) (1,4) (1,21) (1,16) (1,3) (1,19) (1,10) (1,18) (1,2) (2,9) (2,24) (2,11) (2,14) (2,8) (2,20) (2,5) (2,21) (2,6) (2,16) (2,3) (2,19) (2,12) (2,10) (2,18) (3,9) (3,11) (3,14) (3,8) (3,5) (3,21) (3,6) (3,16) (3,19) (3,12) (3,10) (3,18) (4,9) (4,11) (4,13) (4,14) (4,20) (4,5) (4,21) (4,16) (4,19) (4,12) (4,18) (5,9) (5,11) (5,13) (5,8) (5,20) (5,21) (5,6) (5,16) (5,12) (5,10) (5,18) (6,9) (6,24) (6,11) (6,13) (6,14) (6,20) (6,16) (6,19) (6,10) (6,18) (7,23) (7,15) (8,9) (8,24) (8,11) (8,13) (8,14) (8,20) (8,21) (8,16) (8,10) (8,18) (9,24) (9,11) (9,14) (9,20) (9,21) (9,16) (9,19) (9,10) (9,18) (10,24) (10,11) (10,14) (10,20) (10,16) (10,19) (10,12) (10,18) (11,13) (11,14) (11,20) (11,21) (11,16) (11,12) (11,18) (12,24) (12,13) (12,14) (12,20) (12,21) (12,16) (12,19) (12,18) (13,24) (13,14) (13,21) (13,16) (13,18) (14,24) (14,21) (14,19) (14,18) (15,22) (15,17) (16,24) (16,19) (16,18) (17,23) (17,22) (18,24) (18,19) (19,24) (19,21) (20,24) (20,21) (21,24)\nIs there a path between node 12 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph719-24_6", + "image": "data/connectivity/graph_visual/medium/graph719.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,22) (0,21) (0,7) (0,16) (0,14) (1,22) (1,10) (1,16) (2,6) (2,13) (2,24) (2,19) (2,3) (2,9) (2,23) (2,4) (2,15) (2,17) (2,11) (2,5) (3,6) (3,24) (3,19) (3,9) (3,23) (3,4) (3,12) (3,15) (3,17) (3,11) (3,5) (3,8) (4,6) (4,24) (4,9) (4,23) (4,15) (4,17) (4,18) (4,11) (4,5) (5,6) (5,13) (5,24) (5,19) (5,9) (5,23) (5,15) (5,18) (5,8) (6,24) (6,15) (6,17) (6,18) (6,8) (7,20) (7,22) (7,16) (8,24) (8,9) (8,12) (8,15) (8,17) (8,18) (9,13) (9,24) (9,23) (9,12) (9,17) (9,11) (10,20) (10,21) (10,16) (10,14) (11,24) (11,15) (11,17) (11,18) (12,13) (12,19) (12,17) (12,18) (13,24) (13,23) (13,17) (13,18) (14,20) (14,21) (14,16) (15,24) (15,19) (15,23) (15,18) (16,20) (16,21) (17,24) (17,23) (18,19) (19,24) (20,22) (20,21) (21,22)\nIs there a path between node 24 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph198-10_5", + "image": "data/connectivity/graph_visual/medium/graph198.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,6) (0,3) (0,14) (1,8) (1,6) (1,14) (2,6) (2,12) (2,18) (3,8) (3,6) (3,12) (3,18) (4,12) (4,9) (4,14) (5,15) (5,16) (5,7) (6,8) (6,12) (6,14) (7,10) (9,11) (9,18) (15,17) (15,16)\nIs there a path between node 10 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph348-13_19", + "image": "data/connectivity/graph_visual/medium/graph348.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,2) (0,7) (0,20) (0,1) (0,18) (0,11) (0,5) (0,15) (0,13) (0,14) (0,3) (0,9) (0,6) (0,4) (0,12) (0,17) (0,16) (1,10) (1,2) (1,7) (1,20) (1,18) (1,11) (1,5) (1,15) (1,13) (1,14) (1,3) (1,9) (1,6) (1,4) (1,12) (1,17) (1,16) (2,10) (2,7) (2,20) (2,18) (2,11) (2,5) (2,15) (2,13) (2,14) (2,3) (2,9) (2,6) (2,4) (2,12) (2,17) (2,16) (3,10) (3,7) (3,20) (3,18) (3,11) (3,5) (3,15) (3,13) (3,14) (3,9) (3,6) (3,4) (3,12) (3,17) (3,16) (4,10) (4,7) (4,20) (4,18) (4,11) (4,5) (4,15) (4,13) (4,14) (4,9) (4,6) (4,12) (4,17) (4,16) (5,10) (5,7) (5,20) (5,18) (5,11) (5,15) (5,13) (5,14) (5,9) (5,6) (5,12) (5,17) (5,16) (6,10) (6,7) (6,20) (6,18) (6,11) (6,15) (6,13) (6,14) (6,9) (6,12) (6,17) (6,16) (7,10) (7,20) (7,18) (7,11) (7,15) (7,13) (7,14) (7,9) (7,12) (7,17) (7,16) (8,19) (9,10) (9,20) (9,18) (9,11) (9,15) (9,13) (9,14) (9,12) (9,17) (9,16) (10,20) (10,18) (10,11) (10,15) (10,13) (10,14) (10,12) (10,17) (10,16) (11,20) (11,18) (11,15) (11,13) (11,14) (11,12) (11,17) (11,16) (12,20) (12,18) (12,15) (12,13) (12,14) (12,17) (12,16) (13,20) (13,18) (13,15) (13,14) (13,17) (13,16) (14,20) (14,18) (14,15) (14,17) (14,16) (15,20) (15,18) (15,17) (15,16) (16,20) (16,18) (16,17) (17,20) (17,18) (18,20)\nIs there a path between node 13 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph325-8_7", + "image": "data/connectivity/graph_visual/medium/graph325.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,13) (0,5) (0,11) (0,15) (0,10) (0,16) (0,14) (0,8) (0,9) (1,18) (1,12) (1,7) (1,6) (2,13) (2,11) (2,15) (2,17) (2,16) (2,14) (2,3) (2,8) (2,9) (3,5) (3,11) (3,4) (3,15) (3,10) (3,14) (3,8) (3,9) (4,13) (4,5) (4,17) (4,16) (4,14) (4,8) (5,17) (5,16) (5,14) (6,12) (6,19) (6,20) (6,7) (7,18) (8,15) (8,17) (8,16) (8,14) (8,9) (9,13) (9,11) (9,17) (9,16) (9,14) (10,11) (10,15) (10,17) (10,16) (10,14) (11,13) (11,15) (11,16) (12,18) (12,19) (12,20) (13,17) (13,14) (14,15) (14,17) (14,16) (15,17) (16,17) (18,19) (18,20) (19,20)\nIs there a path between node 8 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph237-8_6", + "image": "data/connectivity/graph_visual/medium/graph237.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,11) (0,17) (0,16) (1,2) (1,12) (1,7) (1,3) (2,15) (2,5) (2,7) (2,3) (3,15) (3,5) (3,12) (3,7) (4,8) (4,10) (4,18) (4,6) (4,11) (4,9) (4,17) (4,14) (4,16) (5,15) (5,7) (6,8) (6,10) (6,18) (6,11) (6,9) (6,17) (6,16) (7,15) (7,12) (8,11) (8,9) (8,17) (8,14) (9,18) (9,11) (10,18) (10,11) (10,14) (10,16) (11,18) (11,17) (11,16) (14,18) (14,16) (16,18) (16,17) (17,18)\nIs there a path between node 8 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph123-7_11", + "image": "data/connectivity/graph_visual/medium/graph123.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,8) (0,10) (0,6) (0,2) (0,5) (0,7) (0,9) (0,13) (1,10) (1,6) (1,14) (1,2) (1,5) (1,4) (1,7) (1,3) (1,9) (1,13) (2,8) (2,10) (2,14) (2,5) (2,4) (2,7) (2,3) (2,15) (2,13) (3,10) (3,6) (3,9) (3,13) (4,10) (4,6) (4,14) (4,15) (4,9) (4,13) (5,10) (5,7) (5,15) (5,9) (5,13) (6,8) (6,15) (6,9) (6,13) (7,14) (7,15) (8,10) (8,15) (8,9) (8,13) (9,14) (10,14) (10,15) (11,12) (11,16) (14,15)\nIs there a path between node 7 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph212-9_10", + "image": "data/connectivity/graph_visual/medium/graph212.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,5) (0,9) (0,14) (0,18) (0,3) (0,1) (0,17) (0,4) (0,8) (0,7) (0,15) (0,11) (0,10) (0,13) (1,5) (1,9) (1,14) (1,18) (1,3) (1,17) (1,4) (1,8) (1,7) (1,15) (1,11) (1,10) (1,13) (3,5) (3,9) (3,14) (3,18) (3,17) (3,4) (3,8) (3,7) (3,15) (3,11) (3,10) (3,13) (4,5) (4,9) (4,14) (4,18) (4,17) (4,8) (4,7) (4,15) (4,11) (4,10) (4,13) (5,9) (5,14) (5,18) (5,17) (5,8) (5,7) (5,15) (5,11) (5,10) (5,13) (6,12) (6,16) (7,9) (7,14) (7,18) (7,17) (7,8) (7,15) (7,11) (7,10) (7,13) (8,9) (8,14) (8,18) (8,17) (8,15) (8,11) (8,10) (8,13) (9,14) (9,18) (9,17) (9,15) (9,11) (9,10) (9,13) (10,14) (10,18) (10,17) (10,15) (10,11) (10,13) (11,14) (11,18) (11,17) (11,15) (11,13) (12,16) (13,14) (13,18) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (15,17) (17,18)\nIs there a path between node 9 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph55-13_3", + "image": "data/connectivity/graph_visual/medium/graph55.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (0,13) (1,10) (1,4) (1,12) (3,11) (3,10) (3,7) (3,12) (4,6) (4,9) (4,10) (5,6) (5,12) (6,11) (6,9) (9,10) (10,12)\nIs there a path between node 13 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph472-16_15", + "image": "data/connectivity/graph_visual/medium/graph472.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,5) (0,9) (0,21) (0,19) (1,2) (1,13) (2,22) (2,10) (3,12) (3,21) (4,12) (5,8) (5,9) (5,21) (5,14) (6,18) (6,7) (7,17) (8,11) (8,9) (8,15) (8,19) (9,11) (9,21) (9,15) (9,14) (10,18) (10,17) (10,20) (12,16) (12,21) (12,19) (13,17) (14,21) (16,21) (16,19) (17,20) (20,22)\nIs there a path between node 16 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph147-15_0", + "image": "data/connectivity/graph_visual/medium/graph147.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,9) (0,7) (0,10) (0,6) (0,14) (0,8) (0,16) (0,13) (1,3) (1,6) (1,17) (1,8) (1,12) (1,16) (1,15) (2,5) (2,4) (3,10) (3,6) (3,14) (3,12) (3,16) (3,15) (4,5) (4,11) (5,11) (6,9) (6,7) (6,10) (6,17) (6,8) (6,12) (6,16) (6,13) (6,15) (7,10) (7,17) (7,14) (7,12) (7,16) (7,13) (7,15) (8,10) (8,17) (8,14) (8,12) (8,16) (8,13) (9,10) (9,17) (9,13) (9,15) (10,17) (10,14) (10,12) (10,13) (10,15) (12,17) (12,13) (12,15) (13,14) (13,15) (14,16) (15,16)\nIs there a path between node 15 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph348-18_13", + "image": "data/connectivity/graph_visual/medium/graph348.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,2) (0,7) (0,20) (0,1) (0,18) (0,11) (0,5) (0,15) (0,13) (0,14) (0,3) (0,9) (0,6) (0,4) (0,12) (0,17) (0,16) (1,10) (1,2) (1,7) (1,20) (1,18) (1,11) (1,5) (1,15) (1,13) (1,14) (1,3) (1,9) (1,6) (1,4) (1,12) (1,17) (1,16) (2,10) (2,7) (2,20) (2,18) (2,11) (2,5) (2,15) (2,13) (2,14) (2,3) (2,9) (2,6) (2,4) (2,12) (2,17) (2,16) (3,10) (3,7) (3,20) (3,18) (3,11) (3,5) (3,15) (3,13) (3,14) (3,9) (3,6) (3,4) (3,12) (3,17) (3,16) (4,10) (4,7) (4,20) (4,18) (4,11) (4,5) (4,15) (4,13) (4,14) (4,9) (4,6) (4,12) (4,17) (4,16) (5,10) (5,7) (5,20) (5,18) (5,11) (5,15) (5,13) (5,14) (5,9) (5,6) (5,12) (5,17) (5,16) (6,10) (6,7) (6,20) (6,18) (6,11) (6,15) (6,13) (6,14) (6,9) (6,12) (6,17) (6,16) (7,10) (7,20) (7,18) (7,11) (7,15) (7,13) (7,14) (7,9) (7,12) (7,17) (7,16) (8,19) (9,10) (9,20) (9,18) (9,11) (9,15) (9,13) (9,14) (9,12) (9,17) (9,16) (10,20) (10,18) (10,11) (10,15) (10,13) (10,14) (10,12) (10,17) (10,16) (11,20) (11,18) (11,15) (11,13) (11,14) (11,12) (11,17) (11,16) (12,20) (12,18) (12,15) (12,13) (12,14) (12,17) (12,16) (13,20) (13,18) (13,15) (13,14) (13,17) (13,16) (14,20) (14,18) (14,15) (14,17) (14,16) (15,20) (15,18) (15,17) (15,16) (16,20) (16,18) (16,17) (17,20) (17,18) (18,20)\nIs there a path between node 18 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph825-13_20", + "image": "data/connectivity/graph_visual/medium/graph825.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,1) (0,6) (0,13) (0,16) (0,21) (0,5) (1,12) (1,15) (1,6) (1,5) (2,8) (2,9) (2,19) (2,7) (2,22) (2,4) (2,17) (2,20) (3,11) (3,8) (3,14) (3,9) (3,23) (3,7) (3,22) (3,17) (3,20) (4,11) (4,8) (4,14) (4,19) (4,23) (4,7) (5,10) (5,15) (5,6) (5,13) (5,18) (5,21) (6,12) (6,15) (6,18) (6,21) (7,8) (7,24) (7,14) (7,9) (7,19) (7,22) (7,17) (7,20) (8,11) (8,14) (8,22) (8,17) (8,20) (9,11) (9,24) (9,14) (9,19) (9,17) (10,12) (10,15) (10,16) (10,18) (10,21) (11,24) (11,14) (11,19) (11,23) (11,22) (11,17) (12,15) (12,16) (12,18) (12,21) (13,15) (13,16) (13,18) (14,24) (14,19) (14,23) (14,20) (15,16) (15,18) (16,18) (16,21) (17,24) (17,23) (17,20) (18,21) (19,23) (19,20) (20,24) (20,23) (20,22) (22,24) (22,23)\nIs there a path between node 13 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph644-7_0", + "image": "data/connectivity/graph_visual/medium/graph644.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,9) (1,4) (2,16) (4,18) (4,11) (5,14) (6,8) (7,15) (7,21) (9,15) (9,19) (13,15) (13,16) (15,20) (16,20) (19,21) (19,20)\nIs there a path between node 7 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph591-14_13", + "image": "data/connectivity/graph_visual/medium/graph591.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,2) (0,1) (0,16) (0,17) (1,12) (1,2) (1,16) (1,21) (1,5) (1,17) (2,12) (2,8) (2,21) (2,17) (3,6) (3,23) (3,18) (3,14) (4,10) (4,7) (4,22) (4,19) (4,11) (4,15) (4,20) (5,12) (5,8) (5,16) (6,23) (6,18) (7,13) (7,22) (7,19) (7,11) (8,16) (8,17) (10,22) (10,19) (10,11) (10,15) (10,20) (11,13) (11,22) (11,15) (11,20) (12,21) (13,19) (13,15) (13,20) (14,23) (14,18) (15,22) (15,19) (16,21) (16,17) (18,23) (19,22) (20,22)\nIs there a path between node 14 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph650-4_8", + "image": "data/connectivity/graph_visual/medium/graph650.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,19) (0,22) (0,8) (0,16) (0,23) (0,21) (0,5) (1,14) (1,12) (1,9) (1,18) (1,17) (1,15) (1,10) (1,13) (2,20) (2,19) (2,22) (2,6) (2,8) (2,16) (2,21) (2,5) (2,4) (3,11) (3,14) (3,7) (3,18) (3,15) (3,10) (4,20) (4,22) (4,8) (4,23) (4,5) (5,20) (5,19) (5,22) (5,6) (5,8) (5,16) (5,21) (6,19) (6,22) (6,8) (6,16) (6,23) (6,21) (7,11) (7,12) (7,18) (7,17) (7,15) (7,10) (7,13) (8,20) (8,19) (8,22) (8,16) (8,21) (9,11) (9,14) (9,12) (9,18) (9,17) (9,13) (10,11) (10,12) (10,17) (10,15) (11,14) (11,12) (11,18) (11,17) (11,15) (11,13) (12,14) (12,17) (12,13) (13,14) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (16,20) (16,19) (16,22) (17,18) (19,20) (19,22) (19,23) (19,21) (20,22) (20,21) (21,22) (22,23)\nIs there a path between node 4 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph12-8_3", + "image": "data/connectivity/graph_visual/medium/graph12.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,3) (0,10) (0,7) (0,2) (0,9) (0,1) (0,8) (0,5) (1,3) (1,10) (1,7) (1,2) (1,9) (1,8) (1,5) (2,3) (2,10) (2,7) (2,9) (2,8) (2,5) (3,10) (3,7) (3,9) (3,8) (3,5) (4,6) (5,10) (5,7) (5,9) (5,8) (7,10) (7,9) (7,8) (8,10) (8,9) (9,10)\nIs there a path between node 8 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph31-3_6", + "image": "data/connectivity/graph_visual/medium/graph31.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,6) (0,9) (0,11) (1,7) (1,3) (1,4) (1,5) (1,8) (1,2) (1,10) (2,7) (2,3) (2,4) (2,5) (2,8) (2,10) (3,7) (3,4) (3,5) (3,8) (3,10) (4,7) (4,5) (4,8) (4,10) (5,7) (5,8) (5,10) (6,9) (6,11) (7,8) (7,10) (8,10) (9,11)\nIs there a path between node 3 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph221-10_2", + "image": "data/connectivity/graph_visual/medium/graph221.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,11) (0,15) (1,12) (1,2) (1,8) (1,3) (1,15) (2,13) (2,3) (2,14) (2,15) (3,6) (3,12) (3,13) (3,11) (3,14) (3,9) (3,7) (4,8) (4,11) (4,14) (4,16) (5,6) (5,17) (5,15) (5,7) (6,8) (6,11) (6,17) (6,16) (7,13) (7,16) (8,12) (8,17) (8,14) (9,13) (9,15) (11,15) (12,17) (13,17) (14,16) (15,17) (16,17)\nIs there a path between node 10 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph514-12_16", + "image": "data/connectivity/graph_visual/medium/graph514.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (0,14) (0,19) (0,12) (0,1) (1,10) (1,19) (1,12) (1,3) (1,21) (2,9) (2,15) (2,4) (2,11) (2,22) (2,17) (2,7) (2,5) (2,18) (3,10) (3,19) (3,12) (3,21) (4,6) (4,16) (4,9) (4,8) (4,15) (4,11) (4,22) (4,7) (4,13) (4,5) (4,18) (5,6) (5,9) (5,8) (5,11) (5,22) (5,17) (5,7) (5,18) (6,16) (6,9) (6,11) (6,22) (6,17) (6,7) (6,13) (7,9) (7,11) (7,22) (7,17) (7,13) (7,18) (8,16) (8,11) (8,22) (8,13) (8,18) (9,16) (9,15) (9,11) (9,22) (9,17) (9,13) (9,18) (10,14) (10,19) (10,12) (10,21) (11,15) (11,17) (11,13) (12,14) (12,19) (12,21) (13,15) (13,22) (13,18) (14,21) (15,16) (15,22) (15,17) (16,22) (16,17) (16,18) (17,22) (17,18) (18,22) (19,21)\nIs there a path between node 12 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph768-21_16", + "image": "data/connectivity/graph_visual/medium/graph768.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,8) (0,1) (0,20) (0,7) (0,24) (0,14) (0,5) (0,9) (0,18) (0,10) (0,4) (0,22) (0,16) (0,21) (0,11) (0,19) (0,6) (1,8) (1,20) (1,7) (1,24) (1,14) (1,5) (1,9) (1,18) (1,10) (1,4) (1,22) (1,16) (1,21) (1,11) (1,19) (1,6) (2,12) (2,3) (2,17) (2,15) (2,23) (3,12) (3,17) (3,15) (3,23) (4,8) (4,20) (4,7) (4,24) (4,14) (4,5) (4,9) (4,18) (4,10) (4,22) (4,16) (4,21) (4,11) (4,19) (4,6) (5,8) (5,20) (5,7) (5,24) (5,14) (5,9) (5,18) (5,10) (5,22) (5,16) (5,21) (5,11) (5,19) (5,6) (6,8) (6,20) (6,7) (6,24) (6,14) (6,9) (6,18) (6,10) (6,22) (6,16) (6,21) (6,11) (6,19) (7,8) (7,20) (7,24) (7,14) (7,9) (7,18) (7,10) (7,22) (7,16) (7,21) (7,11) (7,19) (8,20) (8,24) (8,14) (8,9) (8,18) (8,10) (8,22) (8,16) (8,21) (8,11) (8,19) (9,20) (9,24) (9,14) (9,18) (9,10) (9,22) (9,16) (9,21) (9,11) (9,19) (10,20) (10,24) (10,14) (10,18) (10,22) (10,16) (10,21) (10,11) (10,19) (11,20) (11,24) (11,14) (11,18) (11,22) (11,16) (11,21) (11,19) (12,17) (12,15) (12,23) (14,20) (14,24) (14,18) (14,22) (14,16) (14,21) (14,19) (15,17) (15,23) (16,20) (16,24) (16,18) (16,22) (16,21) (16,19) (17,23) (18,20) (18,24) (18,22) (18,21) (18,19) (19,20) (19,24) (19,22) (19,21) (20,24) (20,22) (20,21) (21,24) (21,22) (22,24)\nIs there a path between node 21 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph790-4_23", + "image": "data/connectivity/graph_visual/medium/graph790.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,23) (1,9) (2,13) (2,16) (2,24) (3,5) (3,7) (3,11) (4,6) (4,12) (4,5) (4,14) (4,7) (5,6) (5,12) (5,14) (5,11) (6,17) (6,20) (6,7) (10,19) (10,23) (10,16) (10,18) (11,12) (11,20) (11,15) (13,16) (13,22) (13,24) (14,17) (14,20) (15,20) (16,23) (17,20) (18,22) (22,23) (23,24)\nIs there a path between node 4 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph575-5_3", + "image": "data/connectivity/graph_visual/medium/graph575.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,7) (0,14) (0,15) (0,9) (1,8) (2,4) (2,13) (2,8) (3,18) (3,20) (4,18) (4,13) (4,20) (4,10) (5,11) (5,22) (5,19) (5,23) (7,23) (8,16) (8,13) (8,20) (8,10) (9,15) (11,22) (12,17) (12,14) (13,20) (15,22) (17,22) (17,23) (19,22) (19,23)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph0-4_5", + "image": "data/connectivity/graph_visual/medium/graph0.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (3,8) (3,9) (4,5) (8,9)\nIs there a path between node 4 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph352-15_0", + "image": "data/connectivity/graph_visual/medium/graph352.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,3) (2,11) (2,19) (2,5) (2,17) (2,10) (3,4) (3,6) (3,18) (3,7) (4,6) (4,19) (5,13) (5,19) (5,10) (6,7) (6,10) (7,13) (7,17) (7,10) (8,9) (10,18) (10,19) (10,17) (11,13)\nIs there a path between node 15 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph365-12_4", + "image": "data/connectivity/graph_visual/medium/graph365.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (0,11) (0,5) (1,6) (1,19) (1,9) (1,10) (1,13) (2,18) (2,4) (2,6) (3,17) (3,7) (3,11) (3,20) (3,13) (4,6) (4,19) (4,10) (4,11) (4,13) (5,19) (5,11) (5,14) (6,19) (6,10) (6,7) (7,19) (7,14) (7,13) (9,13) (10,11) (11,18) (14,18) (14,19) (16,20)\nIs there a path between node 12 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph769-4_17", + "image": "data/connectivity/graph_visual/medium/graph769.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,10) (0,7) (0,11) (0,9) (0,21) (0,12) (0,19) (0,17) (0,24) (0,23) (0,1) (0,4) (0,8) (0,6) (0,16) (0,14) (0,22) (0,20) (0,13) (1,2) (1,10) (1,7) (1,11) (1,9) (1,21) (1,12) (1,19) (1,17) (1,24) (1,23) (1,4) (1,8) (1,6) (1,16) (1,14) (1,22) (1,20) (1,13) (2,10) (2,7) (2,11) (2,9) (2,21) (2,12) (2,19) (2,17) (2,24) (2,23) (2,4) (2,8) (2,6) (2,16) (2,14) (2,22) (2,20) (2,13) (3,5) (3,15) (3,18) (4,10) (4,7) (4,11) (4,9) (4,21) (4,12) (4,19) (4,17) (4,24) (4,23) (4,8) (4,6) (4,16) (4,14) (4,22) (4,20) (4,13) (5,15) (5,18) (6,10) (6,7) (6,11) (6,9) (6,21) (6,12) (6,19) (6,17) (6,24) (6,23) (6,8) (6,16) (6,14) (6,22) (6,20) (6,13) (7,10) (7,11) (7,9) (7,21) (7,12) (7,19) (7,17) (7,24) (7,23) (7,8) (7,16) (7,14) (7,22) (7,20) (7,13) (8,10) (8,11) (8,9) (8,21) (8,12) (8,19) (8,17) (8,24) (8,23) (8,16) (8,14) (8,22) (8,20) (8,13) (9,10) (9,11) (9,21) (9,12) (9,19) (9,17) (9,24) (9,23) (9,16) (9,14) (9,22) (9,20) (9,13) (10,11) (10,21) (10,12) (10,19) (10,17) (10,24) (10,23) (10,16) (10,14) (10,22) (10,20) (10,13) (11,21) (11,12) (11,19) (11,17) (11,24) (11,23) (11,16) (11,14) (11,22) (11,20) (11,13) (12,21) (12,19) (12,17) (12,24) (12,23) (12,16) (12,14) (12,22) (12,20) (12,13) (13,21) (13,19) (13,17) (13,24) (13,23) (13,16) (13,14) (13,22) (13,20) (14,21) (14,19) (14,17) (14,24) (14,23) (14,16) (14,22) (14,20) (15,18) (16,21) (16,19) (16,17) (16,24) (16,23) (16,22) (16,20) (17,21) (17,19) (17,24) (17,23) (17,22) (17,20) (19,21) (19,24) (19,23) (19,22) (19,20) (20,21) (20,24) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nIs there a path between node 4 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph192-0_11", + "image": "data/connectivity/graph_visual/medium/graph192.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,11) (0,14) (0,5) (0,7) (0,9) (0,1) (0,12) (1,11) (1,14) (1,5) (1,7) (1,9) (1,12) (2,6) (2,10) (2,15) (2,8) (2,17) (2,13) (2,16) (2,3) (2,4) (3,6) (3,10) (3,15) (3,8) (3,17) (3,13) (3,16) (3,4) (4,6) (4,10) (4,15) (4,8) (4,17) (4,13) (4,16) (5,11) (5,14) (5,7) (5,9) (5,12) (6,10) (6,15) (6,8) (6,17) (6,13) (6,16) (7,11) (7,14) (7,9) (7,12) (8,10) (8,15) (8,17) (8,13) (8,16) (9,11) (9,14) (9,12) (10,15) (10,17) (10,13) (10,16) (11,14) (11,12) (12,14) (13,15) (13,17) (13,16) (15,17) (15,16) (16,17)\nIs there a path between node 0 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph568-12_7", + "image": "data/connectivity/graph_visual/medium/graph568.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,13) (0,16) (0,1) (1,9) (1,13) (1,16) (2,19) (2,4) (2,18) (2,23) (2,17) (3,5) (3,20) (3,15) (3,6) (3,11) (3,7) (3,10) (3,22) (3,12) (3,14) (3,8) (4,19) (4,18) (4,23) (4,17) (5,20) (5,15) (5,6) (5,11) (5,7) (5,10) (5,22) (5,12) (5,14) (5,8) (6,20) (6,15) (6,11) (6,7) (6,10) (6,22) (6,12) (6,14) (6,8) (7,20) (7,15) (7,11) (7,10) (7,22) (7,12) (7,14) (7,8) (8,20) (8,15) (8,11) (8,10) (8,22) (8,12) (8,14) (9,13) (9,16) (10,20) (10,15) (10,11) (10,22) (10,12) (10,14) (11,20) (11,15) (11,22) (11,12) (11,14) (12,20) (12,15) (12,22) (12,14) (13,16) (14,20) (14,15) (14,22) (15,20) (15,22) (17,19) (17,18) (17,23) (18,19) (18,23) (19,23) (20,22)\nIs there a path between node 12 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph387-4_16", + "image": "data/connectivity/graph_visual/medium/graph387.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (0,2) (0,10) (0,1) (0,4) (0,9) (0,19) (0,8) (0,18) (0,14) (0,6) (1,3) (1,2) (1,10) (1,4) (1,9) (1,19) (1,8) (1,18) (1,14) (1,6) (2,3) (2,10) (2,4) (2,9) (2,19) (2,8) (2,18) (2,14) (2,6) (3,10) (3,4) (3,9) (3,19) (3,8) (3,18) (3,14) (3,6) (4,10) (4,9) (4,19) (4,8) (4,18) (4,14) (4,6) (5,17) (5,11) (5,16) (6,10) (6,9) (6,19) (6,8) (6,18) (6,14) (7,15) (7,20) (7,13) (7,12) (8,10) (8,9) (8,19) (8,18) (8,14) (9,10) (9,19) (9,18) (9,14) (10,19) (10,18) (10,14) (11,17) (11,16) (12,15) (12,20) (12,13) (13,15) (13,20) (14,19) (14,18) (15,20) (16,17) (18,19)\nIs there a path between node 4 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph301-15_9", + "image": "data/connectivity/graph_visual/medium/graph301.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,5) (0,14) (0,8) (0,1) (0,17) (0,2) (0,4) (0,10) (0,12) (0,6) (0,7) (0,3) (0,11) (1,5) (1,14) (1,8) (1,17) (1,12) (1,13) (1,3) (2,5) (2,4) (2,10) (2,12) (2,6) (2,7) (2,13) (2,11) (3,14) (3,8) (3,10) (3,12) (3,6) (3,7) (4,14) (4,8) (4,17) (4,10) (4,12) (4,7) (4,11) (5,8) (5,17) (5,12) (5,6) (5,7) (5,13) (5,11) (6,14) (6,10) (6,12) (6,13) (6,11) (7,14) (7,8) (7,17) (7,10) (7,12) (7,13) (7,11) (8,14) (8,17) (8,10) (8,12) (8,11) (9,15) (10,13) (11,14) (11,12) (11,13) (12,17) (12,13) (15,19) (15,18) (15,16) (16,19) (16,18) (18,19)\nIs there a path between node 15 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph15-3_8", + "image": "data/connectivity/graph_visual/medium/graph15.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,4) (0,8) (1,5) (2,3) (3,5) (3,11) (4,8) (5,9) (5,7) (5,10) (6,11)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph577-15_1", + "image": "data/connectivity/graph_visual/medium/graph577.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,17) (0,12) (0,18) (1,3) (1,16) (1,17) (1,14) (1,9) (1,8) (2,18) (2,9) (2,13) (2,22) (3,17) (3,14) (4,5) (4,21) (5,11) (5,6) (5,10) (6,11) (6,21) (7,19) (8,16) (8,22) (9,20) (9,18) (9,23) (11,19) (11,21) (12,14) (12,23) (12,22) (13,16) (13,20) (13,17) (13,22) (14,16) (15,18) (15,23) (16,18) (17,20) (17,18) (17,23) (17,22) (19,21) (20,23)\nIs there a path between node 15 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph738-4_13", + "image": "data/connectivity/graph_visual/medium/graph738.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (1,24) (2,18) (2,9) (3,10) (3,5) (4,8) (4,9) (5,18) (5,11) (5,13) (6,10) (6,8) (6,13) (7,14) (8,9) (8,20) (9,11) (9,13) (9,20) (10,17) (10,13) (11,18) (11,17) (13,18) (13,17) (14,19) (16,23) (16,21) (18,20) (21,23)\nIs there a path between node 4 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph25-6_5", + "image": "data/connectivity/graph_visual/medium/graph25.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,8) (0,6) (0,5) (0,10) (0,3) (0,1) (1,5) (1,10) (1,3) (1,4) (3,8) (3,11) (4,8) (4,6) (4,11) (4,10) (5,8) (5,6) (5,10) (6,8) (6,11) (7,9) (8,10)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph502-9_10", + "image": "data/connectivity/graph_visual/medium/graph502.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,3) (0,7) (0,6) (1,19) (1,12) (1,9) (1,22) (1,21) (1,17) (1,2) (1,11) (2,14) (2,21) (2,4) (2,11) (4,10) (4,20) (4,21) (4,13) (4,17) (5,7) (8,19) (8,21) (8,17) (8,11) (9,16) (9,12) (9,15) (10,14) (11,19) (12,22) (12,21) (12,17) (13,14) (13,19) (13,15) (13,21) (14,20) (14,15) (15,16) (15,20) (15,19) (15,21) (16,22) (17,20) (17,19) (17,22) (20,21) (21,22)\nIs there a path between node 9 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph408-11_3", + "image": "data/connectivity/graph_visual/medium/graph408.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,17) (0,7) (0,18) (0,14) (0,8) (0,19) (0,15) (0,4) (0,21) (1,3) (1,6) (1,11) (2,7) (2,9) (2,14) (2,8) (2,19) (2,13) (2,15) (2,10) (3,5) (3,20) (3,6) (3,11) (4,17) (4,7) (4,18) (4,9) (4,21) (5,12) (5,6) (5,11) (6,12) (6,20) (7,17) (7,18) (7,9) (7,14) (7,8) (7,13) (7,15) (8,17) (8,18) (8,14) (8,13) (8,15) (8,21) (8,10) (9,17) (9,18) (9,14) (9,13) (9,21) (10,17) (10,18) (10,14) (10,13) (10,15) (11,12) (11,20) (12,20) (12,16) (13,18) (13,14) (13,19) (13,15) (13,21) (14,18) (14,15) (14,21) (15,17) (15,18) (15,19) (15,21) (17,18) (17,19) (18,19) (19,21)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph540-2_9", + "image": "data/connectivity/graph_visual/medium/graph540.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,13) (0,22) (0,15) (0,1) (0,9) (0,14) (0,12) (0,20) (0,5) (0,4) (0,19) (0,18) (0,21) (1,13) (1,22) (1,15) (1,9) (1,14) (1,12) (1,20) (1,5) (1,4) (1,19) (1,18) (1,21) (2,6) (2,11) (2,10) (2,17) (2,7) (2,3) (3,6) (3,11) (3,10) (3,17) (3,7) (4,13) (4,22) (4,15) (4,9) (4,14) (4,12) (4,20) (4,5) (4,19) (4,18) (4,21) (5,13) (5,22) (5,15) (5,9) (5,14) (5,12) (5,20) (5,19) (5,18) (5,21) (6,11) (6,10) (6,17) (6,7) (7,11) (7,10) (7,17) (8,16) (9,13) (9,22) (9,15) (9,14) (9,12) (9,20) (9,19) (9,18) (9,21) (10,11) (10,17) (11,17) (12,13) (12,22) (12,15) (12,14) (12,20) (12,19) (12,18) (12,21) (13,22) (13,15) (13,14) (13,20) (13,19) (13,18) (13,21) (14,22) (14,15) (14,20) (14,19) (14,18) (14,21) (15,22) (15,20) (15,19) (15,18) (15,21) (18,22) (18,20) (18,19) (18,21) (19,22) (19,20) (19,21) (20,22) (20,21) (21,22)\nIs there a path between node 2 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph614-23_20", + "image": "data/connectivity/graph_visual/medium/graph614.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,18) (0,1) (0,6) (0,10) (1,8) (1,18) (1,6) (1,10) (2,21) (2,20) (2,19) (2,14) (2,16) (2,13) (2,3) (2,12) (2,4) (2,22) (2,11) (2,9) (2,17) (2,15) (3,21) (3,20) (3,19) (3,14) (3,16) (3,13) (3,12) (3,4) (3,22) (3,11) (3,9) (3,17) (3,15) (4,21) (4,20) (4,19) (4,14) (4,16) (4,13) (4,12) (4,22) (4,11) (4,9) (4,17) (4,15) (5,7) (6,8) (6,18) (6,10) (8,18) (8,10) (9,21) (9,20) (9,19) (9,14) (9,16) (9,13) (9,12) (9,22) (9,11) (9,17) (9,15) (10,18) (11,21) (11,20) (11,19) (11,14) (11,16) (11,13) (11,12) (11,22) (11,17) (11,15) (12,21) (12,20) (12,19) (12,14) (12,16) (12,13) (12,22) (12,17) (12,15) (13,21) (13,20) (13,19) (13,14) (13,16) (13,22) (13,17) (13,15) (14,21) (14,20) (14,19) (14,16) (14,22) (14,17) (14,15) (15,21) (15,20) (15,19) (15,16) (15,22) (15,17) (16,21) (16,20) (16,19) (16,22) (16,17) (17,21) (17,20) (17,19) (17,22) (19,21) (19,20) (19,22) (20,21) (20,22) (21,22)\nIs there a path between node 23 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph184-5_3", + "image": "data/connectivity/graph_visual/medium/graph184.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,4) (0,2) (0,8) (0,1) (0,12) (0,9) (0,6) (0,5) (0,11) (0,13) (0,17) (0,7) (0,14) (0,15) (1,4) (1,2) (1,8) (1,12) (1,9) (1,6) (1,5) (1,11) (1,13) (1,17) (1,7) (1,14) (1,15) (2,4) (2,8) (2,12) (2,9) (2,6) (2,5) (2,11) (2,13) (2,17) (2,7) (2,14) (2,15) (3,10) (4,8) (4,12) (4,9) (4,6) (4,5) (4,11) (4,13) (4,17) (4,7) (4,14) (4,15) (5,8) (5,12) (5,9) (5,6) (5,11) (5,13) (5,17) (5,7) (5,14) (5,15) (6,8) (6,12) (6,9) (6,11) (6,13) (6,17) (6,7) (6,14) (6,15) (7,8) (7,12) (7,9) (7,11) (7,13) (7,17) (7,14) (7,15) (8,12) (8,9) (8,11) (8,13) (8,17) (8,14) (8,15) (9,12) (9,11) (9,13) (9,17) (9,14) (9,15) (11,12) (11,13) (11,17) (11,14) (11,15) (12,13) (12,17) (12,14) (12,15) (13,17) (13,14) (13,15) (14,17) (14,15) (15,17)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph452-18_3", + "image": "data/connectivity/graph_visual/medium/graph452.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,5) (0,13) (0,16) (0,4) (0,12) (1,5) (1,13) (1,9) (1,16) (1,4) (1,2) (2,13) (2,14) (2,4) (3,11) (3,19) (3,18) (3,15) (3,20) (3,6) (3,8) (3,10) (3,21) (4,13) (4,14) (4,9) (4,12) (5,13) (5,14) (5,9) (5,16) (6,11) (6,19) (6,18) (6,15) (6,17) (6,10) (6,21) (6,7) (7,11) (7,19) (7,18) (7,15) (7,20) (7,17) (7,8) (7,10) (7,21) (8,11) (8,18) (8,15) (8,20) (8,21) (9,13) (9,14) (9,16) (9,12) (10,11) (10,19) (10,18) (10,20) (10,17) (10,21) (11,18) (11,20) (14,16) (15,19) (15,18) (15,20) (15,17) (15,21) (17,19) (17,18) (17,20) (17,21) (18,19) (18,20) (19,20) (19,21) (20,21)\nIs there a path between node 18 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph238-8_5", + "image": "data/connectivity/graph_visual/medium/graph238.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,2) (0,5) (0,7) (0,18) (0,13) (0,11) (0,17) (1,8) (1,7) (1,18) (1,13) (1,9) (1,15) (1,11) (1,10) (2,8) (2,5) (2,7) (2,15) (3,14) (3,4) (3,12) (4,12) (5,8) (5,18) (5,13) (5,9) (5,11) (5,17) (6,16) (7,18) (7,13) (7,9) (7,11) (7,17) (8,18) (8,13) (8,9) (8,15) (8,11) (8,17) (8,10) (9,18) (9,13) (9,15) (9,17) (10,15) (10,17) (11,18) (11,13) (11,15) (11,17) (12,14) (13,18) (13,15) (15,18) (15,17) (17,18)\nIs there a path between node 8 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph72-0_8", + "image": "data/connectivity/graph_visual/medium/graph72.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (0,9) (1,10) (1,3) (2,6) (2,4) (2,7) (3,6) (3,10) (3,9) (3,12) (4,8) (5,9) (5,12) (6,9) (6,12) (6,7) (7,10) (7,9) (7,14) (8,10) (8,9) (8,14) (12,14)\nIs there a path between node 0 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph438-7_18", + "image": "data/connectivity/graph_visual/medium/graph438.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,10) (0,5) (0,20) (0,7) (0,19) (0,1) (0,14) (0,12) (0,15) (0,18) (0,4) (1,10) (1,5) (1,7) (1,2) (1,14) (1,12) (1,3) (1,15) (1,16) (1,4) (2,10) (2,5) (2,20) (2,7) (2,19) (2,14) (2,12) (2,15) (2,16) (2,17) (2,18) (2,4) (3,5) (3,20) (3,7) (3,19) (3,14) (3,16) (3,17) (3,18) (4,10) (4,5) (4,20) (4,7) (4,19) (4,14) (4,12) (4,15) (4,16) (4,17) (5,20) (5,7) (5,19) (5,14) (5,12) (5,16) (5,17) (5,18) (6,11) (6,8) (7,10) (7,19) (7,14) (7,12) (7,15) (7,16) (7,17) (7,18) (8,11) (9,21) (9,13) (10,19) (10,14) (10,12) (10,16) (10,18) (12,20) (12,19) (12,14) (12,15) (12,16) (12,17) (14,20) (14,19) (14,15) (14,16) (14,17) (15,20) (15,19) (15,16) (15,17) (15,18) (16,20) (16,19) (16,17) (16,18) (17,20) (17,19) (17,18) (18,19) (19,20)\nIs there a path between node 7 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph814-12_22", + "image": "data/connectivity/graph_visual/medium/graph814.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,8) (0,9) (0,6) (0,18) (0,13) (0,19) (1,21) (1,5) (1,17) (2,16) (2,20) (2,10) (2,12) (2,23) (2,7) (3,4) (3,14) (4,14) (5,21) (6,8) (6,18) (6,13) (6,19) (7,16) (7,10) (7,12) (7,23) (8,9) (8,18) (8,13) (8,19) (9,15) (9,18) (9,13) (10,16) (10,24) (10,23) (10,11) (10,22) (11,24) (11,20) (11,12) (11,23) (11,22) (12,24) (12,20) (13,15) (13,18) (15,18) (16,23) (16,22) (17,21) (18,19) (20,24) (20,23) (20,22) (22,23)\nIs there a path between node 12 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph285-16_18", + "image": "data/connectivity/graph_visual/medium/graph285.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,14) (1,9) (1,2) (1,8) (2,18) (2,6) (2,5) (2,8) (2,11) (3,7) (5,13) (5,6) (5,9) (5,8) (6,12) (6,13) (6,18) (6,10) (6,9) (6,8) (6,11) (7,15) (8,16) (8,9) (9,13) (9,10) (10,16) (10,11) (11,12) (11,16) (12,16) (13,16) (14,15)\nIs there a path between node 16 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph595-3_16", + "image": "data/connectivity/graph_visual/medium/graph595.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,5) (0,23) (0,17) (1,16) (1,11) (1,6) (2,7) (2,12) (2,5) (3,11) (3,6) (4,15) (4,19) (4,10) (4,9) (4,21) (4,14) (4,8) (5,12) (5,18) (5,23) (5,17) (6,11) (7,18) (7,17) (8,19) (8,10) (8,21) (8,14) (9,15) (9,19) (9,13) (9,14) (10,15) (10,19) (10,21) (10,14) (11,16) (12,18) (12,23) (12,17) (13,15) (13,21) (13,14) (14,15) (14,19) (14,21) (15,19) (15,21) (17,18) (17,23) (18,23) (19,21)\nIs there a path between node 3 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph543-8_16", + "image": "data/connectivity/graph_visual/medium/graph543.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,15) (0,8) (0,12) (0,14) (0,2) (0,9) (0,1) (1,15) (1,20) (1,12) (2,20) (2,12) (2,7) (2,16) (3,15) (3,7) (3,16) (3,13) (3,14) (3,17) (3,21) (4,22) (4,8) (4,12) (4,17) (4,11) (6,23) (7,15) (7,17) (7,11) (7,21) (7,18) (8,22) (8,15) (8,20) (8,16) (8,9) (9,22) (9,13) (9,11) (9,21) (9,18) (10,22) (10,13) (10,21) (11,22) (11,15) (11,20) (11,12) (11,21) (11,18) (12,15) (12,13) (13,20) (13,18) (14,20) (17,22) (17,18) (18,20) (19,23) (20,22) (21,22)\nIs there a path between node 8 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph251-18_16", + "image": "data/connectivity/graph_visual/medium/graph251.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,3) (0,1) (0,15) (0,9) (0,2) (0,6) (0,14) (0,8) (0,11) (0,10) (0,7) (1,13) (1,3) (1,15) (1,9) (1,2) (1,6) (1,14) (1,8) (1,11) (1,10) (1,7) (2,13) (2,3) (2,15) (2,9) (2,6) (2,14) (2,8) (2,11) (2,10) (2,7) (3,13) (3,15) (3,9) (3,6) (3,14) (3,8) (3,11) (3,10) (3,7) (4,12) (5,16) (5,18) (5,17) (6,13) (6,15) (6,9) (6,14) (6,8) (6,11) (6,10) (6,7) (7,13) (7,15) (7,9) (7,14) (7,8) (7,11) (7,10) (8,13) (8,15) (8,9) (8,14) (8,11) (8,10) (9,13) (9,15) (9,14) (9,11) (9,10) (10,13) (10,15) (10,14) (10,11) (11,13) (11,15) (11,14) (13,15) (13,14) (14,15) (16,18) (16,17) (17,18)\nIs there a path between node 18 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph482-14_12", + "image": "data/connectivity/graph_visual/medium/graph482.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,5) (0,15) (0,19) (0,21) (0,13) (0,10) (0,6) (0,17) (0,18) (0,9) (0,7) (0,4) (1,15) (1,19) (1,21) (1,2) (1,13) (1,3) (1,8) (1,12) (1,18) (1,20) (1,9) (1,7) (1,4) (1,11) (2,5) (2,15) (2,19) (2,21) (2,3) (2,10) (2,16) (2,6) (2,8) (2,17) (2,12) (2,20) (2,9) (2,7) (2,4) (2,11) (3,5) (3,15) (3,21) (3,13) (3,10) (3,8) (3,12) (3,18) (3,9) (3,7) (3,11) (4,5) (4,15) (4,19) (4,21) (4,10) (4,16) (4,6) (4,8) (4,12) (4,20) (5,15) (5,19) (5,21) (5,13) (5,10) (5,6) (5,17) (5,12) (5,18) (5,20) (5,9) (5,7) (6,15) (6,13) (6,8) (6,17) (6,12) (6,18) (6,7) (6,11) (7,21) (7,13) (7,10) (7,8) (7,17) (7,12) (7,18) (7,20) (7,11) (8,15) (8,19) (8,21) (8,13) (8,10) (8,16) (8,17) (8,12) (8,18) (8,20) (9,15) (9,19) (9,21) (9,16) (9,17) (9,12) (9,18) (9,20) (10,15) (10,19) (10,21) (10,13) (10,16) (10,17) (10,18) (11,19) (11,21) (11,13) (11,17) (11,20) (12,15) (12,21) (12,13) (12,16) (12,17) (12,18) (12,20) (13,15) (13,19) (13,16) (13,17) (13,18) (13,20) (15,19) (15,21) (15,18) (15,20) (16,19) (16,21) (16,17) (16,18) (16,20) (17,19) (18,19) (18,20) (19,21) (19,20) (20,21)\nIs there a path between node 14 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph261-16_4", + "image": "data/connectivity/graph_visual/medium/graph261.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,2) (0,19) (1,11) (2,4) (2,13) (3,17) (3,10) (3,11) (5,8) (5,13) (6,10) (6,12) (7,18) (7,9) (10,17) (10,12) (11,12) (12,17) (13,16) (13,15) (14,18)\nIs there a path between node 16 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph406-19_3", + "image": "data/connectivity/graph_visual/medium/graph406.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,14) (0,13) (1,20) (1,12) (1,3) (1,15) (1,19) (2,3) (2,15) (3,11) (3,10) (4,20) (4,8) (4,19) (4,10) (5,9) (8,20) (8,15) (8,10) (9,13) (10,20) (11,15) (12,20) (12,15) (13,18) (15,20) (18,21) (19,20)\nIs there a path between node 19 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph31-0_6", + "image": "data/connectivity/graph_visual/medium/graph31.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,6) (0,9) (0,11) (1,7) (1,3) (1,4) (1,5) (1,8) (1,2) (1,10) (2,7) (2,3) (2,4) (2,5) (2,8) (2,10) (3,7) (3,4) (3,5) (3,8) (3,10) (4,7) (4,5) (4,8) (4,10) (5,7) (5,8) (5,10) (6,9) (6,11) (7,8) (7,10) (8,10) (9,11)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph209-5_7", + "image": "data/connectivity/graph_visual/medium/graph209.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,7) (0,6) (0,13) (0,12) (0,9) (0,18) (0,15) (0,17) (1,16) (1,2) (1,3) (2,3) (4,11) (4,8) (4,7) (4,9) (4,18) (4,14) (4,15) (5,8) (5,12) (5,10) (5,15) (6,11) (6,8) (6,7) (6,12) (6,18) (6,10) (6,14) (6,15) (6,17) (7,11) (7,8) (7,13) (7,12) (7,9) (7,10) (7,14) (7,15) (8,13) (8,12) (8,9) (8,18) (8,14) (8,17) (9,11) (9,12) (9,18) (9,10) (9,14) (9,15) (9,17) (10,11) (10,13) (10,18) (10,14) (10,17) (11,13) (11,18) (11,14) (12,18) (12,15) (12,17) (13,18) (13,14) (13,15) (14,18) (14,15) (14,17) (15,18) (15,17) (17,18)\nIs there a path between node 5 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph272-0_3", + "image": "data/connectivity/graph_visual/medium/graph272.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,13) (0,9) (0,7) (0,12) (0,4) (0,5) (0,19) (0,6) (0,1) (0,17) (1,14) (1,9) (1,3) (1,7) (1,12) (1,4) (1,5) (1,19) (1,15) (1,17) (2,11) (2,8) (2,10) (3,13) (3,14) (3,9) (3,7) (3,12) (3,4) (3,5) (3,6) (3,18) (3,15) (4,13) (4,9) (4,12) (4,19) (4,6) (4,18) (4,15) (4,17) (5,13) (5,14) (5,7) (5,12) (5,19) (5,15) (5,17) (6,13) (6,9) (6,7) (6,19) (6,15) (6,17) (7,13) (7,14) (7,9) (7,12) (7,19) (7,18) (7,17) (8,11) (8,16) (8,10) (9,14) (9,18) (9,17) (10,11) (11,16) (12,14) (12,19) (12,18) (12,15) (12,17) (13,14) (13,19) (13,18) (13,17) (14,19) (14,18) (14,15) (14,17) (15,17) (17,19) (17,18) (18,19)\nIs there a path between node 0 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph703-2_18", + "image": "data/connectivity/graph_visual/medium/graph703.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,13) (0,17) (0,11) (0,16) (0,14) (0,8) (1,3) (1,20) (2,3) (2,20) (2,21) (3,23) (3,20) (3,18) (6,13) (6,22) (6,14) (6,9) (7,17) (7,22) (7,14) (7,24) (7,9) (8,13) (8,17) (8,22) (8,16) (8,14) (8,24) (9,15) (9,17) (9,11) (9,19) (9,10) (9,24) (9,12) (10,15) (10,17) (10,11) (11,15) (11,22) (12,22) (12,24) (13,15) (13,22) (13,16) (13,24) (14,15) (14,19) (15,24) (16,22) (16,24) (18,20) (18,21) (21,23) (22,24)\nIs there a path between node 2 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph372-5_10", + "image": "data/connectivity/graph_visual/medium/graph372.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (0,6) (0,13) (0,9) (0,16) (0,8) (0,3) (0,1) (0,2) (0,18) (0,19) (1,17) (1,6) (1,13) (1,9) (1,16) (1,8) (1,3) (1,10) (1,2) (1,4) (1,18) (2,17) (2,6) (2,9) (2,16) (2,8) (2,3) (2,4) (2,19) (3,17) (3,6) (3,13) (3,9) (3,8) (3,4) (3,19) (4,6) (4,9) (4,16) (4,18) (5,12) (5,14) (5,7) (5,11) (5,15) (5,20) (6,13) (6,16) (6,10) (6,18) (6,19) (7,12) (7,11) (7,20) (8,19) (9,13) (9,16) (9,10) (9,18) (10,16) (11,12) (11,14) (11,20) (12,20) (13,16) (13,18) (13,19) (14,20) (15,20) (16,17) (16,19) (17,18) (18,19)\nIs there a path between node 5 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph223-0_12", + "image": "data/connectivity/graph_visual/medium/graph223.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,1) (1,12) (2,18) (2,14) (3,17) (4,5) (4,11) (6,11) (6,13) (9,14) (13,17)\nIs there a path between node 0 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph151-0_8", + "image": "data/connectivity/graph_visual/medium/graph151.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,13) (0,14) (0,7) (0,8) (0,17) (0,4) (1,5) (1,3) (1,15) (1,16) (1,11) (1,12) (1,10) (1,9) (1,6) (1,2) (2,5) (2,3) (2,15) (2,16) (2,11) (2,12) (2,10) (2,9) (2,6) (3,5) (3,15) (3,16) (3,11) (3,12) (3,10) (3,9) (3,6) (4,13) (4,14) (4,7) (4,8) (4,17) (5,15) (5,16) (5,11) (5,12) (5,10) (5,9) (5,6) (6,15) (6,16) (6,11) (6,12) (6,10) (6,9) (7,13) (7,14) (7,8) (7,17) (8,13) (8,14) (8,17) (9,15) (9,16) (9,11) (9,12) (9,10) (10,15) (10,16) (10,11) (10,12) (11,15) (11,16) (11,12) (12,15) (12,16) (13,14) (13,17) (14,17) (15,16)\nIs there a path between node 0 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph144-1_15", + "image": "data/connectivity/graph_visual/medium/graph144.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,14) (0,8) (0,3) (0,12) (0,17) (0,2) (0,15) (1,13) (1,8) (1,17) (1,16) (1,2) (1,9) (2,3) (2,12) (2,16) (3,6) (3,14) (3,8) (3,17) (3,16) (3,15) (4,7) (4,5) (4,11) (5,11) (6,10) (6,13) (6,14) (6,8) (6,17) (6,9) (7,11) (8,13) (8,14) (8,12) (8,17) (8,16) (8,9) (9,10) (9,13) (9,14) (9,12) (9,17) (9,16) (9,15) (10,12) (10,17) (10,16) (10,15) (12,13) (12,14) (12,17) (12,16) (12,15) (13,17) (13,16) (13,15) (14,17) (14,15) (15,16) (16,17)\nIs there a path between node 1 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph307-11_19", + "image": "data/connectivity/graph_visual/medium/graph307.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,11) (0,12) (0,1) (0,6) (0,2) (1,3) (1,11) (1,13) (1,12) (1,6) (1,19) (1,2) (2,3) (2,11) (2,13) (2,12) (2,19) (3,13) (3,12) (3,10) (3,19) (4,18) (5,16) (5,17) (5,9) (5,15) (5,7) (6,13) (6,12) (6,10) (7,14) (8,18) (9,16) (9,14) (9,17) (9,15) (10,11) (10,12) (10,19) (11,13) (11,12) (11,19) (12,13) (12,19) (13,19) (14,15) (15,16) (15,17) (16,17)\nIs there a path between node 11 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph310-2_1", + "image": "data/connectivity/graph_visual/medium/graph310.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (0,10) (0,19) (0,16) (0,7) (0,8) (0,4) (0,3) (0,11) (0,1) (0,18) (0,9) (0,5) (0,2) (0,13) (1,17) (1,10) (1,19) (1,16) (1,7) (1,8) (1,4) (1,3) (1,11) (1,18) (1,9) (1,5) (1,2) (1,13) (2,17) (2,10) (2,19) (2,16) (2,7) (2,8) (2,4) (2,3) (2,11) (2,18) (2,9) (2,5) (2,13) (3,17) (3,10) (3,19) (3,16) (3,7) (3,8) (3,4) (3,11) (3,18) (3,9) (3,5) (3,13) (4,17) (4,10) (4,19) (4,16) (4,7) (4,8) (4,11) (4,18) (4,9) (4,5) (4,13) (5,17) (5,10) (5,19) (5,16) (5,7) (5,8) (5,11) (5,18) (5,9) (5,13) (6,15) (7,17) (7,10) (7,19) (7,16) (7,8) (7,11) (7,18) (7,9) (7,13) (8,17) (8,10) (8,19) (8,16) (8,11) (8,18) (8,9) (8,13) (9,17) (9,10) (9,19) (9,16) (9,11) (9,18) (9,13) (10,17) (10,19) (10,16) (10,11) (10,18) (10,13) (11,17) (11,19) (11,16) (11,18) (11,13) (12,14) (13,17) (13,19) (13,16) (13,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nIs there a path between node 2 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph241-9_12", + "image": "data/connectivity/graph_visual/medium/graph241.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,10) (1,14) (1,18) (1,4) (1,11) (1,15) (1,7) (1,5) (1,3) (2,14) (2,18) (2,16) (2,6) (2,4) (2,9) (2,11) (2,15) (2,7) (2,5) (2,3) (3,14) (3,16) (3,6) (3,4) (3,9) (3,11) (3,15) (3,7) (3,5) (4,14) (4,8) (4,9) (4,11) (4,15) (5,18) (5,16) (5,8) (5,6) (5,9) (5,11) (5,15) (5,7) (6,14) (6,16) (6,12) (6,15) (6,7) (7,14) (7,18) (7,16) (7,12) (7,8) (7,9) (7,15) (8,14) (8,18) (8,16) (8,9) (8,11) (8,15) (9,18) (9,16) (9,11) (11,18) (11,16) (11,12) (11,15) (12,14) (12,18) (12,16) (12,15) (14,18) (14,16) (14,15) (15,16) (16,18)\nIs there a path between node 9 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph585-9_13", + "image": "data/connectivity/graph_visual/medium/graph585.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,10) (0,11) (0,13) (0,8) (0,22) (1,18) (2,16) (2,14) (2,21) (2,22) (2,12) (3,17) (4,10) (4,11) (4,16) (4,9) (4,13) (4,14) (4,21) (4,15) (4,22) (4,5) (5,23) (6,11) (6,16) (6,23) (8,11) (8,15) (8,22) (9,10) (9,11) (9,15) (9,22) (10,16) (10,21) (10,15) (11,15) (11,22) (12,16) (12,21) (13,16) (13,22) (14,22) (14,23) (15,22) (16,21) (21,22) (21,23) (22,23)\nIs there a path between node 9 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph743-22_7", + "image": "data/connectivity/graph_visual/medium/graph743.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (1,22) (1,6) (1,2) (1,14) (2,16) (2,20) (2,5) (2,23) (3,16) (3,20) (3,8) (3,5) (3,6) (4,10) (4,24) (5,17) (5,22) (5,20) (5,7) (6,17) (6,9) (6,23) (7,22) (7,20) (8,16) (8,22) (8,14) (9,16) (9,22) (9,20) (9,12) (9,23) (10,11) (12,22) (12,23) (13,18) (14,16) (14,22) (16,17) (16,22) (16,20) (20,22) (20,23)\nIs there a path between node 22 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph5-10_6", + "image": "data/connectivity/graph_visual/medium/graph5.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,10) (1,8) (1,9) (2,10) (2,3) (3,7) (5,10) (6,8) (7,8) (7,9)\nIs there a path between node 10 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph725-14_21", + "image": "data/connectivity/graph_visual/medium/graph725.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,20) (0,7) (0,2) (0,5) (0,18) (0,9) (0,16) (0,21) (0,13) (0,11) (0,14) (0,22) (0,15) (0,6) (2,20) (2,7) (2,5) (2,18) (2,9) (2,16) (2,21) (2,13) (2,11) (2,14) (2,22) (2,15) (2,6) (3,4) (3,10) (3,8) (3,17) (3,19) (3,23) (3,24) (4,10) (4,8) (4,17) (4,19) (4,23) (4,24) (5,20) (5,7) (5,18) (5,9) (5,16) (5,21) (5,13) (5,11) (5,14) (5,22) (5,15) (5,6) (6,20) (6,7) (6,18) (6,9) (6,16) (6,21) (6,13) (6,11) (6,14) (6,22) (6,15) (7,20) (7,18) (7,9) (7,16) (7,21) (7,13) (7,11) (7,14) (7,22) (7,15) (8,10) (8,17) (8,19) (8,23) (8,24) (9,20) (9,18) (9,16) (9,21) (9,13) (9,11) (9,14) (9,22) (9,15) (10,17) (10,19) (10,23) (10,24) (11,20) (11,18) (11,16) (11,21) (11,13) (11,14) (11,22) (11,15) (13,20) (13,18) (13,16) (13,21) (13,14) (13,22) (13,15) (14,20) (14,18) (14,16) (14,21) (14,22) (14,15) (15,20) (15,18) (15,16) (15,21) (15,22) (16,20) (16,18) (16,21) (16,22) (17,19) (17,23) (17,24) (18,20) (18,21) (18,22) (19,23) (19,24) (20,21) (20,22) (21,22) (23,24)\nIs there a path between node 14 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph145-13_2", + "image": "data/connectivity/graph_visual/medium/graph145.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (0,12) (0,4) (0,11) (0,17) (0,2) (0,5) (0,9) (0,8) (0,16) (0,10) (1,3) (1,12) (1,4) (1,11) (1,17) (1,7) (1,2) (1,5) (1,9) (1,8) (1,10) (2,3) (2,12) (2,4) (2,11) (2,17) (2,7) (2,5) (2,8) (2,16) (3,12) (3,7) (3,9) (3,8) (4,12) (4,11) (4,17) (4,5) (4,9) (4,8) (4,16) (4,10) (5,12) (5,11) (5,17) (5,7) (5,14) (5,9) (5,16) (5,10) (6,15) (6,13) (7,12) (7,11) (7,17) (7,9) (7,16) (7,10) (8,11) (8,14) (8,9) (8,16) (8,10) (9,12) (9,17) (9,10) (10,11) (10,17) (10,14) (10,16) (11,17) (11,16) (14,16) (16,17)\nIs there a path between node 13 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph344-1_16", + "image": "data/connectivity/graph_visual/medium/graph344.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,14) (0,8) (0,2) (0,1) (0,18) (0,4) (0,5) (0,16) (0,10) (0,19) (0,6) (0,7) (1,14) (1,8) (1,2) (1,18) (1,4) (1,5) (1,16) (1,10) (1,19) (1,6) (1,7) (2,14) (2,8) (2,18) (2,4) (2,5) (2,16) (2,10) (2,19) (2,6) (2,7) (3,17) (3,11) (3,9) (3,15) (3,20) (3,12) (3,13) (4,14) (4,8) (4,18) (4,5) (4,16) (4,10) (4,19) (4,6) (4,7) (5,14) (5,8) (5,18) (5,16) (5,10) (5,19) (5,6) (5,7) (6,14) (6,8) (6,18) (6,16) (6,10) (6,19) (6,7) (7,14) (7,8) (7,18) (7,16) (7,10) (7,19) (8,14) (8,18) (8,16) (8,10) (8,19) (9,17) (9,11) (9,15) (9,20) (9,12) (9,13) (10,14) (10,18) (10,16) (10,19) (11,17) (11,15) (11,20) (11,12) (11,13) (12,17) (12,15) (12,20) (12,13) (13,17) (13,15) (13,20) (14,18) (14,16) (14,19) (15,17) (15,20) (16,18) (16,19) (17,20) (18,19)\nIs there a path between node 1 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph567-23_16", + "image": "data/connectivity/graph_visual/medium/graph567.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,14) (0,6) (0,18) (0,11) (0,5) (0,21) (0,10) (1,22) (1,16) (1,2) (1,9) (1,7) (1,13) (1,20) (1,19) (1,15) (1,23) (1,4) (1,3) (1,12) (1,8) (1,17) (2,22) (2,16) (2,9) (2,7) (2,13) (2,20) (2,19) (2,15) (2,23) (2,4) (2,3) (2,12) (2,8) (2,17) (3,22) (3,16) (3,9) (3,7) (3,13) (3,20) (3,19) (3,15) (3,23) (3,4) (3,12) (3,8) (3,17) (4,22) (4,16) (4,9) (4,7) (4,13) (4,20) (4,19) (4,15) (4,23) (4,12) (4,8) (4,17) (5,14) (5,6) (5,18) (5,11) (5,21) (5,10) (6,14) (6,18) (6,11) (6,21) (6,10) (7,22) (7,16) (7,9) (7,13) (7,20) (7,19) (7,15) (7,23) (7,12) (7,8) (7,17) (8,22) (8,16) (8,9) (8,13) (8,20) (8,19) (8,15) (8,23) (8,12) (8,17) (9,22) (9,16) (9,13) (9,20) (9,19) (9,15) (9,23) (9,12) (9,17) (10,14) (10,18) (10,11) (10,21) (11,14) (11,18) (11,21) (12,22) (12,16) (12,13) (12,20) (12,19) (12,15) (12,23) (12,17) (13,22) (13,16) (13,20) (13,19) (13,15) (13,23) (13,17) (14,18) (14,21) (15,22) (15,16) (15,20) (15,19) (15,23) (15,17) (16,22) (16,20) (16,19) (16,23) (16,17) (17,22) (17,20) (17,19) (17,23) (18,21) (19,22) (19,20) (19,23) (20,22) (20,23) (22,23)\nIs there a path between node 23 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph855-15_1", + "image": "data/connectivity/graph_visual/medium/graph855.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (0,13) (0,18) (0,21) (0,5) (0,12) (0,10) (0,7) (0,20) (0,17) (0,8) (0,24) (0,3) (0,9) (0,22) (0,16) (0,6) (0,19) (0,15) (1,4) (1,11) (1,23) (1,14) (2,13) (2,18) (2,21) (2,5) (2,12) (2,10) (2,7) (2,20) (2,17) (2,8) (2,24) (2,3) (2,9) (2,22) (2,16) (2,6) (2,19) (2,15) (3,13) (3,18) (3,21) (3,5) (3,12) (3,10) (3,7) (3,20) (3,17) (3,8) (3,24) (3,9) (3,22) (3,16) (3,6) (3,19) (3,15) (4,11) (4,23) (4,14) (5,13) (5,18) (5,21) (5,12) (5,10) (5,7) (5,20) (5,17) (5,8) (5,24) (5,9) (5,22) (5,16) (5,6) (5,19) (5,15) (6,13) (6,18) (6,21) (6,12) (6,10) (6,7) (6,20) (6,17) (6,8) (6,24) (6,9) (6,22) (6,16) (6,19) (6,15) (7,13) (7,18) (7,21) (7,12) (7,10) (7,20) (7,17) (7,8) (7,24) (7,9) (7,22) (7,16) (7,19) (7,15) (8,13) (8,18) (8,21) (8,12) (8,10) (8,20) (8,17) (8,24) (8,9) (8,22) (8,16) (8,19) (8,15) (9,13) (9,18) (9,21) (9,12) (9,10) (9,20) (9,17) (9,24) (9,22) (9,16) (9,19) (9,15) (10,13) (10,18) (10,21) (10,12) (10,20) (10,17) (10,24) (10,22) (10,16) (10,19) (10,15) (11,23) (11,14) (12,13) (12,18) (12,21) (12,20) (12,17) (12,24) (12,22) (12,16) (12,19) (12,15) (13,18) (13,21) (13,20) (13,17) (13,24) (13,22) (13,16) (13,19) (13,15) (14,23) (15,18) (15,21) (15,20) (15,17) (15,24) (15,22) (15,16) (15,19) (16,18) (16,21) (16,20) (16,17) (16,24) (16,22) (16,19) (17,18) (17,21) (17,20) (17,24) (17,22) (17,19) (18,21) (18,20) (18,24) (18,22) (18,19) (19,21) (19,20) (19,24) (19,22) (20,21) (20,24) (20,22) (21,24) (21,22) (22,24)\nIs there a path between node 15 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph331-19_18", + "image": "data/connectivity/graph_visual/medium/graph331.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,12) (0,16) (0,17) (0,18) (0,14) (0,7) (2,15) (2,13) (2,4) (4,8) (5,8) (7,16) (7,18) (8,20) (8,13) (9,14) (10,16) (10,18) (15,19) (19,20)\nIs there a path between node 19 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph21-6_0", + "image": "data/connectivity/graph_visual/medium/graph21.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,9) (0,1) (1,7) (1,9) (2,3) (2,6) (3,10) (4,8) (7,9) (8,9) (10,11)\nIs there a path between node 6 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph73-6_4", + "image": "data/connectivity/graph_visual/medium/graph73.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (0,12) (0,5) (1,12) (1,8) (2,3) (2,8) (2,5) (3,9) (3,10) (3,12) (3,8) (5,12) (6,13) (7,10) (7,14) (8,10) (9,10) (12,14)\nIs there a path between node 6 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph294-17_12", + "image": "data/connectivity/graph_visual/medium/graph294.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,1) (0,19) (1,13) (1,19) (1,11) (1,14) (1,2) (2,4) (2,18) (3,10) (4,13) (4,11) (5,6) (5,10) (5,7) (6,12) (6,7) (7,10) (8,18) (9,15) (10,12) (11,19) (12,15) (13,18)\nIs there a path between node 17 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph19-6_9", + "image": "data/connectivity/graph_visual/medium/graph19.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,8) (0,4) (0,11) (1,3) (3,9) (3,7) (4,8) (5,11) (6,10) (6,9) (6,7) (8,11)\nIs there a path between node 6 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph38-0_12", + "image": "data/connectivity/graph_visual/medium/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,12) (1,9) (2,10) (2,4) (2,12) (3,7) (4,12) (8,10) (8,11) (10,11)\nIs there a path between node 0 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph579-4_11", + "image": "data/connectivity/graph_visual/medium/graph579.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,3) (0,8) (0,10) (0,2) (0,13) (0,19) (1,23) (2,6) (2,20) (2,11) (2,12) (2,8) (2,17) (2,22) (2,5) (2,19) (3,11) (3,12) (3,21) (3,22) (5,16) (5,6) (5,8) (5,17) (5,13) (5,19) (6,20) (6,22) (6,7) (7,8) (7,10) (7,13) (8,11) (8,10) (8,13) (9,20) (9,10) (10,16) (10,11) (11,16) (12,17) (12,22) (12,13) (13,21) (14,23) (14,15) (17,20) (17,21) (21,22)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph444-6_3", + "image": "data/connectivity/graph_visual/medium/graph444.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,3) (0,15) (0,21) (0,17) (0,7) (0,12) (0,5) (0,9) (0,2) (0,19) (0,14) (0,20) (1,3) (1,15) (1,16) (1,17) (1,11) (1,7) (1,12) (1,13) (1,8) (1,18) (1,9) (1,2) (1,19) (1,14) (1,20) (2,15) (2,21) (2,17) (2,11) (2,7) (2,12) (2,5) (2,8) (2,19) (2,14) (2,10) (2,20) (3,15) (3,21) (3,16) (3,17) (3,11) (3,13) (3,5) (3,8) (3,18) (3,14) (3,10) (3,20) (5,15) (5,21) (5,16) (5,17) (5,11) (5,7) (5,12) (5,13) (5,9) (5,19) (5,14) (5,10) (5,20) (7,21) (7,17) (7,11) (7,12) (7,8) (7,18) (7,19) (7,10) (7,20) (8,15) (8,21) (8,16) (8,17) (8,9) (8,19) (8,14) (8,10) (8,20) (9,15) (9,21) (9,16) (9,13) (9,18) (9,14) (10,15) (10,21) (10,16) (10,17) (10,11) (10,12) (10,13) (10,18) (10,19) (10,14) (10,20) (11,15) (11,21) (11,16) (11,17) (11,13) (11,18) (11,14) (11,20) (12,16) (12,17) (12,13) (12,18) (12,20) (13,15) (13,21) (13,16) (13,17) (13,18) (13,14) (13,20) (14,16) (14,17) (14,19) (14,20) (15,16) (15,17) (15,19) (16,17) (16,18) (16,19) (16,20) (17,21) (17,18) (18,19) (18,20) (19,21) (20,21)\nIs there a path between node 6 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph279-2_7", + "image": "data/connectivity/graph_visual/medium/graph279.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,19) (0,2) (0,14) (0,16) (0,7) (0,10) (1,12) (1,11) (1,13) (1,8) (1,17) (1,4) (2,19) (2,14) (2,16) (2,7) (2,10) (3,5) (3,15) (3,18) (3,6) (3,9) (4,12) (4,11) (4,13) (4,8) (4,17) (5,15) (5,18) (5,6) (5,9) (6,15) (6,18) (6,9) (7,19) (7,14) (7,16) (7,10) (8,12) (8,11) (8,13) (8,17) (9,15) (9,18) (10,19) (10,14) (10,16) (11,12) (11,13) (11,17) (12,13) (12,17) (13,17) (14,19) (14,16) (15,18) (16,19)\nIs there a path between node 2 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph634-20_6", + "image": "data/connectivity/graph_visual/medium/graph634.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,3) (0,9) (0,18) (0,2) (0,14) (0,20) (0,22) (0,4) (0,1) (0,19) (1,23) (1,2) (1,16) (1,20) (1,22) (1,11) (1,4) (1,12) (2,3) (2,5) (2,7) (2,9) (2,18) (2,16) (2,14) (2,20) (2,8) (2,4) (2,19) (3,15) (3,5) (3,18) (3,16) (3,8) (3,22) (3,11) (4,15) (4,5) (4,18) (4,11) (4,12) (4,19) (5,23) (5,15) (5,16) (5,12) (5,19) (6,17) (7,18) (7,14) (7,20) (8,15) (8,18) (8,21) (12,21) (12,22) (12,19) (14,23) (14,19) (15,19) (16,18) (18,19) (19,23) (19,20) (19,22) (20,23)\nIs there a path between node 20 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph589-22_5", + "image": "data/connectivity/graph_visual/medium/graph589.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,20) (0,6) (0,23) (0,19) (1,8) (1,4) (2,20) (2,17) (2,19) (2,15) (3,13) (3,15) (5,23) (5,12) (5,15) (5,18) (7,9) (9,14) (10,11) (12,23) (12,22) (12,15) (13,21) (13,15) (16,23) (16,17) (16,22) (16,18) (17,22) (18,21) (18,20) (18,22) (19,23) (20,23)\nIs there a path between node 22 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph598-19_16", + "image": "data/connectivity/graph_visual/medium/graph598.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,23) (0,22) (0,12) (0,10) (0,7) (0,5) (0,14) (0,9) (1,13) (1,6) (1,21) (1,18) (1,20) (1,3) (2,23) (2,22) (2,12) (2,10) (2,17) (2,15) (2,5) (2,14) (2,9) (3,13) (3,21) (3,18) (3,20) (3,4) (4,6) (4,21) (4,18) (4,20) (5,16) (5,22) (5,12) (5,17) (5,8) (5,19) (5,7) (5,15) (6,13) (6,21) (6,18) (7,23) (7,22) (7,12) (7,14) (7,9) (8,23) (8,16) (8,22) (8,12) (8,10) (8,17) (8,19) (8,15) (8,14) (9,16) (9,12) (9,10) (9,17) (9,19) (9,15) (9,14) (10,23) (10,16) (10,22) (10,12) (10,19) (10,14) (12,16) (12,22) (12,17) (12,19) (12,14) (13,21) (13,18) (13,20) (14,23) (14,16) (14,19) (14,15) (15,23) (15,16) (15,22) (15,17) (15,19) (16,23) (16,22) (16,19) (17,23) (17,19) (18,21) (18,20) (19,22) (22,23)\nIs there a path between node 19 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph350-17_18", + "image": "data/connectivity/graph_visual/medium/graph350.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (0,20) (0,4) (0,9) (0,18) (0,12) (0,5) (0,1) (0,17) (0,13) (0,2) (0,10) (0,7) (0,19) (0,15) (0,11) (0,8) (1,16) (1,20) (1,4) (1,9) (1,18) (1,12) (1,5) (1,17) (1,13) (1,2) (1,10) (1,7) (1,19) (1,15) (1,11) (1,8) (2,16) (2,20) (2,4) (2,9) (2,18) (2,12) (2,5) (2,17) (2,13) (2,10) (2,7) (2,19) (2,15) (2,11) (2,8) (3,14) (3,6) (4,16) (4,20) (4,9) (4,18) (4,12) (4,5) (4,17) (4,13) (4,10) (4,7) (4,19) (4,15) (4,11) (4,8) (5,16) (5,20) (5,9) (5,18) (5,12) (5,17) (5,13) (5,10) (5,7) (5,19) (5,15) (5,11) (5,8) (6,14) (7,16) (7,20) (7,9) (7,18) (7,12) (7,17) (7,13) (7,10) (7,19) (7,15) (7,11) (7,8) (8,16) (8,20) (8,9) (8,18) (8,12) (8,17) (8,13) (8,10) (8,19) (8,15) (8,11) (9,16) (9,20) (9,18) (9,12) (9,17) (9,13) (9,10) (9,19) (9,15) (9,11) (10,16) (10,20) (10,18) (10,12) (10,17) (10,13) (10,19) (10,15) (10,11) (11,16) (11,20) (11,18) (11,12) (11,17) (11,13) (11,19) (11,15) (12,16) (12,20) (12,18) (12,17) (12,13) (12,19) (12,15) (13,16) (13,20) (13,18) (13,17) (13,19) (13,15) (15,16) (15,20) (15,18) (15,17) (15,19) (16,20) (16,18) (16,17) (16,19) (17,20) (17,18) (17,19) (18,20) (18,19) (19,20)\nIs there a path between node 17 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph237-0_12", + "image": "data/connectivity/graph_visual/medium/graph237.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (0,11) (0,17) (0,16) (1,2) (1,12) (1,7) (1,3) (2,15) (2,5) (2,7) (2,3) (3,15) (3,5) (3,12) (3,7) (4,8) (4,10) (4,18) (4,6) (4,11) (4,9) (4,17) (4,14) (4,16) (5,15) (5,7) (6,8) (6,10) (6,18) (6,11) (6,9) (6,17) (6,16) (7,15) (7,12) (8,11) (8,9) (8,17) (8,14) (9,18) (9,11) (10,18) (10,11) (10,14) (10,16) (11,18) (11,17) (11,16) (14,18) (14,16) (16,18) (16,17) (17,18)\nIs there a path between node 0 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph287-17_5", + "image": "data/connectivity/graph_visual/medium/graph287.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,14) (0,4) (0,7) (1,17) (1,6) (1,2) (1,18) (2,5) (2,18) (3,10) (3,9) (3,19) (3,12) (3,8) (4,10) (4,15) (4,12) (5,18) (6,11) (6,16) (6,18) (7,10) (7,19) (7,12) (9,15) (10,14) (11,18) (12,13) (12,15) (13,19) (14,15) (15,19) (17,18)\nIs there a path between node 17 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph520-22_6", + "image": "data/connectivity/graph_visual/medium/graph520.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,18) (0,19) (0,3) (0,17) (0,2) (0,21) (0,13) (0,22) (1,19) (1,3) (1,2) (1,13) (2,18) (2,19) (2,5) (2,3) (2,17) (2,13) (2,22) (3,18) (3,5) (3,17) (4,8) (4,9) (4,7) (4,20) (4,12) (5,19) (5,21) (5,13) (6,8) (6,9) (6,20) (6,14) (6,10) (6,15) (6,12) (6,16) (7,9) (7,10) (7,15) (7,12) (7,16) (8,14) (8,16) (9,14) (9,11) (9,15) (9,12) (9,16) (10,20) (10,14) (10,11) (10,16) (11,20) (11,14) (11,12) (11,16) (12,15) (13,18) (13,17) (13,21) (14,20) (14,15) (14,16) (15,20) (15,16) (17,18) (17,21) (17,22) (18,19) (18,22)\nIs there a path between node 22 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph265-8_17", + "image": "data/connectivity/graph_visual/medium/graph265.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,12) (0,19) (0,11) (0,8) (0,10) (1,14) (1,13) (2,11) (2,6) (3,12) (3,19) (3,9) (4,7) (5,11) (5,10) (6,10) (7,16) (7,13) (8,19) (8,11) (9,12) (9,11) (9,18) (11,12) (11,19) (13,16) (13,17) (14,16) (14,17)\nIs there a path between node 8 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph688-2_19", + "image": "data/connectivity/graph_visual/medium/graph688.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,6) (0,11) (0,14) (0,2) (1,20) (1,8) (1,7) (1,16) (1,21) (1,9) (1,17) (1,5) (1,23) (1,12) (1,22) (2,4) (2,6) (2,11) (2,14) (3,15) (3,18) (3,13) (3,19) (3,10) (4,6) (4,11) (4,14) (5,20) (5,8) (5,7) (5,16) (5,21) (5,9) (5,17) (5,23) (5,12) (5,22) (6,11) (6,14) (7,20) (7,8) (7,16) (7,21) (7,9) (7,17) (7,23) (7,12) (7,22) (8,20) (8,16) (8,21) (8,9) (8,17) (8,23) (8,12) (8,22) (9,20) (9,16) (9,21) (9,17) (9,23) (9,12) (9,22) (10,15) (10,18) (10,13) (10,19) (11,14) (12,20) (12,16) (12,21) (12,17) (12,23) (12,22) (13,15) (13,18) (13,19) (15,18) (15,19) (16,20) (16,21) (16,17) (16,23) (16,22) (17,20) (17,21) (17,23) (17,22) (18,19) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nIs there a path between node 2 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph737-13_14", + "image": "data/connectivity/graph_visual/medium/graph737.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,6) (0,3) (0,16) (0,24) (0,7) (1,17) (1,2) (2,9) (2,20) (2,8) (3,22) (3,12) (3,23) (3,21) (4,9) (4,13) (4,18) (5,11) (5,23) (5,21) (6,15) (6,7) (7,11) (7,22) (7,12) (7,16) (7,23) (7,14) (7,21) (8,20) (8,17) (8,18) (10,20) (10,17) (10,18) (11,21) (12,22) (12,14) (14,22) (15,16) (15,24) (16,23) (17,18) (19,21) (21,24) (22,24)\nIs there a path between node 13 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph541-6_12", + "image": "data/connectivity/graph_visual/medium/graph541.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,10) (0,11) (0,12) (0,6) (0,14) (0,21) (1,10) (1,11) (1,12) (1,6) (1,14) (1,21) (2,4) (2,20) (2,5) (2,13) (3,15) (3,8) (3,18) (3,17) (3,22) (3,9) (3,16) (3,7) (3,19) (4,20) (4,5) (4,13) (5,20) (5,13) (6,10) (6,11) (6,12) (6,14) (6,21) (7,15) (7,8) (7,18) (7,17) (7,22) (7,9) (7,16) (7,19) (8,15) (8,18) (8,17) (8,22) (8,9) (8,16) (8,19) (9,15) (9,18) (9,17) (9,22) (9,16) (9,19) (10,11) (10,12) (10,14) (10,21) (11,12) (11,14) (11,21) (12,14) (12,21) (13,20) (14,21) (15,18) (15,17) (15,22) (15,16) (15,19) (16,18) (16,17) (16,22) (16,19) (17,18) (17,22) (17,19) (18,22) (18,19) (19,22)\nIs there a path between node 6 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph644-19_13", + "image": "data/connectivity/graph_visual/medium/graph644.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (0,9) (1,4) (2,16) (4,18) (4,11) (5,14) (6,8) (7,15) (7,21) (9,15) (9,19) (13,15) (13,16) (15,20) (16,20) (19,21) (19,20)\nIs there a path between node 19 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph379-12_1", + "image": "data/connectivity/graph_visual/medium/graph379.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,18) (0,10) (1,4) (1,12) (1,15) (1,7) (1,17) (1,16) (2,18) (3,19) (3,14) (4,12) (4,13) (4,11) (4,15) (4,7) (4,17) (4,16) (4,20) (5,12) (5,13) (5,11) (5,15) (5,7) (5,9) (5,16) (6,12) (6,13) (6,11) (6,15) (6,7) (6,17) (6,16) (6,20) (7,12) (7,13) (7,11) (7,16) (7,20) (8,19) (9,12) (9,13) (9,15) (9,16) (9,20) (10,18) (11,12) (11,13) (11,17) (11,16) (11,20) (12,17) (12,16) (12,20) (13,15) (13,17) (13,16) (13,20) (14,19) (15,17) (15,16) (16,17) (16,20) (17,20)\nIs there a path between node 12 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph796-13_3", + "image": "data/connectivity/graph_visual/medium/graph796.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,1) (1,16) (1,12) (1,19) (1,21) (4,16) (4,9) (4,17) (4,15) (4,23) (4,21) (6,10) (7,13) (8,23) (8,19) (8,21) (8,18) (8,22) (9,16) (9,24) (9,15) (9,23) (9,12) (9,19) (9,21) (12,15) (15,16) (15,24) (15,23) (15,19) (15,21) (15,18) (16,24) (16,18) (17,23) (18,19) (18,21) (19,23) (21,24) (21,23)\nIs there a path between node 13 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph452-2_10", + "image": "data/connectivity/graph_visual/medium/graph452.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,5) (0,13) (0,16) (0,4) (0,12) (1,5) (1,13) (1,9) (1,16) (1,4) (1,2) (2,13) (2,14) (2,4) (3,11) (3,19) (3,18) (3,15) (3,20) (3,6) (3,8) (3,10) (3,21) (4,13) (4,14) (4,9) (4,12) (5,13) (5,14) (5,9) (5,16) (6,11) (6,19) (6,18) (6,15) (6,17) (6,10) (6,21) (6,7) (7,11) (7,19) (7,18) (7,15) (7,20) (7,17) (7,8) (7,10) (7,21) (8,11) (8,18) (8,15) (8,20) (8,21) (9,13) (9,14) (9,16) (9,12) (10,11) (10,19) (10,18) (10,20) (10,17) (10,21) (11,18) (11,20) (14,16) (15,19) (15,18) (15,20) (15,17) (15,21) (17,19) (17,18) (17,20) (17,21) (18,19) (18,20) (19,20) (19,21) (20,21)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph129-8_13", + "image": "data/connectivity/graph_visual/medium/graph129.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,12) (0,13) (0,2) (0,16) (0,7) (0,6) (0,9) (0,5) (0,1) (0,8) (1,12) (1,13) (1,2) (1,16) (1,7) (1,6) (1,9) (1,5) (1,8) (2,12) (2,13) (2,16) (2,7) (2,6) (2,9) (2,5) (2,8) (3,10) (3,14) (3,4) (3,11) (3,15) (4,10) (4,14) (4,11) (4,15) (5,12) (5,13) (5,16) (5,7) (5,6) (5,9) (5,8) (6,12) (6,13) (6,16) (6,7) (6,9) (6,8) (7,12) (7,13) (7,16) (7,9) (7,8) (8,12) (8,13) (8,16) (8,9) (9,12) (9,13) (9,16) (10,14) (10,11) (10,15) (11,14) (11,15) (12,13) (12,16) (13,16) (14,15)\nIs there a path between node 8 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph214-15_11", + "image": "data/connectivity/graph_visual/medium/graph214.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,11) (0,1) (0,6) (0,17) (0,10) (0,16) (0,13) (1,11) (1,6) (1,17) (1,10) (1,16) (1,13) (2,12) (2,8) (2,15) (2,14) (2,3) (2,9) (2,7) (2,4) (2,18) (2,5) (3,12) (3,8) (3,15) (3,14) (3,9) (3,7) (3,4) (3,18) (3,5) (4,12) (4,8) (4,15) (4,14) (4,9) (4,7) (4,18) (4,5) (5,12) (5,8) (5,15) (5,14) (5,9) (5,7) (5,18) (6,11) (6,17) (6,10) (6,16) (6,13) (7,12) (7,8) (7,15) (7,14) (7,9) (7,18) (8,12) (8,15) (8,14) (8,9) (8,18) (9,12) (9,15) (9,14) (9,18) (10,11) (10,17) (10,16) (10,13) (11,17) (11,16) (11,13) (12,15) (12,14) (12,18) (13,17) (13,16) (14,15) (14,18) (15,18) (16,17)\nIs there a path between node 15 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph520-7_10", + "image": "data/connectivity/graph_visual/medium/graph520.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,18) (0,19) (0,3) (0,17) (0,2) (0,21) (0,13) (0,22) (1,19) (1,3) (1,2) (1,13) (2,18) (2,19) (2,5) (2,3) (2,17) (2,13) (2,22) (3,18) (3,5) (3,17) (4,8) (4,9) (4,7) (4,20) (4,12) (5,19) (5,21) (5,13) (6,8) (6,9) (6,20) (6,14) (6,10) (6,15) (6,12) (6,16) (7,9) (7,10) (7,15) (7,12) (7,16) (8,14) (8,16) (9,14) (9,11) (9,15) (9,12) (9,16) (10,20) (10,14) (10,11) (10,16) (11,20) (11,14) (11,12) (11,16) (12,15) (13,18) (13,17) (13,21) (14,20) (14,15) (14,16) (15,20) (15,16) (17,18) (17,21) (17,22) (18,19) (18,22)\nIs there a path between node 7 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph230-9_7", + "image": "data/connectivity/graph_visual/medium/graph230.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,9) (1,14) (1,2) (1,17) (1,16) (1,8) (2,4) (2,17) (3,7) (4,12) (4,18) (4,17) (4,10) (5,14) (5,18) (5,17) (5,10) (5,8) (6,18) (6,17) (6,10) (8,12) (8,10) (8,16) (10,12) (10,14) (12,15) (12,17) (12,16) (14,15) (14,17) (15,17) (15,16) (16,18) (17,18)\nIs there a path between node 9 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph327-2_13", + "image": "data/connectivity/graph_visual/medium/graph327.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,4) (1,13) (2,11) (3,4) (3,6) (3,19) (4,20) (4,12) (4,16) (5,14) (5,9) (6,18) (6,8) (7,13) (7,8) (7,19) (7,15) (8,18) (8,20) (8,15) (11,14) (12,20) (12,13) (12,19) (12,16) (13,18) (13,15) (15,18) (15,19) (18,20) (18,19)\nIs there a path between node 2 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph760-19_16", + "image": "data/connectivity/graph_visual/medium/graph760.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,1) (0,19) (0,21) (1,9) (1,19) (1,21) (2,7) (3,11) (3,14) (3,6) (3,18) (4,23) (4,16) (4,10) (4,17) (4,13) (5,9) (5,21) (6,11) (6,12) (6,14) (6,15) (6,8) (8,12) (8,14) (8,15) (8,18) (9,19) (9,21) (10,23) (10,16) (10,20) (10,13) (11,12) (11,14) (11,15) (11,18) (12,14) (12,18) (13,23) (13,16) (13,20) (13,24) (14,15) (15,18) (16,23) (16,20) (16,24) (17,20) (20,23) (20,24) (23,24)\nIs there a path between node 19 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph301-6_0", + "image": "data/connectivity/graph_visual/medium/graph301.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,5) (0,14) (0,8) (0,1) (0,17) (0,2) (0,4) (0,10) (0,12) (0,6) (0,7) (0,3) (0,11) (1,5) (1,14) (1,8) (1,17) (1,12) (1,13) (1,3) (2,5) (2,4) (2,10) (2,12) (2,6) (2,7) (2,13) (2,11) (3,14) (3,8) (3,10) (3,12) (3,6) (3,7) (4,14) (4,8) (4,17) (4,10) (4,12) (4,7) (4,11) (5,8) (5,17) (5,12) (5,6) (5,7) (5,13) (5,11) (6,14) (6,10) (6,12) (6,13) (6,11) (7,14) (7,8) (7,17) (7,10) (7,12) (7,13) (7,11) (8,14) (8,17) (8,10) (8,12) (8,11) (9,15) (10,13) (11,14) (11,12) (11,13) (12,17) (12,13) (15,19) (15,18) (15,16) (16,19) (16,18) (18,19)\nIs there a path between node 6 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph331-8_13", + "image": "data/connectivity/graph_visual/medium/graph331.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,12) (0,16) (0,17) (0,18) (0,14) (0,7) (2,15) (2,13) (2,4) (4,8) (5,8) (7,16) (7,18) (8,20) (8,13) (9,14) (10,16) (10,18) (15,19) (19,20)\nIs there a path between node 8 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph118-13_1", + "image": "data/connectivity/graph_visual/medium/graph118.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,4) (1,3) (1,7) (1,13) (1,6) (1,10) (2,12) (2,8) (3,8) (3,11) (3,6) (3,10) (5,12) (5,15) (5,9) (7,16) (7,13) (7,8) (8,15) (8,16) (8,9) (9,15) (9,13) (10,12) (11,14) (11,12) (11,13) (12,15) (13,14) (14,16)\nIs there a path between node 13 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph467-13_19", + "image": "data/connectivity/graph_visual/medium/graph467.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,11) (0,7) (0,1) (0,18) (0,12) (0,2) (0,4) (0,21) (0,16) (0,20) (0,15) (0,10) (0,19) (0,17) (0,13) (1,11) (1,7) (1,18) (1,12) (1,2) (1,4) (1,21) (1,16) (1,20) (1,15) (1,10) (1,19) (1,17) (1,13) (2,11) (2,7) (2,18) (2,12) (2,4) (2,21) (2,16) (2,20) (2,15) (2,10) (2,19) (2,17) (2,13) (3,5) (4,11) (4,7) (4,18) (4,12) (4,21) (4,16) (4,20) (4,15) (4,10) (4,19) (4,17) (4,13) (6,9) (6,8) (6,14) (7,11) (7,18) (7,12) (7,21) (7,16) (7,20) (7,15) (7,10) (7,19) (7,17) (7,13) (8,9) (8,14) (9,14) (10,11) (10,18) (10,12) (10,21) (10,16) (10,20) (10,15) (10,19) (10,17) (10,13) (11,18) (11,12) (11,21) (11,16) (11,20) (11,15) (11,19) (11,17) (11,13) (12,18) (12,21) (12,16) (12,20) (12,15) (12,19) (12,17) (12,13) (13,18) (13,21) (13,16) (13,20) (13,15) (13,19) (13,17) (15,18) (15,21) (15,16) (15,20) (15,19) (15,17) (16,18) (16,21) (16,20) (16,19) (16,17) (17,18) (17,21) (17,20) (17,19) (18,21) (18,20) (18,19) (19,21) (19,20) (20,21)\nIs there a path between node 13 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph825-10_12", + "image": "data/connectivity/graph_visual/medium/graph825.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,1) (0,6) (0,13) (0,16) (0,21) (0,5) (1,12) (1,15) (1,6) (1,5) (2,8) (2,9) (2,19) (2,7) (2,22) (2,4) (2,17) (2,20) (3,11) (3,8) (3,14) (3,9) (3,23) (3,7) (3,22) (3,17) (3,20) (4,11) (4,8) (4,14) (4,19) (4,23) (4,7) (5,10) (5,15) (5,6) (5,13) (5,18) (5,21) (6,12) (6,15) (6,18) (6,21) (7,8) (7,24) (7,14) (7,9) (7,19) (7,22) (7,17) (7,20) (8,11) (8,14) (8,22) (8,17) (8,20) (9,11) (9,24) (9,14) (9,19) (9,17) (10,12) (10,15) (10,16) (10,18) (10,21) (11,24) (11,14) (11,19) (11,23) (11,22) (11,17) (12,15) (12,16) (12,18) (12,21) (13,15) (13,16) (13,18) (14,24) (14,19) (14,23) (14,20) (15,16) (15,18) (16,18) (16,21) (17,24) (17,23) (17,20) (18,21) (19,23) (19,20) (20,24) (20,23) (20,22) (22,24) (22,23)\nIs there a path between node 10 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph245-6_1", + "image": "data/connectivity/graph_visual/medium/graph245.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,3) (0,13) (0,2) (0,15) (0,6) (0,17) (0,8) (0,16) (0,18) (0,9) (0,12) (0,11) (1,10) (1,14) (1,7) (1,5) (1,4) (2,3) (2,13) (2,15) (2,6) (2,17) (2,8) (2,16) (2,18) (2,9) (2,12) (2,11) (3,13) (3,15) (3,6) (3,17) (3,8) (3,16) (3,18) (3,9) (3,12) (3,11) (4,10) (4,14) (4,7) (4,5) (5,10) (5,14) (5,7) (6,13) (6,15) (6,17) (6,8) (6,16) (6,18) (6,9) (6,12) (6,11) (7,10) (7,14) (8,13) (8,15) (8,17) (8,16) (8,18) (8,9) (8,12) (8,11) (9,13) (9,15) (9,17) (9,16) (9,18) (9,12) (9,11) (10,14) (11,13) (11,15) (11,17) (11,16) (11,18) (11,12) (12,13) (12,15) (12,17) (12,16) (12,18) (13,15) (13,17) (13,16) (13,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph703-22_5", + "image": "data/connectivity/graph_visual/medium/graph703.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,15) (0,13) (0,17) (0,11) (0,16) (0,14) (0,8) (1,3) (1,20) (2,3) (2,20) (2,21) (3,23) (3,20) (3,18) (6,13) (6,22) (6,14) (6,9) (7,17) (7,22) (7,14) (7,24) (7,9) (8,13) (8,17) (8,22) (8,16) (8,14) (8,24) (9,15) (9,17) (9,11) (9,19) (9,10) (9,24) (9,12) (10,15) (10,17) (10,11) (11,15) (11,22) (12,22) (12,24) (13,15) (13,22) (13,16) (13,24) (14,15) (14,19) (15,24) (16,22) (16,24) (18,20) (18,21) (21,23) (22,24)\nIs there a path between node 22 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph91-10_9", + "image": "data/connectivity/graph_visual/medium/graph91.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,15) (1,14) (1,3) (1,9) (1,10) (1,4) (1,7) (1,6) (1,13) (1,12) (1,11) (2,15) (3,14) (3,8) (3,9) (3,10) (3,4) (3,12) (3,11) (4,8) (4,9) (4,10) (4,7) (4,5) (4,11) (5,9) (5,7) (5,13) (5,12) (5,11) (6,14) (6,8) (6,7) (6,13) (6,11) (7,8) (7,9) (7,10) (7,11) (8,14) (8,10) (8,12) (8,11) (9,14) (9,10) (9,13) (9,12) (10,14) (10,13) (10,12) (11,14) (11,13) (11,12) (12,14)\nIs there a path between node 10 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph324-3_5", + "image": "data/connectivity/graph_visual/medium/graph324.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,17) (0,8) (0,18) (0,6) (0,1) (0,12) (0,3) (0,7) (0,14) (0,10) (0,19) (0,16) (0,13) (1,17) (1,8) (1,18) (1,2) (1,19) (2,8) (2,6) (2,20) (2,14) (3,17) (3,18) (3,6) (3,14) (3,10) (3,19) (4,17) (4,18) (4,6) (4,19) (4,13) (5,15) (6,17) (6,8) (6,18) (6,13) (7,17) (7,14) (7,10) (8,20) (9,15) (9,11) (10,17) (10,18) (11,15) (12,17) (12,18) (12,14) (12,19) (13,17) (13,18) (13,20) (14,17) (14,18) (14,20) (18,20) (19,20)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph95-7_15", + "image": "data/connectivity/graph_visual/medium/graph95.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,6) (0,8) (0,15) (1,10) (2,5) (3,9) (3,10) (4,11) (5,6) (5,7) (5,11) (6,13) (6,11) (7,13) (8,12) (8,13) (11,12) (11,15) (12,15) (13,15)\nIs there a path between node 7 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph427-20_18", + "image": "data/connectivity/graph_visual/medium/graph427.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (0,8) (1,11) (1,9) (1,17) (3,21) (3,11) (3,18) (3,6) (3,10) (3,15) (4,8) (5,18) (5,6) (5,9) (5,15) (6,16) (6,21) (6,11) (6,10) (7,14) (7,9) (7,17) (7,15) (8,12) (8,13) (9,21) (9,17) (9,10) (9,19) (11,14) (11,21) (11,19) (13,20) (14,16) (14,18) (14,17) (14,15) (14,19) (15,16) (16,18) (16,17) (18,21)\nIs there a path between node 20 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph694-8_7", + "image": "data/connectivity/graph_visual/medium/graph694.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,23) (0,1) (0,3) (0,5) (0,12) (0,10) (0,15) (0,11) (0,18) (0,19) (0,13) (0,6) (0,14) (0,17) (0,9) (0,7) (0,16) (0,20) (1,4) (1,23) (1,3) (1,5) (1,12) (1,10) (1,15) (1,11) (1,18) (1,19) (1,13) (1,6) (1,14) (1,17) (1,9) (1,7) (1,16) (1,20) (2,22) (2,21) (2,8) (3,4) (3,23) (3,5) (3,12) (3,10) (3,15) (3,11) (3,18) (3,19) (3,13) (3,6) (3,14) (3,17) (3,9) (3,7) (3,16) (3,20) (4,23) (4,5) (4,12) (4,10) (4,15) (4,11) (4,18) (4,19) (4,13) (4,6) (4,14) (4,17) (4,9) (4,7) (4,16) (4,20) (5,23) (5,12) (5,10) (5,15) (5,11) (5,18) (5,19) (5,13) (5,6) (5,14) (5,17) (5,9) (5,7) (5,16) (5,20) (6,23) (6,12) (6,10) (6,15) (6,11) (6,18) (6,19) (6,13) (6,14) (6,17) (6,9) (6,7) (6,16) (6,20) (7,23) (7,12) (7,10) (7,15) (7,11) (7,18) (7,19) (7,13) (7,14) (7,17) (7,9) (7,16) (7,20) (8,22) (8,21) (9,23) (9,12) (9,10) (9,15) (9,11) (9,18) (9,19) (9,13) (9,14) (9,17) (9,16) (9,20) (10,23) (10,12) (10,15) (10,11) (10,18) (10,19) (10,13) (10,14) (10,17) (10,16) (10,20) (11,23) (11,12) (11,15) (11,18) (11,19) (11,13) (11,14) (11,17) (11,16) (11,20) (12,23) (12,15) (12,18) (12,19) (12,13) (12,14) (12,17) (12,16) (12,20) (13,23) (13,15) (13,18) (13,19) (13,14) (13,17) (13,16) (13,20) (14,23) (14,15) (14,18) (14,19) (14,17) (14,16) (14,20) (15,23) (15,18) (15,19) (15,17) (15,16) (15,20) (16,23) (16,18) (16,19) (16,17) (16,20) (17,23) (17,18) (17,19) (17,20) (18,23) (18,19) (18,20) (19,23) (19,20) (20,23) (21,22)\nIs there a path between node 8 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph750-2_15", + "image": "data/connectivity/graph_visual/medium/graph750.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,11) (0,22) (0,19) (0,13) (0,3) (0,16) (0,24) (0,1) (0,4) (0,7) (0,6) (0,15) (0,9) (1,11) (1,2) (1,22) (1,10) (1,5) (1,14) (1,13) (1,3) (1,16) (1,24) (1,7) (1,6) (1,20) (1,9) (2,11) (2,22) (2,10) (2,5) (2,14) (2,13) (2,3) (2,16) (2,18) (2,24) (2,4) (2,7) (2,6) (2,15) (2,20) (2,9) (3,11) (3,22) (3,19) (3,10) (3,5) (3,13) (3,18) (3,24) (3,7) (3,6) (3,15) (3,20) (3,9) (4,22) (4,19) (4,5) (4,14) (4,13) (4,16) (4,18) (4,20) (4,9) (5,22) (5,19) (5,10) (5,13) (5,16) (5,18) (5,24) (5,6) (5,15) (6,11) (6,22) (6,19) (6,10) (6,16) (6,18) (6,24) (6,7) (6,15) (6,9) (7,11) (7,22) (7,19) (7,10) (7,14) (7,13) (7,18) (7,24) (7,15) (7,20) (7,9) (8,23) (8,17) (9,22) (9,19) (9,10) (9,14) (9,18) (9,24) (9,15) (9,20) (10,11) (10,22) (10,19) (10,14) (10,13) (10,16) (10,18) (10,24) (10,15) (10,20) (11,22) (11,19) (11,14) (11,13) (11,16) (11,24) (11,15) (11,20) (12,23) (12,21) (13,19) (13,16) (13,18) (13,24) (13,15) (13,20) (14,22) (14,16) (14,18) (14,15) (14,20) (15,16) (15,18) (15,24) (16,22) (16,19) (16,18) (16,24) (17,23) (17,21) (18,19) (19,22) (19,24) (19,20) (20,22) (20,24)\nIs there a path between node 2 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph482-22_3", + "image": "data/connectivity/graph_visual/medium/graph482.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (0,5) (0,15) (0,19) (0,21) (0,13) (0,10) (0,6) (0,17) (0,18) (0,9) (0,7) (0,4) (1,15) (1,19) (1,21) (1,2) (1,13) (1,3) (1,8) (1,12) (1,18) (1,20) (1,9) (1,7) (1,4) (1,11) (2,5) (2,15) (2,19) (2,21) (2,3) (2,10) (2,16) (2,6) (2,8) (2,17) (2,12) (2,20) (2,9) (2,7) (2,4) (2,11) (3,5) (3,15) (3,21) (3,13) (3,10) (3,8) (3,12) (3,18) (3,9) (3,7) (3,11) (4,5) (4,15) (4,19) (4,21) (4,10) (4,16) (4,6) (4,8) (4,12) (4,20) (5,15) (5,19) (5,21) (5,13) (5,10) (5,6) (5,17) (5,12) (5,18) (5,20) (5,9) (5,7) (6,15) (6,13) (6,8) (6,17) (6,12) (6,18) (6,7) (6,11) (7,21) (7,13) (7,10) (7,8) (7,17) (7,12) (7,18) (7,20) (7,11) (8,15) (8,19) (8,21) (8,13) (8,10) (8,16) (8,17) (8,12) (8,18) (8,20) (9,15) (9,19) (9,21) (9,16) (9,17) (9,12) (9,18) (9,20) (10,15) (10,19) (10,21) (10,13) (10,16) (10,17) (10,18) (11,19) (11,21) (11,13) (11,17) (11,20) (12,15) (12,21) (12,13) (12,16) (12,17) (12,18) (12,20) (13,15) (13,19) (13,16) (13,17) (13,18) (13,20) (15,19) (15,21) (15,18) (15,20) (16,19) (16,21) (16,17) (16,18) (16,20) (17,19) (18,19) (18,20) (19,21) (19,20) (20,21)\nIs there a path between node 22 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph775-23_1", + "image": "data/connectivity/graph_visual/medium/graph775.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,5) (0,11) (0,24) (0,6) (0,21) (0,14) (0,16) (0,2) (0,23) (0,1) (0,8) (0,19) (0,7) (0,15) (0,17) (0,20) (0,3) (0,22) (0,13) (0,10) (1,5) (1,11) (1,24) (1,6) (1,21) (1,14) (1,16) (1,2) (1,23) (1,8) (1,19) (1,7) (1,15) (1,17) (1,20) (1,3) (1,22) (1,13) (1,10) (2,5) (2,11) (2,24) (2,6) (2,21) (2,14) (2,16) (2,23) (2,8) (2,19) (2,7) (2,15) (2,17) (2,20) (2,3) (2,22) (2,13) (2,10) (3,5) (3,11) (3,24) (3,6) (3,21) (3,14) (3,16) (3,23) (3,8) (3,19) (3,7) (3,15) (3,17) (3,20) (3,22) (3,13) (3,10) (4,18) (4,12) (4,9) (5,11) (5,24) (5,6) (5,21) (5,14) (5,16) (5,23) (5,8) (5,19) (5,7) (5,15) (5,17) (5,20) (5,22) (5,13) (5,10) (6,11) (6,24) (6,21) (6,14) (6,16) (6,23) (6,8) (6,19) (6,7) (6,15) (6,17) (6,20) (6,22) (6,13) (6,10) (7,11) (7,24) (7,21) (7,14) (7,16) (7,23) (7,8) (7,19) (7,15) (7,17) (7,20) (7,22) (7,13) (7,10) (8,11) (8,24) (8,21) (8,14) (8,16) (8,23) (8,19) (8,15) (8,17) (8,20) (8,22) (8,13) (8,10) (9,18) (9,12) (10,11) (10,24) (10,21) (10,14) (10,16) (10,23) (10,19) (10,15) (10,17) (10,20) (10,22) (10,13) (11,24) (11,21) (11,14) (11,16) (11,23) (11,19) (11,15) (11,17) (11,20) (11,22) (11,13) (12,18) (13,24) (13,21) (13,14) (13,16) (13,23) (13,19) (13,15) (13,17) (13,20) (13,22) (14,24) (14,21) (14,16) (14,23) (14,19) (14,15) (14,17) (14,20) (14,22) (15,24) (15,21) (15,16) (15,23) (15,19) (15,17) (15,20) (15,22) (16,24) (16,21) (16,23) (16,19) (16,17) (16,20) (16,22) (17,24) (17,21) (17,23) (17,19) (17,20) (17,22) (19,24) (19,21) (19,23) (19,20) (19,22) (20,24) (20,21) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nIs there a path between node 23 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph619-17_19", + "image": "data/connectivity/graph_visual/medium/graph619.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,18) (0,8) (0,2) (0,12) (0,22) (0,19) (0,10) (0,21) (0,3) (0,14) (0,20) (0,6) (0,15) (0,23) (0,16) (0,4) (0,17) (0,1) (1,18) (1,8) (1,2) (1,12) (1,22) (1,19) (1,10) (1,21) (1,3) (1,14) (1,20) (1,6) (1,15) (1,23) (1,16) (1,4) (1,17) (2,18) (2,8) (2,12) (2,22) (2,19) (2,10) (2,21) (2,3) (2,14) (2,20) (2,6) (2,15) (2,23) (2,16) (2,4) (2,17) (3,18) (3,8) (3,12) (3,22) (3,19) (3,10) (3,21) (3,14) (3,20) (3,6) (3,15) (3,23) (3,16) (3,4) (3,17) (4,18) (4,8) (4,12) (4,22) (4,19) (4,10) (4,21) (4,14) (4,20) (4,6) (4,15) (4,23) (4,16) (4,17) (5,9) (5,11) (5,7) (5,13) (6,18) (6,8) (6,12) (6,22) (6,19) (6,10) (6,21) (6,14) (6,20) (6,15) (6,23) (6,16) (6,17) (7,9) (7,11) (7,13) (8,18) (8,12) (8,22) (8,19) (8,10) (8,21) (8,14) (8,20) (8,15) (8,23) (8,16) (8,17) (9,11) (9,13) (10,18) (10,12) (10,22) (10,19) (10,21) (10,14) (10,20) (10,15) (10,23) (10,16) (10,17) (11,13) (12,18) (12,22) (12,19) (12,21) (12,14) (12,20) (12,15) (12,23) (12,16) (12,17) (14,18) (14,22) (14,19) (14,21) (14,20) (14,15) (14,23) (14,16) (14,17) (15,18) (15,22) (15,19) (15,21) (15,20) (15,23) (15,16) (15,17) (16,18) (16,22) (16,19) (16,21) (16,20) (16,23) (16,17) (17,18) (17,22) (17,19) (17,21) (17,20) (17,23) (18,22) (18,19) (18,21) (18,20) (18,23) (19,22) (19,21) (19,20) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 17 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph179-16_5", + "image": "data/connectivity/graph_visual/medium/graph179.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,16) (0,13) (0,14) (0,9) (0,7) (1,16) (1,12) (1,9) (1,7) (1,4) (2,17) (2,6) (2,11) (2,10) (2,3) (2,15) (3,17) (3,6) (3,11) (3,10) (3,15) (4,16) (4,5) (4,12) (4,13) (4,9) (4,7) (5,16) (5,13) (5,14) (5,9) (5,7) (6,17) (6,10) (6,15) (7,16) (7,12) (7,13) (7,14) (7,9) (8,17) (8,10) (8,15) (9,16) (9,12) (9,13) (9,14) (10,17) (10,11) (11,17) (11,15) (12,16) (12,13) (12,14) (13,16) (13,14) (14,16)\nIs there a path between node 16 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph19-0_9", + "image": "data/connectivity/graph_visual/medium/graph19.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,8) (0,4) (0,11) (1,3) (3,9) (3,7) (4,8) (5,11) (6,10) (6,9) (6,7) (8,11)\nIs there a path between node 0 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph181-2_16", + "image": "data/connectivity/graph_visual/medium/graph181.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,17) (0,16) (0,5) (0,12) (0,13) (0,14) (0,7) (0,1) (1,5) (1,12) (1,9) (3,11) (3,6) (3,15) (5,17) (5,16) (5,12) (5,14) (5,7) (6,8) (7,16) (7,12) (7,14) (7,10) (7,9) (9,17) (9,16) (9,12) (9,14) (10,17) (10,16) (10,12) (10,13) (10,14) (11,15) (12,17) (12,16) (13,16) (13,14) (14,17) (14,16) (16,17)\nIs there a path between node 2 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph508-10_12", + "image": "data/connectivity/graph_visual/medium/graph508.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (0,1) (0,21) (0,13) (0,10) (1,15) (1,11) (1,17) (1,21) (1,3) (1,16) (1,20) (2,17) (2,21) (3,15) (3,8) (4,18) (4,20) (5,22) (6,17) (6,16) (6,8) (8,18) (8,11) (8,17) (10,15) (10,11) (11,13) (13,18) (13,16) (15,17) (15,20) (16,18) (17,18) (17,21) (19,22)\nIs there a path between node 10 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph4-7_3", + "image": "data/connectivity/graph_visual/medium/graph4.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,7) (0,10) (1,8) (2,9) (3,6) (3,4) (5,7) (5,8) (7,8) (7,10)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph619-12_20", + "image": "data/connectivity/graph_visual/medium/graph619.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,18) (0,8) (0,2) (0,12) (0,22) (0,19) (0,10) (0,21) (0,3) (0,14) (0,20) (0,6) (0,15) (0,23) (0,16) (0,4) (0,17) (0,1) (1,18) (1,8) (1,2) (1,12) (1,22) (1,19) (1,10) (1,21) (1,3) (1,14) (1,20) (1,6) (1,15) (1,23) (1,16) (1,4) (1,17) (2,18) (2,8) (2,12) (2,22) (2,19) (2,10) (2,21) (2,3) (2,14) (2,20) (2,6) (2,15) (2,23) (2,16) (2,4) (2,17) (3,18) (3,8) (3,12) (3,22) (3,19) (3,10) (3,21) (3,14) (3,20) (3,6) (3,15) (3,23) (3,16) (3,4) (3,17) (4,18) (4,8) (4,12) (4,22) (4,19) (4,10) (4,21) (4,14) (4,20) (4,6) (4,15) (4,23) (4,16) (4,17) (5,9) (5,11) (5,7) (5,13) (6,18) (6,8) (6,12) (6,22) (6,19) (6,10) (6,21) (6,14) (6,20) (6,15) (6,23) (6,16) (6,17) (7,9) (7,11) (7,13) (8,18) (8,12) (8,22) (8,19) (8,10) (8,21) (8,14) (8,20) (8,15) (8,23) (8,16) (8,17) (9,11) (9,13) (10,18) (10,12) (10,22) (10,19) (10,21) (10,14) (10,20) (10,15) (10,23) (10,16) (10,17) (11,13) (12,18) (12,22) (12,19) (12,21) (12,14) (12,20) (12,15) (12,23) (12,16) (12,17) (14,18) (14,22) (14,19) (14,21) (14,20) (14,15) (14,23) (14,16) (14,17) (15,18) (15,22) (15,19) (15,21) (15,20) (15,23) (15,16) (15,17) (16,18) (16,22) (16,19) (16,21) (16,20) (16,23) (16,17) (17,18) (17,22) (17,19) (17,21) (17,20) (17,23) (18,22) (18,19) (18,21) (18,20) (18,23) (19,22) (19,21) (19,20) (19,23) (20,22) (20,21) (20,23) (21,22) (21,23) (22,23)\nIs there a path between node 12 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph146-10_12", + "image": "data/connectivity/graph_visual/medium/graph146.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,2) (0,7) (0,3) (0,14) (0,4) (0,9) (0,5) (0,16) (1,8) (1,10) (2,12) (2,17) (2,14) (2,11) (2,9) (2,16) (3,12) (3,17) (3,14) (3,11) (3,4) (3,9) (3,5) (3,16) (4,7) (4,14) (4,11) (4,9) (5,12) (5,7) (5,14) (5,16) (6,8) (6,10) (7,14) (7,11) (7,9) (7,16) (8,10) (9,12) (9,17) (9,11) (11,16) (12,17) (12,14) (12,16) (13,15) (14,17) (14,16) (16,17)\nIs there a path between node 10 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph686-19_12", + "image": "data/connectivity/graph_visual/medium/graph686.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,8) (0,18) (1,14) (1,6) (1,16) (1,4) (1,15) (1,19) (1,20) (1,23) (1,7) (1,13) (1,22) (1,9) (1,21) (1,2) (2,14) (2,6) (2,16) (2,4) (2,15) (2,19) (2,20) (2,23) (2,7) (2,13) (2,22) (2,9) (2,21) (3,5) (3,10) (3,12) (3,11) (3,17) (4,14) (4,6) (4,16) (4,15) (4,19) (4,20) (4,23) (4,7) (4,13) (4,22) (4,9) (4,21) (5,10) (5,12) (5,11) (5,17) (6,14) (6,16) (6,15) (6,19) (6,20) (6,23) (6,7) (6,13) (6,22) (6,9) (6,21) (7,14) (7,16) (7,15) (7,19) (7,20) (7,23) (7,13) (7,22) (7,9) (7,21) (8,18) (9,14) (9,16) (9,15) (9,19) (9,20) (9,23) (9,13) (9,22) (9,21) (10,12) (10,11) (10,17) (11,12) (11,17) (12,17) (13,14) (13,16) (13,15) (13,19) (13,20) (13,23) (13,22) (13,21) (14,16) (14,15) (14,19) (14,20) (14,23) (14,22) (14,21) (15,16) (15,19) (15,20) (15,23) (15,22) (15,21) (16,19) (16,20) (16,23) (16,22) (16,21) (19,20) (19,23) (19,22) (19,21) (20,23) (20,22) (20,21) (21,23) (21,22) (22,23)\nIs there a path between node 19 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph429-7_21", + "image": "data/connectivity/graph_visual/medium/graph429.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,10) (0,2) (0,8) (0,13) (1,11) (1,21) (1,7) (2,20) (2,6) (2,10) (2,3) (2,4) (2,12) (2,18) (3,17) (3,6) (3,4) (3,19) (3,18) (4,17) (4,19) (4,13) (6,17) (6,10) (6,19) (7,14) (8,15) (8,20) (9,20) (9,16) (9,18) (10,20) (10,16) (10,19) (12,19) (12,13) (13,17) (13,15) (13,16) (15,17) (15,19) (16,17) (17,20) (18,19) (19,20)\nIs there a path between node 7 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph674-3_11", + "image": "data/connectivity/graph_visual/medium/graph674.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (0,13) (0,19) (0,11) (0,16) (0,20) (0,8) (0,5) (0,3) (0,2) (0,7) (0,6) (0,17) (0,14) (0,12) (0,1) (0,18) (0,10) (0,23) (0,9) (1,4) (1,13) (1,19) (1,11) (1,16) (1,20) (1,8) (1,5) (1,3) (1,2) (1,7) (1,6) (1,17) (1,14) (1,12) (1,18) (1,10) (1,23) (1,9) (2,4) (2,13) (2,19) (2,11) (2,16) (2,20) (2,8) (2,5) (2,3) (2,7) (2,6) (2,17) (2,14) (2,12) (2,18) (2,10) (2,23) (2,9) (3,4) (3,13) (3,19) (3,11) (3,16) (3,20) (3,8) (3,5) (3,7) (3,6) (3,17) (3,14) (3,12) (3,18) (3,10) (3,23) (3,9) (4,13) (4,19) (4,11) (4,16) (4,20) (4,8) (4,5) (4,7) (4,6) (4,17) (4,14) (4,12) (4,18) (4,10) (4,23) (4,9) (5,13) (5,19) (5,11) (5,16) (5,20) (5,8) (5,7) (5,6) (5,17) (5,14) (5,12) (5,18) (5,10) (5,23) (5,9) (6,13) (6,19) (6,11) (6,16) (6,20) (6,8) (6,7) (6,17) (6,14) (6,12) (6,18) (6,10) (6,23) (6,9) (7,13) (7,19) (7,11) (7,16) (7,20) (7,8) (7,17) (7,14) (7,12) (7,18) (7,10) (7,23) (7,9) (8,13) (8,19) (8,11) (8,16) (8,20) (8,17) (8,14) (8,12) (8,18) (8,10) (8,23) (8,9) (9,13) (9,19) (9,11) (9,16) (9,20) (9,17) (9,14) (9,12) (9,18) (9,10) (9,23) (10,13) (10,19) (10,11) (10,16) (10,20) (10,17) (10,14) (10,12) (10,18) (10,23) (11,13) (11,19) (11,16) (11,20) (11,17) (11,14) (11,12) (11,18) (11,23) (12,13) (12,19) (12,16) (12,20) (12,17) (12,14) (12,18) (12,23) (13,19) (13,16) (13,20) (13,17) (13,14) (13,18) (13,23) (14,19) (14,16) (14,20) (14,17) (14,18) (14,23) (15,21) (15,22) (16,19) (16,20) (16,17) (16,18) (16,23) (17,19) (17,20) (17,18) (17,23) (18,19) (18,20) (18,23) (19,20) (19,23) (20,23) (21,22)\nIs there a path between node 3 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph348-19_18", + "image": "data/connectivity/graph_visual/medium/graph348.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,10) (0,2) (0,7) (0,20) (0,1) (0,18) (0,11) (0,5) (0,15) (0,13) (0,14) (0,3) (0,9) (0,6) (0,4) (0,12) (0,17) (0,16) (1,10) (1,2) (1,7) (1,20) (1,18) (1,11) (1,5) (1,15) (1,13) (1,14) (1,3) (1,9) (1,6) (1,4) (1,12) (1,17) (1,16) (2,10) (2,7) (2,20) (2,18) (2,11) (2,5) (2,15) (2,13) (2,14) (2,3) (2,9) (2,6) (2,4) (2,12) (2,17) (2,16) (3,10) (3,7) (3,20) (3,18) (3,11) (3,5) (3,15) (3,13) (3,14) (3,9) (3,6) (3,4) (3,12) (3,17) (3,16) (4,10) (4,7) (4,20) (4,18) (4,11) (4,5) (4,15) (4,13) (4,14) (4,9) (4,6) (4,12) (4,17) (4,16) (5,10) (5,7) (5,20) (5,18) (5,11) (5,15) (5,13) (5,14) (5,9) (5,6) (5,12) (5,17) (5,16) (6,10) (6,7) (6,20) (6,18) (6,11) (6,15) (6,13) (6,14) (6,9) (6,12) (6,17) (6,16) (7,10) (7,20) (7,18) (7,11) (7,15) (7,13) (7,14) (7,9) (7,12) (7,17) (7,16) (8,19) (9,10) (9,20) (9,18) (9,11) (9,15) (9,13) (9,14) (9,12) (9,17) (9,16) (10,20) (10,18) (10,11) (10,15) (10,13) (10,14) (10,12) (10,17) (10,16) (11,20) (11,18) (11,15) (11,13) (11,14) (11,12) (11,17) (11,16) (12,20) (12,18) (12,15) (12,13) (12,14) (12,17) (12,16) (13,20) (13,18) (13,15) (13,14) (13,17) (13,16) (14,20) (14,18) (14,15) (14,17) (14,16) (15,20) (15,18) (15,17) (15,16) (16,20) (16,18) (16,17) (17,20) (17,18) (18,20)\nIs there a path between node 19 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph190-11_7", + "image": "data/connectivity/graph_visual/medium/graph190.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,10) (0,11) (0,5) (0,8) (0,12) (0,17) (0,13) (0,16) (0,6) (0,2) (0,9) (1,10) (1,11) (1,5) (1,8) (1,12) (1,17) (1,13) (1,16) (1,6) (1,2) (1,9) (2,10) (2,11) (2,5) (2,8) (2,12) (2,17) (2,13) (2,16) (2,6) (2,9) (3,15) (3,4) (3,7) (3,14) (4,15) (4,7) (4,14) (5,10) (5,11) (5,8) (5,12) (5,17) (5,13) (5,16) (5,6) (5,9) (6,10) (6,11) (6,8) (6,12) (6,17) (6,13) (6,16) (6,9) (7,15) (7,14) (8,10) (8,11) (8,12) (8,17) (8,13) (8,16) (8,9) (9,10) (9,11) (9,12) (9,17) (9,13) (9,16) (10,11) (10,12) (10,17) (10,13) (10,16) (11,12) (11,17) (11,13) (11,16) (12,17) (12,13) (12,16) (13,17) (13,16) (14,15) (16,17)\nIs there a path between node 11 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph407-5_11", + "image": "data/connectivity/graph_visual/medium/graph407.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (0,8) (0,11) (0,17) (0,1) (0,2) (0,12) (0,6) (0,18) (0,7) (0,15) (1,19) (1,8) (1,9) (1,11) (1,2) (1,12) (1,6) (1,7) (1,15) (2,19) (2,4) (2,9) (2,11) (2,17) (2,12) (2,6) (2,18) (2,15) (3,5) (3,13) (3,10) (4,19) (4,8) (4,9) (4,11) (4,17) (4,12) (4,6) (4,7) (4,15) (5,13) (5,10) (6,9) (6,11) (6,12) (6,18) (7,19) (7,8) (7,9) (7,11) (7,17) (7,15) (8,19) (8,11) (8,17) (8,12) (9,17) (9,12) (9,18) (10,13) (11,17) (11,15) (12,19) (12,17) (12,18) (12,15) (14,20) (14,21) (15,17) (15,18) (17,19) (17,18) (18,19) (20,21)\nIs there a path between node 5 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph560-7_15", + "image": "data/connectivity/graph_visual/medium/graph560.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,15) (0,22) (0,18) (0,2) (1,7) (1,19) (1,23) (1,3) (1,10) (1,13) (1,16) (1,11) (1,12) (1,21) (1,5) (2,9) (2,15) (2,22) (2,17) (2,8) (3,7) (3,19) (3,10) (3,13) (3,16) (3,11) (3,6) (3,20) (3,21) (4,19) (4,23) (4,10) (4,13) (4,16) (4,11) (4,6) (4,20) (4,5) (5,7) (5,19) (5,23) (5,13) (5,16) (5,11) (5,12) (5,6) (5,20) (5,21) (6,7) (6,23) (6,10) (6,13) (6,16) (6,12) (6,20) (6,21) (7,19) (7,23) (7,10) (7,13) (7,16) (7,11) (7,21) (8,15) (8,14) (9,15) (9,22) (9,14) (9,17) (10,13) (10,16) (10,11) (10,12) (11,19) (11,23) (11,12) (11,20) (11,21) (12,16) (12,21) (13,19) (13,16) (13,20) (13,21) (14,22) (14,18) (14,17) (15,22) (15,17) (16,19) (16,23) (16,20) (16,21) (17,18) (18,22) (19,20) (19,21) (20,23) (20,21)\nIs there a path between node 7 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph249-0_15", + "image": "data/connectivity/graph_visual/medium/graph249.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,6) (0,2) (0,17) (0,4) (0,5) (0,15) (0,9) (0,12) (0,11) (0,16) (0,8) (0,10) (0,18) (0,14) (1,7) (2,13) (2,6) (2,17) (2,4) (2,5) (2,15) (2,9) (2,12) (2,11) (2,16) (2,8) (2,10) (2,18) (2,14) (4,13) (4,6) (4,17) (4,5) (4,15) (4,9) (4,12) (4,11) (4,16) (4,8) (4,10) (4,18) (4,14) (5,13) (5,6) (5,17) (5,15) (5,9) (5,12) (5,11) (5,16) (5,8) (5,10) (5,18) (5,14) (6,13) (6,17) (6,15) (6,9) (6,12) (6,11) (6,16) (6,8) (6,10) (6,18) (6,14) (8,13) (8,17) (8,15) (8,9) (8,12) (8,11) (8,16) (8,10) (8,18) (8,14) (9,13) (9,17) (9,15) (9,12) (9,11) (9,16) (9,10) (9,18) (9,14) (10,13) (10,17) (10,15) (10,12) (10,11) (10,16) (10,18) (10,14) (11,13) (11,17) (11,15) (11,12) (11,16) (11,18) (11,14) (12,13) (12,17) (12,15) (12,16) (12,18) (12,14) (13,17) (13,15) (13,16) (13,18) (13,14) (14,17) (14,15) (14,16) (14,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 0 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph641-7_22", + "image": "data/connectivity/graph_visual/medium/graph641.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,14) (0,16) (0,22) (1,3) (1,8) (2,10) (3,20) (3,7) (3,13) (3,15) (3,18) (4,14) (4,16) (4,11) (5,16) (6,9) (8,17) (9,12) (9,11) (10,14) (10,11) (11,14) (11,19) (12,14) (13,23) (13,15) (13,18) (14,22) (15,21) (16,22) (17,23) (17,18) (19,22)\nIs there a path between node 7 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph458-6_2", + "image": "data/connectivity/graph_visual/medium/graph458.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,19) (0,7) (0,5) (0,11) (0,3) (0,10) (0,6) (0,18) (0,15) (0,2) (0,13) (0,16) (0,8) (0,20) (1,12) (1,14) (1,21) (1,9) (1,4) (1,17) (2,19) (2,7) (2,5) (2,11) (2,3) (2,10) (2,6) (2,18) (2,15) (2,13) (2,16) (2,8) (2,20) (3,19) (3,7) (3,5) (3,11) (3,10) (3,6) (3,18) (3,15) (3,13) (3,16) (3,8) (3,20) (4,12) (4,14) (4,21) (4,9) (4,17) (5,19) (5,7) (5,11) (5,10) (5,6) (5,18) (5,15) (5,13) (5,16) (5,8) (5,20) (6,19) (6,7) (6,11) (6,10) (6,18) (6,15) (6,13) (6,16) (6,8) (6,20) (7,19) (7,11) (7,10) (7,18) (7,15) (7,13) (7,16) (7,8) (7,20) (8,19) (8,11) (8,10) (8,18) (8,15) (8,13) (8,16) (8,20) (9,12) (9,14) (9,21) (9,17) (10,19) (10,11) (10,18) (10,15) (10,13) (10,16) (10,20) (11,19) (11,18) (11,15) (11,13) (11,16) (11,20) (12,14) (12,21) (12,17) (13,19) (13,18) (13,15) (13,16) (13,20) (14,21) (14,17) (15,19) (15,18) (15,16) (15,20) (16,19) (16,18) (16,20) (17,21) (18,19) (18,20) (19,20)\nIs there a path between node 6 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph340-18_12", + "image": "data/connectivity/graph_visual/medium/graph340.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,9) (0,11) (0,6) (0,14) (0,8) (0,19) (0,16) (0,4) (0,13) (0,17) (0,15) (1,9) (1,5) (1,14) (1,8) (1,16) (1,12) (1,13) (1,17) (1,15) (2,9) (2,11) (2,6) (2,20) (2,5) (2,14) (2,16) (2,4) (2,17) (2,15) (3,18) (4,9) (4,11) (4,6) (4,5) (4,14) (4,8) (4,19) (4,16) (4,12) (5,11) (5,6) (5,20) (5,8) (5,17) (5,15) (6,9) (6,20) (6,14) (6,8) (6,19) (6,16) (6,12) (6,13) (6,17) (6,15) (8,11) (8,20) (8,14) (8,19) (8,16) (8,12) (8,13) (8,17) (8,15) (9,11) (9,20) (9,14) (9,19) (9,16) (9,13) (9,17) (9,15) (11,20) (11,16) (11,13) (11,17) (11,15) (12,20) (12,14) (12,19) (12,13) (12,17) (12,15) (13,20) (13,14) (13,19) (13,17) (13,15) (14,19) (14,16) (14,17) (15,20) (15,19) (15,17) (16,19) (16,17) (17,19) (19,20)\nIs there a path between node 18 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph335-10_20", + "image": "data/connectivity/graph_visual/medium/graph335.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,6) (0,19) (0,17) (0,3) (0,10) (0,14) (1,7) (1,8) (1,15) (1,13) (2,9) (2,12) (2,18) (2,4) (3,6) (3,19) (3,17) (3,16) (3,10) (3,14) (4,12) (4,18) (5,9) (5,18) (6,19) (6,17) (6,16) (6,14) (6,20) (7,8) (7,15) (7,13) (9,12) (9,18) (10,16) (10,14) (10,20) (11,15) (12,18) (13,15) (14,19) (14,17) (14,20) (16,19) (16,17) (17,20) (19,20)\nIs there a path between node 10 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph70-0_10", + "image": "data/connectivity/graph_visual/medium/graph70.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,5) (0,1) (1,11) (1,5) (1,8) (2,14) (2,10) (2,6) (2,3) (2,13) (2,4) (3,7) (3,14) (3,6) (3,12) (3,13) (3,4) (4,9) (4,7) (4,10) (4,12) (4,13) (5,11) (5,8) (6,7) (6,10) (6,12) (6,13) (7,9) (7,14) (7,10) (7,13) (8,11) (10,14) (10,12) (10,13) (12,14) (12,13) (13,14)\nIs there a path between node 0 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph621-4_1", + "image": "data/connectivity/graph_visual/medium/graph621.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (0,17) (0,21) (0,2) (0,19) (0,5) (0,7) (0,10) (0,13) (0,1) (0,9) (0,20) (1,22) (1,17) (1,21) (1,2) (1,19) (1,5) (1,7) (1,10) (1,13) (1,9) (1,20) (2,22) (2,17) (2,21) (2,19) (2,5) (2,7) (2,10) (2,13) (2,9) (2,20) (3,18) (3,12) (3,11) (3,16) (3,23) (3,6) (3,4) (3,8) (3,14) (3,15) (4,18) (4,12) (4,11) (4,16) (4,23) (4,6) (4,8) (4,14) (4,15) (5,22) (5,17) (5,21) (5,19) (5,7) (5,10) (5,13) (5,9) (5,20) (6,18) (6,12) (6,11) (6,16) (6,23) (6,8) (6,14) (6,15) (7,22) (7,17) (7,21) (7,19) (7,10) (7,13) (7,9) (7,20) (8,18) (8,12) (8,11) (8,16) (8,23) (8,14) (8,15) (9,22) (9,17) (9,21) (9,19) (9,10) (9,13) (9,20) (10,22) (10,17) (10,21) (10,19) (10,13) (10,20) (11,18) (11,12) (11,16) (11,23) (11,14) (11,15) (12,18) (12,16) (12,23) (12,14) (12,15) (13,22) (13,17) (13,21) (13,19) (13,20) (14,18) (14,16) (14,23) (14,15) (15,18) (15,16) (15,23) (16,18) (16,23) (17,22) (17,21) (17,19) (17,20) (18,23) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph50-5_6", + "image": "data/connectivity/graph_visual/medium/graph50.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,1) (0,3) (1,3) (2,12) (2,6) (2,4) (2,5) (2,9) (2,11) (2,10) (2,8) (2,7) (4,12) (4,6) (4,5) (4,9) (4,11) (4,10) (4,8) (4,7) (5,12) (5,6) (5,9) (5,11) (5,10) (5,8) (5,7) (6,12) (6,9) (6,11) (6,10) (6,8) (6,7) (7,12) (7,9) (7,11) (7,10) (7,8) (8,12) (8,9) (8,11) (8,10) (9,12) (9,11) (9,10) (10,12) (10,11) (11,12)\nIs there a path between node 5 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph233-6_18", + "image": "data/connectivity/graph_visual/medium/graph233.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,7) (0,4) (0,1) (0,2) (0,14) (0,15) (0,8) (0,11) (0,9) (0,16) (1,17) (1,2) (1,15) (1,8) (1,9) (1,18) (2,7) (2,4) (2,14) (2,15) (2,12) (2,8) (2,18) (3,5) (3,13) (4,17) (4,15) (4,12) (4,6) (4,11) (4,16) (4,18) (6,17) (6,7) (6,14) (6,12) (6,11) (6,9) (6,16) (6,18) (7,17) (7,14) (7,15) (7,11) (7,9) (7,16) (8,17) (8,15) (8,18) (9,17) (9,14) (9,15) (9,12) (9,11) (9,18) (10,13) (11,17) (11,14) (11,15) (11,12) (11,16) (11,18) (12,17) (12,14) (12,16) (12,18) (14,17) (14,15) (14,16) (15,16) (15,18) (17,18)\nIs there a path between node 6 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph651-1_21", + "image": "data/connectivity/graph_visual/medium/graph651.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,4) (0,11) (0,18) (0,2) (0,8) (0,19) (0,23) (0,13) (0,7) (0,3) (0,16) (1,21) (1,22) (1,14) (1,17) (2,9) (2,4) (2,11) (2,18) (2,8) (2,19) (2,23) (2,13) (2,7) (2,3) (2,6) (3,9) (3,4) (3,11) (3,18) (3,8) (3,23) (3,13) (3,7) (3,6) (4,9) (4,11) (4,18) (4,23) (5,20) (5,10) (6,9) (6,18) (6,8) (6,13) (6,7) (6,16) (7,9) (7,11) (7,18) (7,8) (7,19) (7,23) (7,13) (7,16) (8,9) (8,11) (8,18) (8,19) (8,23) (8,13) (9,19) (9,23) (9,13) (11,18) (11,19) (11,23) (11,16) (12,21) (12,22) (12,15) (13,19) (13,23) (14,21) (14,22) (14,15) (15,21) (15,22) (16,18) (16,23) (17,21) (18,19) (19,23) (21,22)\nIs there a path between node 1 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-medium-graph147-4_1", + "image": "data/connectivity/graph_visual/medium/graph147.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (0,9) (0,7) (0,10) (0,6) (0,14) (0,8) (0,16) (0,13) (1,3) (1,6) (1,17) (1,8) (1,12) (1,16) (1,15) (2,5) (2,4) (3,10) (3,6) (3,14) (3,12) (3,16) (3,15) (4,5) (4,11) (5,11) (6,9) (6,7) (6,10) (6,17) (6,8) (6,12) (6,16) (6,13) (6,15) (7,10) (7,17) (7,14) (7,12) (7,16) (7,13) (7,15) (8,10) (8,17) (8,14) (8,12) (8,16) (8,13) (9,10) (9,17) (9,13) (9,15) (10,17) (10,14) (10,12) (10,13) (10,15) (12,17) (12,13) (12,15) (13,14) (13,15) (14,16) (15,16)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph708-13_5", + "image": "data/connectivity/graph_visual/medium/graph708.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,13) (0,14) (0,4) (1,9) (1,2) (1,15) (1,23) (2,9) (2,10) (2,18) (3,5) (3,8) (3,15) (3,18) (4,24) (4,13) (5,8) (5,15) (5,10) (5,23) (6,15) (6,10) (7,20) (8,15) (9,21) (10,15) (10,21) (10,18) (11,22) (11,13) (11,14) (12,22) (12,24) (12,13) (12,14) (13,17) (13,19) (13,22) (13,24) (14,24) (14,20) (15,18) (17,19) (17,20) (19,20)\nIs there a path between node 13 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph340-9_10", + "image": "data/connectivity/graph_visual/medium/graph340.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,9) (0,11) (0,6) (0,14) (0,8) (0,19) (0,16) (0,4) (0,13) (0,17) (0,15) (1,9) (1,5) (1,14) (1,8) (1,16) (1,12) (1,13) (1,17) (1,15) (2,9) (2,11) (2,6) (2,20) (2,5) (2,14) (2,16) (2,4) (2,17) (2,15) (3,18) (4,9) (4,11) (4,6) (4,5) (4,14) (4,8) (4,19) (4,16) (4,12) (5,11) (5,6) (5,20) (5,8) (5,17) (5,15) (6,9) (6,20) (6,14) (6,8) (6,19) (6,16) (6,12) (6,13) (6,17) (6,15) (8,11) (8,20) (8,14) (8,19) (8,16) (8,12) (8,13) (8,17) (8,15) (9,11) (9,20) (9,14) (9,19) (9,16) (9,13) (9,17) (9,15) (11,20) (11,16) (11,13) (11,17) (11,15) (12,20) (12,14) (12,19) (12,13) (12,17) (12,15) (13,20) (13,14) (13,19) (13,17) (13,15) (14,19) (14,16) (14,17) (15,20) (15,19) (15,17) (16,19) (16,17) (17,19) (19,20)\nIs there a path between node 9 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph613-20_10", + "image": "data/connectivity/graph_visual/medium/graph613.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,9) (0,17) (0,8) (0,22) (0,21) (0,12) (0,6) (0,3) (0,11) (0,20) (0,7) (0,18) (0,19) (0,13) (0,16) (0,4) (0,14) (0,1) (1,9) (1,17) (1,8) (1,22) (1,21) (1,12) (1,6) (1,3) (1,11) (1,20) (1,7) (1,18) (1,19) (1,13) (1,16) (1,4) (1,14) (2,5) (2,15) (2,10) (2,23) (3,9) (3,17) (3,8) (3,22) (3,21) (3,12) (3,6) (3,11) (3,20) (3,7) (3,18) (3,19) (3,13) (3,16) (3,4) (3,14) (4,9) (4,17) (4,8) (4,22) (4,21) (4,12) (4,6) (4,11) (4,20) (4,7) (4,18) (4,19) (4,13) (4,16) (4,14) (5,15) (5,10) (5,23) (6,9) (6,17) (6,8) (6,22) (6,21) (6,12) (6,11) (6,20) (6,7) (6,18) (6,19) (6,13) (6,16) (6,14) (7,9) (7,17) (7,8) (7,22) (7,21) (7,12) (7,11) (7,20) (7,18) (7,19) (7,13) (7,16) (7,14) (8,9) (8,17) (8,22) (8,21) (8,12) (8,11) (8,20) (8,18) (8,19) (8,13) (8,16) (8,14) (9,17) (9,22) (9,21) (9,12) (9,11) (9,20) (9,18) (9,19) (9,13) (9,16) (9,14) (10,15) (10,23) (11,17) (11,22) (11,21) (11,12) (11,20) (11,18) (11,19) (11,13) (11,16) (11,14) (12,17) (12,22) (12,21) (12,20) (12,18) (12,19) (12,13) (12,16) (12,14) (13,17) (13,22) (13,21) (13,20) (13,18) (13,19) (13,16) (13,14) (14,17) (14,22) (14,21) (14,20) (14,18) (14,19) (14,16) (15,23) (16,17) (16,22) (16,21) (16,20) (16,18) (16,19) (17,22) (17,21) (17,20) (17,18) (17,19) (18,22) (18,21) (18,20) (18,19) (19,22) (19,21) (19,20) (20,22) (20,21) (21,22)\nIs there a path between node 20 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph249-3_7", + "image": "data/connectivity/graph_visual/medium/graph249.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,13) (0,6) (0,2) (0,17) (0,4) (0,5) (0,15) (0,9) (0,12) (0,11) (0,16) (0,8) (0,10) (0,18) (0,14) (1,7) (2,13) (2,6) (2,17) (2,4) (2,5) (2,15) (2,9) (2,12) (2,11) (2,16) (2,8) (2,10) (2,18) (2,14) (4,13) (4,6) (4,17) (4,5) (4,15) (4,9) (4,12) (4,11) (4,16) (4,8) (4,10) (4,18) (4,14) (5,13) (5,6) (5,17) (5,15) (5,9) (5,12) (5,11) (5,16) (5,8) (5,10) (5,18) (5,14) (6,13) (6,17) (6,15) (6,9) (6,12) (6,11) (6,16) (6,8) (6,10) (6,18) (6,14) (8,13) (8,17) (8,15) (8,9) (8,12) (8,11) (8,16) (8,10) (8,18) (8,14) (9,13) (9,17) (9,15) (9,12) (9,11) (9,16) (9,10) (9,18) (9,14) (10,13) (10,17) (10,15) (10,12) (10,11) (10,16) (10,18) (10,14) (11,13) (11,17) (11,15) (11,12) (11,16) (11,18) (11,14) (12,13) (12,17) (12,15) (12,16) (12,18) (12,14) (13,17) (13,15) (13,16) (13,18) (13,14) (14,17) (14,15) (14,16) (14,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nIs there a path between node 3 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-medium-graph837-22_20", + "image": "data/connectivity/graph_visual/medium/graph837.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,10) (0,24) (0,6) (1,2) (1,21) (1,9) (1,8) (1,17) (1,5) (1,3) (1,11) (1,4) (1,15) (2,21) (2,9) (2,8) (2,17) (2,5) (2,3) (2,11) (2,4) (2,15) (3,21) (3,9) (3,8) (3,17) (3,5) (3,11) (3,4) (3,15) (4,21) (4,9) (4,8) (4,17) (4,5) (4,11) (4,15) (5,21) (5,9) (5,8) (5,17) (5,11) (5,15) (6,10) (6,24) (7,12) (7,18) (7,16) (7,23) (7,13) (7,20) (7,22) (7,14) (7,19) (8,21) (8,9) (8,17) (8,11) (8,15) (9,21) (9,17) (9,11) (9,15) (10,24) (11,21) (11,17) (11,15) (12,18) (12,16) (12,23) (12,13) (12,20) (12,22) (12,14) (12,19) (13,18) (13,16) (13,23) (13,20) (13,22) (13,14) (13,19) (14,18) (14,16) (14,23) (14,20) (14,22) (14,19) (15,21) (15,17) (16,18) (16,23) (16,20) (16,22) (16,19) (17,21) (18,23) (18,20) (18,22) (18,19) (19,23) (19,20) (19,22) (20,23) (20,22) (22,23)\nIs there a path between node 22 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph203-16_29", + "image": "data/connectivity/graph_visual/hard/graph203.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,5) (0,11) (0,13) (3,4) (3,21) (5,14) (5,27) (5,6) (5,19) (5,29) (5,25) (5,16) (5,13) (6,8) (6,9) (6,20) (6,29) (6,16) (6,11) (7,8) (7,26) (7,20) (7,12) (8,9) (8,19) (8,20) (8,28) (8,10) (8,22) (9,19) (9,20) (9,25) (9,11) (9,12) (9,22) (10,20) (10,25) (10,24) (10,15) (10,22) (11,26) (11,20) (11,28) (11,16) (11,24) (11,15) (12,25) (12,16) (12,23) (12,22) (13,18) (14,26) (14,24) (15,26) (15,20) (15,28) (16,27) (16,18) (16,26) (16,25) (16,23) (16,22) (18,27) (18,19) (18,20) (18,28) (18,25) (19,26) (19,20) (20,29) (20,25) (20,22) (22,24) (23,27) (23,29) (24,26) (24,28) (24,29) (25,27) (25,26)\nIs there a path between node 16 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph695-0_5", + "image": "data/connectivity/graph_visual/hard/graph695.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,21) (0,22) (0,25) (0,23) (0,10) (0,16) (0,3) (0,4) (0,7) (0,34) (0,27) (0,28) (0,19) (0,1) (0,20) (1,14) (1,6) (1,12) (1,25) (1,8) (1,16) (1,4) (1,7) (1,34) (1,27) (1,28) (1,26) (2,5) (2,17) (2,18) (2,15) (2,11) (3,14) (3,13) (3,6) (3,21) (3,12) (3,25) (3,33) (3,8) (3,10) (3,4) (3,7) (3,34) (3,28) (3,19) (3,26) (4,13) (4,6) (4,21) (4,22) (4,12) (4,8) (4,23) (4,10) (4,16) (4,34) (4,29) (4,28) (4,20) (5,30) (5,24) (5,9) (5,31) (5,15) (5,11) (6,14) (6,13) (6,21) (6,25) (6,23) (6,16) (6,7) (6,34) (6,27) (6,29) (6,28) (6,19) (7,14) (7,22) (7,12) (7,33) (7,23) (7,10) (7,16) (7,28) (7,19) (7,26) (7,20) (8,14) (8,13) (8,22) (8,12) (8,25) (8,33) (8,23) (8,10) (8,16) (8,34) (8,27) (8,19) (8,26) (8,20) (9,30) (9,24) (9,18) (9,31) (9,32) (10,14) (10,21) (10,22) (10,12) (10,23) (10,34) (10,27) (10,28) (10,19) (10,26) (11,30) (11,24) (11,17) (11,18) (11,31) (11,15) (11,32) (12,14) (12,13) (12,22) (12,25) (12,33) (12,23) (12,34) (12,27) (12,29) (12,28) (12,19) (12,26) (13,21) (13,22) (13,25) (13,33) (13,23) (13,16) (13,34) (13,27) (13,26) (13,20) (14,21) (14,33) (14,16) (14,34) (14,27) (14,29) (14,26) (14,20) (15,30) (15,24) (15,31) (16,25) (16,33) (16,23) (16,27) (16,19) (16,26) (16,20) (18,30) (18,24) (18,31) (18,32) (19,25) (19,33) (19,23) (19,34) (19,27) (19,29) (19,26) (19,20) (20,22) (20,25) (20,33) (20,23) (20,34) (20,27) (20,28) (20,26) (21,33) (21,23) (21,34) (21,27) (21,29) (22,33) (22,23) (22,27) (22,28) (23,25) (23,33) (23,34) (23,29) (23,28) (23,26) (24,31) (25,33) (25,34) (25,27) (25,28) (25,26) (26,33) (26,34) (26,27) (26,28) (27,33) (27,34) (27,29) (27,28) (28,33) (28,34) (29,33) (29,34) (30,32)\nIs there a path between node 0 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph114-23_3", + "image": "data/connectivity/graph_visual/hard/graph114.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,11) (0,16) (1,13) (2,27) (2,10) (2,5) (2,25) (2,16) (2,4) (3,10) (3,21) (3,7) (4,5) (4,22) (4,25) (4,21) (4,16) (4,6) (4,14) (5,10) (5,22) (5,25) (5,21) (5,11) (5,16) (5,19) (6,21) (6,19) (7,10) (7,21) (7,14) (7,19) (8,15) (9,13) (9,20) (9,23) (10,22) (10,11) (10,16) (10,19) (11,25) (12,15) (13,20) (14,16) (14,19) (15,24) (15,20) (16,27) (16,22) (16,25) (17,27) (17,22) (17,25) (19,27) (19,26) (20,23) (21,25) (21,26) (25,27) (26,27)\nIs there a path between node 23 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph416-3_8", + "image": "data/connectivity/graph_visual/hard/graph416.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,25) (0,27) (1,14) (1,23) (1,5) (1,6) (1,20) (1,8) (2,10) (2,25) (2,22) (3,19) (3,26) (4,32) (4,7) (4,20) (4,8) (5,17) (6,17) (6,8) (8,14) (8,23) (8,32) (9,19) (9,26) (9,13) (10,25) (10,12) (10,11) (11,25) (11,22) (12,24) (12,16) (12,25) (12,21) (13,15) (15,29) (15,19) (16,25) (17,31) (17,23) (17,32) (18,29) (18,30) (21,24) (21,25) (24,27) (26,30)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph474-25_27", + "image": "data/connectivity/graph_visual/hard/graph474.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (0,2) (0,21) (0,11) (0,16) (0,30) (0,29) (0,24) (0,14) (0,3) (0,15) (0,17) (0,7) (0,18) (0,8) (0,23) (0,5) (1,21) (1,11) (1,12) (1,26) (1,30) (1,20) (1,29) (1,31) (1,24) (1,14) (1,15) (1,17) (1,7) (1,18) (1,22) (1,23) (1,5) (2,21) (2,11) (2,12) (2,26) (2,30) (2,20) (2,29) (2,31) (2,24) (2,4) (2,3) (2,15) (2,7) (2,13) (2,22) (2,8) (2,23) (3,28) (3,21) (3,11) (3,12) (3,16) (3,30) (3,20) (3,29) (3,31) (3,14) (3,4) (3,17) (3,7) (3,13) (3,8) (3,23) (3,5) (4,28) (4,11) (4,12) (4,16) (4,6) (4,30) (4,29) (4,31) (4,25) (4,14) (4,15) (4,7) (4,22) (4,23) (4,5) (5,28) (5,11) (5,16) (5,26) (5,30) (5,31) (5,25) (5,14) (5,15) (5,17) (5,7) (5,18) (5,22) (5,8) (5,23) (6,28) (6,21) (6,26) (6,30) (6,20) (6,31) (6,25) (6,14) (6,15) (6,17) (6,7) (6,13) (6,18) (6,22) (6,23) (7,28) (7,11) (7,12) (7,16) (7,26) (7,20) (7,24) (7,25) (7,14) (7,23) (8,21) (8,11) (8,12) (8,16) (8,30) (8,20) (8,31) (8,24) (8,25) (8,17) (8,13) (8,18) (10,19) (11,28) (11,21) (11,12) (11,16) (11,26) (11,20) (11,29) (11,31) (11,14) (11,15) (11,17) (11,13) (11,18) (11,23) (12,21) (12,16) (12,26) (12,30) (12,29) (12,25) (12,15) (12,13) (12,18) (12,22) (13,28) (13,21) (13,16) (13,26) (13,30) (13,20) (13,29) (13,31) (13,24) (13,25) (13,14) (13,15) (13,17) (13,18) (13,23) (14,28) (14,21) (14,16) (14,26) (14,30) (14,29) (14,15) (14,17) (14,18) (14,22) (15,28) (15,21) (15,16) (15,30) (15,20) (15,31) (15,24) (15,17) (15,18) (15,23) (16,28) (16,21) (16,26) (16,20) (16,29) (16,31) (16,24) (16,25) (16,17) (16,18) (16,22) (16,23) (17,28) (17,30) (17,20) (17,29) (17,31) (17,24) (17,25) (17,18) (17,22) (18,28) (18,21) (18,26) (18,30) (18,23) (19,32) (20,21) (20,26) (20,30) (20,29) (20,31) (20,24) (20,25) (20,22) (20,23) (21,30) (21,29) (21,31) (21,25) (21,22) (21,23) (22,28) (22,30) (22,29) (22,25) (23,26) (23,30) (23,29) (23,31) (24,26) (24,29) (24,25) (25,26) (26,30) (26,29) (28,30) (28,29) (28,31) (29,30) (30,31)\nIs there a path between node 25 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph224-15_8", + "image": "data/connectivity/graph_visual/hard/graph224.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,4) (0,19) (0,29) (0,8) (0,20) (0,3) (0,17) (0,26) (0,18) (0,23) (0,28) (0,24) (0,14) (1,15) (1,11) (1,9) (1,16) (1,5) (1,2) (1,6) (1,12) (2,15) (2,21) (2,25) (2,16) (2,5) (2,7) (2,12) (3,10) (3,4) (3,27) (3,29) (3,8) (3,13) (3,20) (3,26) (3,18) (3,23) (3,24) (3,22) (3,14) (4,10) (4,27) (4,29) (4,8) (4,20) (4,17) (4,26) (4,18) (4,23) (4,28) (4,22) (4,14) (5,21) (5,11) (5,9) (5,16) (5,6) (5,7) (6,15) (6,11) (6,25) (6,9) (6,16) (6,7) (6,12) (7,21) (7,11) (7,25) (7,9) (7,12) (8,10) (8,27) (8,19) (8,13) (8,20) (8,17) (8,18) (8,23) (8,28) (8,24) (8,22) (9,15) (9,11) (9,16) (10,27) (10,19) (10,29) (10,13) (10,17) (10,26) (10,23) (10,28) (10,24) (10,22) (10,14) (11,15) (11,25) (11,16) (11,12) (12,15) (12,25) (12,16) (13,19) (13,29) (13,20) (13,17) (13,18) (13,28) (13,24) (13,22) (13,14) (14,27) (14,19) (14,29) (14,17) (14,26) (14,18) (14,23) (14,22) (15,21) (15,25) (15,16) (16,21) (16,25) (17,27) (17,19) (17,26) (17,18) (17,23) (17,28) (18,29) (18,26) (18,28) (18,24) (18,22) (19,27) (19,26) (19,23) (19,22) (20,27) (20,29) (20,26) (20,23) (20,28) (20,24) (21,25) (22,27) (22,29) (22,26) (22,23) (22,28) (22,24) (23,27) (23,26) (23,28) (24,27) (24,29) (24,26) (26,28) (27,29) (27,28) (28,29)\nIs there a path between node 15 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph158-19_23", + "image": "data/connectivity/graph_visual/hard/graph158.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,21) (0,2) (0,13) (0,26) (1,24) (1,22) (1,17) (2,11) (2,15) (2,10) (2,19) (3,4) (3,6) (3,22) (3,17) (3,20) (4,8) (4,24) (5,8) (5,24) (5,20) (6,8) (6,22) (6,20) (6,7) (7,24) (7,22) (7,25) (9,11) (9,12) (9,18) (9,23) (9,14) (9,19) (9,26) (10,19) (10,28) (11,21) (11,14) (11,15) (11,19) (11,16) (11,28) (11,26) (12,26) (13,28) (14,18) (15,21) (15,18) (15,23) (17,27) (17,24) (17,25) (17,20) (19,21) (19,23) (19,26) (20,22) (23,26)\nIs there a path between node 19 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph454-2_30", + "image": "data/connectivity/graph_visual/hard/graph454.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,7) (0,4) (0,23) (0,21) (0,18) (1,10) (1,19) (1,24) (1,18) (1,5) (2,11) (2,14) (2,22) (2,23) (2,13) (2,15) (2,31) (2,20) (3,11) (3,22) (3,16) (3,30) (3,13) (3,20) (3,18) (4,11) (4,14) (4,6) (4,23) (4,24) (4,31) (4,32) (4,18) (4,5) (5,19) (5,11) (5,7) (5,23) (5,15) (5,31) (6,19) (6,7) (6,13) (6,8) (7,11) (7,22) (7,28) (7,30) (7,21) (7,31) (8,10) (8,12) (8,14) (8,16) (8,30) (8,21) (9,17) (10,12) (10,24) (10,21) (10,32) (10,20) (11,22) (11,23) (11,13) (11,15) (11,18) (12,22) (12,31) (12,18) (13,16) (13,30) (13,23) (13,21) (13,15) (13,32) (14,19) (14,30) (14,23) (14,31) (15,30) (15,31) (15,32) (15,20) (16,30) (16,24) (16,21) (16,32) (17,25) (18,19) (18,28) (18,24) (19,21) (20,22) (20,21) (22,30) (22,23) (22,32) (24,28) (24,31) (24,32) (25,26) (25,27)\nIs there a path between node 2 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph370-22_18", + "image": "data/connectivity/graph_visual/hard/graph370.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,20) (0,26) (0,29) (0,27) (0,5) (0,30) (0,6) (0,1) (0,21) (0,10) (0,11) (0,16) (0,23) (1,24) (1,20) (1,13) (1,26) (1,29) (1,9) (1,27) (1,5) (1,30) (1,21) (1,16) (1,23) (1,22) (2,3) (2,28) (3,28) (4,24) (4,20) (4,26) (4,9) (4,27) (4,15) (4,5) (4,30) (4,16) (4,12) (4,22) (5,24) (5,26) (5,9) (5,27) (5,15) (5,30) (5,21) (5,10) (5,16) (5,12) (5,23) (6,24) (6,20) (6,9) (6,27) (6,30) (6,10) (6,11) (6,12) (6,23) (7,18) (7,25) (7,8) (7,14) (7,17) (8,18) (8,14) (8,17) (9,24) (9,20) (9,29) (9,27) (9,15) (9,21) (9,16) (9,12) (9,23) (9,22) (10,24) (10,13) (10,27) (10,15) (10,30) (10,21) (10,11) (10,16) (10,23) (10,22) (11,20) (11,13) (11,26) (11,29) (11,15) (11,30) (11,12) (11,23) (11,22) (12,20) (12,13) (12,29) (12,27) (12,15) (12,30) (12,21) (12,16) (12,23) (13,24) (13,20) (13,26) (13,30) (13,16) (14,18) (14,25) (15,20) (15,26) (15,29) (15,27) (15,30) (15,21) (15,22) (16,24) (16,20) (16,29) (16,27) (16,23) (17,18) (19,31) (19,28) (20,24) (20,27) (20,30) (20,21) (20,22) (21,26) (21,29) (21,30) (21,22) (22,24) (22,29) (22,27) (22,30) (23,26) (23,30) (24,26) (24,29) (24,27) (24,30) (26,29) (26,27) (26,30) (27,29) (27,30) (28,31) (29,30)\nIs there a path between node 22 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph114-15_19", + "image": "data/connectivity/graph_visual/hard/graph114.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,11) (0,16) (1,13) (2,27) (2,10) (2,5) (2,25) (2,16) (2,4) (3,10) (3,21) (3,7) (4,5) (4,22) (4,25) (4,21) (4,16) (4,6) (4,14) (5,10) (5,22) (5,25) (5,21) (5,11) (5,16) (5,19) (6,21) (6,19) (7,10) (7,21) (7,14) (7,19) (8,15) (9,13) (9,20) (9,23) (10,22) (10,11) (10,16) (10,19) (11,25) (12,15) (13,20) (14,16) (14,19) (15,24) (15,20) (16,27) (16,22) (16,25) (17,27) (17,22) (17,25) (19,27) (19,26) (20,23) (21,25) (21,26) (25,27) (26,27)\nIs there a path between node 15 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph410-5_30", + "image": "data/connectivity/graph_visual/hard/graph410.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,2) (0,8) (1,11) (1,10) (1,31) (1,4) (2,7) (2,28) (2,29) (2,6) (3,28) (3,21) (4,13) (4,9) (4,18) (4,26) (4,24) (4,25) (4,15) (4,22) (4,23) (5,11) (5,18) (5,14) (5,17) (5,31) (5,23) (6,28) (6,20) (6,19) (7,19) (7,21) (7,27) (8,20) (8,19) (9,11) (9,18) (9,26) (9,12) (9,24) (9,17) (10,31) (11,13) (11,17) (11,25) (11,31) (11,15) (11,22) (12,31) (12,22) (12,23) (13,18) (13,26) (13,14) (13,16) (13,24) (13,17) (13,15) (13,22) (13,23) (14,32) (14,17) (14,23) (15,24) (15,31) (16,24) (16,17) (16,31) (17,32) (17,25) (18,24) (18,23) (19,28) (19,30) (19,21) (19,27) (20,30) (20,29) (21,28) (21,30) (21,29) (22,25) (23,32) (24,32) (25,32) (26,32) (26,31) (27,29) (28,29) (29,30)\nIs there a path between node 5 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph493-12_24", + "image": "data/connectivity/graph_visual/hard/graph493.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,4) (0,1) (0,5) (0,24) (0,3) (0,21) (0,19) (0,9) (0,15) (0,20) (0,27) (0,13) (1,24) (1,21) (1,31) (1,10) (1,7) (1,20) (1,27) (1,13) (2,6) (2,5) (2,24) (2,3) (2,21) (2,19) (2,9) (2,31) (2,15) (2,7) (2,27) (2,13) (3,6) (3,4) (3,5) (3,22) (3,24) (3,21) (3,19) (3,9) (3,31) (3,18) (3,7) (3,20) (4,5) (4,21) (4,19) (4,9) (4,31) (4,7) (4,20) (4,27) (4,13) (5,6) (5,22) (5,24) (5,21) (5,9) (5,31) (5,10) (5,15) (5,18) (5,20) (5,27) (5,13) (6,22) (6,21) (6,19) (6,9) (6,31) (6,10) (6,15) (6,18) (6,7) (6,27) (6,13) (7,22) (7,9) (7,10) (7,15) (7,18) (7,20) (7,27) (7,13) (8,16) (8,11) (8,28) (8,12) (8,25) (8,30) (8,14) (8,32) (8,29) (9,22) (9,24) (9,21) (9,19) (9,31) (9,10) (9,15) (9,18) (9,20) (10,22) (10,19) (10,31) (10,15) (10,20) (10,27) (10,13) (11,16) (11,28) (11,26) (11,23) (11,30) (11,14) (11,32) (11,17) (12,16) (12,28) (12,23) (12,30) (12,14) (12,33) (12,32) (12,17) (12,29) (13,22) (13,24) (13,21) (13,19) (13,15) (13,18) (13,20) (14,28) (14,26) (14,23) (14,25) (14,33) (14,32) (14,29) (15,22) (15,24) (15,21) (15,19) (15,20) (15,27) (16,26) (16,25) (16,30) (16,33) (16,32) (16,17) (16,29) (17,28) (17,26) (17,25) (17,30) (17,33) (17,32) (17,29) (18,24) (18,19) (18,31) (19,22) (19,24) (19,31) (19,20) (19,27) (20,21) (20,31) (20,27) (21,31) (23,28) (23,26) (23,25) (23,30) (24,31) (24,27) (25,26) (25,30) (25,33) (25,32) (25,29) (26,28) (26,33) (26,32) (28,30) (28,29) (29,30) (29,33) (29,32) (30,32)\nIs there a path between node 12 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph483-30_15", + "image": "data/connectivity/graph_visual/hard/graph483.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,6) (0,15) (0,2) (0,10) (0,20) (0,13) (0,30) (0,17) (0,32) (0,22) (0,24) (1,31) (1,8) (1,4) (2,19) (2,15) (2,27) (2,10) (2,11) (2,20) (2,13) (2,17) (2,32) (2,22) (2,7) (3,18) (3,31) (3,8) (3,4) (4,18) (4,8) (5,25) (5,9) (6,19) (6,16) (6,15) (6,11) (6,13) (6,30) (6,17) (6,32) (6,24) (6,7) (7,19) (7,16) (7,15) (7,10) (7,20) (7,13) (7,30) (7,17) (7,32) (7,22) (7,24) (8,18) (8,31) (9,25) (9,23) (9,28) (10,19) (10,16) (10,27) (10,11) (10,20) (10,13) (10,30) (10,32) (10,22) (10,24) (11,19) (11,16) (11,15) (11,27) (11,13) (11,30) (11,17) (11,32) (11,24) (12,18) (13,19) (13,16) (13,27) (13,20) (13,30) (13,17) (13,22) (13,24) (14,29) (14,26) (15,19) (15,16) (15,27) (15,20) (15,30) (15,17) (15,32) (15,24) (16,19) (16,27) (16,20) (16,30) (16,17) (16,32) (16,24) (17,19) (17,20) (17,30) (17,22) (17,24) (18,31) (19,27) (19,20) (19,30) (19,32) (19,24) (20,27) (20,32) (20,22) (20,24) (21,29) (21,26) (22,27) (22,30) (22,32) (22,24) (23,25) (23,28) (24,27) (24,30) (24,32) (26,29) (27,30)\nIs there a path between node 30 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph185-7_26", + "image": "data/connectivity/graph_visual/hard/graph185.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,3) (0,18) (0,24) (0,5) (0,12) (0,26) (0,14) (0,16) (0,21) (0,9) (0,1) (0,28) (0,25) (1,3) (1,18) (1,24) (1,5) (1,12) (1,26) (1,14) (1,16) (1,21) (1,2) (1,23) (1,20) (1,28) (1,25) (2,3) (2,18) (2,10) (2,24) (2,5) (2,12) (2,26) (2,14) (2,16) (2,9) (2,23) (2,20) (2,28) (2,7) (2,25) (2,22) (2,13) (3,18) (3,24) (3,12) (3,26) (3,16) (3,9) (3,19) (3,7) (3,25) (3,22) (4,11) (4,27) (4,17) (4,15) (4,8) (5,18) (5,24) (5,12) (5,26) (5,14) (5,16) (5,21) (5,9) (5,23) (5,19) (5,20) (5,7) (5,13) (6,11) (6,27) (6,29) (6,15) (6,8) (7,18) (7,10) (7,12) (7,26) (7,14) (7,16) (7,21) (7,9) (7,20) (7,25) (7,22) (7,13) (8,11) (8,27) (8,29) (8,17) (8,15) (9,18) (9,10) (9,24) (9,16) (9,21) (9,19) (9,20) (9,28) (9,25) (9,13) (10,18) (10,24) (10,12) (10,26) (10,14) (10,16) (10,23) (10,20) (10,28) (10,25) (10,22) (10,13) (11,27) (11,29) (12,18) (12,24) (12,16) (12,21) (12,23) (12,20) (12,28) (12,22) (12,13) (13,18) (13,24) (13,26) (13,14) (13,16) (13,21) (13,23) (13,20) (13,28) (13,25) (13,22) (14,26) (14,16) (14,21) (14,23) (14,19) (14,20) (14,28) (14,25) (15,27) (15,17) (16,18) (16,24) (16,26) (16,20) (16,25) (16,22) (17,29) (18,24) (18,26) (18,23) (18,19) (18,20) (18,25) (18,22) (19,21) (19,23) (19,28) (19,25) (20,26) (20,23) (20,28) (20,25) (20,22) (21,26) (21,23) (21,28) (21,22) (22,26) (22,23) (22,25) (23,24) (23,26) (24,26) (24,28) (25,26)\nIs there a path between node 7 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph306-0_14", + "image": "data/connectivity/graph_visual/hard/graph306.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,8) (0,24) (0,6) (0,14) (0,26) (0,29) (0,10) (0,27) (0,5) (1,15) (2,18) (2,3) (2,6) (2,7) (2,13) (2,17) (2,20) (3,24) (3,22) (3,21) (3,12) (3,7) (3,19) (3,13) (3,25) (5,31) (5,16) (5,22) (5,7) (5,9) (5,14) (5,26) (5,25) (5,29) (5,30) (6,12) (6,14) (6,17) (6,20) (6,29) (6,27) (7,8) (7,18) (7,22) (7,28) (7,14) (7,26) (7,25) (7,30) (8,16) (8,9) (8,14) (8,19) (8,10) (9,31) (9,16) (9,21) (9,12) (9,13) (9,27) (10,31) (10,26) (10,17) (10,25) (10,29) (12,18) (12,26) (12,20) (13,28) (13,26) (13,29) (14,24) (14,21) (14,26) (14,17) (14,29) (15,23) (16,24) (16,31) (16,21) (16,26) (16,20) (16,29) (16,30) (17,31) (17,22) (17,19) (17,20) (17,29) (18,22) (18,21) (18,25) (18,29) (19,31) (19,22) (19,26) (19,20) (19,30) (20,25) (21,25) (22,26) (24,28) (25,28) (25,29) (25,27) (25,30) (27,31) (28,31)\nIs there a path between node 0 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph430-32_20", + "image": "data/connectivity/graph_visual/hard/graph430.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,12) (0,17) (0,11) (0,31) (0,25) (0,27) (0,28) (0,8) (0,16) (1,23) (1,3) (1,15) (1,10) (2,18) (2,24) (2,19) (2,4) (2,5) (2,26) (2,6) (2,7) (2,32) (3,23) (3,15) (3,10) (4,18) (4,22) (4,20) (4,6) (4,7) (4,32) (5,18) (5,29) (5,22) (5,24) (5,19) (5,20) (5,13) (5,6) (5,7) (6,24) (6,13) (6,7) (7,18) (7,29) (7,24) (7,32) (8,14) (8,12) (8,21) (8,17) (8,31) (8,25) (8,9) (9,30) (9,14) (9,12) (9,21) (9,17) (9,11) (9,31) (9,27) (9,28) (9,16) (10,23) (10,15) (11,14) (11,21) (11,17) (11,31) (11,25) (11,27) (11,28) (12,30) (12,31) (12,16) (13,18) (13,22) (13,24) (13,19) (13,20) (13,32) (14,30) (14,21) (14,17) (14,27) (14,28) (14,16) (15,23) (16,21) (16,17) (16,31) (16,27) (16,28) (17,21) (17,25) (17,27) (17,28) (18,22) (18,19) (18,20) (18,26) (18,32) (19,22) (19,24) (19,20) (19,26) (19,32) (20,29) (20,24) (20,26) (20,32) (21,31) (21,25) (21,27) (21,28) (22,29) (22,26) (22,32) (24,32) (25,30) (25,27) (25,28) (26,29) (26,32) (27,30) (27,31) (27,28) (28,30) (29,32) (30,31)\nIs there a path between node 32 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph460-26_12", + "image": "data/connectivity/graph_visual/hard/graph460.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (0,16) (0,12) (0,2) (0,27) (0,30) (0,19) (0,28) (0,21) (0,13) (0,18) (1,5) (1,7) (1,4) (1,30) (1,24) (1,3) (2,5) (2,6) (2,22) (2,29) (2,19) (2,24) (2,21) (2,3) (3,31) (3,5) (3,16) (3,6) (3,12) (3,22) (3,29) (3,28) (3,24) (3,21) (3,18) (4,31) (4,16) (4,7) (4,23) (5,17) (5,22) (5,13) (6,32) (6,25) (6,19) (6,23) (6,15) (7,31) (7,25) (7,21) (7,13) (7,18) (8,26) (8,11) (10,12) (10,19) (10,13) (10,18) (11,20) (12,16) (12,27) (12,22) (12,30) (12,28) (12,21) (12,13) (12,15) (13,25) (13,27) (13,30) (13,19) (13,24) (13,18) (15,16) (15,22) (15,21) (15,18) (16,31) (16,32) (16,25) (16,22) (16,29) (16,24) (17,32) (17,19) (17,28) (17,21) (17,23) (18,32) (18,22) (18,19) (18,28) (18,21) (19,31) (19,27) (19,22) (19,29) (19,24) (19,21) (20,26) (21,32) (21,24) (22,31) (22,32) (23,31) (23,25) (23,27) (23,29) (24,25) (28,30) (31,32)\nIs there a path between node 26 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph121-18_1", + "image": "data/connectivity/graph_visual/hard/graph121.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,12) (0,8) (0,5) (0,4) (0,25) (0,22) (0,16) (0,24) (0,21) (2,15) (2,23) (2,26) (2,10) (2,3) (2,11) (2,6) (2,27) (3,15) (3,23) (3,14) (3,26) (3,10) (3,11) (3,27) (4,8) (4,13) (4,5) (4,20) (4,18) (4,7) (4,22) (4,16) (4,24) (5,8) (5,13) (5,20) (5,7) (5,22) (5,24) (5,21) (6,15) (6,23) (6,14) (6,26) (6,10) (6,11) (6,27) (7,12) (7,20) (7,25) (7,16) (7,21) (8,12) (8,20) (8,25) (8,16) (8,24) (10,15) (10,23) (10,14) (10,26) (10,19) (10,11) (10,27) (11,15) (11,23) (11,26) (11,27) (12,16) (12,24) (12,21) (13,20) (13,18) (13,25) (13,22) (13,16) (13,24) (13,21) (14,15) (14,26) (15,26) (15,27) (16,22) (16,24) (16,21) (18,25) (18,22) (18,21) (19,23) (19,26) (19,27) (20,25) (20,24) (21,25) (21,24) (22,25) (22,24) (23,26) (23,27) (24,25) (26,27)\nIs there a path between node 18 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph608-27_32", + "image": "data/connectivity/graph_visual/hard/graph608.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,16) (0,32) (0,6) (0,11) (0,34) (1,26) (1,18) (2,13) (2,8) (2,34) (2,20) (3,30) (3,8) (3,11) (4,10) (5,7) (5,29) (6,32) (6,13) (6,28) (6,20) (7,22) (7,12) (7,23) (7,33) (8,16) (8,32) (8,13) (8,28) (8,20) (9,31) (10,19) (11,34) (13,34) (13,28) (13,20) (14,21) (16,32) (16,30) (16,28) (17,34) (17,28) (19,21) (20,32) (21,25) (22,26) (25,27) (28,30) (30,32)\nIs there a path between node 27 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph111-7_15", + "image": "data/connectivity/graph_visual/hard/graph111.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,16) (0,20) (0,1) (0,19) (0,18) (0,7) (0,17) (0,11) (0,13) (0,5) (0,3) (1,16) (1,9) (1,27) (1,19) (1,18) (1,2) (2,20) (2,10) (2,24) (2,23) (3,10) (3,13) (3,12) (4,9) (4,8) (4,14) (4,19) (4,18) (4,7) (4,17) (4,13) (4,5) (4,12) (4,23) (5,16) (5,6) (5,8) (5,19) (5,24) (5,17) (5,26) (6,20) (6,10) (6,18) (6,7) (6,11) (6,25) (7,8) (7,18) (7,17) (8,19) (8,24) (8,11) (8,13) (9,19) (9,11) (9,25) (10,27) (10,19) (10,18) (10,17) (11,14) (11,18) (11,25) (12,16) (12,14) (13,24) (13,25) (14,25) (15,22) (16,19) (16,24) (16,25) (17,19) (17,25) (18,19) (19,20) (24,27)\nIs there a path between node 7 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph131-6_9", + "image": "data/connectivity/graph_visual/hard/graph131.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,7) (0,18) (0,14) (0,6) (0,13) (1,12) (1,2) (1,11) (1,16) (1,21) (1,20) (1,4) (1,10) (1,27) (2,15) (2,12) (2,11) (2,16) (2,21) (2,17) (2,20) (2,4) (2,10) (3,19) (4,15) (4,16) (4,21) (4,17) (4,20) (4,5) (4,10) (5,15) (5,12) (5,16) (5,21) (5,17) (5,10) (5,27) (6,26) (6,8) (6,23) (6,9) (6,18) (7,26) (7,8) (7,9) (7,25) (8,26) (8,23) (8,18) (8,25) (8,14) (8,13) (9,25) (9,14) (10,15) (10,12) (10,11) (11,12) (11,16) (11,21) (11,17) (11,20) (11,27) (12,15) (12,16) (12,21) (12,20) (12,27) (13,23) (13,18) (13,25) (13,14) (14,26) (14,25) (15,16) (15,21) (15,17) (15,20) (15,27) (16,17) (16,20) (16,27) (17,21) (17,20) (17,27) (18,26) (18,25) (19,22) (20,21) (20,27) (23,26) (23,25) (25,26)\nIs there a path between node 6 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph445-26_24", + "image": "data/connectivity/graph_visual/hard/graph445.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,25) (0,13) (0,7) (0,20) (0,19) (0,10) (1,20) (1,19) (1,31) (1,24) (1,9) (1,3) (2,25) (2,13) (2,22) (2,31) (2,14) (2,24) (2,4) (2,30) (2,3) (2,5) (2,10) (3,6) (3,14) (3,18) (3,30) (4,13) (4,24) (4,21) (4,30) (4,5) (5,12) (5,31) (5,14) (6,20) (6,12) (6,9) (6,27) (7,13) (7,18) (7,10) (8,28) (8,32) (8,23) (8,17) (8,16) (8,26) (9,25) (9,20) (9,12) (9,19) (9,14) (10,13) (10,19) (10,24) (10,21) (10,30) (10,27) (11,15) (11,29) (11,32) (11,23) (11,26) (12,25) (12,22) (12,31) (12,30) (13,20) (13,14) (13,24) (13,30) (14,25) (14,24) (15,29) (15,32) (15,26) (17,23) (17,26) (18,24) (18,30) (19,25) (19,21) (19,30) (19,27) (20,31) (21,25) (21,30) (22,24) (23,28) (23,32) (25,30) (26,28) (26,32) (27,31)\nIs there a path between node 26 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph141-17_16", + "image": "data/connectivity/graph_visual/hard/graph141.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,4) (0,12) (0,17) (0,3) (0,24) (0,10) (1,16) (1,24) (1,7) (1,2) (2,14) (2,11) (2,22) (2,15) (3,11) (3,24) (3,10) (4,17) (4,24) (4,10) (5,27) (5,23) (6,18) (7,22) (7,17) (7,15) (7,24) (9,27) (9,25) (10,14) (10,12) (10,15) (11,14) (11,12) (13,19) (14,16) (14,17) (15,22) (15,16) (16,17) (17,24) (19,26) (21,27) (23,27) (23,25) (25,28)\nIs there a path between node 17 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph525-2_15", + "image": "data/connectivity/graph_visual/hard/graph525.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,12) (0,30) (0,8) (0,15) (1,20) (1,21) (1,29) (1,19) (1,5) (1,16) (2,32) (2,4) (2,27) (2,24) (2,19) (2,18) (2,16) (3,20) (3,18) (3,16) (4,20) (4,21) (4,14) (4,5) (4,16) (5,20) (5,17) (5,31) (6,28) (6,30) (7,29) (7,31) (8,30) (8,15) (9,21) (9,27) (9,14) (9,29) (10,25) (13,22) (13,28) (14,21) (14,27) (14,17) (16,32) (16,20) (16,24) (16,29) (17,21) (17,27) (17,31) (18,20) (18,21) (18,24) (19,24) (20,21) (20,24) (20,31) (21,24) (21,29) (21,31) (27,29)\nIs there a path between node 2 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph328-5_26", + "image": "data/connectivity/graph_visual/hard/graph328.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,21) (0,17) (0,19) (0,2) (0,25) (0,23) (0,14) (0,8) (0,7) (0,28) (0,29) (0,16) (0,5) (0,12) (0,11) (0,18) (0,6) (0,24) (1,4) (1,17) (1,19) (1,14) (1,8) (1,31) (1,27) (1,7) (1,29) (1,16) (1,5) (1,12) (1,11) (1,20) (1,3) (1,18) (1,6) (1,13) (2,21) (2,17) (2,19) (2,25) (2,31) (2,15) (2,27) (2,7) (2,29) (2,16) (2,5) (2,26) (2,12) (2,11) (2,3) (2,18) (2,10) (2,13) (3,4) (3,21) (3,17) (3,19) (3,23) (3,14) (3,31) (3,15) (3,27) (3,7) (3,28) (3,16) (3,26) (3,11) (3,20) (3,18) (3,24) (3,10) (3,13) (4,21) (4,19) (4,25) (4,23) (4,8) (4,31) (4,15) (4,27) (4,7) (4,29) (4,16) (4,5) (4,26) (4,20) (4,18) (4,10) (4,13) (5,21) (5,17) (5,19) (5,23) (5,14) (5,8) (5,31) (5,15) (5,7) (5,28) (5,26) (5,12) (5,11) (5,20) (5,24) (5,10) (5,13) (6,21) (6,17) (6,23) (6,14) (6,8) (6,31) (6,15) (6,27) (6,7) (6,12) (6,11) (6,18) (6,24) (6,10) (6,13) (7,17) (7,19) (7,25) (7,14) (7,31) (7,15) (7,27) (7,28) (7,29) (7,16) (7,26) (7,12) (7,11) (7,20) (7,10) (7,13) (8,21) (8,17) (8,19) (8,25) (8,14) (8,31) (8,28) (8,29) (8,16) (8,20) (8,18) (8,24) (8,10) (8,13) (9,30) (10,21) (10,17) (10,25) (10,23) (10,14) (10,31) (10,15) (10,28) (10,29) (10,16) (10,12) (10,20) (10,18) (10,24) (11,21) (11,17) (11,19) (11,25) (11,23) (11,15) (11,28) (11,16) (11,12) (11,20) (11,18) (11,24) (11,13) (12,19) (12,25) (12,23) (12,14) (12,31) (12,15) (12,27) (12,28) (12,29) (12,16) (12,26) (12,20) (12,18) (12,24) (13,21) (13,19) (13,25) (13,23) (13,14) (13,31) (13,15) (13,29) (13,16) (13,26) (13,20) (13,24) (14,17) (14,23) (14,31) (14,15) (14,28) (14,29) (14,16) (14,26) (14,20) (14,24) (15,17) (15,25) (15,23) (15,31) (15,27) (15,28) (15,29) (15,16) (15,26) (15,20) (16,21) (16,19) (16,25) (16,23) (16,31) (16,27) (16,28) (16,29) (16,26) (16,18) (16,24) (17,21) (17,19) (17,25) (17,23) (17,31) (17,29) (17,18) (17,24) (18,21) (18,19) (18,25) (18,28) (18,29) (18,26) (18,20) (19,21) (19,25) (19,23) (19,27) (19,28) (19,29) (19,20) (20,21) (20,25) (20,23) (20,27) (20,28) (20,26) (20,24) (21,25) (21,23) (21,31) (21,27) (21,28) (21,24) (22,30) (23,31) (23,27) (24,25) (24,31) (24,27) (24,28) (24,29) (24,26) (26,31) (26,27) (26,29) (28,29) (29,31)\nIs there a path between node 5 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph384-24_14", + "image": "data/connectivity/graph_visual/hard/graph384.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,5) (0,30) (0,29) (0,17) (0,3) (0,22) (0,12) (0,15) (0,27) (1,2) (1,9) (1,31) (1,13) (1,16) (1,20) (1,18) (1,25) (2,9) (2,31) (2,13) (2,21) (2,16) (2,10) (2,20) (3,23) (3,4) (3,5) (3,24) (3,17) (3,7) (3,22) (3,19) (3,15) (3,27) (3,14) (4,23) (4,24) (4,30) (4,29) (4,7) (4,22) (4,26) (4,19) (4,28) (4,15) (4,27) (4,14) (5,23) (5,24) (5,29) (5,7) (5,26) (5,19) (5,12) (5,28) (5,15) (5,27) (6,9) (6,31) (6,13) (6,21) (6,16) (6,10) (6,18) (6,25) (7,23) (7,24) (7,30) (7,29) (7,17) (7,22) (7,28) (7,15) (7,27) (8,11) (9,13) (9,21) (9,16) (9,10) (9,18) (9,25) (10,31) (10,13) (10,21) (10,16) (12,23) (12,30) (12,17) (12,22) (12,26) (12,19) (12,28) (12,27) (13,31) (13,21) (13,25) (14,24) (14,30) (14,29) (14,17) (14,22) (14,19) (14,28) (14,15) (14,27) (15,23) (15,24) (15,17) (15,22) (15,26) (15,28) (15,27) (16,31) (16,18) (16,25) (17,23) (17,24) (17,30) (17,22) (17,28) (18,31) (18,20) (18,25) (19,23) (19,24) (19,29) (19,22) (19,27) (20,31) (21,25) (22,23) (22,30) (22,29) (22,26) (22,28) (22,27) (23,30) (23,29) (23,26) (23,28) (24,30) (24,29) (24,28) (24,27) (25,31) (26,30) (26,29) (26,28) (26,27) (27,28) (28,30) (28,29)\nIs there a path between node 24 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph294-9_2", + "image": "data/connectivity/graph_visual/hard/graph294.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,22) (0,13) (0,31) (0,25) (1,23) (2,17) (3,8) (3,11) (3,19) (5,16) (5,17) (5,9) (6,22) (6,26) (6,19) (6,31) (8,28) (8,12) (8,13) (9,23) (10,22) (10,25) (11,28) (11,26) (11,12) (11,19) (12,22) (12,26) (12,25) (13,28) (13,26) (13,31) (14,30) (15,22) (15,28) (15,26) (15,29) (15,31) (15,25) (16,21) (16,18) (17,18) (18,23) (18,21) (19,28) (19,26) (19,29) (19,27) (19,31) (20,30) (20,24) (22,28) (22,26) (22,29) (24,30) (25,26) (26,29) (26,31) (27,28) (29,31)\nIs there a path between node 9 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph622-14_34", + "image": "data/connectivity/graph_visual/hard/graph622.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,25) (0,13) (1,16) (1,27) (1,32) (1,4) (1,31) (1,34) (2,16) (2,27) (2,32) (2,6) (2,19) (2,9) (3,25) (3,28) (3,7) (3,18) (3,21) (4,29) (4,33) (4,23) (4,12) (4,9) (4,34) (5,27) (5,11) (5,19) (5,9) (6,33) (6,27) (6,34) (7,25) (7,18) (8,10) (9,16) (9,19) (9,34) (10,30) (11,29) (11,16) (11,19) (11,31) (11,14) (11,12) (12,33) (12,26) (12,19) (12,34) (13,25) (13,28) (14,32) (15,30) (16,29) (16,27) (16,32) (18,21) (20,24) (21,25) (22,25) (22,28) (23,27) (26,33) (26,27) (26,34) (27,29) (27,33) (27,34) (29,33)\nIs there a path between node 14 and node 34 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph105-3_27", + "image": "data/connectivity/graph_visual/hard/graph105.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,7) (0,2) (0,24) (0,25) (0,12) (0,3) (0,1) (0,14) (0,26) (0,11) (0,10) (0,6) (0,16) (0,22) (0,9) (1,18) (1,7) (1,2) (1,21) (1,15) (1,24) (1,4) (1,12) (1,26) (1,11) (1,10) (1,16) (1,9) (2,7) (2,21) (2,23) (2,25) (2,12) (2,3) (2,26) (2,11) (2,6) (3,18) (3,7) (3,21) (3,19) (3,24) (3,4) (3,14) (3,26) (3,11) (3,20) (3,6) (3,16) (3,22) (3,9) (4,7) (4,17) (4,19) (4,15) (4,25) (4,14) (4,26) (4,20) (4,10) (4,6) (4,16) (4,9) (5,8) (6,7) (6,21) (6,19) (6,15) (6,23) (6,25) (6,12) (6,14) (6,26) (6,11) (6,20) (6,10) (6,16) (6,22) (6,9) (7,17) (7,21) (7,19) (7,15) (7,24) (7,25) (7,12) (7,14) (7,26) (7,10) (7,22) (8,13) (9,18) (9,17) (9,19) (9,23) (9,24) (9,25) (9,12) (9,14) (9,26) (9,11) (9,20) (9,22) (10,18) (10,17) (10,21) (10,19) (10,24) (10,25) (10,11) (10,22) (11,17) (11,21) (11,15) (11,23) (11,24) (11,25) (11,14) (11,20) (11,16) (11,22) (12,18) (12,17) (12,21) (12,15) (12,23) (12,14) (12,26) (12,20) (12,16) (12,22) (14,18) (14,17) (14,21) (14,19) (14,24) (14,25) (14,26) (14,20) (15,18) (15,17) (15,21) (15,23) (15,24) (15,25) (15,20) (15,16) (15,22) (16,17) (16,21) (16,23) (16,24) (16,25) (16,26) (16,20) (16,22) (17,18) (17,21) (17,19) (17,23) (17,24) (17,25) (17,26) (17,20) (18,19) (18,23) (18,24) (18,25) (18,26) (18,20) (18,22) (19,23) (19,25) (19,26) (20,23) (20,24) (20,26) (20,22) (21,25) (21,26) (21,22) (22,23) (22,24) (22,26) (23,24) (23,26) (24,25) (24,26)\nIs there a path between node 3 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph418-12_32", + "image": "data/connectivity/graph_visual/hard/graph418.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,23) (1,29) (1,2) (2,10) (2,7) (2,14) (2,30) (3,31) (3,13) (3,17) (3,12) (5,15) (5,22) (6,13) (6,26) (6,8) (6,25) (8,17) (9,27) (10,11) (10,14) (10,16) (11,18) (12,31) (12,24) (13,31) (13,28) (13,25) (14,30) (15,19) (17,26) (17,24) (18,29) (20,27) (25,28) (25,32) (26,28) (26,32) (28,32) (31,32)\nIs there a path between node 12 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph96-9_3", + "image": "data/connectivity/graph_visual/hard/graph96.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,20) (0,8) (0,13) (0,11) (0,22) (0,15) (1,24) (2,3) (3,24) (4,18) (5,13) (5,27) (5,11) (5,7) (5,21) (6,11) (6,22) (6,17) (7,25) (7,8) (7,23) (7,11) (7,12) (7,22) (7,17) (8,20) (8,10) (8,12) (8,21) (10,20) (10,25) (10,13) (10,22) (10,16) (10,21) (11,20) (11,25) (11,16) (11,15) (12,23) (12,16) (12,21) (13,20) (13,23) (13,22) (13,17) (13,15) (15,26) (15,25) (15,22) (16,27) (17,26) (17,23) (17,27) (20,26) (20,22) (21,25) (22,25) (23,25) (25,26) (26,27)\nIs there a path between node 9 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph651-26_16", + "image": "data/connectivity/graph_visual/hard/graph651.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,5) (0,7) (0,9) (0,30) (0,26) (0,11) (0,28) (0,22) (0,34) (0,14) (0,20) (0,17) (0,29) (0,21) (0,25) (0,24) (1,5) (1,10) (1,9) (1,30) (1,26) (1,18) (1,11) (1,28) (1,22) (1,4) (1,34) (1,32) (1,17) (1,16) (1,29) (1,19) (1,21) (1,23) (1,24) (2,7) (2,10) (2,9) (2,26) (2,33) (2,18) (2,11) (2,28) (2,3) (2,22) (2,4) (2,34) (2,6) (2,8) (2,31) (2,12) (2,20) (2,17) (2,16) (2,29) (2,19) (2,25) (2,24) (3,5) (3,7) (3,10) (3,9) (3,30) (3,26) (3,33) (3,18) (3,11) (3,28) (3,22) (3,34) (3,6) (3,8) (3,32) (3,31) (3,14) (3,12) (3,17) (3,16) (3,29) (3,25) (3,23) (4,10) (4,26) (4,33) (4,18) (4,28) (4,22) (4,34) (4,6) (4,32) (4,14) (4,12) (4,20) (4,17) (4,16) (4,29) (4,19) (4,21) (4,25) (4,24) (5,10) (5,9) (5,30) (5,18) (5,11) (5,28) (5,34) (5,6) (5,8) (5,32) (5,14) (5,20) (5,16) (5,19) (5,21) (5,25) (5,23) (6,7) (6,10) (6,9) (6,33) (6,18) (6,11) (6,28) (6,22) (6,8) (6,17) (6,29) (6,19) (6,21) (6,25) (6,24) (7,10) (7,9) (7,33) (7,18) (7,11) (7,28) (7,22) (7,34) (7,32) (7,31) (7,14) (7,12) (7,17) (7,16) (7,29) (7,21) (7,25) (7,23) (7,24) (8,10) (8,9) (8,30) (8,26) (8,33) (8,18) (8,34) (8,14) (8,12) (8,16) (8,19) (8,21) (8,23) (9,10) (9,30) (9,26) (9,33) (9,18) (9,11) (9,28) (9,22) (9,34) (9,32) (9,14) (9,20) (9,17) (9,29) (9,19) (9,21) (9,25) (9,23) (9,24) (10,26) (10,18) (10,11) (10,28) (10,34) (10,32) (10,31) (10,14) (10,20) (10,29) (10,19) (10,21) (10,25) (10,23) (10,24) (11,26) (11,33) (11,18) (11,28) (11,22) (11,34) (11,31) (11,14) (11,20) (11,16) (11,29) (11,21) (11,25) (11,24) (12,30) (12,26) (12,33) (12,28) (12,22) (12,31) (12,14) (12,20) (12,19) (12,25) (12,23) (12,24) (13,15) (13,27) (14,30) (14,26) (14,28) (14,34) (14,31) (14,17) (14,29) (14,25) (15,27) (16,30) (16,26) (16,18) (16,22) (16,34) (16,31) (16,17) (16,29) (16,19) (16,21) (16,25) (16,23) (16,24) (17,30) (17,26) (17,33) (17,18) (17,28) (17,31) (17,20) (17,29) (17,19) (17,21) (17,25) (17,23) (17,24) (18,30) (18,26) (18,33) (18,28) (18,32) (18,31) (18,29) (18,21) (18,25) (18,23) (18,24) (19,30) (19,33) (19,32) (19,20) (19,29) (19,21) (19,23) (19,24) (20,30) (20,26) (20,33) (20,28) (20,22) (20,34) (20,32) (20,31) (20,21) (20,25) (20,23) (20,24) (21,26) (21,33) (21,28) (21,22) (21,34) (21,31) (21,29) (21,25) (21,24) (22,26) (22,33) (22,28) (22,32) (22,31) (22,23) (22,24) (23,26) (23,28) (23,32) (23,31) (23,29) (24,30) (24,26) (24,33) (24,28) (24,34) (24,32) (24,31) (24,29) (24,25) (25,30) (25,26) (25,33) (25,28) (25,31) (25,29) (26,33) (26,28) (26,34) (26,32) (26,29) (28,34) (28,31) (29,33) (29,32) (29,31) (30,33) (30,34) (30,32) (30,31) (31,34) (31,32) (32,33) (33,34)\nIs there a path between node 26 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph390-20_16", + "image": "data/connectivity/graph_visual/hard/graph390.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,2) (0,17) (1,4) (2,10) (3,19) (3,30) (3,13) (3,25) (3,8) (4,31) (5,16) (6,29) (6,11) (6,32) (7,14) (7,17) (8,21) (8,30) (8,13) (8,28) (9,20) (9,25) (11,29) (11,26) (11,22) (13,21) (13,15) (13,28) (13,23) (15,31) (15,16) (15,28) (15,23) (16,21) (16,25) (16,23) (18,29) (18,24) (20,31) (20,30) (20,25) (21,25) (22,24) (23,25) (23,28) (24,29) (24,32) (25,30) (26,32) (28,30)\nIs there a path between node 20 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph332-11_6", + "image": "data/connectivity/graph_visual/hard/graph332.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,23) (0,2) (0,30) (0,21) (0,10) (0,18) (0,28) (0,12) (0,24) (0,19) (0,3) (0,14) (0,13) (1,26) (1,16) (1,11) (1,20) (1,8) (1,6) (1,25) (2,15) (2,29) (2,23) (2,7) (2,21) (2,10) (2,18) (2,12) (2,24) (2,27) (2,19) (2,14) (2,17) (2,13) (3,29) (3,23) (3,30) (3,7) (3,10) (3,24) (3,27) (3,19) (3,14) (3,31) (3,17) (3,4) (3,13) (4,23) (4,21) (4,10) (4,12) (4,27) (4,19) (4,14) (4,31) (4,17) (4,13) (5,26) (5,16) (5,20) (5,8) (5,6) (5,25) (6,9) (6,16) (6,11) (6,8) (7,29) (7,23) (7,30) (7,21) (7,10) (7,18) (7,28) (7,12) (7,24) (7,27) (7,19) (7,17) (7,22) (7,13) (8,9) (8,26) (8,16) (8,11) (8,20) (8,25) (9,26) (9,11) (9,20) (9,25) (10,15) (10,29) (10,28) (10,12) (10,24) (10,27) (10,31) (10,13) (11,16) (11,20) (11,25) (12,15) (12,29) (12,21) (12,24) (12,27) (12,19) (12,14) (12,31) (12,22) (13,15) (13,23) (13,30) (13,21) (13,18) (13,28) (13,24) (13,27) (13,19) (13,14) (13,22) (14,15) (14,29) (14,30) (14,21) (14,18) (14,24) (14,27) (14,19) (14,31) (14,22) (15,29) (15,23) (15,30) (15,21) (15,24) (15,19) (15,17) (16,26) (16,25) (17,21) (17,18) (17,28) (17,24) (17,27) (17,19) (17,31) (17,22) (18,23) (18,30) (18,21) (18,28) (18,27) (18,19) (18,31) (18,22) (19,23) (19,21) (19,28) (19,24) (19,27) (19,31) (19,22) (20,26) (20,25) (21,29) (21,23) (21,28) (21,24) (21,27) (21,22) (22,29) (22,23) (22,30) (22,24) (22,27) (22,31) (23,28) (23,31) (24,30) (24,27) (24,31) (25,26) (27,29) (27,28) (27,31) (28,29) (28,30) (28,31) (29,30) (29,31)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph243-21_12", + "image": "data/connectivity/graph_visual/hard/graph243.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,20) (0,10) (0,25) (0,16) (0,1) (0,3) (0,2) (0,17) (1,11) (1,22) (1,6) (1,24) (1,9) (1,30) (1,16) (1,17) (1,13) (2,11) (2,8) (2,19) (2,6) (2,12) (2,27) (2,3) (2,17) (3,5) (3,18) (3,24) (3,12) (3,25) (3,30) (4,21) (5,26) (5,22) (5,24) (5,12) (5,29) (5,25) (5,14) (5,30) (6,26) (6,18) (6,15) (8,20) (8,22) (8,12) (8,9) (8,13) (9,20) (9,18) (9,15) (9,23) (9,17) (9,13) (10,11) (10,15) (10,14) (10,30) (10,13) (11,22) (11,30) (11,27) (11,23) (11,17) (12,26) (12,19) (12,15) (12,25) (12,23) (12,17) (13,19) (13,15) (13,30) (14,22) (14,16) (14,17) (15,26) (15,19) (15,18) (15,25) (16,24) (16,25) (16,23) (17,26) (18,25) (19,26) (19,20) (19,22) (19,24) (20,26) (20,24) (20,25) (20,27) (21,28) (22,26) (22,29) (22,30) (22,27) (22,23) (23,30) (24,30) (25,29) (25,27) (26,30) (26,27) (29,30)\nIs there a path between node 21 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph515-7_19", + "image": "data/connectivity/graph_visual/hard/graph515.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,4) (0,20) (0,31) (0,15) (0,28) (0,12) (0,18) (1,4) (1,10) (1,8) (1,16) (1,29) (1,15) (1,28) (1,23) (1,32) (1,6) (1,26) (2,14) (2,11) (3,17) (4,8) (4,23) (4,12) (4,32) (4,26) (5,10) (5,16) (5,29) (5,23) (5,12) (5,32) (6,8) (6,29) (6,12) (6,18) (6,26) (7,10) (7,8) (7,29) (7,15) (7,28) (8,29) (8,28) (8,12) (9,10) (9,31) (9,15) (9,23) (9,12) (9,18) (9,24) (9,32) (9,26) (10,20) (10,31) (10,23) (10,26) (11,14) (12,23) (12,18) (14,33) (14,25) (15,31) (15,29) (15,23) (15,18) (16,20) (16,28) (16,24) (17,19) (17,30) (17,27) (18,20) (18,29) (18,32) (20,29) (20,28) (20,23) (21,22) (22,25) (23,31) (23,29) (23,28) (24,32) (24,26) (26,31) (31,32)\nIs there a path between node 7 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph172-13_6", + "image": "data/connectivity/graph_visual/hard/graph172.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,17) (0,11) (0,6) (0,9) (1,23) (1,21) (1,3) (1,19) (1,15) (1,22) (1,24) (1,5) (1,14) (1,25) (1,27) (1,18) (2,28) (2,13) (2,6) (3,23) (3,21) (3,12) (3,19) (3,15) (3,22) (3,24) (3,10) (3,14) (3,26) (3,25) (3,27) (4,21) (4,12) (4,15) (4,22) (4,24) (4,5) (4,14) (4,26) (4,25) (4,16) (4,27) (5,23) (5,21) (5,19) (5,15) (5,24) (5,10) (5,26) (5,8) (5,27) (6,28) (6,13) (6,17) (6,11) (7,28) (7,13) (7,11) (7,20) (8,21) (8,12) (8,19) (8,15) (8,22) (8,14) (8,26) (8,25) (8,16) (8,27) (9,17) (9,11) (9,20) (10,23) (10,12) (10,15) (10,22) (10,24) (10,14) (10,26) (10,25) (10,16) (10,18) (11,28) (11,13) (11,17) (11,20) (12,23) (12,21) (12,15) (12,22) (12,24) (12,16) (12,18) (13,28) (13,17) (13,20) (14,23) (14,21) (14,19) (14,15) (14,24) (14,25) (14,16) (14,27) (15,23) (15,19) (15,26) (15,25) (15,16) (15,27) (15,18) (16,23) (16,21) (16,19) (16,24) (16,26) (16,27) (16,18) (17,28) (18,23) (18,21) (18,19) (18,22) (18,24) (18,26) (18,25) (19,23) (19,22) (19,24) (19,26) (19,25) (19,27) (20,28) (21,23) (21,22) (21,24) (21,26) (21,25) (21,27) (22,24) (22,25) (23,24) (24,26) (24,25) (24,27)\nIs there a path between node 13 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph467-4_11", + "image": "data/connectivity/graph_visual/hard/graph467.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,29) (0,10) (0,18) (0,21) (0,30) (0,28) (0,15) (1,27) (1,24) (1,22) (1,32) (1,14) (1,5) (2,29) (2,10) (2,18) (2,21) (2,19) (2,30) (2,16) (2,28) (2,15) (3,24) (3,13) (3,22) (3,20) (3,5) (4,17) (4,11) (4,6) (4,26) (4,23) (4,31) (4,25) (5,27) (5,13) (5,22) (5,20) (5,32) (5,14) (6,17) (6,9) (6,23) (6,31) (6,25) (7,29) (7,10) (7,18) (7,19) (7,30) (7,16) (7,15) (8,17) (8,11) (8,26) (8,23) (8,31) (9,17) (9,26) (9,23) (9,31) (9,25) (10,29) (10,18) (10,21) (10,30) (10,28) (10,15) (11,17) (11,26) (11,23) (12,27) (12,24) (12,13) (12,22) (12,32) (13,27) (13,24) (13,22) (13,20) (13,32) (13,14) (14,27) (14,22) (14,32) (15,29) (15,18) (15,21) (15,19) (15,28) (16,29) (16,21) (16,19) (16,28) (17,23) (18,29) (18,21) (18,30) (18,28) (19,29) (19,21) (19,30) (19,28) (20,24) (20,22) (20,32) (21,29) (21,30) (21,28) (22,27) (22,24) (22,32) (23,31) (24,27) (25,26) (26,31) (28,30)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph226-17_12", + "image": "data/connectivity/graph_visual/hard/graph226.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,17) (0,29) (0,18) (0,24) (0,27) (0,12) (0,14) (0,21) (0,7) (0,15) (0,6) (1,25) (1,9) (1,5) (1,8) (1,2) (1,13) (1,10) (1,23) (2,19) (2,3) (2,25) (2,9) (2,5) (2,16) (2,8) (2,13) (2,10) (2,23) (3,19) (3,28) (3,25) (3,5) (3,13) (3,10) (4,17) (4,18) (4,24) (4,27) (4,12) (4,14) (4,20) (4,7) (4,15) (4,6) (4,11) (4,26) (5,19) (5,28) (5,25) (5,9) (5,16) (5,8) (5,10) (5,23) (6,22) (6,17) (6,29) (6,18) (6,24) (6,27) (6,14) (6,21) (6,7) (7,22) (7,17) (7,29) (7,18) (7,24) (7,14) (7,21) (7,20) (7,15) (7,11) (7,26) (8,19) (8,28) (8,9) (8,16) (8,13) (8,10) (8,23) (9,19) (9,28) (9,25) (9,16) (9,13) (9,10) (9,23) (10,28) (10,16) (10,13) (10,23) (11,22) (11,17) (11,24) (11,27) (11,12) (11,14) (11,21) (11,26) (12,22) (12,18) (12,24) (12,15) (12,26) (13,19) (13,28) (13,25) (13,23) (14,22) (14,17) (14,29) (14,18) (14,24) (14,27) (14,21) (14,20) (14,15) (14,26) (15,22) (15,17) (15,29) (15,18) (15,24) (15,27) (15,21) (15,20) (15,26) (16,19) (16,25) (17,22) (17,29) (17,18) (17,27) (17,21) (17,20) (17,26) (18,22) (18,26) (19,28) (19,23) (20,22) (20,24) (20,27) (21,24) (21,27) (21,26) (22,29) (22,24) (22,26) (23,25) (24,29) (25,28) (26,29) (26,27) (27,29)\nIs there a path between node 17 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph22-16_11", + "image": "data/connectivity/graph_visual/hard/graph22.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,19) (0,16) (1,3) (1,4) (1,19) (1,16) (1,10) (2,17) (2,7) (2,9) (2,23) (2,5) (2,18) (3,19) (3,6) (4,14) (5,24) (5,15) (8,13) (8,20) (8,25) (8,23) (8,15) (8,12) (9,17) (9,22) (9,23) (9,21) (11,13) (11,24) (11,22) (11,25) (11,15) (12,13) (12,17) (12,22) (12,18) (13,24) (15,24) (15,17) (15,22) (15,20) (15,18) (15,21) (17,22) (18,22) (20,22) (21,23) (22,24) (24,25)\nIs there a path between node 16 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph17-9_3", + "image": "data/connectivity/graph_visual/hard/graph17.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,24) (0,22) (0,1) (0,16) (1,4) (1,9) (1,12) (1,22) (2,14) (2,9) (2,19) (2,12) (2,16) (2,25) (2,11) (3,13) (3,7) (3,10) (3,21) (3,15) (4,23) (4,9) (4,19) (4,18) (4,11) (4,17) (5,15) (6,18) (6,25) (6,8) (8,14) (8,19) (8,24) (8,12) (8,16) (8,25) (8,17) (9,16) (9,17) (10,21) (11,23) (11,17) (11,20) (12,20) (13,15) (14,19) (14,22) (14,16) (14,17) (14,20) (16,23) (16,18) (16,17) (16,20) (17,23) (17,22) (18,19) (18,24) (18,25) (20,22) (22,23) (22,24) (23,25) (24,25)\nIs there a path between node 9 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph77-16_8", + "image": "data/connectivity/graph_visual/hard/graph77.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,14) (0,7) (0,20) (0,17) (0,19) (0,8) (0,11) (0,18) (0,10) (0,23) (0,15) (0,25) (0,24) (1,14) (1,7) (1,9) (1,17) (1,19) (1,5) (1,8) (1,11) (1,18) (1,10) (1,3) (1,23) (1,25) (1,24) (2,4) (2,26) (2,13) (2,12) (2,21) (2,22) (3,14) (3,7) (3,9) (3,17) (3,19) (3,5) (3,8) (3,6) (3,10) (3,23) (3,25) (3,24) (4,21) (4,16) (5,14) (5,20) (5,9) (5,17) (5,8) (5,6) (5,18) (5,10) (5,15) (5,25) (5,24) (6,7) (6,20) (6,8) (6,18) (6,10) (6,23) (6,15) (6,25) (6,24) (7,14) (7,20) (7,9) (7,19) (7,11) (7,10) (7,15) (8,20) (8,17) (8,19) (8,11) (8,18) (8,10) (8,23) (8,24) (9,20) (9,19) (9,11) (9,18) (9,10) (9,23) (9,25) (10,14) (10,17) (10,19) (10,11) (10,18) (10,23) (10,15) (10,24) (11,14) (11,20) (11,18) (11,23) (11,15) (11,25) (12,26) (12,16) (12,22) (13,26) (13,16) (13,22) (14,20) (14,17) (14,19) (14,18) (14,23) (14,25) (15,20) (15,19) (15,18) (15,25) (16,21) (16,22) (17,20) (17,19) (17,23) (18,20) (18,19) (18,23) (18,24) (19,20) (19,23) (19,25) (20,23) (20,25) (20,24) (21,22) (22,26)\nIs there a path between node 16 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph558-6_33", + "image": "data/connectivity/graph_visual/hard/graph558.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,29) (0,18) (0,4) (0,10) (1,12) (1,28) (1,2) (1,6) (1,27) (1,8) (1,15) (2,9) (2,25) (2,29) (2,16) (2,20) (2,4) (2,10) (2,5) (2,15) (3,28) (3,25) (3,11) (3,6) (3,13) (3,21) (3,15) (4,32) (4,29) (4,6) (4,27) (4,21) (4,19) (4,10) (4,23) (5,16) (5,27) (5,20) (5,31) (5,17) (6,12) (6,28) (6,32) (6,25) (6,13) (6,27) (6,18) (6,17) (6,15) (7,30) (7,12) (7,25) (7,29) (7,14) (7,13) (7,10) (7,33) (8,9) (8,28) (8,32) (8,25) (8,13) (8,27) (8,31) (8,23) (8,15) (9,32) (9,11) (9,29) (9,16) (9,18) (9,31) (9,19) (9,17) (9,33) (9,15) (10,30) (10,12) (10,32) (10,11) (10,20) (10,19) (10,15) (11,12) (11,32) (11,18) (11,20) (11,23) (11,15) (12,18) (12,21) (12,31) (12,19) (12,23) (13,32) (13,14) (13,20) (13,21) (13,31) (13,23) (14,25) (14,16) (14,27) (14,31) (14,19) (14,15) (15,28) (15,25) (15,29) (15,16) (15,19) (15,17) (15,33) (16,28) (16,29) (16,18) (16,31) (16,19) (16,33) (17,32) (17,27) (17,31) (17,33) (18,30) (18,25) (18,20) (18,19) (19,28) (19,27) (19,20) (19,21) (20,30) (20,28) (20,27) (20,31) (21,30) (21,25) (22,24) (23,27) (23,33) (25,32) (27,29) (27,33) (28,33) (30,33) (31,33)\nIs there a path between node 6 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph273-15_21", + "image": "data/connectivity/graph_visual/hard/graph273.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,21) (0,13) (0,15) (0,6) (0,18) (0,26) (0,20) (0,23) (0,10) (0,30) (0,8) (1,24) (2,3) (2,6) (2,18) (2,30) (2,25) (2,8) (3,21) (3,15) (3,6) (3,18) (3,26) (3,10) (3,14) (3,25) (3,7) (4,12) (4,19) (4,29) (4,16) (4,11) (4,22) (5,12) (5,17) (5,29) (5,16) (5,11) (6,21) (6,13) (6,28) (6,15) (6,18) (6,26) (6,20) (6,10) (6,30) (6,25) (6,7) (7,13) (7,15) (7,18) (7,26) (7,20) (7,23) (7,10) (7,14) (7,25) (7,8) (8,21) (8,13) (8,28) (8,15) (8,26) (8,23) (8,30) (9,24) (10,21) (10,13) (10,28) (10,15) (10,26) (10,20) (10,23) (10,14) (10,30) (11,12) (11,27) (11,19) (11,16) (12,29) (12,22) (13,21) (13,15) (13,18) (13,26) (13,20) (13,14) (14,28) (14,15) (14,18) (14,26) (14,20) (14,23) (14,30) (14,25) (15,28) (15,18) (15,26) (15,20) (15,25) (16,17) (16,22) (17,27) (17,19) (17,29) (17,22) (18,21) (18,28) (18,26) (18,20) (18,23) (18,30) (18,25) (19,29) (19,22) (20,21) (20,28) (20,30) (20,25) (21,28) (21,23) (22,29) (23,26) (23,30) (23,25) (25,28) (25,30) (26,28) (26,30) (27,29)\nIs there a path between node 15 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph673-4_11", + "image": "data/connectivity/graph_visual/hard/graph673.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,24) (0,27) (0,26) (0,2) (0,33) (2,19) (2,15) (2,7) (2,18) (2,24) (2,32) (2,26) (2,6) (2,16) (2,34) (2,21) (3,29) (4,19) (4,15) (4,7) (4,8) (4,18) (4,5) (4,31) (4,10) (4,13) (4,34) (4,20) (5,15) (5,11) (5,24) (5,27) (5,21) (6,18) (6,27) (6,26) (6,28) (6,23) (6,12) (6,21) (6,22) (7,27) (7,26) (7,34) (7,23) (7,22) (8,14) (8,26) (8,33) (8,22) (10,11) (10,24) (10,27) (10,28) (10,23) (10,12) (10,21) (10,22) (11,15) (11,30) (11,31) (11,26) (11,16) (11,33) (12,14) (12,15) (12,18) (12,24) (12,33) (12,21) (13,24) (13,33) (13,20) (13,21) (13,22) (14,24) (14,27) (14,16) (14,20) (14,21) (14,22) (15,16) (15,23) (15,21) (15,22) (16,24) (16,34) (16,20) (17,29) (18,19) (18,21) (19,24) (19,31) (19,32) (19,26) (19,28) (19,34) (20,31) (20,26) (20,28) (20,21) (20,22) (21,26) (21,28) (21,34) (21,23) (22,30) (22,27) (22,34) (22,33) (23,27) (23,33) (24,30) (24,27) (24,26) (25,29) (26,33) (27,28) (27,33) (32,34)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph502-10_7", + "image": "data/connectivity/graph_visual/hard/graph502.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,3) (0,19) (0,28) (0,27) (1,22) (1,11) (2,33) (2,17) (3,33) (3,16) (3,7) (3,9) (5,21) (5,18) (7,25) (7,12) (7,17) (7,29) (7,9) (8,15) (8,24) (8,14) (9,25) (9,29) (10,26) (10,13) (11,23) (12,25) (12,16) (12,28) (13,30) (14,15) (14,26) (15,26) (16,27) (17,33) (17,25) (17,29) (19,25) (19,27) (20,33) (20,25) (20,29) (22,31) (24,26) (26,30) (27,33) (27,29)\nIs there a path between node 10 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph566-1_18", + "image": "data/connectivity/graph_visual/hard/graph566.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,33) (0,17) (1,5) (1,18) (1,25) (1,23) (2,13) (2,28) (2,9) (2,21) (2,22) (2,20) (3,16) (3,20) (4,6) (4,19) (4,15) (4,18) (4,30) (4,17) (5,6) (5,32) (5,10) (5,18) (5,33) (6,32) (6,19) (6,15) (6,27) (6,26) (6,18) (6,17) (6,24) (6,25) (8,12) (9,21) (9,22) (10,32) (10,18) (10,30) (10,17) (10,25) (10,23) (11,28) (11,31) (11,16) (11,20) (13,22) (15,19) (15,27) (15,18) (15,33) (15,30) (15,24) (15,25) (15,23) (16,20) (17,27) (17,18) (17,33) (17,24) (17,29) (18,26) (18,33) (18,25) (19,27) (20,21) (21,31) (23,30) (23,25) (24,32) (24,29) (24,25) (25,33) (26,33) (26,29) (27,30) (27,29) (29,30) (30,32) (30,33) (32,33)\nIs there a path between node 1 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph345-0_7", + "image": "data/connectivity/graph_visual/hard/graph345.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,30) (0,19) (0,26) (0,8) (0,7) (2,6) (3,15) (3,9) (4,27) (4,17) (5,16) (5,26) (5,21) (7,30) (7,8) (7,21) (7,29) (7,25) (8,11) (8,31) (8,21) (8,29) (9,15) (9,27) (10,11) (10,19) (10,26) (10,21) (11,30) (11,23) (11,31) (11,21) (11,29) (12,15) (12,22) (12,17) (14,17) (15,27) (16,25) (17,22) (17,27) (19,23) (19,29) (21,23) (21,31) (21,25) (23,30) (25,26)\nIs there a path between node 0 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph648-5_9", + "image": "data/connectivity/graph_visual/hard/graph648.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,1) (0,27) (0,3) (0,2) (1,3) (1,2) (2,27) (3,27) (4,9) (4,7) (4,29) (4,34) (4,31) (4,21) (4,16) (4,17) (4,15) (4,25) (4,18) (4,5) (4,6) (4,20) (4,11) (5,9) (5,7) (5,24) (5,32) (5,23) (5,30) (5,31) (5,16) (5,17) (5,25) (5,26) (5,18) (5,6) (5,13) (5,11) (6,7) (6,29) (6,34) (6,24) (6,32) (6,23) (6,31) (6,21) (6,26) (6,18) (6,20) (6,11) (7,24) (7,32) (7,31) (7,16) (7,17) (7,15) (7,25) (7,12) (7,26) (7,20) (7,13) (7,11) (8,10) (8,14) (8,22) (8,19) (9,29) (9,24) (9,32) (9,23) (9,31) (9,21) (9,16) (9,17) (9,25) (9,12) (9,26) (9,18) (9,20) (9,13) (9,11) (10,33) (10,28) (10,22) (10,19) (11,29) (11,34) (11,24) (11,32) (11,30) (11,31) (11,21) (11,25) (11,12) (11,26) (11,18) (11,13) (12,29) (12,34) (12,24) (12,32) (12,23) (12,15) (12,25) (12,18) (12,20) (12,13) (13,29) (13,34) (13,24) (13,30) (13,17) (13,15) (13,18) (13,20) (14,28) (14,22) (14,19) (15,29) (15,34) (15,24) (15,32) (15,23) (15,21) (15,16) (15,17) (15,25) (15,26) (15,18) (15,20) (16,29) (16,34) (16,24) (16,32) (16,23) (16,30) (16,31) (16,21) (16,25) (16,26) (17,29) (17,34) (17,32) (17,23) (17,30) (17,31) (17,21) (17,26) (17,18) (17,20) (18,24) (18,32) (18,30) (18,31) (18,21) (18,25) (18,20) (19,33) (19,28) (19,22) (20,29) (20,34) (20,30) (20,31) (20,21) (20,25) (20,26) (21,29) (21,34) (21,24) (21,31) (21,25) (21,26) (22,33) (22,28) (23,29) (23,24) (23,32) (23,30) (23,25) (23,26) (24,29) (24,32) (24,31) (24,25) (24,26) (25,34) (25,32) (25,30) (25,26) (26,34) (26,30) (29,32) (29,30) (29,31) (30,32) (31,34) (31,32) (32,34)\nIs there a path between node 5 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph382-13_20", + "image": "data/connectivity/graph_visual/hard/graph382.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,16) (0,4) (0,22) (0,1) (0,23) (0,11) (0,21) (0,2) (0,13) (0,31) (0,19) (0,27) (0,17) (0,14) (0,3) (0,6) (0,12) (1,15) (1,9) (1,16) (1,4) (1,22) (1,23) (1,11) (1,21) (1,30) (1,13) (1,31) (1,19) (1,27) (1,17) (1,14) (1,12) (1,10) (2,9) (2,4) (2,23) (2,21) (2,30) (2,13) (2,31) (2,26) (2,19) (2,14) (2,3) (2,18) (3,15) (3,9) (3,16) (3,4) (3,22) (3,23) (3,11) (3,13) (3,31) (3,19) (3,17) (3,6) (4,15) (4,9) (4,16) (4,11) (4,21) (4,30) (4,13) (4,19) (4,27) (4,17) (4,14) (4,18) (4,12) (5,24) (5,20) (5,29) (5,8) (5,28) (6,15) (6,16) (6,22) (6,23) (6,21) (6,27) (6,14) (6,12) (6,10) (7,25) (8,24) (8,20) (8,28) (9,15) (9,16) (9,23) (9,30) (9,31) (9,26) (9,17) (9,14) (9,12) (9,10) (10,15) (10,16) (10,22) (10,11) (10,21) (10,30) (10,13) (10,31) (10,26) (10,19) (10,27) (10,18) (10,12) (11,16) (11,22) (11,23) (11,21) (11,30) (11,13) (11,31) (11,19) (11,17) (12,16) (12,22) (12,23) (12,30) (12,13) (12,31) (12,26) (12,19) (12,27) (12,17) (12,14) (13,15) (13,16) (13,22) (13,23) (13,30) (13,26) (13,19) (13,27) (13,17) (13,14) (14,16) (14,23) (14,21) (14,30) (14,31) (14,26) (14,19) (14,27) (14,17) (14,18) (15,16) (15,22) (15,23) (15,21) (15,26) (15,19) (15,17) (15,18) (16,22) (16,23) (16,30) (16,31) (16,26) (16,19) (16,27) (16,17) (16,18) (17,23) (17,21) (17,30) (17,31) (17,26) (17,19) (18,22) (18,23) (18,30) (18,26) (18,27) (19,22) (19,23) (19,21) (19,30) (19,26) (20,24) (20,29) (20,28) (21,22) (21,30) (21,27) (22,23) (22,31) (22,27) (23,30) (23,31) (23,26) (23,27) (24,28) (26,30) (26,31) (27,30) (27,31) (28,29) (30,31)\nIs there a path between node 13 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph415-8_19", + "image": "data/connectivity/graph_visual/hard/graph415.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,10) (0,2) (0,31) (0,17) (1,10) (1,26) (1,25) (1,31) (1,17) (2,25) (2,31) (3,18) (3,23) (3,15) (3,11) (3,22) (4,5) (4,13) (4,6) (4,11) (4,16) (4,24) (5,28) (5,23) (5,19) (5,7) (5,22) (6,18) (6,28) (6,11) (7,28) (7,23) (7,13) (7,21) (9,18) (9,15) (9,12) (9,11) (10,29) (11,30) (11,18) (11,14) (11,28) (11,15) (11,19) (12,30) (12,13) (12,19) (13,16) (13,19) (13,22) (14,28) (14,16) (15,30) (15,22) (16,30) (18,30) (18,21) (18,19) (18,24) (19,23) (19,24) (20,29) (23,24) (24,30) (25,27) (25,29) (26,27) (27,31) (29,32)\nIs there a path between node 8 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph268-8_11", + "image": "data/connectivity/graph_visual/hard/graph268.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,5) (0,11) (0,22) (0,30) (0,25) (0,19) (0,12) (0,13) (0,10) (0,29) (1,17) (1,4) (1,18) (1,7) (1,27) (1,2) (1,3) (1,9) (1,23) (1,28) (2,4) (2,21) (2,26) (2,7) (2,27) (2,9) (2,23) (2,28) (3,17) (3,4) (3,21) (3,26) (3,18) (3,7) (3,27) (3,14) (3,9) (3,23) (3,28) (3,24) (4,17) (4,21) (4,26) (4,18) (4,14) (4,9) (4,28) (4,24) (5,11) (5,22) (5,20) (5,25) (5,29) (6,8) (7,21) (7,26) (7,18) (7,27) (7,23) (7,28) (7,24) (9,21) (9,26) (9,18) (9,27) (9,14) (9,23) (9,28) (9,24) (10,11) (10,22) (10,20) (10,30) (10,25) (10,16) (10,19) (10,15) (10,13) (10,29) (11,22) (11,20) (11,30) (11,25) (11,16) (11,19) (11,12) (11,15) (11,13) (11,29) (12,22) (12,20) (12,30) (12,16) (12,15) (12,13) (13,22) (13,20) (13,30) (13,25) (13,16) (13,19) (13,15) (13,29) (14,26) (14,18) (14,23) (14,28) (14,24) (15,22) (15,30) (15,16) (15,19) (15,29) (16,22) (16,30) (16,25) (16,19) (16,29) (17,26) (17,18) (17,27) (17,23) (17,28) (18,21) (18,26) (18,27) (18,24) (19,20) (19,30) (19,25) (19,29) (20,22) (20,25) (20,29) (21,26) (21,27) (21,28) (21,24) (22,30) (22,29) (23,26) (23,27) (23,28) (23,24) (24,27) (24,28) (25,29) (26,27) (27,28) (29,30)\nIs there a path between node 8 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph335-28_12", + "image": "data/connectivity/graph_visual/hard/graph335.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,12) (0,9) (0,4) (0,16) (0,26) (1,19) (1,31) (1,9) (1,4) (1,21) (1,26) (2,13) (2,19) (2,12) (2,31) (2,4) (2,21) (2,26) (3,22) (3,11) (3,6) (3,7) (3,5) (3,8) (3,17) (3,29) (3,28) (3,23) (3,10) (3,25) (3,24) (4,13) (4,16) (4,21) (5,22) (5,7) (5,15) (5,30) (5,8) (5,17) (5,29) (5,27) (5,28) (5,23) (5,10) (6,7) (6,8) (6,17) (6,27) (6,18) (6,28) (6,10) (6,25) (6,24) (6,20) (7,22) (7,11) (7,15) (7,30) (7,29) (7,18) (7,28) (7,23) (7,10) (7,25) (7,20) (8,11) (8,30) (8,17) (8,29) (8,27) (8,23) (8,10) (8,25) (8,20) (9,13) (9,12) (9,31) (9,14) (9,16) (9,26) (10,22) (10,15) (10,30) (10,17) (10,29) (10,27) (10,18) (10,28) (10,23) (10,24) (11,15) (11,17) (11,29) (11,18) (11,28) (11,23) (11,25) (11,24) (12,13) (12,19) (12,31) (12,14) (12,16) (13,31) (13,14) (13,21) (13,26) (14,19) (14,31) (14,16) (14,21) (14,26) (15,22) (15,30) (15,27) (15,28) (15,23) (15,25) (15,20) (16,19) (16,21) (17,22) (17,30) (17,29) (17,27) (17,18) (17,28) (17,23) (17,25) (17,20) (18,22) (18,29) (18,28) (18,25) (18,24) (19,31) (19,21) (19,26) (20,27) (20,28) (20,23) (20,25) (20,24) (21,31) (21,26) (22,27) (22,28) (22,23) (22,25) (22,24) (23,30) (23,29) (23,27) (23,28) (23,25) (23,24) (24,30) (24,29) (24,27) (24,25) (25,29) (25,28) (26,31) (27,30) (27,29) (27,28) (28,30) (28,29) (29,30)\nIs there a path between node 28 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph19-13_24", + "image": "data/connectivity/graph_visual/hard/graph19.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,21) (0,9) (0,6) (0,8) (1,21) (1,19) (1,13) (1,9) (1,3) (2,17) (3,21) (3,16) (3,19) (3,13) (3,8) (4,12) (4,13) (4,6) (4,7) (6,12) (6,16) (6,20) (6,13) (6,18) (6,11) (6,7) (7,20) (7,9) (8,12) (8,16) (8,20) (8,18) (8,11) (9,21) (10,25) (10,24) (11,20) (12,19) (12,13) (13,21) (13,19) (15,23) (18,21) (18,20) (19,20) (23,24)\nIs there a path between node 13 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph39-10_2", + "image": "data/connectivity/graph_visual/hard/graph39.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,10) (0,2) (0,25) (0,7) (0,19) (0,4) (0,15) (0,17) (0,8) (0,6) (0,20) (0,14) (0,12) (0,21) (1,10) (1,24) (1,2) (1,25) (1,7) (1,4) (1,18) (1,15) (1,13) (1,8) (1,6) (1,12) (1,3) (1,21) (2,11) (2,25) (2,7) (2,19) (2,18) (2,15) (2,9) (2,13) (2,8) (2,6) (2,14) (2,3) (2,21) (3,24) (3,25) (3,7) (3,19) (3,4) (3,18) (3,9) (3,17) (3,8) (3,14) (3,12) (3,21) (4,11) (4,10) (4,24) (4,25) (4,19) (4,15) (4,13) (4,17) (4,8) (4,6) (4,20) (4,12) (5,16) (5,22) (5,23) (6,11) (6,24) (6,25) (6,7) (6,18) (6,15) (6,9) (6,17) (6,8) (6,20) (6,14) (6,12) (6,21) (7,10) (7,24) (7,25) (7,19) (7,18) (7,15) (7,13) (7,17) (7,8) (7,20) (7,14) (8,11) (8,10) (8,15) (8,9) (8,17) (8,20) (8,14) (8,12) (9,11) (9,10) (9,24) (9,25) (9,19) (9,15) (9,13) (9,17) (9,20) (9,14) (9,12) (9,21) (10,11) (10,25) (10,19) (10,18) (10,15) (10,13) (10,17) (10,20) (10,12) (10,21) (11,24) (11,25) (11,18) (11,13) (11,17) (11,20) (11,12) (12,25) (12,19) (12,18) (12,15) (12,13) (12,17) (12,20) (12,21) (13,24) (13,25) (13,19) (13,18) (13,15) (13,17) (13,20) (13,21) (14,24) (14,19) (14,18) (14,15) (14,20) (15,24) (15,25) (15,19) (15,17) (15,20) (15,21) (16,22) (16,23) (17,24) (17,19) (17,18) (17,21) (18,25) (18,20) (19,24) (19,25) (20,24) (20,25) (20,21) (21,25) (24,25)\nIs there a path between node 10 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph69-22_5", + "image": "data/connectivity/graph_visual/hard/graph69.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,17) (1,15) (1,8) (1,4) (1,18) (2,14) (2,8) (2,6) (2,26) (3,17) (4,20) (5,16) (5,14) (5,22) (5,6) (5,10) (6,15) (6,23) (6,8) (6,22) (6,18) (6,10) (7,14) (7,8) (7,22) (7,10) (8,23) (8,12) (8,26) (8,18) (9,21) (9,17) (9,19) (10,16) (10,12) (10,26) (11,15) (11,22) (11,18) (12,16) (12,20) (12,14) (12,22) (14,16) (15,16) (15,26) (15,18) (16,23) (20,23) (20,26) (20,25) (22,26) (23,26) (25,26)\nIs there a path between node 22 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph394-32_5", + "image": "data/connectivity/graph_visual/hard/graph394.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,12) (0,24) (0,5) (0,32) (0,18) (0,23) (0,25) (1,20) (2,21) (2,13) (2,29) (3,12) (3,7) (3,11) (3,23) (3,25) (4,27) (4,12) (4,32) (5,30) (5,14) (7,10) (7,11) (7,23) (7,25) (8,27) (8,18) (8,30) (8,11) (8,25) (9,28) (10,27) (10,24) (10,32) (10,18) (10,23) (11,22) (11,14) (12,27) (12,24) (12,25) (13,15) (13,21) (13,29) (14,27) (14,32) (14,23) (15,21) (19,20) (22,30) (22,23) (23,30) (24,32) (24,30) (24,25) (25,27)\nIs there a path between node 32 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph495-10_28", + "image": "data/connectivity/graph_visual/hard/graph495.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,31) (0,22) (0,13) (0,7) (0,1) (0,30) (0,6) (0,15) (0,14) (0,12) (1,13) (1,4) (1,33) (1,24) (1,30) (1,27) (1,28) (1,25) (1,15) (1,21) (1,18) (1,5) (1,12) (3,31) (3,23) (3,27) (3,28) (3,25) (3,15) (4,33) (4,24) (4,25) (4,8) (5,33) (5,30) (5,27) (5,6) (5,15) (6,22) (6,11) (6,19) (6,33) (6,8) (7,31) (7,22) (7,19) (7,33) (7,24) (7,30) (7,18) (8,24) (8,18) (9,29) (11,15) (11,14) (11,18) (12,31) (12,13) (12,24) (12,27) (12,25) (13,24) (13,15) (14,22) (14,30) (14,21) (14,18) (15,31) (15,25) (16,20) (18,33) (19,23) (19,28) (19,21) (19,32) (20,26) (21,27) (21,32) (22,28) (22,25) (22,32) (23,30) (23,25) (23,32) (24,30) (24,28) (24,32) (25,31) (25,33) (27,33) (27,30) (27,28) (28,32) (30,31) (31,32)\nIs there a path between node 10 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph504-30_18", + "image": "data/connectivity/graph_visual/hard/graph504.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,23) (0,22) (0,17) (0,15) (0,9) (0,8) (0,6) (0,13) (0,7) (0,18) (0,12) (0,20) (0,24) (0,33) (0,27) (0,11) (0,30) (1,2) (1,16) (2,16) (2,5) (3,23) (3,19) (3,25) (3,22) (3,32) (3,15) (3,21) (3,8) (3,10) (3,14) (3,6) (3,13) (3,7) (3,18) (3,24) (3,31) (3,33) (3,27) (3,11) (3,30) (4,16) (4,5) (6,23) (6,28) (6,19) (6,25) (6,26) (6,29) (6,22) (6,17) (6,8) (6,10) (6,14) (6,13) (6,18) (6,12) (6,20) (6,24) (6,31) (6,33) (6,27) (6,30) (7,23) (7,28) (7,19) (7,26) (7,29) (7,22) (7,17) (7,21) (7,9) (7,10) (7,14) (7,13) (7,18) (7,12) (7,31) (7,33) (7,27) (7,11) (8,23) (8,25) (8,26) (8,29) (8,32) (8,17) (8,21) (8,9) (8,10) (8,14) (8,13) (8,18) (8,12) (8,20) (8,24) (8,31) (8,33) (8,27) (8,11) (9,25) (9,26) (9,29) (9,22) (9,32) (9,17) (9,21) (9,14) (9,13) (9,18) (9,12) (9,20) (9,24) (9,33) (9,11) (10,28) (10,19) (10,26) (10,22) (10,32) (10,17) (10,15) (10,13) (10,18) (10,12) (10,24) (10,33) (10,27) (10,30) (11,23) (11,28) (11,25) (11,26) (11,29) (11,32) (11,17) (11,13) (11,12) (11,20) (11,24) (11,27) (11,30) (12,28) (12,25) (12,26) (12,29) (12,32) (12,13) (12,18) (12,20) (12,31) (12,27) (12,30) (13,23) (13,19) (13,25) (13,26) (13,29) (13,22) (13,32) (13,17) (13,14) (13,24) (13,31) (13,33) (13,27) (14,23) (14,28) (14,19) (14,25) (14,22) (14,15) (14,21) (14,18) (14,20) (14,24) (14,27) (14,30) (15,28) (15,26) (15,29) (15,22) (15,20) (15,31) (15,33) (15,27) (15,30) (17,23) (17,28) (17,19) (17,25) (17,26) (17,22) (17,32) (17,21) (17,18) (17,20) (17,24) (17,27) (17,30) (18,23) (18,28) (18,19) (18,25) (18,26) (18,32) (18,21) (18,20) (18,24) (18,31) (18,33) (18,27) (18,30) (19,23) (19,28) (19,25) (19,26) (19,29) (19,22) (19,32) (19,21) (19,30) (20,22) (20,32) (20,21) (20,31) (20,33) (20,27) (21,23) (21,25) (21,26) (21,22) (21,32) (21,24) (21,31) (21,33) (21,27) (21,30) (22,23) (22,26) (22,29) (22,32) (22,31) (22,33) (22,30) (23,26) (23,29) (23,32) (23,24) (23,31) (23,33) (24,25) (24,26) (24,29) (24,32) (24,31) (24,33) (24,27) (24,30) (25,26) (25,32) (25,31) (25,33) (25,30) (26,28) (26,29) (26,32) (26,31) (26,27) (27,28) (27,29) (27,31) (27,33) (27,30) (28,29) (28,31) (28,33) (29,32) (29,33) (29,30) (30,32) (30,31) (30,33) (31,32) (31,33) (32,33)\nIs there a path between node 30 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph63-11_13", + "image": "data/connectivity/graph_visual/hard/graph63.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (2,26) (3,4) (3,5) (3,6) (3,15) (3,7) (3,18) (3,23) (3,22) (4,6) (4,9) (4,15) (4,7) (4,21) (4,17) (4,8) (4,23) (4,16) (4,24) (5,11) (5,9) (5,15) (5,23) (5,14) (5,24) (5,10) (6,20) (6,7) (6,17) (6,23) (6,14) (6,25) (7,15) (7,18) (7,12) (7,14) (7,25) (8,15) (8,21) (8,22) (8,12) (8,14) (8,25) (9,15) (9,18) (9,23) (9,14) (10,21) (10,17) (10,12) (10,24) (10,25) (11,21) (11,23) (11,22) (11,14) (12,21) (12,14) (12,25) (13,26) (14,17) (14,16) (14,24) (15,21) (15,23) (15,24) (16,20) (17,20) (17,25) (18,21) (20,25) (21,24) (21,25)\nIs there a path between node 11 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph282-9_2", + "image": "data/connectivity/graph_visual/hard/graph282.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,13) (0,28) (0,2) (0,25) (0,9) (0,3) (0,1) (0,19) (0,23) (0,29) (0,16) (0,8) (0,27) (0,14) (0,22) (1,28) (1,2) (1,25) (1,9) (1,11) (1,3) (1,10) (1,20) (1,19) (1,29) (1,16) (1,8) (1,14) (1,26) (1,22) (1,4) (2,28) (2,25) (2,11) (2,10) (2,20) (2,19) (2,23) (2,29) (2,8) (2,21) (2,22) (3,13) (3,25) (3,9) (3,11) (3,20) (3,23) (3,29) (3,27) (3,26) (3,21) (3,22) (3,4) (4,25) (4,9) (4,11) (4,10) (4,20) (4,23) (4,29) (4,16) (4,14) (4,21) (4,22) (5,24) (6,12) (6,15) (6,18) (7,12) (7,18) (8,13) (8,28) (8,25) (8,9) (8,11) (8,10) (8,20) (8,23) (8,29) (8,16) (8,27) (8,26) (9,13) (9,28) (9,25) (9,10) (9,20) (9,19) (9,23) (9,29) (9,16) (9,27) (9,14) (9,26) (9,21) (9,22) (10,13) (10,28) (10,25) (10,11) (10,20) (10,19) (10,23) (10,29) (10,16) (10,27) (10,14) (10,21) (10,22) (11,13) (11,25) (11,20) (11,19) (11,23) (11,29) (11,16) (11,27) (11,14) (11,26) (11,21) (11,22) (12,15) (12,18) (13,28) (13,25) (13,20) (13,19) (13,29) (13,14) (13,26) (13,22) (14,20) (14,19) (14,23) (14,29) (14,27) (14,26) (14,22) (15,18) (16,28) (16,25) (16,20) (16,23) (16,27) (16,26) (16,22) (17,30) (17,24) (19,28) (19,25) (19,23) (19,27) (19,26) (19,21) (19,22) (20,28) (20,25) (20,29) (20,26) (20,21) (20,22) (21,25) (21,23) (21,27) (21,22) (22,28) (22,29) (22,27) (22,26) (23,28) (23,25) (23,29) (23,27) (24,30) (25,28) (25,29) (25,27) (25,26) (26,28) (26,29) (27,28) (27,29) (28,29)\nIs there a path between node 9 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph621-22_11", + "image": "data/connectivity/graph_visual/hard/graph621.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,9) (0,26) (0,24) (0,27) (0,11) (1,3) (1,2) (1,20) (1,6) (1,31) (2,3) (2,33) (2,30) (2,32) (2,19) (2,7) (3,31) (3,5) (4,33) (4,9) (4,30) (4,16) (4,25) (4,24) (5,30) (5,26) (5,27) (5,15) (6,33) (6,20) (6,24) (6,27) (6,11) (6,7) (7,33) (7,23) (7,30) (9,26) (9,29) (9,24) (9,31) (9,15) (10,28) (10,13) (10,22) (10,21) (11,16) (11,24) (12,15) (13,14) (13,17) (15,23) (15,20) (15,31) (16,20) (16,24) (16,19) (17,21) (19,33) (19,23) (19,25) (19,32) (20,33) (20,23) (20,32) (20,24) (20,27) (21,28) (23,33) (23,32) (24,30) (24,32) (24,29) (25,30) (25,32) (25,29) (25,27) (26,30) (26,32) (26,29) (27,33) (27,30) (29,30) (29,31) (30,32) (31,32)\nIs there a path between node 22 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph409-15_19", + "image": "data/connectivity/graph_visual/hard/graph409.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (0,19) (0,13) (0,15) (0,24) (0,12) (0,8) (1,3) (1,14) (1,21) (1,25) (1,17) (1,4) (1,13) (1,18) (2,14) (2,21) (2,17) (2,29) (2,13) (2,24) (3,17) (3,4) (4,32) (4,21) (4,19) (4,29) (4,15) (4,24) (4,8) (5,22) (5,23) (5,7) (5,28) (6,22) (6,27) (6,30) (7,31) (7,23) (8,14) (8,29) (8,13) (8,10) (10,14) (10,21) (10,25) (10,24) (11,16) (12,29) (12,24) (13,17) (13,19) (13,29) (14,32) (14,25) (14,19) (14,29) (14,18) (15,32) (15,21) (15,19) (15,29) (16,23) (16,28) (17,29) (17,20) (18,29) (19,24) (20,25) (22,26) (22,31) (22,28) (24,32) (26,27)\nIs there a path between node 15 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph381-31_18", + "image": "data/connectivity/graph_visual/hard/graph381.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,17) (0,4) (0,14) (0,22) (0,9) (0,5) (0,16) (0,25) (0,31) (0,23) (0,28) (0,15) (0,2) (0,8) (0,19) (0,6) (1,12) (1,3) (1,21) (2,13) (2,17) (2,4) (2,24) (2,14) (2,30) (2,22) (2,9) (2,16) (2,25) (2,29) (2,31) (2,20) (2,28) (2,15) (2,8) (2,19) (2,6) (3,18) (3,12) (3,21) (4,13) (4,7) (4,14) (4,30) (4,22) (4,9) (4,5) (4,26) (4,23) (4,20) (4,28) (4,15) (4,8) (4,19) (4,6) (5,24) (5,7) (5,14) (5,30) (5,22) (5,9) (5,29) (5,26) (5,23) (5,28) (5,15) (5,8) (5,19) (5,6) (6,13) (6,17) (6,11) (6,24) (6,14) (6,22) (6,16) (6,29) (6,31) (6,23) (6,20) (6,28) (7,13) (7,17) (7,11) (7,24) (7,30) (7,9) (7,16) (7,25) (7,29) (7,26) (7,31) (7,23) (7,20) (7,28) (7,8) (7,19) (8,17) (8,24) (8,14) (8,30) (8,22) (8,9) (8,16) (8,20) (8,28) (8,15) (8,19) (9,13) (9,17) (9,11) (9,24) (9,14) (9,30) (9,22) (9,16) (9,25) (9,29) (9,26) (9,23) (9,20) (9,15) (9,19) (11,13) (11,14) (11,30) (11,22) (11,16) (11,29) (11,26) (11,23) (11,20) (11,15) (11,19) (12,18) (12,21) (13,14) (13,25) (13,26) (13,31) (13,20) (13,15) (13,19) (14,17) (14,24) (14,22) (14,16) (14,25) (14,26) (14,31) (14,20) (14,28) (15,17) (15,24) (15,30) (15,22) (15,16) (15,25) (15,29) (15,19) (16,17) (16,24) (16,30) (16,29) (16,26) (16,31) (16,23) (16,20) (16,28) (16,19) (17,24) (17,30) (17,22) (17,31) (17,23) (17,20) (17,28) (17,19) (19,24) (19,25) (19,26) (19,31) (19,23) (19,20) (20,30) (20,22) (20,26) (20,23) (22,30) (22,25) (22,29) (22,23) (22,28) (23,24) (23,30) (23,25) (23,29) (23,26) (24,30) (24,25) (24,29) (24,28) (25,30) (25,26) (25,31) (25,28) (26,30) (26,29) (26,31) (28,30) (28,29) (30,31)\nIs there a path between node 31 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph461-28_26", + "image": "data/connectivity/graph_visual/hard/graph461.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,10) (0,23) (0,27) (0,9) (1,16) (1,3) (1,4) (1,21) (1,26) (1,2) (2,31) (2,16) (2,15) (2,6) (2,17) (3,24) (3,8) (3,19) (3,16) (3,30) (3,5) (3,4) (3,15) (3,7) (3,11) (4,24) (4,8) (4,30) (4,21) (4,12) (4,26) (4,7) (4,11) (5,21) (5,6) (5,26) (6,30) (6,21) (6,11) (7,24) (8,31) (8,24) (8,19) (8,12) (9,27) (10,18) (10,23) (10,14) (11,31) (11,24) (11,21) (12,24) (12,19) (12,30) (12,15) (12,21) (13,32) (13,18) (13,29) (14,32) (14,23) (15,19) (15,16) (16,24) (16,19) (17,19) (18,32) (18,23) (18,28) (19,24) (19,30) (19,26) (21,31) (21,30) (21,26) (26,30) (27,32) (28,32) (30,31)\nIs there a path between node 28 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph320-4_24", + "image": "data/connectivity/graph_visual/hard/graph320.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,6) (0,28) (1,30) (1,7) (1,26) (1,29) (1,8) (2,19) (2,22) (2,9) (2,20) (3,13) (3,23) (3,26) (3,17) (3,8) (3,4) (4,5) (4,28) (4,17) (5,10) (5,27) (5,26) (5,6) (6,15) (6,7) (6,27) (6,21) (6,23) (6,29) (6,28) (7,30) (7,10) (7,23) (7,26) (7,29) (8,15) (8,30) (8,29) (8,28) (9,18) (10,15) (10,27) (10,23) (10,26) (10,28) (11,14) (11,16) (11,18) (12,19) (12,20) (13,17) (14,19) (14,24) (14,25) (14,31) (15,21) (15,28) (16,22) (16,24) (17,30) (17,23) (17,29) (18,19) (18,22) (18,31) (19,31) (20,24) (21,30) (21,28) (26,30) (26,29) (28,30)\nIs there a path between node 4 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph390-31_5", + "image": "data/connectivity/graph_visual/hard/graph390.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,2) (0,17) (1,4) (2,10) (3,19) (3,30) (3,13) (3,25) (3,8) (4,31) (5,16) (6,29) (6,11) (6,32) (7,14) (7,17) (8,21) (8,30) (8,13) (8,28) (9,20) (9,25) (11,29) (11,26) (11,22) (13,21) (13,15) (13,28) (13,23) (15,31) (15,16) (15,28) (15,23) (16,21) (16,25) (16,23) (18,29) (18,24) (20,31) (20,30) (20,25) (21,25) (22,24) (23,25) (23,28) (24,29) (24,32) (25,30) (26,32) (28,30)\nIs there a path between node 31 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph116-22_14", + "image": "data/connectivity/graph_visual/hard/graph116.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,21) (0,18) (0,16) (0,12) (1,15) (1,2) (1,24) (1,20) (2,10) (2,15) (2,9) (2,24) (2,14) (3,6) (3,8) (3,24) (3,20) (3,14) (4,22) (4,10) (4,15) (4,8) (4,5) (4,23) (5,22) (5,15) (5,19) (5,17) (5,23) (6,15) (6,17) (6,23) (7,9) (7,19) (7,17) (7,23) (8,23) (9,15) (9,19) (9,23) (10,20) (10,17) (11,27) (11,25) (12,21) (12,26) (12,16) (12,13) (13,27) (14,15) (14,19) (15,19) (15,17) (17,22) (17,20) (18,27) (18,26) (19,20) (20,22) (20,24) (21,27) (22,24) (22,23) (25,26)\nIs there a path between node 22 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph393-12_1", + "image": "data/connectivity/graph_visual/hard/graph393.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,6) (0,1) (0,4) (0,30) (0,11) (0,19) (0,17) (0,2) (1,6) (1,4) (1,30) (1,3) (1,22) (2,31) (2,23) (2,22) (2,11) (2,19) (2,17) (3,28) (3,5) (3,18) (3,23) (3,21) (3,11) (3,20) (3,10) (3,32) (4,6) (4,5) (4,31) (4,9) (4,25) (4,20) (4,10) (5,28) (5,23) (5,16) (5,26) (5,9) (5,25) (5,11) (5,17) (5,29) (5,12) (5,32) (6,14) (6,18) (6,21) (6,22) (6,25) (6,17) (6,20) (7,24) (8,13) (8,27) (9,23) (9,26) (10,14) (10,31) (10,23) (10,26) (10,30) (10,25) (10,19) (11,14) (11,31) (11,18) (11,23) (11,30) (11,19) (12,14) (12,30) (13,15) (14,31) (14,18) (14,30) (14,17) (16,28) (16,31) (16,18) (16,21) (16,30) (16,22) (16,25) (16,17) (16,29) (16,32) (17,31) (17,18) (18,23) (18,26) (18,19) (18,20) (19,23) (19,21) (20,28) (20,31) (20,30) (20,25) (20,29) (21,23) (21,22) (22,26) (23,26) (23,30) (24,27) (25,29) (28,31) (28,32)\nIs there a path between node 12 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph437-7_32", + "image": "data/connectivity/graph_visual/hard/graph437.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (0,30) (0,13) (0,2) (0,23) (0,28) (0,8) (0,26) (0,25) (0,21) (0,15) (0,14) (0,31) (1,16) (1,5) (1,20) (1,6) (1,30) (1,13) (1,2) (1,28) (1,8) (1,25) (1,7) (1,15) (1,4) (1,17) (2,16) (2,20) (2,6) (2,30) (2,23) (2,28) (2,3) (2,26) (2,4) (2,17) (2,14) (2,22) (2,31) (3,16) (3,20) (3,30) (3,13) (3,23) (3,28) (3,21) (3,15) (3,14) (3,31) (4,16) (4,5) (4,6) (4,30) (4,13) (4,23) (4,28) (4,8) (4,26) (4,25) (4,21) (4,7) (4,15) (4,17) (4,14) (4,22) (5,16) (5,30) (5,23) (5,28) (5,8) (5,26) (5,15) (5,17) (5,22) (5,31) (6,16) (6,20) (6,30) (6,13) (6,23) (6,28) (6,26) (6,25) (6,21) (6,7) (6,14) (6,22) (6,31) (7,16) (7,30) (7,13) (7,28) (7,26) (7,25) (7,21) (7,14) (8,20) (8,13) (8,28) (8,21) (8,14) (8,22) (9,29) (9,10) (9,27) (9,19) (9,11) (9,18) (10,12) (10,29) (10,27) (10,18) (11,12) (11,29) (11,32) (12,29) (12,27) (12,32) (12,19) (12,18) (13,16) (13,20) (13,30) (13,28) (13,21) (13,15) (13,17) (13,22) (13,31) (14,16) (14,23) (14,28) (14,26) (14,25) (14,15) (14,17) (14,22) (14,31) (15,16) (15,30) (15,23) (15,28) (15,26) (15,25) (15,21) (15,17) (15,22) (15,31) (16,30) (16,23) (16,28) (16,17) (16,22) (16,31) (17,20) (17,30) (17,23) (17,28) (17,22) (17,31) (18,29) (18,27) (18,32) (19,32) (20,30) (20,23) (20,28) (20,26) (20,25) (20,21) (20,22) (20,31) (21,30) (21,28) (21,26) (21,22) (22,23) (22,25) (23,30) (23,26) (23,25) (25,30) (25,28) (25,26) (26,31) (27,29) (27,32) (28,30) (29,32) (30,31)\nIs there a path between node 7 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph172-19_5", + "image": "data/connectivity/graph_visual/hard/graph172.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,17) (0,11) (0,6) (0,9) (1,23) (1,21) (1,3) (1,19) (1,15) (1,22) (1,24) (1,5) (1,14) (1,25) (1,27) (1,18) (2,28) (2,13) (2,6) (3,23) (3,21) (3,12) (3,19) (3,15) (3,22) (3,24) (3,10) (3,14) (3,26) (3,25) (3,27) (4,21) (4,12) (4,15) (4,22) (4,24) (4,5) (4,14) (4,26) (4,25) (4,16) (4,27) (5,23) (5,21) (5,19) (5,15) (5,24) (5,10) (5,26) (5,8) (5,27) (6,28) (6,13) (6,17) (6,11) (7,28) (7,13) (7,11) (7,20) (8,21) (8,12) (8,19) (8,15) (8,22) (8,14) (8,26) (8,25) (8,16) (8,27) (9,17) (9,11) (9,20) (10,23) (10,12) (10,15) (10,22) (10,24) (10,14) (10,26) (10,25) (10,16) (10,18) (11,28) (11,13) (11,17) (11,20) (12,23) (12,21) (12,15) (12,22) (12,24) (12,16) (12,18) (13,28) (13,17) (13,20) (14,23) (14,21) (14,19) (14,15) (14,24) (14,25) (14,16) (14,27) (15,23) (15,19) (15,26) (15,25) (15,16) (15,27) (15,18) (16,23) (16,21) (16,19) (16,24) (16,26) (16,27) (16,18) (17,28) (18,23) (18,21) (18,19) (18,22) (18,24) (18,26) (18,25) (19,23) (19,22) (19,24) (19,26) (19,25) (19,27) (20,28) (21,23) (21,22) (21,24) (21,26) (21,25) (21,27) (22,24) (22,25) (23,24) (24,26) (24,25) (24,27)\nIs there a path between node 19 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph478-1_16", + "image": "data/connectivity/graph_visual/hard/graph478.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (0,6) (0,31) (0,20) (0,8) (0,4) (0,2) (0,28) (0,32) (0,3) (0,10) (0,5) (0,27) (0,16) (0,15) (0,14) (0,9) (0,26) (0,19) (1,17) (1,31) (1,20) (1,4) (1,29) (1,28) (1,32) (1,3) (1,10) (1,5) (1,16) (1,15) (1,9) (1,26) (1,19) (1,24) (2,17) (2,31) (2,20) (2,8) (2,4) (2,29) (2,3) (2,5) (2,27) (2,15) (2,14) (2,9) (3,6) (3,17) (3,31) (3,20) (3,8) (3,4) (3,28) (3,32) (3,10) (3,27) (3,15) (3,14) (3,9) (3,19) (4,6) (4,17) (4,31) (4,20) (4,8) (4,29) (4,28) (4,32) (4,10) (4,5) (4,27) (4,14) (4,26) (4,19) (4,24) (5,6) (5,17) (5,20) (5,8) (5,29) (5,32) (5,10) (5,27) (5,15) (5,14) (5,9) (5,26) (5,19) (5,24) (6,17) (6,8) (6,29) (6,32) (6,10) (6,16) (6,14) (6,9) (6,19) (6,24) (7,23) (7,25) (7,13) (7,21) (7,22) (7,30) (7,12) (8,17) (8,31) (8,20) (8,29) (8,28) (8,32) (8,10) (8,27) (8,16) (8,15) (8,14) (8,19) (8,24) (9,31) (9,28) (9,32) (9,10) (9,27) (9,16) (9,15) (9,14) (9,26) (9,19) (9,24) (10,17) (10,28) (10,32) (10,27) (10,16) (10,15) (10,26) (10,19) (10,24) (11,23) (11,18) (11,25) (11,13) (11,21) (11,22) (11,12) (12,18) (12,25) (12,13) (12,22) (12,30) (13,23) (13,18) (13,25) (13,21) (13,22) (14,17) (14,28) (14,27) (14,16) (14,15) (14,26) (14,19) (15,31) (15,20) (15,28) (15,32) (15,27) (15,26) (15,19) (15,24) (16,17) (16,31) (16,20) (16,29) (16,28) (16,26) (16,19) (16,24) (17,29) (17,28) (17,26) (17,19) (18,23) (18,25) (19,31) (19,20) (19,29) (19,32) (19,27) (20,31) (20,29) (20,28) (20,26) (21,25) (21,22) (21,30) (22,23) (22,25) (22,30) (23,30) (24,31) (24,29) (24,32) (24,26) (25,30) (26,31) (26,29) (26,28) (26,32) (27,31) (27,29) (27,28) (27,32) (28,31) (28,29) (28,32) (29,31) (29,32) (31,32)\nIs there a path between node 1 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph197-2_12", + "image": "data/connectivity/graph_visual/hard/graph197.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,5) (0,18) (0,28) (0,10) (0,13) (0,8) (0,22) (0,20) (1,3) (1,29) (1,23) (1,26) (1,6) (1,24) (1,15) (2,4) (2,27) (3,25) (3,29) (3,23) (3,26) (3,6) (3,24) (3,14) (3,16) (3,9) (4,27) (5,11) (5,18) (5,7) (5,10) (5,8) (5,22) (5,21) (5,20) (6,25) (6,29) (6,23) (6,12) (6,26) (6,24) (6,16) (6,15) (6,9) (7,11) (7,28) (7,19) (7,10) (7,13) (7,8) (7,22) (7,21) (7,20) (8,11) (8,18) (8,19) (8,10) (8,13) (8,22) (8,21) (8,20) (9,25) (9,29) (9,12) (9,26) (9,24) (9,14) (9,16) (9,15) (10,11) (10,18) (10,28) (10,19) (10,13) (10,22) (10,21) (11,18) (11,28) (11,19) (11,13) (11,22) (11,21) (12,25) (12,29) (12,23) (12,24) (12,14) (12,15) (13,18) (13,28) (13,19) (13,21) (14,25) (14,29) (14,16) (15,29) (15,23) (15,26) (15,24) (15,16) (16,25) (16,23) (16,26) (16,24) (18,28) (18,21) (19,28) (19,22) (19,21) (19,20) (20,28) (20,21) (21,22) (22,28) (23,29) (24,25) (24,29) (24,26) (25,29)\nIs there a path between node 2 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph534-3_25", + "image": "data/connectivity/graph_visual/hard/graph534.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,1) (0,3) (0,22) (0,28) (0,2) (0,26) (0,14) (0,10) (0,32) (0,30) (0,16) (0,31) (0,9) (0,23) (0,20) (0,4) (0,19) (0,17) (0,18) (1,21) (1,22) (1,28) (1,15) (1,16) (1,31) (1,20) (1,13) (1,8) (1,19) (1,18) (2,3) (2,28) (2,29) (2,14) (2,10) (2,32) (2,30) (2,16) (2,9) (2,23) (2,20) (2,13) (2,5) (2,4) (2,8) (2,19) (2,17) (2,18) (3,21) (3,22) (3,28) (3,26) (3,10) (3,32) (3,15) (3,31) (3,9) (3,23) (3,20) (3,5) (3,7) (3,4) (3,19) (3,18) (4,22) (4,28) (4,29) (4,14) (4,10) (4,32) (4,15) (4,30) (4,31) (4,23) (4,20) (4,13) (4,7) (4,17) (4,18) (5,22) (5,28) (5,10) (5,9) (5,20) (5,13) (5,7) (5,19) (5,17) (5,18) (6,25) (6,33) (6,24) (6,11) (6,27) (7,21) (7,22) (7,28) (7,26) (7,14) (7,10) (7,32) (7,15) (7,30) (7,9) (7,20) (7,19) (7,18) (8,22) (8,28) (8,29) (8,26) (8,14) (8,10) (8,32) (8,15) (8,30) (8,31) (8,23) (8,20) (8,19) (8,17) (9,21) (9,29) (9,26) (9,10) (9,32) (9,30) (9,16) (9,23) (9,20) (9,13) (9,19) (9,17) (10,21) (10,22) (10,28) (10,29) (10,26) (10,14) (10,32) (10,15) (10,30) (10,16) (10,31) (10,23) (10,20) (10,17) (11,12) (11,27) (12,24) (13,21) (13,22) (13,32) (13,15) (13,30) (13,23) (13,20) (13,19) (13,17) (13,18) (14,21) (14,22) (14,28) (14,26) (14,15) (14,30) (14,16) (14,23) (14,19) (14,17) (14,18) (15,21) (15,22) (15,26) (15,32) (15,30) (15,16) (15,31) (15,23) (15,20) (15,17) (15,18) (16,21) (16,28) (16,29) (16,32) (16,19) (16,17) (16,18) (17,21) (17,22) (17,28) (17,29) (17,26) (17,32) (17,30) (17,23) (17,20) (17,19) (18,21) (18,22) (18,28) (18,29) (18,26) (18,32) (18,30) (18,31) (18,23) (18,20) (18,19) (19,21) (19,22) (19,28) (19,29) (19,26) (19,30) (19,31) (19,23) (19,20) (20,28) (20,29) (20,23) (21,22) (21,28) (21,26) (21,32) (21,30) (21,31) (21,23) (22,28) (22,29) (22,26) (22,32) (23,28) (23,26) (23,31) (24,25) (24,33) (24,27) (25,33) (25,27) (26,29) (26,32) (26,30) (26,31) (27,33) (28,29) (28,32) (28,30) (28,31) (29,32) (29,30) (29,31) (30,31) (31,32)\nIs there a path between node 3 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph6-17_20", + "image": "data/connectivity/graph_visual/hard/graph6.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,7) (0,11) (0,22) (0,23) (1,11) (1,21) (1,2) (1,24) (1,8) (2,19) (2,13) (4,17) (4,5) (5,17) (5,10) (6,25) (7,11) (7,21) (7,24) (8,11) (8,21) (8,18) (8,13) (9,15) (9,10) (10,17) (10,15) (11,19) (11,16) (11,21) (11,22) (11,12) (13,16) (13,22) (13,23) (13,24) (14,19) (14,24) (16,24) (18,19) (18,21) (19,21) (19,23) (20,22) (21,22) (22,24)\nIs there a path between node 17 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph77-25_0", + "image": "data/connectivity/graph_visual/hard/graph77.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,14) (0,7) (0,20) (0,17) (0,19) (0,8) (0,11) (0,18) (0,10) (0,23) (0,15) (0,25) (0,24) (1,14) (1,7) (1,9) (1,17) (1,19) (1,5) (1,8) (1,11) (1,18) (1,10) (1,3) (1,23) (1,25) (1,24) (2,4) (2,26) (2,13) (2,12) (2,21) (2,22) (3,14) (3,7) (3,9) (3,17) (3,19) (3,5) (3,8) (3,6) (3,10) (3,23) (3,25) (3,24) (4,21) (4,16) (5,14) (5,20) (5,9) (5,17) (5,8) (5,6) (5,18) (5,10) (5,15) (5,25) (5,24) (6,7) (6,20) (6,8) (6,18) (6,10) (6,23) (6,15) (6,25) (6,24) (7,14) (7,20) (7,9) (7,19) (7,11) (7,10) (7,15) (8,20) (8,17) (8,19) (8,11) (8,18) (8,10) (8,23) (8,24) (9,20) (9,19) (9,11) (9,18) (9,10) (9,23) (9,25) (10,14) (10,17) (10,19) (10,11) (10,18) (10,23) (10,15) (10,24) (11,14) (11,20) (11,18) (11,23) (11,15) (11,25) (12,26) (12,16) (12,22) (13,26) (13,16) (13,22) (14,20) (14,17) (14,19) (14,18) (14,23) (14,25) (15,20) (15,19) (15,18) (15,25) (16,21) (16,22) (17,20) (17,19) (17,23) (18,20) (18,19) (18,23) (18,24) (19,20) (19,23) (19,25) (20,23) (20,25) (20,24) (21,22) (22,26)\nIs there a path between node 25 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph2-23_0", + "image": "data/connectivity/graph_visual/hard/graph2.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,24) (0,1) (0,6) (0,14) (1,10) (2,25) (2,5) (2,20) (2,18) (3,22) (3,6) (3,19) (3,23) (4,9) (4,18) (5,15) (5,25) (5,17) (5,20) (6,11) (6,24) (6,14) (6,7) (6,21) (7,24) (8,25) (8,17) (8,20) (8,18) (9,25) (10,24) (10,22) (10,21) (11,22) (11,19) (11,23) (12,15) (12,16) (12,17) (13,19) (13,14) (14,22) (14,19) (15,16) (15,18) (16,17) (17,20) (18,25) (19,24) (19,22) (20,25) (21,23) (22,24) (22,23)\nIs there a path between node 23 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph163-28_18", + "image": "data/connectivity/graph_visual/hard/graph163.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,8) (0,11) (0,14) (0,13) (0,3) (1,28) (1,10) (1,21) (1,18) (1,14) (1,13) (2,28) (2,8) (2,27) (2,23) (2,7) (2,4) (2,25) (2,20) (2,26) (2,9) (3,28) (3,6) (3,11) (3,23) (3,21) (3,14) (4,19) (4,23) (4,18) (4,20) (4,9) (5,15) (6,28) (6,8) (6,23) (6,21) (6,25) (6,20) (6,26) (7,27) (7,25) (7,20) (7,13) (7,24) (7,26) (8,28) (8,19) (8,14) (8,26) (8,12) (9,19) (9,21) (9,14) (9,26) (10,14) (10,13) (10,12) (11,28) (11,16) (11,27) (11,14) (11,20) (11,13) (11,24) (11,26) (11,12) (12,20) (13,16) (13,21) (13,18) (14,28) (14,19) (14,23) (14,21) (14,25) (14,24) (15,17) (16,23) (16,24) (18,28) (18,27) (18,26) (19,27) (19,24) (19,26) (20,28) (20,27) (20,23) (21,23) (21,25) (21,26) (23,26) (26,27)\nIs there a path between node 28 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph611-17_30", + "image": "data/connectivity/graph_visual/hard/graph611.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,4) (1,32) (1,22) (1,34) (1,7) (1,5) (1,28) (1,11) (1,13) (1,30) (1,31) (1,26) (2,12) (2,3) (2,24) (2,15) (2,18) (2,8) (2,20) (2,25) (2,19) (2,17) (2,16) (3,10) (3,24) (3,15) (3,18) (3,8) (3,20) (3,14) (3,19) (3,21) (4,23) (4,6) (5,32) (5,22) (5,7) (5,33) (5,11) (5,13) (5,27) (5,31) (5,26) (6,23) (7,22) (7,34) (7,28) (7,13) (7,27) (7,30) (7,26) (7,29) (8,10) (8,24) (8,15) (8,18) (8,20) (8,14) (8,17) (8,21) (8,16) (9,32) (9,22) (9,34) (9,28) (9,13) (9,27) (9,31) (9,26) (9,29) (10,12) (10,24) (10,15) (10,18) (10,20) (10,25) (10,17) (11,32) (11,22) (11,34) (11,28) (11,13) (11,27) (11,30) (11,31) (11,26) (12,24) (12,25) (12,14) (12,17) (12,21) (12,16) (13,34) (13,33) (13,27) (13,30) (13,31) (13,29) (14,15) (14,18) (14,20) (14,25) (14,19) (14,17) (14,21) (14,16) (15,24) (15,18) (15,20) (15,17) (15,21) (16,24) (16,20) (16,19) (16,17) (17,24) (17,20) (17,21) (18,20) (18,25) (18,19) (20,24) (20,25) (20,21) (21,25) (22,32) (22,28) (22,27) (22,30) (22,31) (22,26) (24,25) (26,34) (26,33) (26,31) (27,34) (27,33) (27,28) (27,30) (27,31) (27,29) (28,32) (28,33) (28,30) (28,31) (28,29) (29,32) (29,33) (30,32) (31,32) (31,34) (32,34) (32,33) (33,34)\nIs there a path between node 17 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph107-15_4", + "image": "data/connectivity/graph_visual/hard/graph107.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,27) (0,4) (0,11) (0,9) (0,25) (1,12) (1,16) (2,3) (2,27) (2,11) (2,12) (2,22) (2,25) (2,15) (3,25) (3,15) (4,18) (4,11) (4,26) (4,22) (4,9) (4,24) (4,13) (5,7) (5,14) (5,19) (5,17) (6,14) (7,17) (9,20) (9,26) (9,12) (9,25) (9,15) (10,20) (10,27) (10,11) (10,21) (10,26) (10,16) (11,27) (11,25) (12,27) (12,21) (12,26) (12,24) (13,24) (14,17) (15,20) (15,27) (15,18) (15,26) (15,22) (15,25) (16,20) (16,27) (18,26) (18,25) (20,25) (25,26)\nIs there a path between node 15 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph562-4_13", + "image": "data/connectivity/graph_visual/hard/graph562.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,27) (0,10) (0,8) (0,23) (1,2) (1,21) (1,17) (1,31) (2,6) (2,33) (2,9) (2,3) (2,21) (2,7) (2,16) (3,17) (3,24) (3,5) (4,32) (4,22) (4,12) (5,33) (5,28) (6,24) (6,26) (6,19) (6,16) (6,28) (7,33) (7,24) (7,13) (8,27) (9,31) (9,16) (9,13) (10,27) (10,29) (10,20) (10,12) (11,32) (12,29) (12,22) (13,15) (13,21) (13,26) (13,19) (13,18) (15,21) (16,24) (16,26) (16,18) (17,21) (17,28) (18,33) (18,21) (18,26) (19,21) (19,28) (20,25) (20,22) (21,26) (21,28) (22,30) (22,29) (22,23) (23,29) (23,25) (24,33) (25,29) (26,28) (28,33) (28,31) (29,32) (30,32)\nIs there a path between node 4 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph151-0_27", + "image": "data/connectivity/graph_visual/hard/graph151.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,6) (0,27) (0,11) (0,4) (0,9) (0,25) (0,16) (0,2) (0,23) (0,3) (0,28) (0,10) (0,5) (1,6) (1,27) (1,20) (1,11) (1,24) (1,4) (1,14) (1,13) (1,9) (1,25) (1,2) (1,17) (1,23) (1,3) (1,28) (1,10) (1,22) (2,6) (2,24) (2,4) (2,14) (2,17) (2,23) (2,28) (2,22) (2,5) (3,6) (3,27) (3,20) (3,11) (3,4) (3,16) (3,17) (3,23) (3,28) (3,22) (3,5) (4,27) (4,20) (4,14) (4,9) (4,25) (4,16) (4,17) (4,23) (4,28) (4,10) (4,22) (5,27) (5,20) (5,11) (5,24) (5,13) (5,9) (5,16) (5,17) (5,28) (5,10) (6,20) (6,11) (6,24) (6,13) (6,9) (6,25) (6,16) (6,17) (6,28) (6,10) (6,22) (7,12) (7,26) (7,21) (8,15) (8,18) (9,27) (9,20) (9,11) (9,24) (9,14) (9,13) (9,25) (9,16) (9,10) (9,22) (10,27) (10,20) (10,24) (10,13) (10,25) (10,16) (10,17) (10,23) (10,28) (11,20) (11,24) (11,14) (11,16) (11,17) (11,28) (12,26) (12,21) (13,27) (13,24) (13,25) (13,17) (13,23) (14,20) (14,25) (14,16) (14,23) (14,28) (15,19) (15,18) (16,27) (16,20) (16,24) (16,25) (16,17) (16,23) (16,28) (16,22) (17,27) (17,24) (17,25) (18,19) (20,24) (20,25) (20,22) (21,26) (22,27) (22,24) (22,25) (23,24) (23,25) (24,27) (24,25) (24,28) (25,28) (27,28)\nIs there a path between node 0 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph514-5_22", + "image": "data/connectivity/graph_visual/hard/graph514.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,9) (0,23) (0,19) (0,11) (0,14) (0,29) (0,4) (0,7) (1,33) (1,27) (1,20) (1,12) (1,11) (1,30) (1,14) (1,29) (1,4) (1,15) (2,9) (2,33) (2,19) (2,20) (2,14) (2,32) (3,26) (3,25) (3,16) (4,23) (4,31) (4,32) (5,10) (5,25) (5,6) (5,28) (6,26) (6,22) (7,13) (7,24) (7,27) (7,31) (7,11) (7,29) (7,32) (7,8) (7,15) (8,24) (8,33) (8,12) (8,11) (8,30) (8,14) (8,32) (9,24) (9,33) (9,21) (9,11) (9,14) (9,29) (10,26) (11,19) (11,27) (12,23) (12,20) (13,24) (13,20) (14,30) (14,29) (14,32) (15,23) (15,24) (15,33) (15,30) (15,32) (18,24) (18,33) (18,19) (18,20) (19,30) (19,32) (20,24) (20,27) (21,24) (21,27) (21,31) (22,26) (22,25) (23,32) (26,28) (27,31) (27,30) (27,29) (27,32) (29,33) (29,30) (29,32) (30,32) (31,33) (32,33)\nIs there a path between node 5 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph327-18_24", + "image": "data/connectivity/graph_visual/hard/graph327.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,3) (0,10) (0,27) (0,1) (0,29) (0,7) (0,14) (0,13) (0,20) (0,6) (1,3) (1,4) (1,10) (1,27) (1,7) (1,16) (1,14) (1,13) (1,20) (1,15) (1,6) (2,30) (2,12) (2,5) (2,11) (2,21) (2,28) (2,22) (2,25) (2,31) (2,19) (3,4) (3,29) (3,16) (3,14) (3,13) (3,20) (3,15) (4,10) (4,7) (4,16) (4,13) (4,15) (4,6) (5,12) (5,23) (5,24) (5,21) (5,28) (5,25) (5,31) (5,19) (6,27) (6,29) (6,7) (6,14) (6,13) (6,20) (6,15) (7,10) (7,27) (7,20) (8,18) (9,26) (9,18) (10,27) (10,29) (10,16) (10,13) (10,15) (11,30) (11,24) (11,21) (11,17) (11,28) (11,25) (12,23) (12,24) (12,21) (12,17) (12,28) (12,22) (12,25) (12,19) (13,27) (13,16) (13,20) (13,15) (14,27) (14,29) (14,16) (14,15) (15,27) (15,29) (15,16) (15,20) (16,27) (16,29) (16,20) (17,30) (17,23) (17,24) (17,21) (17,28) (17,22) (17,25) (17,31) (17,19) (18,26) (19,30) (19,23) (19,24) (19,21) (19,28) (19,25) (19,31) (20,27) (21,30) (21,24) (21,28) (21,22) (21,25) (21,31) (22,30) (22,23) (22,24) (22,28) (22,25) (22,31) (23,30) (23,24) (23,25) (23,31) (24,28) (24,25) (24,31) (25,30) (25,28) (25,31) (27,29) (28,30) (30,31)\nIs there a path between node 18 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph491-6_23", + "image": "data/connectivity/graph_visual/hard/graph491.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (0,15) (0,32) (0,3) (0,13) (0,19) (0,17) (1,14) (1,10) (1,21) (1,5) (1,29) (1,2) (2,14) (2,12) (2,21) (2,22) (2,29) (2,6) (2,4) (3,18) (3,13) (3,11) (3,19) (3,9) (3,17) (4,14) (4,12) (4,21) (4,5) (4,29) (4,6) (5,14) (5,22) (6,14) (6,12) (6,10) (6,21) (6,22) (6,29) (7,23) (7,30) (7,18) (7,32) (7,11) (8,25) (8,31) (8,20) (8,16) (9,23) (9,18) (9,32) (9,13) (9,11) (9,19) (9,17) (10,22) (10,29) (11,23) (11,15) (11,30) (11,18) (11,32) (11,19) (11,17) (12,14) (12,22) (12,29) (13,23) (13,15) (13,18) (13,32) (13,17) (14,22) (15,23) (15,30) (15,32) (15,19) (15,17) (16,25) (16,31) (16,24) (16,20) (16,28) (16,26) (16,27) (17,30) (17,18) (17,32) (17,19) (19,30) (19,32) (20,24) (20,27) (21,22) (21,29) (22,29) (23,32) (24,28) (24,26) (24,27) (25,31) (25,28) (25,27) (26,28) (26,27) (27,31) (27,28) (28,31) (30,32)\nIs there a path between node 6 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph704-2_0", + "image": "data/connectivity/graph_visual/hard/graph704.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,8) (0,6) (0,7) (0,28) (0,4) (0,33) (0,32) (0,3) (0,24) (0,16) (0,9) (0,29) (0,14) (0,11) (0,17) (0,22) (0,5) (1,23) (1,8) (1,6) (1,7) (1,28) (1,12) (1,4) (1,33) (1,16) (1,9) (1,10) (1,14) (1,17) (2,26) (2,15) (2,19) (2,21) (3,20) (3,13) (3,25) (3,23) (3,8) (3,6) (3,7) (3,28) (3,12) (3,31) (3,4) (3,30) (3,33) (3,32) (3,27) (3,24) (3,10) (3,22) (3,5) (4,20) (4,23) (4,8) (4,6) (4,7) (4,28) (4,12) (4,30) (4,33) (4,32) (4,27) (4,24) (4,16) (4,9) (4,14) (4,17) (4,22) (4,5) (5,20) (5,6) (5,28) (5,12) (5,31) (5,30) (5,32) (5,24) (5,9) (5,29) (5,14) (5,11) (5,17) (5,22) (6,20) (6,13) (6,25) (6,23) (6,8) (6,7) (6,28) (6,12) (6,30) (6,32) (6,27) (6,24) (6,9) (6,10) (6,29) (6,14) (6,11) (6,22) (7,20) (7,25) (7,23) (7,8) (7,12) (7,31) (7,33) (7,27) (7,24) (7,16) (7,10) (7,14) (7,17) (7,22) (8,20) (8,13) (8,23) (8,12) (8,33) (8,32) (8,27) (8,24) (8,16) (8,9) (8,10) (8,29) (8,14) (8,11) (8,17) (8,22) (9,13) (9,25) (9,12) (9,31) (9,30) (9,33) (9,32) (9,27) (9,24) (9,16) (9,10) (9,29) (9,14) (9,17) (10,13) (10,25) (10,23) (10,28) (10,12) (10,32) (10,24) (10,16) (10,14) (10,11) (10,22) (11,13) (11,23) (11,28) (11,12) (11,31) (11,30) (11,32) (11,27) (11,24) (11,16) (11,29) (11,14) (11,17) (11,22) (12,20) (12,25) (12,23) (12,28) (12,31) (12,30) (12,27) (12,24) (12,16) (12,29) (12,14) (12,22) (13,20) (13,25) (13,28) (13,31) (13,30) (13,33) (13,32) (13,24) (13,16) (13,29) (13,14) (13,17) (13,22) (14,25) (14,28) (14,31) (14,30) (14,33) (14,32) (14,24) (14,16) (14,29) (14,17) (15,26) (15,19) (15,21) (16,20) (16,23) (16,28) (16,31) (16,33) (16,29) (16,17) (16,22) (17,25) (17,23) (17,28) (17,31) (17,32) (17,24) (17,29) (17,22) (19,26) (19,34) (20,25) (20,23) (20,30) (20,32) (20,27) (20,29) (20,22) (21,34) (22,23) (22,28) (22,31) (22,30) (22,33) (22,27) (22,29) (23,25) (23,30) (23,33) (23,32) (23,27) (23,24) (23,29) (24,25) (24,28) (24,31) (24,30) (24,32) (24,27) (25,28) (25,31) (25,30) (25,32) (25,29) (26,34) (27,28) (27,30) (27,33) (27,32) (27,29) (28,31) (28,32) (29,30) (29,32) (30,31) (30,33) (31,32)\nIs there a path between node 2 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph699-9_26", + "image": "data/connectivity/graph_visual/hard/graph699.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,22) (0,23) (0,24) (0,19) (0,4) (0,7) (0,10) (0,3) (0,20) (0,28) (0,2) (0,26) (0,29) (0,21) (1,17) (1,5) (1,14) (1,30) (1,16) (2,13) (2,27) (2,23) (2,24) (2,34) (2,32) (2,10) (2,33) (2,20) (2,26) (2,9) (3,13) (3,27) (3,6) (3,23) (3,24) (3,19) (3,34) (3,10) (3,33) (3,20) (3,28) (3,26) (3,9) (3,29) (3,21) (4,13) (4,27) (4,22) (4,24) (4,19) (4,7) (4,10) (4,33) (4,20) (4,28) (4,26) (4,9) (4,29) (4,21) (5,17) (5,14) (5,15) (5,12) (5,30) (5,18) (5,16) (6,13) (6,22) (6,23) (6,34) (6,32) (6,10) (6,20) (6,26) (6,9) (6,8) (7,13) (7,23) (7,24) (7,19) (7,34) (7,10) (7,33) (7,20) (7,28) (7,8) (7,29) (7,21) (8,27) (8,23) (8,24) (8,34) (8,10) (8,28) (8,9) (8,29) (8,21) (9,13) (9,27) (9,22) (9,23) (9,34) (9,32) (9,10) (9,20) (9,28) (9,26) (9,21) (10,13) (10,27) (10,22) (10,24) (10,19) (10,34) (10,32) (10,33) (10,20) (10,26) (10,29) (10,21) (11,17) (11,31) (11,14) (11,15) (11,18) (11,16) (12,31) (12,15) (12,30) (12,18) (13,27) (13,22) (13,24) (13,32) (13,33) (13,20) (13,28) (13,26) (13,21) (14,17) (14,31) (14,15) (14,30) (14,18) (14,16) (15,17) (15,30) (15,18) (15,16) (16,17) (16,31) (16,30) (16,18) (17,31) (17,18) (18,31) (18,30) (19,22) (19,23) (19,24) (19,34) (19,32) (19,33) (19,20) (19,28) (19,26) (19,29) (19,21) (20,22) (20,23) (20,34) (20,21) (21,27) (21,22) (21,23) (21,34) (21,32) (21,33) (21,28) (21,26) (21,29) (22,27) (22,24) (22,33) (22,28) (22,26) (22,29) (23,27) (23,32) (23,33) (23,26) (23,29) (24,27) (24,34) (24,33) (24,28) (24,26) (24,29) (26,27) (26,34) (26,32) (26,29) (27,34) (27,32) (27,33) (27,28) (27,29) (28,32) (28,33) (28,29) (29,34) (29,32) (32,34) (32,33)\nIs there a path between node 9 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph415-5_11", + "image": "data/connectivity/graph_visual/hard/graph415.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,10) (0,2) (0,31) (0,17) (1,10) (1,26) (1,25) (1,31) (1,17) (2,25) (2,31) (3,18) (3,23) (3,15) (3,11) (3,22) (4,5) (4,13) (4,6) (4,11) (4,16) (4,24) (5,28) (5,23) (5,19) (5,7) (5,22) (6,18) (6,28) (6,11) (7,28) (7,23) (7,13) (7,21) (9,18) (9,15) (9,12) (9,11) (10,29) (11,30) (11,18) (11,14) (11,28) (11,15) (11,19) (12,30) (12,13) (12,19) (13,16) (13,19) (13,22) (14,28) (14,16) (15,30) (15,22) (16,30) (18,30) (18,21) (18,19) (18,24) (19,23) (19,24) (20,29) (23,24) (24,30) (25,27) (25,29) (26,27) (27,31) (29,32)\nIs there a path between node 5 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph44-2_13", + "image": "data/connectivity/graph_visual/hard/graph44.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,26) (0,15) (0,25) (0,14) (0,7) (0,2) (0,9) (0,5) (1,26) (1,15) (1,25) (1,7) (1,6) (1,2) (1,20) (1,22) (2,25) (2,19) (2,14) (2,4) (3,12) (3,16) (4,15) (4,7) (4,6) (4,8) (5,26) (5,20) (5,8) (5,9) (5,22) (5,13) (6,19) (6,17) (6,7) (6,20) (6,22) (7,19) (7,17) (7,9) (8,19) (9,26) (9,14) (9,24) (11,12) (12,21) (12,18) (12,16) (13,17) (13,22) (14,26) (14,22) (15,19) (15,20) (16,21) (18,23) (19,20) (19,22) (25,26)\nIs there a path between node 2 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph399-0_25", + "image": "data/connectivity/graph_visual/hard/graph399.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,4) (0,12) (0,11) (0,10) (0,3) (0,17) (0,21) (0,27) (0,15) (0,23) (0,31) (0,29) (0,2) (0,8) (0,9) (0,14) (0,18) (1,5) (1,26) (1,13) (1,20) (1,32) (1,7) (2,19) (2,4) (2,28) (2,22) (2,16) (2,12) (2,10) (2,3) (2,17) (2,21) (2,27) (2,15) (2,23) (2,31) (2,29) (2,8) (2,9) (2,14) (2,18) (3,4) (3,22) (3,16) (3,12) (3,10) (3,17) (3,21) (3,27) (3,23) (3,31) (3,29) (3,6) (3,9) (3,14) (3,18) (4,16) (4,12) (4,11) (4,17) (4,21) (4,15) (4,30) (4,23) (4,29) (4,6) (4,8) (4,9) (4,18) (5,26) (5,13) (5,25) (5,24) (5,32) (5,7) (6,19) (6,22) (6,12) (6,11) (6,10) (6,17) (6,21) (6,27) (6,15) (6,30) (6,23) (6,31) (6,29) (6,9) (6,14) (7,26) (7,25) (7,32) (8,19) (8,28) (8,10) (8,17) (8,27) (8,15) (8,30) (8,23) (9,19) (9,28) (9,22) (9,16) (9,12) (9,10) (9,17) (9,21) (9,15) (9,30) (9,23) (9,29) (9,18) (10,19) (10,28) (10,22) (10,12) (10,11) (10,17) (10,21) (10,27) (10,15) (10,30) (10,23) (10,31) (10,29) (10,14) (10,18) (11,16) (11,12) (11,17) (11,21) (11,27) (11,15) (11,30) (11,31) (11,29) (11,14) (11,18) (12,19) (12,28) (12,22) (12,17) (12,27) (12,15) (12,30) (12,23) (12,31) (12,29) (12,14) (12,18) (13,26) (13,25) (13,20) (13,32) (14,28) (14,16) (14,17) (14,21) (14,27) (14,15) (14,31) (14,29) (14,18) (15,19) (15,22) (15,16) (15,17) (15,21) (15,27) (15,30) (15,23) (15,31) (15,29) (15,18) (16,19) (16,28) (16,22) (16,17) (16,21) (16,27) (16,30) (16,31) (16,18) (17,22) (17,21) (17,30) (17,31) (17,29) (17,18) (18,19) (18,28) (18,22) (18,21) (18,27) (18,29) (19,28) (19,22) (19,21) (19,30) (19,31) (19,29) (20,32) (21,28) (21,22) (21,27) (21,29) (22,28) (22,30) (22,23) (22,31) (22,29) (23,28) (23,27) (23,30) (23,31) (23,29) (24,26) (24,25) (25,26) (25,32) (26,32) (27,28) (27,30) (27,29) (28,30) (28,31) (28,29) (29,30) (29,31)\nIs there a path between node 0 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph523-2_10", + "image": "data/connectivity/graph_visual/hard/graph523.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,30) (0,1) (0,22) (0,18) (0,3) (1,7) (1,22) (1,14) (1,20) (1,32) (1,17) (1,23) (1,12) (2,7) (2,11) (2,16) (2,31) (2,14) (2,20) (2,17) (3,7) (3,11) (3,33) (3,30) (3,22) (3,9) (3,14) (3,5) (3,6) (3,24) (3,12) (4,30) (4,31) (4,29) (4,5) (4,25) (4,24) (4,28) (4,23) (5,27) (5,7) (5,22) (5,16) (5,20) (5,26) (5,13) (5,23) (6,11) (6,30) (6,16) (6,14) (6,20) (6,25) (7,11) (7,30) (7,29) (7,20) (7,32) (7,28) (8,19) (9,27) (9,29) (9,14) (9,32) (9,28) (9,23) (9,12) (10,19) (11,33) (11,21) (11,16) (11,31) (11,18) (11,26) (11,25) (12,22) (12,18) (12,14) (12,17) (12,25) (12,24) (13,21) (13,22) (13,16) (13,32) (13,17) (13,25) (13,24) (14,33) (14,15) (14,16) (14,28) (15,22) (15,18) (15,26) (15,17) (15,25) (16,21) (16,29) (16,20) (16,32) (16,17) (17,31) (17,25) (17,28) (18,21) (18,25) (18,23) (20,33) (20,22) (20,32) (21,27) (21,30) (22,23) (23,33) (23,29) (23,26) (24,33) (24,30) (24,31) (24,32) (24,28) (25,31) (25,29) (25,26) (26,29) (26,28) (27,29) (27,28) (29,32) (31,32) (32,33)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph565-7_28", + "image": "data/connectivity/graph_visual/hard/graph565.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,13) (1,11) (1,26) (1,32) (1,29) (1,15) (1,18) (1,2) (1,6) (1,22) (1,9) (1,16) (2,7) (2,30) (2,22) (4,12) (5,12) (5,17) (6,30) (6,11) (6,26) (6,25) (6,15) (6,21) (6,33) (6,9) (7,19) (7,13) (7,32) (7,15) (7,18) (7,16) (7,10) (9,30) (9,31) (9,29) (9,21) (9,28) (9,14) (9,33) (9,10) (10,27) (10,31) (10,26) (10,32) (10,21) (10,14) (11,27) (11,31) (11,26) (11,32) (11,18) (11,14) (11,16) (12,24) (13,30) (13,26) (13,29) (13,21) (13,22) (14,32) (14,29) (14,25) (15,19) (15,16) (16,19) (16,27) (16,30) (16,26) (16,32) (16,21) (17,24) (18,33) (18,22) (19,30) (19,26) (19,25) (19,21) (20,23) (21,26) (21,28) (22,25) (25,31) (26,30) (26,31) (26,29) (26,28) (26,33) (28,33) (29,30) (29,31) (29,32) (29,33) (30,31) (32,33)\nIs there a path between node 7 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph429-2_4", + "image": "data/connectivity/graph_visual/hard/graph429.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,30) (0,15) (0,16) (0,27) (0,1) (0,13) (1,14) (1,30) (1,27) (1,13) (2,9) (2,25) (2,22) (2,8) (2,5) (2,26) (2,20) (2,10) (2,6) (2,31) (2,32) (2,19) (2,17) (2,18) (2,23) (2,4) (2,11) (3,9) (3,25) (3,22) (3,8) (3,26) (3,20) (3,24) (3,10) (3,6) (3,31) (3,17) (3,18) (3,12) (3,23) (3,4) (4,25) (4,22) (4,8) (4,5) (4,20) (4,31) (4,32) (4,19) (4,17) (4,23) (4,11) (5,9) (5,25) (5,22) (5,8) (5,10) (5,6) (5,32) (5,19) (5,18) (5,12) (5,23) (5,11) (6,9) (6,25) (6,22) (6,26) (6,24) (6,31) (6,32) (6,19) (6,17) (6,18) (7,29) (7,28) (8,22) (8,26) (8,20) (8,10) (8,31) (8,19) (8,18) (8,11) (9,25) (9,22) (9,26) (9,20) (9,24) (9,31) (9,32) (9,19) (9,17) (9,12) (9,23) (10,25) (10,22) (10,20) (10,24) (10,31) (10,32) (10,19) (10,17) (10,18) (10,12) (10,23) (10,11) (11,26) (11,20) (11,24) (11,31) (11,19) (11,17) (12,25) (12,26) (12,20) (12,24) (12,31) (12,32) (12,19) (13,14) (13,30) (13,27) (14,30) (14,15) (14,16) (15,16) (17,25) (17,22) (17,26) (17,20) (17,24) (17,31) (17,32) (17,23) (18,25) (18,22) (18,26) (18,32) (19,25) (19,22) (19,26) (19,20) (19,32) (19,23) (20,25) (20,22) (20,26) (20,24) (20,31) (21,29) (22,25) (22,26) (22,24) (22,32) (23,25) (23,26) (23,24) (23,31) (24,26) (24,31) (24,32) (25,26) (25,31) (25,32) (27,30) (28,29)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph117-0_5", + "image": "data/connectivity/graph_visual/hard/graph117.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,19) (0,15) (0,14) (0,24) (0,5) (0,25) (0,2) (1,7) (1,11) (1,8) (1,17) (1,25) (1,16) (1,21) (1,2) (2,15) (2,12) (2,3) (2,16) (3,15) (3,11) (3,10) (3,20) (3,16) (3,21) (5,7) (5,14) (5,12) (5,11) (5,24) (5,10) (5,26) (5,6) (6,19) (6,9) (6,14) (6,11) (6,24) (6,10) (6,25) (6,21) (7,19) (7,15) (7,18) (7,11) (7,24) (8,19) (8,24) (8,10) (9,15) (9,18) (9,11) (9,27) (9,26) (9,20) (9,25) (9,21) (9,23) (10,17) (10,25) (11,27) (11,26) (11,17) (11,20) (11,16) (12,19) (12,14) (12,24) (12,17) (14,26) (15,18) (15,17) (16,24) (16,26) (16,17) (17,27) (17,25) (18,24) (18,25) (19,27) (19,23) (20,24) (20,27) (20,23) (21,24) (21,27)\nIs there a path between node 0 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph359-31_6", + "image": "data/connectivity/graph_visual/hard/graph359.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,13) (0,12) (0,15) (1,18) (1,31) (1,20) (1,30) (2,6) (2,14) (2,17) (2,5) (3,9) (3,29) (3,23) (3,17) (4,9) (4,21) (4,8) (4,14) (4,10) (5,16) (5,9) (5,21) (5,8) (5,10) (5,28) (6,11) (6,29) (6,22) (6,27) (7,18) (7,30) (7,26) (7,19) (8,29) (8,22) (8,14) (8,17) (8,10) (8,27) (9,16) (9,11) (9,14) (9,10) (10,16) (10,27) (11,21) (11,17) (12,30) (12,13) (12,25) (13,18) (13,24) (13,25) (13,19) (14,21) (14,22) (15,24) (16,21) (16,22) (16,28) (17,29) (17,21) (18,20) (19,20) (19,30) (19,25) (21,27) (22,28) (22,27) (23,29) (25,26)\nIs there a path between node 31 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph445-2_9", + "image": "data/connectivity/graph_visual/hard/graph445.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,25) (0,13) (0,7) (0,20) (0,19) (0,10) (1,20) (1,19) (1,31) (1,24) (1,9) (1,3) (2,25) (2,13) (2,22) (2,31) (2,14) (2,24) (2,4) (2,30) (2,3) (2,5) (2,10) (3,6) (3,14) (3,18) (3,30) (4,13) (4,24) (4,21) (4,30) (4,5) (5,12) (5,31) (5,14) (6,20) (6,12) (6,9) (6,27) (7,13) (7,18) (7,10) (8,28) (8,32) (8,23) (8,17) (8,16) (8,26) (9,25) (9,20) (9,12) (9,19) (9,14) (10,13) (10,19) (10,24) (10,21) (10,30) (10,27) (11,15) (11,29) (11,32) (11,23) (11,26) (12,25) (12,22) (12,31) (12,30) (13,20) (13,14) (13,24) (13,30) (14,25) (14,24) (15,29) (15,32) (15,26) (17,23) (17,26) (18,24) (18,30) (19,25) (19,21) (19,30) (19,27) (20,31) (21,25) (21,30) (22,24) (23,28) (23,32) (25,30) (26,28) (26,32) (27,31)\nIs there a path between node 2 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph161-2_22", + "image": "data/connectivity/graph_visual/hard/graph161.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,13) (0,10) (0,15) (0,22) (1,5) (1,18) (1,10) (1,12) (1,22) (2,5) (2,24) (2,7) (3,14) (4,20) (5,13) (5,7) (5,12) (7,27) (7,20) (7,26) (7,24) (7,22) (9,19) (9,23) (10,18) (10,27) (10,26) (10,16) (11,21) (11,14) (12,20) (12,26) (12,24) (12,17) (13,20) (13,16) (15,16) (16,18) (17,20) (17,26) (18,26) (18,22) (19,28) (20,22) (22,27) (24,26)\nIs there a path between node 2 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph278-7_3", + "image": "data/connectivity/graph_visual/hard/graph278.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,10) (0,1) (0,15) (0,17) (0,12) (0,8) (1,16) (1,10) (1,18) (1,15) (1,2) (1,17) (1,28) (2,12) (2,8) (3,29) (3,24) (3,25) (3,6) (3,27) (3,19) (3,11) (3,4) (3,5) (4,9) (4,30) (4,22) (4,11) (5,29) (5,24) (5,23) (5,9) (5,25) (5,30) (5,6) (5,22) (5,19) (5,11) (6,29) (6,24) (6,23) (6,25) (6,30) (6,27) (6,22) (6,11) (7,20) (7,21) (7,13) (7,26) (7,14) (8,16) (8,10) (8,18) (8,15) (8,17) (8,12) (8,28) (9,29) (9,23) (9,30) (9,27) (9,22) (9,19) (10,16) (10,18) (10,15) (10,17) (10,12) (10,28) (11,29) (11,25) (11,22) (12,16) (12,15) (12,17) (13,26) (13,14) (14,20) (14,21) (15,16) (15,18) (15,28) (16,18) (16,17) (16,28) (17,18) (17,28) (18,28) (19,29) (19,23) (19,25) (19,30) (19,22) (20,21) (22,29) (22,24) (22,25) (22,30) (23,24) (23,25) (23,27) (24,25) (25,29) (25,30) (25,27) (27,29) (29,30)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph640-22_15", + "image": "data/connectivity/graph_visual/hard/graph640.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,23) (0,29) (0,27) (0,21) (1,2) (1,8) (1,26) (2,5) (2,8) (2,26) (3,30) (3,16) (3,18) (3,20) (3,4) (3,22) (3,17) (3,32) (3,10) (3,13) (3,31) (4,30) (4,16) (4,12) (4,18) (4,20) (4,10) (4,15) (4,13) (4,31) (4,24) (5,8) (6,14) (6,23) (6,29) (6,27) (6,21) (7,16) (7,12) (7,18) (7,22) (7,17) (7,32) (7,34) (7,15) (7,13) (7,31) (7,24) (9,33) (10,30) (10,16) (10,12) (10,18) (10,22) (10,32) (10,34) (10,15) (11,14) (11,23) (11,29) (11,27) (11,19) (11,28) (12,16) (12,18) (12,20) (12,17) (12,34) (12,15) (12,13) (12,31) (12,24) (13,30) (13,16) (13,17) (13,32) (13,15) (13,24) (14,25) (14,29) (14,27) (14,28) (14,21) (15,30) (15,16) (15,18) (15,20) (15,17) (15,32) (15,34) (15,31) (16,30) (16,22) (16,17) (16,32) (16,31) (17,18) (17,22) (17,32) (17,34) (17,31) (18,30) (18,20) (18,22) (18,32) (18,24) (19,23) (19,28) (19,21) (20,30) (20,22) (20,32) (20,34) (20,31) (20,24) (21,25) (21,23) (21,29) (22,31) (22,24) (23,25) (23,27) (23,28) (24,32) (24,34) (25,29) (25,27) (25,28) (28,29) (30,32) (30,34) (31,32) (31,34) (32,34)\nIs there a path between node 22 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph93-17_16", + "image": "data/connectivity/graph_visual/hard/graph93.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,19) (0,18) (0,16) (0,13) (0,4) (0,8) (0,10) (0,22) (1,2) (2,7) (3,19) (3,18) (3,12) (3,20) (3,10) (4,11) (4,14) (4,5) (4,20) (4,8) (5,11) (5,14) (5,18) (5,16) (5,13) (5,12) (6,19) (6,11) (6,12) (6,20) (6,8) (7,26) (8,24) (8,14) (8,18) (8,25) (9,17) (10,15) (10,27) (10,21) (10,18) (10,13) (10,12) (10,20) (11,27) (11,21) (11,13) (11,12) (11,25) (12,24) (12,16) (12,25) (13,24) (13,27) (13,25) (13,20) (13,22) (14,16) (14,22) (15,20) (16,25) (17,26) (17,23) (18,27) (19,25) (19,20) (20,24) (20,25) (20,22) (21,27) (22,25) (23,26) (25,27)\nIs there a path between node 17 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph350-14_25", + "image": "data/connectivity/graph_visual/hard/graph350.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,21) (0,2) (1,19) (1,26) (2,27) (2,9) (3,31) (3,4) (3,25) (3,11) (4,31) (4,6) (4,20) (4,5) (4,10) (4,25) (4,24) (5,31) (5,21) (6,20) (6,21) (6,10) (6,18) (6,11) (6,24) (7,15) (7,17) (8,27) (8,11) (8,9) (9,18) (10,28) (10,16) (10,24) (11,28) (13,22) (13,17) (15,17) (16,21) (16,27) (17,26) (18,21) (18,25) (18,28) (18,24) (20,31) (21,28) (24,29) (24,27) (27,31) (28,31)\nIs there a path between node 14 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph458-27_29", + "image": "data/connectivity/graph_visual/hard/graph458.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,32) (0,6) (0,21) (1,7) (2,18) (3,17) (3,23) (4,27) (4,7) (4,18) (5,27) (6,12) (7,27) (8,28) (8,26) (9,29) (9,31) (10,30) (10,16) (10,25) (10,12) (13,18) (14,30) (14,32) (14,15) (15,19) (15,32) (15,25) (16,19) (16,30) (16,25) (16,21) (17,28) (17,29) (21,30) (21,25) (23,28) (23,29) (26,29) (26,31) (30,32)\nIs there a path between node 27 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph20-10_1", + "image": "data/connectivity/graph_visual/hard/graph20.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,5) (0,14) (0,23) (1,10) (1,6) (1,3) (1,22) (2,16) (2,12) (3,8) (3,14) (3,22) (4,21) (4,25) (6,7) (6,18) (6,14) (6,15) (6,22) (7,18) (7,22) (8,10) (8,23) (11,16) (11,21) (12,17) (12,21) (12,25) (13,20) (14,20) (14,22) (15,18) (16,21) (16,25) (17,21) (19,21) (20,23) (21,25)\nIs there a path between node 10 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph404-29_18", + "image": "data/connectivity/graph_visual/hard/graph404.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,31) (0,26) (0,2) (0,22) (0,1) (0,13) (0,16) (0,18) (0,30) (0,14) (0,21) (1,31) (1,4) (1,26) (1,2) (1,22) (1,7) (1,16) (1,18) (1,11) (1,29) (1,30) (1,23) (1,14) (1,10) (1,32) (1,27) (1,12) (1,21) (2,31) (2,4) (2,26) (2,22) (2,7) (2,13) (2,16) (2,18) (2,11) (2,29) (2,30) (2,23) (2,14) (2,32) (2,12) (4,26) (4,7) (4,16) (4,18) (4,11) (4,29) (4,23) (4,14) (4,10) (4,12) (4,21) (5,17) (5,28) (5,6) (5,15) (5,25) (5,20) (5,8) (6,24) (6,25) (6,20) (6,8) (7,26) (7,18) (7,11) (7,29) (7,23) (7,14) (7,10) (7,32) (7,27) (7,12) (7,21) (8,17) (8,19) (8,28) (8,9) (8,15) (8,24) (9,17) (9,19) (9,28) (9,15) (9,24) (9,25) (9,20) (10,26) (10,22) (10,16) (10,11) (10,29) (10,30) (10,23) (10,14) (10,32) (10,27) (10,12) (11,31) (11,26) (11,22) (11,13) (11,16) (11,18) (11,30) (11,23) (11,14) (11,32) (12,26) (12,13) (12,16) (12,18) (12,29) (12,30) (12,23) (12,14) (12,32) (12,27) (12,21) (13,31) (13,18) (13,29) (13,30) (13,32) (13,21) (14,31) (14,26) (14,22) (14,16) (14,18) (14,29) (14,30) (14,23) (14,32) (14,27) (15,19) (15,28) (15,20) (16,31) (16,22) (16,29) (16,30) (16,23) (16,32) (16,27) (17,28) (17,20) (18,31) (18,22) (18,29) (18,23) (18,32) (18,27) (18,21) (19,28) (19,24) (19,20) (20,28) (20,24) (20,25) (21,22) (21,30) (21,32) (21,27) (22,31) (22,26) (22,29) (22,30) (22,23) (22,32) (22,27) (23,31) (23,30) (23,32) (23,27) (24,28) (24,25) (26,31) (26,30) (26,32) (26,27) (27,31) (27,29) (29,30) (29,32) (30,31) (31,32)\nIs there a path between node 29 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph630-3_12", + "image": "data/connectivity/graph_visual/hard/graph630.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,30) (1,27) (1,11) (2,17) (2,15) (2,32) (3,24) (3,15) (3,10) (3,25) (3,32) (4,21) (4,12) (4,27) (4,8) (5,9) (5,34) (6,30) (6,11) (6,8) (7,29) (7,24) (7,15) (7,14) (8,30) (8,11) (10,19) (10,14) (11,16) (11,31) (11,21) (11,27) (11,23) (12,27) (13,25) (13,20) (14,17) (15,29) (15,24) (15,32) (15,20) (16,31) (17,29) (17,24) (17,19) (17,25) (17,20) (19,24) (19,25) (19,20) (20,32) (21,27) (21,23) (23,31) (24,32) (26,28) (27,30) (29,32)\nIs there a path between node 3 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph624-29_1", + "image": "data/connectivity/graph_visual/hard/graph624.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,16) (0,7) (0,10) (0,15) (1,22) (1,11) (1,34) (1,29) (1,14) (2,27) (2,8) (2,32) (2,28) (2,9) (2,21) (2,4) (3,29) (3,20) (3,24) (4,27) (4,6) (4,28) (4,33) (4,15) (5,25) (5,26) (6,8) (6,7) (6,9) (6,18) (7,16) (7,32) (7,10) (7,33) (7,18) (7,15) (8,32) (8,10) (8,9) (8,18) (9,27) (9,16) (9,28) (9,33) (9,15) (10,15) (11,22) (11,30) (11,14) (11,12) (12,30) (12,29) (12,20) (12,31) (14,17) (14,29) (16,33) (17,30) (17,29) (18,27) (18,28) (18,33) (19,25) (20,22) (20,34) (20,24) (21,28) (22,30) (22,24) (23,24) (24,29)\nIs there a path between node 29 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph198-24_9", + "image": "data/connectivity/graph_visual/hard/graph198.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,20) (0,29) (0,25) (0,15) (0,10) (0,23) (0,1) (0,13) (1,22) (1,24) (1,10) (1,6) (2,27) (2,26) (2,3) (3,12) (3,27) (3,26) (3,9) (3,21) (3,8) (4,14) (4,19) (4,7) (4,17) (4,18) (4,5) (5,19) (5,7) (5,17) (6,11) (6,20) (6,24) (6,25) (6,15) (6,23) (7,19) (7,16) (7,18) (8,12) (8,28) (8,26) (8,9) (9,12) (9,28) (10,15) (11,24) (11,29) (11,25) (11,23) (11,13) (12,27) (12,21) (13,22) (13,20) (13,24) (13,29) (13,23) (14,19) (14,17) (14,16) (14,18) (15,22) (15,20) (15,24) (15,29) (15,25) (15,23) (16,17) (16,18) (17,19) (17,18) (18,19) (20,22) (20,24) (20,29) (20,25) (21,28) (21,26) (22,25) (23,24) (26,28) (26,27) (27,28)\nIs there a path between node 24 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph400-29_1", + "image": "data/connectivity/graph_visual/hard/graph400.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,2) (0,31) (0,22) (0,30) (0,29) (0,8) (0,21) (0,13) (0,24) (0,3) (0,23) (0,11) (0,4) (0,14) (0,32) (0,27) (1,16) (1,9) (1,12) (1,19) (1,28) (1,20) (1,10) (2,31) (2,22) (2,26) (2,8) (2,6) (2,18) (2,24) (2,5) (2,3) (2,23) (2,11) (2,4) (2,14) (2,17) (2,27) (3,31) (3,22) (3,26) (3,30) (3,8) (3,13) (3,7) (3,18) (3,5) (3,23) (3,14) (3,17) (3,32) (3,27) (4,29) (4,8) (4,21) (4,6) (4,13) (4,7) (4,11) (4,14) (4,17) (4,32) (4,27) (5,22) (5,29) (5,8) (5,21) (5,13) (5,7) (5,18) (5,24) (5,23) (5,11) (5,17) (5,32) (6,31) (6,30) (6,8) (6,21) (6,13) (6,7) (6,18) (6,24) (6,11) (6,32) (6,27) (7,31) (7,26) (7,30) (7,29) (7,8) (7,21) (7,13) (7,24) (7,11) (7,32) (7,27) (8,31) (8,22) (8,26) (8,30) (8,29) (8,13) (8,18) (8,24) (8,23) (8,14) (8,17) (8,32) (8,27) (9,16) (9,12) (9,19) (9,28) (9,15) (9,20) (9,10) (10,16) (10,25) (10,12) (10,19) (11,31) (11,22) (11,26) (11,29) (11,21) (11,13) (11,18) (11,24) (11,23) (11,14) (11,17) (11,32) (12,25) (12,19) (12,15) (12,20) (13,22) (13,30) (13,29) (13,18) (13,24) (13,23) (13,14) (13,17) (13,32) (14,31) (14,22) (14,26) (14,30) (14,21) (14,18) (14,24) (14,17) (14,32) (14,27) (15,16) (15,25) (15,28) (15,20) (16,19) (17,30) (17,29) (17,21) (17,18) (17,23) (17,32) (17,27) (18,31) (18,22) (18,26) (18,29) (18,21) (18,24) (18,32) (18,27) (19,28) (19,20) (20,25) (20,28) (21,31) (21,30) (21,29) (21,24) (21,23) (22,31) (22,26) (22,24) (22,23) (23,26) (23,30) (23,32) (23,27) (24,31) (24,26) (24,30) (24,29) (24,32) (24,27) (26,29) (26,32) (27,31) (27,30) (27,32) (29,31) (29,30) (30,31) (30,32) (31,32)\nIs there a path between node 29 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph503-3_8", + "image": "data/connectivity/graph_visual/hard/graph503.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,29) (0,30) (0,27) (0,33) (0,11) (0,5) (0,12) (0,20) (0,7) (0,28) (0,17) (0,6) (0,4) (0,32) (0,13) (0,3) (0,22) (0,31) (1,25) (1,29) (1,30) (1,27) (1,33) (1,2) (1,5) (1,12) (1,20) (1,28) (1,18) (1,16) (1,24) (1,6) (1,13) (1,3) (1,22) (1,31) (2,25) (2,23) (2,29) (2,30) (2,27) (2,33) (2,11) (2,5) (2,12) (2,7) (2,18) (2,16) (2,17) (2,24) (2,13) (2,22) (2,15) (3,25) (3,23) (3,29) (3,30) (3,12) (3,7) (3,18) (3,16) (3,24) (3,4) (3,13) (3,22) (3,31) (4,23) (4,29) (4,27) (4,33) (4,11) (4,5) (4,7) (4,18) (4,24) (4,32) (4,15) (4,31) (5,25) (5,23) (5,30) (5,27) (5,33) (5,11) (5,12) (5,20) (5,7) (5,28) (5,24) (5,6) (5,32) (5,13) (5,22) (5,15) (5,31) (6,25) (6,23) (6,30) (6,27) (6,33) (6,12) (6,20) (6,7) (6,18) (6,24) (6,32) (6,13) (7,25) (7,30) (7,27) (7,33) (7,20) (7,28) (7,18) (7,24) (7,32) (7,13) (7,22) (7,15) (7,31) (8,14) (8,26) (8,19) (9,14) (9,26) (9,19) (9,21) (9,10) (10,14) (10,26) (10,19) (11,23) (11,29) (11,30) (11,27) (11,33) (11,20) (11,18) (11,16) (11,17) (11,32) (11,13) (11,22) (11,15) (11,31) (12,25) (12,23) (12,29) (12,27) (12,33) (12,28) (12,16) (12,24) (12,13) (12,22) (12,15) (12,31) (13,25) (13,23) (13,29) (13,27) (13,33) (13,20) (13,28) (13,18) (13,16) (13,17) (13,24) (13,32) (13,15) (13,31) (14,26) (15,25) (15,23) (15,29) (15,30) (15,33) (15,16) (15,17) (15,24) (15,22) (15,31) (16,25) (16,23) (16,29) (16,30) (16,27) (16,28) (16,17) (16,24) (16,32) (16,22) (17,25) (17,23) (17,29) (17,33) (17,20) (17,18) (17,24) (17,31) (18,25) (18,29) (18,30) (18,33) (18,28) (18,24) (18,31) (20,25) (20,23) (20,30) (20,24) (20,32) (20,22) (20,31) (21,26) (22,25) (22,29) (22,30) (22,28) (22,24) (23,25) (23,29) (23,27) (23,28) (23,24) (23,32) (24,25) (24,29) (24,27) (24,33) (24,28) (24,31) (25,29) (25,30) (25,27) (25,28) (25,32) (25,31) (27,29) (27,30) (27,33) (27,28) (28,29) (28,30) (28,33) (28,32) (28,31) (29,30) (29,33) (29,32) (29,31) (30,33) (30,32) (30,31) (31,33) (31,32) (32,33)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph256-8_14", + "image": "data/connectivity/graph_visual/hard/graph256.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,16) (0,13) (0,1) (0,18) (0,12) (0,23) (1,20) (1,30) (1,16) (1,27) (1,15) (1,7) (1,18) (1,11) (1,23) (2,3) (3,28) (4,27) (4,15) (4,8) (4,11) (4,25) (5,26) (5,6) (5,21) (5,25) (6,9) (6,26) (6,30) (6,24) (6,13) (6,15) (6,7) (7,18) (7,23) (8,26) (8,15) (8,14) (8,22) (8,12) (9,26) (9,30) (9,16) (9,17) (9,15) (9,14) (9,12) (9,23) (11,30) (11,16) (11,17) (11,27) (11,15) (11,14) (11,22) (11,12) (12,16) (12,15) (12,18) (12,22) (12,19) (12,25) (12,23) (13,16) (13,27) (13,14) (13,18) (13,23) (14,30) (14,16) (14,27) (14,22) (15,30) (15,17) (15,18) (15,19) (15,23) (16,21) (17,24) (17,25) (18,22) (19,30) (19,27) (19,23) (20,26) (21,24) (21,27) (21,25) (21,23) (22,27) (23,25) (24,26) (24,25) (25,30) (28,29)\nIs there a path between node 8 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph213-19_23", + "image": "data/connectivity/graph_visual/hard/graph213.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,26) (0,1) (0,27) (0,11) (1,27) (1,17) (1,8) (1,20) (1,28) (1,11) (1,18) (1,12) (1,22) (2,24) (2,13) (2,3) (2,7) (3,13) (3,10) (3,4) (3,14) (4,15) (4,21) (4,24) (4,13) (4,10) (5,15) (5,21) (5,24) (5,7) (6,27) (6,29) (6,8) (6,20) (6,9) (6,28) (6,18) (6,25) (7,13) (7,16) (8,27) (8,28) (8,18) (9,17) (9,28) (9,25) (10,16) (11,28) (11,18) (11,25) (12,27) (12,17) (12,28) (12,19) (13,15) (14,15) (14,24) (14,23) (15,16) (15,23) (17,19) (18,25) (18,19) (19,20) (19,28) (19,25) (20,27) (23,24) (25,29) (25,28) (26,29) (28,29)\nIs there a path between node 19 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph228-23_7", + "image": "data/connectivity/graph_visual/hard/graph228.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,18) (0,15) (0,8) (0,20) (1,22) (1,4) (1,25) (1,11) (1,7) (1,24) (1,28) (1,21) (2,23) (2,27) (2,18) (2,16) (2,3) (2,8) (2,5) (2,20) (3,27) (3,16) (3,12) (3,15) (3,8) (3,5) (4,29) (4,22) (4,6) (4,10) (4,17) (4,14) (4,25) (4,11) (4,7) (4,24) (4,28) (4,21) (4,26) (5,23) (5,27) (5,18) (5,16) (5,12) (5,15) (5,8) (5,20) (6,29) (6,22) (6,19) (6,10) (6,25) (6,9) (6,7) (6,13) (6,24) (6,28) (6,26) (7,10) (7,17) (7,14) (7,25) (7,9) (7,13) (7,24) (7,28) (7,21) (7,26) (8,23) (8,18) (8,12) (8,20) (9,29) (9,22) (9,19) (9,10) (9,25) (9,11) (9,13) (9,24) (9,28) (9,26) (10,29) (10,22) (10,19) (10,14) (10,25) (10,11) (10,13) (10,24) (10,26) (11,22) (11,19) (11,17) (11,25) (11,13) (11,24) (11,21) (11,26) (12,23) (12,27) (12,18) (12,16) (12,15) (13,29) (13,19) (13,17) (13,14) (13,25) (13,28) (13,21) (13,26) (14,19) (14,17) (14,25) (14,28) (14,21) (14,26) (15,23) (15,27) (15,18) (15,16) (15,20) (16,23) (16,18) (16,20) (17,22) (17,19) (17,25) (17,28) (17,26) (18,23) (18,27) (19,22) (19,25) (19,28) (19,26) (21,29) (21,25) (21,24) (21,28) (21,26) (22,29) (22,25) (22,28) (22,26) (23,27) (24,29) (24,25) (24,28) (24,26) (25,29) (25,28) (25,26) (26,29) (26,28)\nIs there a path between node 23 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph57-9_11", + "image": "data/connectivity/graph_visual/hard/graph57.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,19) (0,15) (0,8) (0,10) (0,6) (0,16) (0,21) (0,22) (0,11) (0,2) (0,5) (0,7) (0,24) (0,18) (0,26) (0,14) (0,4) (1,12) (1,19) (1,3) (1,15) (1,8) (1,10) (1,6) (1,16) (1,21) (1,22) (1,11) (1,2) (1,5) (1,20) (1,7) (1,24) (1,26) (1,14) (2,12) (2,19) (2,15) (2,10) (2,6) (2,21) (2,22) (2,11) (2,5) (2,20) (2,7) (2,24) (2,18) (2,26) (2,14) (2,4) (3,12) (3,19) (3,15) (3,8) (3,10) (3,6) (3,16) (3,21) (3,11) (3,5) (3,20) (3,7) (3,24) (3,18) (3,26) (3,4) (4,25) (4,19) (4,15) (4,10) (4,6) (4,16) (4,22) (4,11) (4,20) (4,7) (4,18) (5,25) (5,19) (5,15) (5,8) (5,6) (5,16) (5,21) (5,22) (5,11) (5,24) (5,18) (5,26) (5,14) (6,25) (6,19) (6,8) (6,16) (6,21) (6,22) (6,20) (6,7) (6,24) (6,18) (6,14) (7,12) (7,19) (7,15) (7,10) (7,16) (7,21) (7,11) (7,20) (7,18) (7,26) (7,14) (8,12) (8,25) (8,15) (8,10) (8,16) (8,21) (8,11) (8,20) (8,18) (8,26) (9,17) (9,13) (9,23) (10,12) (10,25) (10,19) (10,15) (10,16) (10,22) (10,11) (10,18) (10,26) (10,14) (11,12) (11,25) (11,19) (11,16) (11,22) (11,20) (11,24) (11,18) (11,26) (11,14) (12,19) (12,15) (12,16) (12,21) (12,20) (12,26) (13,17) (13,23) (14,19) (14,16) (14,21) (14,20) (14,24) (14,18) (14,26) (15,25) (15,19) (15,22) (15,24) (15,18) (15,26) (16,21) (16,22) (16,18) (17,23) (18,25) (18,19) (18,21) (18,22) (18,20) (18,24) (18,26) (19,25) (19,21) (19,20) (19,24) (19,26) (20,25) (20,24) (21,22) (21,24) (21,26) (22,24) (22,26) (24,25) (24,26) (25,26)\nIs there a path between node 9 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph542-8_12", + "image": "data/connectivity/graph_visual/hard/graph542.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,19) (0,10) (0,11) (0,4) (0,22) (0,30) (0,5) (0,31) (0,14) (0,12) (1,8) (1,11) (1,4) (1,22) (1,33) (1,5) (1,9) (1,14) (1,12) (2,13) (2,26) (2,27) (2,28) (2,18) (2,29) (2,24) (2,3) (2,17) (2,25) (3,20) (3,15) (3,23) (3,28) (3,18) (3,29) (3,32) (3,24) (3,7) (3,21) (3,17) (3,25) (4,8) (4,10) (4,22) (4,33) (4,9) (4,31) (5,8) (5,19) (5,11) (5,33) (5,9) (5,31) (5,14) (5,12) (6,23) (6,27) (6,28) (6,18) (6,29) (6,32) (6,24) (6,7) (6,21) (6,25) (7,20) (7,13) (7,26) (7,23) (7,28) (7,18) (7,21) (7,17) (7,25) (8,19) (8,22) (8,33) (8,30) (8,31) (8,14) (8,12) (9,19) (9,10) (9,11) (9,22) (9,30) (9,31) (10,19) (10,11) (10,22) (10,30) (10,31) (10,14) (11,22) (11,31) (11,12) (12,19) (12,30) (12,14) (13,20) (13,26) (13,15) (13,23) (13,27) (13,28) (13,29) (13,32) (13,24) (14,19) (14,22) (14,33) (15,20) (15,23) (15,27) (15,18) (15,29) (15,32) (15,24) (15,17) (17,26) (17,23) (17,28) (17,18) (17,29) (17,32) (17,24) (17,21) (17,25) (18,20) (18,29) (19,33) (19,30) (19,31) (20,26) (20,23) (20,27) (20,28) (20,25) (21,23) (21,27) (21,28) (21,29) (21,32) (21,24) (21,25) (22,33) (22,30) (23,27) (23,28) (23,29) (23,32) (23,25) (24,26) (24,27) (24,32) (25,27) (25,28) (25,29) (26,27) (26,28) (26,32) (27,28) (27,29) (27,32) (29,32) (30,33) (30,31) (31,33)\nIs there a path between node 8 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph222-29_20", + "image": "data/connectivity/graph_visual/hard/graph222.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,2) (0,11) (1,20) (1,26) (1,8) (1,14) (1,16) (1,5) (1,18) (1,15) (1,17) (1,10) (1,22) (1,27) (1,24) (1,28) (1,29) (2,11) (3,9) (3,21) (3,12) (3,13) (4,25) (4,26) (4,8) (4,14) (4,6) (4,23) (4,16) (4,5) (4,18) (4,15) (4,17) (4,19) (4,10) (4,27) (4,24) (4,7) (5,20) (5,26) (5,14) (5,6) (5,23) (5,16) (5,15) (5,17) (5,19) (5,22) (5,24) (5,28) (5,29) (6,26) (6,8) (6,14) (6,23) (6,18) (6,15) (6,19) (6,10) (6,22) (6,27) (6,28) (6,29) (6,7) (7,25) (7,26) (7,14) (7,16) (7,18) (7,22) (7,27) (7,28) (8,25) (8,20) (8,26) (8,14) (8,23) (8,16) (8,18) (8,17) (8,10) (8,27) (8,24) (8,28) (8,29) (9,21) (9,12) (9,13) (10,25) (10,20) (10,26) (10,14) (10,23) (10,18) (10,15) (10,17) (10,19) (10,22) (10,24) (10,28) (10,29) (12,21) (12,13) (13,21) (14,25) (14,23) (14,16) (14,18) (14,15) (14,17) (14,22) (14,27) (14,24) (14,28) (15,25) (15,20) (15,26) (15,16) (15,18) (15,22) (15,27) (15,28) (15,29) (16,25) (16,20) (16,26) (16,23) (16,18) (16,19) (16,22) (16,27) (16,24) (17,25) (17,26) (17,18) (17,24) (18,25) (18,20) (18,26) (18,23) (18,22) (18,27) (18,28) (18,29) (19,25) (19,20) (19,23) (19,22) (19,27) (19,24) (19,28) (19,29) (20,25) (20,22) (20,27) (20,28) (22,25) (22,26) (22,23) (22,27) (22,28) (22,29) (23,27) (23,28) (23,29) (24,26) (24,29) (25,26) (25,27) (25,28) (26,27) (26,28) (26,29) (27,28) (27,29) (28,29)\nIs there a path between node 29 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph602-12_31", + "image": "data/connectivity/graph_visual/hard/graph602.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,7) (0,20) (0,27) (0,29) (0,26) (0,17) (0,3) (0,1) (0,16) (1,6) (1,7) (1,20) (1,19) (1,3) (1,33) (1,4) (2,27) (2,34) (2,26) (2,19) (2,17) (2,3) (2,21) (2,4) (3,6) (3,7) (3,11) (3,28) (3,29) (4,6) (4,28) (4,27) (4,29) (4,26) (4,19) (4,33) (4,23) (5,7) (5,11) (5,28) (5,19) (5,33) (5,16) (6,7) (6,28) (6,27) (6,26) (6,21) (7,34) (8,13) (8,12) (8,22) (8,15) (9,24) (9,12) (9,10) (10,25) (11,16) (11,23) (12,32) (12,18) (12,22) (12,15) (13,14) (14,18) (14,15) (15,30) (15,18) (16,27) (16,17) (16,23) (17,29) (17,19) (17,33) (17,23) (18,31) (18,24) (19,28) (19,27) (19,34) (19,29) (19,33) (19,21) (20,21) (21,26) (21,33) (22,30) (22,25) (25,30) (25,31) (26,28) (26,34) (26,29) (27,28) (30,32) (31,32)\nIs there a path between node 12 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph637-1_24", + "image": "data/connectivity/graph_visual/hard/graph637.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,24) (0,28) (0,32) (0,1) (0,27) (0,13) (0,9) (1,31) (1,8) (1,15) (1,14) (1,21) (1,28) (1,4) (1,6) (2,3) (2,11) (2,24) (2,31) (2,14) (2,32) (2,4) (2,27) (2,9) (3,22) (3,14) (3,32) (3,20) (3,9) (4,11) (4,24) (4,34) (4,7) (4,19) (4,18) (4,29) (4,28) (4,32) (4,27) (4,13) (5,22) (5,7) (5,18) (5,6) (5,27) (5,13) (6,15) (6,29) (6,27) (6,13) (7,22) (7,33) (7,24) (7,8) (7,19) (7,25) (7,18) (7,30) (7,21) (7,28) (8,11) (8,33) (8,14) (8,25) (8,30) (8,32) (9,27) (9,20) (10,23) (11,22) (11,31) (11,15) (11,19) (11,30) (11,29) (12,17) (13,22) (13,33) (13,19) (13,16) (13,30) (13,21) (13,20) (14,34) (14,30) (15,22) (15,33) (15,24) (15,31) (15,18) (15,30) (15,21) (15,27) (16,24) (16,30) (18,22) (18,33) (18,31) (18,32) (19,22) (19,26) (19,25) (19,28) (19,32) (20,33) (20,24) (20,28) (21,25) (21,30) (21,29) (22,31) (22,28) (22,27) (24,34) (24,31) (24,26) (25,26) (25,29) (25,28) (26,34) (26,30) (26,28) (27,34) (27,28) (28,31) (30,31) (31,34) (32,33) (33,34)\nIs there a path between node 1 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph118-2_19", + "image": "data/connectivity/graph_visual/hard/graph118.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,9) (0,22) (0,15) (0,19) (0,17) (1,12) (2,21) (3,7) (3,18) (3,16) (3,22) (3,24) (3,4) (3,17) (4,7) (4,6) (4,18) (4,13) (4,16) (4,19) (4,14) (4,5) (5,9) (5,7) (5,10) (5,13) (5,20) (5,26) (5,24) (5,17) (6,16) (6,22) (6,15) (6,19) (6,17) (7,10) (7,18) (7,20) (7,16) (7,26) (7,19) (7,14) (8,9) (8,10) (8,16) (8,23) (8,15) (8,19) (8,24) (8,17) (9,10) (9,16) (9,22) (9,17) (10,18) (10,22) (10,19) (10,17) (11,22) (11,26) (11,15) (11,17) (12,27) (13,18) (13,20) (13,25) (13,14) (14,16) (14,26) (14,25) (14,17) (15,18) (15,20) (15,26) (15,17) (16,18) (16,20) (16,26) (17,25) (19,23) (20,22) (22,26) (23,24)\nIs there a path between node 2 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph6-25_19", + "image": "data/connectivity/graph_visual/hard/graph6.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,7) (0,11) (0,22) (0,23) (1,11) (1,21) (1,2) (1,24) (1,8) (2,19) (2,13) (4,17) (4,5) (5,17) (5,10) (6,25) (7,11) (7,21) (7,24) (8,11) (8,21) (8,18) (8,13) (9,15) (9,10) (10,17) (10,15) (11,19) (11,16) (11,21) (11,22) (11,12) (13,16) (13,22) (13,23) (13,24) (14,19) (14,24) (16,24) (18,19) (18,21) (19,21) (19,23) (20,22) (21,22) (22,24)\nIs there a path between node 25 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph300-9_25", + "image": "data/connectivity/graph_visual/hard/graph300.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,22) (0,19) (0,24) (0,1) (0,2) (0,5) (0,28) (0,29) (0,31) (0,12) (0,23) (0,15) (0,11) (0,10) (1,6) (1,22) (1,19) (1,24) (1,2) (1,5) (1,28) (1,29) (1,31) (1,14) (1,23) (1,15) (1,11) (2,6) (2,22) (2,19) (2,5) (2,28) (2,18) (2,31) (2,14) (2,12) (2,15) (2,11) (2,10) (3,6) (3,19) (3,28) (3,29) (3,18) (3,23) (3,15) (3,10) (4,25) (4,20) (4,17) (4,30) (4,27) (4,9) (4,21) (4,26) (4,13) (4,7) (4,16) (5,6) (5,19) (5,24) (5,28) (5,18) (5,31) (5,14) (5,12) (5,23) (5,15) (5,11) (6,19) (6,24) (6,29) (6,18) (6,31) (6,12) (6,15) (6,10) (7,25) (7,20) (7,17) (7,30) (7,27) (7,9) (7,21) (7,26) (7,13) (7,16) (8,25) (8,9) (9,25) (9,20) (9,17) (9,30) (9,21) (9,26) (9,13) (9,16) (10,22) (10,24) (10,28) (10,29) (10,18) (10,31) (10,14) (10,15) (11,24) (11,28) (11,29) (11,18) (11,14) (11,12) (11,15) (12,29) (12,18) (12,31) (12,15) (13,20) (13,17) (13,30) (13,27) (13,21) (13,26) (13,16) (14,22) (14,19) (14,24) (14,18) (14,31) (14,23) (14,15) (15,22) (15,19) (15,24) (15,28) (15,29) (15,18) (16,20) (16,17) (16,30) (16,21) (16,26) (17,25) (17,20) (17,27) (18,22) (18,19) (18,24) (18,28) (18,29) (18,31) (19,22) (19,24) (19,28) (19,29) (19,23) (20,30) (20,27) (20,21) (20,26) (21,25) (21,30) (21,27) (21,26) (22,24) (22,28) (22,31) (22,23) (23,28) (23,29) (23,31) (24,28) (24,31) (25,30) (26,30) (26,27) (28,29) (28,31) (29,31)\nIs there a path between node 9 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph610-32_25", + "image": "data/connectivity/graph_visual/hard/graph610.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,31) (0,11) (0,18) (0,1) (1,28) (1,31) (1,13) (1,8) (1,5) (1,32) (1,34) (2,17) (3,14) (3,15) (3,24) (4,32) (4,34) (5,8) (5,9) (6,25) (6,10) (6,15) (6,7) (6,19) (7,14) (7,10) (7,16) (7,12) (7,21) (8,18) (9,31) (9,11) (9,34) (10,23) (10,29) (10,33) (10,16) (10,30) (11,20) (11,18) (12,23) (12,14) (12,25) (12,19) (12,24) (13,34) (14,25) (15,23) (15,25) (15,24) (16,23) (16,25) (16,29) (16,33) (16,17) (17,30) (17,21) (17,24) (18,22) (18,20) (19,24) (20,28) (20,32) (20,34) (22,26) (22,34) (23,25) (23,30) (24,33) (24,30) (25,29) (25,33) (26,27) (27,32) (28,32) (28,34) (29,30) (30,33) (31,32)\nIs there a path between node 32 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph67-26_8", + "image": "data/connectivity/graph_visual/hard/graph67.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,2) (0,12) (0,8) (1,23) (1,22) (1,26) (1,24) (1,13) (2,12) (2,20) (3,12) (3,20) (4,15) (4,10) (4,21) (5,11) (6,11) (7,10) (9,13) (10,15) (11,18) (11,19) (13,23) (13,26) (16,23) (16,26) (17,26) (22,26) (23,26) (23,24)\nIs there a path between node 26 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph235-0_26", + "image": "data/connectivity/graph_visual/hard/graph235.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,29) (0,27) (0,23) (0,4) (0,20) (0,17) (0,6) (1,5) (1,22) (1,11) (1,19) (1,24) (1,2) (1,15) (1,8) (1,30) (1,9) (1,28) (1,18) (2,5) (2,22) (2,24) (2,15) (2,8) (2,30) (2,9) (2,28) (2,18) (3,26) (3,13) (4,21) (4,29) (4,23) (4,20) (4,17) (4,6) (5,22) (5,19) (5,24) (5,14) (5,30) (5,28) (5,18) (6,21) (6,29) (6,27) (6,23) (6,20) (6,17) (7,26) (7,10) (7,13) (7,16) (7,12) (8,11) (8,24) (8,14) (8,30) (8,9) (8,28) (8,18) (9,22) (9,11) (9,19) (9,15) (9,28) (10,16) (10,12) (11,15) (11,30) (11,28) (11,18) (12,13) (12,16) (13,26) (13,16) (13,25) (14,22) (14,19) (14,15) (14,30) (15,19) (15,30) (15,28) (15,18) (16,26) (16,25) (17,29) (17,23) (18,19) (18,24) (18,28) (19,30) (19,28) (20,21) (20,27) (21,29) (21,27) (21,23) (22,24) (22,28) (23,27) (24,30) (24,28) (25,26) (28,30)\nIs there a path between node 0 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph495-4_5", + "image": "data/connectivity/graph_visual/hard/graph495.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,31) (0,22) (0,13) (0,7) (0,1) (0,30) (0,6) (0,15) (0,14) (0,12) (1,13) (1,4) (1,33) (1,24) (1,30) (1,27) (1,28) (1,25) (1,15) (1,21) (1,18) (1,5) (1,12) (3,31) (3,23) (3,27) (3,28) (3,25) (3,15) (4,33) (4,24) (4,25) (4,8) (5,33) (5,30) (5,27) (5,6) (5,15) (6,22) (6,11) (6,19) (6,33) (6,8) (7,31) (7,22) (7,19) (7,33) (7,24) (7,30) (7,18) (8,24) (8,18) (9,29) (11,15) (11,14) (11,18) (12,31) (12,13) (12,24) (12,27) (12,25) (13,24) (13,15) (14,22) (14,30) (14,21) (14,18) (15,31) (15,25) (16,20) (18,33) (19,23) (19,28) (19,21) (19,32) (20,26) (21,27) (21,32) (22,28) (22,25) (22,32) (23,30) (23,25) (23,32) (24,30) (24,28) (24,32) (25,31) (25,33) (27,33) (27,30) (27,28) (28,32) (30,31) (31,32)\nIs there a path between node 4 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph664-13_25", + "image": "data/connectivity/graph_visual/hard/graph664.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,14) (0,16) (0,33) (0,10) (0,7) (0,25) (1,28) (1,2) (1,12) (1,17) (1,13) (1,18) (1,32) (1,20) (1,16) (1,30) (1,7) (1,25) (1,31) (2,17) (2,18) (2,21) (2,33) (2,8) (2,11) (3,24) (3,6) (3,19) (4,6) (4,23) (4,34) (4,26) (5,24) (5,23) (5,26) (6,23) (6,19) (7,28) (7,13) (7,20) (7,22) (8,17) (8,20) (8,16) (8,22) (9,28) (9,18) (9,32) (9,16) (9,30) (9,11) (10,28) (10,14) (10,22) (10,25) (11,28) (11,12) (11,17) (11,18) (11,22) (11,33) (12,28) (12,15) (12,14) (12,16) (12,29) (12,33) (12,25) (13,30) (14,17) (14,18) (14,16) (14,22) (14,31) (15,18) (15,21) (15,16) (15,30) (16,28) (16,21) (16,20) (16,22) (16,31) (17,28) (17,18) (17,32) (17,20) (18,32) (18,21) (18,22) (18,30) (19,23) (19,34) (20,27) (20,25) (20,31) (21,32) (21,29) (21,33) (21,31) (22,31) (25,28) (25,32) (25,27) (26,34) (27,29) (30,31) (31,32) (31,33) (32,33)\nIs there a path between node 13 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph199-21_10", + "image": "data/connectivity/graph_visual/hard/graph199.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,13) (0,15) (0,27) (0,28) (0,14) (0,17) (0,2) (0,19) (0,5) (0,26) (0,29) (0,4) (0,22) (0,6) (0,11) (0,25) (1,12) (1,28) (1,14) (1,17) (1,10) (1,19) (1,20) (1,18) (1,23) (1,26) (1,29) (1,8) (1,4) (1,22) (1,3) (1,11) (1,25) (2,12) (2,13) (2,15) (2,7) (2,27) (2,28) (2,14) (2,10) (2,19) (2,5) (2,20) (2,18) (2,23) (2,26) (2,29) (2,8) (2,4) (2,22) (2,6) (2,3) (2,11) (2,25) (3,12) (3,27) (3,19) (3,20) (3,18) (3,23) (3,26) (3,29) (3,8) (3,4) (3,22) (3,6) (3,25) (4,12) (4,13) (4,10) (4,5) (4,20) (4,18) (4,26) (4,22) (4,6) (4,11) (4,25) (5,12) (5,15) (5,7) (5,28) (5,17) (5,10) (5,19) (5,20) (5,18) (5,26) (5,29) (5,8) (5,22) (6,12) (6,13) (6,15) (6,27) (6,28) (6,17) (6,10) (6,19) (6,20) (6,18) (6,23) (6,26) (6,25) (7,12) (7,13) (7,15) (7,27) (7,10) (7,23) (7,29) (7,8) (7,22) (7,11) (8,13) (8,15) (8,28) (8,14) (8,17) (8,10) (8,19) (8,20) (8,18) (8,23) (8,26) (8,22) (8,11) (9,16) (9,21) (10,12) (10,13) (10,15) (10,28) (10,17) (10,19) (10,20) (10,18) (10,23) (10,29) (10,11) (11,28) (11,14) (11,17) (11,19) (11,20) (11,18) (11,23) (11,26) (11,29) (11,22) (11,25) (12,13) (12,15) (12,28) (12,14) (12,17) (12,19) (12,20) (12,23) (12,26) (12,29) (12,22) (12,25) (13,15) (13,28) (13,17) (13,20) (13,23) (13,26) (13,29) (13,22) (14,15) (14,27) (14,28) (14,17) (14,19) (14,20) (14,23) (14,26) (14,29) (14,25) (15,27) (15,28) (15,17) (15,19) (15,20) (15,18) (15,26) (15,22) (15,25) (16,21) (17,27) (17,19) (17,20) (17,18) (17,23) (17,26) (17,29) (17,22) (18,27) (18,28) (18,23) (18,26) (18,22) (19,27) (19,28) (19,22) (19,25) (20,26) (20,29) (20,25) (21,24) (22,27) (22,26) (22,29) (22,25) (23,27) (23,28) (23,29) (23,25) (25,28) (25,29) (26,27) (26,28) (27,28) (28,29)\nIs there a path between node 21 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph629-20_26", + "image": "data/connectivity/graph_visual/hard/graph629.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,1) (0,28) (0,7) (0,32) (0,34) (0,29) (1,16) (1,9) (1,27) (1,4) (1,22) (1,34) (2,16) (2,28) (2,9) (2,5) (2,31) (2,22) (3,13) (3,17) (3,26) (3,12) (4,24) (4,11) (4,7) (4,5) (4,27) (4,22) (5,16) (5,9) (5,31) (5,23) (6,17) (6,12) (7,24) (7,32) (7,31) (7,23) (8,21) (9,28) (9,11) (11,31) (11,19) (11,23) (12,18) (12,17) (13,20) (13,26) (14,24) (14,32) (14,27) (14,19) (14,29) (15,30) (16,24) (16,23) (19,27) (20,33) (21,25) (22,32) (22,29) (23,28) (23,24) (23,27) (24,27) (24,31) (27,32) (27,34) (31,34)\nIs there a path between node 20 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph104-26_11", + "image": "data/connectivity/graph_visual/hard/graph104.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,27) (0,14) (0,21) (0,10) (0,18) (0,12) (1,20) (1,17) (1,9) (1,4) (1,5) (1,24) (1,3) (1,2) (1,16) (1,13) (2,20) (2,19) (2,6) (2,9) (2,4) (2,5) (2,8) (2,22) (2,24) (2,11) (2,3) (2,16) (2,13) (2,7) (3,20) (3,19) (3,9) (3,4) (3,5) (3,8) (3,24) (3,16) (3,13) (3,7) (4,19) (4,17) (4,6) (4,9) (4,5) (4,8) (4,22) (4,11) (4,16) (4,13) (4,7) (5,20) (5,19) (5,17) (5,6) (5,9) (5,8) (5,22) (5,24) (5,11) (5,13) (6,20) (6,19) (6,17) (6,9) (6,22) (6,24) (6,16) (6,7) (7,19) (7,17) (7,9) (7,8) (7,22) (7,24) (7,11) (7,13) (8,20) (8,17) (8,9) (8,24) (8,11) (8,16) (8,13) (9,20) (9,19) (9,24) (9,11) (9,13) (10,25) (10,15) (10,26) (10,27) (10,14) (10,21) (10,23) (10,12) (11,20) (11,17) (11,22) (11,24) (11,13) (12,15) (12,14) (12,18) (13,20) (13,17) (13,22) (13,24) (13,16) (14,25) (14,15) (14,26) (14,27) (14,23) (15,25) (15,26) (15,21) (15,18) (16,20) (16,22) (16,24) (17,20) (17,19) (18,25) (18,26) (18,27) (18,21) (18,23) (19,24) (20,22) (21,25) (21,27) (23,25) (23,26) (25,26) (25,27) (26,27)\nIs there a path between node 26 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph134-27_23", + "image": "data/connectivity/graph_visual/hard/graph134.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,16) (0,4) (1,27) (1,26) (1,10) (1,13) (1,12) (1,24) (1,19) (1,11) (1,7) (1,6) (1,14) (1,3) (1,18) (1,20) (2,4) (3,9) (3,27) (3,10) (3,21) (3,25) (3,13) (3,24) (3,15) (3,23) (3,19) (3,11) (3,7) (3,6) (3,14) (3,18) (5,9) (5,26) (5,22) (5,10) (5,13) (5,12) (5,15) (5,17) (5,23) (5,19) (5,11) (5,7) (5,6) (5,14) (6,27) (6,26) (6,10) (6,21) (6,25) (6,13) (6,12) (6,8) (6,17) (6,23) (6,19) (6,11) (6,7) (6,14) (6,18) (6,20) (7,9) (7,27) (7,22) (7,10) (7,21) (7,13) (7,12) (7,8) (7,24) (7,15) (7,17) (7,19) (7,11) (7,14) (8,9) (8,27) (8,22) (8,10) (8,21) (8,25) (8,13) (8,12) (8,15) (8,17) (8,23) (8,19) (8,11) (8,14) (8,18) (8,20) (9,27) (9,10) (9,21) (9,13) (9,12) (9,24) (9,15) (9,17) (9,23) (9,19) (9,11) (9,20) (10,27) (10,26) (10,22) (10,21) (10,25) (10,13) (10,24) (10,15) (10,17) (10,19) (10,11) (10,14) (11,27) (11,26) (11,22) (11,25) (11,13) (11,15) (11,17) (11,14) (11,18) (11,20) (12,27) (12,26) (12,22) (12,21) (12,13) (12,15) (12,17) (12,23) (12,19) (12,18) (12,20) (13,22) (13,21) (13,24) (13,15) (13,17) (13,23) (13,19) (13,14) (13,18) (13,20) (14,27) (14,26) (14,24) (14,15) (14,17) (14,23) (14,19) (14,20) (15,27) (15,22) (15,25) (15,24) (15,17) (15,23) (15,20) (17,22) (17,25) (17,23) (17,19) (17,18) (17,20) (18,26) (18,24) (18,23) (18,19) (19,26) (19,21) (19,25) (19,24) (19,23) (19,20) (20,27) (20,26) (20,21) (20,24) (20,23) (21,27) (21,22) (21,25) (21,24) (22,27) (22,26) (23,27) (23,26) (23,24) (25,27) (25,26)\nIs there a path between node 27 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph336-3_13", + "image": "data/connectivity/graph_visual/hard/graph336.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,22) (0,14) (0,4) (0,15) (0,20) (0,3) (0,18) (0,26) (1,7) (1,19) (1,6) (1,27) (1,11) (1,12) (1,31) (1,13) (1,24) (1,16) (1,10) (1,29) (2,7) (2,23) (2,6) (2,27) (2,17) (2,12) (2,28) (2,24) (2,10) (2,29) (2,21) (2,8) (3,14) (3,4) (3,20) (3,18) (3,26) (4,22) (4,14) (4,15) (4,20) (4,18) (4,26) (5,30) (5,25) (6,7) (6,27) (6,17) (6,11) (6,31) (6,13) (6,10) (6,8) (7,23) (7,27) (7,17) (7,11) (7,12) (7,31) (7,13) (7,24) (7,16) (7,10) (7,29) (7,8) (8,23) (8,17) (8,11) (8,12) (8,28) (8,31) (8,13) (8,24) (8,16) (8,29) (10,11) (10,12) (10,31) (10,24) (10,16) (10,29) (10,21) (11,23) (11,19) (11,27) (11,17) (11,12) (11,28) (11,13) (11,24) (12,23) (12,17) (12,28) (12,31) (12,16) (12,21) (13,23) (13,19) (13,27) (13,28) (13,31) (13,21) (14,22) (14,15) (14,18) (14,26) (15,20) (15,26) (16,23) (16,27) (16,17) (16,31) (16,24) (16,29) (16,21) (17,23) (17,19) (17,27) (17,28) (17,31) (17,24) (18,22) (18,26) (19,27) (19,31) (19,24) (19,29) (19,21) (20,22) (20,26) (21,27) (21,28) (21,31) (21,29) (22,26) (23,28) (23,31) (23,24) (23,29) (24,27) (24,31) (24,29) (25,30) (27,28) (28,31)\nIs there a path between node 3 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph347-21_20", + "image": "data/connectivity/graph_visual/hard/graph347.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,6) (0,15) (0,10) (0,16) (0,25) (1,13) (1,6) (1,3) (1,22) (1,31) (1,9) (1,4) (1,27) (1,29) (2,21) (2,28) (3,13) (3,6) (3,10) (3,26) (3,20) (3,16) (4,19) (4,23) (4,18) (4,27) (4,25) (4,14) (5,30) (5,28) (5,11) (6,19) (6,7) (6,31) (6,9) (6,25) (7,18) (7,26) (7,25) (7,14) (8,21) (9,19) (9,12) (9,15) (9,26) (9,27) (9,29) (10,19) (10,31) (10,16) (10,25) (10,24) (11,30) (11,28) (12,19) (12,13) (12,17) (12,22) (12,31) (12,20) (12,16) (12,29) (13,18) (13,26) (13,16) (13,27) (14,22) (14,23) (15,19) (15,18) (15,29) (16,19) (16,22) (16,23) (16,18) (16,27) (16,29) (17,19) (17,20) (17,29) (18,19) (18,22) (18,23) (18,26) (18,27) (18,25) (18,29) (19,23) (19,20) (19,24) (20,27) (20,24) (20,29) (21,30) (22,26) (22,27) (23,31) (23,26) (23,27) (23,29) (24,26) (24,27) (24,25) (25,31) (25,27)\nIs there a path between node 21 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph71-18_17", + "image": "data/connectivity/graph_visual/hard/graph71.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,7) (0,14) (0,16) (0,2) (0,26) (0,17) (0,9) (1,7) (1,14) (1,21) (1,16) (1,20) (1,2) (1,6) (1,8) (1,19) (1,11) (1,17) (2,13) (2,21) (2,22) (2,16) (2,3) (2,24) (2,6) (2,11) (3,13) (3,7) (3,25) (3,20) (3,24) (3,6) (3,23) (4,5) (4,16) (4,24) (4,6) (4,8) (4,19) (5,25) (5,15) (5,19) (6,13) (6,14) (6,21) (6,25) (6,22) (6,16) (6,24) (6,19) (6,23) (6,17) (7,22) (7,16) (7,8) (7,17) (7,9) (8,13) (8,15) (8,11) (8,23) (8,17) (8,9) (9,14) (9,25) (9,22) (9,16) (9,20) (9,15) (9,19) (9,11) (9,26) (10,18) (11,21) (11,16) (11,20) (11,24) (11,23) (11,17) (12,18) (13,22) (13,20) (13,24) (13,23) (14,21) (14,25) (14,22) (14,16) (14,20) (14,15) (14,19) (15,25) (15,19) (15,26) (15,17) (16,25) (16,19) (16,23) (16,26) (16,17) (17,20) (17,23) (17,26) (19,25) (19,20) (19,24) (20,22) (21,22) (22,23) (23,25)\nIs there a path between node 18 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph9-10_23", + "image": "data/connectivity/graph_visual/hard/graph9.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,2) (0,10) (0,13) (0,12) (0,9) (0,18) (0,24) (0,5) (0,20) (0,21) (0,7) (0,3) (0,23) (1,2) (1,13) (1,16) (1,12) (1,18) (1,24) (1,20) (1,4) (1,7) (1,3) (1,19) (1,23) (2,13) (2,16) (2,12) (2,9) (2,11) (2,18) (2,24) (2,5) (2,20) (2,4) (2,21) (2,7) (2,3) (2,23) (3,13) (3,16) (3,12) (3,9) (3,11) (3,24) (3,5) (3,20) (3,21) (3,7) (3,19) (3,23) (4,10) (4,16) (4,12) (4,11) (4,18) (4,24) (4,5) (4,20) (4,21) (4,7) (4,19) (4,23) (5,13) (5,12) (5,11) (5,18) (5,24) (5,20) (5,21) (5,7) (5,23) (6,15) (6,25) (6,22) (6,8) (7,13) (7,12) (7,9) (7,11) (7,18) (7,20) (7,21) (7,19) (8,17) (8,15) (8,22) (8,14) (9,10) (9,13) (9,16) (9,11) (9,18) (9,21) (9,19) (9,23) (10,13) (10,12) (10,11) (10,24) (10,20) (10,21) (10,19) (10,23) (11,13) (11,16) (11,24) (11,20) (11,21) (11,19) (11,23) (12,13) (12,16) (12,18) (12,24) (12,20) (12,21) (12,19) (12,23) (13,16) (13,24) (13,21) (13,23) (14,17) (14,15) (14,22) (15,17) (15,25) (15,22) (16,18) (16,24) (16,21) (16,23) (17,25) (17,22) (18,20) (18,21) (18,19) (18,23) (19,20) (19,23) (20,24) (20,21) (21,23) (22,25) (23,24)\nIs there a path between node 10 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph643-1_8", + "image": "data/connectivity/graph_visual/hard/graph643.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,19) (0,3) (0,23) (0,8) (0,1) (0,28) (0,27) (0,9) (0,11) (0,32) (1,3) (1,26) (1,8) (1,15) (1,28) (1,27) (1,9) (1,11) (1,32) (2,29) (2,20) (2,12) (2,5) (2,33) (2,6) (2,18) (2,21) (2,25) (2,31) (2,14) (2,24) (2,16) (3,19) (3,23) (3,26) (3,8) (3,34) (3,27) (3,11) (3,32) (3,30) (4,20) (4,12) (4,5) (4,6) (4,18) (4,21) (4,7) (4,25) (4,13) (4,14) (4,16) (4,22) (5,29) (5,20) (5,12) (5,6) (5,17) (5,7) (5,25) (5,31) (5,24) (5,22) (6,29) (6,12) (6,33) (6,17) (6,7) (6,25) (6,13) (6,31) (6,24) (6,16) (6,22) (7,29) (7,18) (7,13) (7,14) (7,24) (8,19) (8,23) (8,26) (8,28) (8,9) (8,11) (8,32) (8,30) (9,19) (9,26) (9,34) (9,15) (9,28) (9,27) (9,11) (9,32) (10,29) (10,12) (10,33) (10,21) (10,25) (10,13) (10,31) (10,14) (10,24) (10,16) (11,23) (11,26) (11,34) (11,15) (11,28) (11,27) (11,32) (12,29) (12,20) (12,33) (12,17) (12,18) (12,21) (12,25) (12,13) (12,24) (12,16) (12,22) (13,29) (13,20) (13,33) (13,17) (13,18) (13,25) (13,31) (13,24) (13,16) (14,20) (14,18) (14,21) (14,25) (14,31) (14,24) (14,16) (14,22) (15,19) (15,23) (15,34) (15,28) (15,27) (15,32) (15,30) (16,29) (16,20) (16,33) (16,17) (16,31) (16,24) (17,29) (17,33) (17,18) (17,21) (17,31) (17,24) (17,22) (18,29) (18,20) (18,25) (18,31) (18,24) (18,22) (19,26) (19,34) (19,28) (19,27) (19,32) (19,30) (20,21) (20,25) (20,31) (20,24) (20,22) (21,29) (21,33) (21,31) (21,24) (21,22) (22,29) (22,33) (22,25) (22,31) (22,24) (23,26) (23,28) (23,27) (23,30) (24,33) (24,25) (24,31) (25,29) (25,33) (25,31) (26,34) (26,28) (26,27) (26,30) (27,34) (27,30) (28,32) (28,30) (29,33) (29,31) (30,34) (30,32) (31,33) (32,34)\nIs there a path between node 1 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph66-26_8", + "image": "data/connectivity/graph_visual/hard/graph66.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,23) (0,10) (0,15) (0,1) (0,24) (1,17) (1,11) (1,23) (1,18) (1,13) (1,6) (1,24) (2,25) (3,21) (3,18) (3,10) (3,13) (3,20) (3,24) (5,21) (5,12) (5,23) (5,15) (5,6) (5,24) (6,7) (6,17) (6,13) (6,19) (6,24) (7,16) (7,15) (7,19) (7,24) (8,25) (8,26) (9,26) (10,13) (11,23) (12,21) (12,18) (13,17) (13,15) (13,22) (13,19) (15,20) (16,22) (17,18) (17,22) (19,20) (19,24) (20,21) (21,22) (23,24)\nIs there a path between node 26 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph360-3_12", + "image": "data/connectivity/graph_visual/hard/graph360.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,28) (0,24) (0,31) (0,30) (0,27) (0,20) (1,21) (1,6) (1,19) (1,12) (1,22) (1,4) (1,17) (1,13) (1,30) (2,23) (2,3) (2,14) (3,25) (4,5) (4,17) (4,27) (5,17) (5,31) (5,20) (6,26) (6,16) (6,28) (6,10) (6,19) (6,12) (6,22) (6,13) (7,21) (7,28) (7,19) (7,17) (7,13) (7,18) (7,27) (8,23) (8,11) (8,25) (10,26) (10,28) (10,22) (10,31) (10,18) (11,23) (12,30) (13,21) (13,19) (13,31) (15,26) (15,16) (15,17) (15,18) (15,20) (16,21) (16,28) (16,19) (16,30) (16,27) (16,20) (17,24) (17,22) (17,18) (18,22) (19,22) (19,31) (19,20) (20,28) (21,22) (21,31) (22,30) (24,31) (27,28) (28,31)\nIs there a path between node 3 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph625-26_6", + "image": "data/connectivity/graph_visual/hard/graph625.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,30) (0,9) (0,23) (0,3) (2,19) (2,6) (2,31) (2,21) (2,18) (2,11) (3,7) (3,10) (3,34) (3,27) (3,23) (4,16) (4,14) (4,21) (4,18) (4,11) (4,33) (5,17) (6,21) (7,15) (7,13) (7,9) (8,16) (8,31) (8,11) (9,10) (9,15) (9,26) (9,27) (9,23) (10,34) (10,13) (10,28) (11,16) (11,19) (11,31) (12,34) (12,13) (12,30) (12,27) (12,23) (13,26) (13,27) (13,28) (14,31) (14,21) (14,32) (15,27) (15,22) (16,19) (16,25) (17,20) (18,21) (18,33) (18,32) (19,29) (19,21) (19,32) (21,29) (21,25) (21,32) (22,24) (22,28) (23,30) (23,28) (24,34) (24,30) (24,28) (25,31) (26,30) (29,31) (29,33) (29,32) (30,34) (31,33)\nIs there a path between node 26 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph73-11_26", + "image": "data/connectivity/graph_visual/hard/graph73.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,7) (0,16) (0,14) (0,13) (0,25) (0,4) (0,19) (0,9) (0,10) (2,13) (2,15) (2,10) (3,18) (3,14) (3,25) (3,23) (3,15) (3,10) (3,24) (4,16) (4,23) (4,19) (4,15) (4,11) (5,21) (5,8) (5,26) (6,20) (6,19) (6,15) (6,10) (6,24) (7,20) (7,11) (8,21) (9,20) (9,22) (9,25) (9,11) (9,24) (10,17) (10,25) (11,17) (11,13) (11,23) (12,16) (12,14) (12,25) (12,15) (13,17) (13,25) (14,17) (14,16) (14,25) (14,15) (15,17) (15,16) (15,20) (15,24) (16,18) (16,17) (16,20) (16,22) (16,19) (17,23) (18,22) (18,23) (19,22) (19,25) (22,23) (24,25)\nIs there a path between node 11 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph431-13_18", + "image": "data/connectivity/graph_visual/hard/graph431.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,3) (0,7) (0,5) (0,9) (0,25) (0,26) (0,15) (0,22) (0,13) (0,31) (0,1) (0,20) (1,3) (1,7) (1,5) (1,28) (1,9) (1,15) (1,22) (1,31) (1,30) (2,16) (2,17) (2,6) (2,14) (2,21) (2,32) (2,24) (2,8) (2,27) (2,10) (2,29) (2,19) (3,23) (3,18) (3,5) (3,28) (3,9) (3,25) (3,20) (3,30) (4,16) (4,17) (4,14) (4,21) (4,32) (4,12) (4,24) (4,8) (4,27) (4,10) (4,29) (4,11) (4,19) (5,23) (5,18) (5,7) (5,28) (5,9) (5,25) (5,26) (5,15) (5,22) (5,20) (5,30) (6,17) (6,14) (6,32) (6,12) (6,24) (6,8) (6,27) (6,19) (7,18) (7,9) (7,25) (7,26) (7,22) (7,13) (7,31) (7,20) (8,16) (8,17) (8,14) (8,32) (8,24) (8,27) (8,29) (8,19) (9,23) (9,18) (9,28) (9,25) (9,15) (9,22) (9,13) (9,31) (9,20) (10,16) (10,17) (10,21) (10,32) (10,12) (10,19) (11,16) (11,14) (11,21) (11,12) (11,24) (11,27) (11,29) (11,19) (12,16) (12,17) (12,14) (12,32) (12,27) (12,29) (12,19) (13,23) (13,18) (13,26) (13,15) (13,20) (13,30) (14,16) (14,32) (14,24) (14,27) (14,19) (15,23) (15,18) (15,28) (15,25) (15,26) (15,22) (15,31) (15,20) (16,17) (16,21) (16,32) (16,29) (17,21) (17,32) (17,24) (17,27) (17,29) (17,19) (18,25) (18,26) (18,22) (18,31) (18,30) (19,21) (19,32) (19,24) (19,27) (19,29) (20,28) (20,25) (20,26) (20,22) (20,31) (21,32) (21,24) (21,27) (22,23) (22,28) (22,25) (22,30) (23,28) (23,31) (23,30) (24,32) (24,29) (25,28) (25,26) (26,28) (26,30) (27,32) (27,29) (28,31) (28,30) (29,32)\nIs there a path between node 13 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph298-24_23", + "image": "data/connectivity/graph_visual/hard/graph298.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,31) (0,27) (0,3) (0,21) (0,19) (0,23) (0,18) (0,29) (0,16) (0,24) (1,25) (1,5) (1,6) (2,12) (2,10) (2,17) (2,13) (3,4) (3,31) (3,27) (3,21) (3,15) (3,23) (3,18) (3,16) (3,24) (4,27) (4,15) (4,23) (4,18) (4,29) (4,22) (4,16) (4,24) (5,25) (5,6) (6,25) (7,20) (7,11) (8,25) (9,12) (9,14) (9,10) (9,17) (9,13) (10,12) (10,14) (10,17) (10,13) (11,26) (11,20) (11,28) (12,17) (13,14) (13,17) (14,17) (15,31) (15,27) (15,21) (15,30) (15,23) (15,29) (15,22) (15,24) (16,27) (16,30) (16,19) (16,23) (16,22) (16,24) (18,31) (18,27) (18,21) (18,30) (18,19) (18,23) (18,22) (19,31) (19,27) (19,21) (19,24) (20,26) (21,27) (21,30) (21,23) (21,29) (21,22) (22,31) (22,27) (22,30) (22,29) (23,31) (23,29) (24,27) (24,29) (26,28) (29,31) (29,30) (30,31)\nIs there a path between node 24 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph660-10_29", + "image": "data/connectivity/graph_visual/hard/graph660.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,31) (0,28) (0,12) (0,20) (0,22) (0,16) (0,7) (1,25) (1,28) (1,27) (1,29) (1,20) (1,16) (1,17) (2,31) (2,18) (2,12) (2,24) (2,29) (2,13) (2,19) (2,26) (2,16) (3,14) (3,28) (3,27) (3,29) (3,19) (3,22) (4,21) (4,31) (4,25) (4,28) (4,18) (4,11) (4,8) (4,10) (5,6) (6,9) (6,33) (7,23) (7,31) (7,24) (7,29) (7,13) (7,20) (8,21) (8,31) (8,14) (8,27) (8,12) (8,29) (8,20) (9,33) (10,23) (10,14) (10,27) (10,29) (10,19) (10,11) (10,26) (11,23) (11,31) (11,14) (11,28) (11,27) (11,18) (11,12) (11,29) (11,20) (11,16) (12,15) (12,28) (12,18) (12,13) (12,20) (13,31) (13,25) (13,15) (13,28) (13,22) (13,26) (13,32) (13,16) (13,17) (14,31) (14,15) (14,28) (14,27) (15,23) (15,25) (15,27) (15,18) (15,30) (15,26) (15,32) (16,25) (16,27) (16,24) (16,29) (16,20) (16,26) (17,23) (17,25) (17,27) (17,30) (17,32) (18,25) (18,28) (18,24) (18,20) (18,30) (18,32) (19,24) (19,29) (19,26) (20,21) (20,31) (20,22) (21,25) (21,29) (22,24) (23,26) (24,31) (24,25) (24,27) (24,32) (27,30) (28,29) (28,32)\nIs there a path between node 10 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph66-26_22", + "image": "data/connectivity/graph_visual/hard/graph66.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,23) (0,10) (0,15) (0,1) (0,24) (1,17) (1,11) (1,23) (1,18) (1,13) (1,6) (1,24) (2,25) (3,21) (3,18) (3,10) (3,13) (3,20) (3,24) (5,21) (5,12) (5,23) (5,15) (5,6) (5,24) (6,7) (6,17) (6,13) (6,19) (6,24) (7,16) (7,15) (7,19) (7,24) (8,25) (8,26) (9,26) (10,13) (11,23) (12,21) (12,18) (13,17) (13,15) (13,22) (13,19) (15,20) (16,22) (17,18) (17,22) (19,20) (19,24) (20,21) (21,22) (23,24)\nIs there a path between node 26 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph400-26_28", + "image": "data/connectivity/graph_visual/hard/graph400.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,2) (0,31) (0,22) (0,30) (0,29) (0,8) (0,21) (0,13) (0,24) (0,3) (0,23) (0,11) (0,4) (0,14) (0,32) (0,27) (1,16) (1,9) (1,12) (1,19) (1,28) (1,20) (1,10) (2,31) (2,22) (2,26) (2,8) (2,6) (2,18) (2,24) (2,5) (2,3) (2,23) (2,11) (2,4) (2,14) (2,17) (2,27) (3,31) (3,22) (3,26) (3,30) (3,8) (3,13) (3,7) (3,18) (3,5) (3,23) (3,14) (3,17) (3,32) (3,27) (4,29) (4,8) (4,21) (4,6) (4,13) (4,7) (4,11) (4,14) (4,17) (4,32) (4,27) (5,22) (5,29) (5,8) (5,21) (5,13) (5,7) (5,18) (5,24) (5,23) (5,11) (5,17) (5,32) (6,31) (6,30) (6,8) (6,21) (6,13) (6,7) (6,18) (6,24) (6,11) (6,32) (6,27) (7,31) (7,26) (7,30) (7,29) (7,8) (7,21) (7,13) (7,24) (7,11) (7,32) (7,27) (8,31) (8,22) (8,26) (8,30) (8,29) (8,13) (8,18) (8,24) (8,23) (8,14) (8,17) (8,32) (8,27) (9,16) (9,12) (9,19) (9,28) (9,15) (9,20) (9,10) (10,16) (10,25) (10,12) (10,19) (11,31) (11,22) (11,26) (11,29) (11,21) (11,13) (11,18) (11,24) (11,23) (11,14) (11,17) (11,32) (12,25) (12,19) (12,15) (12,20) (13,22) (13,30) (13,29) (13,18) (13,24) (13,23) (13,14) (13,17) (13,32) (14,31) (14,22) (14,26) (14,30) (14,21) (14,18) (14,24) (14,17) (14,32) (14,27) (15,16) (15,25) (15,28) (15,20) (16,19) (17,30) (17,29) (17,21) (17,18) (17,23) (17,32) (17,27) (18,31) (18,22) (18,26) (18,29) (18,21) (18,24) (18,32) (18,27) (19,28) (19,20) (20,25) (20,28) (21,31) (21,30) (21,29) (21,24) (21,23) (22,31) (22,26) (22,24) (22,23) (23,26) (23,30) (23,32) (23,27) (24,31) (24,26) (24,30) (24,29) (24,32) (24,27) (26,29) (26,32) (27,31) (27,30) (27,32) (29,31) (29,30) (30,31) (30,32) (31,32)\nIs there a path between node 26 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph519-15_10", + "image": "data/connectivity/graph_visual/hard/graph519.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,24) (0,8) (0,19) (0,17) (0,22) (1,24) (1,12) (1,29) (1,11) (1,25) (1,10) (2,31) (2,8) (2,12) (2,6) (2,16) (2,23) (3,15) (4,32) (4,8) (4,12) (4,19) (4,11) (4,6) (4,7) (4,16) (4,18) (4,13) (4,22) (5,32) (5,31) (5,27) (5,29) (5,6) (5,16) (5,13) (5,22) (6,7) (6,16) (6,21) (6,18) (6,13) (7,9) (7,8) (7,30) (7,16) (7,33) (7,17) (7,10) (8,31) (8,11) (8,16) (8,33) (8,17) (9,20) (9,32) (9,24) (9,18) (9,23) (9,10) (10,32) (10,19) (10,29) (10,21) (10,13) (11,32) (11,24) (11,12) (11,29) (11,33) (11,13) (11,23) (12,13) (12,22) (13,20) (13,16) (13,22) (14,26) (15,26) (16,24) (16,18) (16,25) (16,22) (17,31) (17,29) (17,23) (18,31) (18,24) (18,19) (18,25) (19,20) (19,27) (20,32) (20,31) (20,27) (20,29) (20,25) (21,32) (21,30) (21,29) (21,25) (21,23) (22,24) (22,29) (22,33) (23,24) (23,27) (23,33) (23,25) (24,31) (24,30) (25,32) (26,28) (27,30) (29,31) (29,30) (29,33) (31,33) (32,33)\nIs there a path between node 15 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph324-11_3", + "image": "data/connectivity/graph_visual/hard/graph324.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,10) (0,28) (0,11) (0,21) (0,9) (0,12) (0,14) (0,26) (0,19) (0,29) (0,16) (0,25) (0,23) (1,18) (1,10) (1,7) (1,27) (1,13) (1,20) (1,6) (1,5) (1,9) (1,12) (1,19) (1,31) (1,16) (1,23) (2,3) (2,17) (2,24) (2,4) (3,15) (3,17) (3,24) (3,4) (4,15) (4,17) (4,24) (5,13) (5,6) (5,21) (5,12) (5,14) (5,8) (5,26) (5,19) (5,31) (5,16) (5,23) (6,18) (6,10) (6,27) (6,11) (6,12) (6,8) (6,19) (6,29) (6,25) (6,23) (7,18) (7,27) (7,20) (7,11) (7,21) (7,9) (7,12) (7,14) (7,8) (7,19) (7,29) (7,31) (7,23) (8,10) (8,27) (8,28) (8,21) (8,12) (8,14) (8,26) (8,29) (8,31) (8,16) (8,25) (9,18) (9,10) (9,27) (9,21) (9,26) (9,16) (10,27) (10,28) (10,20) (10,11) (10,21) (10,12) (10,14) (10,19) (10,29) (10,31) (10,16) (10,25) (11,18) (11,28) (11,20) (11,21) (11,12) (11,26) (11,19) (11,29) (11,31) (11,16) (11,25) (11,23) (12,18) (12,28) (12,13) (12,21) (12,14) (12,26) (12,19) (12,29) (12,31) (12,16) (12,23) (13,18) (13,27) (13,20) (13,21) (13,14) (13,26) (13,29) (13,16) (13,25) (13,23) (14,27) (14,26) (14,31) (14,16) (14,25) (14,23) (15,17) (15,24) (16,18) (16,27) (16,20) (16,21) (16,26) (16,19) (16,29) (16,31) (17,24) (18,27) (18,28) (18,20) (18,21) (18,26) (18,19) (18,29) (18,31) (18,25) (18,23) (19,27) (19,28) (19,20) (19,21) (19,26) (19,29) (19,31) (19,25) (20,27) (20,21) (20,26) (20,25) (20,23) (21,27) (21,28) (21,29) (21,31) (23,27) (23,29) (23,25) (25,28) (25,26) (25,29) (25,31) (26,27) (26,28) (26,29) (26,31) (27,28) (27,29) (28,29) (28,31) (29,31)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph439-10_17", + "image": "data/connectivity/graph_visual/hard/graph439.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,12) (0,15) (0,27) (0,11) (0,32) (0,23) (0,17) (0,21) (0,19) (0,14) (0,22) (0,29) (0,16) (0,5) (0,4) (0,2) (0,1) (1,15) (1,27) (1,32) (1,23) (1,21) (1,3) (1,14) (1,20) (1,7) (1,29) (1,16) (1,5) (1,4) (1,2) (1,13) (2,12) (2,15) (2,11) (2,18) (2,32) (2,23) (2,3) (2,19) (2,14) (2,28) (2,22) (2,7) (2,29) (2,16) (2,4) (2,13) (3,27) (3,11) (3,32) (3,23) (3,21) (3,10) (3,19) (3,14) (3,28) (3,7) (3,29) (3,16) (3,4) (4,15) (4,27) (4,11) (4,18) (4,32) (4,23) (4,17) (4,21) (4,10) (4,19) (4,14) (4,20) (4,29) (4,5) (4,8) (4,13) (5,12) (5,15) (5,27) (5,11) (5,18) (5,32) (5,23) (5,17) (5,21) (5,10) (5,28) (5,29) (5,16) (5,8) (6,25) (7,12) (7,15) (7,27) (7,11) (7,18) (7,32) (7,23) (7,17) (7,21) (7,10) (7,19) (7,20) (7,29) (7,16) (7,13) (8,15) (8,11) (8,18) (8,32) (8,23) (8,17) (8,28) (8,22) (8,20) (8,13) (9,31) (9,26) (9,30) (10,27) (10,32) (10,23) (10,17) (10,21) (10,19) (10,14) (10,28) (10,22) (10,20) (10,29) (10,16) (11,12) (11,15) (11,27) (11,18) (11,32) (11,23) (11,21) (11,14) (11,28) (11,22) (11,29) (11,16) (11,13) (12,18) (12,32) (12,23) (12,17) (12,21) (12,19) (12,22) (12,29) (12,13) (13,15) (13,27) (13,18) (13,32) (13,23) (13,14) (13,28) (13,22) (13,20) (13,29) (13,16) (14,15) (14,18) (14,32) (14,17) (14,21) (14,19) (14,22) (14,29) (15,27) (15,18) (15,32) (15,21) (15,28) (15,16) (16,27) (16,18) (16,32) (16,23) (16,17) (16,21) (16,28) (16,29) (17,23) (17,21) (17,19) (17,22) (17,20) (17,29) (18,27) (18,32) (18,23) (18,21) (18,19) (18,28) (18,22) (19,32) (19,23) (19,21) (19,28) (19,20) (19,29) (20,27) (20,21) (20,22) (20,29) (21,27) (21,32) (21,23) (21,28) (21,22) (21,29) (22,27) (22,23) (22,28) (22,29) (23,27) (23,32) (23,28) (24,26) (26,31) (26,30) (27,32) (27,28) (27,29) (28,29) (29,32) (30,31)\nIs there a path between node 10 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph657-15_3", + "image": "data/connectivity/graph_visual/hard/graph657.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,34) (0,7) (0,3) (0,15) (0,22) (0,33) (0,13) (1,9) (1,3) (1,16) (1,20) (1,6) (1,12) (2,34) (2,7) (2,27) (2,15) (2,16) (2,22) (2,33) (2,13) (3,34) (3,27) (3,16) (3,29) (3,13) (3,6) (3,11) (4,26) (4,5) (4,24) (5,18) (5,28) (5,24) (6,34) (6,19) (6,15) (6,22) (6,33) (6,20) (6,11) (6,12) (7,34) (7,19) (7,22) (8,25) (8,34) (8,27) (8,29) (8,20) (8,12) (9,25) (9,19) (9,15) (9,33) (9,12) (10,17) (10,28) (11,34) (11,19) (11,16) (11,29) (11,20) (12,19) (12,16) (13,25) (13,19) (13,15) (14,32) (14,23) (14,24) (15,34) (15,27) (15,20) (16,22) (17,31) (17,32) (17,18) (18,32) (18,28) (19,25) (19,22) (20,34) (21,31) (21,23) (22,25) (22,29) (23,30) (23,28) (24,31) (24,26) (25,34) (25,33) (26,28) (27,29) (28,32) (28,30) (29,33) (30,32) (33,34)\nIs there a path between node 15 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph404-0_13", + "image": "data/connectivity/graph_visual/hard/graph404.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,31) (0,26) (0,2) (0,22) (0,1) (0,13) (0,16) (0,18) (0,30) (0,14) (0,21) (1,31) (1,4) (1,26) (1,2) (1,22) (1,7) (1,16) (1,18) (1,11) (1,29) (1,30) (1,23) (1,14) (1,10) (1,32) (1,27) (1,12) (1,21) (2,31) (2,4) (2,26) (2,22) (2,7) (2,13) (2,16) (2,18) (2,11) (2,29) (2,30) (2,23) (2,14) (2,32) (2,12) (4,26) (4,7) (4,16) (4,18) (4,11) (4,29) (4,23) (4,14) (4,10) (4,12) (4,21) (5,17) (5,28) (5,6) (5,15) (5,25) (5,20) (5,8) (6,24) (6,25) (6,20) (6,8) (7,26) (7,18) (7,11) (7,29) (7,23) (7,14) (7,10) (7,32) (7,27) (7,12) (7,21) (8,17) (8,19) (8,28) (8,9) (8,15) (8,24) (9,17) (9,19) (9,28) (9,15) (9,24) (9,25) (9,20) (10,26) (10,22) (10,16) (10,11) (10,29) (10,30) (10,23) (10,14) (10,32) (10,27) (10,12) (11,31) (11,26) (11,22) (11,13) (11,16) (11,18) (11,30) (11,23) (11,14) (11,32) (12,26) (12,13) (12,16) (12,18) (12,29) (12,30) (12,23) (12,14) (12,32) (12,27) (12,21) (13,31) (13,18) (13,29) (13,30) (13,32) (13,21) (14,31) (14,26) (14,22) (14,16) (14,18) (14,29) (14,30) (14,23) (14,32) (14,27) (15,19) (15,28) (15,20) (16,31) (16,22) (16,29) (16,30) (16,23) (16,32) (16,27) (17,28) (17,20) (18,31) (18,22) (18,29) (18,23) (18,32) (18,27) (18,21) (19,28) (19,24) (19,20) (20,28) (20,24) (20,25) (21,22) (21,30) (21,32) (21,27) (22,31) (22,26) (22,29) (22,30) (22,23) (22,32) (22,27) (23,31) (23,30) (23,32) (23,27) (24,28) (24,25) (26,31) (26,30) (26,32) (26,27) (27,31) (27,29) (29,30) (29,32) (30,31) (31,32)\nIs there a path between node 0 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph175-11_14", + "image": "data/connectivity/graph_visual/hard/graph175.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,5) (0,7) (0,6) (0,26) (0,24) (0,15) (0,22) (0,18) (1,2) (1,28) (1,3) (1,13) (1,9) (1,8) (1,4) (2,27) (2,11) (2,14) (2,17) (2,16) (2,28) (2,3) (2,9) (2,4) (3,27) (3,11) (3,25) (3,28) (3,13) (3,9) (3,8) (3,23) (3,12) (4,10) (4,11) (4,25) (4,14) (4,17) (4,16) (4,28) (4,13) (4,23) (5,21) (5,6) (5,26) (5,20) (5,19) (5,15) (5,22) (5,18) (6,7) (6,24) (6,20) (6,19) (6,22) (6,18) (7,21) (7,26) (7,20) (7,15) (8,27) (8,10) (8,11) (8,25) (8,14) (8,16) (8,23) (8,12) (9,27) (9,16) (9,28) (9,13) (9,23) (9,12) (10,27) (10,11) (10,25) (10,14) (10,17) (10,28) (10,13) (10,23) (10,12) (11,14) (11,16) (11,13) (11,12) (12,27) (12,14) (12,17) (12,28) (12,13) (13,27) (13,25) (13,14) (13,17) (13,16) (13,28) (13,23) (14,27) (14,17) (14,16) (14,28) (14,23) (15,21) (15,26) (15,24) (15,20) (15,22) (16,27) (16,25) (16,17) (16,28) (16,23) (17,27) (17,28) (18,21) (18,26) (18,20) (18,19) (19,26) (20,21) (20,26) (20,24) (21,26) (21,24) (22,26) (22,24) (23,27) (23,25) (25,28) (27,28)\nIs there a path between node 11 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph195-3_28", + "image": "data/connectivity/graph_visual/hard/graph195.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,28) (0,13) (0,26) (0,17) (0,6) (0,29) (0,18) (0,27) (1,12) (1,9) (1,20) (1,4) (1,7) (1,22) (1,11) (1,15) (2,12) (2,9) (2,23) (2,20) (2,24) (2,22) (2,11) (2,15) (3,8) (3,28) (3,26) (3,17) (3,6) (3,29) (3,25) (3,18) (3,27) (4,12) (4,9) (4,20) (4,24) (4,22) (4,11) (5,10) (5,21) (6,8) (6,28) (6,13) (6,26) (6,17) (6,25) (6,18) (7,24) (7,22) (7,11) (7,15) (8,13) (8,19) (8,29) (8,25) (8,27) (9,23) (9,20) (9,24) (9,22) (10,16) (10,14) (10,21) (11,12) (11,23) (11,20) (11,24) (12,23) (12,20) (12,24) (13,28) (13,26) (13,17) (13,19) (13,29) (13,25) (13,18) (13,27) (14,16) (15,23) (15,20) (15,24) (15,22) (17,28) (17,26) (17,19) (17,29) (17,25) (17,18) (17,27) (18,28) (18,26) (18,19) (18,25) (18,27) (19,28) (19,26) (19,29) (19,25) (20,23) (20,22) (22,23) (22,24) (23,24) (25,26) (25,29) (25,27) (26,28) (26,29) (27,28)\nIs there a path between node 3 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph187-27_7", + "image": "data/connectivity/graph_visual/hard/graph187.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,20) (1,9) (1,25) (1,14) (1,8) (1,7) (1,27) (1,3) (1,13) (2,4) (2,10) (3,14) (3,7) (3,21) (3,13) (4,5) (5,18) (6,9) (6,16) (6,28) (6,8) (6,17) (6,7) (6,15) (6,24) (6,22) (6,13) (7,29) (7,17) (8,28) (8,23) (8,29) (8,17) (8,27) (9,14) (9,15) (10,20) (10,18) (11,15) (11,24) (11,22) (13,25) (13,23) (13,21) (14,28) (14,23) (14,29) (14,24) (15,16) (15,28) (15,29) (15,27) (15,22) (16,29) (16,27) (17,25) (17,29) (17,27) (21,25) (21,28) (22,25) (23,28) (23,29) (27,29)\nIs there a path between node 27 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph67-5_16", + "image": "data/connectivity/graph_visual/hard/graph67.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,2) (0,12) (0,8) (1,23) (1,22) (1,26) (1,24) (1,13) (2,12) (2,20) (3,12) (3,20) (4,15) (4,10) (4,21) (5,11) (6,11) (7,10) (9,13) (10,15) (11,18) (11,19) (13,23) (13,26) (16,23) (16,26) (17,26) (22,26) (23,26) (23,24)\nIs there a path between node 5 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph460-8_1", + "image": "data/connectivity/graph_visual/hard/graph460.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (0,16) (0,12) (0,2) (0,27) (0,30) (0,19) (0,28) (0,21) (0,13) (0,18) (1,5) (1,7) (1,4) (1,30) (1,24) (1,3) (2,5) (2,6) (2,22) (2,29) (2,19) (2,24) (2,21) (2,3) (3,31) (3,5) (3,16) (3,6) (3,12) (3,22) (3,29) (3,28) (3,24) (3,21) (3,18) (4,31) (4,16) (4,7) (4,23) (5,17) (5,22) (5,13) (6,32) (6,25) (6,19) (6,23) (6,15) (7,31) (7,25) (7,21) (7,13) (7,18) (8,26) (8,11) (10,12) (10,19) (10,13) (10,18) (11,20) (12,16) (12,27) (12,22) (12,30) (12,28) (12,21) (12,13) (12,15) (13,25) (13,27) (13,30) (13,19) (13,24) (13,18) (15,16) (15,22) (15,21) (15,18) (16,31) (16,32) (16,25) (16,22) (16,29) (16,24) (17,32) (17,19) (17,28) (17,21) (17,23) (18,32) (18,22) (18,19) (18,28) (18,21) (19,31) (19,27) (19,22) (19,29) (19,24) (19,21) (20,26) (21,32) (21,24) (22,31) (22,32) (23,31) (23,25) (23,27) (23,29) (24,25) (28,30) (31,32)\nIs there a path between node 8 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph14-21_16", + "image": "data/connectivity/graph_visual/hard/graph14.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,11) (0,13) (0,25) (0,21) (0,14) (0,4) (0,1) (1,3) (1,11) (1,13) (1,21) (1,14) (1,4) (2,6) (2,19) (2,12) (2,8) (2,9) (2,24) (2,17) (2,10) (2,7) (2,22) (2,16) (2,18) (3,5) (3,11) (3,13) (3,25) (3,21) (3,4) (4,5) (4,11) (4,13) (4,25) (4,21) (5,11) (5,25) (5,14) (6,19) (6,12) (6,8) (6,20) (6,9) (6,24) (6,17) (6,7) (6,22) (6,15) (6,18) (7,19) (7,12) (7,8) (7,23) (7,20) (7,24) (7,17) (7,22) (7,15) (7,16) (7,18) (8,12) (8,23) (8,20) (8,9) (8,24) (8,17) (8,22) (8,15) (8,16) (9,23) (9,20) (9,10) (9,22) (9,16) (10,19) (10,12) (10,23) (10,24) (10,17) (11,13) (11,25) (12,17) (12,22) (12,16) (13,25) (14,21) (15,19) (15,23) (15,20) (15,17) (15,16) (16,17) (16,22) (16,18) (17,20) (17,22) (18,23) (18,20) (18,24) (18,22) (19,23) (19,24) (19,22) (20,23) (20,24) (20,22) (21,25) (22,23) (22,24) (23,24)\nIs there a path between node 21 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph299-0_27", + "image": "data/connectivity/graph_visual/hard/graph299.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,31) (0,14) (0,18) (0,24) (0,23) (0,25) (0,30) (0,21) (0,26) (1,5) (1,19) (1,15) (1,28) (1,20) (1,2) (1,17) (1,27) (1,6) (2,5) (2,19) (2,15) (2,28) (2,20) (2,16) (2,17) (2,4) (2,8) (2,10) (2,6) (2,29) (2,12) (3,7) (3,31) (3,11) (3,14) (3,18) (3,24) (3,23) (3,25) (3,30) (4,5) (4,19) (4,15) (4,20) (4,16) (4,10) (4,6) (5,13) (5,22) (5,28) (5,20) (5,8) (5,6) (5,29) (5,12) (6,19) (6,13) (6,22) (6,20) (6,17) (6,8) (6,10) (6,27) (7,31) (7,11) (7,14) (7,23) (7,25) (7,30) (7,21) (7,26) (8,19) (8,20) (8,16) (8,27) (8,29) (8,12) (9,31) (9,11) (9,14) (9,24) (9,23) (9,30) (9,21) (9,26) (10,15) (10,13) (10,22) (10,28) (10,20) (10,16) (10,17) (10,12) (11,31) (11,18) (11,24) (11,30) (11,21) (11,26) (12,19) (12,15) (12,22) (12,28) (12,20) (12,16) (13,19) (13,15) (13,22) (13,28) (13,16) (13,27) (13,29) (14,31) (14,18) (14,23) (14,25) (14,30) (14,21) (15,22) (15,28) (15,20) (15,16) (15,17) (15,27) (15,29) (16,19) (16,22) (16,28) (16,17) (16,29) (17,19) (17,22) (17,20) (17,29) (18,31) (18,23) (18,25) (18,21) (19,20) (19,27) (20,22) (20,28) (20,27) (20,29) (21,24) (21,25) (21,30) (21,26) (22,28) (22,27) (23,25) (23,30) (23,26) (24,31) (24,25) (24,30) (24,26) (25,31) (25,30) (25,26) (26,31) (27,28) (27,29) (30,31)\nIs there a path between node 0 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph305-29_30", + "image": "data/connectivity/graph_visual/hard/graph305.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,29) (0,19) (0,26) (0,23) (0,7) (0,1) (1,2) (1,18) (1,23) (1,6) (2,10) (2,25) (2,6) (2,24) (3,20) (3,30) (3,4) (4,27) (4,28) (4,12) (5,27) (5,15) (6,10) (6,29) (6,25) (6,22) (6,7) (7,10) (7,29) (7,18) (8,29) (8,25) (8,18) (10,19) (10,25) (10,26) (10,24) (11,27) (11,15) (12,21) (13,28) (14,31) (15,30) (16,17) (17,19) (17,22) (18,25) (18,26) (18,24) (19,25) (19,26) (19,24) (20,21) (22,26) (22,24) (23,26) (24,26) (25,26) (26,29) (27,30)\nIs there a path between node 29 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph120-22_23", + "image": "data/connectivity/graph_visual/hard/graph120.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,22) (0,13) (0,25) (2,21) (2,6) (2,3) (3,27) (3,24) (4,14) (4,21) (4,27) (5,17) (6,27) (7,18) (7,22) (8,18) (8,26) (8,20) (9,15) (10,22) (10,12) (10,16) (10,25) (12,18) (12,15) (12,26) (13,22) (13,26) (13,20) (14,21) (14,19) (15,22) (17,19) (17,23) (18,22) (19,21) (20,26) (21,27) (21,23)\nIs there a path between node 22 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph133-21_25", + "image": "data/connectivity/graph_visual/hard/graph133.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,6) (0,2) (0,5) (0,27) (0,8) (0,1) (0,21) (0,24) (0,10) (0,4) (0,11) (0,19) (0,25) (0,7) (0,9) (0,13) (0,18) (1,6) (1,12) (1,27) (1,8) (1,21) (1,10) (1,4) (1,11) (1,19) (1,25) (1,7) (1,26) (1,18) (2,6) (2,12) (2,27) (2,8) (2,21) (2,24) (2,22) (2,10) (2,4) (2,3) (2,19) (2,7) (2,9) (2,13) (2,18) (3,6) (3,5) (3,12) (3,27) (3,8) (3,21) (3,24) (3,22) (3,10) (3,4) (3,11) (3,25) (3,9) (3,13) (3,18) (4,6) (4,5) (4,12) (4,27) (4,21) (4,24) (4,22) (4,10) (4,19) (4,25) (4,7) (4,13) (5,6) (5,27) (5,22) (5,10) (5,11) (5,19) (5,25) (5,7) (5,13) (5,26) (5,18) (6,12) (6,27) (6,8) (6,24) (6,22) (6,10) (6,11) (6,19) (6,25) (6,7) (6,13) (6,26) (7,12) (7,27) (7,8) (7,21) (7,24) (7,22) (7,25) (7,9) (7,13) (7,26) (7,18) (8,12) (8,27) (8,21) (8,24) (8,22) (8,11) (8,19) (8,25) (8,9) (8,13) (8,26) (9,12) (9,21) (9,24) (9,22) (9,11) (9,19) (9,25) (9,13) (9,26) (10,27) (10,21) (10,24) (10,22) (10,19) (10,25) (10,13) (11,12) (11,27) (11,24) (11,22) (11,19) (11,25) (11,13) (11,26) (11,18) (12,21) (12,25) (12,13) (12,26) (12,18) (13,27) (13,24) (13,22) (13,19) (13,25) (13,26) (13,18) (14,15) (14,17) (14,23) (14,16) (14,20) (15,17) (15,23) (15,20) (16,17) (16,20) (18,22) (18,19) (18,26) (19,27) (19,21) (19,26) (20,23) (21,27) (21,24) (21,22) (21,26) (22,27) (22,26) (24,25) (25,26) (26,27)\nIs there a path between node 21 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph557-17_22", + "image": "data/connectivity/graph_visual/hard/graph557.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,10) (0,11) (1,18) (4,10) (4,11) (4,24) (4,12) (5,30) (5,9) (5,32) (5,26) (5,8) (6,30) (6,19) (7,28) (8,19) (8,15) (8,13) (9,19) (9,13) (10,11) (10,31) (10,17) (10,12) (11,14) (11,22) (12,23) (12,16) (13,15) (14,24) (14,16) (15,26) (15,29) (16,22) (16,17) (17,22) (17,23) (19,26) (20,28) (21,23) (22,23) (22,31) (23,31) (29,32)\nIs there a path between node 17 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph343-30_16", + "image": "data/connectivity/graph_visual/hard/graph343.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,23) (0,28) (0,25) (0,17) (0,3) (0,10) (0,31) (0,7) (0,12) (0,14) (1,18) (1,28) (1,2) (1,3) (1,7) (1,30) (1,5) (2,24) (2,25) (2,29) (2,8) (2,30) (2,19) (2,5) (3,22) (3,25) (3,4) (3,29) (3,17) (3,21) (4,23) (4,21) (4,8) (4,19) (5,22) (5,9) (5,21) (5,10) (5,8) (5,30) (5,14) (6,18) (6,9) (6,10) (6,7) (6,14) (7,22) (7,18) (7,24) (7,9) (7,29) (7,8) (7,30) (7,13) (8,26) (8,23) (8,28) (8,9) (8,21) (9,26) (9,22) (9,25) (9,17) (9,31) (9,12) (9,14) (9,13) (10,22) (10,23) (10,28) (10,17) (10,21) (10,12) (10,13) (11,22) (11,24) (11,30) (12,23) (12,17) (12,30) (12,14) (13,23) (13,28) (13,30) (13,14) (14,22) (14,24) (14,25) (14,17) (14,21) (14,31) (14,30) (17,26) (17,22) (17,24) (18,26) (18,24) (18,30) (19,23) (19,29) (19,31) (21,23) (22,24) (22,29) (22,31) (23,26) (23,24) (23,28) (23,31) (24,28) (24,31) (25,28) (28,31) (29,31) (30,31)\nIs there a path between node 30 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph487-13_12", + "image": "data/connectivity/graph_visual/hard/graph487.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,8) (0,30) (0,9) (0,18) (0,2) (0,4) (0,20) (0,28) (0,1) (0,7) (0,16) (0,5) (0,17) (0,32) (0,26) (0,29) (0,21) (0,25) (0,11) (0,13) (0,31) (0,27) (1,8) (1,9) (1,18) (1,15) (1,4) (1,20) (1,28) (1,7) (1,16) (1,5) (1,32) (1,21) (1,25) (1,22) (1,11) (1,13) (1,31) (1,3) (1,27) (2,18) (2,15) (2,4) (2,20) (2,28) (2,7) (2,16) (2,23) (2,32) (2,26) (2,21) (2,25) (2,22) (2,12) (2,13) (2,31) (2,27) (3,8) (3,9) (3,18) (3,15) (3,4) (3,20) (3,7) (3,16) (3,23) (3,29) (3,21) (3,25) (3,22) (3,11) (3,27) (4,8) (4,30) (4,9) (4,18) (4,15) (4,7) (4,16) (4,5) (4,17) (4,26) (4,21) (4,25) (4,22) (4,12) (4,13) (4,31) (4,27) (5,30) (5,18) (5,15) (5,28) (5,7) (5,32) (5,26) (5,29) (5,21) (5,25) (5,22) (5,12) (5,11) (5,13) (5,31) (5,27) (6,24) (6,10) (6,19) (6,14) (7,9) (7,18) (7,15) (7,28) (7,16) (7,17) (7,23) (7,32) (7,21) (7,25) (7,22) (7,12) (7,31) (8,30) (8,9) (8,15) (8,28) (8,16) (8,17) (8,23) (8,26) (8,29) (8,21) (8,22) (8,11) (8,13) (8,27) (9,28) (9,17) (9,32) (9,26) (9,21) (9,25) (9,11) (9,31) (9,27) (10,24) (10,19) (10,14) (11,18) (11,15) (11,28) (11,16) (11,32) (11,21) (11,22) (11,13) (11,31) (11,27) (12,30) (12,18) (12,15) (12,32) (12,26) (12,21) (12,22) (12,13) (12,31) (13,18) (13,28) (13,17) (13,32) (13,26) (13,29) (13,21) (13,25) (13,22) (13,31) (13,27) (14,24) (14,19) (15,18) (15,20) (15,28) (15,17) (15,23) (15,32) (15,29) (15,25) (15,22) (15,31) (16,30) (16,18) (16,20) (16,28) (16,17) (16,26) (16,21) (16,31) (16,27) (17,30) (17,18) (17,20) (17,23) (17,32) (17,26) (17,29) (17,25) (17,31) (17,27) (18,30) (18,20) (18,28) (18,23) (18,32) (18,26) (18,29) (18,21) (18,25) (18,31) (18,27) (19,24) (20,30) (20,28) (20,32) (20,26) (20,29) (20,31) (20,27) (21,30) (21,23) (21,32) (21,29) (21,25) (21,27) (22,28) (22,26) (22,29) (22,25) (22,31) (22,27) (23,30) (23,32) (23,29) (23,25) (23,31) (23,27) (25,30) (25,28) (25,26) (25,31) (26,30) (26,28) (26,27) (27,30) (27,28) (27,32) (28,29) (28,31) (29,30) (29,32) (29,31) (30,32) (31,32)\nIs there a path between node 13 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph600-19_25", + "image": "data/connectivity/graph_visual/hard/graph600.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,29) (0,1) (0,9) (0,20) (0,34) (0,7) (0,19) (0,22) (0,31) (1,11) (1,30) (1,6) (1,21) (1,14) (1,28) (1,19) (1,31) (1,4) (2,3) (2,11) (2,18) (2,21) (2,20) (2,14) (2,7) (2,17) (3,11) (3,33) (3,15) (3,30) (3,18) (3,21) (3,14) (3,5) (4,10) (4,26) (4,27) (4,21) (4,34) (5,9) (5,27) (5,30) (5,6) (5,24) (5,14) (5,34) (5,28) (5,17) (6,11) (6,25) (6,10) (6,26) (6,29) (6,15) (6,16) (6,14) (6,7) (6,12) (6,22) (7,10) (7,26) (7,27) (7,18) (7,24) (7,8) (7,31) (8,11) (8,33) (8,9) (8,30) (8,24) (8,20) (8,16) (8,22) (8,17) (9,10) (9,20) (9,16) (9,14) (10,25) (10,33) (10,30) (10,18) (10,24) (10,20) (10,31) (11,15) (11,12) (11,19) (11,17) (12,25) (12,29) (12,27) (12,30) (12,34) (12,28) (12,17) (14,25) (14,33) (14,26) (14,29) (14,30) (14,21) (14,17) (15,20) (15,17) (16,21) (16,28) (16,19) (16,22) (17,27) (17,30) (17,24) (17,19) (18,26) (18,21) (18,28) (19,33) (19,27) (19,34) (19,22) (20,25) (20,26) (20,27) (20,21) (20,28) (20,31) (21,22) (22,24) (22,31) (24,34) (24,28) (25,26) (25,29) (25,27) (26,33) (26,27) (26,30) (27,30) (27,28) (28,31) (29,30) (29,34) (29,31) (30,33) (30,34) (31,33) (31,34)\nIs there a path between node 19 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph290-29_30", + "image": "data/connectivity/graph_visual/hard/graph290.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,12) (0,29) (1,12) (1,26) (1,18) (1,15) (1,27) (1,28) (1,2) (2,13) (2,29) (2,8) (2,22) (2,28) (3,31) (4,25) (4,24) (5,13) (5,12) (5,23) (5,7) (5,18) (5,27) (5,22) (6,23) (6,7) (6,15) (7,13) (7,19) (7,23) (7,18) (7,15) (8,23) (8,29) (8,18) (8,15) (8,27) (8,22) (9,10) (9,16) (10,11) (11,31) (12,19) (12,23) (12,18) (12,27) (13,19) (13,26) (13,29) (13,18) (13,28) (14,19) (14,26) (14,20) (14,15) (14,22) (15,19) (15,26) (18,29) (18,20) (19,26) (19,20) (19,28) (20,23) (20,29) (21,24) (25,31) (26,29) (26,27) (28,30)\nIs there a path between node 29 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph554-30_21", + "image": "data/connectivity/graph_visual/hard/graph554.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,3) (0,14) (0,1) (0,17) (1,23) (1,3) (1,13) (1,14) (2,30) (2,20) (2,31) (3,25) (3,14) (3,6) (3,7) (3,10) (3,33) (4,27) (4,8) (4,5) (4,20) (5,27) (5,22) (5,15) (5,8) (5,29) (6,11) (6,19) (6,18) (6,13) (6,7) (6,17) (7,13) (7,33) (8,26) (8,12) (8,29) (8,24) (9,19) (9,33) (10,11) (10,23) (10,19) (11,23) (11,19) (11,13) (11,21) (12,30) (12,22) (12,31) (13,23) (13,19) (13,14) (14,28) (15,30) (15,16) (15,32) (15,31) (15,24) (16,32) (16,20) (17,18) (17,33) (18,25) (18,21) (19,25) (19,21) (20,30) (20,31) (20,24) (22,24) (23,25) (23,28) (24,27) (24,30) (24,31) (25,33) (26,29) (29,32) (31,32)\nIs there a path between node 30 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph126-22_13", + "image": "data/connectivity/graph_visual/hard/graph126.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,4) (0,12) (0,27) (0,10) (0,21) (0,22) (0,8) (0,15) (0,19) (0,20) (0,23) (0,25) (0,14) (0,5) (0,18) (1,2) (1,17) (1,3) (2,24) (2,26) (2,3) (3,17) (3,26) (3,16) (4,12) (4,10) (4,7) (4,9) (4,22) (4,8) (4,19) (4,11) (4,14) (4,13) (4,5) (4,18) (5,12) (5,10) (5,21) (5,7) (5,9) (5,22) (5,8) (5,15) (5,19) (5,11) (5,14) (5,18) (6,12) (6,10) (6,21) (6,9) (6,22) (6,8) (6,15) (6,19) (6,20) (6,25) (6,11) (6,13) (6,18) (7,12) (7,21) (7,9) (7,22) (7,8) (7,15) (7,19) (7,20) (7,25) (7,11) (7,14) (7,13) (7,18) (8,10) (8,21) (8,9) (8,22) (8,15) (8,23) (8,25) (8,11) (8,14) (8,13) (8,18) (9,12) (9,10) (9,22) (9,19) (9,20) (9,23) (9,11) (9,14) (10,12) (10,27) (10,19) (10,23) (10,11) (10,14) (10,13) (10,18) (11,27) (11,21) (11,22) (11,20) (11,18) (12,27) (12,22) (12,15) (12,20) (12,13) (12,18) (13,21) (13,22) (13,15) (13,19) (13,20) (13,23) (13,25) (13,18) (14,22) (14,15) (14,19) (14,20) (14,23) (14,25) (14,18) (15,22) (15,19) (15,20) (15,25) (15,18) (16,24) (16,17) (16,26) (17,24) (17,26) (18,21) (18,22) (18,20) (18,23) (19,27) (19,21) (19,22) (19,23) (19,25) (20,21) (20,22) (20,23) (20,25) (21,27) (21,22) (21,23) (22,27) (22,23) (24,26)\nIs there a path between node 22 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph78-21_17", + "image": "data/connectivity/graph_visual/hard/graph78.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,7) (0,24) (0,8) (1,10) (1,22) (1,4) (1,5) (1,11) (1,13) (1,12) (1,14) (1,18) (1,20) (1,25) (1,6) (1,15) (1,26) (1,3) (2,10) (2,22) (2,4) (2,5) (2,11) (2,21) (2,12) (2,14) (2,18) (2,20) (2,25) (2,23) (2,6) (2,15) (2,26) (2,3) (3,19) (3,16) (3,22) (3,4) (3,5) (3,11) (3,25) (3,23) (3,15) (3,26) (4,19) (4,16) (4,22) (4,5) (4,11) (4,13) (4,12) (4,14) (4,15) (4,26) (5,19) (5,10) (5,16) (5,21) (5,13) (5,14) (5,18) (5,20) (5,25) (5,23) (5,6) (6,19) (6,10) (6,16) (6,22) (6,18) (6,20) (6,25) (6,23) (6,15) (7,17) (7,9) (7,24) (7,8) (8,17) (8,9) (9,17) (9,24) (10,19) (10,16) (10,22) (10,11) (10,21) (10,13) (10,12) (10,18) (10,20) (10,23) (10,15) (11,19) (11,16) (11,13) (11,12) (11,14) (11,18) (11,20) (11,25) (11,23) (12,19) (12,16) (12,21) (12,13) (12,14) (12,20) (12,25) (12,23) (13,19) (13,16) (13,22) (13,18) (13,20) (13,15) (13,26) (14,19) (14,22) (14,21) (14,18) (14,20) (14,15) (15,16) (15,22) (15,21) (15,20) (15,23) (15,26) (16,19) (16,21) (16,18) (16,20) (16,25) (16,23) (16,26) (17,24) (18,19) (18,22) (18,21) (18,20) (18,23) (19,22) (19,21) (19,20) (19,25) (19,23) (20,22) (20,21) (20,25) (20,23) (20,26) (21,22) (21,23) (22,25) (22,23) (22,26) (23,26) (25,26)\nIs there a path between node 21 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph23-23_14", + "image": "data/connectivity/graph_visual/hard/graph23.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,21) (0,24) (0,3) (0,23) (0,2) (0,1) (0,22) (1,7) (1,2) (1,8) (1,11) (1,22) (2,23) (2,8) (2,10) (3,19) (3,20) (3,8) (4,9) (5,21) (5,24) (5,17) (5,15) (5,8) (6,14) (7,21) (7,24) (7,13) (7,15) (8,21) (8,16) (8,23) (8,22) (10,17) (10,18) (10,25) (10,22) (11,24) (11,23) (13,24) (13,20) (13,22) (15,20) (15,23) (15,25) (16,19) (16,20) (16,23) (17,21) (17,20) (17,23) (18,24) (18,23) (18,25) (21,22) (22,23) (23,24)\nIs there a path between node 23 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph574-33_27", + "image": "data/connectivity/graph_visual/hard/graph574.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,16) (0,28) (0,26) (0,7) (0,22) (0,6) (0,1) (0,30) (0,3) (1,16) (1,28) (1,26) (1,22) (1,10) (1,30) (2,4) (2,29) (2,24) (2,14) (2,21) (2,25) (2,13) (2,12) (2,31) (2,19) (2,33) (2,27) (2,23) (2,8) (2,18) (3,16) (3,28) (3,26) (3,9) (3,7) (3,10) (4,29) (4,32) (4,24) (4,21) (4,25) (4,15) (4,12) (4,31) (4,19) (4,33) (4,27) (4,17) (4,23) (4,18) (5,32) (5,14) (5,21) (5,15) (5,12) (5,19) (5,33) (5,27) (5,23) (5,8) (6,28) (6,26) (6,7) (6,22) (6,10) (7,16) (7,9) (7,22) (7,10) (8,29) (8,32) (8,24) (8,21) (8,15) (8,13) (8,33) (8,27) (8,23) (8,18) (9,16) (9,28) (9,26) (9,22) (9,10) (10,28) (10,22) (10,30) (12,29) (12,14) (12,21) (12,25) (12,15) (12,13) (12,31) (12,19) (12,33) (12,17) (12,23) (12,18) (13,20) (13,29) (13,24) (13,21) (13,25) (13,15) (13,31) (13,19) (13,33) (13,27) (13,17) (13,23) (13,18) (14,20) (14,29) (14,32) (14,24) (14,21) (14,15) (14,31) (14,19) (14,33) (14,17) (14,18) (15,20) (15,29) (15,32) (15,24) (15,21) (15,25) (15,31) (15,19) (15,33) (15,27) (15,17) (15,23) (15,18) (16,28) (16,26) (16,22) (16,30) (17,20) (17,29) (17,32) (17,24) (17,21) (17,25) (17,31) (17,19) (17,18) (18,20) (18,29) (18,32) (18,24) (18,21) (18,25) (18,31) (18,19) (18,27) (18,23) (19,32) (19,24) (19,33) (19,27) (19,23) (20,29) (20,32) (20,24) (20,21) (20,25) (20,31) (20,33) (20,27) (20,23) (21,32) (21,24) (21,25) (21,31) (21,33) (21,27) (21,23) (22,26) (22,30) (23,29) (23,32) (23,24) (23,25) (23,31) (23,33) (23,27) (24,32) (24,25) (24,31) (24,27) (25,29) (25,33) (25,27) (26,28) (26,30) (27,29) (27,31) (27,33) (28,30) (29,32) (29,31) (29,33) (31,32) (31,33) (32,33)\nIs there a path between node 33 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph537-30_2", + "image": "data/connectivity/graph_visual/hard/graph537.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,16) (0,17) (0,4) (0,8) (0,12) (0,31) (1,19) (1,21) (1,2) (1,30) (1,26) (1,3) (1,9) (1,22) (1,6) (1,23) (1,18) (2,21) (2,28) (2,26) (2,3) (2,25) (2,20) (2,33) (2,9) (2,22) (2,6) (2,15) (2,7) (2,23) (2,18) (3,19) (3,30) (3,28) (3,26) (3,22) (3,32) (3,6) (3,15) (3,23) (3,18) (4,10) (4,16) (4,17) (4,5) (4,8) (4,12) (5,10) (5,13) (5,24) (5,16) (5,31) (6,19) (6,14) (6,30) (6,26) (6,25) (6,20) (6,11) (6,9) (6,22) (6,27) (6,32) (6,15) (6,29) (7,21) (7,30) (7,28) (7,26) (7,25) (7,33) (7,22) (7,27) (7,32) (7,15) (7,29) (7,23) (7,18) (8,13) (8,24) (8,16) (8,17) (8,31) (9,19) (9,21) (9,30) (9,20) (9,11) (9,22) (9,15) (9,23) (9,18) (10,13) (10,24) (10,16) (10,17) (10,12) (10,31) (11,19) (11,21) (11,14) (11,28) (11,26) (11,25) (11,20) (11,22) (11,32) (11,15) (11,29) (11,23) (11,18) (12,24) (12,17) (13,24) (13,16) (13,17) (14,19) (14,21) (14,30) (14,28) (14,25) (14,20) (14,33) (14,32) (14,15) (14,29) (14,23) (14,18) (15,30) (15,28) (15,26) (15,25) (15,20) (15,33) (15,22) (15,32) (15,29) (15,23) (15,18) (16,24) (16,17) (17,31) (18,19) (18,28) (18,26) (18,20) (18,33) (18,22) (18,27) (18,29) (18,23) (19,21) (19,28) (19,26) (19,20) (19,22) (19,29) (19,23) (20,21) (20,30) (20,26) (20,25) (20,22) (20,32) (20,29) (20,23) (21,28) (21,33) (21,22) (21,27) (21,32) (21,29) (22,30) (22,28) (22,26) (22,25) (22,27) (22,32) (22,23) (23,30) (23,28) (23,26) (23,33) (23,27) (23,32) (23,29) (24,31) (25,30) (25,26) (25,33) (25,27) (25,32) (25,29) (26,28) (26,27) (26,32) (26,29) (27,30) (27,28) (27,32) (27,29) (28,30) (28,33) (28,29) (29,32) (30,32) (32,33)\nIs there a path between node 30 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph284-18_30", + "image": "data/connectivity/graph_visual/hard/graph284.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,31) (0,11) (0,27) (0,18) (1,4) (1,12) (1,31) (1,7) (1,25) (1,8) (1,18) (2,17) (2,14) (2,6) (2,10) (2,19) (3,17) (3,22) (3,9) (4,12) (4,30) (4,31) (4,13) (4,27) (4,18) (5,29) (5,16) (5,22) (5,21) (5,20) (5,28) (5,19) (6,29) (6,9) (6,10) (6,28) (7,11) (7,27) (7,15) (7,18) (8,30) (8,23) (8,11) (9,14) (9,21) (9,10) (11,23) (11,18) (12,30) (12,31) (12,27) (12,25) (12,15) (12,18) (13,23) (13,25) (13,15) (14,29) (14,17) (16,24) (16,17) (16,20) (17,29) (18,30) (18,26) (20,29) (21,24) (22,24) (23,27) (23,25) (25,26) (25,27) (26,31) (27,31) (28,29)\nIs there a path between node 18 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph287-12_13", + "image": "data/connectivity/graph_visual/hard/graph287.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,16) (0,19) (1,31) (1,27) (1,7) (2,26) (2,12) (2,4) (2,7) (2,23) (3,28) (3,10) (3,14) (3,19) (3,11) (3,25) (4,27) (4,24) (4,17) (5,20) (5,13) (5,10) (5,14) (5,19) (6,31) (6,15) (6,27) (6,21) (8,13) (9,13) (9,11) (9,18) (10,28) (10,14) (10,16) (10,19) (10,11) (10,18) (11,20) (11,22) (11,14) (11,16) (11,18) (12,31) (12,30) (12,27) (12,24) (12,23) (13,22) (13,14) (13,25) (14,22) (14,25) (14,18) (15,31) (15,26) (15,24) (16,18) (17,31) (17,26) (17,23) (18,19) (19,22) (20,25) (21,31) (21,24) (21,29) (21,23) (22,28) (22,25) (23,27) (23,29) (24,30) (26,27) (29,31)\nIs there a path between node 12 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph132-20_4", + "image": "data/connectivity/graph_visual/hard/graph132.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,23) (0,17) (0,27) (0,18) (0,13) (0,9) (0,19) (0,8) (0,16) (0,22) (0,25) (0,3) (1,4) (1,12) (1,7) (1,20) (1,26) (2,23) (2,27) (2,13) (2,9) (2,24) (2,14) (2,19) (2,16) (2,22) (2,3) (3,21) (3,23) (3,15) (3,27) (3,18) (3,9) (3,24) (3,14) (3,8) (3,16) (3,22) (3,25) (4,12) (4,11) (4,20) (4,26) (4,5) (5,12) (5,7) (5,11) (5,20) (5,26) (6,10) (7,12) (7,20) (8,21) (8,17) (8,15) (8,27) (8,9) (8,24) (8,14) (8,19) (8,16) (8,22) (9,17) (9,27) (9,24) (11,12) (11,20) (12,26) (13,21) (13,23) (13,17) (13,15) (13,18) (13,14) (13,19) (13,22) (13,25) (14,21) (14,23) (14,17) (14,27) (14,18) (14,24) (14,19) (14,22) (14,25) (15,21) (15,23) (15,17) (15,27) (15,18) (15,24) (15,19) (15,16) (15,22) (15,25) (16,21) (16,23) (16,27) (16,18) (16,24) (16,22) (16,25) (17,23) (17,27) (18,21) (18,27) (18,24) (18,19) (18,22) (18,25) (19,23) (19,27) (19,22) (19,25) (20,26) (21,23) (21,27) (22,27) (23,27) (24,27) (24,25) (25,27)\nIs there a path between node 20 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph661-3_32", + "image": "data/connectivity/graph_visual/hard/graph661.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,27) (0,32) (0,11) (0,33) (0,5) (0,31) (0,30) (0,2) (0,9) (1,26) (1,25) (1,4) (2,24) (2,17) (2,3) (2,34) (2,10) (2,9) (2,29) (3,24) (3,14) (3,34) (3,5) (3,30) (3,9) (5,33) (5,10) (5,9) (6,17) (6,20) (6,15) (6,30) (7,24) (7,16) (7,20) (7,33) (8,21) (8,13) (8,19) (8,18) (9,27) (9,30) (10,24) (10,16) (10,15) (10,11) (10,28) (10,30) (11,27) (11,33) (11,28) (11,34) (11,30) (12,13) (12,19) (12,18) (13,19) (13,18) (13,22) (14,24) (14,27) (14,32) (15,17) (15,20) (15,33) (15,29) (16,24) (17,24) (17,27) (17,32) (17,33) (17,28) (17,30) (18,22) (19,26) (19,25) (19,23) (19,22) (21,25) (24,33) (25,26) (27,34) (28,32) (28,33) (28,31) (30,34) (31,33) (31,34) (33,34)\nIs there a path between node 3 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph442-12_18", + "image": "data/connectivity/graph_visual/hard/graph442.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,11) (0,32) (0,29) (0,7) (0,15) (1,30) (1,10) (1,8) (2,27) (2,18) (2,20) (2,7) (2,26) (3,14) (3,9) (4,18) (4,11) (4,13) (4,15) (5,30) (5,21) (6,14) (6,21) (6,17) (7,18) (7,22) (7,31) (7,29) (7,26) (8,14) (8,10) (9,21) (10,12) (10,21) (10,17) (11,19) (11,22) (11,28) (11,32) (11,29) (11,15) (11,26) (12,30) (12,21) (13,27) (13,20) (13,28) (13,31) (14,17) (15,20) (15,31) (15,26) (16,27) (16,32) (17,30) (18,27) (18,28) (18,32) (18,26) (18,24) (18,23) (19,27) (19,20) (19,31) (19,29) (19,26) (19,24) (20,25) (20,28) (20,32) (20,26) (22,31) (22,23) (23,27) (23,28) (23,26) (25,26) (26,27) (26,28) (26,29) (28,32) (28,31) (29,31)\nIs there a path between node 12 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph650-14_15", + "image": "data/connectivity/graph_visual/hard/graph650.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,19) (0,29) (0,25) (0,12) (0,30) (0,27) (0,3) (0,15) (0,32) (0,9) (0,7) (0,31) (0,13) (0,2) (0,33) (0,20) (0,17) (0,4) (0,34) (1,21) (1,28) (1,6) (1,5) (1,25) (1,12) (1,30) (1,27) (1,3) (1,32) (1,9) (1,7) (1,31) (1,22) (1,33) (1,20) (1,17) (1,26) (1,4) (1,34) (2,11) (2,18) (2,21) (2,19) (2,28) (2,5) (2,29) (2,25) (2,12) (2,30) (2,27) (2,3) (2,15) (2,7) (2,22) (2,24) (2,33) (2,20) (2,17) (2,26) (2,34) (3,11) (3,18) (3,21) (3,19) (3,28) (3,5) (3,29) (3,25) (3,12) (3,30) (3,27) (3,14) (3,32) (3,7) (3,31) (3,13) (3,22) (3,20) (3,17) (3,4) (4,11) (4,18) (4,19) (4,28) (4,6) (4,5) (4,29) (4,25) (4,12) (4,30) (4,27) (4,14) (4,15) (4,32) (4,9) (4,7) (4,13) (4,24) (4,17) (4,34) (5,11) (5,18) (5,21) (5,6) (5,29) (5,25) (5,27) (5,14) (5,15) (5,9) (5,23) (5,31) (5,22) (5,24) (5,33) (5,20) (5,17) (5,26) (5,34) (6,21) (6,19) (6,28) (6,29) (6,25) (6,12) (6,27) (6,14) (6,15) (6,32) (6,9) (6,23) (6,7) (6,31) (6,22) (6,24) (6,33) (6,20) (6,17) (6,26) (6,34) (7,11) (7,18) (7,19) (7,28) (7,30) (7,27) (7,14) (7,32) (7,23) (7,13) (7,22) (7,24) (7,33) (7,20) (7,17) (7,26) (7,34) (8,16) (9,11) (9,18) (9,21) (9,19) (9,28) (9,29) (9,25) (9,12) (9,30) (9,15) (9,32) (9,23) (9,31) (9,13) (9,22) (9,24) (9,33) (9,20) (9,17) (9,34) (10,16) (11,18) (11,21) (11,19) (11,12) (11,30) (11,27) (11,15) (11,32) (11,23) (11,31) (11,13) (11,22) (11,24) (11,20) (11,17) (11,26) (11,34) (12,18) (12,21) (12,28) (12,29) (12,25) (12,30) (12,27) (12,14) (12,32) (12,13) (12,22) (12,24) (12,33) (12,20) (12,26) (12,34) (13,18) (13,21) (13,19) (13,28) (13,29) (13,25) (13,30) (13,27) (13,32) (13,23) (13,31) (13,22) (13,24) (13,20) (13,17) (13,26) (13,34) (14,18) (14,21) (14,19) (14,28) (14,29) (14,30) (14,27) (14,15) (14,32) (14,23) (14,31) (14,22) (14,33) (14,20) (14,17) (14,26) (15,18) (15,21) (15,29) (15,25) (15,30) (15,23) (15,31) (15,22) (15,33) (15,17) (15,26) (17,18) (17,21) (17,19) (17,28) (17,29) (17,25) (17,30) (17,27) (17,32) (17,23) (17,31) (17,22) (17,24) (17,33) (17,26) (17,34) (18,19) (18,28) (18,23) (18,22) (18,33) (18,20) (19,21) (19,28) (19,25) (19,30) (19,27) (19,31) (19,24) (19,33) (19,26) (19,34) (20,21) (20,28) (20,25) (20,27) (20,32) (20,31) (20,24) (21,28) (21,29) (21,25) (21,30) (21,27) (21,31) (21,22) (21,24) (21,26) (21,34) (22,28) (22,25) (22,27) (22,32) (22,23) (22,24) (22,33) (22,26) (22,34) (23,28) (23,25) (23,30) (23,27) (23,32) (23,31) (23,24) (23,33) (23,26) (23,34) (24,28) (24,29) (24,25) (24,30) (24,31) (24,33) (24,26) (24,34) (25,28) (25,30) (25,27) (25,32) (25,33) (25,26) (25,34) (26,28) (26,27) (26,32) (26,31) (26,33) (27,29) (27,32) (27,33) (27,34) (28,29) (28,30) (28,32) (28,31) (28,34) (29,32) (29,31) (29,34) (30,32) (30,31) (31,32) (31,33) (32,33) (33,34)\nIs there a path between node 14 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph412-15_23", + "image": "data/connectivity/graph_visual/hard/graph412.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,16) (0,14) (0,20) (1,32) (1,25) (1,21) (1,22) (1,23) (1,26) (2,9) (2,20) (3,32) (3,28) (4,9) (4,5) (4,17) (4,31) (5,13) (5,31) (5,11) (6,32) (6,26) (7,32) (7,27) (7,25) (7,28) (7,22) (7,23) (8,30) (8,31) (8,20) (9,24) (9,12) (9,11) (10,18) (10,29) (10,25) (10,28) (10,26) (11,17) (11,14) (12,14) (12,20) (13,16) (13,17) (14,24) (14,16) (14,20) (15,32) (15,25) (15,28) (15,23) (16,17) (16,20) (17,30) (18,29) (18,21) (18,28) (18,22) (19,28) (19,26) (20,30) (21,25) (21,23) (21,26) (22,25) (22,28) (22,26) (25,27) (25,29) (25,28) (27,28)\nIs there a path between node 15 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph408-26_0", + "image": "data/connectivity/graph_visual/hard/graph408.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,21) (0,17) (0,7) (0,29) (1,20) (2,32) (2,6) (2,13) (3,22) (3,23) (3,8) (4,30) (4,31) (6,23) (6,16) (6,32) (7,19) (8,14) (8,23) (8,16) (8,32) (8,13) (9,24) (9,17) (9,29) (13,14) (13,32) (14,16) (14,32) (16,20) (16,28) (17,24) (20,28) (21,29) (24,29) (27,30) (30,31)\nIs there a path between node 26 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph258-14_26", + "image": "data/connectivity/graph_visual/hard/graph258.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,17) (0,11) (0,7) (0,15) (0,30) (0,25) (1,14) (1,6) (1,8) (2,26) (2,28) (3,11) (3,5) (3,15) (3,23) (3,16) (3,19) (3,10) (4,17) (4,22) (4,15) (4,16) (4,19) (4,30) (4,10) (5,9) (5,13) (5,22) (5,24) (5,19) (5,27) (5,21) (6,29) (7,17) (7,20) (7,16) (8,14) (9,17) (9,20) (9,15) (9,24) (9,30) (9,21) (10,16) (10,24) (10,30) (10,21) (10,25) (11,17) (11,12) (11,27) (11,21) (12,17) (12,20) (12,21) (13,17) (13,20) (15,24) (15,27) (15,30) (16,22) (16,21) (17,19) (17,30) (17,21) (17,25) (18,26) (19,20) (20,24) (20,27) (20,21) (21,24) (21,27) (21,30) (21,25) (22,23) (22,30) (25,27) (25,30) (26,28) (27,30)\nIs there a path between node 14 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph531-21_15", + "image": "data/connectivity/graph_visual/hard/graph531.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,7) (0,14) (0,15) (0,29) (0,19) (0,11) (0,32) (0,13) (0,3) (0,6) (0,8) (0,23) (0,10) (0,17) (1,7) (1,14) (1,27) (1,24) (1,29) (1,33) (1,19) (1,11) (1,26) (1,13) (1,3) (1,6) (1,10) (1,17) (2,22) (2,25) (2,31) (2,12) (2,16) (3,7) (3,14) (3,27) (3,33) (3,9) (3,30) (3,13) (3,6) (3,8) (3,17) (4,22) (4,28) (4,12) (4,16) (4,21) (4,18) (5,7) (5,14) (5,15) (5,24) (5,29) (5,19) (5,9) (5,30) (5,32) (5,26) (5,8) (5,10) (5,17) (6,11) (6,9) (6,26) (6,13) (6,8) (6,23) (6,17) (7,14) (7,27) (7,29) (7,33) (7,9) (7,30) (7,13) (7,8) (7,10) (8,14) (8,27) (8,15) (8,24) (8,29) (8,11) (8,9) (8,30) (8,32) (8,13) (8,23) (8,10) (8,17) (9,27) (9,15) (9,24) (9,29) (9,33) (9,19) (9,11) (9,30) (9,32) (9,13) (9,23) (9,10) (10,14) (10,27) (10,24) (10,29) (10,33) (10,19) (10,11) (10,30) (10,32) (10,26) (10,23) (10,17) (11,27) (11,15) (11,29) (11,33) (11,19) (11,30) (11,32) (11,26) (11,23) (11,17) (12,22) (12,25) (12,31) (12,28) (12,16) (12,21) (12,20) (12,18) (13,14) (13,27) (13,15) (13,24) (13,29) (13,33) (13,19) (13,32) (13,26) (13,23) (13,17) (14,15) (14,24) (14,29) (14,19) (14,30) (14,32) (14,17) (15,33) (15,30) (15,32) (15,23) (15,17) (16,22) (16,25) (16,31) (16,28) (16,21) (16,18) (17,27) (17,29) (17,26) (18,22) (18,25) (18,31) (18,28) (18,21) (18,20) (19,27) (19,24) (19,29) (19,33) (19,30) (19,32) (19,23) (20,25) (20,31) (21,22) (21,31) (22,31) (22,28) (23,24) (23,29) (23,32) (23,26) (24,29) (24,33) (24,30) (24,32) (25,31) (25,28) (26,27) (26,29) (26,33) (26,30) (26,32) (27,29) (27,30) (27,32) (28,31) (29,33) (29,30) (32,33)\nIs there a path between node 21 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph150-25_7", + "image": "data/connectivity/graph_visual/hard/graph150.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,7) (0,8) (0,4) (0,20) (0,15) (0,26) (0,19) (0,10) (0,11) (0,23) (0,14) (0,27) (0,16) (1,6) (1,5) (1,28) (2,13) (2,21) (2,25) (2,22) (2,24) (2,3) (2,9) (3,13) (3,21) (3,17) (3,22) (3,9) (4,7) (4,8) (4,20) (4,12) (4,15) (4,19) (4,10) (4,11) (4,23) (4,14) (4,27) (5,6) (6,18) (6,28) (7,8) (7,20) (7,23) (7,14) (7,27) (7,16) (8,26) (8,19) (8,10) (8,11) (8,27) (9,21) (9,17) (9,25) (9,22) (9,24) (10,20) (10,12) (10,26) (10,19) (10,11) (10,23) (10,14) (10,27) (10,16) (11,20) (11,12) (11,15) (11,26) (11,19) (11,23) (11,14) (11,27) (11,16) (12,20) (12,15) (12,19) (12,23) (12,14) (12,27) (12,16) (13,25) (13,24) (14,20) (14,15) (14,27) (14,16) (15,20) (15,23) (15,27) (15,16) (16,20) (16,26) (16,19) (17,21) (17,25) (17,24) (18,28) (19,20) (19,26) (19,23) (20,26) (20,23) (20,27) (21,25) (21,22) (21,24) (22,25) (22,24) (23,26) (23,27) (26,27)\nIs there a path between node 25 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph159-11_6", + "image": "data/connectivity/graph_visual/hard/graph159.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,2) (0,26) (0,21) (0,9) (0,24) (0,17) (0,22) (1,16) (2,20) (2,11) (2,26) (2,27) (2,21) (2,12) (2,9) (2,23) (2,4) (2,19) (3,25) (4,8) (4,23) (4,17) (4,7) (4,13) (6,16) (7,10) (7,20) (7,12) (7,9) (7,23) (7,17) (7,22) (7,13) (7,19) (8,18) (8,11) (8,9) (8,17) (9,10) (9,11) (9,24) (9,23) (10,20) (10,11) (10,24) (10,13) (11,18) (11,12) (12,20) (12,24) (13,18) (13,20) (13,22) (13,14) (14,20) (14,24) (14,23) (14,19) (15,27) (15,23) (15,19) (17,28) (17,23) (18,21) (18,24) (18,19) (19,22) (20,28) (20,24) (21,28) (21,27) (22,28) (22,27) (23,26) (23,27) (23,24) (24,26) (26,28) (26,27) (27,28)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph294-15_10", + "image": "data/connectivity/graph_visual/hard/graph294.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,22) (0,13) (0,31) (0,25) (1,23) (2,17) (3,8) (3,11) (3,19) (5,16) (5,17) (5,9) (6,22) (6,26) (6,19) (6,31) (8,28) (8,12) (8,13) (9,23) (10,22) (10,25) (11,28) (11,26) (11,12) (11,19) (12,22) (12,26) (12,25) (13,28) (13,26) (13,31) (14,30) (15,22) (15,28) (15,26) (15,29) (15,31) (15,25) (16,21) (16,18) (17,18) (18,23) (18,21) (19,28) (19,26) (19,29) (19,27) (19,31) (20,30) (20,24) (22,28) (22,26) (22,29) (24,30) (25,26) (26,29) (26,31) (27,28) (29,31)\nIs there a path between node 15 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph628-1_8", + "image": "data/connectivity/graph_visual/hard/graph628.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,33) (1,28) (1,34) (2,27) (2,4) (2,15) (2,23) (2,12) (3,33) (3,30) (3,26) (4,27) (4,15) (4,8) (5,26) (6,17) (6,22) (6,23) (6,11) (7,12) (7,32) (8,27) (8,10) (8,15) (8,9) (8,14) (8,20) (9,21) (9,11) (10,23) (10,32) (11,27) (11,15) (11,12) (11,32) (11,20) (12,17) (12,22) (12,32) (14,27) (14,19) (14,20) (15,27) (15,32) (15,21) (16,19) (16,32) (17,32) (18,28) (19,20) (20,22) (21,27) (22,27) (22,29) (22,23) (22,32) (23,27) (24,30) (24,26) (25,33) (27,29) (28,31) (29,32) (30,33)\nIs there a path between node 1 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph613-28_25", + "image": "data/connectivity/graph_visual/hard/graph613.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,13) (0,19) (0,6) (0,21) (0,10) (0,31) (0,16) (0,7) (0,20) (0,8) (0,17) (0,12) (0,3) (0,11) (0,23) (0,2) (0,22) (0,1) (0,18) (1,33) (1,32) (1,13) (1,19) (1,29) (1,26) (1,27) (1,6) (1,21) (1,10) (1,31) (1,16) (1,28) (1,7) (1,20) (1,8) (1,17) (1,12) (1,3) (1,2) (1,14) (1,22) (1,18) (1,5) (2,33) (2,13) (2,19) (2,29) (2,26) (2,27) (2,6) (2,10) (2,31) (2,16) (2,28) (2,7) (2,20) (2,24) (2,8) (2,17) (2,12) (2,22) (2,18) (3,32) (3,29) (3,27) (3,6) (3,21) (3,31) (3,16) (3,28) (3,7) (3,20) (3,8) (3,12) (3,23) (3,14) (3,22) (3,18) (3,5) (4,25) (4,34) (5,33) (5,32) (5,13) (5,19) (5,29) (5,26) (5,27) (5,6) (5,21) (5,10) (5,31) (5,16) (5,28) (5,20) (5,8) (5,12) (5,11) (5,23) (5,14) (5,22) (5,18) (6,32) (6,13) (6,19) (6,26) (6,27) (6,21) (6,10) (6,16) (6,28) (6,7) (6,20) (6,17) (6,12) (6,11) (6,23) (6,14) (6,22) (6,18) (7,32) (7,13) (7,29) (7,27) (7,21) (7,10) (7,16) (7,28) (7,20) (7,24) (7,17) (7,12) (7,11) (7,23) (7,14) (7,22) (7,18) (8,33) (8,32) (8,13) (8,19) (8,29) (8,26) (8,21) (8,10) (8,31) (8,16) (8,28) (8,20) (8,24) (8,17) (8,12) (8,11) (8,23) (8,14) (8,22) (8,18) (9,25) (9,34) (9,15) (9,30) (10,33) (10,32) (10,13) (10,19) (10,29) (10,26) (10,27) (10,16) (10,28) (10,12) (10,11) (10,14) (10,22) (11,33) (11,32) (11,13) (11,19) (11,29) (11,21) (11,28) (11,20) (11,24) (11,17) (11,12) (11,23) (11,14) (11,22) (11,18) (12,33) (12,32) (12,13) (12,19) (12,29) (12,26) (12,31) (12,16) (12,28) (12,20) (12,23) (12,18) (13,33) (13,32) (13,19) (13,29) (13,26) (13,27) (13,21) (13,31) (13,16) (13,28) (13,20) (13,17) (13,23) (13,14) (13,18) (14,33) (14,32) (14,19) (14,29) (14,26) (14,27) (14,21) (14,31) (14,16) (14,28) (14,20) (14,17) (14,22) (15,25) (15,30) (16,33) (16,32) (16,19) (16,29) (16,26) (16,27) (16,21) (16,31) (16,28) (16,20) (16,24) (16,17) (16,23) (16,22) (17,33) (17,32) (17,19) (17,29) (17,21) (17,28) (17,20) (17,24) (17,23) (17,22) (17,18) (18,32) (18,19) (18,29) (18,26) (18,27) (18,21) (18,31) (18,28) (18,24) (18,23) (18,22) (19,29) (19,27) (19,21) (19,31) (19,28) (19,20) (19,23) (20,33) (20,29) (20,26) (20,31) (20,28) (20,22) (21,33) (21,32) (21,29) (21,31) (21,24) (21,23) (22,29) (22,31) (22,24) (23,29) (23,26) (23,27) (23,31) (23,28) (23,24) (24,32) (24,26) (24,27) (24,31) (25,34) (26,32) (26,29) (26,27) (26,31) (26,28) (27,33) (27,29) (27,31) (28,33) (28,31) (29,33) (29,32) (30,34) (31,33) (31,32) (32,33)\nIs there a path between node 28 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph464-9_16", + "image": "data/connectivity/graph_visual/hard/graph464.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,17) (0,8) (0,21) (0,6) (1,14) (1,13) (1,30) (1,12) (1,24) (2,15) (3,8) (3,5) (4,9) (5,7) (6,32) (6,19) (7,17) (7,25) (8,32) (9,26) (9,15) (10,14) (10,13) (10,24) (11,14) (11,13) (12,13) (12,30) (12,24) (13,29) (13,24) (13,27) (14,27) (15,16) (15,18) (16,31) (17,32) (17,25) (18,26) (19,23) (20,26) (21,32) (23,25)\nIs there a path between node 9 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph189-26_16", + "image": "data/connectivity/graph_visual/hard/graph189.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,1) (0,17) (0,3) (0,23) (0,10) (0,12) (1,21) (1,26) (1,24) (2,4) (2,22) (2,26) (2,12) (3,17) (3,29) (3,24) (3,12) (3,16) (4,17) (4,23) (4,10) (5,6) (5,27) (5,14) (5,19) (6,8) (6,11) (6,25) (6,27) (7,22) (7,13) (8,11) (8,9) (9,11) (9,20) (9,15) (9,25) (10,18) (10,17) (10,22) (10,28) (11,20) (11,15) (11,19) (12,17) (12,23) (12,16) (12,13) (13,18) (13,29) (13,22) (13,24) (13,16) (14,15) (14,19) (16,17) (16,29) (16,26) (17,28) (17,26) (18,28) (18,23) (21,29) (23,28) (23,26) (23,24) (26,29)\nIs there a path between node 26 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph134-1_4", + "image": "data/connectivity/graph_visual/hard/graph134.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,16) (0,4) (1,27) (1,26) (1,10) (1,13) (1,12) (1,24) (1,19) (1,11) (1,7) (1,6) (1,14) (1,3) (1,18) (1,20) (2,4) (3,9) (3,27) (3,10) (3,21) (3,25) (3,13) (3,24) (3,15) (3,23) (3,19) (3,11) (3,7) (3,6) (3,14) (3,18) (5,9) (5,26) (5,22) (5,10) (5,13) (5,12) (5,15) (5,17) (5,23) (5,19) (5,11) (5,7) (5,6) (5,14) (6,27) (6,26) (6,10) (6,21) (6,25) (6,13) (6,12) (6,8) (6,17) (6,23) (6,19) (6,11) (6,7) (6,14) (6,18) (6,20) (7,9) (7,27) (7,22) (7,10) (7,21) (7,13) (7,12) (7,8) (7,24) (7,15) (7,17) (7,19) (7,11) (7,14) (8,9) (8,27) (8,22) (8,10) (8,21) (8,25) (8,13) (8,12) (8,15) (8,17) (8,23) (8,19) (8,11) (8,14) (8,18) (8,20) (9,27) (9,10) (9,21) (9,13) (9,12) (9,24) (9,15) (9,17) (9,23) (9,19) (9,11) (9,20) (10,27) (10,26) (10,22) (10,21) (10,25) (10,13) (10,24) (10,15) (10,17) (10,19) (10,11) (10,14) (11,27) (11,26) (11,22) (11,25) (11,13) (11,15) (11,17) (11,14) (11,18) (11,20) (12,27) (12,26) (12,22) (12,21) (12,13) (12,15) (12,17) (12,23) (12,19) (12,18) (12,20) (13,22) (13,21) (13,24) (13,15) (13,17) (13,23) (13,19) (13,14) (13,18) (13,20) (14,27) (14,26) (14,24) (14,15) (14,17) (14,23) (14,19) (14,20) (15,27) (15,22) (15,25) (15,24) (15,17) (15,23) (15,20) (17,22) (17,25) (17,23) (17,19) (17,18) (17,20) (18,26) (18,24) (18,23) (18,19) (19,26) (19,21) (19,25) (19,24) (19,23) (19,20) (20,27) (20,26) (20,21) (20,24) (20,23) (21,27) (21,22) (21,25) (21,24) (22,27) (22,26) (23,27) (23,26) (23,24) (25,27) (25,26)\nIs there a path between node 1 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph289-30_3", + "image": "data/connectivity/graph_visual/hard/graph289.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,21) (0,23) (0,2) (0,8) (1,18) (1,3) (1,16) (2,4) (2,5) (3,25) (3,13) (4,6) (4,27) (4,17) (4,8) (5,26) (5,19) (5,30) (5,28) (5,23) (5,15) (5,8) (6,26) (6,19) (6,30) (6,8) (8,26) (8,21) (8,23) (8,27) (9,14) (11,20) (11,16) (12,19) (12,30) (13,18) (13,29) (15,28) (16,24) (16,20) (16,29) (17,30) (17,21) (17,27) (19,30) (19,27) (20,25) (21,26) (21,28) (23,27) (25,29) (27,30) (27,28)\nIs there a path between node 30 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph288-11_17", + "image": "data/connectivity/graph_visual/hard/graph288.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,23) (1,9) (1,11) (1,25) (1,30) (1,15) (1,21) (1,26) (2,16) (2,5) (2,19) (2,25) (2,24) (3,8) (4,27) (4,19) (4,30) (4,15) (4,20) (4,21) (5,27) (5,16) (5,18) (5,19) (5,15) (5,14) (5,31) (6,13) (7,10) (7,23) (8,12) (8,9) (8,28) (8,20) (9,11) (9,20) (9,21) (9,14) (10,29) (11,12) (11,30) (11,20) (11,21) (11,26) (12,19) (12,20) (12,14) (12,26) (13,17) (13,29) (14,28) (14,21) (14,26) (14,24) (15,27) (15,18) (15,21) (16,22) (16,25) (16,26) (16,24) (18,25) (18,31) (19,27) (19,28) (19,21) (20,28) (20,25) (20,30) (20,24) (21,28) (21,30) (21,26) (21,31) (22,27) (22,28) (22,31) (23,29) (24,28) (24,26) (24,31) (25,31) (26,27) (26,31) (27,31) (30,31)\nIs there a path between node 11 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph422-13_4", + "image": "data/connectivity/graph_visual/hard/graph422.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,21) (0,6) (0,13) (0,26) (1,27) (1,28) (1,6) (1,17) (1,13) (1,24) (1,10) (1,15) (2,9) (2,31) (2,19) (2,17) (2,29) (3,16) (3,9) (3,18) (3,26) (3,29) (4,20) (4,16) (4,9) (4,17) (4,18) (4,24) (6,27) (6,20) (6,9) (6,14) (6,13) (6,26) (6,24) (7,28) (7,9) (7,31) (7,30) (7,19) (7,17) (7,22) (7,29) (8,32) (9,16) (9,21) (9,30) (9,17) (9,22) (9,18) (10,20) (10,16) (10,14) (10,21) (10,18) (10,15) (13,20) (13,17) (13,26) (13,29) (14,28) (14,21) (14,19) (14,18) (15,17) (15,18) (15,29) (16,20) (16,31) (16,17) (16,18) (16,29) (17,27) (17,28) (17,20) (17,18) (17,26) (18,31) (19,21) (19,30) (19,22) (20,27) (20,28) (21,27) (21,31) (21,30) (22,30) (24,28) (24,29) (26,27) (26,29) (27,31) (27,30) (29,31) (29,30)\nIs there a path between node 13 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph199-8_23", + "image": "data/connectivity/graph_visual/hard/graph199.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,13) (0,15) (0,27) (0,28) (0,14) (0,17) (0,2) (0,19) (0,5) (0,26) (0,29) (0,4) (0,22) (0,6) (0,11) (0,25) (1,12) (1,28) (1,14) (1,17) (1,10) (1,19) (1,20) (1,18) (1,23) (1,26) (1,29) (1,8) (1,4) (1,22) (1,3) (1,11) (1,25) (2,12) (2,13) (2,15) (2,7) (2,27) (2,28) (2,14) (2,10) (2,19) (2,5) (2,20) (2,18) (2,23) (2,26) (2,29) (2,8) (2,4) (2,22) (2,6) (2,3) (2,11) (2,25) (3,12) (3,27) (3,19) (3,20) (3,18) (3,23) (3,26) (3,29) (3,8) (3,4) (3,22) (3,6) (3,25) (4,12) (4,13) (4,10) (4,5) (4,20) (4,18) (4,26) (4,22) (4,6) (4,11) (4,25) (5,12) (5,15) (5,7) (5,28) (5,17) (5,10) (5,19) (5,20) (5,18) (5,26) (5,29) (5,8) (5,22) (6,12) (6,13) (6,15) (6,27) (6,28) (6,17) (6,10) (6,19) (6,20) (6,18) (6,23) (6,26) (6,25) (7,12) (7,13) (7,15) (7,27) (7,10) (7,23) (7,29) (7,8) (7,22) (7,11) (8,13) (8,15) (8,28) (8,14) (8,17) (8,10) (8,19) (8,20) (8,18) (8,23) (8,26) (8,22) (8,11) (9,16) (9,21) (10,12) (10,13) (10,15) (10,28) (10,17) (10,19) (10,20) (10,18) (10,23) (10,29) (10,11) (11,28) (11,14) (11,17) (11,19) (11,20) (11,18) (11,23) (11,26) (11,29) (11,22) (11,25) (12,13) (12,15) (12,28) (12,14) (12,17) (12,19) (12,20) (12,23) (12,26) (12,29) (12,22) (12,25) (13,15) (13,28) (13,17) (13,20) (13,23) (13,26) (13,29) (13,22) (14,15) (14,27) (14,28) (14,17) (14,19) (14,20) (14,23) (14,26) (14,29) (14,25) (15,27) (15,28) (15,17) (15,19) (15,20) (15,18) (15,26) (15,22) (15,25) (16,21) (17,27) (17,19) (17,20) (17,18) (17,23) (17,26) (17,29) (17,22) (18,27) (18,28) (18,23) (18,26) (18,22) (19,27) (19,28) (19,22) (19,25) (20,26) (20,29) (20,25) (21,24) (22,27) (22,26) (22,29) (22,25) (23,27) (23,28) (23,29) (23,25) (25,28) (25,29) (26,27) (26,28) (27,28) (28,29)\nIs there a path between node 8 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph599-24_3", + "image": "data/connectivity/graph_visual/hard/graph599.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,25) (0,32) (0,24) (0,10) (0,1) (0,28) (0,17) (0,3) (0,16) (0,7) (0,29) (0,5) (1,6) (1,25) (1,32) (1,24) (1,13) (1,10) (1,11) (1,28) (1,16) (1,7) (1,29) (2,14) (2,15) (2,8) (2,33) (3,18) (3,25) (3,24) (3,13) (3,10) (3,11) (3,28) (3,17) (3,16) (3,7) (3,29) (4,12) (4,27) (4,21) (5,18) (5,6) (5,25) (5,24) (5,13) (5,10) (5,11) (5,17) (5,29) (6,18) (6,25) (6,24) (6,13) (6,10) (6,11) (6,28) (7,18) (7,25) (7,32) (7,24) (7,13) (7,10) (7,28) (7,17) (7,29) (8,19) (8,33) (8,30) (9,22) (9,31) (10,25) (10,32) (10,24) (10,13) (10,28) (10,16) (10,29) (11,25) (11,32) (11,24) (11,13) (11,28) (11,17) (11,29) (12,26) (13,18) (13,25) (13,32) (13,28) (13,16) (14,19) (14,20) (14,15) (14,33) (15,19) (15,20) (15,33) (15,30) (16,32) (16,24) (16,28) (16,17) (16,29) (17,32) (17,24) (17,28) (17,29) (18,32) (18,24) (18,29) (19,20) (19,33) (19,30) (20,33) (20,30) (21,26) (22,31) (22,23) (23,31) (24,25) (24,32) (24,28) (24,29) (25,28) (26,27) (28,32) (28,29) (30,33)\nIs there a path between node 24 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph530-29_32", + "image": "data/connectivity/graph_visual/hard/graph530.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,19) (0,4) (1,23) (1,7) (1,18) (1,24) (1,32) (1,31) (1,21) (1,27) (1,11) (1,6) (1,29) (1,17) (1,20) (2,23) (2,7) (2,18) (2,33) (2,24) (2,31) (2,21) (2,8) (2,27) (2,11) (2,29) (2,17) (2,26) (3,9) (3,22) (3,13) (3,5) (3,30) (3,28) (3,16) (3,14) (3,15) (4,19) (4,10) (5,9) (5,22) (5,13) (5,28) (5,16) (5,14) (6,18) (6,32) (6,25) (6,21) (6,8) (6,11) (6,17) (6,20) (6,26) (7,18) (7,33) (7,24) (7,32) (7,25) (7,31) (7,21) (7,17) (7,20) (7,26) (8,18) (8,33) (8,32) (8,25) (8,31) (8,27) (8,11) (8,29) (8,20) (8,26) (9,22) (9,13) (9,30) (9,28) (9,14) (9,15) (10,19) (10,12) (11,18) (11,33) (11,24) (11,25) (11,31) (11,27) (11,29) (11,26) (12,19) (13,28) (13,15) (14,30) (14,28) (14,16) (14,15) (15,22) (15,30) (15,16) (16,22) (17,23) (17,18) (17,33) (17,25) (17,31) (17,21) (17,27) (17,29) (17,20) (17,26) (18,23) (18,32) (18,25) (18,21) (18,29) (18,20) (18,26) (20,23) (20,33) (20,32) (20,25) (20,31) (20,21) (20,27) (20,29) (20,26) (21,23) (21,33) (21,24) (21,25) (21,29) (23,33) (23,24) (23,25) (23,31) (23,27) (23,29) (23,26) (24,33) (24,32) (24,25) (24,27) (24,29) (24,26) (25,32) (25,31) (25,27) (25,29) (25,26) (26,33) (26,31) (26,27) (27,31) (27,29) (28,30) (31,32) (32,33)\nIs there a path between node 29 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph434-23_27", + "image": "data/connectivity/graph_visual/hard/graph434.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (0,5) (0,6) (0,2) (0,23) (0,3) (0,26) (0,7) (1,5) (1,6) (1,24) (1,30) (1,2) (1,3) (1,17) (1,26) (1,18) (1,21) (2,5) (2,6) (2,24) (2,30) (2,13) (2,23) (2,18) (3,5) (3,6) (3,24) (3,30) (3,13) (3,23) (3,17) (3,7) (4,28) (4,27) (4,31) (5,6) (5,30) (5,13) (5,17) (5,26) (6,24) (6,30) (6,13) (6,23) (6,18) (6,7) (7,24) (7,30) (7,23) (7,17) (7,26) (8,22) (8,10) (8,25) (8,12) (8,11) (8,15) (8,16) (8,32) (8,19) (8,9) (8,14) (8,20) (9,10) (9,25) (9,12) (9,11) (9,16) (9,32) (9,19) (9,20) (10,22) (10,25) (10,12) (10,11) (10,15) (10,16) (10,32) (10,20) (11,14) (11,20) (12,22) (12,15) (12,16) (12,20) (13,24) (13,17) (13,26) (13,18) (13,21) (14,25) (14,15) (14,16) (14,32) (14,19) (15,25) (15,16) (15,32) (15,19) (15,20) (16,22) (16,25) (16,19) (16,20) (17,30) (17,23) (17,26) (18,24) (18,30) (18,26) (18,21) (19,22) (19,32) (20,25) (21,24) (21,23) (21,26) (22,25) (22,32) (23,24) (23,30) (24,30) (24,26) (25,32) (26,30) (27,28) (27,31) (28,29) (28,31) (29,31)\nIs there a path between node 23 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph86-16_3", + "image": "data/connectivity/graph_visual/hard/graph86.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,25) (0,5) (0,14) (0,24) (1,7) (1,23) (1,18) (1,15) (1,26) (1,9) (1,22) (1,2) (1,3) (2,12) (2,16) (2,7) (2,15) (2,26) (2,9) (2,22) (2,3) (3,12) (3,16) (3,23) (3,8) (3,18) (3,26) (3,9) (3,22) (3,19) (4,10) (4,25) (4,20) (4,11) (4,14) (4,24) (4,13) (5,25) (5,14) (6,10) (6,21) (6,20) (6,13) (7,16) (7,23) (7,15) (7,26) (7,9) (7,22) (7,17) (7,19) (8,12) (8,16) (8,23) (8,18) (8,15) (8,26) (8,9) (8,22) (8,17) (8,19) (9,16) (9,18) (9,15) (9,26) (10,21) (10,20) (10,11) (10,14) (10,13) (11,21) (11,25) (11,20) (11,13) (12,16) (12,23) (12,15) (12,26) (12,22) (12,19) (13,21) (13,25) (13,20) (13,14) (13,24) (14,25) (15,16) (15,23) (15,18) (15,22) (15,17) (16,23) (16,26) (16,17) (16,19) (17,23) (17,18) (17,26) (17,22) (17,19) (18,23) (18,26) (18,22) (19,23) (19,26) (19,22) (20,21) (20,25) (20,24) (21,25) (21,24) (22,23) (22,26) (23,26) (24,25)\nIs there a path between node 16 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph661-14_16", + "image": "data/connectivity/graph_visual/hard/graph661.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,27) (0,32) (0,11) (0,33) (0,5) (0,31) (0,30) (0,2) (0,9) (1,26) (1,25) (1,4) (2,24) (2,17) (2,3) (2,34) (2,10) (2,9) (2,29) (3,24) (3,14) (3,34) (3,5) (3,30) (3,9) (5,33) (5,10) (5,9) (6,17) (6,20) (6,15) (6,30) (7,24) (7,16) (7,20) (7,33) (8,21) (8,13) (8,19) (8,18) (9,27) (9,30) (10,24) (10,16) (10,15) (10,11) (10,28) (10,30) (11,27) (11,33) (11,28) (11,34) (11,30) (12,13) (12,19) (12,18) (13,19) (13,18) (13,22) (14,24) (14,27) (14,32) (15,17) (15,20) (15,33) (15,29) (16,24) (17,24) (17,27) (17,32) (17,33) (17,28) (17,30) (18,22) (19,26) (19,25) (19,23) (19,22) (21,25) (24,33) (25,26) (27,34) (28,32) (28,33) (28,31) (30,34) (31,33) (31,34) (33,34)\nIs there a path between node 14 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph137-7_22", + "image": "data/connectivity/graph_visual/hard/graph137.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,16) (0,13) (0,1) (0,9) (0,5) (0,7) (0,3) (0,10) (0,23) (0,26) (0,27) (0,8) (0,14) (0,22) (0,20) (0,15) (0,4) (0,2) (1,25) (1,11) (1,21) (1,13) (1,9) (1,3) (1,10) (1,23) (1,26) (1,27) (1,14) (1,20) (1,15) (1,2) (1,28) (2,25) (2,11) (2,16) (2,21) (2,6) (2,13) (2,9) (2,7) (2,23) (2,26) (2,8) (2,20) (2,15) (3,25) (3,6) (3,13) (3,9) (3,10) (3,27) (3,20) (3,15) (3,4) (3,28) (4,11) (4,16) (4,6) (4,13) (4,10) (4,23) (4,26) (4,27) (4,8) (4,14) (4,22) (4,15) (4,28) (5,25) (5,16) (5,21) (5,6) (5,13) (5,9) (5,7) (5,26) (5,8) (5,22) (5,15) (5,28) (6,11) (6,16) (6,21) (6,13) (6,9) (6,7) (6,10) (6,27) (6,22) (6,20) (6,15) (7,25) (7,16) (7,21) (7,9) (7,10) (7,27) (7,8) (7,14) (7,22) (7,20) (7,15) (7,28) (8,25) (8,13) (8,23) (8,26) (8,27) (8,14) (8,20) (8,28) (9,25) (9,11) (9,16) (9,21) (9,10) (9,23) (9,26) (9,27) (9,22) (9,20) (9,28) (10,11) (10,16) (10,21) (10,13) (10,23) (10,26) (10,27) (10,14) (10,22) (10,20) (10,15) (10,28) (11,25) (11,16) (11,21) (11,13) (11,23) (11,26) (11,27) (11,14) (11,22) (11,20) (12,24) (12,19) (13,25) (13,16) (13,14) (13,22) (13,15) (13,28) (14,25) (14,21) (14,23) (14,26) (14,20) (14,15) (15,16) (15,21) (15,26) (15,27) (15,22) (15,28) (16,21) (16,23) (16,26) (16,27) (16,28) (17,18) (20,25) (20,23) (20,26) (20,27) (20,22) (20,28) (21,25) (21,23) (21,26) (21,22) (22,25) (22,23) (22,27) (23,25) (23,26) (23,27) (23,28) (25,26) (25,27) (26,27) (27,28)\nIs there a path between node 7 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph62-11_16", + "image": "data/connectivity/graph_visual/hard/graph62.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,5) (0,23) (0,20) (0,12) (1,9) (1,17) (1,16) (1,13) (2,9) (2,12) (3,10) (3,24) (3,21) (5,23) (6,10) (6,24) (7,10) (7,22) (7,25) (8,23) (8,17) (8,20) (9,17) (9,20) (9,26) (9,12) (10,18) (10,14) (12,23) (12,20) (12,26) (12,16) (12,19) (13,20) (14,22) (15,17) (15,20) (16,19) (17,23) (17,26) (17,19) (18,24) (18,21) (20,23) (20,26) (21,22) (21,24) (22,25)\nIs there a path between node 11 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph340-31_4", + "image": "data/connectivity/graph_visual/hard/graph340.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,14) (0,13) (0,27) (1,21) (1,24) (1,13) (1,5) (2,19) (3,30) (3,26) (3,10) (3,25) (5,15) (5,9) (5,27) (5,19) (6,22) (6,29) (6,16) (7,15) (7,24) (7,9) (7,19) (9,21) (9,15) (9,24) (10,31) (10,11) (10,23) (11,23) (11,26) (11,17) (12,22) (12,29) (12,16) (13,14) (13,24) (14,21) (14,24) (14,27) (15,21) (16,29) (17,23) (17,25) (18,20) (18,29) (20,22) (21,27) (24,27) (25,28)\nIs there a path between node 31 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph119-25_15", + "image": "data/connectivity/graph_visual/hard/graph119.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,11) (0,8) (0,1) (0,7) (0,18) (1,3) (1,4) (2,16) (3,17) (3,4) (3,7) (4,17) (6,7) (6,18) (7,22) (7,8) (8,17) (9,23) (9,21) (10,12) (11,17) (12,25) (13,23) (13,15) (13,21) (13,20) (14,24) (14,27) (14,20) (16,25) (17,18) (18,22) (19,26) (19,25) (20,27) (23,27) (24,27)\nIs there a path between node 25 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph408-17_12", + "image": "data/connectivity/graph_visual/hard/graph408.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,21) (0,17) (0,7) (0,29) (1,20) (2,32) (2,6) (2,13) (3,22) (3,23) (3,8) (4,30) (4,31) (6,23) (6,16) (6,32) (7,19) (8,14) (8,23) (8,16) (8,32) (8,13) (9,24) (9,17) (9,29) (13,14) (13,32) (14,16) (14,32) (16,20) (16,28) (17,24) (20,28) (21,29) (24,29) (27,30) (30,31)\nIs there a path between node 17 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph559-8_24", + "image": "data/connectivity/graph_visual/hard/graph559.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,1) (0,29) (0,8) (0,19) (0,26) (0,7) (0,10) (0,24) (1,8) (1,5) (1,19) (2,11) (2,29) (2,8) (2,6) (2,5) (2,19) (2,26) (2,7) (2,27) (2,14) (2,24) (3,33) (3,32) (4,18) (5,29) (5,10) (6,8) (6,10) (7,29) (7,10) (7,14) (8,26) (9,33) (9,17) (9,30) (9,20) (10,27) (11,24) (12,18) (12,16) (12,20) (13,22) (13,31) (13,15) (14,26) (15,31) (16,17) (16,32) (16,30) (16,20) (17,32) (19,24) (20,33) (21,32) (21,30) (22,23) (23,25) (27,29) (28,31)\nIs there a path between node 8 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph601-25_18", + "image": "data/connectivity/graph_visual/hard/graph601.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,25) (0,3) (1,25) (1,29) (2,14) (2,13) (2,20) (2,18) (2,31) (2,9) (2,27) (2,21) (2,12) (2,7) (2,33) (2,11) (2,24) (2,26) (2,30) (3,25) (4,23) (4,22) (4,34) (4,5) (5,23) (5,22) (5,34) (6,14) (6,13) (6,20) (6,18) (6,27) (6,21) (6,12) (6,7) (6,28) (6,24) (6,26) (6,30) (7,14) (7,13) (7,20) (7,31) (7,17) (7,9) (7,27) (7,21) (7,12) (7,10) (7,33) (7,28) (7,30) (8,14) (8,13) (8,31) (8,17) (8,9) (8,27) (8,12) (8,33) (8,11) (8,28) (8,26) (8,30) (9,14) (9,13) (9,20) (9,18) (9,27) (9,21) (9,12) (9,10) (9,33) (9,24) (9,26) (9,19) (9,30) (10,13) (10,20) (10,18) (10,31) (10,17) (10,27) (10,12) (10,33) (10,11) (10,28) (10,24) (11,14) (11,13) (11,20) (11,18) (11,31) (11,12) (11,33) (11,28) (11,24) (11,26) (11,30) (12,14) (12,13) (12,20) (12,18) (12,17) (12,27) (12,21) (12,33) (12,19) (13,14) (13,20) (13,18) (13,31) (13,17) (13,21) (13,28) (13,24) (13,26) (14,18) (14,31) (14,17) (14,27) (14,21) (14,33) (14,26) (15,32) (17,18) (17,31) (17,27) (17,33) (17,28) (17,24) (17,26) (17,19) (17,30) (18,20) (18,31) (18,33) (18,24) (18,26) (18,19) (18,30) (19,31) (19,27) (19,21) (19,33) (19,28) (19,26) (20,31) (20,27) (20,21) (20,33) (20,24) (20,26) (20,30) (21,27) (21,33) (21,28) (21,24) (21,30) (22,23) (22,34) (23,34) (24,33) (24,26) (25,29) (26,31) (26,33) (26,30) (27,31) (27,33) (27,28) (27,30) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nIs there a path between node 25 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph103-1_14", + "image": "data/connectivity/graph_visual/hard/graph103.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,20) (0,2) (0,21) (0,26) (0,24) (0,9) (0,18) (0,8) (0,23) (0,5) (0,4) (0,7) (0,14) (0,17) (0,12) (0,10) (0,25) (0,27) (2,20) (2,21) (2,24) (2,9) (2,18) (2,8) (2,6) (2,23) (2,4) (2,11) (2,7) (2,14) (2,17) (2,12) (2,10) (2,25) (2,13) (2,27) (4,20) (4,22) (4,21) (4,24) (4,9) (4,8) (4,6) (4,23) (4,5) (4,11) (4,14) (4,15) (4,12) (4,10) (4,25) (4,13) (4,16) (4,27) (5,22) (5,21) (5,26) (5,6) (5,23) (5,7) (5,14) (5,15) (5,10) (5,13) (6,20) (6,22) (6,24) (6,11) (6,7) (6,17) (6,12) (6,25) (6,13) (6,16) (7,20) (7,22) (7,21) (7,9) (7,23) (7,14) (7,17) (7,10) (7,25) (7,13) (7,16) (8,20) (8,22) (8,26) (8,18) (8,23) (8,11) (8,14) (8,15) (8,17) (8,12) (8,13) (8,16) (9,20) (9,22) (9,21) (9,24) (9,18) (9,23) (9,14) (9,15) (9,17) (9,10) (9,25) (9,13) (9,16) (10,20) (10,21) (10,26) (10,23) (10,11) (10,14) (10,15) (10,17) (10,12) (10,25) (10,13) (10,16) (10,27) (11,21) (11,26) (11,18) (11,23) (11,14) (11,15) (11,17) (11,12) (11,25) (11,13) (11,27) (12,20) (12,21) (12,26) (12,18) (12,23) (12,14) (12,15) (12,25) (12,13) (12,16) (13,20) (13,21) (13,24) (13,18) (13,14) (13,15) (13,17) (13,27) (14,20) (14,22) (14,21) (14,26) (14,24) (14,23) (14,25) (14,27) (15,20) (15,22) (15,21) (15,26) (15,25) (15,16) (15,27) (16,20) (16,22) (16,21) (16,26) (16,24) (16,18) (16,23) (16,17) (17,20) (17,22) (17,21) (17,26) (17,24) (17,18) (17,23) (17,25) (17,27) (18,20) (18,26) (18,24) (18,23) (20,22) (20,21) (20,26) (20,24) (20,25) (20,27) (21,26) (21,24) (21,23) (21,25) (22,26) (22,24) (22,23) (22,25) (23,26) (23,24) (23,25) (23,27) (24,26) (24,25) (24,27)\nIs there a path between node 1 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph276-14_26", + "image": "data/connectivity/graph_visual/hard/graph276.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,15) (0,11) (0,30) (0,8) (0,25) (0,7) (0,17) (0,23) (0,3) (0,27) (0,10) (0,28) (0,26) (0,14) (0,29) (1,15) (1,11) (1,20) (1,25) (1,17) (1,23) (1,3) (1,27) (1,10) (1,28) (1,26) (1,14) (2,9) (2,13) (2,18) (2,22) (3,30) (3,8) (3,20) (3,7) (3,23) (3,27) (3,10) (3,28) (3,26) (3,14) (3,29) (4,21) (4,19) (4,12) (4,24) (4,16) (5,9) (5,18) (5,22) (6,21) (6,19) (6,12) (6,24) (7,15) (7,11) (7,8) (7,17) (7,23) (7,10) (7,28) (7,26) (7,14) (8,15) (8,11) (8,30) (8,17) (8,10) (8,26) (8,29) (9,13) (9,18) (10,11) (10,30) (10,20) (10,25) (10,17) (10,28) (10,26) (10,14) (10,29) (11,15) (11,25) (11,17) (11,23) (11,27) (11,29) (12,21) (12,19) (13,18) (13,22) (14,15) (14,20) (14,25) (14,17) (14,23) (14,28) (14,26) (14,29) (15,30) (15,20) (15,25) (15,17) (15,23) (15,27) (15,29) (16,19) (17,20) (17,25) (17,23) (17,27) (17,28) (17,29) (20,30) (20,25) (20,27) (20,28) (20,26) (20,29) (21,24) (23,30) (23,25) (23,28) (23,26) (23,29) (25,27) (25,26) (26,29) (27,30) (27,29) (28,30) (28,29) (29,30)\nIs there a path between node 14 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph653-18_27", + "image": "data/connectivity/graph_visual/hard/graph653.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,20) (0,13) (0,1) (1,4) (1,12) (1,34) (1,6) (1,28) (3,32) (4,20) (4,12) (4,34) (4,6) (4,28) (4,13) (5,26) (5,23) (5,18) (5,24) (5,30) (5,8) (5,21) (5,10) (5,25) (5,29) (5,22) (5,33) (5,15) (5,11) (6,20) (6,12) (6,28) (6,13) (7,16) (8,9) (8,31) (8,26) (8,23) (8,18) (8,24) (8,19) (8,21) (8,10) (8,25) (8,22) (8,33) (8,11) (8,17) (9,31) (9,26) (9,23) (9,18) (9,24) (9,21) (9,10) (9,25) (9,29) (9,22) (9,33) (9,15) (9,17) (10,31) (10,26) (10,23) (10,18) (10,24) (10,30) (10,19) (10,21) (10,29) (10,33) (10,15) (11,31) (11,23) (11,18) (11,24) (11,30) (11,19) (11,21) (11,25) (11,29) (11,33) (11,15) (11,17) (12,20) (12,34) (12,13) (13,20) (14,16) (15,31) (15,26) (15,18) (15,24) (15,30) (15,19) (15,21) (15,25) (15,22) (15,17) (15,27) (17,31) (17,23) (17,18) (17,24) (17,22) (17,27) (18,31) (18,26) (18,23) (18,24) (18,30) (18,19) (18,21) (18,25) (18,29) (18,22) (18,27) (19,31) (19,26) (19,24) (19,21) (19,25) (19,22) (19,33) (19,27) (20,34) (20,28) (21,31) (21,26) (21,23) (21,25) (21,29) (21,22) (21,33) (21,27) (22,24) (22,25) (22,29) (22,33) (22,27) (23,26) (23,29) (23,27) (24,31) (24,26) (24,30) (24,25) (24,29) (25,26) (25,30) (25,29) (25,33) (25,27) (26,31) (26,30) (26,29) (26,33) (26,27) (27,30) (27,29) (27,33) (28,34) (29,31) (29,33) (30,31) (31,33)\nIs there a path between node 18 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph388-13_2", + "image": "data/connectivity/graph_visual/hard/graph388.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,17) (0,10) (0,28) (0,30) (0,29) (0,3) (1,14) (1,2) (2,25) (2,20) (2,7) (2,32) (2,22) (3,24) (3,19) (3,23) (3,4) (3,12) (3,29) (4,26) (4,24) (4,23) (4,8) (4,13) (5,26) (5,19) (5,23) (5,8) (5,15) (5,21) (6,14) (7,32) (8,16) (8,12) (8,29) (9,26) (9,13) (9,18) (9,29) (9,31) (10,17) (10,11) (10,30) (10,23) (10,13) (11,16) (11,17) (11,19) (11,28) (11,23) (12,26) (12,24) (12,21) (13,26) (13,17) (13,19) (13,30) (13,31) (14,25) (14,22) (15,16) (15,17) (15,23) (15,18) (15,29) (16,26) (16,24) (16,18) (16,21) (17,24) (17,19) (17,28) (17,30) (17,23) (18,24) (18,21) (19,26) (19,24) (19,28) (19,23) (20,32) (22,32) (22,27) (24,26) (24,30) (26,29) (28,29)\nIs there a path between node 13 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph340-26_0", + "image": "data/connectivity/graph_visual/hard/graph340.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,14) (0,13) (0,27) (1,21) (1,24) (1,13) (1,5) (2,19) (3,30) (3,26) (3,10) (3,25) (5,15) (5,9) (5,27) (5,19) (6,22) (6,29) (6,16) (7,15) (7,24) (7,9) (7,19) (9,21) (9,15) (9,24) (10,31) (10,11) (10,23) (11,23) (11,26) (11,17) (12,22) (12,29) (12,16) (13,14) (13,24) (14,21) (14,24) (14,27) (15,21) (16,29) (17,23) (17,25) (18,20) (18,29) (20,22) (21,27) (24,27) (25,28)\nIs there a path between node 26 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph607-0_31", + "image": "data/connectivity/graph_visual/hard/graph607.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,2) (0,29) (0,27) (0,13) (0,14) (0,6) (0,33) (0,24) (2,8) (2,20) (2,4) (2,16) (2,15) (2,11) (2,24) (2,25) (3,8) (3,22) (3,32) (3,28) (3,10) (3,27) (3,30) (3,13) (3,33) (3,24) (4,8) (4,17) (4,29) (4,10) (4,30) (4,16) (4,26) (4,15) (4,14) (4,33) (6,20) (6,22) (6,32) (6,19) (6,10) (6,13) (6,31) (6,24) (6,25) (8,22) (8,12) (8,27) (8,14) (8,11) (8,25) (9,32) (9,17) (9,30) (9,16) (9,33) (9,24) (9,25) (10,22) (10,26) (10,11) (10,25) (11,20) (11,27) (11,33) (11,25) (12,20) (12,22) (12,32) (12,29) (12,27) (12,14) (12,33) (12,24) (13,26) (13,31) (13,33) (13,24) (13,25) (14,32) (14,19) (14,27) (14,16) (14,15) (15,32) (15,19) (15,16) (15,25) (16,19) (16,17) (16,30) (16,31) (16,24) (16,25) (17,32) (17,28) (17,27) (17,33) (18,34) (19,20) (20,22) (20,30) (22,29) (22,30) (24,27) (24,30) (24,31) (24,33) (25,28) (25,26) (25,31) (26,27) (26,30) (27,28) (27,29) (27,30) (28,31) (28,33) (29,33) (31,32)\nIs there a path between node 0 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph359-12_10", + "image": "data/connectivity/graph_visual/hard/graph359.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,13) (0,12) (0,15) (1,18) (1,31) (1,20) (1,30) (2,6) (2,14) (2,17) (2,5) (3,9) (3,29) (3,23) (3,17) (4,9) (4,21) (4,8) (4,14) (4,10) (5,16) (5,9) (5,21) (5,8) (5,10) (5,28) (6,11) (6,29) (6,22) (6,27) (7,18) (7,30) (7,26) (7,19) (8,29) (8,22) (8,14) (8,17) (8,10) (8,27) (9,16) (9,11) (9,14) (9,10) (10,16) (10,27) (11,21) (11,17) (12,30) (12,13) (12,25) (13,18) (13,24) (13,25) (13,19) (14,21) (14,22) (15,24) (16,21) (16,22) (16,28) (17,29) (17,21) (18,20) (19,20) (19,30) (19,25) (21,27) (22,28) (22,27) (23,29) (25,26)\nIs there a path between node 12 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph667-7_4", + "image": "data/connectivity/graph_visual/hard/graph667.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,15) (0,11) (1,29) (2,9) (2,22) (2,23) (2,18) (2,33) (2,8) (2,5) (2,17) (3,4) (3,29) (4,24) (4,21) (4,12) (5,13) (5,23) (5,18) (5,16) (5,8) (5,27) (5,17) (6,14) (6,22) (6,7) (6,10) (6,27) (6,28) (6,11) (7,9) (7,34) (7,23) (7,18) (7,33) (7,17) (8,14) (8,22) (8,15) (8,34) (8,32) (8,19) (8,33) (8,30) (8,27) (9,16) (10,22) (10,34) (10,23) (10,32) (10,33) (10,30) (10,11) (11,15) (11,18) (11,16) (11,19) (11,30) (12,24) (12,31) (13,22) (13,32) (13,19) (14,18) (14,32) (14,17) (15,33) (16,26) (17,26) (17,33) (17,27) (18,23) (18,19) (18,30) (18,27) (18,28) (19,27) (20,31) (22,34) (22,32) (22,30) (23,30) (23,27) (23,28) (24,25) (26,27) (27,32) (27,33) (28,34) (29,31) (30,33)\nIs there a path between node 7 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph641-5_24", + "image": "data/connectivity/graph_visual/hard/graph641.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,28) (0,15) (0,19) (0,6) (0,2) (0,33) (0,18) (0,5) (0,7) (0,9) (0,34) (1,26) (1,23) (1,3) (1,4) (1,20) (1,25) (1,13) (1,11) (2,28) (2,14) (2,15) (2,19) (2,6) (2,27) (2,8) (2,24) (2,5) (2,7) (2,9) (3,26) (3,31) (3,23) (3,4) (3,17) (3,29) (3,20) (3,25) (3,13) (3,11) (3,30) (4,26) (4,31) (4,23) (4,29) (4,20) (4,25) (4,13) (4,11) (5,28) (5,14) (5,10) (5,19) (5,6) (5,27) (5,33) (5,8) (5,18) (5,24) (5,7) (6,28) (6,15) (6,10) (6,19) (6,27) (6,8) (6,18) (6,7) (6,9) (6,34) (7,28) (7,14) (7,10) (7,19) (7,27) (7,8) (7,18) (7,9) (7,34) (8,28) (8,14) (8,10) (8,27) (8,33) (8,24) (8,34) (9,28) (9,15) (9,10) (9,33) (9,18) (9,24) (9,34) (10,28) (10,15) (10,19) (10,27) (11,23) (11,17) (11,29) (11,20) (11,13) (12,21) (12,22) (12,16) (13,23) (13,17) (13,29) (13,25) (13,30) (14,28) (14,15) (14,27) (14,33) (14,24) (14,34) (15,28) (15,19) (15,27) (15,18) (16,21) (16,32) (17,26) (17,23) (17,29) (17,30) (18,28) (18,19) (18,27) (18,24) (19,27) (19,24) (19,34) (20,26) (20,31) (20,29) (20,30) (21,22) (21,32) (23,26) (23,29) (23,25) (24,28) (24,27) (25,26) (25,31) (25,29) (25,30) (26,31) (26,29) (26,30) (27,34) (28,33) (28,34) (29,31) (29,30) (30,31) (33,34)\nIs there a path between node 5 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph708-14_13", + "image": "data/connectivity/graph_visual/hard/graph708.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,33) (0,7) (0,24) (0,22) (0,27) (0,17) (0,20) (1,21) (1,9) (1,15) (1,33) (1,7) (1,25) (1,24) (1,22) (1,8) (1,27) (1,20) (2,23) (2,14) (2,31) (2,10) (2,4) (2,30) (2,26) (2,6) (2,16) (2,11) (3,29) (4,23) (4,14) (4,31) (4,10) (4,12) (4,30) (4,26) (4,32) (4,16) (4,18) (4,19) (4,11) (4,34) (5,21) (5,9) (5,15) (5,33) (5,7) (5,25) (5,24) (5,22) (5,8) (5,27) (5,17) (5,20) (6,23) (6,13) (6,14) (6,31) (6,12) (6,30) (6,26) (6,16) (6,19) (6,11) (6,34) (7,21) (7,9) (7,15) (7,33) (7,25) (7,24) (7,22) (7,27) (7,17) (8,21) (8,9) (8,33) (8,25) (8,24) (8,22) (8,27) (8,17) (9,21) (9,15) (9,33) (9,24) (9,22) (9,27) (9,17) (9,20) (10,14) (10,31) (10,12) (10,30) (10,26) (10,32) (10,18) (10,19) (11,23) (11,13) (11,14) (11,31) (11,30) (11,32) (11,16) (11,18) (11,19) (12,13) (12,14) (12,31) (12,30) (12,26) (12,16) (12,19) (12,34) (13,23) (13,14) (13,31) (13,30) (13,32) (13,16) (13,19) (13,34) (14,23) (14,31) (14,30) (14,26) (14,32) (14,16) (14,19) (15,21) (15,33) (15,25) (15,24) (15,22) (15,27) (15,20) (16,23) (16,31) (16,26) (16,32) (16,18) (16,19) (16,34) (17,25) (17,24) (18,23) (18,31) (18,26) (18,32) (18,19) (19,31) (19,30) (19,32) (20,21) (20,22) (21,33) (21,25) (21,22) (21,27) (22,33) (22,25) (22,24) (22,27) (23,31) (23,26) (23,32) (23,34) (24,33) (24,25) (24,27) (25,33) (26,31) (26,30) (26,34) (27,33) (28,29) (30,31) (32,34)\nIs there a path between node 14 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph599-20_24", + "image": "data/connectivity/graph_visual/hard/graph599.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,25) (0,32) (0,24) (0,10) (0,1) (0,28) (0,17) (0,3) (0,16) (0,7) (0,29) (0,5) (1,6) (1,25) (1,32) (1,24) (1,13) (1,10) (1,11) (1,28) (1,16) (1,7) (1,29) (2,14) (2,15) (2,8) (2,33) (3,18) (3,25) (3,24) (3,13) (3,10) (3,11) (3,28) (3,17) (3,16) (3,7) (3,29) (4,12) (4,27) (4,21) (5,18) (5,6) (5,25) (5,24) (5,13) (5,10) (5,11) (5,17) (5,29) (6,18) (6,25) (6,24) (6,13) (6,10) (6,11) (6,28) (7,18) (7,25) (7,32) (7,24) (7,13) (7,10) (7,28) (7,17) (7,29) (8,19) (8,33) (8,30) (9,22) (9,31) (10,25) (10,32) (10,24) (10,13) (10,28) (10,16) (10,29) (11,25) (11,32) (11,24) (11,13) (11,28) (11,17) (11,29) (12,26) (13,18) (13,25) (13,32) (13,28) (13,16) (14,19) (14,20) (14,15) (14,33) (15,19) (15,20) (15,33) (15,30) (16,32) (16,24) (16,28) (16,17) (16,29) (17,32) (17,24) (17,28) (17,29) (18,32) (18,24) (18,29) (19,20) (19,33) (19,30) (20,33) (20,30) (21,26) (22,31) (22,23) (23,31) (24,25) (24,32) (24,28) (24,29) (25,28) (26,27) (28,32) (28,29) (30,33)\nIs there a path between node 20 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph272-2_22", + "image": "data/connectivity/graph_visual/hard/graph272.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,12) (0,19) (0,23) (0,5) (0,25) (0,29) (0,11) (0,28) (0,21) (0,30) (0,16) (0,6) (0,13) (0,14) (1,12) (1,19) (1,23) (1,3) (1,15) (1,10) (1,18) (1,29) (1,11) (1,28) (1,21) (1,26) (1,16) (1,8) (1,6) (1,13) (1,14) (2,12) (2,19) (2,23) (2,3) (2,10) (2,5) (2,9) (2,25) (2,29) (2,11) (2,28) (2,21) (2,26) (2,16) (2,8) (2,13) (2,14) (3,19) (3,15) (3,10) (3,18) (3,9) (3,25) (3,29) (3,21) (3,30) (3,26) (3,16) (3,13) (3,14) (4,24) (4,7) (5,12) (5,19) (5,23) (5,15) (5,18) (5,25) (5,29) (5,28) (5,30) (5,26) (5,16) (5,8) (5,6) (5,14) (6,12) (6,19) (6,23) (6,15) (6,10) (6,18) (6,9) (6,25) (6,29) (6,21) (6,30) (6,26) (6,16) (6,8) (6,13) (6,14) (7,24) (8,12) (8,23) (8,15) (8,10) (8,18) (8,9) (8,25) (8,29) (8,11) (8,28) (8,16) (8,14) (9,19) (9,18) (9,25) (9,29) (9,11) (9,21) (9,30) (9,16) (9,13) (9,14) (10,12) (10,19) (10,23) (10,25) (10,29) (10,11) (10,28) (10,21) (10,30) (11,12) (11,19) (11,23) (11,15) (11,18) (11,29) (11,21) (11,16) (11,13) (12,19) (12,23) (12,15) (12,21) (12,30) (12,16) (12,13) (12,14) (13,19) (13,15) (13,28) (13,30) (13,26) (13,16) (13,14) (14,23) (14,15) (14,18) (14,25) (14,28) (14,21) (14,26) (14,16) (15,23) (15,25) (15,29) (15,21) (15,26) (15,16) (16,25) (16,29) (16,28) (16,30) (16,26) (18,19) (18,23) (18,25) (18,28) (18,26) (19,23) (19,25) (19,28) (19,30) (19,26) (20,27) (20,22) (21,23) (21,25) (21,29) (21,30) (21,26) (22,27) (23,25) (23,29) (23,28) (23,30) (23,26) (25,29) (25,28) (25,30) (25,26) (26,29) (26,28) (26,30) (28,30)\nIs there a path between node 2 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph38-2_17", + "image": "data/connectivity/graph_visual/hard/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,7) (0,4) (0,24) (0,15) (1,2) (1,19) (1,6) (1,23) (1,13) (1,5) (1,20) (1,16) (1,25) (1,9) (1,21) (2,3) (2,6) (2,12) (2,23) (2,13) (2,5) (2,20) (2,16) (2,25) (2,9) (2,21) (2,8) (3,10) (3,22) (3,19) (3,6) (3,12) (3,14) (3,23) (3,13) (3,5) (3,20) (3,25) (3,9) (3,8) (4,11) (4,15) (5,6) (5,12) (5,23) (5,20) (5,17) (5,8) (6,22) (6,19) (6,14) (6,23) (6,13) (6,25) (6,17) (6,9) (7,15) (8,10) (8,22) (8,12) (8,13) (8,20) (8,16) (8,25) (8,9) (8,21) (9,22) (9,19) (9,12) (9,14) (9,23) (9,16) (9,25) (9,21) (10,12) (10,14) (10,20) (10,16) (10,25) (11,24) (11,15) (12,22) (12,16) (12,25) (12,17) (12,21) (13,22) (13,19) (13,14) (13,23) (13,20) (13,16) (13,17) (14,22) (14,19) (14,23) (14,25) (14,21) (15,18) (16,22) (16,23) (16,20) (16,25) (17,22) (17,19) (17,23) (17,20) (18,24) (19,22) (19,21) (20,23) (20,25) (21,22) (21,25) (22,25) (23,25)\nIs there a path between node 2 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph346-29_24", + "image": "data/connectivity/graph_visual/hard/graph346.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,29) (0,31) (0,26) (0,27) (0,19) (1,28) (2,30) (4,6) (5,29) (5,31) (6,17) (6,30) (7,24) (7,29) (7,31) (8,21) (8,28) (10,11) (10,15) (12,28) (14,15) (14,20) (15,20) (18,29) (18,26) (20,23) (21,28) (24,26) (24,27)\nIs there a path between node 29 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph104-19_7", + "image": "data/connectivity/graph_visual/hard/graph104.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,27) (0,14) (0,21) (0,10) (0,18) (0,12) (1,20) (1,17) (1,9) (1,4) (1,5) (1,24) (1,3) (1,2) (1,16) (1,13) (2,20) (2,19) (2,6) (2,9) (2,4) (2,5) (2,8) (2,22) (2,24) (2,11) (2,3) (2,16) (2,13) (2,7) (3,20) (3,19) (3,9) (3,4) (3,5) (3,8) (3,24) (3,16) (3,13) (3,7) (4,19) (4,17) (4,6) (4,9) (4,5) (4,8) (4,22) (4,11) (4,16) (4,13) (4,7) (5,20) (5,19) (5,17) (5,6) (5,9) (5,8) (5,22) (5,24) (5,11) (5,13) (6,20) (6,19) (6,17) (6,9) (6,22) (6,24) (6,16) (6,7) (7,19) (7,17) (7,9) (7,8) (7,22) (7,24) (7,11) (7,13) (8,20) (8,17) (8,9) (8,24) (8,11) (8,16) (8,13) (9,20) (9,19) (9,24) (9,11) (9,13) (10,25) (10,15) (10,26) (10,27) (10,14) (10,21) (10,23) (10,12) (11,20) (11,17) (11,22) (11,24) (11,13) (12,15) (12,14) (12,18) (13,20) (13,17) (13,22) (13,24) (13,16) (14,25) (14,15) (14,26) (14,27) (14,23) (15,25) (15,26) (15,21) (15,18) (16,20) (16,22) (16,24) (17,20) (17,19) (18,25) (18,26) (18,27) (18,21) (18,23) (19,24) (20,22) (21,25) (21,27) (23,25) (23,26) (25,26) (25,27) (26,27)\nIs there a path between node 19 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph234-25_4", + "image": "data/connectivity/graph_visual/hard/graph234.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,9) (0,30) (0,6) (0,12) (1,15) (2,17) (2,4) (3,25) (3,30) (3,12) (4,18) (4,16) (4,20) (4,22) (4,28) (4,8) (4,17) (5,12) (5,11) (6,19) (7,9) (7,10) (8,22) (8,28) (8,21) (9,23) (10,12) (10,11) (11,30) (11,19) (11,12) (12,25) (12,19) (13,27) (13,26) (15,26) (16,18) (16,29) (16,20) (16,24) (16,22) (16,28) (16,17) (17,22) (17,28) (17,21) (18,29) (18,20) (18,24) (18,22) (19,30) (20,22) (20,28) (21,24) (24,28) (25,30)\nIs there a path between node 25 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph303-24_15", + "image": "data/connectivity/graph_visual/hard/graph303.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,29) (0,24) (0,6) (0,31) (0,23) (0,26) (0,25) (0,15) (0,8) (0,1) (0,28) (0,21) (0,27) (0,7) (0,22) (0,9) (0,17) (0,30) (0,14) (0,2) (0,12) (1,29) (1,6) (1,31) (1,26) (1,25) (1,15) (1,8) (1,28) (1,21) (1,27) (1,17) (1,30) (1,14) (1,2) (1,12) (2,29) (2,31) (2,23) (2,26) (2,25) (2,15) (2,28) (2,27) (2,9) (2,30) (2,16) (2,14) (2,12) (3,11) (3,20) (3,18) (4,13) (4,10) (5,29) (5,6) (5,23) (5,26) (5,25) (5,15) (5,28) (5,21) (5,22) (5,9) (5,17) (5,30) (5,16) (5,14) (6,29) (6,31) (6,26) (6,25) (6,15) (6,8) (6,27) (6,7) (6,30) (6,14) (6,12) (7,29) (7,24) (7,31) (7,23) (7,25) (7,15) (7,8) (7,28) (7,21) (7,27) (7,22) (7,9) (7,17) (7,30) (7,16) (7,14) (8,24) (8,26) (8,25) (8,15) (8,28) (8,21) (8,27) (8,22) (8,9) (8,30) (8,14) (8,12) (9,29) (9,24) (9,31) (9,23) (9,26) (9,25) (9,28) (9,21) (9,27) (9,22) (9,17) (9,16) (9,12) (10,13) (11,19) (11,18) (12,24) (12,31) (12,23) (12,26) (12,15) (12,28) (12,21) (12,22) (12,17) (12,30) (12,16) (12,14) (14,29) (14,23) (14,26) (14,25) (14,15) (14,17) (14,16) (15,29) (15,24) (15,25) (15,28) (15,21) (15,27) (15,22) (15,17) (15,30) (16,29) (16,31) (16,23) (16,26) (16,25) (16,21) (16,27) (16,22) (16,30) (17,29) (17,31) (17,23) (17,28) (17,21) (17,22) (17,30) (18,20) (19,20) (21,29) (21,24) (21,31) (21,23) (21,28) (21,27) (21,22) (21,30) (22,29) (22,24) (22,31) (22,26) (22,25) (22,27) (23,24) (23,31) (23,26) (23,25) (23,27) (24,31) (24,25) (24,27) (25,26) (25,28) (25,27) (25,30) (26,29) (26,31) (26,27) (27,29) (27,31) (28,29) (28,30) (29,30)\nIs there a path between node 24 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph616-17_1", + "image": "data/connectivity/graph_visual/hard/graph616.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,33) (0,24) (0,27) (0,12) (0,16) (0,20) (0,5) (0,14) (0,17) (0,34) (0,29) (0,23) (0,22) (0,10) (0,28) (0,2) (0,15) (0,11) (0,8) (1,3) (1,6) (1,33) (1,27) (1,16) (1,20) (1,5) (1,26) (1,7) (1,19) (1,34) (1,29) (1,23) (1,22) (1,10) (1,28) (1,2) (1,9) (1,15) (1,11) (1,31) (1,8) (2,13) (2,33) (2,27) (2,12) (2,20) (2,7) (2,14) (2,19) (2,34) (2,29) (2,15) (2,11) (2,31) (3,6) (3,33) (3,12) (3,20) (3,5) (3,21) (3,7) (3,14) (3,17) (3,34) (3,29) (3,23) (3,22) (3,10) (3,28) (3,15) (3,11) (3,31) (3,8) (4,32) (4,30) (4,18) (5,13) (5,6) (5,33) (5,24) (5,12) (5,16) (5,20) (5,21) (5,26) (5,7) (5,14) (5,19) (5,17) (5,34) (5,29) (5,23) (5,22) (5,10) (5,28) (5,9) (5,15) (5,11) (6,13) (6,33) (6,27) (6,12) (6,20) (6,21) (6,26) (6,7) (6,14) (6,34) (6,23) (6,22) (6,10) (6,15) (6,31) (6,8) (7,13) (7,33) (7,24) (7,27) (7,16) (7,20) (7,21) (7,14) (7,19) (7,17) (7,29) (7,23) (7,10) (7,28) (7,9) (7,15) (7,11) (7,31) (7,8) (8,33) (8,24) (8,27) (8,26) (8,34) (8,29) (8,23) (8,10) (8,28) (8,9) (8,15) (8,11) (8,31) (9,13) (9,33) (9,24) (9,27) (9,16) (9,20) (9,21) (9,26) (9,14) (9,19) (9,17) (9,34) (9,22) (9,15) (9,11) (9,31) (10,13) (10,33) (10,24) (10,20) (10,14) (10,19) (10,17) (10,34) (10,29) (10,23) (10,28) (10,11) (10,31) (11,13) (11,33) (11,24) (11,27) (11,12) (11,16) (11,20) (11,21) (11,26) (11,19) (11,29) (11,22) (12,13) (12,24) (12,27) (12,16) (12,20) (12,21) (12,26) (12,14) (12,19) (12,34) (12,23) (12,22) (12,28) (12,15) (12,31) (13,24) (13,27) (13,16) (13,20) (13,21) (13,14) (13,19) (13,17) (13,34) (13,23) (13,22) (13,28) (13,15) (13,31) (14,24) (14,27) (14,16) (14,20) (14,26) (14,17) (14,34) (14,22) (14,28) (15,33) (15,24) (15,16) (15,26) (15,17) (15,34) (15,29) (15,22) (15,28) (15,31) (16,33) (16,24) (16,20) (16,21) (16,17) (16,34) (16,29) (16,31) (17,33) (17,24) (17,27) (17,20) (17,26) (17,19) (17,34) (17,29) (17,23) (17,22) (17,28) (17,31) (18,32) (18,25) (19,33) (19,24) (19,20) (19,21) (19,26) (19,29) (19,23) (19,31) (20,33) (20,24) (20,27) (20,21) (20,26) (20,34) (20,29) (20,23) (20,22) (20,28) (20,31) (21,33) (21,24) (21,27) (21,26) (21,23) (21,22) (21,28) (21,31) (22,33) (22,24) (22,27) (22,26) (22,34) (22,29) (22,23) (22,28) (22,31) (23,33) (23,27) (23,26) (23,34) (23,29) (23,28) (23,31) (24,33) (24,27) (24,34) (24,31) (25,32) (25,30) (26,33) (26,27) (26,34) (26,29) (26,28) (26,31) (27,33) (27,28) (27,31) (28,33) (28,34) (29,33) (29,34) (29,31) (30,32) (31,33) (31,34)\nIs there a path between node 17 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph497-15_6", + "image": "data/connectivity/graph_visual/hard/graph497.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,19) (0,32) (0,26) (0,31) (0,9) (0,8) (0,18) (1,27) (1,23) (1,31) (1,9) (1,8) (1,7) (1,22) (1,10) (1,29) (1,28) (2,12) (2,23) (2,9) (2,13) (2,7) (2,3) (2,28) (3,16) (3,32) (3,21) (3,27) (3,14) (3,20) (3,31) (3,24) (3,7) (3,10) (3,4) (4,19) (4,32) (4,21) (4,26) (4,24) (4,9) (4,8) (4,13) (4,28) (6,12) (6,15) (6,22) (6,29) (6,18) (7,32) (7,26) (7,18) (8,32) (8,14) (8,15) (8,22) (8,28) (9,16) (9,27) (9,31) (9,24) (9,15) (9,29) (9,18) (9,28) (10,12) (10,19) (10,32) (10,21) (10,33) (10,17) (10,15) (10,22) (10,18) (11,16) (11,32) (11,26) (11,20) (11,31) (11,24) (11,22) (11,29) (12,16) (12,19) (12,14) (12,26) (12,23) (12,20) (12,22) (12,18) (13,16) (13,19) (13,24) (13,15) (14,32) (14,21) (14,27) (14,20) (14,31) (14,24) (14,15) (14,29) (15,32) (15,21) (15,24) (15,28) (16,21) (16,23) (16,22) (16,28) (17,23) (17,29) (17,28) (18,31) (18,22) (19,26) (19,23) (19,20) (19,31) (20,28) (21,33) (21,31) (22,28) (23,27) (23,28) (24,26) (24,31) (25,30) (26,32) (27,31) (28,32) (28,33) (32,33)\nIs there a path between node 15 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph34-14_5", + "image": "data/connectivity/graph_visual/hard/graph34.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,6) (0,8) (0,5) (0,13) (0,16) (0,19) (0,1) (0,21) (0,14) (1,25) (1,17) (1,5) (1,10) (1,16) (1,9) (1,19) (1,21) (1,14) (2,23) (2,22) (2,4) (2,3) (2,20) (2,24) (2,12) (2,7) (2,11) (3,22) (3,4) (3,20) (3,24) (3,15) (4,23) (4,22) (4,20) (4,24) (4,15) (4,7) (4,11) (5,6) (5,8) (5,25) (5,13) (5,10) (5,9) (5,19) (5,21) (5,14) (6,8) (6,17) (6,13) (6,10) (6,16) (6,9) (6,19) (6,21) (6,14) (7,22) (7,24) (7,15) (7,12) (7,11) (8,25) (8,13) (8,10) (8,9) (8,19) (8,14) (9,25) (9,13) (9,10) (9,19) (9,21) (10,25) (10,17) (10,13) (10,16) (10,19) (11,23) (11,22) (11,24) (11,15) (11,12) (12,23) (12,20) (12,24) (12,15) (13,17) (13,16) (13,14) (14,25) (14,17) (14,16) (14,19) (15,23) (15,20) (15,24) (16,17) (16,21) (17,21) (19,21) (20,23) (21,25) (23,24)\nIs there a path between node 14 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph569-25_33", + "image": "data/connectivity/graph_visual/hard/graph569.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,13) (0,29) (0,27) (0,23) (0,33) (0,26) (1,10) (1,5) (2,13) (2,17) (2,23) (2,22) (2,9) (2,3) (2,20) (3,23) (3,19) (3,7) (3,30) (3,21) (3,4) (3,33) (3,24) (3,8) (4,6) (4,27) (4,23) (4,22) (4,30) (4,20) (4,26) (4,8) (5,12) (6,13) (6,31) (6,27) (6,7) (6,21) (6,33) (6,26) (7,13) (7,17) (7,23) (7,22) (7,30) (7,21) (7,24) (8,25) (8,23) (8,19) (8,9) (8,30) (8,33) (8,24) (9,17) (9,31) (9,27) (10,28) (12,28) (13,31) (13,19) (13,30) (13,20) (13,26) (14,16) (15,23) (15,33) (17,25) (17,29) (17,27) (17,26) (17,24) (19,30) (19,20) (19,21) (20,25) (20,30) (20,33) (21,31) (21,33) (22,30) (22,33) (22,24) (23,29) (23,27) (23,33) (23,26) (23,24) (24,31) (25,31) (26,29) (30,31)\nIs there a path between node 25 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph69-22_20", + "image": "data/connectivity/graph_visual/hard/graph69.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,17) (1,15) (1,8) (1,4) (1,18) (2,14) (2,8) (2,6) (2,26) (3,17) (4,20) (5,16) (5,14) (5,22) (5,6) (5,10) (6,15) (6,23) (6,8) (6,22) (6,18) (6,10) (7,14) (7,8) (7,22) (7,10) (8,23) (8,12) (8,26) (8,18) (9,21) (9,17) (9,19) (10,16) (10,12) (10,26) (11,15) (11,22) (11,18) (12,16) (12,20) (12,14) (12,22) (14,16) (15,16) (15,26) (15,18) (16,23) (20,23) (20,26) (20,25) (22,26) (23,26) (25,26)\nIs there a path between node 22 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph461-7_32", + "image": "data/connectivity/graph_visual/hard/graph461.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,10) (0,23) (0,27) (0,9) (1,16) (1,3) (1,4) (1,21) (1,26) (1,2) (2,31) (2,16) (2,15) (2,6) (2,17) (3,24) (3,8) (3,19) (3,16) (3,30) (3,5) (3,4) (3,15) (3,7) (3,11) (4,24) (4,8) (4,30) (4,21) (4,12) (4,26) (4,7) (4,11) (5,21) (5,6) (5,26) (6,30) (6,21) (6,11) (7,24) (8,31) (8,24) (8,19) (8,12) (9,27) (10,18) (10,23) (10,14) (11,31) (11,24) (11,21) (12,24) (12,19) (12,30) (12,15) (12,21) (13,32) (13,18) (13,29) (14,32) (14,23) (15,19) (15,16) (16,24) (16,19) (17,19) (18,32) (18,23) (18,28) (19,24) (19,30) (19,26) (21,31) (21,30) (21,26) (26,30) (27,32) (28,32) (30,31)\nIs there a path between node 7 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph159-18_1", + "image": "data/connectivity/graph_visual/hard/graph159.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,2) (0,26) (0,21) (0,9) (0,24) (0,17) (0,22) (1,16) (2,20) (2,11) (2,26) (2,27) (2,21) (2,12) (2,9) (2,23) (2,4) (2,19) (3,25) (4,8) (4,23) (4,17) (4,7) (4,13) (6,16) (7,10) (7,20) (7,12) (7,9) (7,23) (7,17) (7,22) (7,13) (7,19) (8,18) (8,11) (8,9) (8,17) (9,10) (9,11) (9,24) (9,23) (10,20) (10,11) (10,24) (10,13) (11,18) (11,12) (12,20) (12,24) (13,18) (13,20) (13,22) (13,14) (14,20) (14,24) (14,23) (14,19) (15,27) (15,23) (15,19) (17,28) (17,23) (18,21) (18,24) (18,19) (19,22) (20,28) (20,24) (21,28) (21,27) (22,28) (22,27) (23,26) (23,27) (23,24) (24,26) (26,28) (26,27) (27,28)\nIs there a path between node 18 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph228-4_2", + "image": "data/connectivity/graph_visual/hard/graph228.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,18) (0,15) (0,8) (0,20) (1,22) (1,4) (1,25) (1,11) (1,7) (1,24) (1,28) (1,21) (2,23) (2,27) (2,18) (2,16) (2,3) (2,8) (2,5) (2,20) (3,27) (3,16) (3,12) (3,15) (3,8) (3,5) (4,29) (4,22) (4,6) (4,10) (4,17) (4,14) (4,25) (4,11) (4,7) (4,24) (4,28) (4,21) (4,26) (5,23) (5,27) (5,18) (5,16) (5,12) (5,15) (5,8) (5,20) (6,29) (6,22) (6,19) (6,10) (6,25) (6,9) (6,7) (6,13) (6,24) (6,28) (6,26) (7,10) (7,17) (7,14) (7,25) (7,9) (7,13) (7,24) (7,28) (7,21) (7,26) (8,23) (8,18) (8,12) (8,20) (9,29) (9,22) (9,19) (9,10) (9,25) (9,11) (9,13) (9,24) (9,28) (9,26) (10,29) (10,22) (10,19) (10,14) (10,25) (10,11) (10,13) (10,24) (10,26) (11,22) (11,19) (11,17) (11,25) (11,13) (11,24) (11,21) (11,26) (12,23) (12,27) (12,18) (12,16) (12,15) (13,29) (13,19) (13,17) (13,14) (13,25) (13,28) (13,21) (13,26) (14,19) (14,17) (14,25) (14,28) (14,21) (14,26) (15,23) (15,27) (15,18) (15,16) (15,20) (16,23) (16,18) (16,20) (17,22) (17,19) (17,25) (17,28) (17,26) (18,23) (18,27) (19,22) (19,25) (19,28) (19,26) (21,29) (21,25) (21,24) (21,28) (21,26) (22,29) (22,25) (22,28) (22,26) (23,27) (24,29) (24,25) (24,28) (24,26) (25,29) (25,28) (25,26) (26,29) (26,28)\nIs there a path between node 4 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph111-0_2", + "image": "data/connectivity/graph_visual/hard/graph111.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,16) (0,20) (0,1) (0,19) (0,18) (0,7) (0,17) (0,11) (0,13) (0,5) (0,3) (1,16) (1,9) (1,27) (1,19) (1,18) (1,2) (2,20) (2,10) (2,24) (2,23) (3,10) (3,13) (3,12) (4,9) (4,8) (4,14) (4,19) (4,18) (4,7) (4,17) (4,13) (4,5) (4,12) (4,23) (5,16) (5,6) (5,8) (5,19) (5,24) (5,17) (5,26) (6,20) (6,10) (6,18) (6,7) (6,11) (6,25) (7,8) (7,18) (7,17) (8,19) (8,24) (8,11) (8,13) (9,19) (9,11) (9,25) (10,27) (10,19) (10,18) (10,17) (11,14) (11,18) (11,25) (12,16) (12,14) (13,24) (13,25) (14,25) (15,22) (16,19) (16,24) (16,25) (17,19) (17,25) (18,19) (19,20) (24,27)\nIs there a path between node 0 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph69-13_18", + "image": "data/connectivity/graph_visual/hard/graph69.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,17) (1,15) (1,8) (1,4) (1,18) (2,14) (2,8) (2,6) (2,26) (3,17) (4,20) (5,16) (5,14) (5,22) (5,6) (5,10) (6,15) (6,23) (6,8) (6,22) (6,18) (6,10) (7,14) (7,8) (7,22) (7,10) (8,23) (8,12) (8,26) (8,18) (9,21) (9,17) (9,19) (10,16) (10,12) (10,26) (11,15) (11,22) (11,18) (12,16) (12,20) (12,14) (12,22) (14,16) (15,16) (15,26) (15,18) (16,23) (20,23) (20,26) (20,25) (22,26) (23,26) (25,26)\nIs there a path between node 13 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph101-24_21", + "image": "data/connectivity/graph_visual/hard/graph101.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,14) (0,21) (0,23) (0,9) (0,6) (0,17) (0,2) (0,10) (0,25) (0,7) (0,27) (0,26) (0,8) (0,5) (1,22) (1,24) (1,20) (1,4) (1,15) (1,12) (2,21) (2,9) (2,6) (2,17) (2,18) (2,3) (2,27) (2,26) (2,5) (3,23) (3,9) (3,6) (3,17) (3,19) (3,16) (3,18) (3,11) (3,10) (3,7) (3,26) (3,8) (3,5) (4,22) (4,20) (4,13) (4,15) (5,14) (5,23) (5,9) (5,6) (5,17) (5,16) (5,18) (5,11) (5,10) (5,25) (5,7) (5,27) (5,26) (5,8) (6,14) (6,21) (6,23) (6,9) (6,17) (6,19) (6,16) (6,18) (6,10) (6,7) (6,27) (6,8) (7,14) (7,21) (7,23) (7,9) (7,17) (7,19) (7,18) (7,11) (7,10) (7,25) (7,26) (7,8) (8,14) (8,21) (8,23) (8,9) (8,17) (8,19) (8,18) (8,11) (8,10) (8,25) (8,27) (8,26) (9,21) (9,19) (9,10) (9,25) (9,27) (9,26) (10,21) (10,19) (10,11) (10,25) (10,27) (10,26) (11,14) (11,21) (11,23) (11,17) (11,19) (11,16) (11,18) (11,25) (12,22) (12,24) (12,13) (13,22) (13,24) (13,20) (14,21) (14,23) (14,17) (14,19) (14,16) (14,18) (14,25) (14,26) (15,22) (15,20) (16,21) (16,23) (16,17) (16,19) (16,18) (16,26) (17,21) (17,23) (17,25) (17,27) (17,26) (18,21) (18,23) (19,21) (19,23) (19,25) (19,27) (19,26) (20,22) (20,24) (21,23) (21,25) (22,24) (23,25) (25,27) (25,26) (26,27)\nIs there a path between node 24 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph308-8_25", + "image": "data/connectivity/graph_visual/hard/graph308.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,23) (0,26) (1,11) (2,28) (2,12) (3,5) (3,18) (3,31) (4,7) (4,18) (4,24) (4,9) (4,11) (4,19) (5,16) (5,24) (5,11) (5,25) (6,23) (6,13) (6,29) (6,20) (6,14) (8,26) (8,22) (9,17) (9,11) (9,19) (10,27) (10,21) (10,24) (11,16) (11,24) (11,25) (12,29) (13,15) (14,15) (14,30) (14,28) (15,23) (15,30) (15,28) (15,20) (16,17) (16,24) (17,19) (18,21) (18,19) (19,25) (20,26) (20,30) (20,28) (21,31) (24,27) (27,31) (28,29)\nIs there a path between node 8 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph515-20_28", + "image": "data/connectivity/graph_visual/hard/graph515.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,4) (0,20) (0,31) (0,15) (0,28) (0,12) (0,18) (1,4) (1,10) (1,8) (1,16) (1,29) (1,15) (1,28) (1,23) (1,32) (1,6) (1,26) (2,14) (2,11) (3,17) (4,8) (4,23) (4,12) (4,32) (4,26) (5,10) (5,16) (5,29) (5,23) (5,12) (5,32) (6,8) (6,29) (6,12) (6,18) (6,26) (7,10) (7,8) (7,29) (7,15) (7,28) (8,29) (8,28) (8,12) (9,10) (9,31) (9,15) (9,23) (9,12) (9,18) (9,24) (9,32) (9,26) (10,20) (10,31) (10,23) (10,26) (11,14) (12,23) (12,18) (14,33) (14,25) (15,31) (15,29) (15,23) (15,18) (16,20) (16,28) (16,24) (17,19) (17,30) (17,27) (18,20) (18,29) (18,32) (20,29) (20,28) (20,23) (21,22) (22,25) (23,31) (23,29) (23,28) (24,32) (24,26) (26,31) (31,32)\nIs there a path between node 20 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph407-19_32", + "image": "data/connectivity/graph_visual/hard/graph407.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,12) (0,24) (0,31) (0,6) (0,1) (0,2) (0,19) (0,30) (1,26) (1,24) (1,31) (1,6) (1,2) (1,15) (1,5) (1,19) (1,30) (1,13) (2,22) (2,26) (2,24) (2,15) (2,5) (2,19) (2,30) (3,29) (3,16) (3,4) (3,28) (3,7) (3,8) (3,11) (3,20) (3,21) (3,25) (3,32) (3,23) (3,18) (4,29) (4,16) (4,28) (4,7) (4,8) (4,11) (4,21) (4,27) (4,17) (4,32) (4,23) (4,18) (5,22) (5,12) (5,24) (5,31) (5,6) (5,15) (5,19) (5,30) (6,26) (6,12) (6,24) (6,15) (6,19) (6,30) (6,13) (7,29) (7,16) (7,28) (7,8) (7,25) (7,27) (7,17) (7,32) (7,23) (7,18) (7,9) (8,28) (8,11) (8,25) (8,27) (8,17) (8,18) (8,9) (9,29) (9,28) (9,20) (9,21) (9,25) (9,27) (9,17) (9,32) (9,23) (9,18) (10,14) (11,29) (11,28) (11,20) (11,21) (11,25) (11,27) (11,17) (11,32) (11,23) (11,18) (12,24) (12,15) (12,19) (13,22) (13,26) (13,24) (13,31) (13,15) (13,19) (13,30) (15,26) (15,30) (16,29) (16,20) (16,21) (16,27) (16,17) (16,18) (17,29) (17,28) (17,20) (17,25) (17,27) (17,23) (17,18) (18,29) (18,28) (18,20) (18,21) (18,32) (19,26) (19,24) (19,31) (20,28) (20,27) (20,32) (20,23) (21,29) (21,28) (21,25) (21,32) (21,23) (22,24) (23,29) (23,25) (23,27) (23,32) (24,30) (25,29) (25,28) (25,27) (25,32) (26,30) (27,29) (27,28) (27,32) (28,32) (29,32) (30,31)\nIs there a path between node 19 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph7-18_2", + "image": "data/connectivity/graph_visual/hard/graph7.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,5) (0,1) (0,4) (0,12) (0,23) (0,19) (0,14) (0,21) (0,15) (0,7) (0,22) (1,24) (1,6) (1,20) (1,23) (1,25) (1,3) (1,9) (1,16) (1,7) (2,6) (2,19) (2,14) (2,10) (2,3) (2,8) (2,9) (2,7) (3,5) (3,24) (3,14) (3,25) (3,22) (4,24) (4,19) (4,10) (4,16) (5,24) (5,14) (5,15) (5,9) (6,23) (6,14) (6,15) (7,24) (7,23) (7,14) (7,15) (7,10) (7,22) (8,19) (8,14) (8,21) (8,25) (8,22) (9,23) (10,24) (10,16) (11,18) (11,17) (12,20) (12,14) (12,25) (12,16) (14,24) (14,23) (14,19) (14,15) (15,20) (15,19) (15,21) (15,22) (16,25) (17,18) (19,21) (20,24) (20,23) (20,25) (21,23) (22,23)\nIs there a path between node 18 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph261-20_22", + "image": "data/connectivity/graph_visual/hard/graph261.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,23) (0,17) (1,9) (2,21) (2,30) (3,9) (3,7) (4,17) (4,20) (5,28) (5,26) (5,24) (6,21) (7,21) (7,9) (7,11) (8,16) (8,18) (9,21) (10,11) (12,28) (12,19) (12,26) (12,17) (12,13) (13,23) (13,24) (14,15) (14,29) (15,16) (16,18) (16,29) (17,23) (19,23) (19,24) (20,28) (20,23) (20,22)\nIs there a path between node 20 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph669-17_7", + "image": "data/connectivity/graph_visual/hard/graph669.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,17) (0,33) (0,14) (1,18) (1,14) (2,28) (2,24) (2,25) (2,20) (2,31) (2,22) (2,8) (3,30) (3,23) (3,17) (3,29) (3,21) (4,7) (4,11) (4,31) (4,22) (4,8) (5,28) (5,9) (5,34) (5,22) (6,20) (6,9) (6,15) (6,8) (7,11) (7,16) (8,25) (8,20) (8,9) (8,31) (8,15) (8,22) (8,19) (9,28) (9,32) (9,11) (9,31) (10,32) (10,20) (10,15) (10,22) (10,19) (11,28) (11,31) (11,15) (11,34) (12,18) (12,23) (12,13) (13,23) (13,29) (13,33) (14,26) (14,17) (14,29) (14,33) (16,24) (16,32) (16,22) (17,30) (17,23) (18,26) (18,23) (18,29) (18,21) (21,26) (21,23) (22,34) (23,26) (24,28) (24,32) (25,28) (25,34) (28,32) (29,30)\nIs there a path between node 17 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph454-27_16", + "image": "data/connectivity/graph_visual/hard/graph454.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,7) (0,4) (0,23) (0,21) (0,18) (1,10) (1,19) (1,24) (1,18) (1,5) (2,11) (2,14) (2,22) (2,23) (2,13) (2,15) (2,31) (2,20) (3,11) (3,22) (3,16) (3,30) (3,13) (3,20) (3,18) (4,11) (4,14) (4,6) (4,23) (4,24) (4,31) (4,32) (4,18) (4,5) (5,19) (5,11) (5,7) (5,23) (5,15) (5,31) (6,19) (6,7) (6,13) (6,8) (7,11) (7,22) (7,28) (7,30) (7,21) (7,31) (8,10) (8,12) (8,14) (8,16) (8,30) (8,21) (9,17) (10,12) (10,24) (10,21) (10,32) (10,20) (11,22) (11,23) (11,13) (11,15) (11,18) (12,22) (12,31) (12,18) (13,16) (13,30) (13,23) (13,21) (13,15) (13,32) (14,19) (14,30) (14,23) (14,31) (15,30) (15,31) (15,32) (15,20) (16,30) (16,24) (16,21) (16,32) (17,25) (18,19) (18,28) (18,24) (19,21) (20,22) (20,21) (22,30) (22,23) (22,32) (24,28) (24,31) (24,32) (25,26) (25,27)\nIs there a path between node 27 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph326-13_19", + "image": "data/connectivity/graph_visual/hard/graph326.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,21) (0,6) (0,10) (0,29) (0,17) (0,1) (0,7) (0,13) (0,19) (0,20) (1,18) (1,21) (1,5) (1,6) (1,29) (1,3) (1,25) (1,17) (1,7) (1,13) (1,2) (1,30) (1,19) (2,18) (2,21) (2,5) (2,6) (2,10) (2,29) (2,3) (2,25) (2,7) (2,13) (2,19) (3,18) (3,21) (3,6) (3,10) (3,25) (3,31) (3,17) (3,16) (3,7) (3,30) (3,19) (4,12) (4,27) (4,9) (4,14) (4,23) (4,8) (4,26) (4,11) (5,21) (5,6) (5,10) (5,29) (5,25) (5,31) (5,17) (5,16) (5,7) (5,20) (6,21) (6,10) (6,25) (6,31) (6,16) (6,30) (7,18) (7,21) (7,29) (7,25) (7,31) (7,17) (7,13) (7,30) (7,20) (8,12) (8,22) (8,27) (8,28) (8,9) (8,15) (8,14) (8,23) (8,26) (8,11) (9,12) (9,22) (9,27) (9,28) (9,15) (9,14) (9,23) (9,11) (10,18) (10,21) (10,25) (10,31) (10,17) (10,16) (10,13) (10,30) (10,19) (10,20) (11,22) (11,28) (11,15) (11,23) (11,26) (12,27) (12,15) (12,14) (12,23) (12,26) (13,29) (13,16) (13,30) (13,19) (13,20) (14,22) (14,27) (14,28) (14,15) (14,23) (14,24) (15,22) (15,27) (15,23) (15,24) (16,18) (16,25) (16,17) (16,30) (16,20) (17,18) (17,21) (17,29) (17,25) (17,31) (17,30) (17,19) (17,20) (18,29) (18,25) (18,31) (18,30) (18,19) (18,20) (19,21) (19,29) (19,25) (19,30) (20,21) (20,29) (20,25) (20,31) (20,30) (21,25) (21,31) (21,30) (22,27) (22,28) (22,26) (22,24) (23,27) (23,28) (23,24) (24,27) (24,28) (25,31) (26,28) (27,28) (29,31) (29,30)\nIs there a path between node 13 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph93-0_23", + "image": "data/connectivity/graph_visual/hard/graph93.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,19) (0,18) (0,16) (0,13) (0,4) (0,8) (0,10) (0,22) (1,2) (2,7) (3,19) (3,18) (3,12) (3,20) (3,10) (4,11) (4,14) (4,5) (4,20) (4,8) (5,11) (5,14) (5,18) (5,16) (5,13) (5,12) (6,19) (6,11) (6,12) (6,20) (6,8) (7,26) (8,24) (8,14) (8,18) (8,25) (9,17) (10,15) (10,27) (10,21) (10,18) (10,13) (10,12) (10,20) (11,27) (11,21) (11,13) (11,12) (11,25) (12,24) (12,16) (12,25) (13,24) (13,27) (13,25) (13,20) (13,22) (14,16) (14,22) (15,20) (16,25) (17,26) (17,23) (18,27) (19,25) (19,20) (20,24) (20,25) (20,22) (21,27) (22,25) (23,26) (25,27)\nIs there a path between node 0 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph81-4_0", + "image": "data/connectivity/graph_visual/hard/graph81.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,7) (0,10) (0,11) (0,20) (0,14) (0,24) (0,16) (0,25) (0,3) (0,12) (0,8) (0,19) (0,6) (1,23) (1,7) (1,10) (1,11) (1,20) (1,14) (1,24) (1,3) (1,6) (2,7) (2,10) (2,11) (2,20) (2,14) (2,24) (2,16) (2,25) (2,3) (2,12) (2,13) (2,6) (3,23) (3,7) (3,10) (3,11) (3,20) (3,14) (3,24) (3,16) (3,25) (3,12) (3,8) (3,13) (4,26) (4,5) (4,9) (4,17) (5,26) (5,15) (5,9) (5,18) (5,17) (5,22) (6,10) (6,11) (6,14) (6,24) (6,25) (6,12) (6,8) (6,19) (6,13) (7,23) (7,10) (7,20) (7,14) (7,16) (7,25) (7,19) (8,23) (8,10) (8,11) (8,14) (8,24) (8,16) (8,25) (8,12) (8,13) (9,26) (9,15) (9,21) (9,18) (9,17) (9,22) (10,23) (10,20) (10,16) (10,25) (10,12) (10,13) (11,20) (11,14) (11,25) (11,12) (11,19) (11,13) (12,20) (12,24) (12,16) (12,19) (13,14) (13,24) (13,16) (13,25) (13,19) (14,23) (15,26) (15,18) (16,23) (16,20) (16,24) (16,25) (17,21) (17,18) (17,22) (18,26) (18,21) (18,22) (19,23) (19,25) (20,23) (20,24) (21,26) (21,22) (22,26) (23,24) (23,25) (24,25)\nIs there a path between node 4 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph510-28_16", + "image": "data/connectivity/graph_visual/hard/graph510.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,31) (0,1) (0,27) (0,13) (0,10) (0,25) (0,7) (0,21) (0,19) (0,15) (0,16) (0,17) (0,9) (0,20) (0,26) (0,30) (0,28) (0,2) (0,5) (0,24) (0,3) (1,10) (1,33) (1,23) (1,25) (1,8) (1,7) (1,21) (1,19) (1,16) (1,17) (1,26) (1,30) (1,22) (1,28) (1,5) (1,24) (1,3) (2,31) (2,13) (2,10) (2,33) (2,14) (2,23) (2,25) (2,8) (2,7) (2,21) (2,19) (2,15) (2,20) (2,26) (2,30) (2,22) (2,24) (2,3) (3,31) (3,27) (3,13) (3,33) (3,14) (3,23) (3,25) (3,21) (3,15) (3,16) (3,9) (3,30) (3,5) (3,24) (4,18) (4,11) (4,12) (4,29) (5,31) (5,27) (5,13) (5,10) (5,33) (5,25) (5,8) (5,7) (5,21) (5,19) (5,16) (5,20) (5,26) (5,30) (5,22) (6,12) (6,29) (6,32) (7,31) (7,13) (7,33) (7,25) (7,8) (7,19) (7,16) (7,17) (7,9) (7,20) (7,26) (7,30) (7,22) (7,28) (7,24) (8,31) (8,27) (8,10) (8,14) (8,21) (8,19) (8,15) (8,17) (8,9) (8,22) (8,28) (8,24) (9,31) (9,27) (9,13) (9,33) (9,23) (9,25) (9,16) (9,17) (9,26) (9,30) (9,28) (9,24) (10,31) (10,27) (10,13) (10,14) (10,23) (10,25) (10,21) (10,19) (10,15) (10,20) (10,26) (10,30) (10,22) (11,12) (11,29) (11,32) (12,18) (12,32) (13,31) (13,27) (13,33) (13,23) (13,25) (13,19) (13,15) (13,17) (13,20) (13,26) (13,22) (13,28) (13,24) (14,31) (14,27) (14,33) (14,23) (14,25) (14,21) (14,16) (14,17) (14,20) (14,26) (14,30) (14,22) (14,24) (15,31) (15,27) (15,33) (15,23) (15,25) (15,19) (15,17) (15,20) (15,30) (15,22) (15,24) (16,31) (16,17) (16,20) (16,30) (16,28) (16,24) (17,31) (17,27) (17,33) (17,25) (17,20) (17,30) (17,22) (19,31) (19,25) (19,21) (19,20) (19,26) (19,22) (19,28) (19,24) (20,27) (20,33) (20,23) (20,21) (20,26) (20,22) (20,28) (20,24) (21,31) (21,33) (21,23) (21,30) (21,28) (21,24) (22,31) (22,27) (22,23) (22,25) (22,30) (22,28) (22,24) (23,31) (23,27) (23,33) (24,31) (24,27) (24,33) (24,26) (24,30) (24,28) (25,30) (25,28) (26,31) (26,33) (26,30) (27,31) (27,30) (27,28) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nIs there a path between node 28 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph81-13_1", + "image": "data/connectivity/graph_visual/hard/graph81.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,7) (0,10) (0,11) (0,20) (0,14) (0,24) (0,16) (0,25) (0,3) (0,12) (0,8) (0,19) (0,6) (1,23) (1,7) (1,10) (1,11) (1,20) (1,14) (1,24) (1,3) (1,6) (2,7) (2,10) (2,11) (2,20) (2,14) (2,24) (2,16) (2,25) (2,3) (2,12) (2,13) (2,6) (3,23) (3,7) (3,10) (3,11) (3,20) (3,14) (3,24) (3,16) (3,25) (3,12) (3,8) (3,13) (4,26) (4,5) (4,9) (4,17) (5,26) (5,15) (5,9) (5,18) (5,17) (5,22) (6,10) (6,11) (6,14) (6,24) (6,25) (6,12) (6,8) (6,19) (6,13) (7,23) (7,10) (7,20) (7,14) (7,16) (7,25) (7,19) (8,23) (8,10) (8,11) (8,14) (8,24) (8,16) (8,25) (8,12) (8,13) (9,26) (9,15) (9,21) (9,18) (9,17) (9,22) (10,23) (10,20) (10,16) (10,25) (10,12) (10,13) (11,20) (11,14) (11,25) (11,12) (11,19) (11,13) (12,20) (12,24) (12,16) (12,19) (13,14) (13,24) (13,16) (13,25) (13,19) (14,23) (15,26) (15,18) (16,23) (16,20) (16,24) (16,25) (17,21) (17,18) (17,22) (18,26) (18,21) (18,22) (19,23) (19,25) (20,23) (20,24) (21,26) (21,22) (22,26) (23,24) (23,25) (24,25)\nIs there a path between node 13 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph204-25_23", + "image": "data/connectivity/graph_visual/hard/graph204.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,15) (0,26) (0,23) (0,4) (0,6) (0,3) (0,24) (2,17) (2,6) (2,3) (2,9) (2,11) (3,18) (3,14) (3,9) (3,11) (4,17) (4,15) (4,21) (4,29) (4,23) (4,13) (4,27) (4,9) (4,8) (5,22) (5,10) (5,15) (5,23) (5,9) (5,8) (6,22) (6,10) (6,26) (6,27) (6,24) (6,8) (6,11) (8,10) (8,21) (9,19) (9,17) (9,15) (9,29) (9,25) (9,23) (9,14) (9,27) (10,22) (10,29) (10,25) (10,23) (10,18) (10,13) (10,24) (10,11) (11,22) (11,19) (11,15) (11,29) (11,14) (13,19) (13,17) (13,29) (13,26) (13,23) (13,27) (13,24) (14,17) (14,21) (14,29) (14,23) (14,18) (14,27) (14,28) (15,19) (15,29) (15,25) (17,22) (17,21) (17,26) (17,23) (18,22) (18,29) (18,26) (18,28) (19,22) (19,26) (21,25) (21,28) (22,25) (22,26) (22,23) (22,24) (24,28) (25,28) (26,27) (27,28)\nIs there a path between node 25 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph630-33_11", + "image": "data/connectivity/graph_visual/hard/graph630.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,30) (1,27) (1,11) (2,17) (2,15) (2,32) (3,24) (3,15) (3,10) (3,25) (3,32) (4,21) (4,12) (4,27) (4,8) (5,9) (5,34) (6,30) (6,11) (6,8) (7,29) (7,24) (7,15) (7,14) (8,30) (8,11) (10,19) (10,14) (11,16) (11,31) (11,21) (11,27) (11,23) (12,27) (13,25) (13,20) (14,17) (15,29) (15,24) (15,32) (15,20) (16,31) (17,29) (17,24) (17,19) (17,25) (17,20) (19,24) (19,25) (19,20) (20,32) (21,27) (21,23) (23,31) (24,32) (26,28) (27,30) (29,32)\nIs there a path between node 33 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph676-30_26", + "image": "data/connectivity/graph_visual/hard/graph676.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,10) (0,26) (0,32) (0,20) (0,28) (0,15) (0,17) (0,3) (0,12) (0,9) (1,10) (1,24) (1,26) (1,34) (1,18) (1,25) (1,15) (1,27) (1,21) (1,29) (1,12) (1,9) (2,13) (2,4) (2,17) (3,10) (3,11) (3,33) (3,18) (3,4) (3,27) (3,17) (3,30) (4,18) (4,25) (4,27) (4,29) (4,7) (5,16) (7,11) (7,33) (7,34) (7,18) (7,13) (7,19) (7,28) (7,27) (7,31) (7,12) (7,9) (9,26) (9,32) (9,20) (9,13) (9,14) (9,12) (10,26) (10,34) (10,14) (10,31) (10,30) (11,24) (11,34) (11,18) (11,14) (11,15) (11,27) (12,33) (12,20) (12,28) (12,27) (13,33) (13,18) (13,32) (13,15) (13,22) (13,17) (13,31) (14,33) (14,26) (14,19) (15,33) (15,18) (15,28) (15,25) (15,23) (17,18) (17,32) (17,29) (18,33) (18,24) (18,34) (18,20) (18,25) (18,27) (18,30) (19,28) (19,25) (19,22) (19,21) (20,33) (20,26) (20,32) (20,22) (21,33) (21,24) (21,34) (21,28) (21,25) (21,27) (22,33) (22,26) (22,29) (23,33) (23,34) (23,28) (23,31) (23,29) (24,32) (24,31) (24,30) (25,33) (25,32) (25,27) (26,32) (27,31) (28,33) (30,34) (31,34) (32,33) (33,34)\nIs there a path between node 30 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph702-21_30", + "image": "data/connectivity/graph_visual/hard/graph702.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,12) (0,4) (0,34) (0,32) (0,13) (0,20) (0,11) (0,14) (0,6) (0,3) (1,12) (1,17) (1,33) (1,20) (1,23) (1,11) (1,6) (1,3) (2,31) (2,30) (2,21) (2,27) (2,7) (2,29) (2,15) (2,19) (2,5) (2,9) (2,16) (2,18) (2,24) (2,26) (3,12) (3,33) (3,4) (3,34) (3,32) (3,20) (3,11) (3,6) (4,33) (4,13) (4,14) (5,25) (5,10) (5,21) (5,27) (5,7) (5,29) (5,8) (5,16) (5,18) (5,22) (5,24) (6,34) (6,13) (6,23) (6,11) (6,14) (7,31) (7,25) (7,30) (7,27) (7,29) (7,9) (7,8) (7,18) (7,22) (7,24) (7,26) (8,25) (8,30) (8,21) (8,27) (8,19) (8,9) (8,16) (8,22) (8,28) (8,24) (9,31) (9,25) (9,30) (9,21) (9,27) (9,29) (9,16) (9,22) (9,28) (9,24) (10,31) (10,25) (10,30) (10,21) (10,29) (10,15) (10,19) (10,16) (10,18) (10,22) (10,26) (11,33) (11,34) (11,32) (11,23) (11,14) (12,17) (12,32) (12,23) (12,14) (13,17) (13,33) (13,34) (13,32) (13,20) (13,23) (13,14) (14,17) (14,34) (14,32) (14,20) (15,25) (15,21) (15,29) (15,19) (15,16) (15,18) (15,28) (15,24) (16,31) (16,25) (16,21) (16,27) (16,29) (16,19) (16,22) (16,28) (16,24) (16,26) (17,33) (17,34) (17,32) (17,20) (18,31) (18,25) (18,30) (18,21) (18,27) (18,29) (18,19) (18,22) (18,28) (18,24) (18,26) (19,31) (19,25) (19,21) (19,28) (19,26) (20,33) (20,34) (20,32) (20,23) (21,31) (21,25) (21,30) (21,27) (21,24) (22,31) (22,25) (22,30) (22,27) (22,29) (22,28) (22,24) (22,26) (23,34) (23,32) (24,31) (24,25) (24,30) (24,29) (24,28) (25,31) (25,30) (25,29) (25,28) (25,26) (26,27) (26,29) (26,28) (27,31) (27,29) (27,28) (28,30) (29,31) (29,30) (30,31) (33,34)\nIs there a path between node 21 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph258-11_12", + "image": "data/connectivity/graph_visual/hard/graph258.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,17) (0,11) (0,7) (0,15) (0,30) (0,25) (1,14) (1,6) (1,8) (2,26) (2,28) (3,11) (3,5) (3,15) (3,23) (3,16) (3,19) (3,10) (4,17) (4,22) (4,15) (4,16) (4,19) (4,30) (4,10) (5,9) (5,13) (5,22) (5,24) (5,19) (5,27) (5,21) (6,29) (7,17) (7,20) (7,16) (8,14) (9,17) (9,20) (9,15) (9,24) (9,30) (9,21) (10,16) (10,24) (10,30) (10,21) (10,25) (11,17) (11,12) (11,27) (11,21) (12,17) (12,20) (12,21) (13,17) (13,20) (15,24) (15,27) (15,30) (16,22) (16,21) (17,19) (17,30) (17,21) (17,25) (18,26) (19,20) (20,24) (20,27) (20,21) (21,24) (21,27) (21,30) (21,25) (22,23) (22,30) (25,27) (25,30) (26,28) (27,30)\nIs there a path between node 11 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph202-23_22", + "image": "data/connectivity/graph_visual/hard/graph202.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,29) (1,27) (1,24) (1,21) (1,3) (2,10) (2,22) (2,6) (2,18) (2,25) (2,12) (3,19) (3,27) (3,24) (4,10) (4,6) (4,18) (4,25) (5,28) (5,16) (6,10) (6,13) (6,25) (6,12) (6,9) (7,28) (8,10) (8,14) (8,18) (8,29) (8,25) (8,23) (9,13) (9,14) (10,29) (10,25) (12,22) (12,18) (12,17) (13,29) (13,26) (14,20) (14,17) (15,19) (17,25) (18,20) (18,25) (20,29) (20,26) (20,23) (21,27) (21,24) (23,26) (23,25) (24,27) (26,29)\nIs there a path between node 23 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph96-12_14", + "image": "data/connectivity/graph_visual/hard/graph96.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,20) (0,8) (0,13) (0,11) (0,22) (0,15) (1,24) (2,3) (3,24) (4,18) (5,13) (5,27) (5,11) (5,7) (5,21) (6,11) (6,22) (6,17) (7,25) (7,8) (7,23) (7,11) (7,12) (7,22) (7,17) (8,20) (8,10) (8,12) (8,21) (10,20) (10,25) (10,13) (10,22) (10,16) (10,21) (11,20) (11,25) (11,16) (11,15) (12,23) (12,16) (12,21) (13,20) (13,23) (13,22) (13,17) (13,15) (15,26) (15,25) (15,22) (16,27) (17,26) (17,23) (17,27) (20,26) (20,22) (21,25) (22,25) (23,25) (25,26) (26,27)\nIs there a path between node 12 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph709-9_34", + "image": "data/connectivity/graph_visual/hard/graph709.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,10) (0,2) (0,34) (0,21) (1,18) (1,31) (1,3) (1,4) (1,8) (1,20) (1,23) (1,14) (1,26) (1,16) (1,5) (1,17) (1,27) (1,9) (1,19) (1,15) (1,33) (2,10) (3,31) (3,29) (3,22) (3,12) (3,7) (3,4) (3,28) (3,8) (3,6) (3,20) (3,23) (3,14) (3,16) (3,13) (3,17) (3,24) (3,27) (3,15) (4,29) (4,22) (4,12) (4,11) (4,28) (4,20) (4,23) (4,14) (4,26) (4,16) (4,5) (4,13) (4,24) (4,27) (4,19) (4,33) (5,18) (5,31) (5,29) (5,12) (5,11) (5,7) (5,28) (5,8) (5,6) (5,20) (5,32) (5,23) (5,26) (5,16) (5,13) (5,17) (5,24) (5,9) (5,15) (5,33) (6,18) (6,31) (6,22) (6,12) (6,11) (6,7) (6,20) (6,23) (6,14) (6,16) (6,17) (6,27) (6,9) (6,19) (6,15) (7,18) (7,22) (7,12) (7,11) (7,8) (7,20) (7,14) (7,26) (7,16) (7,13) (7,17) (7,24) (7,9) (7,15) (7,33) (8,18) (8,29) (8,12) (8,11) (8,28) (8,20) (8,32) (8,23) (8,26) (8,17) (8,24) (8,27) (8,9) (8,19) (8,15) (8,33) (9,31) (9,22) (9,12) (9,28) (9,20) (9,32) (9,23) (9,14) (9,16) (9,13) (9,17) (9,24) (9,15) (10,30) (10,25) (10,34) (11,18) (11,31) (11,22) (11,12) (11,28) (11,20) (11,32) (11,23) (11,26) (11,13) (11,17) (11,24) (11,27) (11,19) (11,15) (12,18) (12,31) (12,29) (12,22) (12,20) (12,23) (12,14) (12,26) (12,17) (12,27) (12,19) (12,15) (12,33) (13,18) (13,29) (13,28) (13,20) (13,32) (13,23) (13,26) (13,16) (13,24) (13,15) (14,29) (14,22) (14,20) (14,32) (14,23) (14,16) (14,17) (14,27) (14,19) (15,18) (15,31) (15,29) (15,22) (15,28) (15,32) (15,23) (15,26) (15,16) (15,17) (15,24) (15,19) (15,33) (16,18) (16,31) (16,22) (16,28) (16,26) (16,27) (16,33) (17,28) (17,32) (17,23) (17,24) (17,27) (17,19) (18,31) (18,29) (18,22) (18,32) (18,26) (18,24) (18,19) (18,33) (19,31) (19,28) (19,20) (19,23) (19,33) (20,31) (20,32) (20,26) (21,25) (21,34) (22,29) (22,28) (22,32) (22,23) (22,27) (22,33) (23,31) (23,29) (23,28) (23,32) (23,26) (23,24) (23,27) (24,28) (24,26) (24,27) (24,33) (25,30) (26,31) (26,29) (26,28) (26,33) (27,31) (27,28) (27,32) (27,33) (28,29) (28,32) (29,32) (29,33) (31,33) (32,33)\nIs there a path between node 9 and node 34 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph500-13_8", + "image": "data/connectivity/graph_visual/hard/graph500.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,24) (0,14) (0,1) (0,12) (0,7) (1,15) (1,10) (1,12) (1,25) (3,9) (3,13) (3,23) (3,7) (4,14) (4,20) (4,23) (4,12) (4,16) (4,8) (4,6) (5,18) (6,24) (6,15) (6,14) (6,12) (7,15) (7,20) (7,12) (7,25) (7,16) (7,27) (8,24) (8,10) (8,14) (8,9) (8,13) (8,23) (8,12) (8,16) (8,27) (9,20) (9,12) (9,25) (9,16) (10,14) (10,12) (10,16) (10,27) (12,23) (13,24) (13,15) (13,20) (13,33) (14,24) (14,20) (14,23) (14,33) (14,16) (14,27) (15,24) (15,25) (16,24) (19,31) (20,33) (20,27) (23,25) (26,29) (28,32)\nIs there a path between node 13 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph496-29_13", + "image": "data/connectivity/graph_visual/hard/graph496.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,15) (0,27) (0,3) (1,6) (1,8) (1,12) (1,4) (1,10) (1,19) (2,9) (2,8) (2,26) (2,31) (2,18) (2,4) (3,15) (3,5) (4,6) (4,8) (4,28) (4,18) (4,13) (4,10) (4,23) (5,15) (5,27) (6,31) (6,10) (6,20) (7,25) (8,29) (8,28) (8,18) (9,26) (9,13) (9,10) (9,33) (10,26) (10,13) (11,26) (11,12) (11,22) (11,24) (11,13) (11,20) (12,26) (12,22) (12,24) (12,18) (12,20) (12,23) (12,33) (13,33) (14,17) (14,25) (14,32) (18,29) (18,22) (19,28) (19,24) (19,33) (20,29) (21,25) (21,32) (22,26) (22,23) (22,33) (23,28) (23,31) (23,33) (24,33) (26,28) (26,31) (26,33) (28,29) (29,31) (29,33) (30,32) (31,33)\nIs there a path between node 29 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph589-17_19", + "image": "data/connectivity/graph_visual/hard/graph589.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,11) (0,16) (0,3) (0,26) (0,15) (0,30) (0,20) (0,27) (0,17) (0,18) (0,7) (0,1) (0,23) (0,24) (0,12) (1,8) (1,16) (1,25) (1,10) (1,5) (1,26) (1,15) (1,20) (1,27) (1,18) (1,13) (1,23) (1,2) (1,24) (1,31) (1,33) (1,12) (1,4) (1,6) (2,8) (2,11) (2,21) (2,25) (2,3) (2,10) (2,5) (2,26) (2,15) (2,27) (2,28) (2,14) (2,13) (2,31) (2,33) (2,4) (3,8) (3,9) (3,16) (3,25) (3,5) (3,26) (3,22) (3,30) (3,20) (3,17) (3,7) (3,28) (3,23) (3,24) (3,12) (3,4) (4,8) (4,11) (4,21) (4,25) (4,10) (4,15) (4,22) (4,20) (4,27) (4,18) (4,7) (4,28) (4,14) (4,23) (4,24) (4,31) (4,12) (5,8) (5,11) (5,9) (5,16) (5,21) (5,25) (5,10) (5,26) (5,15) (5,22) (5,30) (5,27) (5,18) (5,7) (5,28) (5,14) (5,13) (5,31) (6,8) (6,21) (6,25) (6,10) (6,26) (6,15) (6,22) (6,30) (6,20) (6,27) (6,28) (6,13) (6,31) (6,33) (7,11) (7,9) (7,16) (7,21) (7,25) (7,10) (7,26) (7,15) (7,22) (7,30) (7,20) (7,27) (7,28) (7,14) (7,13) (7,23) (7,24) (7,31) (7,12) (8,11) (8,9) (8,16) (8,21) (8,25) (8,10) (8,26) (8,30) (8,20) (8,17) (8,18) (8,28) (8,14) (8,23) (8,24) (8,31) (8,12) (9,11) (9,16) (9,21) (9,10) (9,26) (9,15) (9,22) (9,30) (9,27) (9,17) (9,18) (9,28) (9,14) (9,13) (9,24) (9,31) (10,26) (10,30) (10,27) (10,17) (10,18) (10,28) (10,14) (10,13) (10,31) (10,33) (10,12) (11,16) (11,21) (11,25) (11,26) (11,15) (11,22) (11,30) (11,20) (11,27) (11,17) (11,18) (11,28) (11,14) (11,13) (11,24) (11,31) (11,33) (11,12) (12,21) (12,25) (12,26) (12,22) (12,20) (12,17) (12,18) (12,28) (12,14) (12,13) (12,23) (12,31) (12,33) (13,25) (13,26) (13,15) (13,30) (13,20) (13,17) (13,18) (13,14) (13,23) (13,24) (13,31) (13,33) (14,16) (14,21) (14,25) (14,26) (14,22) (14,20) (14,17) (14,18) (14,28) (14,23) (14,31) (14,33) (15,16) (15,22) (15,30) (15,18) (15,28) (15,23) (15,24) (15,31) (15,33) (16,21) (16,25) (16,22) (16,20) (16,27) (16,17) (16,18) (16,28) (16,23) (16,33) (17,25) (17,22) (17,30) (17,20) (17,27) (17,18) (17,28) (17,23) (17,24) (17,33) (18,25) (18,22) (18,30) (18,20) (18,27) (18,23) (18,24) (18,33) (19,29) (19,32) (20,26) (20,22) (20,30) (20,27) (20,28) (20,23) (20,24) (20,31) (20,33) (21,25) (21,26) (21,30) (21,27) (21,28) (21,23) (21,33) (22,26) (22,30) (22,23) (22,33) (23,25) (23,26) (23,27) (23,28) (23,24) (23,31) (23,33) (24,25) (24,26) (24,28) (24,31) (25,26) (25,30) (25,27) (25,28) (25,33) (26,30) (26,27) (26,28) (26,31) (27,30) (27,28) (27,33) (28,31) (28,33) (29,32) (30,33) (31,33)\nIs there a path between node 17 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph519-26_12", + "image": "data/connectivity/graph_visual/hard/graph519.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,24) (0,8) (0,19) (0,17) (0,22) (1,24) (1,12) (1,29) (1,11) (1,25) (1,10) (2,31) (2,8) (2,12) (2,6) (2,16) (2,23) (3,15) (4,32) (4,8) (4,12) (4,19) (4,11) (4,6) (4,7) (4,16) (4,18) (4,13) (4,22) (5,32) (5,31) (5,27) (5,29) (5,6) (5,16) (5,13) (5,22) (6,7) (6,16) (6,21) (6,18) (6,13) (7,9) (7,8) (7,30) (7,16) (7,33) (7,17) (7,10) (8,31) (8,11) (8,16) (8,33) (8,17) (9,20) (9,32) (9,24) (9,18) (9,23) (9,10) (10,32) (10,19) (10,29) (10,21) (10,13) (11,32) (11,24) (11,12) (11,29) (11,33) (11,13) (11,23) (12,13) (12,22) (13,20) (13,16) (13,22) (14,26) (15,26) (16,24) (16,18) (16,25) (16,22) (17,31) (17,29) (17,23) (18,31) (18,24) (18,19) (18,25) (19,20) (19,27) (20,32) (20,31) (20,27) (20,29) (20,25) (21,32) (21,30) (21,29) (21,25) (21,23) (22,24) (22,29) (22,33) (23,24) (23,27) (23,33) (23,25) (24,31) (24,30) (25,32) (26,28) (27,30) (29,31) (29,30) (29,33) (31,33) (32,33)\nIs there a path between node 26 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph241-12_30", + "image": "data/connectivity/graph_visual/hard/graph241.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,22) (0,15) (0,7) (0,13) (0,8) (1,2) (1,11) (1,29) (1,15) (1,20) (1,17) (1,23) (1,6) (2,12) (2,11) (2,5) (2,29) (2,10) (2,16) (2,28) (2,13) (2,8) (4,22) (4,9) (4,15) (4,16) (4,19) (4,20) (5,11) (5,22) (5,16) (5,19) (5,18) (5,23) (5,13) (6,22) (6,27) (6,10) (6,18) (6,17) (6,7) (7,27) (7,10) (7,9) (7,15) (7,14) (7,23) (7,8) (8,26) (8,27) (8,29) (8,14) (8,16) (8,28) (8,17) (9,12) (9,11) (9,26) (9,29) (9,16) (9,18) (9,24) (9,23) (9,13) (10,12) (10,11) (10,27) (10,15) (10,28) (10,18) (10,24) (11,27) (11,20) (11,25) (12,29) (12,19) (12,18) (12,25) (12,17) (12,24) (13,15) (13,16) (13,25) (13,24) (14,18) (14,25) (14,23) (15,29) (15,16) (15,28) (15,19) (15,24) (15,23) (16,24) (16,23) (17,29) (17,19) (18,27) (18,19) (19,20) (19,25) (20,27) (20,24) (22,29) (23,26) (23,24) (24,26) (24,27) (26,27) (26,29) (27,28) (28,29)\nIs there a path between node 12 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph214-23_2", + "image": "data/connectivity/graph_visual/hard/graph214.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,5) (0,4) (0,22) (0,15) (2,28) (4,9) (4,15) (5,20) (5,22) (5,18) (6,25) (6,12) (7,10) (7,11) (8,21) (8,20) (8,15) (9,22) (9,18) (10,11) (11,24) (11,17) (11,27) (12,19) (12,13) (12,25) (13,25) (14,17) (15,20) (16,28) (18,21) (19,26) (21,22) (24,27) (25,29) (26,29)\nIs there a path between node 23 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph229-29_16", + "image": "data/connectivity/graph_visual/hard/graph229.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,26) (0,13) (1,23) (1,10) (1,16) (1,11) (1,19) (1,8) (1,2) (1,14) (1,29) (1,25) (1,9) (1,17) (1,28) (2,24) (2,23) (2,10) (2,16) (2,11) (2,19) (2,20) (2,21) (2,14) (2,25) (2,9) (2,4) (2,17) (2,28) (3,5) (3,15) (3,6) (3,7) (4,24) (4,16) (4,11) (4,19) (4,8) (4,18) (4,14) (4,29) (4,25) (4,22) (4,17) (4,28) (5,27) (5,15) (5,6) (6,27) (7,27) (7,15) (8,24) (8,23) (8,10) (8,19) (8,20) (8,18) (8,29) (8,25) (8,17) (8,28) (9,24) (9,23) (9,10) (9,19) (9,18) (9,29) (9,25) (9,22) (9,17) (10,24) (10,23) (10,16) (10,11) (10,19) (10,20) (10,21) (10,18) (10,29) (10,25) (10,22) (10,17) (10,28) (11,24) (11,23) (11,16) (11,19) (11,21) (11,18) (11,14) (11,29) (11,22) (11,28) (12,26) (13,26) (14,24) (14,16) (14,20) (14,21) (14,18) (14,29) (14,25) (14,22) (15,27) (16,23) (16,20) (16,18) (16,29) (16,25) (17,23) (17,20) (17,29) (17,22) (17,28) (18,23) (18,19) (18,20) (18,21) (18,29) (18,25) (18,28) (19,24) (19,21) (19,29) (19,25) (19,22) (19,28) (20,24) (20,21) (20,25) (20,22) (20,28) (21,23) (21,29) (21,22) (22,23) (22,29) (23,29) (23,25) (23,28) (24,25) (25,28) (28,29)\nIs there a path between node 29 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph638-6_13", + "image": "data/connectivity/graph_visual/hard/graph638.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,1) (0,19) (0,15) (0,20) (0,9) (0,21) (0,3) (0,22) (0,32) (0,24) (0,14) (0,11) (0,17) (0,5) (0,34) (0,4) (0,26) (0,10) (0,8) (1,27) (1,23) (1,30) (1,6) (1,19) (1,20) (1,2) (1,9) (1,21) (1,3) (1,22) (1,24) (1,14) (1,11) (1,17) (1,5) (1,4) (1,26) (1,8) (2,27) (2,30) (2,6) (2,19) (2,20) (2,9) (2,21) (2,3) (2,22) (2,32) (2,7) (2,11) (2,17) (2,5) (2,34) (2,4) (2,26) (2,12) (2,10) (3,27) (3,23) (3,30) (3,6) (3,19) (3,15) (3,20) (3,9) (3,22) (3,24) (3,14) (3,34) (3,4) (3,12) (3,10) (3,8) (3,28) (4,27) (4,23) (4,30) (4,19) (4,15) (4,20) (4,9) (4,21) (4,32) (4,24) (4,14) (4,7) (4,11) (4,17) (4,5) (4,26) (4,12) (4,8) (4,28) (5,30) (5,19) (5,9) (5,21) (5,24) (5,7) (5,11) (5,17) (5,34) (5,12) (6,27) (6,23) (6,30) (6,19) (6,20) (6,9) (6,21) (6,22) (6,32) (6,24) (6,14) (6,7) (6,11) (6,17) (6,34) (6,26) (6,8) (6,28) (7,23) (7,30) (7,19) (7,15) (7,20) (7,21) (7,32) (7,24) (7,11) (7,17) (7,34) (7,12) (7,10) (7,8) (7,28) (8,23) (8,15) (8,20) (8,24) (8,14) (8,11) (8,17) (8,34) (8,26) (8,12) (8,10) (8,28) (9,30) (9,19) (9,15) (9,20) (9,22) (9,32) (9,24) (9,11) (9,34) (9,12) (9,10) (9,28) (10,27) (10,23) (10,30) (10,19) (10,21) (10,32) (10,24) (10,26) (10,12) (11,27) (11,30) (11,19) (11,20) (11,21) (11,22) (11,32) (11,24) (11,14) (11,17) (11,34) (11,12) (12,27) (12,30) (12,19) (12,20) (12,22) (12,32) (12,24) (12,14) (12,17) (12,34) (12,28) (14,27) (14,23) (14,30) (14,19) (14,15) (14,21) (14,22) (14,32) (14,17) (14,34) (14,28) (15,19) (15,20) (15,21) (15,22) (15,32) (15,24) (15,34) (15,26) (15,28) (16,33) (16,29) (16,18) (16,31) (17,27) (17,23) (17,30) (17,19) (17,20) (17,21) (17,22) (17,32) (17,24) (17,34) (17,28) (18,33) (18,31) (18,25) (19,27) (19,23) (19,30) (19,20) (19,22) (19,32) (19,34) (19,26) (19,28) (20,23) (20,30) (20,21) (20,22) (20,32) (20,24) (20,34) (20,26) (21,27) (21,23) (21,30) (21,22) (21,32) (21,24) (21,34) (21,26) (21,28) (22,27) (22,23) (22,24) (22,34) (22,26) (22,28) (23,32) (23,26) (23,28) (24,27) (24,32) (24,34) (24,26) (25,33) (26,30) (26,32) (26,34) (27,30) (27,32) (27,28) (28,30) (28,32) (28,34) (29,33) (29,31) (31,33) (32,34)\nIs there a path between node 6 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph681-5_16", + "image": "data/connectivity/graph_visual/hard/graph681.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,20) (0,9) (0,16) (0,8) (0,23) (0,1) (0,32) (0,3) (0,10) (0,25) (0,11) (0,5) (1,16) (1,32) (1,3) (1,25) (1,26) (1,27) (3,30) (3,8) (3,14) (3,25) (3,33) (4,7) (4,9) (4,15) (4,30) (4,19) (4,32) (4,22) (4,6) (4,28) (4,14) (4,5) (4,27) (5,9) (5,8) (5,19) (5,31) (5,25) (5,33) (6,13) (6,30) (6,21) (6,19) (6,31) (6,29) (6,11) (7,20) (7,30) (7,8) (7,23) (7,34) (7,31) (7,28) (7,10) (7,14) (7,25) (7,33) (8,30) (8,32) (8,22) (8,14) (8,18) (8,11) (9,20) (9,15) (9,23) (9,21) (9,19) (9,22) (9,33) (9,11) (10,20) (10,16) (10,15) (10,32) (10,31) (10,22) (10,28) (10,25) (10,27) (11,20) (11,16) (11,15) (11,23) (11,25) (11,26) (11,27) (12,16) (12,13) (12,25) (13,23) (13,19) (13,31) (13,14) (13,25) (13,26) (13,33) (13,18) (14,16) (14,15) (14,34) (14,21) (14,31) (15,16) (15,26) (16,34) (16,21) (16,19) (16,22) (16,26) (16,33) (17,24) (18,30) (18,28) (19,27) (20,31) (20,26) (20,33) (21,23) (21,28) (21,25) (21,29) (22,30) (22,23) (22,34) (22,31) (22,25) (23,29) (23,33) (23,27) (26,28) (26,33) (26,27) (27,34) (27,31) (28,30) (28,34) (28,32) (29,30)\nIs there a path between node 5 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph68-23_6", + "image": "data/connectivity/graph_visual/hard/graph68.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,24) (0,11) (0,6) (1,22) (1,26) (1,12) (2,14) (2,11) (2,4) (3,21) (3,11) (3,18) (3,9) (4,17) (4,21) (4,14) (5,7) (5,25) (5,10) (5,20) (6,16) (7,15) (7,26) (8,20) (9,17) (9,23) (9,24) (9,13) (9,11) (9,18) (10,25) (11,14) (12,20) (13,17) (13,21) (13,24) (13,19) (14,18) (15,25) (16,23) (16,21) (18,23) (19,23) (19,24) (20,26) (21,24) (22,25)\nIs there a path between node 23 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph38-25_15", + "image": "data/connectivity/graph_visual/hard/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,7) (0,4) (0,24) (0,15) (1,2) (1,19) (1,6) (1,23) (1,13) (1,5) (1,20) (1,16) (1,25) (1,9) (1,21) (2,3) (2,6) (2,12) (2,23) (2,13) (2,5) (2,20) (2,16) (2,25) (2,9) (2,21) (2,8) (3,10) (3,22) (3,19) (3,6) (3,12) (3,14) (3,23) (3,13) (3,5) (3,20) (3,25) (3,9) (3,8) (4,11) (4,15) (5,6) (5,12) (5,23) (5,20) (5,17) (5,8) (6,22) (6,19) (6,14) (6,23) (6,13) (6,25) (6,17) (6,9) (7,15) (8,10) (8,22) (8,12) (8,13) (8,20) (8,16) (8,25) (8,9) (8,21) (9,22) (9,19) (9,12) (9,14) (9,23) (9,16) (9,25) (9,21) (10,12) (10,14) (10,20) (10,16) (10,25) (11,24) (11,15) (12,22) (12,16) (12,25) (12,17) (12,21) (13,22) (13,19) (13,14) (13,23) (13,20) (13,16) (13,17) (14,22) (14,19) (14,23) (14,25) (14,21) (15,18) (16,22) (16,23) (16,20) (16,25) (17,22) (17,19) (17,23) (17,20) (18,24) (19,22) (19,21) (20,23) (20,25) (21,22) (21,25) (22,25) (23,25)\nIs there a path between node 25 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph292-18_10", + "image": "data/connectivity/graph_visual/hard/graph292.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,29) (0,7) (0,26) (1,20) (1,21) (1,24) (2,13) (3,17) (3,25) (3,26) (4,20) (4,27) (4,24) (5,9) (5,12) (5,8) (6,9) (6,7) (6,26) (6,22) (7,10) (7,9) (7,12) (7,25) (7,22) (8,9) (8,29) (8,22) (9,17) (9,10) (9,25) (10,17) (10,16) (10,29) (10,18) (10,25) (10,22) (11,13) (12,29) (12,26) (13,23) (13,30) (13,28) (13,27) (14,15) (14,19) (15,31) (16,25) (18,26) (18,22) (19,31) (20,27) (20,21) (21,23) (21,30) (21,27) (23,28) (23,27)\nIs there a path between node 18 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph10-25_15", + "image": "data/connectivity/graph_visual/hard/graph10.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,4) (0,16) (0,25) (0,14) (0,21) (0,11) (0,9) (0,5) (0,23) (0,6) (1,4) (1,16) (1,14) (1,13) (1,21) (1,11) (1,9) (1,10) (1,5) (1,23) (1,15) (1,20) (1,6) (2,18) (2,4) (2,16) (2,25) (2,14) (2,21) (2,9) (2,10) (2,5) (2,15) (2,20) (2,6) (3,12) (3,19) (3,24) (3,17) (3,7) (3,22) (3,8) (4,16) (4,25) (4,14) (4,21) (4,11) (4,9) (4,10) (4,5) (4,23) (4,15) (4,20) (4,6) (5,18) (5,16) (5,25) (5,13) (5,21) (5,11) (5,10) (5,15) (5,6) (6,18) (6,16) (6,25) (6,14) (6,13) (6,21) (6,11) (6,9) (6,10) (6,23) (6,20) (7,12) (7,24) (7,17) (7,22) (8,12) (8,19) (9,18) (9,25) (9,14) (9,13) (9,21) (9,11) (9,10) (9,23) (9,20) (10,18) (10,16) (10,25) (10,14) (10,21) (10,11) (10,15) (11,18) (11,16) (11,25) (11,14) (11,21) (11,23) (12,19) (12,24) (12,17) (12,22) (13,16) (13,14) (13,21) (13,23) (13,20) (14,18) (14,25) (14,20) (15,18) (15,16) (15,25) (15,21) (15,23) (15,20) (16,18) (16,25) (16,23) (17,19) (17,24) (17,22) (18,25) (18,21) (18,23) (19,22) (20,25) (20,21) (21,25) (21,23) (22,24) (23,25)\nIs there a path between node 25 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph341-17_21", + "image": "data/connectivity/graph_visual/hard/graph341.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,30) (0,28) (0,1) (0,7) (0,13) (1,3) (1,10) (1,9) (1,14) (1,23) (1,13) (2,26) (2,10) (2,28) (2,7) (2,14) (2,13) (3,26) (3,10) (3,9) (3,11) (3,19) (3,4) (3,14) (3,13) (3,20) (4,26) (4,8) (4,9) (4,17) (4,12) (4,14) (4,23) (5,26) (5,8) (5,11) (5,27) (5,23) (6,21) (6,22) (6,18) (7,15) (7,26) (7,30) (7,10) (7,11) (7,23) (7,13) (7,31) (7,16) (8,15) (8,26) (8,10) (8,28) (8,17) (8,19) (8,23) (8,16) (9,15) (9,28) (9,11) (9,19) (9,27) (10,28) (10,11) (10,17) (10,13) (10,31) (10,16) (11,15) (11,30) (11,17) (11,14) (12,15) (12,23) (12,31) (12,16) (13,26) (13,19) (13,14) (13,27) (13,31) (14,30) (14,28) (14,19) (14,27) (14,20) (14,31) (15,26) (15,30) (15,19) (15,23) (15,20) (16,26) (16,30) (16,31) (17,27) (17,20) (18,22) (18,24) (19,26) (19,20) (20,28) (21,22) (21,25) (22,24) (22,25) (23,26) (24,25) (25,29) (26,30) (27,28) (28,31)\nIs there a path between node 17 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph29-6_24", + "image": "data/connectivity/graph_visual/hard/graph29.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,19) (0,23) (0,18) (0,8) (0,11) (1,13) (1,18) (1,9) (1,24) (1,25) (2,10) (2,19) (2,6) (2,18) (2,5) (2,25) (2,7) (3,19) (3,21) (3,15) (3,25) (3,16) (5,23) (5,8) (5,15) (5,25) (6,13) (6,23) (6,22) (6,24) (6,7) (7,10) (7,18) (7,8) (7,22) (7,15) (7,16) (8,13) (8,10) (8,19) (8,22) (8,11) (8,9) (8,24) (9,13) (9,22) (9,16) (10,12) (11,13) (11,19) (11,15) (11,12) (11,16) (12,20) (12,22) (12,15) (13,23) (13,21) (13,15) (15,18) (15,21) (15,24) (16,21) (16,24) (16,25) (18,23) (18,22) (19,24) (20,23) (20,22) (20,25) (22,23) (22,25) (23,24)\nIs there a path between node 6 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph535-17_13", + "image": "data/connectivity/graph_visual/hard/graph535.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,15) (0,8) (0,32) (0,26) (0,11) (1,29) (1,6) (1,23) (1,31) (1,18) (1,30) (1,4) (1,24) (1,22) (1,16) (1,33) (1,5) (1,25) (2,10) (2,14) (2,28) (2,12) (2,20) (2,27) (3,29) (3,6) (3,23) (3,31) (3,9) (3,4) (3,22) (3,16) (3,33) (3,5) (3,25) (4,29) (4,6) (4,23) (4,31) (4,30) (4,9) (4,24) (4,22) (4,33) (4,25) (5,6) (5,23) (5,31) (5,18) (5,30) (5,9) (5,24) (5,7) (5,16) (5,33) (5,25) (6,29) (6,31) (6,18) (6,30) (6,9) (6,7) (6,22) (6,16) (6,33) (6,25) (7,23) (7,31) (7,18) (7,30) (7,9) (7,24) (7,22) (7,16) (7,25) (8,15) (8,19) (8,26) (9,29) (9,23) (9,18) (9,30) (9,16) (9,25) (10,21) (10,17) (10,28) (10,20) (10,27) (10,13) (11,15) (11,32) (11,19) (11,26) (12,21) (12,17) (12,28) (12,20) (12,27) (12,13) (13,21) (13,17) (13,20) (13,27) (14,21) (14,17) (14,28) (14,27) (15,26) (16,29) (16,23) (16,18) (16,30) (16,24) (16,33) (16,25) (17,21) (17,28) (17,20) (18,31) (18,30) (18,22) (18,33) (18,25) (19,32) (19,26) (20,21) (20,28) (20,27) (21,28) (22,29) (22,30) (22,33) (22,25) (23,31) (23,30) (23,33) (24,29) (24,31) (24,30) (24,33) (24,25) (25,29) (25,31) (26,32) (27,28) (29,31) (29,33) (30,33) (31,33)\nIs there a path between node 17 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph117-21_13", + "image": "data/connectivity/graph_visual/hard/graph117.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,19) (0,15) (0,14) (0,24) (0,5) (0,25) (0,2) (1,7) (1,11) (1,8) (1,17) (1,25) (1,16) (1,21) (1,2) (2,15) (2,12) (2,3) (2,16) (3,15) (3,11) (3,10) (3,20) (3,16) (3,21) (5,7) (5,14) (5,12) (5,11) (5,24) (5,10) (5,26) (5,6) (6,19) (6,9) (6,14) (6,11) (6,24) (6,10) (6,25) (6,21) (7,19) (7,15) (7,18) (7,11) (7,24) (8,19) (8,24) (8,10) (9,15) (9,18) (9,11) (9,27) (9,26) (9,20) (9,25) (9,21) (9,23) (10,17) (10,25) (11,27) (11,26) (11,17) (11,20) (11,16) (12,19) (12,14) (12,24) (12,17) (14,26) (15,18) (15,17) (16,24) (16,26) (16,17) (17,27) (17,25) (18,24) (18,25) (19,27) (19,23) (20,24) (20,27) (20,23) (21,24) (21,27)\nIs there a path between node 21 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph535-1_7", + "image": "data/connectivity/graph_visual/hard/graph535.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,15) (0,8) (0,32) (0,26) (0,11) (1,29) (1,6) (1,23) (1,31) (1,18) (1,30) (1,4) (1,24) (1,22) (1,16) (1,33) (1,5) (1,25) (2,10) (2,14) (2,28) (2,12) (2,20) (2,27) (3,29) (3,6) (3,23) (3,31) (3,9) (3,4) (3,22) (3,16) (3,33) (3,5) (3,25) (4,29) (4,6) (4,23) (4,31) (4,30) (4,9) (4,24) (4,22) (4,33) (4,25) (5,6) (5,23) (5,31) (5,18) (5,30) (5,9) (5,24) (5,7) (5,16) (5,33) (5,25) (6,29) (6,31) (6,18) (6,30) (6,9) (6,7) (6,22) (6,16) (6,33) (6,25) (7,23) (7,31) (7,18) (7,30) (7,9) (7,24) (7,22) (7,16) (7,25) (8,15) (8,19) (8,26) (9,29) (9,23) (9,18) (9,30) (9,16) (9,25) (10,21) (10,17) (10,28) (10,20) (10,27) (10,13) (11,15) (11,32) (11,19) (11,26) (12,21) (12,17) (12,28) (12,20) (12,27) (12,13) (13,21) (13,17) (13,20) (13,27) (14,21) (14,17) (14,28) (14,27) (15,26) (16,29) (16,23) (16,18) (16,30) (16,24) (16,33) (16,25) (17,21) (17,28) (17,20) (18,31) (18,30) (18,22) (18,33) (18,25) (19,32) (19,26) (20,21) (20,28) (20,27) (21,28) (22,29) (22,30) (22,33) (22,25) (23,31) (23,30) (23,33) (24,29) (24,31) (24,30) (24,33) (24,25) (25,29) (25,31) (26,32) (27,28) (29,31) (29,33) (30,33) (31,33)\nIs there a path between node 1 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph416-6_21", + "image": "data/connectivity/graph_visual/hard/graph416.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,25) (0,27) (1,14) (1,23) (1,5) (1,6) (1,20) (1,8) (2,10) (2,25) (2,22) (3,19) (3,26) (4,32) (4,7) (4,20) (4,8) (5,17) (6,17) (6,8) (8,14) (8,23) (8,32) (9,19) (9,26) (9,13) (10,25) (10,12) (10,11) (11,25) (11,22) (12,24) (12,16) (12,25) (12,21) (13,15) (15,29) (15,19) (16,25) (17,31) (17,23) (17,32) (18,29) (18,30) (21,24) (21,25) (24,27) (26,30)\nIs there a path between node 6 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph383-5_1", + "image": "data/connectivity/graph_visual/hard/graph383.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,29) (0,28) (0,8) (0,23) (0,6) (0,10) (0,11) (0,31) (0,2) (0,9) (0,21) (0,12) (0,22) (0,14) (0,30) (1,15) (1,26) (1,19) (1,13) (1,20) (2,29) (2,28) (2,8) (2,6) (2,10) (2,11) (2,31) (2,21) (2,12) (2,14) (3,24) (3,26) (3,19) (3,13) (3,4) (4,15) (4,26) (4,19) (5,16) (5,7) (5,17) (6,28) (6,23) (6,10) (6,11) (6,31) (6,9) (6,22) (6,14) (6,30) (7,27) (8,29) (8,28) (8,23) (8,10) (8,11) (8,31) (8,9) (8,25) (8,21) (8,12) (8,14) (9,18) (9,29) (9,23) (9,10) (9,11) (9,31) (9,25) (9,14) (10,18) (10,28) (10,23) (10,11) (10,21) (10,12) (10,14) (10,30) (11,18) (11,28) (11,23) (11,31) (11,25) (11,21) (11,12) (11,22) (11,14) (11,30) (12,18) (12,29) (12,28) (12,31) (12,25) (12,22) (12,14) (13,24) (13,15) (13,26) (13,19) (14,18) (14,23) (14,31) (14,25) (14,21) (14,22) (14,30) (15,19) (15,20) (16,27) (16,17) (17,27) (18,29) (18,23) (18,31) (18,25) (19,24) (19,26) (19,20) (20,26) (21,29) (21,28) (21,23) (21,25) (21,22) (22,29) (22,28) (22,23) (22,31) (22,25) (22,30) (23,29) (23,28) (23,31) (23,25) (25,29) (25,28) (25,31) (25,30) (28,29) (28,31) (28,30) (29,30) (30,31)\nIs there a path between node 5 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph238-15_8", + "image": "data/connectivity/graph_visual/hard/graph238.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,13) (0,4) (0,26) (1,6) (1,15) (1,30) (1,24) (2,3) (2,20) (2,25) (2,26) (3,12) (3,10) (3,25) (4,12) (4,13) (4,10) (4,7) (4,25) (4,26) (5,29) (5,20) (5,11) (5,25) (5,26) (6,14) (6,30) (6,28) (6,17) (7,29) (7,12) (7,13) (7,10) (7,20) (7,25) (7,26) (8,19) (8,27) (8,24) (9,22) (9,11) (9,25) (10,22) (10,29) (10,12) (10,13) (10,25) (10,26) (11,22) (11,23) (11,20) (12,29) (12,23) (14,27) (14,28) (14,24) (15,21) (15,19) (16,30) (16,24) (17,19) (17,28) (17,24) (18,20) (18,25) (20,22) (20,29) (20,25) (21,30) (21,24) (22,23) (22,25) (22,26) (23,29) (25,29) (25,26) (26,29) (28,30)\nIs there a path between node 15 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph204-7_25", + "image": "data/connectivity/graph_visual/hard/graph204.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,15) (0,26) (0,23) (0,4) (0,6) (0,3) (0,24) (2,17) (2,6) (2,3) (2,9) (2,11) (3,18) (3,14) (3,9) (3,11) (4,17) (4,15) (4,21) (4,29) (4,23) (4,13) (4,27) (4,9) (4,8) (5,22) (5,10) (5,15) (5,23) (5,9) (5,8) (6,22) (6,10) (6,26) (6,27) (6,24) (6,8) (6,11) (8,10) (8,21) (9,19) (9,17) (9,15) (9,29) (9,25) (9,23) (9,14) (9,27) (10,22) (10,29) (10,25) (10,23) (10,18) (10,13) (10,24) (10,11) (11,22) (11,19) (11,15) (11,29) (11,14) (13,19) (13,17) (13,29) (13,26) (13,23) (13,27) (13,24) (14,17) (14,21) (14,29) (14,23) (14,18) (14,27) (14,28) (15,19) (15,29) (15,25) (17,22) (17,21) (17,26) (17,23) (18,22) (18,29) (18,26) (18,28) (19,22) (19,26) (21,25) (21,28) (22,25) (22,26) (22,23) (22,24) (24,28) (25,28) (26,27) (27,28)\nIs there a path between node 7 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph188-17_3", + "image": "data/connectivity/graph_visual/hard/graph188.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,21) (0,7) (0,2) (0,6) (0,14) (0,24) (0,23) (0,20) (1,10) (1,28) (1,3) (1,16) (1,24) (1,5) (2,3) (2,7) (2,24) (2,20) (3,25) (3,28) (3,22) (3,21) (3,16) (3,14) (4,28) (4,22) (4,16) (4,18) (4,14) (5,10) (5,7) (5,16) (6,10) (6,22) (6,7) (6,24) (6,23) (7,25) (7,22) (7,21) (7,14) (7,24) (7,20) (8,13) (10,20) (10,11) (11,18) (11,14) (11,23) (12,13) (12,17) (13,17) (13,19) (14,28) (14,23) (16,21) (16,18) (16,26) (18,22) (18,24) (18,20) (21,28) (21,23) (22,24) (23,24) (25,26)\nIs there a path between node 17 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph706-2_0", + "image": "data/connectivity/graph_visual/hard/graph706.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,21) (0,17) (0,24) (0,27) (0,4) (0,10) (0,7) (1,29) (1,14) (1,5) (1,26) (1,18) (1,23) (1,28) (1,34) (1,8) (1,6) (2,29) (2,16) (2,30) (2,5) (2,26) (2,19) (2,25) (2,11) (2,18) (2,23) (2,28) (2,20) (2,9) (2,8) (2,6) (3,33) (3,32) (4,13) (4,17) (4,22) (4,24) (4,15) (4,27) (4,12) (4,10) (4,7) (5,29) (5,14) (5,26) (5,19) (5,25) (5,11) (5,31) (5,28) (5,34) (5,6) (6,29) (6,14) (6,30) (6,26) (6,19) (6,25) (6,11) (6,18) (6,28) (6,20) (6,9) (6,8) (7,13) (7,21) (7,17) (7,22) (7,24) (7,27) (7,10) (8,16) (8,14) (8,30) (8,26) (8,25) (8,11) (8,31) (8,18) (8,23) (8,20) (8,9) (8,34) (9,29) (9,16) (9,30) (9,26) (9,19) (9,25) (9,11) (9,31) (9,23) (10,13) (10,21) (10,17) (10,24) (10,15) (10,27) (11,29) (11,16) (11,14) (11,30) (11,26) (11,19) (11,25) (11,23) (12,13) (12,17) (12,22) (12,27) (13,21) (13,17) (13,22) (13,24) (13,15) (13,27) (14,29) (14,16) (14,30) (14,26) (14,25) (14,31) (14,18) (14,28) (14,34) (15,22) (15,24) (15,27) (16,29) (16,30) (16,26) (16,25) (16,31) (16,23) (17,21) (17,24) (17,27) (18,29) (18,30) (18,26) (18,19) (18,25) (18,31) (18,23) (18,34) (19,29) (19,30) (19,26) (19,31) (19,23) (19,20) (19,34) (20,29) (20,30) (20,31) (20,23) (20,28) (20,34) (21,22) (21,24) (22,24) (22,27) (23,29) (23,26) (23,34) (24,27) (25,29) (25,30) (25,31) (25,28) (25,34) (26,29) (26,30) (26,31) (26,28) (26,34) (28,29) (28,31) (29,30) (29,31) (29,34) (30,31) (30,34) (31,34)\nIs there a path between node 2 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph74-2_1", + "image": "data/connectivity/graph_visual/hard/graph74.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,4) (0,12) (0,1) (0,13) (0,14) (0,11) (0,20) (0,7) (0,21) (1,4) (1,13) (1,14) (1,16) (1,7) (1,21) (2,5) (2,22) (2,8) (2,15) (2,25) (2,9) (2,17) (2,26) (3,11) (3,20) (3,7) (4,13) (4,14) (4,11) (4,20) (4,21) (5,22) (5,18) (5,15) (5,23) (5,25) (5,17) (5,26) (5,24) (6,19) (7,12) (7,13) (7,14) (7,11) (7,20) (7,21) (8,22) (8,15) (8,23) (8,9) (8,17) (8,24) (9,18) (9,15) (9,23) (9,25) (9,17) (11,13) (11,14) (11,16) (11,20) (12,13) (12,14) (12,16) (12,20) (12,21) (13,16) (13,20) (14,16) (14,20) (14,21) (15,22) (15,18) (15,23) (15,25) (15,26) (15,24) (16,21) (17,22) (17,18) (17,23) (17,25) (18,25) (18,24) (20,21) (22,23) (22,25) (22,26) (22,24) (23,26) (23,24) (24,25) (25,26)\nIs there a path between node 2 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph628-28_25", + "image": "data/connectivity/graph_visual/hard/graph628.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,33) (1,28) (1,34) (2,27) (2,4) (2,15) (2,23) (2,12) (3,33) (3,30) (3,26) (4,27) (4,15) (4,8) (5,26) (6,17) (6,22) (6,23) (6,11) (7,12) (7,32) (8,27) (8,10) (8,15) (8,9) (8,14) (8,20) (9,21) (9,11) (10,23) (10,32) (11,27) (11,15) (11,12) (11,32) (11,20) (12,17) (12,22) (12,32) (14,27) (14,19) (14,20) (15,27) (15,32) (15,21) (16,19) (16,32) (17,32) (18,28) (19,20) (20,22) (21,27) (22,27) (22,29) (22,23) (22,32) (23,27) (24,30) (24,26) (25,33) (27,29) (28,31) (29,32) (30,33)\nIs there a path between node 28 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph260-14_30", + "image": "data/connectivity/graph_visual/hard/graph260.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,18) (0,28) (0,30) (0,24) (0,14) (1,13) (1,12) (2,10) (2,22) (2,12) (3,9) (4,20) (4,6) (4,7) (4,18) (4,30) (4,25) (4,14) (5,21) (5,26) (6,11) (6,15) (6,25) (6,14) (7,20) (7,18) (7,11) (7,28) (7,24) (7,17) (7,15) (7,14) (8,30) (8,24) (8,25) (8,14) (9,26) (11,28) (11,14) (13,16) (13,22) (14,20) (14,28) (14,17) (14,25) (15,25) (16,22) (16,23) (17,28) (17,24) (17,25) (18,19) (19,25) (20,28) (20,30) (20,25) (21,27) (21,26) (22,23) (27,29)\nIs there a path between node 14 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph301-8_29", + "image": "data/connectivity/graph_visual/hard/graph301.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,25) (0,1) (0,26) (0,12) (0,4) (0,31) (0,30) (0,15) (0,3) (0,2) (1,25) (1,26) (1,31) (1,3) (1,2) (2,25) (2,26) (2,12) (2,4) (2,31) (2,15) (2,3) (3,25) (3,26) (3,12) (3,4) (3,31) (3,30) (3,15) (4,12) (4,30) (4,15) (5,27) (5,6) (5,28) (5,24) (5,10) (5,13) (5,19) (6,7) (6,27) (6,17) (6,24) (6,13) (7,27) (7,17) (7,14) (7,28) (7,24) (7,10) (7,13) (7,19) (8,18) (8,22) (8,20) (8,16) (8,23) (9,21) (9,18) (9,11) (9,20) (9,16) (10,17) (10,14) (10,28) (10,24) (10,13) (10,19) (11,21) (11,18) (11,22) (11,20) (11,16) (11,23) (12,25) (12,26) (12,31) (12,30) (12,15) (13,17) (13,14) (13,28) (13,24) (13,19) (14,27) (14,24) (14,19) (15,25) (15,26) (15,31) (15,30) (16,21) (16,18) (16,22) (16,20) (16,23) (16,29) (17,27) (17,24) (17,19) (18,21) (18,20) (18,23) (18,29) (19,27) (19,24) (20,21) (20,22) (20,23) (20,29) (21,23) (22,23) (22,29) (23,29) (25,31) (25,30) (26,31) (26,30) (30,31)\nIs there a path between node 8 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph447-30_31", + "image": "data/connectivity/graph_visual/hard/graph447.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (1,11) (1,25) (1,27) (1,20) (1,24) (2,14) (3,19) (3,17) (5,18) (5,27) (5,28) (6,7) (6,13) (6,29) (7,8) (7,10) (7,17) (8,31) (8,13) (9,10) (9,13) (10,19) (10,12) (11,25) (11,28) (12,13) (12,29) (13,29) (15,22) (15,25) (15,23) (15,27) (18,22) (18,23) (18,24) (19,31) (19,29) (20,23) (20,28) (20,24) (21,26) (22,25) (22,23) (22,27) (25,28) (27,28)\nIs there a path between node 30 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph72-4_24", + "image": "data/connectivity/graph_visual/hard/graph72.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,13) (0,14) (0,10) (0,19) (0,8) (0,26) (0,15) (0,1) (0,4) (1,22) (1,14) (1,23) (1,5) (1,26) (1,15) (1,11) (2,20) (2,14) (2,10) (2,15) (2,6) (2,17) (2,3) (2,11) (3,13) (3,12) (3,10) (3,5) (3,7) (3,4) (4,12) (4,14) (4,10) (4,23) (4,7) (4,26) (4,15) (4,17) (4,11) (5,12) (5,19) (5,26) (5,17) (6,20) (6,13) (6,14) (6,10) (6,19) (6,8) (6,26) (6,15) (6,21) (6,17) (7,13) (7,16) (7,21) (7,17) (7,24) (8,22) (8,15) (8,21) (10,19) (10,23) (10,11) (11,16) (11,21) (12,13) (12,14) (12,23) (12,26) (12,15) (12,24) (13,23) (13,26) (13,17) (14,20) (14,23) (14,17) (14,24) (15,20) (16,20) (16,21) (17,21) (19,22) (20,23) (20,26) (22,23) (24,26)\nIs there a path between node 4 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph123-0_9", + "image": "data/connectivity/graph_visual/hard/graph123.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,13) (0,26) (0,21) (0,20) (0,25) (0,16) (0,22) (0,14) (0,2) (0,27) (0,3) (0,5) (0,4) (0,7) (0,11) (0,24) (0,12) (0,1) (0,6) (0,23) (1,13) (1,26) (1,21) (1,25) (1,16) (1,22) (1,14) (1,2) (1,8) (1,27) (1,3) (1,5) (1,7) (1,11) (1,24) (1,12) (1,6) (1,23) (2,21) (2,25) (2,16) (2,10) (2,14) (2,8) (2,27) (2,3) (2,5) (2,4) (2,7) (2,11) (2,24) (2,12) (3,26) (3,21) (3,25) (3,10) (3,8) (3,4) (3,7) (3,11) (3,24) (3,12) (3,23) (4,13) (4,21) (4,20) (4,16) (4,10) (4,22) (4,8) (4,27) (4,7) (4,11) (4,24) (4,6) (5,21) (5,20) (5,25) (5,10) (5,8) (5,27) (5,11) (5,12) (5,6) (5,23) (6,13) (6,26) (6,21) (6,16) (6,10) (6,22) (6,14) (6,8) (6,11) (6,24) (6,12) (6,23) (7,13) (7,26) (7,21) (7,22) (7,14) (7,8) (7,24) (7,12) (7,23) (8,13) (8,21) (8,20) (8,25) (8,16) (8,22) (8,14) (8,23) (9,17) (9,18) (10,13) (10,26) (10,21) (10,20) (10,16) (10,14) (10,27) (10,11) (10,12) (10,23) (11,26) (11,25) (11,22) (11,27) (11,24) (11,12) (12,13) (12,21) (12,20) (12,16) (12,22) (12,14) (12,27) (12,24) (12,23) (13,26) (13,21) (13,20) (13,16) (13,22) (13,14) (13,27) (13,24) (13,23) (14,26) (14,21) (14,20) (14,25) (14,16) (14,22) (14,27) (14,24) (14,23) (15,18) (15,19) (16,26) (16,21) (16,27) (16,23) (17,18) (17,19) (18,19) (20,26) (20,21) (20,27) (20,24) (20,23) (21,26) (21,22) (21,27) (22,26) (22,25) (22,24) (22,23) (23,25) (23,24) (24,26) (24,25) (24,27)\nIs there a path between node 0 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph376-26_17", + "image": "data/connectivity/graph_visual/hard/graph376.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,17) (0,19) (0,26) (0,29) (0,14) (0,31) (0,23) (0,27) (0,30) (0,2) (0,28) (0,16) (0,9) (1,10) (1,19) (1,8) (1,29) (1,31) (1,23) (1,24) (1,7) (1,22) (1,30) (1,2) (1,28) (1,16) (1,15) (2,5) (2,17) (2,19) (2,8) (2,29) (2,12) (2,14) (2,31) (2,23) (2,24) (2,7) (2,27) (2,30) (2,28) (2,16) (2,9) (2,15) (3,11) (3,6) (3,13) (3,21) (4,5) (4,8) (4,29) (4,12) (4,14) (4,23) (4,22) (4,20) (4,9) (5,19) (5,26) (5,8) (5,12) (5,14) (5,23) (5,24) (5,7) (5,27) (5,30) (5,20) (5,9) (5,15) (6,11) (6,13) (6,21) (6,25) (7,10) (7,17) (7,19) (7,8) (7,14) (7,31) (7,23) (7,24) (7,22) (7,28) (7,16) (7,9) (7,15) (8,10) (8,17) (8,19) (8,26) (8,29) (8,12) (8,14) (8,31) (8,23) (8,24) (8,22) (8,30) (8,28) (8,20) (8,16) (8,9) (8,15) (9,10) (9,17) (9,19) (9,26) (9,29) (9,14) (9,31) (9,23) (9,24) (9,22) (9,27) (9,30) (9,28) (9,20) (9,16) (10,19) (10,12) (10,23) (10,22) (10,27) (10,30) (10,20) (10,16) (10,15) (11,13) (11,25) (12,17) (12,19) (12,14) (12,31) (12,23) (12,24) (12,22) (12,30) (12,28) (12,16) (12,15) (13,18) (13,21) (14,17) (14,26) (14,29) (14,22) (14,27) (14,30) (14,20) (14,16) (15,17) (15,19) (15,26) (15,31) (15,23) (15,24) (15,22) (15,27) (15,28) (15,20) (16,17) (16,26) (16,29) (16,23) (16,24) (16,22) (16,27) (16,30) (16,28) (17,19) (17,29) (17,24) (17,22) (17,30) (17,28) (17,20) (18,25) (19,31) (19,24) (19,22) (19,27) (19,30) (19,28) (20,29) (20,31) (20,23) (20,24) (20,22) (20,27) (20,30) (20,28) (21,25) (22,29) (22,31) (22,23) (22,24) (22,27) (22,30) (22,28) (23,29) (23,31) (23,27) (23,30) (23,28) (24,26) (24,29) (24,30) (24,28) (26,31) (26,27) (26,30) (26,28) (27,29) (27,31) (27,30) (27,28) (28,29) (28,31) (28,30) (29,30) (30,31)\nIs there a path between node 26 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph354-24_1", + "image": "data/connectivity/graph_visual/hard/graph354.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,28) (1,7) (1,14) (1,13) (1,3) (1,5) (1,2) (1,21) (2,8) (2,27) (2,22) (3,8) (3,6) (3,7) (3,14) (4,30) (4,10) (5,14) (5,25) (5,23) (5,19) (6,11) (6,14) (6,22) (6,9) (6,16) (7,27) (7,9) (7,31) (7,23) (8,11) (8,20) (8,16) (8,19) (8,21) (9,25) (9,13) (9,31) (9,23) (9,19) (10,30) (10,12) (10,26) (11,31) (11,19) (11,21) (12,15) (12,30) (13,14) (13,23) (13,21) (14,20) (14,17) (14,23) (15,26) (16,22) (16,31) (17,20) (18,29) (19,23) (20,25) (21,25) (21,22) (22,31) (23,25) (23,31) (24,28) (24,30) (25,31) (26,30) (28,30) (28,29)\nIs there a path between node 24 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph167-9_19", + "image": "data/connectivity/graph_visual/hard/graph167.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,15) (0,8) (0,7) (0,4) (0,28) (0,18) (1,21) (1,15) (1,19) (1,25) (1,10) (1,4) (1,27) (1,5) (2,6) (2,14) (2,12) (2,8) (2,4) (2,11) (2,17) (3,21) (3,15) (3,6) (3,20) (3,23) (3,10) (3,7) (3,16) (3,28) (3,5) (3,18) (4,15) (4,14) (4,24) (4,20) (4,10) (4,11) (5,8) (5,27) (5,16) (5,11) (6,20) (6,16) (6,26) (6,18) (7,14) (7,19) (7,25) (7,12) (7,23) (7,8) (7,17) (7,13) (8,20) (8,16) (8,13) (10,25) (10,11) (10,26) (11,20) (11,28) (11,17) (11,18) (12,20) (12,28) (13,19) (13,27) (13,18) (14,21) (14,15) (14,23) (15,21) (15,19) (15,24) (15,16) (16,21) (16,20) (16,23) (16,26) (17,24) (17,20) (17,27) (18,19) (18,28) (19,21) (19,27) (19,28) (19,26) (20,28) (23,25) (24,25) (24,28) (25,28)\nIs there a path between node 9 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph55-6_10", + "image": "data/connectivity/graph_visual/hard/graph55.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,11) (0,1) (0,5) (0,24) (0,12) (0,4) (0,2) (0,14) (0,7) (0,25) (0,17) (0,9) (0,20) (1,11) (1,18) (1,5) (1,8) (1,6) (1,24) (1,12) (1,3) (1,4) (1,2) (1,14) (1,7) (1,17) (1,16) (1,9) (2,11) (2,18) (2,8) (2,3) (2,14) (2,7) (2,25) (2,17) (2,9) (2,20) (2,26) (3,11) (3,18) (3,5) (3,8) (3,6) (3,24) (3,12) (3,4) (3,7) (3,25) (3,17) (3,16) (3,9) (3,20) (3,26) (4,11) (4,18) (4,5) (4,8) (4,6) (4,24) (4,12) (4,14) (4,17) (4,23) (4,9) (4,20) (4,22) (4,26) (5,11) (5,18) (5,8) (5,6) (5,24) (5,12) (5,25) (5,23) (5,9) (5,20) (5,22) (5,26) (6,18) (6,8) (6,24) (6,14) (6,7) (6,17) (6,23) (6,9) (6,22) (6,26) (7,11) (7,18) (7,8) (7,24) (7,25) (7,23) (7,16) (7,9) (7,20) (7,22) (7,26) (8,24) (8,14) (8,25) (8,23) (8,16) (8,9) (8,20) (8,22) (8,26) (9,11) (9,18) (9,12) (9,14) (9,25) (9,17) (9,23) (9,20) (9,22) (10,13) (10,15) (10,21) (11,24) (11,12) (11,14) (11,25) (11,23) (11,16) (11,22) (11,26) (12,24) (12,25) (12,23) (12,16) (12,20) (12,22) (12,26) (13,19) (13,15) (13,21) (14,18) (14,24) (14,25) (14,23) (14,22) (14,26) (15,19) (15,21) (16,18) (16,24) (16,17) (16,23) (16,20) (17,18) (17,24) (17,23) (17,20) (17,22) (17,26) (18,23) (18,26) (20,25) (20,23) (20,26) (22,24) (22,25) (22,23) (23,25) (23,26) (24,25) (24,26)\nIs there a path between node 6 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph550-14_18", + "image": "data/connectivity/graph_visual/hard/graph550.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,28) (0,23) (0,22) (0,32) (1,28) (1,15) (1,12) (1,13) (2,11) (2,19) (2,9) (4,16) (4,21) (4,24) (5,7) (5,8) (5,20) (6,19) (6,24) (6,27) (7,8) (7,20) (9,19) (9,24) (10,28) (10,12) (10,14) (10,32) (11,21) (12,18) (12,26) (12,22) (13,28) (13,15) (13,26) (14,18) (14,17) (14,22) (15,25) (15,26) (15,23) (16,30) (17,28) (17,32) (19,31) (19,21) (19,24) (19,33) (21,30) (21,24) (21,27) (23,28) (23,25) (25,26) (26,32) (30,31) (30,33)\nIs there a path between node 14 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph488-26_3", + "image": "data/connectivity/graph_visual/hard/graph488.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,9) (0,13) (0,24) (1,21) (1,19) (1,15) (1,10) (1,32) (1,4) (1,11) (1,27) (1,22) (1,20) (1,17) (1,5) (1,29) (1,18) (1,7) (1,3) (1,16) (2,21) (2,19) (2,15) (2,28) (2,32) (2,4) (2,27) (2,22) (2,20) (2,17) (2,5) (2,6) (2,29) (2,18) (2,7) (2,14) (2,16) (3,21) (3,15) (3,28) (3,10) (3,32) (3,4) (3,11) (3,27) (3,22) (3,20) (3,6) (3,29) (3,7) (3,23) (3,14) (4,21) (4,19) (4,15) (4,28) (4,10) (4,20) (4,17) (4,14) (5,21) (5,15) (5,10) (5,22) (5,20) (5,17) (5,29) (5,18) (5,7) (5,23) (5,14) (5,16) (6,28) (6,10) (6,32) (6,11) (6,22) (6,20) (6,17) (6,29) (6,18) (6,7) (6,23) (6,16) (7,15) (7,10) (7,32) (7,11) (7,27) (7,17) (7,29) (7,18) (7,16) (8,24) (9,13) (9,25) (9,24) (10,21) (10,15) (10,28) (10,32) (10,27) (10,22) (10,20) (10,17) (10,29) (10,18) (10,23) (10,16) (11,21) (11,28) (11,27) (11,20) (11,17) (11,14) (11,16) (12,30) (12,31) (13,24) (14,21) (14,19) (14,15) (14,32) (14,27) (14,20) (14,17) (14,29) (14,18) (14,23) (14,16) (15,21) (15,19) (15,28) (15,27) (15,22) (15,17) (15,29) (15,18) (16,21) (16,19) (16,32) (16,27) (16,22) (16,20) (16,17) (16,29) (16,23) (17,27) (17,29) (17,18) (17,23) (18,21) (18,19) (18,32) (18,27) (18,22) (18,29) (19,21) (19,28) (19,32) (19,27) (19,22) (19,20) (19,29) (19,23) (20,27) (21,32) (21,27) (21,22) (22,28) (22,27) (22,29) (22,23) (23,28) (23,32) (23,29) (24,25) (26,31) (27,28) (27,29) (28,32) (28,29) (29,32) (30,31)\nIs there a path between node 26 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph634-18_11", + "image": "data/connectivity/graph_visual/hard/graph634.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,6) (0,1) (0,8) (0,13) (0,32) (0,2) (1,33) (1,34) (1,30) (1,8) (1,10) (1,19) (1,31) (1,2) (2,15) (2,34) (2,18) (2,8) (2,3) (2,16) (2,32) (2,4) (3,5) (3,26) (3,15) (3,11) (3,16) (3,4) (3,14) (4,5) (4,26) (4,12) (4,33) (4,34) (4,30) (4,13) (4,19) (5,34) (5,21) (5,6) (5,8) (5,19) (5,32) (5,31) (6,33) (6,15) (6,34) (6,13) (6,31) (7,23) (7,20) (8,33) (8,15) (8,34) (8,21) (8,11) (9,24) (10,33) (10,21) (10,27) (10,13) (10,11) (10,19) (11,26) (11,33) (11,13) (11,32) (12,30) (12,16) (13,33) (13,34) (13,19) (13,14) (15,33) (15,34) (15,27) (16,34) (16,30) (16,27) (16,32) (17,29) (18,27) (18,32) (19,30) (19,21) (19,32) (20,28) (21,27) (21,32) (26,33) (26,30) (26,31) (27,34)\nIs there a path between node 18 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph104-1_21", + "image": "data/connectivity/graph_visual/hard/graph104.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,27) (0,14) (0,21) (0,10) (0,18) (0,12) (1,20) (1,17) (1,9) (1,4) (1,5) (1,24) (1,3) (1,2) (1,16) (1,13) (2,20) (2,19) (2,6) (2,9) (2,4) (2,5) (2,8) (2,22) (2,24) (2,11) (2,3) (2,16) (2,13) (2,7) (3,20) (3,19) (3,9) (3,4) (3,5) (3,8) (3,24) (3,16) (3,13) (3,7) (4,19) (4,17) (4,6) (4,9) (4,5) (4,8) (4,22) (4,11) (4,16) (4,13) (4,7) (5,20) (5,19) (5,17) (5,6) (5,9) (5,8) (5,22) (5,24) (5,11) (5,13) (6,20) (6,19) (6,17) (6,9) (6,22) (6,24) (6,16) (6,7) (7,19) (7,17) (7,9) (7,8) (7,22) (7,24) (7,11) (7,13) (8,20) (8,17) (8,9) (8,24) (8,11) (8,16) (8,13) (9,20) (9,19) (9,24) (9,11) (9,13) (10,25) (10,15) (10,26) (10,27) (10,14) (10,21) (10,23) (10,12) (11,20) (11,17) (11,22) (11,24) (11,13) (12,15) (12,14) (12,18) (13,20) (13,17) (13,22) (13,24) (13,16) (14,25) (14,15) (14,26) (14,27) (14,23) (15,25) (15,26) (15,21) (15,18) (16,20) (16,22) (16,24) (17,20) (17,19) (18,25) (18,26) (18,27) (18,21) (18,23) (19,24) (20,22) (21,25) (21,27) (23,25) (23,26) (25,26) (25,27) (26,27)\nIs there a path between node 1 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph250-13_6", + "image": "data/connectivity/graph_visual/hard/graph250.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,21) (0,16) (0,11) (0,5) (0,14) (0,8) (0,23) (0,15) (0,10) (0,7) (0,27) (0,6) (0,29) (0,19) (0,18) (0,22) (0,28) (0,2) (0,1) (0,9) (0,4) (1,26) (1,16) (1,11) (1,5) (1,14) (1,8) (1,10) (1,7) (1,6) (1,3) (1,29) (1,19) (1,17) (1,18) (1,28) (1,20) (1,9) (1,4) (2,26) (2,11) (2,5) (2,8) (2,15) (2,10) (2,7) (2,29) (2,19) (2,17) (2,18) (2,22) (2,28) (2,20) (2,4) (3,26) (3,21) (3,16) (3,11) (3,8) (3,15) (3,10) (3,27) (3,6) (3,29) (3,19) (3,17) (3,18) (3,22) (3,28) (3,30) (3,9) (3,4) (4,26) (4,16) (4,11) (4,5) (4,23) (4,15) (4,7) (4,27) (4,29) (4,20) (5,26) (5,16) (5,11) (5,8) (5,23) (5,10) (5,6) (5,29) (5,19) (5,17) (5,18) (5,22) (5,28) (5,30) (5,9) (6,16) (6,11) (6,8) (6,23) (6,15) (6,10) (6,27) (6,29) (6,19) (6,17) (6,18) (6,28) (6,20) (6,30) (6,9) (7,26) (7,21) (7,11) (7,8) (7,23) (7,15) (7,10) (7,27) (7,29) (7,19) (7,18) (7,22) (7,20) (7,30) (8,16) (8,23) (8,17) (8,18) (8,28) (8,20) (8,30) (8,9) (9,21) (9,16) (9,15) (9,10) (9,27) (9,29) (9,19) (9,17) (9,18) (9,22) (9,28) (9,20) (9,30) (10,26) (10,21) (10,16) (10,11) (10,15) (10,29) (10,19) (10,17) (10,18) (10,22) (10,28) (10,20) (10,30) (11,26) (11,21) (11,16) (11,14) (11,23) (11,29) (11,17) (11,18) (11,28) (11,20) (12,24) (13,24) (13,25) (14,26) (14,16) (14,23) (14,27) (14,19) (14,22) (14,28) (15,23) (15,29) (15,19) (15,17) (15,18) (15,22) (15,28) (15,20) (16,26) (16,21) (16,27) (16,19) (16,17) (16,18) (16,20) (17,26) (17,23) (17,19) (17,22) (17,28) (17,20) (18,26) (18,21) (18,23) (18,27) (18,19) (18,28) (18,30) (19,21) (19,23) (19,27) (19,29) (19,22) (19,20) (19,30) (20,26) (20,21) (20,23) (20,27) (20,22) (20,30) (21,26) (21,23) (21,27) (21,29) (21,28) (21,30) (22,26) (22,23) (22,29) (22,28) (22,30) (23,26) (23,27) (23,29) (23,30) (26,27) (26,30) (27,29) (27,28) (27,30) (28,29) (28,30) (29,30)\nIs there a path between node 13 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph10-2_0", + "image": "data/connectivity/graph_visual/hard/graph10.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,4) (0,16) (0,25) (0,14) (0,21) (0,11) (0,9) (0,5) (0,23) (0,6) (1,4) (1,16) (1,14) (1,13) (1,21) (1,11) (1,9) (1,10) (1,5) (1,23) (1,15) (1,20) (1,6) (2,18) (2,4) (2,16) (2,25) (2,14) (2,21) (2,9) (2,10) (2,5) (2,15) (2,20) (2,6) (3,12) (3,19) (3,24) (3,17) (3,7) (3,22) (3,8) (4,16) (4,25) (4,14) (4,21) (4,11) (4,9) (4,10) (4,5) (4,23) (4,15) (4,20) (4,6) (5,18) (5,16) (5,25) (5,13) (5,21) (5,11) (5,10) (5,15) (5,6) (6,18) (6,16) (6,25) (6,14) (6,13) (6,21) (6,11) (6,9) (6,10) (6,23) (6,20) (7,12) (7,24) (7,17) (7,22) (8,12) (8,19) (9,18) (9,25) (9,14) (9,13) (9,21) (9,11) (9,10) (9,23) (9,20) (10,18) (10,16) (10,25) (10,14) (10,21) (10,11) (10,15) (11,18) (11,16) (11,25) (11,14) (11,21) (11,23) (12,19) (12,24) (12,17) (12,22) (13,16) (13,14) (13,21) (13,23) (13,20) (14,18) (14,25) (14,20) (15,18) (15,16) (15,25) (15,21) (15,23) (15,20) (16,18) (16,25) (16,23) (17,19) (17,24) (17,22) (18,25) (18,21) (18,23) (19,22) (20,25) (20,21) (21,25) (21,23) (22,24) (23,25)\nIs there a path between node 2 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph26-25_23", + "image": "data/connectivity/graph_visual/hard/graph26.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,22) (0,2) (0,24) (0,25) (1,22) (1,15) (1,25) (2,22) (2,10) (2,15) (2,12) (2,11) (2,25) (2,20) (2,13) (3,8) (3,4) (4,17) (4,8) (4,5) (5,23) (5,8) (6,10) (6,15) (6,11) (6,9) (7,19) (8,17) (9,15) (9,25) (9,21) (9,13) (10,18) (10,15) (10,11) (10,21) (10,13) (11,22) (11,24) (12,22) (12,14) (12,13) (13,22) (13,14) (13,21) (14,21) (15,22) (15,18) (16,22) (16,24) (17,19) (18,22) (20,22) (20,21) (22,24) (24,25)\nIs there a path between node 25 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph644-28_30", + "image": "data/connectivity/graph_visual/hard/graph644.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,34) (0,17) (0,18) (0,1) (0,4) (0,28) (0,14) (0,22) (0,12) (1,20) (1,5) (1,26) (1,8) (1,34) (1,17) (1,28) (1,22) (2,9) (2,30) (2,6) (2,21) (2,23) (2,19) (2,25) (2,29) (2,13) (2,15) (2,16) (2,10) (2,27) (3,9) (3,31) (3,6) (3,21) (3,23) (3,19) (3,33) (3,25) (3,13) (3,15) (3,7) (3,16) (3,10) (3,24) (3,32) (3,11) (3,27) (4,5) (4,26) (4,8) (4,34) (4,17) (4,18) (4,28) (4,14) (5,20) (5,26) (5,8) (5,34) (5,17) (5,18) (5,14) (6,30) (6,31) (6,23) (6,33) (6,29) (6,7) (6,16) (6,10) (6,11) (7,9) (7,30) (7,31) (7,21) (7,23) (7,19) (7,29) (7,13) (7,16) (7,10) (7,24) (7,32) (7,11) (7,27) (8,20) (8,17) (8,18) (8,28) (8,14) (8,22) (9,30) (9,31) (9,21) (9,19) (9,33) (9,25) (9,10) (9,32) (9,11) (10,23) (10,19) (10,33) (10,25) (10,13) (10,15) (10,16) (10,24) (10,32) (10,27) (11,30) (11,31) (11,21) (11,23) (11,33) (11,25) (11,29) (11,13) (11,15) (11,16) (11,24) (11,27) (12,20) (12,26) (12,34) (12,18) (12,22) (13,31) (13,21) (13,33) (13,25) (13,15) (13,16) (13,27) (14,20) (14,26) (14,34) (14,17) (14,28) (14,22) (15,30) (15,23) (15,19) (15,25) (15,24) (15,32) (15,27) (16,30) (16,31) (16,21) (16,23) (16,24) (16,32) (17,20) (17,26) (17,34) (17,28) (17,22) (18,20) (18,26) (18,34) (18,22) (19,30) (19,31) (19,23) (19,25) (19,27) (20,34) (21,23) (21,33) (21,25) (21,29) (21,24) (21,27) (22,34) (22,28) (23,31) (23,29) (23,24) (23,32) (24,30) (24,31) (24,33) (24,29) (24,32) (24,27) (25,30) (25,31) (25,33) (25,32) (25,27) (26,34) (27,30) (27,33) (29,30) (29,31) (30,33) (30,32) (31,33) (31,32)\nIs there a path between node 28 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph80-15_26", + "image": "data/connectivity/graph_visual/hard/graph80.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,24) (0,26) (0,15) (0,14) (0,22) (0,25) (1,7) (1,24) (1,26) (1,17) (1,4) (1,15) (1,14) (1,9) (1,25) (2,12) (2,20) (2,6) (2,8) (2,18) (2,11) (2,23) (2,10) (3,7) (3,24) (3,26) (3,4) (3,15) (3,14) (3,19) (3,9) (3,21) (3,22) (3,25) (4,24) (4,26) (4,15) (4,9) (4,21) (4,22) (5,20) (5,6) (5,16) (5,8) (5,18) (5,11) (5,23) (5,10) (6,12) (6,20) (6,8) (6,18) (6,11) (6,23) (6,10) (7,13) (7,24) (7,26) (7,15) (7,14) (7,19) (7,9) (7,21) (7,22) (7,25) (8,20) (8,16) (8,10) (9,13) (9,26) (9,17) (9,15) (9,19) (9,21) (9,22) (9,25) (10,12) (10,16) (10,18) (10,11) (11,12) (11,16) (11,18) (11,23) (12,20) (12,23) (13,24) (13,17) (13,15) (13,19) (13,21) (13,22) (13,25) (14,26) (14,15) (14,19) (14,21) (14,22) (14,25) (15,24) (15,26) (15,17) (15,22) (16,20) (16,23) (17,19) (17,22) (17,25) (18,23) (19,26) (19,21) (19,22) (19,25) (20,23) (21,24) (21,26) (21,22) (21,25) (22,25) (24,26) (24,25)\nIs there a path between node 15 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph668-12_5", + "image": "data/connectivity/graph_visual/hard/graph668.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,19) (0,18) (0,12) (0,21) (0,23) (0,5) (0,26) (0,11) (0,30) (1,16) (1,19) (1,21) (1,17) (1,5) (1,26) (2,22) (2,18) (2,27) (2,23) (2,28) (2,24) (3,20) (3,14) (3,5) (3,33) (3,26) (3,25) (3,30) (4,16) (4,18) (4,21) (4,23) (4,28) (4,11) (4,25) (4,6) (5,22) (5,7) (5,18) (5,9) (5,17) (5,29) (5,28) (5,24) (5,11) (6,16) (6,20) (6,7) (6,19) (6,18) (6,14) (6,12) (6,9) (6,21) (6,23) (7,31) (7,18) (7,12) (7,9) (7,32) (7,17) (7,29) (7,26) (8,31) (8,10) (8,14) (8,9) (8,21) (8,32) (8,29) (8,33) (8,26) (9,13) (9,27) (9,12) (9,17) (9,29) (9,33) (9,28) (9,11) (9,25) (10,22) (10,31) (10,20) (10,18) (10,12) (10,23) (10,29) (10,28) (11,16) (11,13) (11,14) (11,17) (11,26) (11,30) (12,16) (12,22) (12,20) (12,13) (12,27) (12,21) (12,32) (12,17) (12,25) (13,18) (14,20) (14,32) (14,28) (14,26) (16,19) (16,17) (16,28) (16,24) (16,25) (16,30) (17,19) (17,18) (17,27) (17,25) (18,20) (18,28) (18,26) (19,22) (19,31) (19,27) (19,23) (19,29) (19,33) (20,22) (20,31) (20,23) (20,32) (20,33) (20,26) (20,30) (21,22) (21,29) (21,24) (21,25) (22,31) (22,23) (22,33) (22,26) (23,32) (23,33) (23,24) (23,30) (24,27) (24,25) (25,27) (25,32) (25,28) (25,26) (26,33) (26,30) (27,33) (27,30) (28,31) (28,29) (29,31) (29,32) (30,31) (30,33) (31,33)\nIs there a path between node 12 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph461-9_18", + "image": "data/connectivity/graph_visual/hard/graph461.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,10) (0,23) (0,27) (0,9) (1,16) (1,3) (1,4) (1,21) (1,26) (1,2) (2,31) (2,16) (2,15) (2,6) (2,17) (3,24) (3,8) (3,19) (3,16) (3,30) (3,5) (3,4) (3,15) (3,7) (3,11) (4,24) (4,8) (4,30) (4,21) (4,12) (4,26) (4,7) (4,11) (5,21) (5,6) (5,26) (6,30) (6,21) (6,11) (7,24) (8,31) (8,24) (8,19) (8,12) (9,27) (10,18) (10,23) (10,14) (11,31) (11,24) (11,21) (12,24) (12,19) (12,30) (12,15) (12,21) (13,32) (13,18) (13,29) (14,32) (14,23) (15,19) (15,16) (16,24) (16,19) (17,19) (18,32) (18,23) (18,28) (19,24) (19,30) (19,26) (21,31) (21,30) (21,26) (26,30) (27,32) (28,32) (30,31)\nIs there a path between node 9 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph284-3_8", + "image": "data/connectivity/graph_visual/hard/graph284.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,31) (0,11) (0,27) (0,18) (1,4) (1,12) (1,31) (1,7) (1,25) (1,8) (1,18) (2,17) (2,14) (2,6) (2,10) (2,19) (3,17) (3,22) (3,9) (4,12) (4,30) (4,31) (4,13) (4,27) (4,18) (5,29) (5,16) (5,22) (5,21) (5,20) (5,28) (5,19) (6,29) (6,9) (6,10) (6,28) (7,11) (7,27) (7,15) (7,18) (8,30) (8,23) (8,11) (9,14) (9,21) (9,10) (11,23) (11,18) (12,30) (12,31) (12,27) (12,25) (12,15) (12,18) (13,23) (13,25) (13,15) (14,29) (14,17) (16,24) (16,17) (16,20) (17,29) (18,30) (18,26) (20,29) (21,24) (22,24) (23,27) (23,25) (25,26) (25,27) (26,31) (27,31) (28,29)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph350-18_1", + "image": "data/connectivity/graph_visual/hard/graph350.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,21) (0,2) (1,19) (1,26) (2,27) (2,9) (3,31) (3,4) (3,25) (3,11) (4,31) (4,6) (4,20) (4,5) (4,10) (4,25) (4,24) (5,31) (5,21) (6,20) (6,21) (6,10) (6,18) (6,11) (6,24) (7,15) (7,17) (8,27) (8,11) (8,9) (9,18) (10,28) (10,16) (10,24) (11,28) (13,22) (13,17) (15,17) (16,21) (16,27) (17,26) (18,21) (18,25) (18,28) (18,24) (20,31) (21,28) (24,29) (24,27) (27,31) (28,31)\nIs there a path between node 18 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph142-7_15", + "image": "data/connectivity/graph_visual/hard/graph142.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,7) (0,23) (0,27) (0,25) (0,3) (1,2) (1,21) (1,25) (1,22) (1,9) (2,10) (2,25) (2,3) (2,8) (3,23) (3,12) (3,25) (3,9) (3,26) (4,20) (4,5) (4,24) (4,18) (5,19) (5,20) (5,17) (6,21) (6,27) (6,22) (6,16) (6,26) (7,23) (7,21) (7,10) (7,22) (7,26) (7,8) (8,21) (8,15) (8,22) (8,16) (9,21) (9,12) (10,13) (10,21) (10,25) (11,18) (12,13) (12,21) (12,27) (12,25) (12,22) (13,21) (14,18) (15,27) (15,22) (16,21) (16,28) (16,26) (17,19) (17,20) (17,18) (19,24) (21,23) (21,25) (21,28) (22,25) (23,28) (27,28)\nIs there a path between node 7 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph176-11_8", + "image": "data/connectivity/graph_visual/hard/graph176.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,19) (0,13) (0,4) (0,28) (0,3) (0,11) (0,9) (0,18) (1,22) (1,6) (1,20) (1,21) (2,8) (2,15) (2,25) (2,19) (2,23) (2,4) (2,28) (2,24) (2,16) (2,11) (2,9) (2,26) (2,18) (3,25) (3,19) (3,23) (3,24) (3,11) (3,12) (3,9) (3,26) (3,18) (4,8) (4,15) (4,25) (4,13) (4,23) (4,28) (4,16) (4,11) (4,12) (4,9) (4,26) (4,18) (5,14) (5,22) (5,10) (5,6) (5,17) (5,21) (5,27) (5,7) (6,14) (6,10) (6,17) (6,27) (7,14) (7,22) (7,10) (8,15) (8,25) (8,19) (8,23) (8,28) (8,16) (8,9) (8,18) (9,19) (9,28) (9,24) (9,11) (9,12) (10,14) (10,22) (10,17) (10,20) (10,21) (10,27) (11,15) (11,23) (11,24) (11,16) (11,26) (11,18) (12,15) (12,25) (12,19) (12,13) (12,23) (12,24) (12,26) (13,15) (13,19) (13,24) (13,16) (13,18) (14,22) (14,17) (14,20) (14,21) (15,25) (15,19) (15,23) (15,16) (15,18) (16,25) (16,19) (16,28) (16,24) (16,26) (16,18) (17,20) (17,21) (17,27) (18,25) (18,19) (18,23) (18,28) (19,25) (19,23) (19,28) (19,24) (19,26) (20,22) (20,21) (21,22) (21,27) (22,27) (23,28) (23,24) (24,25) (24,26) (25,26) (26,28)\nIs there a path between node 11 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph127-23_27", + "image": "data/connectivity/graph_visual/hard/graph127.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,14) (0,20) (0,10) (0,6) (0,18) (1,24) (1,16) (1,27) (1,19) (1,12) (1,11) (1,17) (1,23) (1,26) (1,15) (1,4) (2,14) (2,25) (2,20) (2,6) (3,7) (4,24) (4,16) (4,12) (4,11) (4,8) (4,23) (4,26) (4,5) (5,27) (5,19) (5,17) (5,23) (5,13) (5,26) (5,15) (5,22) (6,14) (6,20) (6,10) (6,21) (6,18) (8,24) (8,16) (8,27) (8,12) (8,11) (8,17) (8,23) (8,26) (8,22) (10,14) (10,20) (10,21) (10,18) (11,24) (11,16) (11,19) (11,17) (11,23) (11,26) (11,15) (11,22) (12,27) (12,19) (12,17) (12,13) (12,26) (12,15) (12,22) (13,24) (13,19) (13,17) (13,23) (13,15) (13,22) (14,25) (14,20) (15,24) (15,16) (15,17) (15,23) (15,26) (15,22) (16,24) (16,17) (16,23) (16,22) (17,24) (17,19) (17,23) (17,22) (18,25) (18,20) (18,21) (19,23) (19,26) (20,25) (22,24) (22,23) (22,26) (24,27) (24,26)\nIs there a path between node 23 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph87-1_25", + "image": "data/connectivity/graph_visual/hard/graph87.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,14) (0,20) (0,2) (0,6) (0,11) (0,8) (0,12) (0,9) (0,5) (0,26) (0,24) (0,17) (1,14) (1,20) (1,6) (1,11) (1,8) (1,12) (1,9) (1,7) (1,13) (1,5) (1,19) (1,16) (1,24) (1,17) (1,25) (2,12) (2,9) (2,7) (2,5) (2,19) (2,16) (2,26) (2,24) (2,17) (2,25) (3,21) (3,4) (3,15) (3,18) (3,22) (3,23) (4,21) (4,15) (4,18) (4,23) (4,10) (5,14) (5,11) (5,8) (5,7) (5,19) (5,16) (5,24) (5,17) (6,20) (6,11) (6,8) (6,12) (6,7) (6,13) (6,19) (6,16) (6,26) (6,17) (7,14) (7,20) (7,11) (7,8) (7,12) (7,9) (7,13) (7,19) (7,16) (7,26) (7,24) (7,17) (7,25) (8,14) (8,20) (8,11) (8,9) (8,19) (8,16) (8,26) (8,24) (9,20) (9,13) (9,19) (9,16) (9,24) (9,17) (10,15) (10,22) (10,23) (11,20) (11,13) (11,19) (12,14) (12,20) (12,13) (12,19) (12,16) (12,24) (12,17) (12,25) (13,20) (13,19) (13,26) (13,24) (13,25) (14,19) (14,16) (14,26) (14,24) (14,17) (15,21) (15,18) (15,23) (16,20) (16,19) (16,26) (16,24) (16,17) (17,20) (17,19) (17,26) (17,24) (17,25) (18,21) (18,22) (19,20) (19,26) (19,24) (19,25) (20,26) (20,24) (21,22) (21,23) (22,23)\nIs there a path between node 1 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph328-6_23", + "image": "data/connectivity/graph_visual/hard/graph328.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,21) (0,17) (0,19) (0,2) (0,25) (0,23) (0,14) (0,8) (0,7) (0,28) (0,29) (0,16) (0,5) (0,12) (0,11) (0,18) (0,6) (0,24) (1,4) (1,17) (1,19) (1,14) (1,8) (1,31) (1,27) (1,7) (1,29) (1,16) (1,5) (1,12) (1,11) (1,20) (1,3) (1,18) (1,6) (1,13) (2,21) (2,17) (2,19) (2,25) (2,31) (2,15) (2,27) (2,7) (2,29) (2,16) (2,5) (2,26) (2,12) (2,11) (2,3) (2,18) (2,10) (2,13) (3,4) (3,21) (3,17) (3,19) (3,23) (3,14) (3,31) (3,15) (3,27) (3,7) (3,28) (3,16) (3,26) (3,11) (3,20) (3,18) (3,24) (3,10) (3,13) (4,21) (4,19) (4,25) (4,23) (4,8) (4,31) (4,15) (4,27) (4,7) (4,29) (4,16) (4,5) (4,26) (4,20) (4,18) (4,10) (4,13) (5,21) (5,17) (5,19) (5,23) (5,14) (5,8) (5,31) (5,15) (5,7) (5,28) (5,26) (5,12) (5,11) (5,20) (5,24) (5,10) (5,13) (6,21) (6,17) (6,23) (6,14) (6,8) (6,31) (6,15) (6,27) (6,7) (6,12) (6,11) (6,18) (6,24) (6,10) (6,13) (7,17) (7,19) (7,25) (7,14) (7,31) (7,15) (7,27) (7,28) (7,29) (7,16) (7,26) (7,12) (7,11) (7,20) (7,10) (7,13) (8,21) (8,17) (8,19) (8,25) (8,14) (8,31) (8,28) (8,29) (8,16) (8,20) (8,18) (8,24) (8,10) (8,13) (9,30) (10,21) (10,17) (10,25) (10,23) (10,14) (10,31) (10,15) (10,28) (10,29) (10,16) (10,12) (10,20) (10,18) (10,24) (11,21) (11,17) (11,19) (11,25) (11,23) (11,15) (11,28) (11,16) (11,12) (11,20) (11,18) (11,24) (11,13) (12,19) (12,25) (12,23) (12,14) (12,31) (12,15) (12,27) (12,28) (12,29) (12,16) (12,26) (12,20) (12,18) (12,24) (13,21) (13,19) (13,25) (13,23) (13,14) (13,31) (13,15) (13,29) (13,16) (13,26) (13,20) (13,24) (14,17) (14,23) (14,31) (14,15) (14,28) (14,29) (14,16) (14,26) (14,20) (14,24) (15,17) (15,25) (15,23) (15,31) (15,27) (15,28) (15,29) (15,16) (15,26) (15,20) (16,21) (16,19) (16,25) (16,23) (16,31) (16,27) (16,28) (16,29) (16,26) (16,18) (16,24) (17,21) (17,19) (17,25) (17,23) (17,31) (17,29) (17,18) (17,24) (18,21) (18,19) (18,25) (18,28) (18,29) (18,26) (18,20) (19,21) (19,25) (19,23) (19,27) (19,28) (19,29) (19,20) (20,21) (20,25) (20,23) (20,27) (20,28) (20,26) (20,24) (21,25) (21,23) (21,31) (21,27) (21,28) (21,24) (22,30) (23,31) (23,27) (24,25) (24,31) (24,27) (24,28) (24,29) (24,26) (26,31) (26,27) (26,29) (28,29) (29,31)\nIs there a path between node 6 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph368-17_31", + "image": "data/connectivity/graph_visual/hard/graph368.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,10) (0,4) (0,3) (0,16) (0,24) (0,17) (0,25) (0,8) (1,18) (1,10) (1,4) (1,30) (1,16) (1,24) (1,17) (2,21) (2,14) (2,29) (2,11) (2,9) (2,5) (2,13) (3,18) (3,4) (3,23) (3,7) (3,16) (3,24) (3,20) (3,17) (3,8) (4,10) (4,30) (4,24) (4,20) (4,17) (4,8) (5,14) (5,11) (5,28) (5,9) (6,22) (6,19) (6,12) (7,18) (7,10) (7,23) (7,16) (7,24) (7,20) (7,17) (7,8) (8,18) (8,10) (8,23) (8,30) (8,16) (8,20) (9,26) (9,14) (9,29) (9,11) (9,28) (9,13) (10,18) (10,23) (10,30) (10,16) (10,24) (10,20) (10,17) (11,26) (11,21) (11,14) (11,29) (11,28) (11,13) (12,22) (12,27) (12,19) (12,31) (13,26) (13,21) (13,14) (13,29) (14,26) (14,21) (14,29) (14,28) (15,27) (15,19) (15,31) (16,18) (16,23) (16,30) (16,24) (16,20) (16,17) (17,30) (17,20) (18,30) (18,24) (18,20) (18,25) (19,22) (19,27) (19,31) (20,25) (21,29) (22,27) (23,30) (23,25) (24,25) (25,30) (26,28) (27,31) (28,29)\nIs there a path between node 17 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph278-0_28", + "image": "data/connectivity/graph_visual/hard/graph278.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,10) (0,1) (0,15) (0,17) (0,12) (0,8) (1,16) (1,10) (1,18) (1,15) (1,2) (1,17) (1,28) (2,12) (2,8) (3,29) (3,24) (3,25) (3,6) (3,27) (3,19) (3,11) (3,4) (3,5) (4,9) (4,30) (4,22) (4,11) (5,29) (5,24) (5,23) (5,9) (5,25) (5,30) (5,6) (5,22) (5,19) (5,11) (6,29) (6,24) (6,23) (6,25) (6,30) (6,27) (6,22) (6,11) (7,20) (7,21) (7,13) (7,26) (7,14) (8,16) (8,10) (8,18) (8,15) (8,17) (8,12) (8,28) (9,29) (9,23) (9,30) (9,27) (9,22) (9,19) (10,16) (10,18) (10,15) (10,17) (10,12) (10,28) (11,29) (11,25) (11,22) (12,16) (12,15) (12,17) (13,26) (13,14) (14,20) (14,21) (15,16) (15,18) (15,28) (16,18) (16,17) (16,28) (17,18) (17,28) (18,28) (19,29) (19,23) (19,25) (19,30) (19,22) (20,21) (22,29) (22,24) (22,25) (22,30) (23,24) (23,25) (23,27) (24,25) (25,29) (25,30) (25,27) (27,29) (29,30)\nIs there a path between node 0 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph321-19_16", + "image": "data/connectivity/graph_visual/hard/graph321.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,5) (0,21) (0,7) (0,6) (0,3) (0,17) (0,20) (0,22) (0,16) (0,23) (0,25) (0,27) (1,5) (1,21) (1,4) (1,7) (1,15) (1,18) (1,2) (1,24) (1,20) (1,11) (1,16) (1,25) (1,27) (2,14) (2,5) (2,21) (2,4) (2,15) (2,24) (2,22) (2,11) (2,23) (2,25) (2,27) (3,14) (3,13) (3,21) (3,7) (3,15) (3,6) (3,17) (3,24) (3,22) (3,11) (3,16) (3,23) (4,14) (4,13) (4,5) (4,19) (4,7) (4,18) (4,17) (4,22) (4,11) (4,23) (4,25) (4,27) (5,13) (5,19) (5,15) (5,18) (5,24) (5,20) (5,22) (5,11) (5,23) (5,27) (6,14) (6,21) (6,19) (6,7) (6,15) (6,18) (6,17) (6,24) (6,20) (6,11) (6,16) (6,25) (6,27) (7,14) (7,13) (7,21) (7,19) (7,15) (7,18) (7,17) (7,20) (7,22) (7,11) (7,23) (7,27) (8,30) (8,28) (9,31) (9,10) (9,26) (9,29) (10,31) (10,26) (10,29) (11,13) (11,21) (11,19) (11,15) (11,24) (11,22) (11,25) (11,27) (12,28) (13,14) (13,21) (13,15) (13,18) (13,17) (13,24) (13,20) (13,16) (13,23) (13,25) (13,27) (14,21) (14,19) (14,24) (14,20) (14,22) (14,16) (14,23) (14,25) (15,21) (15,18) (15,17) (15,24) (15,20) (15,22) (15,16) (15,25) (15,27) (16,21) (16,18) (16,17) (16,24) (16,20) (16,22) (16,25) (17,21) (17,19) (17,18) (17,24) (17,20) (17,22) (17,23) (17,25) (17,27) (18,21) (18,24) (18,20) (18,25) (18,27) (19,21) (19,20) (19,22) (19,27) (20,21) (20,24) (20,22) (20,23) (20,27) (21,24) (21,22) (21,25) (21,27) (22,25) (23,25) (23,27) (25,27) (26,31) (26,29) (29,31)\nIs there a path between node 19 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph196-6_4", + "image": "data/connectivity/graph_visual/hard/graph196.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,29) (0,15) (0,3) (0,14) (0,27) (0,1) (0,25) (0,12) (0,26) (1,22) (1,15) (1,3) (1,14) (1,27) (1,16) (1,5) (1,12) (2,10) (2,23) (3,29) (3,22) (3,15) (3,14) (3,25) (3,5) (3,12) (4,19) (4,11) (4,18) (4,28) (4,17) (5,7) (5,25) (5,16) (5,12) (6,9) (6,18) (6,20) (6,28) (6,13) (7,29) (7,22) (7,15) (7,25) (7,16) (7,26) (8,24) (8,10) (9,21) (9,20) (9,17) (10,23) (11,19) (11,20) (11,28) (12,29) (12,22) (12,14) (12,27) (12,25) (12,26) (13,21) (13,18) (13,17) (14,29) (14,22) (14,15) (14,27) (14,25) (14,16) (14,26) (15,29) (15,25) (15,16) (15,26) (16,29) (16,25) (17,18) (17,28) (18,19) (18,21) (18,20) (19,21) (20,21) (21,28) (22,25) (22,26) (23,24) (25,27) (25,26) (26,29) (26,27) (27,29)\nIs there a path between node 6 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph521-22_12", + "image": "data/connectivity/graph_visual/hard/graph521.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,21) (0,11) (0,23) (1,9) (1,18) (1,8) (1,5) (2,30) (2,12) (2,32) (2,10) (2,17) (3,6) (3,20) (3,19) (3,5) (3,27) (4,33) (4,28) (4,20) (5,6) (5,27) (6,25) (6,7) (6,20) (6,19) (6,8) (6,15) (6,27) (7,14) (7,24) (7,20) (8,9) (8,14) (8,28) (8,19) (9,25) (9,14) (9,20) (9,18) (10,16) (10,26) (10,32) (10,17) (11,30) (11,32) (11,31) (11,21) (11,23) (12,30) (12,21) (12,17) (12,22) (12,23) (13,31) (13,17) (14,25) (14,33) (14,18) (14,19) (16,30) (16,26) (16,21) (16,17) (16,23) (17,23) (18,25) (18,33) (18,19) (19,33) (20,33) (20,28) (21,32) (21,31) (22,30) (23,32) (23,31) (24,25) (24,27) (25,27) (26,30) (27,33) (28,33)\nIs there a path between node 22 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph404-21_32", + "image": "data/connectivity/graph_visual/hard/graph404.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,31) (0,26) (0,2) (0,22) (0,1) (0,13) (0,16) (0,18) (0,30) (0,14) (0,21) (1,31) (1,4) (1,26) (1,2) (1,22) (1,7) (1,16) (1,18) (1,11) (1,29) (1,30) (1,23) (1,14) (1,10) (1,32) (1,27) (1,12) (1,21) (2,31) (2,4) (2,26) (2,22) (2,7) (2,13) (2,16) (2,18) (2,11) (2,29) (2,30) (2,23) (2,14) (2,32) (2,12) (4,26) (4,7) (4,16) (4,18) (4,11) (4,29) (4,23) (4,14) (4,10) (4,12) (4,21) (5,17) (5,28) (5,6) (5,15) (5,25) (5,20) (5,8) (6,24) (6,25) (6,20) (6,8) (7,26) (7,18) (7,11) (7,29) (7,23) (7,14) (7,10) (7,32) (7,27) (7,12) (7,21) (8,17) (8,19) (8,28) (8,9) (8,15) (8,24) (9,17) (9,19) (9,28) (9,15) (9,24) (9,25) (9,20) (10,26) (10,22) (10,16) (10,11) (10,29) (10,30) (10,23) (10,14) (10,32) (10,27) (10,12) (11,31) (11,26) (11,22) (11,13) (11,16) (11,18) (11,30) (11,23) (11,14) (11,32) (12,26) (12,13) (12,16) (12,18) (12,29) (12,30) (12,23) (12,14) (12,32) (12,27) (12,21) (13,31) (13,18) (13,29) (13,30) (13,32) (13,21) (14,31) (14,26) (14,22) (14,16) (14,18) (14,29) (14,30) (14,23) (14,32) (14,27) (15,19) (15,28) (15,20) (16,31) (16,22) (16,29) (16,30) (16,23) (16,32) (16,27) (17,28) (17,20) (18,31) (18,22) (18,29) (18,23) (18,32) (18,27) (18,21) (19,28) (19,24) (19,20) (20,28) (20,24) (20,25) (21,22) (21,30) (21,32) (21,27) (22,31) (22,26) (22,29) (22,30) (22,23) (22,32) (22,27) (23,31) (23,30) (23,32) (23,27) (24,28) (24,25) (26,31) (26,30) (26,32) (26,27) (27,31) (27,29) (29,30) (29,32) (30,31) (31,32)\nIs there a path between node 21 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph381-18_5", + "image": "data/connectivity/graph_visual/hard/graph381.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,17) (0,4) (0,14) (0,22) (0,9) (0,5) (0,16) (0,25) (0,31) (0,23) (0,28) (0,15) (0,2) (0,8) (0,19) (0,6) (1,12) (1,3) (1,21) (2,13) (2,17) (2,4) (2,24) (2,14) (2,30) (2,22) (2,9) (2,16) (2,25) (2,29) (2,31) (2,20) (2,28) (2,15) (2,8) (2,19) (2,6) (3,18) (3,12) (3,21) (4,13) (4,7) (4,14) (4,30) (4,22) (4,9) (4,5) (4,26) (4,23) (4,20) (4,28) (4,15) (4,8) (4,19) (4,6) (5,24) (5,7) (5,14) (5,30) (5,22) (5,9) (5,29) (5,26) (5,23) (5,28) (5,15) (5,8) (5,19) (5,6) (6,13) (6,17) (6,11) (6,24) (6,14) (6,22) (6,16) (6,29) (6,31) (6,23) (6,20) (6,28) (7,13) (7,17) (7,11) (7,24) (7,30) (7,9) (7,16) (7,25) (7,29) (7,26) (7,31) (7,23) (7,20) (7,28) (7,8) (7,19) (8,17) (8,24) (8,14) (8,30) (8,22) (8,9) (8,16) (8,20) (8,28) (8,15) (8,19) (9,13) (9,17) (9,11) (9,24) (9,14) (9,30) (9,22) (9,16) (9,25) (9,29) (9,26) (9,23) (9,20) (9,15) (9,19) (11,13) (11,14) (11,30) (11,22) (11,16) (11,29) (11,26) (11,23) (11,20) (11,15) (11,19) (12,18) (12,21) (13,14) (13,25) (13,26) (13,31) (13,20) (13,15) (13,19) (14,17) (14,24) (14,22) (14,16) (14,25) (14,26) (14,31) (14,20) (14,28) (15,17) (15,24) (15,30) (15,22) (15,16) (15,25) (15,29) (15,19) (16,17) (16,24) (16,30) (16,29) (16,26) (16,31) (16,23) (16,20) (16,28) (16,19) (17,24) (17,30) (17,22) (17,31) (17,23) (17,20) (17,28) (17,19) (19,24) (19,25) (19,26) (19,31) (19,23) (19,20) (20,30) (20,22) (20,26) (20,23) (22,30) (22,25) (22,29) (22,23) (22,28) (23,24) (23,30) (23,25) (23,29) (23,26) (24,30) (24,25) (24,29) (24,28) (25,30) (25,26) (25,31) (25,28) (26,30) (26,29) (26,31) (28,30) (28,29) (30,31)\nIs there a path between node 18 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph7-25_24", + "image": "data/connectivity/graph_visual/hard/graph7.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,5) (0,1) (0,4) (0,12) (0,23) (0,19) (0,14) (0,21) (0,15) (0,7) (0,22) (1,24) (1,6) (1,20) (1,23) (1,25) (1,3) (1,9) (1,16) (1,7) (2,6) (2,19) (2,14) (2,10) (2,3) (2,8) (2,9) (2,7) (3,5) (3,24) (3,14) (3,25) (3,22) (4,24) (4,19) (4,10) (4,16) (5,24) (5,14) (5,15) (5,9) (6,23) (6,14) (6,15) (7,24) (7,23) (7,14) (7,15) (7,10) (7,22) (8,19) (8,14) (8,21) (8,25) (8,22) (9,23) (10,24) (10,16) (11,18) (11,17) (12,20) (12,14) (12,25) (12,16) (14,24) (14,23) (14,19) (14,15) (15,20) (15,19) (15,21) (15,22) (16,25) (17,18) (19,21) (20,24) (20,23) (20,25) (21,23) (22,23)\nIs there a path between node 25 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph338-24_31", + "image": "data/connectivity/graph_visual/hard/graph338.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (1,11) (1,9) (1,19) (1,31) (1,20) (2,15) (2,11) (2,27) (2,29) (2,16) (2,31) (3,8) (3,4) (3,12) (3,18) (3,17) (3,10) (3,25) (3,31) (3,20) (4,30) (4,24) (4,19) (5,26) (5,23) (6,13) (7,15) (7,9) (7,30) (7,12) (7,16) (7,19) (7,10) (7,25) (8,15) (8,11) (8,30) (8,24) (8,10) (8,31) (9,11) (9,30) (9,27) (9,29) (9,10) (10,15) (10,30) (10,12) (10,18) (10,19) (10,17) (10,14) (11,30) (11,29) (11,19) (12,15) (12,19) (12,14) (12,20) (13,28) (14,27) (14,24) (14,20) (15,27) (15,18) (15,25) (15,20) (16,29) (16,24) (16,19) (17,29) (17,19) (17,31) (18,30) (18,24) (18,19) (18,31) (19,30) (19,25) (21,28) (21,23) (22,23) (25,27) (25,31) (26,28) (29,31)\nIs there a path between node 24 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph151-7_10", + "image": "data/connectivity/graph_visual/hard/graph151.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,6) (0,27) (0,11) (0,4) (0,9) (0,25) (0,16) (0,2) (0,23) (0,3) (0,28) (0,10) (0,5) (1,6) (1,27) (1,20) (1,11) (1,24) (1,4) (1,14) (1,13) (1,9) (1,25) (1,2) (1,17) (1,23) (1,3) (1,28) (1,10) (1,22) (2,6) (2,24) (2,4) (2,14) (2,17) (2,23) (2,28) (2,22) (2,5) (3,6) (3,27) (3,20) (3,11) (3,4) (3,16) (3,17) (3,23) (3,28) (3,22) (3,5) (4,27) (4,20) (4,14) (4,9) (4,25) (4,16) (4,17) (4,23) (4,28) (4,10) (4,22) (5,27) (5,20) (5,11) (5,24) (5,13) (5,9) (5,16) (5,17) (5,28) (5,10) (6,20) (6,11) (6,24) (6,13) (6,9) (6,25) (6,16) (6,17) (6,28) (6,10) (6,22) (7,12) (7,26) (7,21) (8,15) (8,18) (9,27) (9,20) (9,11) (9,24) (9,14) (9,13) (9,25) (9,16) (9,10) (9,22) (10,27) (10,20) (10,24) (10,13) (10,25) (10,16) (10,17) (10,23) (10,28) (11,20) (11,24) (11,14) (11,16) (11,17) (11,28) (12,26) (12,21) (13,27) (13,24) (13,25) (13,17) (13,23) (14,20) (14,25) (14,16) (14,23) (14,28) (15,19) (15,18) (16,27) (16,20) (16,24) (16,25) (16,17) (16,23) (16,28) (16,22) (17,27) (17,24) (17,25) (18,19) (20,24) (20,25) (20,22) (21,26) (22,27) (22,24) (22,25) (23,24) (23,25) (24,27) (24,25) (24,28) (25,28) (27,28)\nIs there a path between node 7 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph394-10_7", + "image": "data/connectivity/graph_visual/hard/graph394.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,12) (0,24) (0,5) (0,32) (0,18) (0,23) (0,25) (1,20) (2,21) (2,13) (2,29) (3,12) (3,7) (3,11) (3,23) (3,25) (4,27) (4,12) (4,32) (5,30) (5,14) (7,10) (7,11) (7,23) (7,25) (8,27) (8,18) (8,30) (8,11) (8,25) (9,28) (10,27) (10,24) (10,32) (10,18) (10,23) (11,22) (11,14) (12,27) (12,24) (12,25) (13,15) (13,21) (13,29) (14,27) (14,32) (14,23) (15,21) (19,20) (22,30) (22,23) (23,30) (24,32) (24,30) (24,25) (25,27)\nIs there a path between node 10 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph377-22_9", + "image": "data/connectivity/graph_visual/hard/graph377.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,27) (0,28) (0,4) (1,18) (1,27) (1,28) (1,25) (1,4) (2,30) (2,20) (2,5) (2,21) (2,31) (2,11) (2,9) (2,6) (2,17) (2,29) (2,22) (2,23) (2,15) (2,24) (2,19) (2,3) (2,16) (2,12) (2,14) (3,30) (3,21) (3,7) (3,31) (3,9) (3,8) (3,6) (3,17) (3,13) (3,22) (3,23) (3,15) (3,24) (3,16) (3,12) (3,14) (4,18) (4,27) (4,28) (5,30) (5,21) (5,7) (5,31) (5,11) (5,9) (5,8) (5,6) (5,13) (5,26) (5,15) (5,19) (5,10) (5,12) (5,14) (6,30) (6,20) (6,21) (6,7) (6,31) (6,11) (6,9) (6,29) (6,23) (6,15) (6,19) (6,10) (6,16) (6,12) (6,14) (7,30) (7,20) (7,11) (7,9) (7,8) (7,17) (7,29) (7,13) (7,22) (7,23) (7,15) (7,19) (7,10) (7,12) (8,30) (8,21) (8,31) (8,11) (8,9) (8,29) (8,26) (8,22) (8,23) (8,24) (8,19) (8,10) (8,16) (9,30) (9,20) (9,21) (9,31) (9,11) (9,29) (9,13) (9,26) (9,22) (9,23) (9,24) (9,19) (9,12) (9,14) (10,30) (10,20) (10,21) (10,11) (10,23) (10,15) (10,24) (10,19) (10,16) (11,31) (11,29) (11,13) (11,26) (11,22) (11,23) (11,16) (11,12) (11,14) (12,30) (12,20) (12,21) (12,17) (12,29) (12,13) (12,26) (12,22) (12,23) (12,24) (12,19) (12,16) (12,14) (13,30) (13,21) (13,31) (13,17) (13,29) (13,26) (13,23) (13,15) (13,24) (13,19) (13,16) (13,14) (14,30) (14,21) (14,31) (14,22) (14,19) (14,16) (15,20) (15,29) (15,26) (15,23) (15,24) (16,30) (16,20) (16,31) (16,17) (16,29) (16,19) (17,21) (17,31) (17,26) (17,23) (17,19) (18,27) (19,30) (19,21) (19,29) (19,26) (19,22) (19,23) (20,21) (20,31) (20,29) (20,23) (21,30) (21,31) (21,29) (21,26) (21,23) (21,24) (22,30) (22,31) (22,29) (22,26) (22,23) (22,24) (23,31) (23,29) (23,26) (24,30) (24,29) (24,26) (25,28) (26,29) (29,31) (30,31)\nIs there a path between node 22 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph288-9_2", + "image": "data/connectivity/graph_visual/hard/graph288.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,23) (1,9) (1,11) (1,25) (1,30) (1,15) (1,21) (1,26) (2,16) (2,5) (2,19) (2,25) (2,24) (3,8) (4,27) (4,19) (4,30) (4,15) (4,20) (4,21) (5,27) (5,16) (5,18) (5,19) (5,15) (5,14) (5,31) (6,13) (7,10) (7,23) (8,12) (8,9) (8,28) (8,20) (9,11) (9,20) (9,21) (9,14) (10,29) (11,12) (11,30) (11,20) (11,21) (11,26) (12,19) (12,20) (12,14) (12,26) (13,17) (13,29) (14,28) (14,21) (14,26) (14,24) (15,27) (15,18) (15,21) (16,22) (16,25) (16,26) (16,24) (18,25) (18,31) (19,27) (19,28) (19,21) (20,28) (20,25) (20,30) (20,24) (21,28) (21,30) (21,26) (21,31) (22,27) (22,28) (22,31) (23,29) (24,28) (24,26) (24,31) (25,31) (26,27) (26,31) (27,31) (30,31)\nIs there a path between node 9 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph627-21_11", + "image": "data/connectivity/graph_visual/hard/graph627.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,5) (0,24) (0,14) (0,29) (0,28) (0,32) (0,22) (0,23) (1,4) (1,30) (1,6) (1,14) (1,2) (1,28) (2,4) (2,26) (2,6) (2,17) (2,9) (2,32) (2,10) (3,26) (3,13) (3,6) (3,31) (3,32) (3,20) (3,21) (3,10) (4,26) (4,5) (4,17) (4,21) (4,10) (5,30) (5,26) (5,6) (5,31) (5,22) (5,34) (5,21) (6,19) (6,29) (6,28) (6,9) (6,32) (6,20) (7,12) (7,18) (7,11) (8,12) (8,18) (8,11) (9,19) (9,24) (9,13) (9,32) (9,21) (10,19) (10,24) (10,28) (10,23) (11,12) (11,27) (12,18) (13,26) (13,14) (13,28) (13,31) (13,23) (14,19) (14,24) (14,29) (14,22) (14,34) (14,21) (14,23) (15,25) (17,30) (17,19) (17,24) (17,29) (17,31) (17,32) (17,22) (18,27) (19,24) (19,32) (19,34) (19,33) (20,26) (20,28) (20,21) (20,23) (20,33) (21,30) (21,24) (21,31) (21,34) (21,23) (22,30) (22,26) (22,31) (22,23) (22,33) (23,34) (24,29) (24,33) (26,29) (26,28) (26,32) (28,30) (28,34) (30,31)\nIs there a path between node 21 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph29-6_17", + "image": "data/connectivity/graph_visual/hard/graph29.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,19) (0,23) (0,18) (0,8) (0,11) (1,13) (1,18) (1,9) (1,24) (1,25) (2,10) (2,19) (2,6) (2,18) (2,5) (2,25) (2,7) (3,19) (3,21) (3,15) (3,25) (3,16) (5,23) (5,8) (5,15) (5,25) (6,13) (6,23) (6,22) (6,24) (6,7) (7,10) (7,18) (7,8) (7,22) (7,15) (7,16) (8,13) (8,10) (8,19) (8,22) (8,11) (8,9) (8,24) (9,13) (9,22) (9,16) (10,12) (11,13) (11,19) (11,15) (11,12) (11,16) (12,20) (12,22) (12,15) (13,23) (13,21) (13,15) (15,18) (15,21) (15,24) (16,21) (16,24) (16,25) (18,23) (18,22) (19,24) (20,23) (20,22) (20,25) (22,23) (22,25) (23,24)\nIs there a path between node 6 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph49-23_16", + "image": "data/connectivity/graph_visual/hard/graph49.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,25) (0,23) (0,10) (1,22) (1,7) (1,8) (1,10) (1,20) (2,14) (2,18) (2,12) (2,26) (3,19) (3,8) (4,7) (4,25) (4,20) (5,12) (5,11) (5,26) (5,9) (6,19) (6,23) (6,16) (7,13) (7,23) (7,24) (7,16) (8,20) (9,14) (10,13) (10,22) (10,23) (10,24) (11,14) (11,21) (11,26) (12,21) (13,24) (13,16) (15,22) (15,17) (16,22) (16,20) (17,25) (17,24) (18,26) (19,22) (19,23) (19,20) (20,23) (20,24) (21,26) (23,24) (24,25)\nIs there a path between node 23 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph60-1_23", + "image": "data/connectivity/graph_visual/hard/graph60.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,18) (0,13) (0,22) (1,12) (1,6) (2,20) (2,14) (2,11) (3,5) (3,23) (3,6) (5,17) (6,19) (7,23) (8,13) (8,15) (9,21) (9,18) (12,24) (12,17) (12,19) (13,21) (13,18) (13,25) (13,15) (13,16) (15,16) (16,21) (16,25) (17,23) (17,19) (19,26) (21,22) (22,25)\nIs there a path between node 1 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph293-7_15", + "image": "data/connectivity/graph_visual/hard/graph293.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,20) (0,6) (0,21) (0,9) (0,19) (1,3) (1,7) (1,2) (1,5) (1,30) (2,15) (2,25) (2,26) (2,11) (2,31) (2,12) (2,30) (3,28) (3,11) (3,16) (3,5) (4,28) (4,25) (4,7) (4,11) (4,16) (4,31) (5,15) (5,25) (5,7) (6,20) (6,21) (7,25) (7,26) (7,16) (8,28) (8,26) (8,31) (10,15) (11,15) (11,16) (12,28) (12,16) (12,31) (13,20) (14,22) (15,25) (15,16) (16,31) (17,22) (19,20) (19,27) (20,21) (21,27) (21,24) (23,24) (25,29) (25,31) (25,30)\nIs there a path between node 7 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph534-14_19", + "image": "data/connectivity/graph_visual/hard/graph534.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,1) (0,3) (0,22) (0,28) (0,2) (0,26) (0,14) (0,10) (0,32) (0,30) (0,16) (0,31) (0,9) (0,23) (0,20) (0,4) (0,19) (0,17) (0,18) (1,21) (1,22) (1,28) (1,15) (1,16) (1,31) (1,20) (1,13) (1,8) (1,19) (1,18) (2,3) (2,28) (2,29) (2,14) (2,10) (2,32) (2,30) (2,16) (2,9) (2,23) (2,20) (2,13) (2,5) (2,4) (2,8) (2,19) (2,17) (2,18) (3,21) (3,22) (3,28) (3,26) (3,10) (3,32) (3,15) (3,31) (3,9) (3,23) (3,20) (3,5) (3,7) (3,4) (3,19) (3,18) (4,22) (4,28) (4,29) (4,14) (4,10) (4,32) (4,15) (4,30) (4,31) (4,23) (4,20) (4,13) (4,7) (4,17) (4,18) (5,22) (5,28) (5,10) (5,9) (5,20) (5,13) (5,7) (5,19) (5,17) (5,18) (6,25) (6,33) (6,24) (6,11) (6,27) (7,21) (7,22) (7,28) (7,26) (7,14) (7,10) (7,32) (7,15) (7,30) (7,9) (7,20) (7,19) (7,18) (8,22) (8,28) (8,29) (8,26) (8,14) (8,10) (8,32) (8,15) (8,30) (8,31) (8,23) (8,20) (8,19) (8,17) (9,21) (9,29) (9,26) (9,10) (9,32) (9,30) (9,16) (9,23) (9,20) (9,13) (9,19) (9,17) (10,21) (10,22) (10,28) (10,29) (10,26) (10,14) (10,32) (10,15) (10,30) (10,16) (10,31) (10,23) (10,20) (10,17) (11,12) (11,27) (12,24) (13,21) (13,22) (13,32) (13,15) (13,30) (13,23) (13,20) (13,19) (13,17) (13,18) (14,21) (14,22) (14,28) (14,26) (14,15) (14,30) (14,16) (14,23) (14,19) (14,17) (14,18) (15,21) (15,22) (15,26) (15,32) (15,30) (15,16) (15,31) (15,23) (15,20) (15,17) (15,18) (16,21) (16,28) (16,29) (16,32) (16,19) (16,17) (16,18) (17,21) (17,22) (17,28) (17,29) (17,26) (17,32) (17,30) (17,23) (17,20) (17,19) (18,21) (18,22) (18,28) (18,29) (18,26) (18,32) (18,30) (18,31) (18,23) (18,20) (18,19) (19,21) (19,22) (19,28) (19,29) (19,26) (19,30) (19,31) (19,23) (19,20) (20,28) (20,29) (20,23) (21,22) (21,28) (21,26) (21,32) (21,30) (21,31) (21,23) (22,28) (22,29) (22,26) (22,32) (23,28) (23,26) (23,31) (24,25) (24,33) (24,27) (25,33) (25,27) (26,29) (26,32) (26,30) (26,31) (27,33) (28,29) (28,32) (28,30) (28,31) (29,32) (29,30) (29,31) (30,31) (31,32)\nIs there a path between node 14 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph534-12_3", + "image": "data/connectivity/graph_visual/hard/graph534.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,1) (0,3) (0,22) (0,28) (0,2) (0,26) (0,14) (0,10) (0,32) (0,30) (0,16) (0,31) (0,9) (0,23) (0,20) (0,4) (0,19) (0,17) (0,18) (1,21) (1,22) (1,28) (1,15) (1,16) (1,31) (1,20) (1,13) (1,8) (1,19) (1,18) (2,3) (2,28) (2,29) (2,14) (2,10) (2,32) (2,30) (2,16) (2,9) (2,23) (2,20) (2,13) (2,5) (2,4) (2,8) (2,19) (2,17) (2,18) (3,21) (3,22) (3,28) (3,26) (3,10) (3,32) (3,15) (3,31) (3,9) (3,23) (3,20) (3,5) (3,7) (3,4) (3,19) (3,18) (4,22) (4,28) (4,29) (4,14) (4,10) (4,32) (4,15) (4,30) (4,31) (4,23) (4,20) (4,13) (4,7) (4,17) (4,18) (5,22) (5,28) (5,10) (5,9) (5,20) (5,13) (5,7) (5,19) (5,17) (5,18) (6,25) (6,33) (6,24) (6,11) (6,27) (7,21) (7,22) (7,28) (7,26) (7,14) (7,10) (7,32) (7,15) (7,30) (7,9) (7,20) (7,19) (7,18) (8,22) (8,28) (8,29) (8,26) (8,14) (8,10) (8,32) (8,15) (8,30) (8,31) (8,23) (8,20) (8,19) (8,17) (9,21) (9,29) (9,26) (9,10) (9,32) (9,30) (9,16) (9,23) (9,20) (9,13) (9,19) (9,17) (10,21) (10,22) (10,28) (10,29) (10,26) (10,14) (10,32) (10,15) (10,30) (10,16) (10,31) (10,23) (10,20) (10,17) (11,12) (11,27) (12,24) (13,21) (13,22) (13,32) (13,15) (13,30) (13,23) (13,20) (13,19) (13,17) (13,18) (14,21) (14,22) (14,28) (14,26) (14,15) (14,30) (14,16) (14,23) (14,19) (14,17) (14,18) (15,21) (15,22) (15,26) (15,32) (15,30) (15,16) (15,31) (15,23) (15,20) (15,17) (15,18) (16,21) (16,28) (16,29) (16,32) (16,19) (16,17) (16,18) (17,21) (17,22) (17,28) (17,29) (17,26) (17,32) (17,30) (17,23) (17,20) (17,19) (18,21) (18,22) (18,28) (18,29) (18,26) (18,32) (18,30) (18,31) (18,23) (18,20) (18,19) (19,21) (19,22) (19,28) (19,29) (19,26) (19,30) (19,31) (19,23) (19,20) (20,28) (20,29) (20,23) (21,22) (21,28) (21,26) (21,32) (21,30) (21,31) (21,23) (22,28) (22,29) (22,26) (22,32) (23,28) (23,26) (23,31) (24,25) (24,33) (24,27) (25,33) (25,27) (26,29) (26,32) (26,30) (26,31) (27,33) (28,29) (28,32) (28,30) (28,31) (29,32) (29,30) (29,31) (30,31) (31,32)\nIs there a path between node 12 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph218-5_6", + "image": "data/connectivity/graph_visual/hard/graph218.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,7) (0,15) (0,18) (0,27) (0,9) (0,13) (0,25) (0,3) (1,8) (1,5) (1,26) (1,12) (1,2) (1,16) (1,14) (2,8) (2,26) (2,12) (2,16) (2,14) (3,7) (3,4) (3,15) (3,18) (3,27) (3,13) (4,7) (4,15) (4,18) (4,27) (4,13) (5,8) (5,12) (5,11) (5,16) (5,14) (5,20) (6,17) (6,21) (6,29) (6,28) (7,15) (7,18) (7,27) (7,9) (7,13) (8,26) (8,23) (8,16) (8,14) (9,15) (10,29) (10,24) (11,12) (11,16) (11,14) (11,20) (12,22) (12,23) (12,14) (12,20) (13,18) (13,27) (14,26) (14,22) (14,23) (14,20) (15,18) (15,27) (15,25) (16,26) (16,22) (16,23) (16,20) (17,21) (17,19) (17,24) (17,28) (19,21) (19,29) (19,24) (19,28) (20,26) (20,22) (20,23) (21,29) (21,24) (22,26) (22,23) (24,29) (24,28) (25,27)\nIs there a path between node 5 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph444-31_6", + "image": "data/connectivity/graph_visual/hard/graph444.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,32) (0,17) (0,24) (0,25) (0,20) (0,9) (1,31) (1,3) (1,5) (2,7) (2,16) (2,10) (2,32) (2,19) (2,9) (3,31) (3,12) (3,13) (3,27) (3,29) (4,18) (4,14) (4,29) (4,21) (5,12) (5,18) (6,28) (6,30) (6,19) (6,20) (6,9) (6,11) (7,23) (7,10) (7,19) (7,15) (7,26) (7,24) (7,25) (7,11) (8,26) (8,9) (9,23) (9,10) (9,17) (9,26) (9,24) (9,20) (10,22) (10,30) (10,19) (10,17) (10,25) (10,20) (11,23) (11,25) (12,13) (12,14) (13,31) (14,27) (14,21) (15,22) (15,30) (15,16) (15,24) (15,25) (15,20) (16,22) (16,23) (16,19) (17,30) (17,32) (17,19) (19,23) (19,24) (20,30) (20,25) (21,27) (22,28) (22,32) (22,26) (22,24) (23,28) (23,24) (24,25) (25,28) (25,32) (26,30) (26,32) (27,29) (30,32)\nIs there a path between node 31 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph637-10_1", + "image": "data/connectivity/graph_visual/hard/graph637.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,24) (0,28) (0,32) (0,1) (0,27) (0,13) (0,9) (1,31) (1,8) (1,15) (1,14) (1,21) (1,28) (1,4) (1,6) (2,3) (2,11) (2,24) (2,31) (2,14) (2,32) (2,4) (2,27) (2,9) (3,22) (3,14) (3,32) (3,20) (3,9) (4,11) (4,24) (4,34) (4,7) (4,19) (4,18) (4,29) (4,28) (4,32) (4,27) (4,13) (5,22) (5,7) (5,18) (5,6) (5,27) (5,13) (6,15) (6,29) (6,27) (6,13) (7,22) (7,33) (7,24) (7,8) (7,19) (7,25) (7,18) (7,30) (7,21) (7,28) (8,11) (8,33) (8,14) (8,25) (8,30) (8,32) (9,27) (9,20) (10,23) (11,22) (11,31) (11,15) (11,19) (11,30) (11,29) (12,17) (13,22) (13,33) (13,19) (13,16) (13,30) (13,21) (13,20) (14,34) (14,30) (15,22) (15,33) (15,24) (15,31) (15,18) (15,30) (15,21) (15,27) (16,24) (16,30) (18,22) (18,33) (18,31) (18,32) (19,22) (19,26) (19,25) (19,28) (19,32) (20,33) (20,24) (20,28) (21,25) (21,30) (21,29) (22,31) (22,28) (22,27) (24,34) (24,31) (24,26) (25,26) (25,29) (25,28) (26,34) (26,30) (26,28) (27,34) (27,28) (28,31) (30,31) (31,34) (32,33) (33,34)\nIs there a path between node 10 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph694-27_9", + "image": "data/connectivity/graph_visual/hard/graph694.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,29) (0,33) (0,25) (0,14) (0,16) (0,4) (0,26) (0,5) (0,27) (0,20) (0,1) (0,7) (0,30) (0,2) (0,9) (0,13) (0,23) (1,29) (1,33) (1,25) (1,14) (1,26) (1,5) (1,20) (1,7) (1,31) (1,30) (1,9) (1,13) (1,23) (2,29) (2,33) (2,25) (2,14) (2,16) (2,4) (2,26) (2,5) (2,27) (2,20) (2,7) (2,31) (2,12) (2,9) (2,23) (3,32) (3,10) (3,6) (3,19) (3,8) (3,15) (3,17) (3,22) (3,21) (3,28) (4,29) (4,33) (4,25) (4,16) (4,26) (4,5) (4,27) (4,31) (4,30) (4,12) (4,13) (4,34) (4,23) (5,29) (5,25) (5,26) (5,27) (5,20) (5,7) (5,31) (5,30) (5,12) (5,9) (5,13) (5,34) (5,23) (6,11) (6,32) (6,19) (6,8) (6,24) (6,18) (6,17) (6,22) (6,21) (6,28) (7,29) (7,33) (7,25) (7,14) (7,16) (7,26) (7,31) (7,30) (7,12) (7,9) (7,13) (7,34) (7,23) (8,11) (8,10) (8,19) (8,15) (8,24) (8,17) (8,22) (8,21) (9,33) (9,25) (9,14) (9,16) (9,26) (9,20) (9,31) (9,12) (9,34) (9,23) (10,11) (10,32) (10,24) (10,18) (10,28) (11,32) (11,19) (11,15) (11,24) (11,18) (11,17) (11,21) (12,29) (12,33) (12,25) (12,16) (12,26) (12,27) (12,31) (12,30) (12,13) (12,34) (13,33) (13,25) (13,27) (13,20) (13,31) (13,30) (13,34) (14,29) (14,33) (14,25) (14,16) (14,27) (14,31) (14,34) (14,23) (15,32) (15,19) (15,22) (15,21) (15,28) (16,33) (16,25) (16,26) (16,27) (16,30) (17,32) (17,24) (17,18) (17,22) (17,28) (18,32) (18,19) (18,24) (18,22) (18,21) (18,28) (19,32) (19,24) (19,22) (19,21) (20,25) (20,26) (20,27) (20,31) (20,30) (20,23) (21,24) (21,22) (21,28) (22,24) (22,28) (23,29) (23,33) (23,26) (23,31) (23,34) (24,32) (24,28) (25,29) (25,33) (25,27) (25,31) (25,30) (25,34) (26,33) (26,27) (26,30) (26,34) (27,29) (27,31) (27,30) (27,34) (28,32) (29,33) (29,30) (29,34) (30,33) (30,31) (30,34) (31,33) (31,34) (33,34)\nIs there a path between node 27 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph377-2_20", + "image": "data/connectivity/graph_visual/hard/graph377.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,27) (0,28) (0,4) (1,18) (1,27) (1,28) (1,25) (1,4) (2,30) (2,20) (2,5) (2,21) (2,31) (2,11) (2,9) (2,6) (2,17) (2,29) (2,22) (2,23) (2,15) (2,24) (2,19) (2,3) (2,16) (2,12) (2,14) (3,30) (3,21) (3,7) (3,31) (3,9) (3,8) (3,6) (3,17) (3,13) (3,22) (3,23) (3,15) (3,24) (3,16) (3,12) (3,14) (4,18) (4,27) (4,28) (5,30) (5,21) (5,7) (5,31) (5,11) (5,9) (5,8) (5,6) (5,13) (5,26) (5,15) (5,19) (5,10) (5,12) (5,14) (6,30) (6,20) (6,21) (6,7) (6,31) (6,11) (6,9) (6,29) (6,23) (6,15) (6,19) (6,10) (6,16) (6,12) (6,14) (7,30) (7,20) (7,11) (7,9) (7,8) (7,17) (7,29) (7,13) (7,22) (7,23) (7,15) (7,19) (7,10) (7,12) (8,30) (8,21) (8,31) (8,11) (8,9) (8,29) (8,26) (8,22) (8,23) (8,24) (8,19) (8,10) (8,16) (9,30) (9,20) (9,21) (9,31) (9,11) (9,29) (9,13) (9,26) (9,22) (9,23) (9,24) (9,19) (9,12) (9,14) (10,30) (10,20) (10,21) (10,11) (10,23) (10,15) (10,24) (10,19) (10,16) (11,31) (11,29) (11,13) (11,26) (11,22) (11,23) (11,16) (11,12) (11,14) (12,30) (12,20) (12,21) (12,17) (12,29) (12,13) (12,26) (12,22) (12,23) (12,24) (12,19) (12,16) (12,14) (13,30) (13,21) (13,31) (13,17) (13,29) (13,26) (13,23) (13,15) (13,24) (13,19) (13,16) (13,14) (14,30) (14,21) (14,31) (14,22) (14,19) (14,16) (15,20) (15,29) (15,26) (15,23) (15,24) (16,30) (16,20) (16,31) (16,17) (16,29) (16,19) (17,21) (17,31) (17,26) (17,23) (17,19) (18,27) (19,30) (19,21) (19,29) (19,26) (19,22) (19,23) (20,21) (20,31) (20,29) (20,23) (21,30) (21,31) (21,29) (21,26) (21,23) (21,24) (22,30) (22,31) (22,29) (22,26) (22,23) (22,24) (23,31) (23,29) (23,26) (24,30) (24,29) (24,26) (25,28) (26,29) (29,31) (30,31)\nIs there a path between node 2 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph107-5_7", + "image": "data/connectivity/graph_visual/hard/graph107.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,27) (0,4) (0,11) (0,9) (0,25) (1,12) (1,16) (2,3) (2,27) (2,11) (2,12) (2,22) (2,25) (2,15) (3,25) (3,15) (4,18) (4,11) (4,26) (4,22) (4,9) (4,24) (4,13) (5,7) (5,14) (5,19) (5,17) (6,14) (7,17) (9,20) (9,26) (9,12) (9,25) (9,15) (10,20) (10,27) (10,11) (10,21) (10,26) (10,16) (11,27) (11,25) (12,27) (12,21) (12,26) (12,24) (13,24) (14,17) (15,20) (15,27) (15,18) (15,26) (15,22) (15,25) (16,20) (16,27) (18,26) (18,25) (20,25) (25,26)\nIs there a path between node 5 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph49-1_19", + "image": "data/connectivity/graph_visual/hard/graph49.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,25) (0,23) (0,10) (1,22) (1,7) (1,8) (1,10) (1,20) (2,14) (2,18) (2,12) (2,26) (3,19) (3,8) (4,7) (4,25) (4,20) (5,12) (5,11) (5,26) (5,9) (6,19) (6,23) (6,16) (7,13) (7,23) (7,24) (7,16) (8,20) (9,14) (10,13) (10,22) (10,23) (10,24) (11,14) (11,21) (11,26) (12,21) (13,24) (13,16) (15,22) (15,17) (16,22) (16,20) (17,25) (17,24) (18,26) (19,22) (19,23) (19,20) (20,23) (20,24) (21,26) (23,24) (24,25)\nIs there a path between node 1 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph547-22_8", + "image": "data/connectivity/graph_visual/hard/graph547.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,31) (0,26) (0,8) (0,6) (0,29) (0,20) (0,22) (0,28) (0,17) (0,32) (0,13) (0,19) (0,1) (1,26) (1,6) (1,29) (1,22) (1,28) (1,17) (1,32) (1,19) (1,10) (2,7) (2,5) (2,24) (2,4) (2,18) (2,16) (2,3) (2,30) (2,11) (2,33) (2,15) (2,21) (2,12) (3,7) (3,5) (3,18) (3,30) (3,14) (3,33) (3,23) (3,9) (3,21) (4,5) (4,27) (4,18) (4,25) (4,30) (4,14) (4,11) (4,33) (4,15) (4,23) (4,9) (4,21) (4,12) (5,7) (5,24) (5,27) (5,18) (5,16) (5,25) (5,30) (5,14) (5,11) (5,33) (5,15) (5,23) (5,9) (5,21) (5,12) (6,26) (6,8) (6,29) (6,20) (6,28) (6,17) (6,32) (6,19) (6,10) (7,27) (7,18) (7,16) (7,30) (7,14) (7,33) (7,15) (7,23) (7,12) (8,31) (8,22) (8,28) (8,17) (8,32) (8,13) (8,19) (9,24) (9,27) (9,16) (9,25) (9,30) (9,14) (9,11) (9,33) (9,15) (9,12) (10,31) (10,29) (10,20) (10,32) (10,13) (10,19) (11,27) (11,18) (11,16) (11,25) (11,30) (11,33) (11,21) (11,12) (12,24) (12,18) (12,16) (12,25) (12,30) (12,14) (12,23) (12,21) (13,31) (13,26) (13,29) (13,20) (13,22) (13,28) (13,17) (13,32) (14,27) (14,18) (14,16) (14,25) (14,30) (14,33) (14,15) (14,21) (15,24) (15,18) (15,16) (15,25) (15,33) (15,21) (16,18) (16,30) (16,33) (16,23) (16,21) (17,29) (17,28) (17,32) (17,19) (18,27) (18,25) (18,30) (18,33) (18,21) (19,31) (19,26) (19,20) (19,22) (19,32) (20,31) (20,26) (20,22) (20,32) (21,24) (21,27) (21,30) (22,26) (22,29) (22,28) (22,32) (23,24) (23,27) (23,25) (23,30) (23,33) (24,27) (24,25) (24,30) (24,33) (25,30) (26,29) (26,28) (26,32) (27,30) (27,33) (28,31) (28,29) (28,32) (29,32) (30,33) (31,32)\nIs there a path between node 22 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph326-16_27", + "image": "data/connectivity/graph_visual/hard/graph326.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,21) (0,6) (0,10) (0,29) (0,17) (0,1) (0,7) (0,13) (0,19) (0,20) (1,18) (1,21) (1,5) (1,6) (1,29) (1,3) (1,25) (1,17) (1,7) (1,13) (1,2) (1,30) (1,19) (2,18) (2,21) (2,5) (2,6) (2,10) (2,29) (2,3) (2,25) (2,7) (2,13) (2,19) (3,18) (3,21) (3,6) (3,10) (3,25) (3,31) (3,17) (3,16) (3,7) (3,30) (3,19) (4,12) (4,27) (4,9) (4,14) (4,23) (4,8) (4,26) (4,11) (5,21) (5,6) (5,10) (5,29) (5,25) (5,31) (5,17) (5,16) (5,7) (5,20) (6,21) (6,10) (6,25) (6,31) (6,16) (6,30) (7,18) (7,21) (7,29) (7,25) (7,31) (7,17) (7,13) (7,30) (7,20) (8,12) (8,22) (8,27) (8,28) (8,9) (8,15) (8,14) (8,23) (8,26) (8,11) (9,12) (9,22) (9,27) (9,28) (9,15) (9,14) (9,23) (9,11) (10,18) (10,21) (10,25) (10,31) (10,17) (10,16) (10,13) (10,30) (10,19) (10,20) (11,22) (11,28) (11,15) (11,23) (11,26) (12,27) (12,15) (12,14) (12,23) (12,26) (13,29) (13,16) (13,30) (13,19) (13,20) (14,22) (14,27) (14,28) (14,15) (14,23) (14,24) (15,22) (15,27) (15,23) (15,24) (16,18) (16,25) (16,17) (16,30) (16,20) (17,18) (17,21) (17,29) (17,25) (17,31) (17,30) (17,19) (17,20) (18,29) (18,25) (18,31) (18,30) (18,19) (18,20) (19,21) (19,29) (19,25) (19,30) (20,21) (20,29) (20,25) (20,31) (20,30) (21,25) (21,31) (21,30) (22,27) (22,28) (22,26) (22,24) (23,27) (23,28) (23,24) (24,27) (24,28) (25,31) (26,28) (27,28) (29,31) (29,30)\nIs there a path between node 16 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph379-7_4", + "image": "data/connectivity/graph_visual/hard/graph379.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,2) (0,18) (0,15) (0,10) (0,24) (0,26) (0,5) (0,11) (0,30) (1,12) (1,6) (1,9) (1,25) (1,4) (1,20) (1,19) (1,22) (1,8) (1,28) (1,17) (2,18) (2,14) (2,10) (2,24) (2,26) (2,23) (2,29) (2,31) (2,30) (3,12) (3,13) (3,6) (3,9) (3,4) (3,20) (3,22) (3,8) (3,28) (4,12) (4,27) (4,25) (4,19) (4,22) (4,8) (4,7) (4,17) (4,16) (5,18) (5,15) (5,14) (5,10) (5,24) (5,23) (5,29) (5,31) (5,30) (6,12) (6,13) (6,27) (6,25) (6,20) (6,19) (6,21) (6,28) (6,7) (6,17) (7,13) (7,27) (7,20) (7,19) (7,21) (7,28) (7,17) (7,16) (8,12) (8,13) (8,27) (8,20) (8,19) (8,21) (8,22) (8,28) (8,16) (9,12) (9,13) (9,27) (9,25) (9,20) (9,21) (9,22) (9,28) (9,17) (9,16) (10,18) (10,15) (10,14) (10,24) (10,23) (10,29) (10,11) (10,30) (11,15) (11,23) (11,29) (11,31) (12,25) (12,19) (12,21) (12,22) (12,28) (12,17) (12,16) (13,27) (13,19) (13,21) (13,28) (13,17) (13,16) (14,18) (14,24) (14,26) (14,23) (14,29) (14,31) (14,30) (15,18) (15,24) (15,26) (15,23) (15,29) (15,31) (15,30) (16,27) (16,25) (16,20) (16,19) (16,21) (16,17) (17,27) (17,25) (17,19) (17,22) (17,28) (18,24) (18,29) (18,30) (19,27) (19,25) (19,20) (19,22) (19,28) (20,27) (20,25) (20,21) (20,22) (20,28) (21,25) (21,22) (21,28) (22,27) (22,25) (23,26) (23,29) (23,31) (23,30) (26,29) (26,31) (26,30) (27,28) (29,31) (29,30) (30,31)\nIs there a path between node 7 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph9-25_3", + "image": "data/connectivity/graph_visual/hard/graph9.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,2) (0,10) (0,13) (0,12) (0,9) (0,18) (0,24) (0,5) (0,20) (0,21) (0,7) (0,3) (0,23) (1,2) (1,13) (1,16) (1,12) (1,18) (1,24) (1,20) (1,4) (1,7) (1,3) (1,19) (1,23) (2,13) (2,16) (2,12) (2,9) (2,11) (2,18) (2,24) (2,5) (2,20) (2,4) (2,21) (2,7) (2,3) (2,23) (3,13) (3,16) (3,12) (3,9) (3,11) (3,24) (3,5) (3,20) (3,21) (3,7) (3,19) (3,23) (4,10) (4,16) (4,12) (4,11) (4,18) (4,24) (4,5) (4,20) (4,21) (4,7) (4,19) (4,23) (5,13) (5,12) (5,11) (5,18) (5,24) (5,20) (5,21) (5,7) (5,23) (6,15) (6,25) (6,22) (6,8) (7,13) (7,12) (7,9) (7,11) (7,18) (7,20) (7,21) (7,19) (8,17) (8,15) (8,22) (8,14) (9,10) (9,13) (9,16) (9,11) (9,18) (9,21) (9,19) (9,23) (10,13) (10,12) (10,11) (10,24) (10,20) (10,21) (10,19) (10,23) (11,13) (11,16) (11,24) (11,20) (11,21) (11,19) (11,23) (12,13) (12,16) (12,18) (12,24) (12,20) (12,21) (12,19) (12,23) (13,16) (13,24) (13,21) (13,23) (14,17) (14,15) (14,22) (15,17) (15,25) (15,22) (16,18) (16,24) (16,21) (16,23) (17,25) (17,22) (18,20) (18,21) (18,19) (18,23) (19,20) (19,23) (20,24) (20,21) (21,23) (22,25) (23,24)\nIs there a path between node 25 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph211-13_12", + "image": "data/connectivity/graph_visual/hard/graph211.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,24) (0,29) (0,27) (1,13) (1,20) (1,17) (1,7) (2,28) (2,6) (2,13) (2,17) (2,14) (2,7) (3,6) (3,18) (4,19) (4,12) (4,15) (4,11) (6,13) (7,25) (7,8) (7,18) (7,14) (9,21) (9,27) (12,19) (12,26) (13,18) (13,14) (14,25) (14,20) (17,25) (19,26) (20,28) (21,29) (22,29) (23,24) (23,29) (24,29) (24,27)\nIs there a path between node 13 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph184-28_1", + "image": "data/connectivity/graph_visual/hard/graph184.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,3) (0,4) (0,11) (0,13) (1,8) (1,21) (1,10) (1,7) (1,2) (2,24) (2,8) (2,9) (2,10) (2,22) (3,5) (3,11) (3,13) (4,15) (4,6) (4,16) (4,11) (5,12) (5,15) (5,19) (5,18) (5,27) (6,19) (6,11) (7,26) (7,23) (7,9) (8,23) (8,9) (8,10) (8,22) (9,25) (9,14) (10,25) (10,17) (10,23) (11,20) (11,27) (12,15) (12,16) (12,18) (14,22) (15,19) (15,27) (16,19) (17,26) (17,24) (17,28) (17,23) (17,22) (19,20) (19,27) (21,26) (21,25) (21,29) (21,22) (22,29) (23,24) (23,29) (26,28)\nIs there a path between node 28 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph255-6_1", + "image": "data/connectivity/graph_visual/hard/graph255.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,6) (0,2) (0,10) (0,29) (0,19) (0,5) (0,3) (1,30) (1,8) (1,28) (2,3) (3,6) (3,19) (4,14) (5,25) (6,19) (7,13) (7,30) (7,21) (7,8) (7,11) (8,13) (8,16) (8,30) (9,18) (12,19) (13,20) (13,28) (14,24) (14,18) (14,23) (15,30) (16,22) (16,28) (17,29) (17,19) (18,23) (19,25) (20,30) (20,28)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph327-27_14", + "image": "data/connectivity/graph_visual/hard/graph327.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,3) (0,10) (0,27) (0,1) (0,29) (0,7) (0,14) (0,13) (0,20) (0,6) (1,3) (1,4) (1,10) (1,27) (1,7) (1,16) (1,14) (1,13) (1,20) (1,15) (1,6) (2,30) (2,12) (2,5) (2,11) (2,21) (2,28) (2,22) (2,25) (2,31) (2,19) (3,4) (3,29) (3,16) (3,14) (3,13) (3,20) (3,15) (4,10) (4,7) (4,16) (4,13) (4,15) (4,6) (5,12) (5,23) (5,24) (5,21) (5,28) (5,25) (5,31) (5,19) (6,27) (6,29) (6,7) (6,14) (6,13) (6,20) (6,15) (7,10) (7,27) (7,20) (8,18) (9,26) (9,18) (10,27) (10,29) (10,16) (10,13) (10,15) (11,30) (11,24) (11,21) (11,17) (11,28) (11,25) (12,23) (12,24) (12,21) (12,17) (12,28) (12,22) (12,25) (12,19) (13,27) (13,16) (13,20) (13,15) (14,27) (14,29) (14,16) (14,15) (15,27) (15,29) (15,16) (15,20) (16,27) (16,29) (16,20) (17,30) (17,23) (17,24) (17,21) (17,28) (17,22) (17,25) (17,31) (17,19) (18,26) (19,30) (19,23) (19,24) (19,21) (19,28) (19,25) (19,31) (20,27) (21,30) (21,24) (21,28) (21,22) (21,25) (21,31) (22,30) (22,23) (22,24) (22,28) (22,25) (22,31) (23,30) (23,24) (23,25) (23,31) (24,28) (24,25) (24,31) (25,30) (25,28) (25,31) (27,29) (28,30) (30,31)\nIs there a path between node 27 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph420-32_1", + "image": "data/connectivity/graph_visual/hard/graph420.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,12) (0,5) (0,20) (0,28) (1,14) (1,27) (2,21) (2,16) (3,29) (3,31) (3,22) (3,17) (4,13) (4,9) (5,12) (5,32) (5,11) (6,14) (6,12) (6,32) (6,28) (7,10) (7,20) (7,27) (8,21) (8,15) (9,26) (9,31) (9,30) (9,17) (10,20) (10,28) (11,14) (11,12) (12,20) (12,32) (12,28) (13,29) (13,31) (13,22) (14,28) (15,16) (15,24) (16,19) (17,26) (17,18) (20,23) (21,24) (22,26) (22,31) (26,30)\nIs there a path between node 32 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph354-19_7", + "image": "data/connectivity/graph_visual/hard/graph354.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,28) (1,7) (1,14) (1,13) (1,3) (1,5) (1,2) (1,21) (2,8) (2,27) (2,22) (3,8) (3,6) (3,7) (3,14) (4,30) (4,10) (5,14) (5,25) (5,23) (5,19) (6,11) (6,14) (6,22) (6,9) (6,16) (7,27) (7,9) (7,31) (7,23) (8,11) (8,20) (8,16) (8,19) (8,21) (9,25) (9,13) (9,31) (9,23) (9,19) (10,30) (10,12) (10,26) (11,31) (11,19) (11,21) (12,15) (12,30) (13,14) (13,23) (13,21) (14,20) (14,17) (14,23) (15,26) (16,22) (16,31) (17,20) (18,29) (19,23) (20,25) (21,25) (21,22) (22,31) (23,25) (23,31) (24,28) (24,30) (25,31) (26,30) (28,30) (28,29)\nIs there a path between node 19 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph173-20_3", + "image": "data/connectivity/graph_visual/hard/graph173.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,24) (0,8) (0,18) (0,26) (0,14) (0,15) (0,9) (0,25) (0,17) (0,4) (0,2) (1,27) (1,16) (1,5) (1,22) (1,19) (2,26) (2,13) (2,14) (2,3) (2,15) (2,25) (2,4) (2,21) (3,8) (3,13) (3,23) (3,15) (3,17) (3,6) (3,21) (4,24) (4,8) (4,18) (4,26) (4,13) (4,14) (4,25) (4,6) (4,21) (5,16) (5,10) (5,19) (6,24) (6,8) (6,13) (6,23) (6,14) (6,15) (6,9) (6,17) (6,21) (7,28) (7,20) (7,11) (8,24) (8,18) (8,13) (8,23) (8,14) (8,9) (8,21) (9,24) (9,26) (9,23) (9,14) (9,25) (10,27) (10,16) (10,22) (10,19) (12,27) (12,16) (12,22) (13,24) (13,26) (13,23) (13,14) (13,15) (13,25) (13,17) (13,21) (14,26) (14,15) (14,25) (15,26) (15,23) (15,25) (15,17) (15,21) (16,27) (16,22) (16,19) (17,24) (17,18) (17,23) (18,24) (18,26) (18,21) (19,27) (19,22) (20,28) (21,24) (21,23) (21,25) (23,26) (23,25) (24,26) (24,25) (25,26)\nIs there a path between node 20 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph605-1_33", + "image": "data/connectivity/graph_visual/hard/graph605.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,3) (0,18) (0,9) (1,3) (1,31) (1,23) (2,22) (2,5) (3,27) (3,20) (4,12) (4,22) (4,33) (4,10) (4,26) (5,22) (5,17) (5,33) (5,14) (6,32) (6,29) (7,26) (8,28) (8,25) (8,17) (9,34) (9,13) (10,28) (10,17) (10,16) (11,18) (11,13) (11,19) (12,24) (12,22) (12,17) (12,16) (13,31) (13,20) (14,28) (14,30) (14,17) (15,25) (15,30) (15,17) (16,30) (16,26) (18,27) (18,20) (20,23) (22,25) (22,30) (22,33) (22,26) (23,27) (25,28) (26,28) (28,33)\nIs there a path between node 1 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph322-12_21", + "image": "data/connectivity/graph_visual/hard/graph322.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,31) (0,23) (0,26) (0,5) (0,11) (0,19) (0,13) (0,27) (0,16) (0,7) (1,4) (1,6) (1,2) (1,30) (1,29) (1,12) (1,21) (1,10) (2,6) (2,30) (2,28) (2,15) (2,29) (2,12) (2,24) (2,14) (2,10) (3,9) (3,8) (3,31) (3,23) (3,5) (3,11) (3,19) (3,20) (3,16) (3,7) (4,6) (4,30) (4,28) (4,15) (4,29) (4,24) (4,21) (5,23) (5,26) (5,17) (5,11) (5,19) (5,13) (5,20) (5,7) (5,22) (6,18) (6,25) (6,30) (6,29) (6,12) (6,24) (6,21) (6,14) (6,10) (7,9) (7,8) (7,31) (7,26) (7,11) (7,19) (7,27) (7,20) (7,16) (7,22) (8,9) (8,31) (8,26) (8,17) (8,11) (8,13) (8,22) (9,31) (9,26) (9,11) (9,19) (9,13) (9,27) (9,20) (9,22) (10,18) (10,25) (10,28) (10,15) (10,24) (10,21) (11,31) (11,26) (11,17) (11,19) (11,13) (11,20) (12,18) (12,30) (12,29) (12,24) (12,21) (13,31) (13,23) (13,26) (13,17) (13,27) (13,20) (14,18) (14,25) (14,30) (14,15) (14,29) (14,24) (15,18) (15,25) (15,28) (15,29) (15,24) (15,21) (16,31) (16,23) (16,17) (16,27) (16,20) (16,22) (17,27) (17,20) (18,25) (18,28) (18,29) (18,21) (19,31) (19,26) (20,31) (20,23) (20,26) (20,27) (21,25) (21,30) (21,28) (21,29) (21,24) (22,31) (22,26) (23,31) (23,26) (24,30) (24,28) (24,29) (25,30) (25,28) (25,29) (26,31) (27,31) (28,30) (28,29) (29,30)\nIs there a path between node 12 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph699-21_32", + "image": "data/connectivity/graph_visual/hard/graph699.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,22) (0,23) (0,24) (0,19) (0,4) (0,7) (0,10) (0,3) (0,20) (0,28) (0,2) (0,26) (0,29) (0,21) (1,17) (1,5) (1,14) (1,30) (1,16) (2,13) (2,27) (2,23) (2,24) (2,34) (2,32) (2,10) (2,33) (2,20) (2,26) (2,9) (3,13) (3,27) (3,6) (3,23) (3,24) (3,19) (3,34) (3,10) (3,33) (3,20) (3,28) (3,26) (3,9) (3,29) (3,21) (4,13) (4,27) (4,22) (4,24) (4,19) (4,7) (4,10) (4,33) (4,20) (4,28) (4,26) (4,9) (4,29) (4,21) (5,17) (5,14) (5,15) (5,12) (5,30) (5,18) (5,16) (6,13) (6,22) (6,23) (6,34) (6,32) (6,10) (6,20) (6,26) (6,9) (6,8) (7,13) (7,23) (7,24) (7,19) (7,34) (7,10) (7,33) (7,20) (7,28) (7,8) (7,29) (7,21) (8,27) (8,23) (8,24) (8,34) (8,10) (8,28) (8,9) (8,29) (8,21) (9,13) (9,27) (9,22) (9,23) (9,34) (9,32) (9,10) (9,20) (9,28) (9,26) (9,21) (10,13) (10,27) (10,22) (10,24) (10,19) (10,34) (10,32) (10,33) (10,20) (10,26) (10,29) (10,21) (11,17) (11,31) (11,14) (11,15) (11,18) (11,16) (12,31) (12,15) (12,30) (12,18) (13,27) (13,22) (13,24) (13,32) (13,33) (13,20) (13,28) (13,26) (13,21) (14,17) (14,31) (14,15) (14,30) (14,18) (14,16) (15,17) (15,30) (15,18) (15,16) (16,17) (16,31) (16,30) (16,18) (17,31) (17,18) (18,31) (18,30) (19,22) (19,23) (19,24) (19,34) (19,32) (19,33) (19,20) (19,28) (19,26) (19,29) (19,21) (20,22) (20,23) (20,34) (20,21) (21,27) (21,22) (21,23) (21,34) (21,32) (21,33) (21,28) (21,26) (21,29) (22,27) (22,24) (22,33) (22,28) (22,26) (22,29) (23,27) (23,32) (23,33) (23,26) (23,29) (24,27) (24,34) (24,33) (24,28) (24,26) (24,29) (26,27) (26,34) (26,32) (26,29) (27,34) (27,32) (27,33) (27,28) (27,29) (28,32) (28,33) (28,29) (29,34) (29,32) (32,34) (32,33)\nIs there a path between node 21 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph255-2_5", + "image": "data/connectivity/graph_visual/hard/graph255.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,6) (0,2) (0,10) (0,29) (0,19) (0,5) (0,3) (1,30) (1,8) (1,28) (2,3) (3,6) (3,19) (4,14) (5,25) (6,19) (7,13) (7,30) (7,21) (7,8) (7,11) (8,13) (8,16) (8,30) (9,18) (12,19) (13,20) (13,28) (14,24) (14,18) (14,23) (15,30) (16,22) (16,28) (17,29) (17,19) (18,23) (19,25) (20,30) (20,28)\nIs there a path between node 2 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph333-8_16", + "image": "data/connectivity/graph_visual/hard/graph333.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,19) (0,14) (0,10) (1,12) (1,13) (1,17) (1,25) (2,24) (2,12) (2,13) (2,25) (3,27) (3,15) (3,9) (3,18) (3,23) (3,31) (3,28) (3,21) (4,6) (4,14) (4,10) (5,16) (5,26) (5,8) (5,7) (6,19) (6,14) (7,16) (7,20) (7,8) (8,16) (8,20) (9,15) (9,18) (9,29) (9,30) (9,23) (9,31) (9,28) (9,21) (10,14) (11,17) (11,25) (12,13) (12,17) (13,24) (13,17) (13,25) (14,19) (15,27) (15,18) (15,29) (15,22) (15,30) (15,23) (15,31) (15,28) (15,21) (16,26) (17,24) (17,25) (18,29) (18,30) (18,23) (18,31) (18,21) (20,26) (21,27) (21,29) (21,22) (21,30) (21,23) (21,31) (21,28) (22,27) (22,29) (22,30) (22,23) (22,28) (23,27) (23,29) (23,30) (23,28) (24,25) (27,29) (27,30) (27,31) (27,28) (28,29) (28,30) (28,31) (29,30) (29,31) (30,31)\nIs there a path between node 8 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph604-2_30", + "image": "data/connectivity/graph_visual/hard/graph604.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,16) (0,5) (0,18) (1,6) (1,12) (1,2) (1,34) (2,19) (2,11) (2,26) (2,7) (2,12) (2,33) (2,20) (3,15) (4,18) (5,18) (6,19) (6,26) (6,10) (6,23) (6,33) (6,21) (6,20) (7,11) (8,28) (9,14) (10,23) (11,22) (11,27) (11,31) (12,25) (12,33) (12,21) (13,15) (14,15) (14,32) (14,24) (15,29) (16,17) (17,18) (18,30) (19,22) (19,23) (19,21) (19,34) (19,20) (20,22) (20,33) (20,34) (21,26) (21,22) (21,34) (22,27) (22,31) (23,33) (24,32) (24,28) (25,27) (25,33) (27,34) (31,34) (33,34)\nIs there a path between node 2 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph342-6_22", + "image": "data/connectivity/graph_visual/hard/graph342.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,2) (0,20) (1,13) (1,28) (1,18) (1,4) (2,31) (2,23) (2,27) (2,9) (2,24) (3,26) (4,29) (4,14) (4,13) (4,8) (4,30) (5,7) (5,21) (5,31) (5,27) (5,9) (5,12) (5,15) (6,25) (6,21) (6,10) (6,27) (6,20) (7,10) (7,23) (7,9) (7,20) (8,19) (8,18) (9,25) (9,23) (9,27) (9,16) (9,12) (9,22) (10,25) (10,21) (10,27) (10,15) (10,22) (10,20) (11,19) (12,25) (12,21) (12,20) (13,28) (13,30) (14,29) (14,28) (14,19) (14,30) (15,21) (15,23) (15,20) (15,24) (16,31) (18,30) (19,28) (20,25) (20,31) (20,23) (20,22) (22,25) (22,23) (23,25) (24,27) (28,29) (28,30)\nIs there a path between node 6 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph153-12_5", + "image": "data/connectivity/graph_visual/hard/graph153.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,1) (0,21) (0,2) (0,3) (0,10) (0,4) (0,28) (0,26) (0,19) (0,23) (0,18) (0,25) (0,22) (0,16) (0,20) (0,7) (0,27) (0,15) (0,24) (0,12) (0,14) (1,6) (1,21) (1,13) (1,2) (1,3) (1,10) (1,4) (1,9) (1,28) (1,18) (1,25) (1,20) (1,17) (1,27) (1,15) (1,12) (1,14) (2,6) (2,13) (2,3) (2,10) (2,4) (2,9) (2,28) (2,26) (2,19) (2,23) (2,18) (2,22) (2,16) (2,20) (2,27) (2,15) (2,24) (2,12) (2,14) (3,11) (3,6) (3,13) (3,10) (3,4) (3,9) (3,26) (3,23) (3,25) (3,22) (3,16) (3,20) (3,7) (3,15) (3,14) (4,11) (4,21) (4,13) (4,10) (4,9) (4,28) (4,26) (4,23) (4,22) (4,16) (4,17) (4,7) (4,27) (4,15) (4,24) (5,8) (6,11) (6,28) (6,19) (6,23) (6,18) (6,22) (6,20) (6,7) (6,27) (6,15) (7,11) (7,21) (7,13) (7,10) (7,9) (7,28) (7,26) (7,19) (7,18) (7,22) (7,16) (7,17) (7,15) (7,24) (7,14) (9,11) (9,21) (9,10) (9,28) (9,26) (9,23) (9,18) (9,25) (9,22) (9,16) (9,27) (9,24) (9,12) (10,11) (10,13) (10,28) (10,26) (10,19) (10,23) (10,18) (10,25) (10,16) (10,20) (10,17) (10,27) (10,15) (10,24) (10,12) (10,14) (11,19) (11,23) (11,18) (11,25) (11,22) (11,17) (11,24) (11,12) (11,14) (12,21) (12,26) (12,19) (12,23) (12,18) (12,22) (12,20) (12,17) (12,14) (13,21) (13,28) (13,19) (13,23) (13,25) (13,22) (13,16) (13,20) (13,17) (13,27) (13,15) (13,14) (14,21) (14,26) (14,19) (14,23) (14,18) (14,25) (14,16) (14,20) (14,17) (14,27) (15,21) (15,26) (15,18) (15,25) (15,22) (15,16) (15,20) (15,24) (16,21) (16,28) (16,26) (16,23) (16,18) (16,22) (16,17) (16,24) (17,28) (17,19) (17,18) (17,20) (17,27) (17,24) (18,21) (18,19) (18,23) (18,22) (18,20) (19,21) (19,28) (19,26) (19,23) (19,25) (19,22) (19,20) (19,27) (19,24) (20,21) (20,28) (20,25) (20,24) (21,28) (21,26) (21,23) (21,25) (21,22) (21,27) (21,24) (22,28) (22,26) (22,23) (22,25) (23,26) (23,25) (23,27) (24,25) (25,26) (26,28) (27,28)\nIs there a path between node 12 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph27-14_4", + "image": "data/connectivity/graph_visual/hard/graph27.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,17) (0,6) (0,9) (0,20) (0,21) (2,5) (2,9) (2,20) (2,7) (2,21) (3,5) (3,24) (3,6) (3,4) (3,25) (3,19) (3,8) (4,12) (4,6) (5,17) (5,11) (5,9) (5,19) (6,14) (6,20) (6,7) (6,13) (7,11) (7,25) (7,20) (8,12) (8,19) (8,13) (9,12) (9,14) (9,17) (9,25) (9,19) (9,21) (10,23) (12,14) (12,24) (12,17) (12,13) (13,14) (13,24) (13,20) (14,21) (15,16) (17,24) (17,25) (17,19) (18,23) (19,20) (21,25)\nIs there a path between node 14 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph272-1_11", + "image": "data/connectivity/graph_visual/hard/graph272.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,12) (0,19) (0,23) (0,5) (0,25) (0,29) (0,11) (0,28) (0,21) (0,30) (0,16) (0,6) (0,13) (0,14) (1,12) (1,19) (1,23) (1,3) (1,15) (1,10) (1,18) (1,29) (1,11) (1,28) (1,21) (1,26) (1,16) (1,8) (1,6) (1,13) (1,14) (2,12) (2,19) (2,23) (2,3) (2,10) (2,5) (2,9) (2,25) (2,29) (2,11) (2,28) (2,21) (2,26) (2,16) (2,8) (2,13) (2,14) (3,19) (3,15) (3,10) (3,18) (3,9) (3,25) (3,29) (3,21) (3,30) (3,26) (3,16) (3,13) (3,14) (4,24) (4,7) (5,12) (5,19) (5,23) (5,15) (5,18) (5,25) (5,29) (5,28) (5,30) (5,26) (5,16) (5,8) (5,6) (5,14) (6,12) (6,19) (6,23) (6,15) (6,10) (6,18) (6,9) (6,25) (6,29) (6,21) (6,30) (6,26) (6,16) (6,8) (6,13) (6,14) (7,24) (8,12) (8,23) (8,15) (8,10) (8,18) (8,9) (8,25) (8,29) (8,11) (8,28) (8,16) (8,14) (9,19) (9,18) (9,25) (9,29) (9,11) (9,21) (9,30) (9,16) (9,13) (9,14) (10,12) (10,19) (10,23) (10,25) (10,29) (10,11) (10,28) (10,21) (10,30) (11,12) (11,19) (11,23) (11,15) (11,18) (11,29) (11,21) (11,16) (11,13) (12,19) (12,23) (12,15) (12,21) (12,30) (12,16) (12,13) (12,14) (13,19) (13,15) (13,28) (13,30) (13,26) (13,16) (13,14) (14,23) (14,15) (14,18) (14,25) (14,28) (14,21) (14,26) (14,16) (15,23) (15,25) (15,29) (15,21) (15,26) (15,16) (16,25) (16,29) (16,28) (16,30) (16,26) (18,19) (18,23) (18,25) (18,28) (18,26) (19,23) (19,25) (19,28) (19,30) (19,26) (20,27) (20,22) (21,23) (21,25) (21,29) (21,30) (21,26) (22,27) (23,25) (23,29) (23,28) (23,30) (23,26) (25,29) (25,28) (25,30) (25,26) (26,29) (26,28) (26,30) (28,30)\nIs there a path between node 1 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph150-26_0", + "image": "data/connectivity/graph_visual/hard/graph150.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,7) (0,8) (0,4) (0,20) (0,15) (0,26) (0,19) (0,10) (0,11) (0,23) (0,14) (0,27) (0,16) (1,6) (1,5) (1,28) (2,13) (2,21) (2,25) (2,22) (2,24) (2,3) (2,9) (3,13) (3,21) (3,17) (3,22) (3,9) (4,7) (4,8) (4,20) (4,12) (4,15) (4,19) (4,10) (4,11) (4,23) (4,14) (4,27) (5,6) (6,18) (6,28) (7,8) (7,20) (7,23) (7,14) (7,27) (7,16) (8,26) (8,19) (8,10) (8,11) (8,27) (9,21) (9,17) (9,25) (9,22) (9,24) (10,20) (10,12) (10,26) (10,19) (10,11) (10,23) (10,14) (10,27) (10,16) (11,20) (11,12) (11,15) (11,26) (11,19) (11,23) (11,14) (11,27) (11,16) (12,20) (12,15) (12,19) (12,23) (12,14) (12,27) (12,16) (13,25) (13,24) (14,20) (14,15) (14,27) (14,16) (15,20) (15,23) (15,27) (15,16) (16,20) (16,26) (16,19) (17,21) (17,25) (17,24) (18,28) (19,20) (19,26) (19,23) (20,26) (20,23) (20,27) (21,25) (21,22) (21,24) (22,25) (22,24) (23,26) (23,27) (26,27)\nIs there a path between node 26 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph277-20_27", + "image": "data/connectivity/graph_visual/hard/graph277.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,8) (0,30) (0,14) (0,1) (0,10) (0,29) (0,12) (0,2) (0,17) (0,23) (0,7) (1,26) (1,3) (1,10) (1,25) (1,27) (1,29) (1,12) (1,20) (1,17) (1,7) (2,26) (2,3) (2,8) (2,30) (2,14) (2,10) (2,25) (2,27) (2,29) (2,12) (2,17) (2,23) (3,26) (3,30) (3,14) (3,10) (3,25) (3,27) (3,12) (3,20) (3,17) (3,23) (4,9) (4,22) (4,19) (4,21) (4,16) (4,6) (5,18) (5,13) (5,15) (6,9) (6,22) (6,21) (6,16) (7,26) (7,8) (7,30) (7,14) (7,10) (7,25) (7,27) (7,29) (7,12) (7,20) (7,17) (7,23) (8,27) (8,29) (8,12) (8,20) (8,23) (9,22) (9,21) (9,16) (9,28) (10,26) (10,14) (10,25) (10,29) (10,17) (11,21) (11,16) (11,28) (12,26) (12,25) (12,27) (12,29) (12,20) (12,17) (13,18) (13,15) (14,30) (14,25) (14,27) (14,29) (14,20) (14,17) (14,23) (16,22) (16,21) (16,28) (17,30) (17,27) (17,20) (17,23) (18,24) (19,22) (20,26) (20,25) (20,27) (20,23) (22,28) (23,26) (23,30) (23,25) (23,27) (23,29) (25,26) (25,27) (25,29) (26,27) (26,29) (27,30) (27,29)\nIs there a path between node 20 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph188-4_12", + "image": "data/connectivity/graph_visual/hard/graph188.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,21) (0,7) (0,2) (0,6) (0,14) (0,24) (0,23) (0,20) (1,10) (1,28) (1,3) (1,16) (1,24) (1,5) (2,3) (2,7) (2,24) (2,20) (3,25) (3,28) (3,22) (3,21) (3,16) (3,14) (4,28) (4,22) (4,16) (4,18) (4,14) (5,10) (5,7) (5,16) (6,10) (6,22) (6,7) (6,24) (6,23) (7,25) (7,22) (7,21) (7,14) (7,24) (7,20) (8,13) (10,20) (10,11) (11,18) (11,14) (11,23) (12,13) (12,17) (13,17) (13,19) (14,28) (14,23) (16,21) (16,18) (16,26) (18,22) (18,24) (18,20) (21,28) (21,23) (22,24) (23,24) (25,26)\nIs there a path between node 4 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph433-4_11", + "image": "data/connectivity/graph_visual/hard/graph433.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,3) (0,18) (0,20) (0,22) (0,10) (0,26) (0,2) (0,13) (0,29) (0,30) (0,12) (0,23) (1,3) (1,18) (1,24) (1,5) (1,7) (1,22) (1,6) (1,10) (1,26) (1,2) (1,29) (1,30) (1,12) (2,18) (2,24) (2,5) (2,7) (2,22) (2,6) (2,10) (2,26) (2,13) (2,29) (2,30) (2,12) (2,23) (3,18) (3,20) (3,22) (3,6) (3,10) (3,26) (3,29) (3,30) (3,12) (3,23) (4,28) (4,21) (4,32) (4,27) (4,8) (4,25) (4,17) (4,19) (4,9) (4,11) (5,18) (5,20) (5,22) (5,6) (5,26) (5,13) (5,29) (5,12) (5,23) (6,7) (6,20) (6,10) (6,26) (6,29) (6,30) (6,23) (7,24) (7,22) (7,10) (7,26) (7,29) (7,30) (7,12) (7,23) (8,28) (8,21) (8,15) (8,32) (8,27) (8,17) (8,16) (8,19) (8,9) (8,11) (9,28) (9,21) (9,31) (9,15) (9,32) (9,16) (9,14) (10,24) (10,20) (10,22) (10,26) (10,29) (10,12) (10,23) (11,28) (11,21) (11,31) (11,15) (11,32) (11,27) (11,25) (11,16) (11,19) (12,18) (12,24) (12,20) (12,22) (12,26) (12,29) (12,23) (13,18) (13,24) (13,20) (13,22) (13,29) (13,30) (14,28) (14,21) (14,15) (14,32) (14,19) (15,28) (15,21) (15,31) (15,27) (15,25) (15,17) (15,16) (16,28) (16,21) (16,32) (16,27) (17,28) (17,21) (17,32) (17,27) (17,25) (17,19) (18,24) (18,22) (18,26) (18,29) (18,23) (19,28) (19,31) (19,25) (20,24) (20,22) (20,29) (20,30) (20,23) (21,28) (21,31) (21,27) (21,25) (22,29) (22,30) (22,23) (23,24) (24,26) (24,29) (25,28) (25,31) (26,29) (26,30) (27,31) (27,32) (28,31) (28,32) (31,32)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph430-31_8", + "image": "data/connectivity/graph_visual/hard/graph430.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,12) (0,17) (0,11) (0,31) (0,25) (0,27) (0,28) (0,8) (0,16) (1,23) (1,3) (1,15) (1,10) (2,18) (2,24) (2,19) (2,4) (2,5) (2,26) (2,6) (2,7) (2,32) (3,23) (3,15) (3,10) (4,18) (4,22) (4,20) (4,6) (4,7) (4,32) (5,18) (5,29) (5,22) (5,24) (5,19) (5,20) (5,13) (5,6) (5,7) (6,24) (6,13) (6,7) (7,18) (7,29) (7,24) (7,32) (8,14) (8,12) (8,21) (8,17) (8,31) (8,25) (8,9) (9,30) (9,14) (9,12) (9,21) (9,17) (9,11) (9,31) (9,27) (9,28) (9,16) (10,23) (10,15) (11,14) (11,21) (11,17) (11,31) (11,25) (11,27) (11,28) (12,30) (12,31) (12,16) (13,18) (13,22) (13,24) (13,19) (13,20) (13,32) (14,30) (14,21) (14,17) (14,27) (14,28) (14,16) (15,23) (16,21) (16,17) (16,31) (16,27) (16,28) (17,21) (17,25) (17,27) (17,28) (18,22) (18,19) (18,20) (18,26) (18,32) (19,22) (19,24) (19,20) (19,26) (19,32) (20,29) (20,24) (20,26) (20,32) (21,31) (21,25) (21,27) (21,28) (22,29) (22,26) (22,32) (24,32) (25,30) (25,27) (25,28) (26,29) (26,32) (27,30) (27,31) (27,28) (28,30) (29,32) (30,31)\nIs there a path between node 31 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph705-10_11", + "image": "data/connectivity/graph_visual/hard/graph705.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,17) (0,1) (0,20) (0,5) (0,16) (0,34) (1,17) (1,9) (1,5) (1,16) (1,34) (2,30) (2,26) (2,25) (2,24) (3,18) (3,12) (3,4) (3,32) (3,7) (3,33) (3,22) (3,13) (3,15) (3,6) (3,10) (3,27) (4,12) (4,11) (4,7) (4,22) (4,19) (4,13) (4,15) (4,6) (4,21) (4,27) (5,17) (5,9) (5,20) (5,34) (6,18) (6,32) (6,11) (6,7) (6,33) (6,22) (6,19) (6,15) (6,21) (7,18) (7,11) (7,33) (7,22) (7,19) (7,13) (7,10) (7,27) (8,31) (8,29) (9,17) (9,20) (9,16) (9,34) (10,12) (10,32) (10,19) (10,13) (10,15) (10,27) (11,12) (11,32) (11,33) (11,22) (11,19) (11,13) (11,27) (12,22) (12,19) (12,13) (12,15) (12,27) (13,18) (13,32) (13,33) (13,19) (13,15) (13,21) (13,27) (14,28) (14,30) (14,25) (14,24) (15,18) (15,33) (15,22) (15,19) (15,21) (15,27) (16,20) (17,20) (18,33) (18,19) (18,27) (19,32) (19,33) (19,21) (19,27) (20,34) (21,32) (21,27) (22,32) (22,33) (22,27) (23,31) (23,29) (24,28) (24,25) (25,28) (25,26) (26,28) (26,30) (28,30) (29,31) (32,33)\nIs there a path between node 10 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph444-19_11", + "image": "data/connectivity/graph_visual/hard/graph444.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,32) (0,17) (0,24) (0,25) (0,20) (0,9) (1,31) (1,3) (1,5) (2,7) (2,16) (2,10) (2,32) (2,19) (2,9) (3,31) (3,12) (3,13) (3,27) (3,29) (4,18) (4,14) (4,29) (4,21) (5,12) (5,18) (6,28) (6,30) (6,19) (6,20) (6,9) (6,11) (7,23) (7,10) (7,19) (7,15) (7,26) (7,24) (7,25) (7,11) (8,26) (8,9) (9,23) (9,10) (9,17) (9,26) (9,24) (9,20) (10,22) (10,30) (10,19) (10,17) (10,25) (10,20) (11,23) (11,25) (12,13) (12,14) (13,31) (14,27) (14,21) (15,22) (15,30) (15,16) (15,24) (15,25) (15,20) (16,22) (16,23) (16,19) (17,30) (17,32) (17,19) (19,23) (19,24) (20,30) (20,25) (21,27) (22,28) (22,32) (22,26) (22,24) (23,28) (23,24) (24,25) (25,28) (25,32) (26,30) (26,32) (27,29) (30,32)\nIs there a path between node 19 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph130-22_2", + "image": "data/connectivity/graph_visual/hard/graph130.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,27) (0,16) (0,21) (0,4) (0,6) (0,15) (0,5) (0,23) (0,26) (0,10) (0,14) (0,20) (0,19) (0,25) (0,13) (0,24) (1,16) (1,21) (1,4) (1,23) (1,26) (1,2) (1,14) (1,20) (1,19) (1,25) (1,22) (2,16) (2,3) (2,21) (2,4) (2,6) (2,15) (2,23) (2,26) (2,8) (2,10) (2,20) (2,19) (2,25) (2,22) (2,13) (2,24) (3,27) (3,16) (3,21) (3,15) (3,5) (3,23) (3,8) (3,14) (3,19) (3,25) (3,22) (3,13) (3,24) (4,27) (4,16) (4,21) (4,6) (4,5) (4,23) (4,26) (4,8) (4,20) (4,25) (4,13) (5,27) (5,16) (5,21) (5,6) (5,23) (5,8) (5,10) (5,14) (5,20) (5,19) (5,25) (5,22) (5,13) (5,24) (6,16) (6,21) (6,15) (6,23) (6,26) (6,10) (6,14) (6,20) (6,22) (6,13) (7,17) (7,9) (7,18) (7,12) (8,16) (8,21) (8,23) (8,26) (8,10) (8,14) (8,19) (8,25) (8,22) (8,24) (9,17) (9,12) (10,27) (10,16) (10,15) (10,26) (10,19) (10,25) (10,22) (10,13) (10,24) (11,17) (11,18) (11,12) (12,17) (12,18) (13,27) (13,16) (13,21) (13,15) (13,23) (13,14) (13,19) (13,22) (14,16) (14,21) (14,15) (14,23) (14,26) (14,19) (14,22) (15,27) (15,16) (15,21) (15,23) (15,26) (15,25) (15,22) (16,21) (16,23) (16,20) (16,19) (16,25) (16,22) (16,24) (17,18) (19,21) (19,23) (19,24) (20,27) (20,23) (20,26) (20,25) (20,22) (21,27) (21,23) (21,25) (21,22) (22,27) (22,23) (22,26) (22,25) (22,24) (23,27) (23,26) (23,24) (24,25) (25,26) (26,27)\nIs there a path between node 22 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph414-1_6", + "image": "data/connectivity/graph_visual/hard/graph414.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,2) (0,26) (0,21) (0,6) (0,12) (0,28) (0,15) (0,7) (1,21) (1,14) (1,25) (1,8) (1,18) (1,15) (1,27) (1,7) (2,26) (2,21) (2,14) (2,8) (2,24) (2,16) (2,13) (2,19) (2,28) (2,15) (2,27) (2,7) (3,26) (3,13) (3,18) (3,12) (3,9) (3,15) (3,27) (3,7) (3,4) (4,17) (4,8) (4,16) (4,12) (4,20) (5,14) (5,25) (5,13) (5,18) (5,28) (5,27) (5,32) (6,17) (6,25) (6,16) (6,9) (6,32) (6,11) (7,21) (7,24) (7,18) (7,12) (7,28) (7,15) (7,31) (8,25) (8,24) (8,9) (8,15) (8,31) (8,27) (8,32) (9,17) (9,16) (9,19) (9,12) (9,28) (9,15) (9,27) (10,22) (11,13) (11,18) (11,19) (11,12) (11,31) (11,27) (12,21) (12,25) (12,24) (12,16) (12,15) (12,32) (13,17) (13,14) (13,24) (13,18) (13,15) (13,20) (13,32) (14,24) (14,19) (14,28) (14,15) (14,20) (14,32) (15,28) (16,24) (16,18) (17,25) (17,28) (17,27) (18,21) (19,25) (19,28) (20,24) (20,32) (21,26) (21,25) (22,30) (23,30) (23,29) (24,25) (25,26) (25,28) (25,32) (26,31) (27,28) (27,31) (28,31) (28,32)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph658-25_10", + "image": "data/connectivity/graph_visual/hard/graph658.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,1) (0,13) (0,27) (0,17) (0,25) (0,30) (0,26) (0,21) (0,7) (1,8) (1,28) (1,30) (1,19) (1,6) (1,23) (2,3) (4,18) (4,15) (4,13) (4,31) (4,9) (4,26) (4,6) (4,11) (5,8) (5,24) (5,13) (5,31) (5,16) (5,23) (6,8) (6,14) (6,20) (6,16) (6,22) (6,25) (6,9) (6,7) (7,32) (7,15) (7,20) (7,25) (7,29) (7,19) (7,23) (8,28) (8,17) (8,11) (8,23) (9,34) (9,24) (9,17) (9,31) (9,22) (9,19) (9,11) (10,12) (11,34) (11,18) (11,27) (11,17) (11,31) (11,25) (11,29) (11,21) (13,24) (13,15) (13,17) (13,29) (13,21) (13,23) (14,18) (14,31) (14,16) (14,25) (14,29) (14,21) (15,34) (15,32) (15,16) (15,22) (15,19) (16,34) (16,32) (16,20) (16,31) (16,25) (16,30) (16,23) (17,18) (17,32) (17,20) (17,29) (17,21) (17,23) (18,27) (18,22) (18,25) (18,30) (18,29) (18,21) (19,24) (19,27) (19,20) (20,32) (20,27) (20,22) (20,26) (20,21) (21,34) (21,24) (21,32) (21,28) (21,22) (21,25) (21,30) (21,29) (21,23) (22,28) (22,31) (22,25) (22,30) (22,26) (23,24) (23,25) (23,29) (24,34) (24,26) (25,32) (25,31) (25,30) (25,29) (26,31) (26,29) (27,32) (28,34) (28,30) (28,29) (30,32) (33,34)\nIs there a path between node 25 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph150-16_15", + "image": "data/connectivity/graph_visual/hard/graph150.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,7) (0,8) (0,4) (0,20) (0,15) (0,26) (0,19) (0,10) (0,11) (0,23) (0,14) (0,27) (0,16) (1,6) (1,5) (1,28) (2,13) (2,21) (2,25) (2,22) (2,24) (2,3) (2,9) (3,13) (3,21) (3,17) (3,22) (3,9) (4,7) (4,8) (4,20) (4,12) (4,15) (4,19) (4,10) (4,11) (4,23) (4,14) (4,27) (5,6) (6,18) (6,28) (7,8) (7,20) (7,23) (7,14) (7,27) (7,16) (8,26) (8,19) (8,10) (8,11) (8,27) (9,21) (9,17) (9,25) (9,22) (9,24) (10,20) (10,12) (10,26) (10,19) (10,11) (10,23) (10,14) (10,27) (10,16) (11,20) (11,12) (11,15) (11,26) (11,19) (11,23) (11,14) (11,27) (11,16) (12,20) (12,15) (12,19) (12,23) (12,14) (12,27) (12,16) (13,25) (13,24) (14,20) (14,15) (14,27) (14,16) (15,20) (15,23) (15,27) (15,16) (16,20) (16,26) (16,19) (17,21) (17,25) (17,24) (18,28) (19,20) (19,26) (19,23) (20,26) (20,23) (20,27) (21,25) (21,22) (21,24) (22,25) (22,24) (23,26) (23,27) (26,27)\nIs there a path between node 16 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph170-10_27", + "image": "data/connectivity/graph_visual/hard/graph170.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,26) (0,12) (0,7) (0,13) (0,3) (0,8) (0,21) (0,18) (0,22) (0,6) (0,28) (0,11) (0,24) (0,4) (0,5) (0,15) (0,20) (0,19) (1,26) (1,12) (1,13) (1,21) (1,18) (1,22) (1,6) (1,17) (1,23) (1,14) (1,11) (1,27) (1,24) (1,4) (1,5) (1,20) (2,25) (2,9) (2,16) (3,7) (3,13) (3,8) (3,18) (3,22) (3,17) (3,23) (3,14) (3,11) (3,27) (3,24) (3,15) (3,20) (3,19) (4,26) (4,12) (4,13) (4,8) (4,21) (4,6) (4,17) (4,23) (4,28) (4,27) (4,24) (4,5) (4,20) (5,12) (5,7) (5,13) (5,8) (5,21) (5,18) (5,22) (5,17) (5,28) (5,27) (5,15) (5,20) (5,19) (6,12) (6,7) (6,13) (6,8) (6,21) (6,22) (6,17) (6,14) (6,28) (6,27) (6,15) (6,20) (6,19) (7,26) (7,12) (7,13) (7,8) (7,21) (7,22) (7,17) (7,23) (7,28) (7,11) (7,24) (7,15) (8,26) (8,13) (8,22) (8,17) (8,11) (8,27) (8,24) (9,25) (9,16) (11,12) (11,13) (11,21) (11,22) (11,17) (11,23) (11,28) (11,27) (11,24) (11,15) (11,20) (11,19) (12,26) (12,18) (12,22) (12,17) (12,14) (12,28) (12,24) (12,15) (12,20) (12,19) (13,26) (13,18) (13,17) (13,23) (13,14) (13,28) (13,15) (13,20) (13,19) (14,22) (14,17) (14,23) (14,28) (14,24) (14,15) (14,19) (15,26) (15,21) (15,17) (15,28) (15,24) (15,20) (16,25) (17,26) (17,21) (17,18) (17,22) (17,27) (17,24) (17,20) (17,19) (18,21) (18,28) (18,27) (18,24) (19,21) (19,22) (19,28) (19,27) (19,24) (19,20) (20,26) (20,22) (20,24) (21,26) (21,22) (21,28) (21,27) (21,24) (22,23) (22,28) (22,27) (22,24) (23,26) (23,27) (23,24) (24,27) (26,27) (27,28)\nIs there a path between node 10 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph314-29_22", + "image": "data/connectivity/graph_visual/hard/graph314.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,7) (1,5) (1,10) (1,23) (1,20) (2,30) (2,24) (2,18) (2,12) (2,16) (2,3) (2,11) (3,30) (3,4) (3,12) (3,10) (3,22) (3,19) (3,20) (4,30) (4,28) (4,18) (4,12) (4,10) (4,23) (4,22) (4,19) (5,28) (5,18) (5,12) (5,10) (5,19) (5,11) (6,8) (6,21) (6,13) (6,29) (7,8) (7,21) (7,13) (7,17) (7,29) (8,17) (8,15) (9,26) (9,23) (9,22) (9,19) (9,25) (9,20) (10,18) (10,16) (10,26) (10,22) (10,11) (11,30) (11,12) (11,22) (12,28) (12,16) (12,23) (13,17) (13,29) (14,31) (15,31) (15,29) (16,24) (16,28) (16,19) (16,20) (17,27) (17,21) (18,26) (18,19) (19,23) (20,24) (20,23) (22,28) (22,23) (22,25) (23,26) (24,28) (24,25) (25,30)\nIs there a path between node 29 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph375-8_12", + "image": "data/connectivity/graph_visual/hard/graph375.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,20) (0,4) (0,29) (0,11) (0,3) (0,1) (0,22) (0,10) (0,13) (0,16) (0,19) (0,7) (0,15) (0,25) (0,2) (0,23) (0,5) (1,18) (1,12) (1,9) (1,27) (1,20) (1,14) (1,11) (1,3) (1,24) (1,28) (1,6) (1,22) (1,10) (1,13) (1,15) (1,25) (1,2) (1,23) (1,5) (1,17) (2,18) (2,12) (2,9) (2,27) (2,29) (2,14) (2,11) (2,28) (2,6) (2,22) (2,10) (2,16) (2,7) (2,15) (2,25) (2,23) (2,17) (3,9) (3,27) (3,4) (3,29) (3,11) (3,24) (3,6) (3,21) (3,22) (3,10) (3,13) (3,16) (3,19) (3,7) (3,15) (3,25) (3,23) (4,18) (4,9) (4,27) (4,29) (4,14) (4,21) (4,22) (4,16) (4,19) (4,25) (4,23) (5,9) (5,27) (5,20) (5,29) (5,14) (5,28) (5,6) (5,22) (5,13) (5,16) (5,15) (5,25) (5,23) (6,12) (6,9) (6,27) (6,20) (6,14) (6,11) (6,24) (6,21) (6,22) (6,10) (6,13) (6,16) (6,19) (6,15) (6,25) (6,23) (7,18) (7,12) (7,9) (7,27) (7,11) (7,24) (7,28) (7,21) (7,13) (7,19) (7,25) (9,18) (9,12) (9,27) (9,20) (9,14) (9,28) (9,21) (9,22) (9,10) (9,19) (9,25) (9,23) (9,17) (10,18) (10,12) (10,20) (10,29) (10,14) (10,11) (10,21) (10,22) (10,13) (10,16) (10,19) (10,15) (10,17) (11,18) (11,27) (11,20) (11,14) (11,28) (11,13) (11,19) (11,15) (11,25) (11,23) (12,27) (12,22) (12,13) (12,16) (12,19) (12,25) (12,23) (13,20) (13,14) (13,24) (13,28) (13,21) (13,22) (13,16) (13,15) (13,25) (13,23) (13,17) (14,18) (14,27) (14,20) (14,29) (14,24) (14,28) (14,21) (14,22) (14,16) (14,19) (14,25) (14,17) (15,27) (15,20) (15,29) (15,24) (15,28) (15,21) (15,22) (15,19) (15,25) (15,17) (16,18) (16,20) (16,29) (16,24) (16,22) (16,19) (16,25) (16,17) (17,18) (17,27) (17,29) (17,24) (17,28) (17,21) (17,22) (17,19) (17,25) (17,23) (18,20) (18,29) (18,24) (18,28) (18,21) (18,19) (18,23) (19,27) (19,20) (19,29) (19,24) (19,28) (19,23) (20,22) (20,25) (21,27) (21,29) (21,24) (21,28) (21,25) (21,23) (22,27) (22,24) (22,28) (22,23) (23,27) (23,29) (23,24) (23,28) (23,25) (24,27) (24,28) (25,29) (25,28) (26,31) (27,29) (27,28) (28,29) (30,31)\nIs there a path between node 8 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph173-25_0", + "image": "data/connectivity/graph_visual/hard/graph173.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,24) (0,8) (0,18) (0,26) (0,14) (0,15) (0,9) (0,25) (0,17) (0,4) (0,2) (1,27) (1,16) (1,5) (1,22) (1,19) (2,26) (2,13) (2,14) (2,3) (2,15) (2,25) (2,4) (2,21) (3,8) (3,13) (3,23) (3,15) (3,17) (3,6) (3,21) (4,24) (4,8) (4,18) (4,26) (4,13) (4,14) (4,25) (4,6) (4,21) (5,16) (5,10) (5,19) (6,24) (6,8) (6,13) (6,23) (6,14) (6,15) (6,9) (6,17) (6,21) (7,28) (7,20) (7,11) (8,24) (8,18) (8,13) (8,23) (8,14) (8,9) (8,21) (9,24) (9,26) (9,23) (9,14) (9,25) (10,27) (10,16) (10,22) (10,19) (12,27) (12,16) (12,22) (13,24) (13,26) (13,23) (13,14) (13,15) (13,25) (13,17) (13,21) (14,26) (14,15) (14,25) (15,26) (15,23) (15,25) (15,17) (15,21) (16,27) (16,22) (16,19) (17,24) (17,18) (17,23) (18,24) (18,26) (18,21) (19,27) (19,22) (20,28) (21,24) (21,23) (21,25) (23,26) (23,25) (24,26) (24,25) (25,26)\nIs there a path between node 25 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph707-7_20", + "image": "data/connectivity/graph_visual/hard/graph707.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,20) (0,7) (0,13) (0,27) (0,34) (0,28) (0,19) (0,3) (0,17) (0,21) (0,6) (0,32) (0,31) (0,25) (0,24) (1,14) (1,29) (1,12) (1,23) (1,33) (1,11) (2,26) (2,18) (2,20) (2,7) (2,34) (2,28) (2,3) (2,15) (2,17) (2,21) (2,6) (2,32) (2,10) (2,31) (2,25) (2,22) (3,26) (3,18) (3,20) (3,7) (3,13) (3,27) (3,6) (3,32) (3,10) (3,9) (3,31) (3,25) (3,24) (4,29) (4,8) (4,5) (4,12) (4,30) (4,16) (5,14) (5,8) (5,12) (5,23) (5,30) (5,16) (5,33) (5,11) (6,7) (6,13) (6,34) (6,28) (6,19) (6,15) (6,17) (6,32) (6,31) (6,25) (6,24) (6,22) (7,18) (7,13) (7,27) (7,32) (7,9) (7,25) (7,24) (7,22) (8,29) (8,12) (8,23) (8,16) (8,33) (9,18) (9,13) (9,27) (9,34) (9,28) (9,19) (9,15) (9,17) (9,21) (9,32) (9,31) (9,25) (9,24) (9,22) (10,26) (10,20) (10,27) (10,34) (10,28) (10,19) (10,17) (10,32) (10,25) (11,29) (11,12) (11,30) (11,16) (12,23) (13,18) (13,20) (13,27) (13,28) (13,15) (13,17) (13,21) (13,32) (13,31) (13,25) (13,22) (14,29) (14,23) (14,16) (14,33) (15,18) (15,27) (15,34) (15,28) (15,19) (15,17) (15,32) (15,31) (15,24) (16,23) (16,30) (16,33) (17,26) (17,20) (17,27) (17,28) (17,19) (17,21) (17,32) (17,31) (17,25) (17,22) (18,20) (18,27) (18,28) (18,19) (18,32) (18,31) (18,25) (19,20) (19,27) (19,34) (19,21) (19,32) (19,31) (19,25) (19,24) (19,22) (20,26) (20,34) (20,21) (20,32) (20,31) (20,24) (21,26) (21,27) (21,32) (21,31) (21,25) (21,22) (22,28) (22,32) (22,31) (22,24) (23,29) (23,30) (23,33) (24,34) (24,28) (24,32) (24,25) (25,26) (25,27) (25,28) (25,32) (25,31) (26,27) (26,34) (26,28) (26,32) (26,31) (27,34) (27,28) (27,32) (27,31) (28,34) (28,32) (28,31) (29,30) (29,33) (30,33) (31,34) (32,34)\nIs there a path between node 7 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph346-18_0", + "image": "data/connectivity/graph_visual/hard/graph346.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,29) (0,31) (0,26) (0,27) (0,19) (1,28) (2,30) (4,6) (5,29) (5,31) (6,17) (6,30) (7,24) (7,29) (7,31) (8,21) (8,28) (10,11) (10,15) (12,28) (14,15) (14,20) (15,20) (18,29) (18,26) (20,23) (21,28) (24,26) (24,27)\nIs there a path between node 18 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph485-30_7", + "image": "data/connectivity/graph_visual/hard/graph485.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,7) (0,31) (0,25) (0,22) (0,24) (0,23) (0,5) (0,9) (0,21) (0,30) (1,26) (1,14) (1,7) (1,6) (1,31) (1,24) (1,23) (1,9) (1,21) (1,30) (2,27) (2,20) (2,12) (2,19) (2,32) (2,28) (2,13) (2,17) (3,26) (3,11) (3,18) (3,7) (3,31) (3,25) (3,22) (3,23) (3,5) (3,9) (3,21) (3,30) (4,27) (4,20) (4,12) (4,19) (4,28) (4,17) (4,29) (5,26) (5,11) (5,14) (5,18) (5,7) (5,6) (5,31) (5,22) (5,24) (5,23) (5,21) (5,30) (6,26) (6,11) (6,18) (6,7) (6,31) (6,25) (6,22) (6,23) (7,11) (7,18) (7,31) (7,25) (7,22) (7,23) (7,9) (8,16) (8,10) (8,15) (9,26) (9,11) (9,18) (9,25) (9,24) (9,23) (9,21) (9,30) (10,16) (11,26) (11,14) (11,31) (11,25) (11,23) (11,21) (11,30) (12,19) (12,28) (12,13) (12,17) (12,29) (13,27) (13,19) (13,32) (13,28) (13,17) (13,29) (14,18) (14,25) (14,22) (14,24) (14,23) (14,21) (14,30) (17,27) (17,19) (17,32) (17,28) (17,29) (18,31) (18,25) (18,22) (18,23) (18,21) (19,27) (19,32) (19,28) (19,29) (20,27) (20,32) (20,28) (20,29) (21,22) (21,24) (21,23) (22,26) (22,31) (22,24) (22,23) (22,30) (23,26) (23,31) (23,25) (24,31) (24,25) (25,26) (26,31) (27,32) (27,29) (29,32)\nIs there a path between node 30 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph592-31_6", + "image": "data/connectivity/graph_visual/hard/graph592.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,10) (0,19) (0,2) (0,33) (0,21) (0,3) (0,18) (0,9) (0,14) (0,6) (0,17) (0,26) (0,25) (0,5) (0,28) (0,20) (0,29) (0,12) (1,19) (1,2) (1,33) (1,23) (1,32) (1,21) (1,24) (1,3) (1,18) (1,9) (1,14) (1,17) (1,15) (1,26) (1,16) (1,22) (1,8) (1,4) (1,20) (1,29) (1,12) (2,19) (2,13) (2,23) (2,3) (2,18) (2,9) (2,14) (2,6) (2,17) (2,16) (2,22) (2,25) (2,5) (2,20) (2,29) (3,10) (3,19) (3,13) (3,23) (3,32) (3,24) (3,9) (3,14) (3,6) (3,17) (3,15) (3,26) (3,16) (3,22) (3,8) (3,25) (3,5) (3,28) (3,4) (3,20) (3,12) (4,10) (4,19) (4,13) (4,23) (4,32) (4,21) (4,18) (4,9) (4,14) (4,6) (4,16) (4,22) (4,5) (4,29) (4,12) (5,10) (5,19) (5,33) (5,13) (5,21) (5,24) (5,18) (5,14) (5,6) (5,15) (5,16) (5,8) (5,25) (5,28) (5,29) (5,12) (6,10) (6,19) (6,33) (6,13) (6,21) (6,18) (6,14) (6,17) (6,16) (6,22) (6,8) (6,20) (6,29) (7,11) (7,27) (7,30) (7,31) (8,10) (8,19) (8,33) (8,13) (8,23) (8,32) (8,21) (8,18) (8,9) (8,14) (8,17) (8,15) (8,26) (8,22) (8,25) (8,28) (8,29) (8,12) (9,10) (9,33) (9,13) (9,23) (9,32) (9,21) (9,24) (9,18) (9,14) (9,26) (9,22) (9,25) (9,29) (9,12) (10,19) (10,13) (10,23) (10,32) (10,21) (10,24) (10,14) (10,17) (10,15) (10,26) (10,16) (10,22) (10,28) (10,29) (10,12) (11,30) (12,33) (12,13) (12,32) (12,21) (12,24) (12,14) (12,17) (12,15) (12,26) (12,16) (12,22) (12,20) (13,19) (13,33) (13,18) (13,14) (13,15) (13,26) (13,16) (13,22) (13,25) (13,20) (13,29) (14,19) (14,33) (14,32) (14,18) (14,17) (14,15) (14,26) (14,16) (14,22) (14,28) (14,20) (14,29) (15,19) (15,23) (15,21) (15,24) (15,18) (15,17) (15,26) (15,16) (15,20) (15,29) (16,19) (16,23) (16,24) (16,18) (16,26) (16,22) (16,28) (16,20) (16,29) (17,33) (17,23) (17,32) (17,21) (17,24) (17,18) (17,26) (17,22) (17,28) (17,29) (18,33) (18,23) (18,32) (18,21) (18,24) (18,25) (18,28) (18,20) (19,33) (19,32) (19,21) (19,24) (19,26) (19,28) (19,20) (20,33) (20,23) (20,32) (20,21) (20,24) (20,26) (20,22) (20,25) (20,28) (21,33) (21,23) (21,32) (21,26) (21,22) (21,25) (22,33) (22,32) (22,24) (22,26) (22,25) (22,29) (23,33) (23,24) (23,26) (23,25) (24,33) (24,32) (24,26) (24,25) (24,28) (24,29) (25,33) (25,26) (25,28) (25,29) (26,28) (26,29) (27,30) (27,31) (28,33) (28,32) (28,29) (29,33) (29,32) (32,33)\nIs there a path between node 31 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph315-30_27", + "image": "data/connectivity/graph_visual/hard/graph315.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,14) (0,31) (0,28) (0,20) (0,26) (0,13) (0,2) (1,7) (1,10) (2,14) (2,17) (2,31) (2,9) (2,15) (2,13) (2,16) (3,21) (3,29) (3,12) (3,15) (3,24) (3,16) (3,27) (4,14) (4,22) (4,15) (4,19) (4,26) (4,24) (4,16) (5,7) (5,18) (5,10) (6,25) (6,10) (7,25) (7,18) (8,11) (9,14) (9,17) (9,31) (9,28) (9,12) (9,20) (9,24) (11,30) (11,25) (11,18) (12,14) (12,21) (13,14) (13,17) (13,29) (13,23) (13,15) (13,20) (13,16) (14,21) (14,29) (14,24) (15,29) (15,28) (15,19) (15,26) (15,27) (16,29) (16,23) (16,19) (16,24) (17,29) (17,22) (17,24) (18,25) (19,24) (20,23) (20,26) (20,27) (21,28) (21,24) (23,31) (23,26) (23,27) (24,28) (24,26)\nIs there a path between node 30 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph617-10_12", + "image": "data/connectivity/graph_visual/hard/graph617.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,19) (0,23) (0,18) (0,2) (0,24) (0,14) (0,6) (0,7) (0,33) (0,30) (0,21) (0,11) (0,29) (0,10) (1,25) (1,31) (1,16) (1,34) (1,28) (2,22) (2,23) (2,18) (2,24) (2,32) (2,14) (2,6) (2,33) (2,8) (2,27) (2,21) (2,4) (2,29) (3,9) (3,13) (3,15) (3,5) (3,26) (4,19) (4,23) (4,18) (4,24) (4,12) (4,32) (4,6) (4,7) (4,33) (4,8) (4,27) (4,30) (4,17) (4,10) (5,9) (5,13) (5,15) (5,26) (6,19) (6,12) (6,32) (6,14) (6,33) (6,27) (6,10) (7,22) (7,19) (7,18) (7,24) (7,32) (7,14) (7,27) (7,30) (7,11) (7,10) (8,22) (8,19) (8,23) (8,12) (8,33) (8,30) (8,17) (8,11) (8,29) (8,10) (9,13) (9,15) (9,26) (10,19) (10,18) (10,12) (10,32) (10,33) (10,27) (10,17) (10,11) (10,29) (11,19) (11,23) (11,18) (11,24) (11,32) (11,33) (11,27) (11,21) (11,29) (12,19) (12,23) (12,18) (12,32) (12,14) (12,33) (12,27) (12,30) (12,21) (12,17) (13,26) (14,22) (14,19) (14,23) (14,18) (14,32) (14,30) (14,21) (14,29) (15,26) (16,25) (16,31) (16,34) (16,28) (17,19) (17,23) (17,18) (17,24) (17,33) (17,27) (17,29) (18,22) (18,19) (18,23) (18,33) (18,27) (18,21) (18,29) (19,22) (19,23) (19,33) (19,27) (19,29) (20,25) (20,31) (20,34) (21,22) (21,23) (21,32) (21,33) (21,27) (21,30) (21,29) (22,33) (22,27) (22,30) (23,24) (23,32) (23,33) (23,27) (23,29) (24,32) (24,33) (24,27) (24,30) (24,29) (25,31) (25,34) (27,32) (27,33) (27,29) (29,33) (30,32) (30,33) (31,34) (32,33)\nIs there a path between node 10 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph561-6_5", + "image": "data/connectivity/graph_visual/hard/graph561.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,23) (0,31) (0,10) (0,14) (0,28) (0,18) (0,8) (0,21) (0,33) (0,22) (0,2) (0,1) (1,12) (1,31) (1,14) (1,28) (1,18) (1,8) (1,21) (1,19) (1,7) (1,5) (2,3) (2,31) (2,16) (2,19) (2,9) (2,22) (2,7) (3,10) (3,29) (3,11) (3,9) (4,23) (4,10) (4,14) (4,16) (4,29) (4,17) (4,8) (4,25) (4,30) (4,15) (5,27) (5,12) (5,23) (5,10) (5,16) (5,18) (5,13) (5,19) (5,9) (6,20) (7,12) (7,14) (7,26) (7,8) (7,30) (8,31) (8,28) (8,29) (8,33) (8,15) (9,12) (9,16) (9,13) (9,19) (9,15) (9,22) (10,27) (10,12) (10,16) (10,28) (11,27) (11,23) (11,31) (11,18) (12,27) (12,13) (12,21) (12,25) (12,19) (13,23) (13,14) (13,28) (13,18) (13,17) (13,33) (13,15) (14,28) (15,27) (15,18) (15,29) (15,25) (15,30) (16,27) (16,28) (16,19) (17,31) (17,28) (17,25) (18,28) (18,25) (19,29) (19,25) (19,22) (21,27) (22,25) (23,29) (23,33) (26,29) (27,28) (27,29) (27,30) (28,31) (29,31) (29,33)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph586-11_33", + "image": "data/connectivity/graph_visual/hard/graph586.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,15) (0,4) (0,8) (0,20) (0,25) (0,27) (0,18) (0,22) (0,19) (0,6) (0,12) (1,15) (1,16) (1,20) (1,18) (1,22) (1,3) (1,19) (1,6) (1,12) (1,29) (2,14) (2,24) (2,28) (2,31) (2,26) (3,4) (3,8) (3,27) (3,7) (3,19) (3,12) (3,29) (4,33) (4,8) (4,16) (4,20) (4,25) (4,18) (4,22) (4,19) (4,6) (4,29) (5,14) (5,24) (5,11) (5,28) (5,17) (5,31) (5,26) (5,32) (6,33) (6,16) (6,20) (6,25) (6,27) (6,22) (6,7) (6,12) (6,29) (7,15) (7,33) (7,8) (7,20) (7,27) (7,18) (7,22) (7,19) (7,29) (8,15) (8,33) (8,16) (8,18) (8,22) (8,19) (8,12) (8,29) (9,14) (9,24) (9,23) (9,11) (9,26) (9,32) (10,21) (11,14) (11,24) (11,23) (11,28) (11,17) (11,31) (11,26) (11,32) (12,15) (12,33) (12,16) (12,20) (12,25) (12,27) (13,21) (14,23) (14,28) (14,26) (14,32) (15,20) (15,18) (15,29) (16,33) (16,20) (16,27) (16,18) (16,22) (16,29) (17,24) (17,23) (17,30) (17,26) (17,32) (18,33) (18,20) (18,25) (18,27) (18,29) (19,33) (19,27) (19,22) (19,29) (20,33) (20,27) (20,22) (20,29) (22,33) (22,25) (22,27) (22,29) (23,24) (23,28) (23,30) (23,31) (23,32) (24,28) (24,30) (24,31) (24,32) (25,33) (25,27) (26,28) (26,30) (26,31) (28,30) (28,32) (29,33) (30,31)\nIs there a path between node 11 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph688-14_5", + "image": "data/connectivity/graph_visual/hard/graph688.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,29) (0,30) (1,19) (1,22) (1,13) (1,28) (1,26) (1,24) (1,3) (1,12) (1,7) (1,16) (1,25) (1,27) (1,11) (2,31) (2,10) (2,18) (2,9) (2,14) (2,23) (2,33) (2,32) (3,19) (3,21) (3,22) (3,28) (3,26) (3,24) (3,12) (3,7) (3,16) (3,25) (3,27) (3,11) (4,17) (5,8) (5,9) (5,23) (5,32) (6,29) (6,15) (7,19) (7,22) (7,28) (7,26) (7,24) (7,12) (7,16) (7,25) (7,27) (8,31) (8,10) (8,18) (8,14) (8,23) (8,33) (8,32) (9,31) (9,10) (9,18) (9,14) (9,23) (9,32) (10,31) (10,18) (10,14) (10,23) (10,33) (10,32) (11,19) (11,21) (11,22) (11,13) (11,28) (11,26) (11,12) (11,16) (11,27) (12,22) (12,13) (12,24) (12,16) (12,25) (12,27) (13,19) (13,22) (13,28) (13,26) (13,24) (13,16) (13,25) (14,31) (14,18) (14,23) (14,33) (14,32) (15,34) (15,30) (16,21) (16,22) (16,25) (16,27) (17,20) (18,31) (18,23) (18,32) (19,21) (19,22) (19,28) (19,26) (19,24) (19,25) (21,22) (21,28) (21,26) (21,24) (21,25) (21,27) (22,28) (22,27) (23,31) (23,33) (23,32) (24,28) (24,26) (24,27) (25,28) (25,26) (25,27) (26,28) (26,27) (30,34) (31,33)\nIs there a path between node 14 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph468-23_27", + "image": "data/connectivity/graph_visual/hard/graph468.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,6) (0,2) (0,22) (0,32) (0,27) (0,5) (0,14) (0,3) (0,21) (0,7) (0,25) (0,29) (0,9) (0,18) (0,19) (0,11) (0,31) (0,10) (0,8) (1,6) (1,2) (1,5) (1,3) (1,21) (1,7) (1,29) (1,9) (1,19) (1,10) (1,8) (2,32) (2,5) (2,14) (2,3) (2,7) (2,29) (2,9) (2,18) (2,23) (2,11) (2,10) (2,8) (3,22) (3,27) (3,5) (3,21) (3,7) (3,25) (3,29) (3,19) (3,23) (3,10) (4,20) (4,15) (4,28) (4,12) (4,30) (5,6) (5,22) (5,32) (5,27) (5,14) (5,21) (5,25) (5,29) (5,9) (5,18) (5,19) (5,11) (5,31) (5,10) (5,8) (6,24) (6,32) (6,27) (6,14) (6,21) (6,25) (6,29) (6,9) (6,18) (6,19) (6,23) (6,8) (7,22) (7,24) (7,27) (7,14) (7,21) (7,29) (7,9) (7,23) (7,11) (7,10) (7,8) (8,24) (8,32) (8,27) (8,14) (8,25) (8,29) (8,9) (8,18) (8,19) (8,23) (8,11) (8,31) (9,22) (9,24) (9,32) (9,27) (9,21) (9,29) (9,18) (9,19) (9,23) (9,11) (9,10) (10,22) (10,32) (10,27) (10,14) (10,21) (10,19) (10,23) (10,31) (11,22) (11,24) (11,32) (11,27) (11,14) (11,21) (11,25) (11,29) (11,18) (11,19) (11,31) (12,20) (12,15) (12,28) (12,30) (13,16) (13,17) (14,24) (14,32) (14,21) (14,25) (14,29) (14,19) (14,23) (14,31) (15,20) (15,28) (15,30) (16,17) (16,26) (17,26) (18,32) (18,27) (18,21) (18,25) (18,29) (18,23) (18,31) (19,22) (19,32) (19,27) (19,21) (19,25) (20,28) (20,30) (21,22) (21,24) (21,32) (21,27) (21,29) (21,23) (22,32) (22,25) (22,29) (22,23) (22,31) (23,24) (23,27) (23,31) (24,32) (24,27) (24,25) (24,31) (25,27) (25,29) (27,29) (27,31) (28,30) (29,32) (31,32)\nIs there a path between node 23 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph648-31_34", + "image": "data/connectivity/graph_visual/hard/graph648.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,1) (0,27) (0,3) (0,2) (1,3) (1,2) (2,27) (3,27) (4,9) (4,7) (4,29) (4,34) (4,31) (4,21) (4,16) (4,17) (4,15) (4,25) (4,18) (4,5) (4,6) (4,20) (4,11) (5,9) (5,7) (5,24) (5,32) (5,23) (5,30) (5,31) (5,16) (5,17) (5,25) (5,26) (5,18) (5,6) (5,13) (5,11) (6,7) (6,29) (6,34) (6,24) (6,32) (6,23) (6,31) (6,21) (6,26) (6,18) (6,20) (6,11) (7,24) (7,32) (7,31) (7,16) (7,17) (7,15) (7,25) (7,12) (7,26) (7,20) (7,13) (7,11) (8,10) (8,14) (8,22) (8,19) (9,29) (9,24) (9,32) (9,23) (9,31) (9,21) (9,16) (9,17) (9,25) (9,12) (9,26) (9,18) (9,20) (9,13) (9,11) (10,33) (10,28) (10,22) (10,19) (11,29) (11,34) (11,24) (11,32) (11,30) (11,31) (11,21) (11,25) (11,12) (11,26) (11,18) (11,13) (12,29) (12,34) (12,24) (12,32) (12,23) (12,15) (12,25) (12,18) (12,20) (12,13) (13,29) (13,34) (13,24) (13,30) (13,17) (13,15) (13,18) (13,20) (14,28) (14,22) (14,19) (15,29) (15,34) (15,24) (15,32) (15,23) (15,21) (15,16) (15,17) (15,25) (15,26) (15,18) (15,20) (16,29) (16,34) (16,24) (16,32) (16,23) (16,30) (16,31) (16,21) (16,25) (16,26) (17,29) (17,34) (17,32) (17,23) (17,30) (17,31) (17,21) (17,26) (17,18) (17,20) (18,24) (18,32) (18,30) (18,31) (18,21) (18,25) (18,20) (19,33) (19,28) (19,22) (20,29) (20,34) (20,30) (20,31) (20,21) (20,25) (20,26) (21,29) (21,34) (21,24) (21,31) (21,25) (21,26) (22,33) (22,28) (23,29) (23,24) (23,32) (23,30) (23,25) (23,26) (24,29) (24,32) (24,31) (24,25) (24,26) (25,34) (25,32) (25,30) (25,26) (26,34) (26,30) (29,32) (29,30) (29,31) (30,32) (31,34) (31,32) (32,34)\nIs there a path between node 31 and node 34 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph284-6_7", + "image": "data/connectivity/graph_visual/hard/graph284.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,31) (0,11) (0,27) (0,18) (1,4) (1,12) (1,31) (1,7) (1,25) (1,8) (1,18) (2,17) (2,14) (2,6) (2,10) (2,19) (3,17) (3,22) (3,9) (4,12) (4,30) (4,31) (4,13) (4,27) (4,18) (5,29) (5,16) (5,22) (5,21) (5,20) (5,28) (5,19) (6,29) (6,9) (6,10) (6,28) (7,11) (7,27) (7,15) (7,18) (8,30) (8,23) (8,11) (9,14) (9,21) (9,10) (11,23) (11,18) (12,30) (12,31) (12,27) (12,25) (12,15) (12,18) (13,23) (13,25) (13,15) (14,29) (14,17) (16,24) (16,17) (16,20) (17,29) (18,30) (18,26) (20,29) (21,24) (22,24) (23,27) (23,25) (25,26) (25,27) (26,31) (27,31) (28,29)\nIs there a path between node 6 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph357-2_21", + "image": "data/connectivity/graph_visual/hard/graph357.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,22) (0,27) (1,18) (1,21) (1,15) (1,6) (1,29) (1,9) (1,4) (1,8) (1,28) (1,17) (2,13) (2,24) (2,14) (2,30) (2,12) (2,17) (2,5) (3,20) (3,14) (3,23) (3,15) (3,26) (3,9) (3,25) (3,8) (3,28) (3,17) (4,20) (4,18) (4,23) (4,15) (4,10) (4,30) (4,6) (4,26) (4,12) (4,16) (5,24) (5,14) (5,15) (5,6) (5,29) (5,12) (5,9) (5,8) (6,18) (6,10) (6,29) (6,28) (6,17) (7,27) (8,18) (8,21) (8,13) (8,23) (8,12) (8,25) (8,19) (8,17) (9,15) (9,30) (9,29) (9,25) (9,19) (9,17) (10,29) (10,26) (10,28) (10,17) (11,18) (11,15) (11,30) (11,26) (11,28) (11,17) (12,20) (12,14) (12,23) (13,18) (13,30) (13,29) (13,26) (13,25) (13,19) (13,28) (13,17) (14,20) (14,19) (15,18) (16,20) (16,26) (16,25) (16,19) (17,30) (17,26) (17,19) (18,21) (18,24) (18,30) (18,25) (18,28) (19,21) (19,23) (20,24) (20,26) (20,28) (21,24) (21,30) (24,30) (24,26) (25,30) (26,29) (26,28)\nIs there a path between node 2 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph454-7_27", + "image": "data/connectivity/graph_visual/hard/graph454.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,7) (0,4) (0,23) (0,21) (0,18) (1,10) (1,19) (1,24) (1,18) (1,5) (2,11) (2,14) (2,22) (2,23) (2,13) (2,15) (2,31) (2,20) (3,11) (3,22) (3,16) (3,30) (3,13) (3,20) (3,18) (4,11) (4,14) (4,6) (4,23) (4,24) (4,31) (4,32) (4,18) (4,5) (5,19) (5,11) (5,7) (5,23) (5,15) (5,31) (6,19) (6,7) (6,13) (6,8) (7,11) (7,22) (7,28) (7,30) (7,21) (7,31) (8,10) (8,12) (8,14) (8,16) (8,30) (8,21) (9,17) (10,12) (10,24) (10,21) (10,32) (10,20) (11,22) (11,23) (11,13) (11,15) (11,18) (12,22) (12,31) (12,18) (13,16) (13,30) (13,23) (13,21) (13,15) (13,32) (14,19) (14,30) (14,23) (14,31) (15,30) (15,31) (15,32) (15,20) (16,30) (16,24) (16,21) (16,32) (17,25) (18,19) (18,28) (18,24) (19,21) (20,22) (20,21) (22,30) (22,23) (22,32) (24,28) (24,31) (24,32) (25,26) (25,27)\nIs there a path between node 7 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph615-14_20", + "image": "data/connectivity/graph_visual/hard/graph615.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,29) (0,8) (0,16) (0,1) (0,28) (0,4) (0,33) (0,21) (0,3) (0,18) (0,17) (0,23) (0,14) (0,27) (0,25) (0,30) (0,11) (0,19) (0,7) (0,26) (0,5) (0,12) (1,8) (1,28) (1,33) (1,3) (1,18) (1,17) (1,23) (1,27) (1,25) (1,30) (1,15) (1,32) (1,19) (1,9) (1,5) (1,20) (1,2) (1,12) (1,34) (2,29) (2,24) (2,8) (2,16) (2,4) (2,33) (2,3) (2,18) (2,17) (2,23) (2,27) (2,25) (2,11) (2,15) (2,32) (2,19) (2,9) (2,26) (2,5) (2,12) (2,34) (3,29) (3,24) (3,8) (3,16) (3,28) (3,4) (3,33) (3,18) (3,17) (3,27) (3,30) (3,11) (3,6) (3,32) (3,9) (3,7) (3,12) (4,29) (4,24) (4,16) (4,33) (4,21) (4,18) (4,17) (4,14) (4,27) (4,25) (4,30) (4,11) (4,15) (4,32) (4,31) (4,19) (4,9) (4,7) (4,26) (4,5) (4,12) (5,29) (5,24) (5,8) (5,16) (5,28) (5,33) (5,18) (5,23) (5,14) (5,27) (5,25) (5,30) (5,15) (5,6) (5,31) (5,19) (5,9) (5,7) (5,26) (5,20) (5,12) (6,24) (6,8) (6,16) (6,28) (6,21) (6,17) (6,14) (6,27) (6,11) (6,15) (6,32) (6,19) (6,9) (6,7) (6,26) (6,20) (6,34) (7,24) (7,8) (7,33) (7,21) (7,18) (7,23) (7,14) (7,25) (7,30) (7,11) (7,15) (7,31) (7,9) (7,26) (7,20) (7,12) (7,34) (8,29) (8,24) (8,16) (8,17) (8,23) (8,14) (8,25) (8,30) (8,32) (8,31) (8,9) (8,20) (8,12) (9,29) (9,24) (9,16) (9,28) (9,21) (9,18) (9,17) (9,23) (9,27) (9,25) (9,15) (9,32) (9,31) (9,19) (9,26) (9,20) (9,12) (9,34) (10,13) (11,29) (11,24) (11,28) (11,33) (11,21) (11,18) (11,23) (11,14) (11,27) (11,25) (11,30) (11,32) (11,31) (11,26) (11,12) (11,34) (12,24) (12,16) (12,28) (12,33) (12,21) (12,18) (12,14) (12,27) (12,25) (12,15) (12,32) (12,26) (12,20) (12,34) (14,29) (14,24) (14,16) (14,28) (14,33) (14,21) (14,17) (14,23) (14,27) (14,25) (14,15) (14,31) (14,26) (14,20) (14,34) (15,29) (15,24) (15,28) (15,18) (15,17) (15,23) (15,27) (15,25) (15,30) (15,31) (15,19) (15,26) (15,34) (16,29) (16,24) (16,28) (16,33) (16,17) (16,27) (16,30) (16,31) (16,26) (16,20) (16,34) (17,24) (17,28) (17,33) (17,18) (17,23) (17,27) (17,30) (17,31) (17,19) (17,20) (17,34) (18,29) (18,28) (18,33) (18,21) (18,23) (18,27) (18,25) (18,30) (18,32) (18,31) (18,19) (18,34) (19,33) (19,21) (19,23) (19,27) (19,25) (19,31) (19,26) (19,20) (19,34) (20,21) (20,23) (20,27) (20,25) (20,30) (20,32) (20,26) (20,34) (21,29) (21,24) (21,33) (21,23) (21,31) (23,24) (23,28) (23,27) (23,25) (23,30) (23,32) (23,31) (23,26) (23,34) (24,29) (24,30) (24,32) (24,31) (24,26) (24,34) (25,29) (25,28) (25,33) (25,27) (25,31) (25,34) (26,28) (26,27) (26,32) (26,31) (26,34) (27,29) (27,33) (27,30) (27,32) (27,31) (28,29) (28,33) (28,30) (28,32) (28,31) (28,34) (29,33) (29,30) (29,32) (29,31) (29,34) (30,33) (30,32) (30,31) (30,34) (31,33) (31,34) (32,33) (32,34) (33,34)\nIs there a path between node 14 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph369-25_4", + "image": "data/connectivity/graph_visual/hard/graph369.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,16) (0,6) (0,12) (0,29) (0,13) (0,3) (0,21) (0,17) (0,30) (0,27) (0,8) (0,10) (1,9) (1,11) (1,16) (1,6) (1,20) (1,24) (1,13) (1,14) (1,3) (1,21) (1,17) (1,30) (1,25) (1,19) (1,27) (1,8) (1,10) (2,4) (3,26) (3,9) (3,11) (3,7) (3,12) (3,24) (3,13) (3,14) (3,17) (3,30) (3,25) (3,27) (3,8) (3,10) (4,23) (5,28) (5,15) (6,26) (6,9) (6,11) (6,16) (6,7) (6,12) (6,24) (6,14) (6,21) (6,17) (6,25) (6,19) (6,27) (6,10) (7,26) (7,11) (7,16) (7,12) (7,29) (7,24) (7,21) (7,17) (7,30) (7,8) (7,10) (8,9) (8,16) (8,12) (8,20) (8,24) (8,13) (8,14) (8,17) (8,30) (8,19) (8,27) (8,10) (9,11) (9,16) (9,12) (9,20) (9,29) (9,24) (9,14) (9,21) (9,17) (9,30) (9,25) (9,19) (9,27) (10,16) (10,12) (10,20) (10,24) (10,13) (10,14) (10,21) (10,17) (10,30) (10,25) (10,19) (10,27) (11,26) (11,16) (11,24) (11,14) (11,21) (11,30) (11,25) (11,19) (11,27) (12,26) (12,16) (12,20) (12,29) (12,24) (12,13) (12,14) (12,21) (12,17) (12,30) (12,19) (12,27) (13,26) (13,16) (13,20) (13,24) (13,14) (13,21) (13,17) (13,30) (13,19) (13,27) (14,26) (14,16) (14,20) (14,29) (14,30) (14,25) (15,31) (16,26) (16,29) (16,21) (16,17) (16,30) (16,25) (16,27) (17,26) (17,29) (17,21) (17,30) (17,25) (17,19) (17,27) (18,23) (18,22) (19,26) (19,20) (19,21) (19,30) (19,25) (19,27) (20,26) (20,29) (20,24) (20,21) (20,30) (20,25) (20,27) (21,26) (21,29) (21,30) (21,25) (21,27) (22,23) (24,29) (24,30) (25,29) (25,30) (25,27) (26,29) (27,29) (27,30) (29,30)\nIs there a path between node 25 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph471-0_25", + "image": "data/connectivity/graph_visual/hard/graph471.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,28) (0,30) (0,13) (0,15) (0,2) (0,1) (0,9) (0,21) (1,25) (1,13) (1,3) (1,29) (1,23) (1,14) (1,12) (2,20) (2,25) (2,30) (2,13) (2,3) (2,29) (2,23) (2,18) (2,9) (2,21) (3,20) (3,25) (3,13) (3,29) (3,18) (3,15) (3,9) (3,12) (3,21) (4,7) (5,6) (5,10) (5,8) (5,19) (5,16) (5,27) (5,26) (5,31) (5,11) (6,10) (6,8) (6,19) (6,27) (6,26) (6,31) (6,22) (6,11) (7,17) (8,32) (8,19) (8,16) (8,27) (8,26) (8,31) (8,22) (8,11) (9,28) (9,20) (9,29) (9,23) (9,15) (9,14) (9,21) (10,32) (10,24) (10,31) (10,22) (10,11) (11,32) (11,19) (11,24) (11,27) (11,31) (11,22) (12,25) (12,30) (12,29) (12,18) (12,15) (12,14) (12,21) (13,20) (13,25) (13,30) (13,23) (13,18) (13,14) (14,28) (14,25) (14,23) (14,15) (14,21) (15,20) (15,25) (15,30) (15,29) (15,23) (15,18) (15,21) (16,19) (16,27) (16,26) (16,22) (18,28) (18,20) (18,25) (18,30) (18,29) (18,23) (18,21) (19,32) (19,27) (19,31) (20,30) (20,29) (20,23) (21,28) (21,25) (21,29) (21,23) (22,32) (22,24) (22,27) (22,26) (22,31) (23,25) (23,30) (24,32) (24,27) (24,26) (25,28) (25,29) (26,32) (27,32) (28,30) (28,29) (31,32)\nIs there a path between node 0 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph686-11_22", + "image": "data/connectivity/graph_visual/hard/graph686.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,24) (0,27) (0,32) (0,33) (0,29) (0,9) (0,21) (0,5) (0,31) (0,14) (0,12) (0,26) (0,11) (0,17) (0,16) (0,34) (0,23) (0,30) (0,7) (0,6) (1,24) (1,32) (1,4) (1,20) (1,9) (1,21) (1,22) (1,12) (1,26) (1,25) (1,11) (1,17) (1,34) (1,23) (1,7) (1,6) (1,8) (2,27) (2,4) (2,29) (2,9) (2,21) (2,5) (2,15) (2,31) (2,22) (2,12) (2,26) (2,25) (2,11) (2,17) (2,18) (2,34) (2,23) (2,30) (3,24) (3,27) (3,32) (3,33) (3,4) (3,20) (3,5) (3,15) (3,31) (3,14) (3,22) (3,25) (3,11) (3,17) (3,16) (3,18) (3,34) (3,30) (3,7) (3,28) (3,6) (3,8) (4,24) (4,27) (4,33) (4,29) (4,20) (4,9) (4,21) (4,5) (4,15) (4,31) (4,14) (4,22) (4,12) (4,25) (4,17) (4,16) (4,18) (4,30) (4,28) (4,6) (4,8) (5,27) (5,29) (5,20) (5,21) (5,15) (5,31) (5,14) (5,12) (5,26) (5,25) (5,11) (5,17) (5,16) (5,30) (5,7) (5,28) (5,8) (6,24) (6,32) (6,33) (6,29) (6,20) (6,9) (6,21) (6,15) (6,14) (6,22) (6,12) (6,26) (6,25) (6,11) (6,16) (6,18) (6,7) (6,28) (6,8) (7,24) (7,27) (7,33) (7,9) (7,21) (7,15) (7,31) (7,14) (7,22) (7,12) (7,26) (7,25) (7,18) (7,23) (7,28) (7,8) (8,24) (8,32) (8,20) (8,9) (8,15) (8,31) (8,14) (8,22) (8,12) (8,17) (8,16) (8,34) (8,23) (8,30) (8,28) (9,27) (9,32) (9,33) (9,29) (9,20) (9,21) (9,31) (9,14) (9,12) (9,26) (9,16) (9,34) (9,23) (9,30) (9,28) (10,19) (10,13) (11,24) (11,32) (11,29) (11,20) (11,21) (11,15) (11,14) (11,22) (11,12) (11,26) (11,17) (11,18) (11,34) (11,23) (11,30) (11,28) (12,24) (12,27) (12,32) (12,33) (12,20) (12,21) (12,31) (12,22) (12,26) (12,25) (12,17) (12,16) (12,18) (12,34) (12,30) (12,28) (13,19) (14,32) (14,29) (14,21) (14,31) (14,26) (14,25) (14,17) (14,16) (14,18) (14,23) (14,30) (15,24) (15,27) (15,32) (15,33) (15,20) (15,31) (15,22) (15,26) (15,25) (15,17) (15,16) (15,34) (15,23) (15,30) (16,27) (16,33) (16,29) (16,20) (16,21) (16,31) (16,22) (16,26) (16,25) (16,17) (16,18) (16,34) (16,23) (16,30) (17,24) (17,32) (17,33) (17,29) (17,20) (17,31) (17,22) (17,26) (17,25) (17,34) (17,23) (17,28) (18,24) (18,32) (18,33) (18,20) (18,31) (18,22) (18,26) (18,34) (18,23) (18,28) (20,24) (20,33) (20,29) (20,31) (20,22) (20,26) (20,34) (20,23) (20,30) (20,28) (21,24) (21,32) (21,26) (21,25) (21,34) (21,23) (21,30) (21,28) (22,24) (22,32) (22,33) (22,29) (22,31) (22,26) (22,25) (22,34) (22,28) (23,27) (23,32) (23,33) (23,29) (23,31) (23,34) (23,30) (23,28) (24,27) (24,33) (24,29) (24,31) (24,26) (24,25) (24,34) (24,30) (24,28) (25,27) (25,32) (25,33) (25,29) (25,26) (25,34) (25,30) (25,28) (26,27) (26,32) (26,33) (26,29) (26,31) (26,28) (27,32) (27,33) (27,29) (27,31) (27,30) (28,32) (28,31) (28,34) (28,30) (29,32) (29,33) (29,34) (30,32) (30,31) (30,34) (31,32) (31,33) (32,33) (32,34) (33,34)\nIs there a path between node 11 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph177-8_22", + "image": "data/connectivity/graph_visual/hard/graph177.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,7) (0,24) (0,22) (0,21) (0,20) (0,3) (1,13) (1,27) (1,23) (1,28) (1,2) (1,10) (1,11) (1,18) (1,14) (1,8) (1,16) (1,12) (2,13) (2,27) (2,23) (2,15) (2,26) (2,10) (2,9) (2,11) (2,14) (2,8) (2,5) (3,24) (3,22) (3,4) (3,21) (3,20) (4,7) (4,24) (4,21) (5,13) (5,23) (5,26) (5,28) (5,17) (5,11) (5,14) (5,8) (5,12) (6,13) (6,27) (6,23) (6,15) (6,26) (6,17) (6,10) (6,9) (6,19) (6,11) (6,14) (6,8) (6,16) (7,24) (7,22) (8,13) (8,27) (8,26) (8,28) (8,17) (8,10) (8,9) (8,19) (8,11) (8,18) (8,16) (9,13) (9,27) (9,15) (9,26) (9,28) (9,17) (9,10) (9,19) (9,11) (9,14) (9,16) (9,12) (10,13) (10,27) (10,23) (10,15) (10,28) (10,17) (10,19) (10,11) (10,18) (10,14) (11,13) (11,27) (11,23) (11,15) (11,28) (11,17) (11,19) (11,18) (11,14) (11,16) (12,23) (12,15) (12,17) (12,19) (12,18) (12,14) (13,27) (13,23) (13,15) (13,26) (13,17) (13,19) (13,18) (13,14) (13,16) (14,23) (14,15) (14,28) (14,17) (14,19) (15,26) (15,28) (15,17) (15,19) (15,16) (16,27) (16,26) (16,28) (16,19) (16,18) (17,27) (17,23) (17,19) (18,26) (18,28) (19,23) (19,26) (19,28) (20,24) (20,21) (21,24) (23,26) (26,28) (27,28)\nIs there a path between node 8 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph128-0_19", + "image": "data/connectivity/graph_visual/hard/graph128.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,12) (0,14) (0,10) (0,17) (0,18) (0,1) (0,13) (0,11) (0,23) (0,4) (1,19) (1,12) (1,14) (1,6) (1,17) (1,18) (1,13) (1,7) (1,27) (1,23) (2,5) (2,8) (3,21) (3,20) (3,15) (3,25) (4,19) (4,22) (4,10) (4,6) (4,17) (4,18) (4,13) (4,7) (4,27) (5,8) (6,22) (6,12) (6,14) (6,10) (6,17) (6,18) (6,13) (6,11) (6,23) (7,22) (7,26) (7,14) (7,10) (7,17) (7,18) (7,9) (9,26) (9,14) (9,10) (9,17) (9,13) (9,11) (9,27) (9,23) (10,19) (10,26) (10,14) (10,17) (10,18) (10,13) (10,27) (10,23) (11,19) (11,22) (11,26) (11,12) (11,14) (11,17) (11,13) (11,27) (12,19) (12,22) (12,14) (12,17) (12,18) (12,27) (13,19) (13,26) (13,14) (13,17) (13,18) (14,19) (14,18) (14,23) (15,21) (15,16) (15,20) (15,25) (16,21) (17,23) (18,19) (18,22) (18,26) (19,27) (20,21) (20,24) (21,25) (22,26) (22,27) (22,23) (23,26) (23,27) (24,25) (26,27)\nIs there a path between node 0 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph397-18_4", + "image": "data/connectivity/graph_visual/hard/graph397.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,27) (0,1) (0,32) (0,9) (1,25) (1,20) (1,23) (1,24) (1,8) (2,25) (2,20) (2,23) (2,16) (2,19) (3,24) (3,32) (3,19) (4,13) (5,13) (5,7) (5,26) (5,29) (5,6) (5,22) (6,28) (7,13) (7,21) (7,22) (7,18) (7,28) (8,24) (8,31) (8,10) (8,9) (9,11) (9,10) (9,32) (9,19) (9,14) (10,24) (10,15) (11,25) (11,20) (11,19) (12,30) (12,20) (12,24) (13,21) (13,29) (13,18) (13,28) (14,20) (14,23) (14,24) (14,27) (14,15) (15,16) (16,27) (16,31) (17,28) (18,21) (18,26) (19,24) (20,30) (20,27) (20,32) (21,28) (24,25) (24,27) (24,31) (24,32) (25,27) (25,31) (27,32)\nIs there a path between node 18 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph41-19_23", + "image": "data/connectivity/graph_visual/hard/graph41.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,17) (0,2) (0,25) (0,14) (0,9) (0,15) (0,12) (0,1) (0,7) (0,16) (0,18) (0,11) (0,10) (0,5) (1,17) (1,2) (1,21) (1,14) (1,9) (1,15) (1,12) (1,19) (1,8) (1,7) (1,18) (1,11) (1,10) (1,5) (2,17) (2,21) (2,14) (2,9) (2,13) (2,3) (2,12) (2,6) (2,19) (2,7) (2,18) (2,11) (2,5) (3,17) (3,22) (3,21) (3,9) (3,15) (3,13) (3,6) (3,19) (3,8) (3,7) (3,16) (3,18) (3,11) (4,20) (4,23) (4,24) (5,17) (5,22) (5,21) (5,9) (5,15) (5,12) (5,19) (5,8) (5,16) (5,11) (5,10) (6,22) (6,25) (6,9) (6,15) (6,13) (6,12) (6,19) (6,8) (6,7) (6,16) (7,17) (7,22) (7,25) (7,9) (7,15) (7,13) (7,12) (7,19) (7,8) (7,16) (7,11) (7,10) (8,17) (8,22) (8,14) (8,12) (8,16) (8,18) (8,11) (9,17) (9,22) (9,25) (9,15) (9,13) (9,12) (9,19) (9,16) (9,18) (9,11) (10,17) (10,22) (10,25) (10,13) (10,19) (10,11) (11,17) (11,25) (11,14) (11,15) (11,13) (11,12) (11,19) (12,22) (12,21) (12,14) (12,19) (12,16) (13,22) (13,25) (13,21) (13,14) (13,16) (14,17) (14,21) (14,15) (14,19) (14,16) (14,18) (15,17) (15,25) (15,21) (15,16) (16,22) (16,25) (16,21) (16,19) (16,18) (17,22) (17,25) (17,21) (17,19) (17,18) (18,22) (18,21) (18,19) (19,22) (19,25) (19,21) (20,23) (20,24) (21,22) (21,25) (23,24)\nIs there a path between node 19 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph374-31_7", + "image": "data/connectivity/graph_visual/hard/graph374.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,25) (0,5) (0,14) (0,10) (0,3) (0,2) (0,18) (1,24) (1,15) (1,12) (2,14) (2,10) (2,3) (2,21) (2,16) (3,25) (3,5) (3,14) (3,10) (3,21) (3,18) (3,16) (4,31) (4,22) (4,20) (4,7) (4,28) (4,30) (4,9) (4,11) (4,17) (4,6) (4,23) (4,26) (5,25) (5,14) (5,10) (5,18) (5,16) (6,7) (6,28) (6,30) (6,9) (6,23) (7,31) (7,22) (7,20) (7,28) (7,19) (7,30) (7,9) (7,11) (7,17) (7,26) (8,29) (9,31) (9,22) (9,20) (9,19) (9,17) (9,23) (9,26) (10,25) (10,14) (10,18) (11,22) (11,20) (11,28) (11,19) (11,30) (11,17) (11,23) (12,27) (12,24) (12,15) (12,13) (13,15) (14,21) (14,18) (14,16) (15,27) (16,21) (16,18) (17,31) (17,20) (17,19) (17,30) (17,26) (18,25) (19,31) (19,22) (19,28) (19,30) (19,23) (20,31) (20,22) (20,28) (20,30) (20,23) (20,26) (22,31) (22,28) (22,23) (23,28) (23,30) (24,27) (26,31) (26,28) (28,31) (28,30) (30,31)\nIs there a path between node 31 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph510-20_26", + "image": "data/connectivity/graph_visual/hard/graph510.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,31) (0,1) (0,27) (0,13) (0,10) (0,25) (0,7) (0,21) (0,19) (0,15) (0,16) (0,17) (0,9) (0,20) (0,26) (0,30) (0,28) (0,2) (0,5) (0,24) (0,3) (1,10) (1,33) (1,23) (1,25) (1,8) (1,7) (1,21) (1,19) (1,16) (1,17) (1,26) (1,30) (1,22) (1,28) (1,5) (1,24) (1,3) (2,31) (2,13) (2,10) (2,33) (2,14) (2,23) (2,25) (2,8) (2,7) (2,21) (2,19) (2,15) (2,20) (2,26) (2,30) (2,22) (2,24) (2,3) (3,31) (3,27) (3,13) (3,33) (3,14) (3,23) (3,25) (3,21) (3,15) (3,16) (3,9) (3,30) (3,5) (3,24) (4,18) (4,11) (4,12) (4,29) (5,31) (5,27) (5,13) (5,10) (5,33) (5,25) (5,8) (5,7) (5,21) (5,19) (5,16) (5,20) (5,26) (5,30) (5,22) (6,12) (6,29) (6,32) (7,31) (7,13) (7,33) (7,25) (7,8) (7,19) (7,16) (7,17) (7,9) (7,20) (7,26) (7,30) (7,22) (7,28) (7,24) (8,31) (8,27) (8,10) (8,14) (8,21) (8,19) (8,15) (8,17) (8,9) (8,22) (8,28) (8,24) (9,31) (9,27) (9,13) (9,33) (9,23) (9,25) (9,16) (9,17) (9,26) (9,30) (9,28) (9,24) (10,31) (10,27) (10,13) (10,14) (10,23) (10,25) (10,21) (10,19) (10,15) (10,20) (10,26) (10,30) (10,22) (11,12) (11,29) (11,32) (12,18) (12,32) (13,31) (13,27) (13,33) (13,23) (13,25) (13,19) (13,15) (13,17) (13,20) (13,26) (13,22) (13,28) (13,24) (14,31) (14,27) (14,33) (14,23) (14,25) (14,21) (14,16) (14,17) (14,20) (14,26) (14,30) (14,22) (14,24) (15,31) (15,27) (15,33) (15,23) (15,25) (15,19) (15,17) (15,20) (15,30) (15,22) (15,24) (16,31) (16,17) (16,20) (16,30) (16,28) (16,24) (17,31) (17,27) (17,33) (17,25) (17,20) (17,30) (17,22) (19,31) (19,25) (19,21) (19,20) (19,26) (19,22) (19,28) (19,24) (20,27) (20,33) (20,23) (20,21) (20,26) (20,22) (20,28) (20,24) (21,31) (21,33) (21,23) (21,30) (21,28) (21,24) (22,31) (22,27) (22,23) (22,25) (22,30) (22,28) (22,24) (23,31) (23,27) (23,33) (24,31) (24,27) (24,33) (24,26) (24,30) (24,28) (25,30) (25,28) (26,31) (26,33) (26,30) (27,31) (27,30) (27,28) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nIs there a path between node 20 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph406-29_18", + "image": "data/connectivity/graph_visual/hard/graph406.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,21) (0,25) (0,3) (0,16) (0,15) (0,5) (0,1) (0,28) (1,25) (1,3) (1,5) (1,28) (2,22) (2,13) (2,24) (2,31) (2,26) (2,32) (2,17) (2,19) (2,30) (3,21) (3,25) (3,15) (3,5) (4,22) (4,13) (4,7) (4,31) (4,26) (4,32) (4,17) (4,30) (5,21) (5,16) (5,15) (6,18) (6,14) (6,9) (6,23) (6,20) (7,22) (7,24) (7,32) (7,17) (7,19) (7,12) (7,30) (9,18) (9,23) (9,20) (9,10) (9,29) (9,27) (10,18) (10,14) (10,11) (10,23) (10,20) (10,29) (10,27) (11,18) (11,23) (11,20) (11,29) (11,27) (12,22) (12,24) (12,31) (12,26) (12,32) (12,17) (12,19) (12,30) (13,22) (13,24) (13,31) (13,26) (13,32) (13,17) (13,30) (14,20) (14,27) (15,16) (15,28) (16,21) (17,24) (17,31) (17,26) (17,32) (17,19) (17,30) (18,23) (18,27) (19,22) (19,31) (19,26) (19,32) (20,23) (20,29) (20,27) (21,25) (22,31) (22,26) (22,32) (23,27) (24,31) (24,26) (24,32) (25,28) (26,31) (26,32) (27,29) (31,32)\nIs there a path between node 29 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph407-4_1", + "image": "data/connectivity/graph_visual/hard/graph407.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,12) (0,24) (0,31) (0,6) (0,1) (0,2) (0,19) (0,30) (1,26) (1,24) (1,31) (1,6) (1,2) (1,15) (1,5) (1,19) (1,30) (1,13) (2,22) (2,26) (2,24) (2,15) (2,5) (2,19) (2,30) (3,29) (3,16) (3,4) (3,28) (3,7) (3,8) (3,11) (3,20) (3,21) (3,25) (3,32) (3,23) (3,18) (4,29) (4,16) (4,28) (4,7) (4,8) (4,11) (4,21) (4,27) (4,17) (4,32) (4,23) (4,18) (5,22) (5,12) (5,24) (5,31) (5,6) (5,15) (5,19) (5,30) (6,26) (6,12) (6,24) (6,15) (6,19) (6,30) (6,13) (7,29) (7,16) (7,28) (7,8) (7,25) (7,27) (7,17) (7,32) (7,23) (7,18) (7,9) (8,28) (8,11) (8,25) (8,27) (8,17) (8,18) (8,9) (9,29) (9,28) (9,20) (9,21) (9,25) (9,27) (9,17) (9,32) (9,23) (9,18) (10,14) (11,29) (11,28) (11,20) (11,21) (11,25) (11,27) (11,17) (11,32) (11,23) (11,18) (12,24) (12,15) (12,19) (13,22) (13,26) (13,24) (13,31) (13,15) (13,19) (13,30) (15,26) (15,30) (16,29) (16,20) (16,21) (16,27) (16,17) (16,18) (17,29) (17,28) (17,20) (17,25) (17,27) (17,23) (17,18) (18,29) (18,28) (18,20) (18,21) (18,32) (19,26) (19,24) (19,31) (20,28) (20,27) (20,32) (20,23) (21,29) (21,28) (21,25) (21,32) (21,23) (22,24) (23,29) (23,25) (23,27) (23,32) (24,30) (25,29) (25,28) (25,27) (25,32) (26,30) (27,29) (27,28) (27,32) (28,32) (29,32) (30,31)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph375-22_6", + "image": "data/connectivity/graph_visual/hard/graph375.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,20) (0,4) (0,29) (0,11) (0,3) (0,1) (0,22) (0,10) (0,13) (0,16) (0,19) (0,7) (0,15) (0,25) (0,2) (0,23) (0,5) (1,18) (1,12) (1,9) (1,27) (1,20) (1,14) (1,11) (1,3) (1,24) (1,28) (1,6) (1,22) (1,10) (1,13) (1,15) (1,25) (1,2) (1,23) (1,5) (1,17) (2,18) (2,12) (2,9) (2,27) (2,29) (2,14) (2,11) (2,28) (2,6) (2,22) (2,10) (2,16) (2,7) (2,15) (2,25) (2,23) (2,17) (3,9) (3,27) (3,4) (3,29) (3,11) (3,24) (3,6) (3,21) (3,22) (3,10) (3,13) (3,16) (3,19) (3,7) (3,15) (3,25) (3,23) (4,18) (4,9) (4,27) (4,29) (4,14) (4,21) (4,22) (4,16) (4,19) (4,25) (4,23) (5,9) (5,27) (5,20) (5,29) (5,14) (5,28) (5,6) (5,22) (5,13) (5,16) (5,15) (5,25) (5,23) (6,12) (6,9) (6,27) (6,20) (6,14) (6,11) (6,24) (6,21) (6,22) (6,10) (6,13) (6,16) (6,19) (6,15) (6,25) (6,23) (7,18) (7,12) (7,9) (7,27) (7,11) (7,24) (7,28) (7,21) (7,13) (7,19) (7,25) (9,18) (9,12) (9,27) (9,20) (9,14) (9,28) (9,21) (9,22) (9,10) (9,19) (9,25) (9,23) (9,17) (10,18) (10,12) (10,20) (10,29) (10,14) (10,11) (10,21) (10,22) (10,13) (10,16) (10,19) (10,15) (10,17) (11,18) (11,27) (11,20) (11,14) (11,28) (11,13) (11,19) (11,15) (11,25) (11,23) (12,27) (12,22) (12,13) (12,16) (12,19) (12,25) (12,23) (13,20) (13,14) (13,24) (13,28) (13,21) (13,22) (13,16) (13,15) (13,25) (13,23) (13,17) (14,18) (14,27) (14,20) (14,29) (14,24) (14,28) (14,21) (14,22) (14,16) (14,19) (14,25) (14,17) (15,27) (15,20) (15,29) (15,24) (15,28) (15,21) (15,22) (15,19) (15,25) (15,17) (16,18) (16,20) (16,29) (16,24) (16,22) (16,19) (16,25) (16,17) (17,18) (17,27) (17,29) (17,24) (17,28) (17,21) (17,22) (17,19) (17,25) (17,23) (18,20) (18,29) (18,24) (18,28) (18,21) (18,19) (18,23) (19,27) (19,20) (19,29) (19,24) (19,28) (19,23) (20,22) (20,25) (21,27) (21,29) (21,24) (21,28) (21,25) (21,23) (22,27) (22,24) (22,28) (22,23) (23,27) (23,29) (23,24) (23,28) (23,25) (24,27) (24,28) (25,29) (25,28) (26,31) (27,29) (27,28) (28,29) (30,31)\nIs there a path between node 22 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph594-15_6", + "image": "data/connectivity/graph_visual/hard/graph594.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,3) (0,26) (0,7) (0,22) (0,17) (0,18) (0,8) (1,20) (1,33) (1,14) (1,30) (1,25) (1,12) (1,24) (1,19) (1,28) (1,9) (1,32) (1,21) (1,13) (1,2) (1,16) (2,33) (2,14) (2,23) (2,25) (2,27) (2,4) (2,19) (2,28) (2,9) (2,32) (2,21) (2,16) (3,6) (3,5) (3,26) (3,7) (3,11) (3,22) (3,17) (3,31) (3,15) (3,18) (3,29) (3,8) (3,10) (4,33) (4,14) (4,23) (4,30) (4,27) (4,24) (4,28) (4,9) (4,32) (4,21) (4,13) (4,16) (5,6) (5,11) (5,22) (5,17) (5,31) (5,15) (5,18) (5,29) (5,10) (6,26) (6,11) (6,22) (6,17) (6,31) (6,15) (6,8) (6,10) (7,26) (7,11) (7,22) (7,31) (7,15) (7,18) (7,29) (7,8) (8,26) (8,11) (8,22) (8,31) (8,15) (8,10) (9,20) (9,33) (9,14) (9,23) (9,12) (9,27) (9,24) (9,19) (9,21) (9,13) (9,16) (10,11) (10,17) (10,31) (10,15) (10,18) (11,17) (11,31) (11,18) (11,29) (12,20) (12,23) (12,25) (12,27) (12,19) (12,28) (12,32) (12,21) (12,13) (13,33) (13,14) (13,23) (13,30) (13,27) (13,24) (13,19) (13,32) (13,21) (13,16) (14,23) (14,30) (14,27) (14,19) (14,32) (14,16) (15,22) (15,31) (15,18) (15,29) (16,20) (16,23) (16,25) (16,19) (16,28) (16,32) (16,21) (17,26) (17,22) (17,31) (17,18) (17,29) (18,31) (18,29) (19,33) (19,25) (19,27) (19,28) (19,21) (20,33) (20,30) (20,25) (20,28) (20,32) (21,23) (21,30) (21,25) (21,27) (21,24) (22,31) (22,29) (23,30) (23,25) (23,27) (23,24) (23,28) (24,33) (24,27) (24,28) (24,32) (25,30) (25,27) (25,28) (25,32) (26,31) (26,29) (27,32) (28,33) (29,31) (30,32) (32,33)\nIs there a path between node 15 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph704-14_17", + "image": "data/connectivity/graph_visual/hard/graph704.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,8) (0,6) (0,7) (0,28) (0,4) (0,33) (0,32) (0,3) (0,24) (0,16) (0,9) (0,29) (0,14) (0,11) (0,17) (0,22) (0,5) (1,23) (1,8) (1,6) (1,7) (1,28) (1,12) (1,4) (1,33) (1,16) (1,9) (1,10) (1,14) (1,17) (2,26) (2,15) (2,19) (2,21) (3,20) (3,13) (3,25) (3,23) (3,8) (3,6) (3,7) (3,28) (3,12) (3,31) (3,4) (3,30) (3,33) (3,32) (3,27) (3,24) (3,10) (3,22) (3,5) (4,20) (4,23) (4,8) (4,6) (4,7) (4,28) (4,12) (4,30) (4,33) (4,32) (4,27) (4,24) (4,16) (4,9) (4,14) (4,17) (4,22) (4,5) (5,20) (5,6) (5,28) (5,12) (5,31) (5,30) (5,32) (5,24) (5,9) (5,29) (5,14) (5,11) (5,17) (5,22) (6,20) (6,13) (6,25) (6,23) (6,8) (6,7) (6,28) (6,12) (6,30) (6,32) (6,27) (6,24) (6,9) (6,10) (6,29) (6,14) (6,11) (6,22) (7,20) (7,25) (7,23) (7,8) (7,12) (7,31) (7,33) (7,27) (7,24) (7,16) (7,10) (7,14) (7,17) (7,22) (8,20) (8,13) (8,23) (8,12) (8,33) (8,32) (8,27) (8,24) (8,16) (8,9) (8,10) (8,29) (8,14) (8,11) (8,17) (8,22) (9,13) (9,25) (9,12) (9,31) (9,30) (9,33) (9,32) (9,27) (9,24) (9,16) (9,10) (9,29) (9,14) (9,17) (10,13) (10,25) (10,23) (10,28) (10,12) (10,32) (10,24) (10,16) (10,14) (10,11) (10,22) (11,13) (11,23) (11,28) (11,12) (11,31) (11,30) (11,32) (11,27) (11,24) (11,16) (11,29) (11,14) (11,17) (11,22) (12,20) (12,25) (12,23) (12,28) (12,31) (12,30) (12,27) (12,24) (12,16) (12,29) (12,14) (12,22) (13,20) (13,25) (13,28) (13,31) (13,30) (13,33) (13,32) (13,24) (13,16) (13,29) (13,14) (13,17) (13,22) (14,25) (14,28) (14,31) (14,30) (14,33) (14,32) (14,24) (14,16) (14,29) (14,17) (15,26) (15,19) (15,21) (16,20) (16,23) (16,28) (16,31) (16,33) (16,29) (16,17) (16,22) (17,25) (17,23) (17,28) (17,31) (17,32) (17,24) (17,29) (17,22) (19,26) (19,34) (20,25) (20,23) (20,30) (20,32) (20,27) (20,29) (20,22) (21,34) (22,23) (22,28) (22,31) (22,30) (22,33) (22,27) (22,29) (23,25) (23,30) (23,33) (23,32) (23,27) (23,24) (23,29) (24,25) (24,28) (24,31) (24,30) (24,32) (24,27) (25,28) (25,31) (25,30) (25,32) (25,29) (26,34) (27,28) (27,30) (27,33) (27,32) (27,29) (28,31) (28,32) (29,30) (29,32) (30,31) (30,33) (31,32)\nIs there a path between node 14 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph5-5_20", + "image": "data/connectivity/graph_visual/hard/graph5.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,15) (0,17) (0,9) (0,4) (0,6) (0,22) (0,23) (2,9) (2,12) (2,4) (2,11) (2,22) (2,23) (2,7) (3,24) (3,25) (3,14) (4,5) (4,22) (5,20) (5,15) (5,17) (5,9) (5,22) (6,15) (6,9) (6,16) (6,8) (6,22) (6,13) (7,11) (7,23) (8,22) (8,13) (9,22) (12,23) (14,18) (15,20) (15,22) (16,20) (17,20) (17,23) (18,24) (18,19) (19,24) (19,25) (20,22) (20,23) (22,23) (24,25)\nIs there a path between node 5 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph214-9_1", + "image": "data/connectivity/graph_visual/hard/graph214.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,5) (0,4) (0,22) (0,15) (2,28) (4,9) (4,15) (5,20) (5,22) (5,18) (6,25) (6,12) (7,10) (7,11) (8,21) (8,20) (8,15) (9,22) (9,18) (10,11) (11,24) (11,17) (11,27) (12,19) (12,13) (12,25) (13,25) (14,17) (15,20) (16,28) (18,21) (19,26) (21,22) (24,27) (25,29) (26,29)\nIs there a path between node 9 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph214-9_10", + "image": "data/connectivity/graph_visual/hard/graph214.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,5) (0,4) (0,22) (0,15) (2,28) (4,9) (4,15) (5,20) (5,22) (5,18) (6,25) (6,12) (7,10) (7,11) (8,21) (8,20) (8,15) (9,22) (9,18) (10,11) (11,24) (11,17) (11,27) (12,19) (12,13) (12,25) (13,25) (14,17) (15,20) (16,28) (18,21) (19,26) (21,22) (24,27) (25,29) (26,29)\nIs there a path between node 9 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph134-16_10", + "image": "data/connectivity/graph_visual/hard/graph134.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,16) (0,4) (1,27) (1,26) (1,10) (1,13) (1,12) (1,24) (1,19) (1,11) (1,7) (1,6) (1,14) (1,3) (1,18) (1,20) (2,4) (3,9) (3,27) (3,10) (3,21) (3,25) (3,13) (3,24) (3,15) (3,23) (3,19) (3,11) (3,7) (3,6) (3,14) (3,18) (5,9) (5,26) (5,22) (5,10) (5,13) (5,12) (5,15) (5,17) (5,23) (5,19) (5,11) (5,7) (5,6) (5,14) (6,27) (6,26) (6,10) (6,21) (6,25) (6,13) (6,12) (6,8) (6,17) (6,23) (6,19) (6,11) (6,7) (6,14) (6,18) (6,20) (7,9) (7,27) (7,22) (7,10) (7,21) (7,13) (7,12) (7,8) (7,24) (7,15) (7,17) (7,19) (7,11) (7,14) (8,9) (8,27) (8,22) (8,10) (8,21) (8,25) (8,13) (8,12) (8,15) (8,17) (8,23) (8,19) (8,11) (8,14) (8,18) (8,20) (9,27) (9,10) (9,21) (9,13) (9,12) (9,24) (9,15) (9,17) (9,23) (9,19) (9,11) (9,20) (10,27) (10,26) (10,22) (10,21) (10,25) (10,13) (10,24) (10,15) (10,17) (10,19) (10,11) (10,14) (11,27) (11,26) (11,22) (11,25) (11,13) (11,15) (11,17) (11,14) (11,18) (11,20) (12,27) (12,26) (12,22) (12,21) (12,13) (12,15) (12,17) (12,23) (12,19) (12,18) (12,20) (13,22) (13,21) (13,24) (13,15) (13,17) (13,23) (13,19) (13,14) (13,18) (13,20) (14,27) (14,26) (14,24) (14,15) (14,17) (14,23) (14,19) (14,20) (15,27) (15,22) (15,25) (15,24) (15,17) (15,23) (15,20) (17,22) (17,25) (17,23) (17,19) (17,18) (17,20) (18,26) (18,24) (18,23) (18,19) (19,26) (19,21) (19,25) (19,24) (19,23) (19,20) (20,27) (20,26) (20,21) (20,24) (20,23) (21,27) (21,22) (21,25) (21,24) (22,27) (22,26) (23,27) (23,26) (23,24) (25,27) (25,26)\nIs there a path between node 16 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph507-16_0", + "image": "data/connectivity/graph_visual/hard/graph507.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,29) (0,21) (0,6) (0,28) (0,24) (0,9) (0,2) (0,13) (0,15) (0,10) (1,30) (1,25) (1,33) (1,5) (1,27) (1,11) (1,22) (2,29) (2,6) (2,14) (2,8) (2,9) (2,13) (2,15) (2,26) (2,17) (2,32) (3,19) (3,20) (5,30) (5,27) (5,11) (5,31) (5,22) (6,29) (6,28) (6,14) (6,8) (6,9) (6,12) (6,18) (6,15) (6,26) (6,17) (6,32) (6,7) (6,10) (7,21) (7,28) (7,14) (7,8) (7,9) (7,16) (7,18) (7,15) (7,17) (7,32) (8,21) (8,28) (8,24) (8,9) (8,16) (8,12) (8,13) (8,23) (8,18) (8,15) (8,26) (8,17) (8,32) (8,10) (9,28) (9,14) (9,24) (9,12) (9,13) (9,23) (9,18) (9,15) (9,26) (9,17) (9,10) (10,29) (10,21) (10,28) (10,14) (10,24) (10,12) (10,13) (10,23) (10,18) (10,17) (11,30) (11,25) (11,33) (11,27) (11,31) (11,22) (12,29) (12,21) (12,28) (12,24) (12,16) (12,13) (12,23) (12,18) (12,15) (12,26) (12,32) (13,21) (13,28) (13,14) (13,24) (13,16) (13,23) (13,18) (13,26) (13,17) (14,29) (14,21) (14,28) (14,24) (14,16) (14,18) (14,32) (15,29) (15,21) (15,28) (15,24) (15,23) (15,32) (16,29) (16,21) (16,28) (16,24) (16,23) (16,18) (16,26) (16,32) (17,21) (17,23) (17,18) (17,26) (18,29) (18,21) (18,28) (18,24) (18,23) (18,26) (18,32) (19,20) (21,28) (21,23) (21,26) (21,32) (22,30) (22,25) (22,33) (22,27) (22,31) (23,29) (23,28) (23,24) (23,26) (23,32) (24,26) (24,32) (25,33) (25,31) (26,29) (26,28) (26,32) (27,30) (27,33) (28,29) (29,32) (30,33) (31,33)\nIs there a path between node 16 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph285-10_26", + "image": "data/connectivity/graph_visual/hard/graph285.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,3) (0,11) (0,15) (0,25) (0,31) (0,23) (0,14) (1,28) (1,20) (1,12) (1,21) (1,19) (1,24) (1,27) (1,13) (1,6) (2,20) (2,22) (2,21) (2,19) (2,13) (2,6) (3,15) (3,4) (3,25) (3,23) (4,9) (4,15) (4,14) (5,8) (5,17) (5,10) (5,26) (5,7) (5,16) (6,20) (6,21) (6,19) (6,27) (6,13) (7,17) (7,16) (7,29) (8,17) (9,11) (9,15) (9,31) (9,23) (9,14) (10,17) (11,15) (11,30) (11,23) (11,14) (12,20) (12,22) (12,19) (12,27) (12,13) (12,18) (13,28) (13,22) (13,21) (13,24) (13,27) (13,18) (14,15) (14,25) (14,31) (14,23) (15,25) (15,30) (15,23) (16,26) (17,26) (17,29) (18,28) (18,20) (18,22) (18,21) (18,19) (18,24) (18,27) (19,22) (19,21) (19,24) (19,27) (20,28) (20,22) (20,21) (20,24) (20,27) (21,28) (21,22) (21,24) (22,24) (22,27) (23,30) (23,31) (24,28) (25,31) (27,28) (30,31)\nIs there a path between node 10 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph300-28_20", + "image": "data/connectivity/graph_visual/hard/graph300.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,22) (0,19) (0,24) (0,1) (0,2) (0,5) (0,28) (0,29) (0,31) (0,12) (0,23) (0,15) (0,11) (0,10) (1,6) (1,22) (1,19) (1,24) (1,2) (1,5) (1,28) (1,29) (1,31) (1,14) (1,23) (1,15) (1,11) (2,6) (2,22) (2,19) (2,5) (2,28) (2,18) (2,31) (2,14) (2,12) (2,15) (2,11) (2,10) (3,6) (3,19) (3,28) (3,29) (3,18) (3,23) (3,15) (3,10) (4,25) (4,20) (4,17) (4,30) (4,27) (4,9) (4,21) (4,26) (4,13) (4,7) (4,16) (5,6) (5,19) (5,24) (5,28) (5,18) (5,31) (5,14) (5,12) (5,23) (5,15) (5,11) (6,19) (6,24) (6,29) (6,18) (6,31) (6,12) (6,15) (6,10) (7,25) (7,20) (7,17) (7,30) (7,27) (7,9) (7,21) (7,26) (7,13) (7,16) (8,25) (8,9) (9,25) (9,20) (9,17) (9,30) (9,21) (9,26) (9,13) (9,16) (10,22) (10,24) (10,28) (10,29) (10,18) (10,31) (10,14) (10,15) (11,24) (11,28) (11,29) (11,18) (11,14) (11,12) (11,15) (12,29) (12,18) (12,31) (12,15) (13,20) (13,17) (13,30) (13,27) (13,21) (13,26) (13,16) (14,22) (14,19) (14,24) (14,18) (14,31) (14,23) (14,15) (15,22) (15,19) (15,24) (15,28) (15,29) (15,18) (16,20) (16,17) (16,30) (16,21) (16,26) (17,25) (17,20) (17,27) (18,22) (18,19) (18,24) (18,28) (18,29) (18,31) (19,22) (19,24) (19,28) (19,29) (19,23) (20,30) (20,27) (20,21) (20,26) (21,25) (21,30) (21,27) (21,26) (22,24) (22,28) (22,31) (22,23) (23,28) (23,29) (23,31) (24,28) (24,31) (25,30) (26,30) (26,27) (28,29) (28,31) (29,31)\nIs there a path between node 28 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph246-23_14", + "image": "data/connectivity/graph_visual/hard/graph246.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,3) (0,15) (0,14) (0,1) (0,10) (0,29) (0,20) (0,26) (0,22) (0,18) (0,7) (0,4) (0,2) (1,27) (1,14) (1,10) (1,12) (1,20) (1,26) (1,22) (1,18) (1,11) (1,7) (1,4) (1,2) (2,3) (2,27) (2,15) (2,10) (2,12) (2,20) (2,26) (2,22) (2,18) (2,11) (2,7) (2,4) (2,25) (2,21) (2,19) (3,27) (3,15) (3,14) (3,10) (3,29) (3,20) (3,22) (3,18) (3,11) (3,4) (3,25) (3,21) (3,19) (4,15) (4,14) (4,10) (4,29) (4,12) (4,20) (4,26) (4,18) (4,25) (4,21) (4,19) (5,17) (5,6) (5,30) (5,16) (5,13) (5,24) (5,9) (6,23) (6,30) (6,16) (6,13) (6,8) (6,24) (6,9) (7,27) (7,15) (7,10) (7,29) (7,12) (7,20) (7,26) (7,22) (7,11) (7,25) (7,19) (8,17) (8,28) (8,23) (8,30) (8,16) (8,13) (8,24) (8,9) (9,28) (9,23) (9,30) (9,16) (10,15) (10,14) (10,12) (10,20) (10,26) (10,22) (10,18) (10,11) (10,25) (10,19) (11,27) (11,15) (11,14) (11,12) (11,20) (11,26) (11,22) (11,18) (11,25) (11,21) (12,27) (12,15) (12,14) (12,20) (12,26) (12,22) (12,21) (13,17) (13,28) (13,23) (13,30) (13,16) (14,27) (14,15) (14,20) (14,26) (14,22) (14,18) (14,25) (14,21) (14,19) (15,20) (15,26) (15,22) (15,18) (15,21) (16,17) (16,28) (16,23) (16,24) (17,28) (17,23) (17,30) (18,27) (18,29) (18,20) (18,21) (18,19) (19,29) (19,20) (19,25) (19,21) (20,27) (20,26) (20,22) (20,25) (20,21) (21,29) (21,26) (21,22) (21,25) (22,29) (22,25) (23,28) (23,30) (24,28) (26,27) (26,29) (27,29)\nIs there a path between node 23 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph115-8_13", + "image": "data/connectivity/graph_visual/hard/graph115.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,13) (1,6) (1,12) (1,20) (1,5) (1,27) (1,24) (1,14) (1,16) (2,7) (3,17) (3,21) (3,26) (3,22) (3,10) (3,24) (3,14) (3,16) (4,19) (4,21) (4,6) (4,20) (4,9) (4,5) (4,23) (4,10) (4,14) (4,15) (4,16) (4,8) (5,13) (5,12) (5,27) (6,21) (6,26) (6,16) (6,8) (8,17) (8,26) (8,23) (8,15) (9,27) (9,22) (9,10) (9,24) (10,12) (10,20) (10,27) (10,22) (10,24) (10,15) (10,16) (12,13) (12,24) (12,15) (12,16) (13,22) (13,15) (14,19) (14,20) (14,26) (14,18) (14,23) (14,24) (15,27) (15,23) (15,24) (16,19) (16,21) (16,20) (16,23) (17,20) (17,23) (18,21) (18,23) (19,23) (19,24) (21,22) (21,24) (22,27) (22,23) (23,26) (23,27) (24,27)\nIs there a path between node 8 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph610-4_6", + "image": "data/connectivity/graph_visual/hard/graph610.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,31) (0,11) (0,18) (0,1) (1,28) (1,31) (1,13) (1,8) (1,5) (1,32) (1,34) (2,17) (3,14) (3,15) (3,24) (4,32) (4,34) (5,8) (5,9) (6,25) (6,10) (6,15) (6,7) (6,19) (7,14) (7,10) (7,16) (7,12) (7,21) (8,18) (9,31) (9,11) (9,34) (10,23) (10,29) (10,33) (10,16) (10,30) (11,20) (11,18) (12,23) (12,14) (12,25) (12,19) (12,24) (13,34) (14,25) (15,23) (15,25) (15,24) (16,23) (16,25) (16,29) (16,33) (16,17) (17,30) (17,21) (17,24) (18,22) (18,20) (19,24) (20,28) (20,32) (20,34) (22,26) (22,34) (23,25) (23,30) (24,33) (24,30) (25,29) (25,33) (26,27) (27,32) (28,32) (28,34) (29,30) (30,33) (31,32)\nIs there a path between node 4 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph189-17_11", + "image": "data/connectivity/graph_visual/hard/graph189.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,1) (0,17) (0,3) (0,23) (0,10) (0,12) (1,21) (1,26) (1,24) (2,4) (2,22) (2,26) (2,12) (3,17) (3,29) (3,24) (3,12) (3,16) (4,17) (4,23) (4,10) (5,6) (5,27) (5,14) (5,19) (6,8) (6,11) (6,25) (6,27) (7,22) (7,13) (8,11) (8,9) (9,11) (9,20) (9,15) (9,25) (10,18) (10,17) (10,22) (10,28) (11,20) (11,15) (11,19) (12,17) (12,23) (12,16) (12,13) (13,18) (13,29) (13,22) (13,24) (13,16) (14,15) (14,19) (16,17) (16,29) (16,26) (17,28) (17,26) (18,28) (18,23) (21,29) (23,28) (23,26) (23,24) (26,29)\nIs there a path between node 17 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph181-28_5", + "image": "data/connectivity/graph_visual/hard/graph181.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,18) (1,25) (1,22) (1,15) (1,20) (1,19) (1,11) (1,2) (1,23) (1,24) (2,25) (2,22) (2,15) (2,3) (2,11) (2,7) (2,6) (2,14) (2,24) (3,22) (3,16) (3,15) (3,19) (3,7) (3,23) (3,6) (3,14) (4,21) (4,9) (4,28) (4,8) (4,26) (4,17) (5,9) (5,12) (5,27) (5,26) (5,17) (6,25) (6,16) (6,15) (6,20) (6,19) (6,7) (6,14) (6,24) (7,25) (7,22) (7,16) (7,20) (7,19) (7,11) (7,23) (7,24) (8,21) (8,9) (8,12) (8,26) (8,17) (9,21) (9,10) (9,28) (9,12) (9,27) (9,26) (9,17) (10,21) (10,28) (10,12) (10,26) (10,17) (11,22) (11,16) (11,15) (11,20) (11,19) (11,23) (11,14) (11,24) (12,27) (12,26) (12,17) (13,18) (14,16) (14,15) (14,20) (14,24) (15,22) (15,16) (15,20) (15,23) (15,24) (16,25) (16,22) (16,20) (16,19) (16,23) (16,24) (17,21) (17,27) (17,26) (19,25) (19,22) (19,23) (19,24) (20,22) (20,23) (20,24) (21,28) (21,27) (21,26) (22,25) (23,25) (23,24) (24,25) (26,27)\nIs there a path between node 28 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph494-14_2", + "image": "data/connectivity/graph_visual/hard/graph494.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,12) (0,13) (0,2) (0,14) (0,23) (0,8) (0,1) (0,25) (0,27) (0,10) (1,29) (1,13) (1,19) (1,28) (1,23) (1,30) (1,25) (1,24) (2,12) (2,5) (2,14) (2,17) (2,23) (3,7) (3,12) (3,19) (3,23) (3,8) (3,30) (3,25) (3,24) (4,33) (5,20) (5,23) (5,30) (6,15) (6,11) (7,32) (7,17) (7,23) (7,8) (7,10) (8,29) (8,12) (8,32) (8,20) (8,19) (8,17) (8,30) (9,29) (9,28) (9,30) (9,24) (10,13) (10,20) (10,14) (10,22) (11,31) (12,13) (12,23) (12,27) (12,26) (13,29) (13,32) (13,14) (13,28) (13,30) (13,24) (14,17) (14,30) (14,22) (14,27) (15,16) (15,31) (15,33) (17,32) (17,20) (17,19) (17,27) (17,24) (17,26) (18,21) (20,28) (20,30) (20,25) (21,31) (22,32) (22,28) (22,30) (23,28) (23,25) (23,27) (24,29) (24,28) (24,26) (25,32) (26,29) (26,27) (27,32) (27,30) (28,32) (28,30)\nIs there a path between node 14 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph662-26_0", + "image": "data/connectivity/graph_visual/hard/graph662.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,7) (0,11) (0,16) (0,3) (0,12) (0,4) (0,34) (0,26) (1,7) (1,10) (1,14) (1,11) (1,30) (1,8) (1,16) (1,29) (2,33) (2,21) (2,10) (2,14) (2,15) (2,3) (2,12) (2,23) (3,31) (3,22) (3,11) (3,32) (3,12) (3,4) (3,34) (3,26) (4,24) (4,5) (4,33) (4,7) (4,11) (4,19) (4,15) (4,30) (4,25) (4,12) (4,9) (4,23) (5,33) (5,22) (5,15) (5,9) (5,23) (6,18) (7,33) (7,31) (7,22) (7,14) (7,30) (7,12) (7,34) (8,33) (8,31) (8,30) (8,25) (8,16) (8,23) (8,29) (9,21) (9,31) (9,22) (9,30) (9,32) (9,26) (10,21) (10,32) (10,23) (11,29) (12,25) (14,24) (14,31) (14,22) (14,16) (14,34) (15,21) (15,31) (15,19) (15,32) (16,24) (16,19) (16,23) (16,26) (18,28) (19,24) (19,21) (19,31) (19,25) (19,23) (21,22) (21,30) (22,24) (22,25) (22,29) (23,31) (23,34) (24,31) (24,34) (25,31) (25,34) (26,33) (26,31) (26,30) (27,28) (29,30) (29,32) (30,33) (30,31)\nIs there a path between node 26 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph431-29_13", + "image": "data/connectivity/graph_visual/hard/graph431.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,3) (0,7) (0,5) (0,9) (0,25) (0,26) (0,15) (0,22) (0,13) (0,31) (0,1) (0,20) (1,3) (1,7) (1,5) (1,28) (1,9) (1,15) (1,22) (1,31) (1,30) (2,16) (2,17) (2,6) (2,14) (2,21) (2,32) (2,24) (2,8) (2,27) (2,10) (2,29) (2,19) (3,23) (3,18) (3,5) (3,28) (3,9) (3,25) (3,20) (3,30) (4,16) (4,17) (4,14) (4,21) (4,32) (4,12) (4,24) (4,8) (4,27) (4,10) (4,29) (4,11) (4,19) (5,23) (5,18) (5,7) (5,28) (5,9) (5,25) (5,26) (5,15) (5,22) (5,20) (5,30) (6,17) (6,14) (6,32) (6,12) (6,24) (6,8) (6,27) (6,19) (7,18) (7,9) (7,25) (7,26) (7,22) (7,13) (7,31) (7,20) (8,16) (8,17) (8,14) (8,32) (8,24) (8,27) (8,29) (8,19) (9,23) (9,18) (9,28) (9,25) (9,15) (9,22) (9,13) (9,31) (9,20) (10,16) (10,17) (10,21) (10,32) (10,12) (10,19) (11,16) (11,14) (11,21) (11,12) (11,24) (11,27) (11,29) (11,19) (12,16) (12,17) (12,14) (12,32) (12,27) (12,29) (12,19) (13,23) (13,18) (13,26) (13,15) (13,20) (13,30) (14,16) (14,32) (14,24) (14,27) (14,19) (15,23) (15,18) (15,28) (15,25) (15,26) (15,22) (15,31) (15,20) (16,17) (16,21) (16,32) (16,29) (17,21) (17,32) (17,24) (17,27) (17,29) (17,19) (18,25) (18,26) (18,22) (18,31) (18,30) (19,21) (19,32) (19,24) (19,27) (19,29) (20,28) (20,25) (20,26) (20,22) (20,31) (21,32) (21,24) (21,27) (22,23) (22,28) (22,25) (22,30) (23,28) (23,31) (23,30) (24,32) (24,29) (25,28) (25,26) (26,28) (26,30) (27,32) (27,29) (28,31) (28,30) (29,32)\nIs there a path between node 29 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph75-15_24", + "image": "data/connectivity/graph_visual/hard/graph75.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,18) (0,16) (0,11) (0,20) (0,22) (0,14) (0,23) (0,25) (0,4) (0,5) (0,2) (1,19) (1,17) (1,21) (1,9) (1,3) (2,10) (2,16) (2,7) (2,20) (2,22) (2,6) (2,8) (2,23) (2,25) (3,19) (3,12) (3,21) (3,9) (4,10) (4,18) (4,16) (4,11) (4,20) (4,22) (4,14) (4,8) (4,13) (4,23) (4,25) (4,5) (5,11) (5,7) (5,20) (5,22) (5,14) (5,8) (5,25) (6,10) (6,18) (6,16) (6,11) (6,7) (6,14) (6,8) (6,13) (6,23) (6,25) (7,10) (7,18) (7,11) (7,20) (7,14) (7,8) (7,13) (7,23) (7,25) (8,10) (8,16) (8,11) (8,20) (8,22) (8,14) (8,13) (8,23) (8,25) (9,15) (9,19) (9,17) (9,21) (10,18) (10,16) (10,11) (10,20) (10,14) (10,13) (10,23) (10,25) (11,18) (11,16) (11,22) (11,13) (12,15) (12,26) (12,21) (13,16) (13,20) (13,22) (13,14) (13,23) (14,18) (14,16) (14,20) (14,22) (14,23) (14,25) (15,26) (15,19) (15,17) (15,21) (16,18) (16,20) (16,22) (16,23) (16,25) (17,19) (18,20) (18,22) (18,23) (19,26) (20,22) (20,23) (21,26) (22,25) (23,25)\nIs there a path between node 15 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph128-17_3", + "image": "data/connectivity/graph_visual/hard/graph128.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,12) (0,14) (0,10) (0,17) (0,18) (0,1) (0,13) (0,11) (0,23) (0,4) (1,19) (1,12) (1,14) (1,6) (1,17) (1,18) (1,13) (1,7) (1,27) (1,23) (2,5) (2,8) (3,21) (3,20) (3,15) (3,25) (4,19) (4,22) (4,10) (4,6) (4,17) (4,18) (4,13) (4,7) (4,27) (5,8) (6,22) (6,12) (6,14) (6,10) (6,17) (6,18) (6,13) (6,11) (6,23) (7,22) (7,26) (7,14) (7,10) (7,17) (7,18) (7,9) (9,26) (9,14) (9,10) (9,17) (9,13) (9,11) (9,27) (9,23) (10,19) (10,26) (10,14) (10,17) (10,18) (10,13) (10,27) (10,23) (11,19) (11,22) (11,26) (11,12) (11,14) (11,17) (11,13) (11,27) (12,19) (12,22) (12,14) (12,17) (12,18) (12,27) (13,19) (13,26) (13,14) (13,17) (13,18) (14,19) (14,18) (14,23) (15,21) (15,16) (15,20) (15,25) (16,21) (17,23) (18,19) (18,22) (18,26) (19,27) (20,21) (20,24) (21,25) (22,26) (22,27) (22,23) (23,26) (23,27) (24,25) (26,27)\nIs there a path between node 17 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph175-20_1", + "image": "data/connectivity/graph_visual/hard/graph175.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,5) (0,7) (0,6) (0,26) (0,24) (0,15) (0,22) (0,18) (1,2) (1,28) (1,3) (1,13) (1,9) (1,8) (1,4) (2,27) (2,11) (2,14) (2,17) (2,16) (2,28) (2,3) (2,9) (2,4) (3,27) (3,11) (3,25) (3,28) (3,13) (3,9) (3,8) (3,23) (3,12) (4,10) (4,11) (4,25) (4,14) (4,17) (4,16) (4,28) (4,13) (4,23) (5,21) (5,6) (5,26) (5,20) (5,19) (5,15) (5,22) (5,18) (6,7) (6,24) (6,20) (6,19) (6,22) (6,18) (7,21) (7,26) (7,20) (7,15) (8,27) (8,10) (8,11) (8,25) (8,14) (8,16) (8,23) (8,12) (9,27) (9,16) (9,28) (9,13) (9,23) (9,12) (10,27) (10,11) (10,25) (10,14) (10,17) (10,28) (10,13) (10,23) (10,12) (11,14) (11,16) (11,13) (11,12) (12,27) (12,14) (12,17) (12,28) (12,13) (13,27) (13,25) (13,14) (13,17) (13,16) (13,28) (13,23) (14,27) (14,17) (14,16) (14,28) (14,23) (15,21) (15,26) (15,24) (15,20) (15,22) (16,27) (16,25) (16,17) (16,28) (16,23) (17,27) (17,28) (18,21) (18,26) (18,20) (18,19) (19,26) (20,21) (20,26) (20,24) (21,26) (21,24) (22,26) (22,24) (23,27) (23,25) (25,28) (27,28)\nIs there a path between node 20 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph554-7_25", + "image": "data/connectivity/graph_visual/hard/graph554.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,3) (0,14) (0,1) (0,17) (1,23) (1,3) (1,13) (1,14) (2,30) (2,20) (2,31) (3,25) (3,14) (3,6) (3,7) (3,10) (3,33) (4,27) (4,8) (4,5) (4,20) (5,27) (5,22) (5,15) (5,8) (5,29) (6,11) (6,19) (6,18) (6,13) (6,7) (6,17) (7,13) (7,33) (8,26) (8,12) (8,29) (8,24) (9,19) (9,33) (10,11) (10,23) (10,19) (11,23) (11,19) (11,13) (11,21) (12,30) (12,22) (12,31) (13,23) (13,19) (13,14) (14,28) (15,30) (15,16) (15,32) (15,31) (15,24) (16,32) (16,20) (17,18) (17,33) (18,25) (18,21) (19,25) (19,21) (20,30) (20,31) (20,24) (22,24) (23,25) (23,28) (24,27) (24,30) (24,31) (25,33) (26,29) (29,32) (31,32)\nIs there a path between node 7 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph394-12_23", + "image": "data/connectivity/graph_visual/hard/graph394.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,12) (0,24) (0,5) (0,32) (0,18) (0,23) (0,25) (1,20) (2,21) (2,13) (2,29) (3,12) (3,7) (3,11) (3,23) (3,25) (4,27) (4,12) (4,32) (5,30) (5,14) (7,10) (7,11) (7,23) (7,25) (8,27) (8,18) (8,30) (8,11) (8,25) (9,28) (10,27) (10,24) (10,32) (10,18) (10,23) (11,22) (11,14) (12,27) (12,24) (12,25) (13,15) (13,21) (13,29) (14,27) (14,32) (14,23) (15,21) (19,20) (22,30) (22,23) (23,30) (24,32) (24,30) (24,25) (25,27)\nIs there a path between node 12 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph112-1_26", + "image": "data/connectivity/graph_visual/hard/graph112.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,22) (0,11) (0,10) (0,23) (0,4) (0,9) (0,19) (1,17) (1,27) (1,15) (1,23) (1,24) (1,5) (1,18) (2,15) (2,10) (2,23) (2,5) (2,6) (2,16) (4,17) (4,27) (4,16) (4,25) (5,27) (5,11) (5,24) (5,7) (5,16) (5,25) (5,21) (5,18) (6,17) (6,13) (6,27) (6,11) (6,10) (6,14) (6,16) (6,8) (6,19) (7,20) (7,15) (7,10) (7,24) (7,16) (7,8) (7,19) (7,25) (7,21) (8,20) (8,17) (8,27) (8,11) (8,24) (8,16) (9,20) (9,27) (9,11) (9,16) (9,25) (10,13) (10,27) (10,15) (10,16) (11,20) (11,13) (11,14) (11,24) (11,21) (13,20) (13,14) (13,16) (14,22) (14,15) (14,23) (14,19) (15,24) (15,19) (15,25) (16,22) (16,17) (16,23) (17,22) (17,23) (17,25) (18,19) (18,21) (19,27) (19,24) (19,25) (21,25) (23,27) (25,27)\nIs there a path between node 1 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph318-19_22", + "image": "data/connectivity/graph_visual/hard/graph318.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,22) (0,20) (0,21) (0,12) (0,4) (1,27) (1,9) (1,14) (1,25) (2,17) (2,14) (2,31) (3,13) (3,6) (3,20) (3,21) (3,19) (4,13) (5,11) (5,8) (5,7) (7,29) (7,16) (7,30) (8,29) (8,11) (8,10) (9,17) (9,27) (9,25) (10,16) (12,21) (12,19) (13,28) (13,20) (13,21) (14,27) (14,23) (14,31) (15,27) (15,23) (15,26) (17,23) (17,26) (18,21) (21,28) (23,31) (25,31) (25,26) (27,31) (29,30)\nIs there a path between node 19 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph586-15_16", + "image": "data/connectivity/graph_visual/hard/graph586.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,15) (0,4) (0,8) (0,20) (0,25) (0,27) (0,18) (0,22) (0,19) (0,6) (0,12) (1,15) (1,16) (1,20) (1,18) (1,22) (1,3) (1,19) (1,6) (1,12) (1,29) (2,14) (2,24) (2,28) (2,31) (2,26) (3,4) (3,8) (3,27) (3,7) (3,19) (3,12) (3,29) (4,33) (4,8) (4,16) (4,20) (4,25) (4,18) (4,22) (4,19) (4,6) (4,29) (5,14) (5,24) (5,11) (5,28) (5,17) (5,31) (5,26) (5,32) (6,33) (6,16) (6,20) (6,25) (6,27) (6,22) (6,7) (6,12) (6,29) (7,15) (7,33) (7,8) (7,20) (7,27) (7,18) (7,22) (7,19) (7,29) (8,15) (8,33) (8,16) (8,18) (8,22) (8,19) (8,12) (8,29) (9,14) (9,24) (9,23) (9,11) (9,26) (9,32) (10,21) (11,14) (11,24) (11,23) (11,28) (11,17) (11,31) (11,26) (11,32) (12,15) (12,33) (12,16) (12,20) (12,25) (12,27) (13,21) (14,23) (14,28) (14,26) (14,32) (15,20) (15,18) (15,29) (16,33) (16,20) (16,27) (16,18) (16,22) (16,29) (17,24) (17,23) (17,30) (17,26) (17,32) (18,33) (18,20) (18,25) (18,27) (18,29) (19,33) (19,27) (19,22) (19,29) (20,33) (20,27) (20,22) (20,29) (22,33) (22,25) (22,27) (22,29) (23,24) (23,28) (23,30) (23,31) (23,32) (24,28) (24,30) (24,31) (24,32) (25,33) (25,27) (26,28) (26,30) (26,31) (28,30) (28,32) (29,33) (30,31)\nIs there a path between node 15 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph641-28_29", + "image": "data/connectivity/graph_visual/hard/graph641.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,28) (0,15) (0,19) (0,6) (0,2) (0,33) (0,18) (0,5) (0,7) (0,9) (0,34) (1,26) (1,23) (1,3) (1,4) (1,20) (1,25) (1,13) (1,11) (2,28) (2,14) (2,15) (2,19) (2,6) (2,27) (2,8) (2,24) (2,5) (2,7) (2,9) (3,26) (3,31) (3,23) (3,4) (3,17) (3,29) (3,20) (3,25) (3,13) (3,11) (3,30) (4,26) (4,31) (4,23) (4,29) (4,20) (4,25) (4,13) (4,11) (5,28) (5,14) (5,10) (5,19) (5,6) (5,27) (5,33) (5,8) (5,18) (5,24) (5,7) (6,28) (6,15) (6,10) (6,19) (6,27) (6,8) (6,18) (6,7) (6,9) (6,34) (7,28) (7,14) (7,10) (7,19) (7,27) (7,8) (7,18) (7,9) (7,34) (8,28) (8,14) (8,10) (8,27) (8,33) (8,24) (8,34) (9,28) (9,15) (9,10) (9,33) (9,18) (9,24) (9,34) (10,28) (10,15) (10,19) (10,27) (11,23) (11,17) (11,29) (11,20) (11,13) (12,21) (12,22) (12,16) (13,23) (13,17) (13,29) (13,25) (13,30) (14,28) (14,15) (14,27) (14,33) (14,24) (14,34) (15,28) (15,19) (15,27) (15,18) (16,21) (16,32) (17,26) (17,23) (17,29) (17,30) (18,28) (18,19) (18,27) (18,24) (19,27) (19,24) (19,34) (20,26) (20,31) (20,29) (20,30) (21,22) (21,32) (23,26) (23,29) (23,25) (24,28) (24,27) (25,26) (25,31) (25,29) (25,30) (26,31) (26,29) (26,30) (27,34) (28,33) (28,34) (29,31) (29,30) (30,31) (33,34)\nIs there a path between node 28 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph17-7_20", + "image": "data/connectivity/graph_visual/hard/graph17.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,24) (0,22) (0,1) (0,16) (1,4) (1,9) (1,12) (1,22) (2,14) (2,9) (2,19) (2,12) (2,16) (2,25) (2,11) (3,13) (3,7) (3,10) (3,21) (3,15) (4,23) (4,9) (4,19) (4,18) (4,11) (4,17) (5,15) (6,18) (6,25) (6,8) (8,14) (8,19) (8,24) (8,12) (8,16) (8,25) (8,17) (9,16) (9,17) (10,21) (11,23) (11,17) (11,20) (12,20) (13,15) (14,19) (14,22) (14,16) (14,17) (14,20) (16,23) (16,18) (16,17) (16,20) (17,23) (17,22) (18,19) (18,24) (18,25) (20,22) (22,23) (22,24) (23,25) (24,25)\nIs there a path between node 7 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph93-8_18", + "image": "data/connectivity/graph_visual/hard/graph93.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,19) (0,18) (0,16) (0,13) (0,4) (0,8) (0,10) (0,22) (1,2) (2,7) (3,19) (3,18) (3,12) (3,20) (3,10) (4,11) (4,14) (4,5) (4,20) (4,8) (5,11) (5,14) (5,18) (5,16) (5,13) (5,12) (6,19) (6,11) (6,12) (6,20) (6,8) (7,26) (8,24) (8,14) (8,18) (8,25) (9,17) (10,15) (10,27) (10,21) (10,18) (10,13) (10,12) (10,20) (11,27) (11,21) (11,13) (11,12) (11,25) (12,24) (12,16) (12,25) (13,24) (13,27) (13,25) (13,20) (13,22) (14,16) (14,22) (15,20) (16,25) (17,26) (17,23) (18,27) (19,25) (19,20) (20,24) (20,25) (20,22) (21,27) (22,25) (23,26) (25,27)\nIs there a path between node 8 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph107-18_14", + "image": "data/connectivity/graph_visual/hard/graph107.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,27) (0,4) (0,11) (0,9) (0,25) (1,12) (1,16) (2,3) (2,27) (2,11) (2,12) (2,22) (2,25) (2,15) (3,25) (3,15) (4,18) (4,11) (4,26) (4,22) (4,9) (4,24) (4,13) (5,7) (5,14) (5,19) (5,17) (6,14) (7,17) (9,20) (9,26) (9,12) (9,25) (9,15) (10,20) (10,27) (10,11) (10,21) (10,26) (10,16) (11,27) (11,25) (12,27) (12,21) (12,26) (12,24) (13,24) (14,17) (15,20) (15,27) (15,18) (15,26) (15,22) (15,25) (16,20) (16,27) (18,26) (18,25) (20,25) (25,26)\nIs there a path between node 18 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph631-33_20", + "image": "data/connectivity/graph_visual/hard/graph631.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,16) (1,33) (1,17) (1,12) (1,25) (1,7) (1,18) (1,32) (1,11) (1,10) (1,15) (1,9) (1,5) (1,26) (1,4) (2,19) (2,33) (2,18) (2,30) (3,34) (3,31) (3,14) (3,6) (3,17) (3,11) (3,22) (3,29) (3,15) (3,24) (3,30) (4,16) (4,6) (4,12) (4,32) (4,24) (5,31) (5,16) (5,8) (5,23) (5,24) (5,21) (6,19) (6,33) (6,25) (6,11) (6,10) (6,24) (6,30) (7,12) (7,15) (7,9) (7,30) (8,17) (8,12) (8,32) (8,22) (8,29) (8,24) (8,30) (9,16) (9,14) (9,12) (9,25) (9,18) (9,23) (9,26) (10,31) (10,14) (10,19) (10,25) (10,32) (10,22) (10,23) (10,21) (11,34) (11,14) (11,17) (11,27) (11,25) (11,18) (11,26) (14,19) (14,33) (14,25) (14,18) (14,30) (14,26) (14,21) (15,34) (15,31) (15,33) (15,32) (15,24) (15,26) (15,21) (16,34) (16,22) (16,29) (16,24) (16,26) (17,31) (17,18) (17,23) (17,26) (18,22) (18,26) (19,33) (19,27) (19,25) (19,29) (19,26) (21,34) (21,31) (21,33) (21,25) (21,22) (21,24) (21,30) (22,34) (22,29) (22,24) (23,33) (23,27) (23,32) (24,33) (24,27) (24,32) (25,34) (25,31) (26,29) (27,34) (27,33) (29,31) (29,33) (29,30) (30,31) (31,34)\nIs there a path between node 33 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph654-21_33", + "image": "data/connectivity/graph_visual/hard/graph654.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,25) (0,10) (0,11) (0,18) (0,15) (0,21) (0,24) (0,26) (0,16) (0,31) (1,13) (1,30) (1,6) (1,22) (1,28) (1,23) (1,20) (1,3) (1,14) (1,29) (1,2) (1,32) (1,27) (1,9) (1,17) (2,13) (2,6) (2,12) (2,22) (2,28) (2,23) (2,20) (2,14) (2,29) (2,32) (2,27) (3,13) (3,30) (3,6) (3,22) (3,28) (3,5) (3,23) (3,29) (3,32) (3,27) (3,9) (3,17) (4,33) (4,19) (4,10) (4,11) (4,18) (4,15) (4,21) (4,24) (4,26) (4,16) (4,31) (5,13) (5,30) (5,6) (5,12) (5,22) (5,28) (5,20) (5,14) (5,32) (5,27) (5,9) (6,12) (6,22) (6,28) (6,23) (6,20) (6,14) (6,29) (6,32) (6,27) (6,9) (6,17) (7,8) (7,25) (7,33) (7,19) (7,10) (7,11) (7,15) (7,34) (7,26) (7,16) (7,31) (8,33) (8,19) (8,10) (8,18) (8,24) (8,26) (8,16) (8,31) (9,13) (9,30) (9,12) (9,28) (9,14) (9,29) (9,32) (9,27) (10,33) (10,19) (10,18) (10,15) (10,34) (10,24) (10,26) (10,16) (10,31) (11,25) (11,33) (11,19) (11,18) (11,34) (11,24) (11,26) (11,16) (11,31) (12,13) (12,30) (12,14) (12,29) (12,32) (12,27) (12,17) (13,30) (13,23) (13,20) (13,14) (13,29) (13,27) (13,17) (14,30) (14,23) (14,20) (14,29) (14,27) (14,17) (15,33) (15,19) (15,21) (15,24) (15,26) (15,16) (15,31) (16,25) (16,33) (16,19) (16,18) (16,21) (16,24) (16,26) (16,31) (17,30) (17,22) (17,20) (17,29) (17,32) (17,27) (18,25) (18,33) (18,19) (18,21) (18,34) (18,31) (19,21) (19,34) (19,24) (20,22) (20,28) (20,23) (20,29) (20,32) (20,27) (21,34) (21,24) (21,26) (22,30) (22,29) (22,27) (23,30) (23,29) (23,32) (24,33) (24,26) (24,31) (25,31) (26,34) (26,31) (27,28) (27,29) (27,32) (28,30) (28,29) (28,32) (29,30) (30,32) (31,33) (31,34) (33,34)\nIs there a path between node 21 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph401-10_6", + "image": "data/connectivity/graph_visual/hard/graph401.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,11) (0,15) (0,31) (0,7) (0,4) (0,28) (0,32) (0,19) (0,16) (0,25) (0,17) (0,12) (0,27) (0,9) (0,23) (0,3) (0,14) (0,1) (0,2) (0,29) (1,30) (1,31) (1,13) (1,7) (1,4) (1,6) (1,32) (1,19) (1,22) (1,26) (1,16) (1,25) (1,17) (1,27) (1,9) (1,24) (1,14) (1,2) (2,15) (2,30) (2,31) (2,13) (2,7) (2,4) (2,6) (2,32) (2,8) (2,19) (2,26) (2,17) (2,12) (2,18) (2,27) (2,9) (2,24) (2,23) (2,5) (2,3) (2,14) (2,29) (3,11) (3,30) (3,31) (3,13) (3,7) (3,4) (3,28) (3,6) (3,32) (3,8) (3,22) (3,26) (3,16) (3,25) (3,17) (3,18) (3,27) (3,23) (3,5) (3,14) (3,29) (4,11) (4,30) (4,31) (4,6) (4,32) (4,19) (4,16) (4,25) (4,17) (4,12) (4,18) (4,27) (4,9) (4,24) (4,5) (4,14) (5,11) (5,31) (5,13) (5,7) (5,28) (5,19) (5,26) (5,25) (5,12) (5,18) (5,24) (5,23) (5,14) (6,11) (6,15) (6,30) (6,31) (6,13) (6,7) (6,28) (6,8) (6,22) (6,26) (6,16) (6,25) (6,17) (6,12) (6,14) (6,29) (7,11) (7,15) (7,30) (7,31) (7,28) (7,32) (7,19) (7,22) (7,17) (7,12) (7,18) (7,27) (7,24) (7,23) (7,29) (8,11) (8,15) (8,30) (8,31) (8,13) (8,28) (8,32) (8,19) (8,26) (8,16) (8,17) (8,12) (8,9) (8,24) (8,23) (8,14) (8,29) (9,11) (9,30) (9,13) (9,32) (9,19) (9,26) (9,16) (9,25) (9,12) (9,18) (9,27) (9,24) (9,29) (10,20) (11,31) (11,13) (11,28) (11,32) (11,19) (11,22) (11,16) (11,25) (11,17) (11,27) (11,24) (11,23) (11,29) (12,15) (12,13) (12,28) (12,32) (12,19) (12,26) (12,25) (12,27) (12,23) (12,29) (13,15) (13,31) (13,28) (13,32) (13,22) (13,26) (13,16) (13,25) (13,18) (13,27) (13,24) (13,23) (13,29) (14,15) (14,30) (14,31) (14,28) (14,32) (14,19) (14,22) (14,26) (14,16) (14,25) (14,17) (14,18) (14,27) (14,24) (14,23) (14,29) (15,31) (15,19) (15,22) (15,17) (15,18) (15,27) (15,24) (15,23) (15,29) (16,30) (16,31) (16,32) (16,19) (16,22) (16,26) (16,27) (16,24) (17,28) (17,32) (17,19) (17,18) (17,27) (18,30) (18,31) (18,28) (18,32) (18,19) (18,22) (18,27) (18,24) (18,23) (19,30) (19,31) (19,28) (19,32) (19,22) (19,25) (19,27) (19,23) (19,29) (20,21) (22,30) (22,26) (22,25) (22,27) (22,29) (23,30) (23,28) (23,32) (23,26) (23,25) (23,27) (23,24) (23,29) (24,30) (24,31) (24,28) (24,32) (24,25) (24,27) (24,29) (25,30) (25,28) (25,32) (25,27) (25,29) (26,30) (26,32) (26,27) (26,29) (27,28) (27,29) (28,29) (29,31) (29,32) (30,32) (31,32)\nIs there a path between node 10 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph631-12_21", + "image": "data/connectivity/graph_visual/hard/graph631.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,16) (1,33) (1,17) (1,12) (1,25) (1,7) (1,18) (1,32) (1,11) (1,10) (1,15) (1,9) (1,5) (1,26) (1,4) (2,19) (2,33) (2,18) (2,30) (3,34) (3,31) (3,14) (3,6) (3,17) (3,11) (3,22) (3,29) (3,15) (3,24) (3,30) (4,16) (4,6) (4,12) (4,32) (4,24) (5,31) (5,16) (5,8) (5,23) (5,24) (5,21) (6,19) (6,33) (6,25) (6,11) (6,10) (6,24) (6,30) (7,12) (7,15) (7,9) (7,30) (8,17) (8,12) (8,32) (8,22) (8,29) (8,24) (8,30) (9,16) (9,14) (9,12) (9,25) (9,18) (9,23) (9,26) (10,31) (10,14) (10,19) (10,25) (10,32) (10,22) (10,23) (10,21) (11,34) (11,14) (11,17) (11,27) (11,25) (11,18) (11,26) (14,19) (14,33) (14,25) (14,18) (14,30) (14,26) (14,21) (15,34) (15,31) (15,33) (15,32) (15,24) (15,26) (15,21) (16,34) (16,22) (16,29) (16,24) (16,26) (17,31) (17,18) (17,23) (17,26) (18,22) (18,26) (19,33) (19,27) (19,25) (19,29) (19,26) (21,34) (21,31) (21,33) (21,25) (21,22) (21,24) (21,30) (22,34) (22,29) (22,24) (23,33) (23,27) (23,32) (24,33) (24,27) (24,32) (25,34) (25,31) (26,29) (27,34) (27,33) (29,31) (29,33) (29,30) (30,31) (31,34)\nIs there a path between node 12 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph671-34_7", + "image": "data/connectivity/graph_visual/hard/graph671.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,17) (0,6) (0,19) (0,28) (0,14) (1,27) (1,3) (2,10) (2,23) (2,4) (2,29) (2,26) (2,9) (3,22) (4,8) (4,18) (4,15) (4,33) (4,34) (4,28) (5,20) (5,8) (5,6) (5,30) (5,9) (6,10) (6,17) (6,8) (6,23) (6,18) (6,19) (6,25) (6,33) (6,32) (6,28) (6,14) (6,9) (8,32) (8,12) (8,29) (8,26) (8,30) (8,9) (8,31) (9,19) (9,33) (9,32) (9,12) (10,11) (10,25) (10,28) (10,14) (11,23) (11,12) (11,26) (11,30) (11,31) (12,15) (12,33) (12,30) (12,14) (13,22) (14,19) (14,31) (15,23) (15,28) (15,29) (16,24) (17,20) (18,32) (18,29) (18,26) (19,34) (19,31) (20,26) (21,27) (22,24) (23,32) (23,28) (24,27) (25,34) (25,28) (25,29) (26,34) (26,28) (28,34) (29,31) (30,33) (30,34) (31,32) (32,34) (33,34)\nIs there a path between node 34 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph674-1_18", + "image": "data/connectivity/graph_visual/hard/graph674.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,6) (0,23) (0,25) (0,8) (0,29) (1,19) (1,30) (2,7) (2,4) (2,3) (2,31) (2,8) (2,34) (3,23) (4,9) (4,17) (4,8) (4,13) (4,34) (5,15) (5,24) (6,9) (6,7) (6,12) (6,23) (6,31) (7,10) (7,23) (7,22) (7,29) (9,10) (9,22) (9,29) (10,12) (10,22) (11,23) (11,22) (12,22) (12,17) (12,13) (12,34) (13,31) (13,17) (14,16) (15,21) (15,19) (15,27) (17,26) (17,25) (17,31) (18,20) (18,33) (19,21) (19,30) (19,32) (19,27) (20,28) (20,33) (21,24) (21,30) (21,27) (22,34) (25,26) (25,34) (26,31) (27,32) (30,32)\nIs there a path between node 1 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph368-10_7", + "image": "data/connectivity/graph_visual/hard/graph368.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,10) (0,4) (0,3) (0,16) (0,24) (0,17) (0,25) (0,8) (1,18) (1,10) (1,4) (1,30) (1,16) (1,24) (1,17) (2,21) (2,14) (2,29) (2,11) (2,9) (2,5) (2,13) (3,18) (3,4) (3,23) (3,7) (3,16) (3,24) (3,20) (3,17) (3,8) (4,10) (4,30) (4,24) (4,20) (4,17) (4,8) (5,14) (5,11) (5,28) (5,9) (6,22) (6,19) (6,12) (7,18) (7,10) (7,23) (7,16) (7,24) (7,20) (7,17) (7,8) (8,18) (8,10) (8,23) (8,30) (8,16) (8,20) (9,26) (9,14) (9,29) (9,11) (9,28) (9,13) (10,18) (10,23) (10,30) (10,16) (10,24) (10,20) (10,17) (11,26) (11,21) (11,14) (11,29) (11,28) (11,13) (12,22) (12,27) (12,19) (12,31) (13,26) (13,21) (13,14) (13,29) (14,26) (14,21) (14,29) (14,28) (15,27) (15,19) (15,31) (16,18) (16,23) (16,30) (16,24) (16,20) (16,17) (17,30) (17,20) (18,30) (18,24) (18,20) (18,25) (19,22) (19,27) (19,31) (20,25) (21,29) (22,27) (23,30) (23,25) (24,25) (25,30) (26,28) (27,31) (28,29)\nIs there a path between node 10 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph534-4_9", + "image": "data/connectivity/graph_visual/hard/graph534.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,1) (0,3) (0,22) (0,28) (0,2) (0,26) (0,14) (0,10) (0,32) (0,30) (0,16) (0,31) (0,9) (0,23) (0,20) (0,4) (0,19) (0,17) (0,18) (1,21) (1,22) (1,28) (1,15) (1,16) (1,31) (1,20) (1,13) (1,8) (1,19) (1,18) (2,3) (2,28) (2,29) (2,14) (2,10) (2,32) (2,30) (2,16) (2,9) (2,23) (2,20) (2,13) (2,5) (2,4) (2,8) (2,19) (2,17) (2,18) (3,21) (3,22) (3,28) (3,26) (3,10) (3,32) (3,15) (3,31) (3,9) (3,23) (3,20) (3,5) (3,7) (3,4) (3,19) (3,18) (4,22) (4,28) (4,29) (4,14) (4,10) (4,32) (4,15) (4,30) (4,31) (4,23) (4,20) (4,13) (4,7) (4,17) (4,18) (5,22) (5,28) (5,10) (5,9) (5,20) (5,13) (5,7) (5,19) (5,17) (5,18) (6,25) (6,33) (6,24) (6,11) (6,27) (7,21) (7,22) (7,28) (7,26) (7,14) (7,10) (7,32) (7,15) (7,30) (7,9) (7,20) (7,19) (7,18) (8,22) (8,28) (8,29) (8,26) (8,14) (8,10) (8,32) (8,15) (8,30) (8,31) (8,23) (8,20) (8,19) (8,17) (9,21) (9,29) (9,26) (9,10) (9,32) (9,30) (9,16) (9,23) (9,20) (9,13) (9,19) (9,17) (10,21) (10,22) (10,28) (10,29) (10,26) (10,14) (10,32) (10,15) (10,30) (10,16) (10,31) (10,23) (10,20) (10,17) (11,12) (11,27) (12,24) (13,21) (13,22) (13,32) (13,15) (13,30) (13,23) (13,20) (13,19) (13,17) (13,18) (14,21) (14,22) (14,28) (14,26) (14,15) (14,30) (14,16) (14,23) (14,19) (14,17) (14,18) (15,21) (15,22) (15,26) (15,32) (15,30) (15,16) (15,31) (15,23) (15,20) (15,17) (15,18) (16,21) (16,28) (16,29) (16,32) (16,19) (16,17) (16,18) (17,21) (17,22) (17,28) (17,29) (17,26) (17,32) (17,30) (17,23) (17,20) (17,19) (18,21) (18,22) (18,28) (18,29) (18,26) (18,32) (18,30) (18,31) (18,23) (18,20) (18,19) (19,21) (19,22) (19,28) (19,29) (19,26) (19,30) (19,31) (19,23) (19,20) (20,28) (20,29) (20,23) (21,22) (21,28) (21,26) (21,32) (21,30) (21,31) (21,23) (22,28) (22,29) (22,26) (22,32) (23,28) (23,26) (23,31) (24,25) (24,33) (24,27) (25,33) (25,27) (26,29) (26,32) (26,30) (26,31) (27,33) (28,29) (28,32) (28,30) (28,31) (29,32) (29,30) (29,31) (30,31) (31,32)\nIs there a path between node 4 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph477-8_31", + "image": "data/connectivity/graph_visual/hard/graph477.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,4) (0,16) (0,9) (1,2) (1,10) (1,26) (1,18) (1,3) (1,31) (1,28) (1,12) (1,23) (1,27) (1,7) (1,32) (1,8) (1,21) (1,6) (2,25) (2,11) (2,10) (2,26) (2,18) (2,3) (2,31) (2,28) (2,23) (2,19) (2,27) (2,32) (2,8) (2,6) (3,10) (3,26) (3,18) (3,12) (3,23) (3,19) (3,27) (3,7) (3,32) (3,29) (3,8) (3,21) (3,6) (4,20) (4,24) (4,30) (4,9) (5,15) (6,25) (6,11) (6,10) (6,26) (6,31) (6,28) (6,23) (6,19) (6,32) (6,29) (6,8) (6,21) (7,11) (7,10) (7,26) (7,31) (7,28) (7,12) (7,19) (7,27) (7,29) (8,25) (8,11) (8,10) (8,26) (8,28) (8,12) (8,23) (8,19) (8,27) (8,29) (8,21) (9,20) (9,24) (9,14) (9,17) (9,16) (9,30) (10,25) (10,11) (10,26) (10,18) (10,31) (10,28) (10,23) (10,19) (10,27) (10,29) (10,21) (11,25) (11,31) (11,28) (11,12) (11,19) (11,27) (11,32) (12,25) (12,26) (12,18) (12,31) (12,23) (12,19) (12,27) (12,32) (13,20) (13,22) (13,14) (13,17) (13,16) (13,30) (14,20) (14,22) (14,17) (14,30) (16,20) (16,22) (17,20) (17,22) (18,25) (18,31) (18,28) (18,23) (18,27) (18,32) (19,26) (19,31) (19,23) (19,27) (19,32) (19,29) (19,21) (20,22) (20,24) (20,30) (21,25) (21,23) (21,32) (21,29) (23,25) (23,26) (23,31) (23,27) (24,30) (25,26) (25,28) (25,27) (25,29) (26,31) (26,32) (26,29) (27,31) (27,28) (27,29) (28,32) (28,29) (29,32) (31,32)\nIs there a path between node 8 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph671-18_13", + "image": "data/connectivity/graph_visual/hard/graph671.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,17) (0,6) (0,19) (0,28) (0,14) (1,27) (1,3) (2,10) (2,23) (2,4) (2,29) (2,26) (2,9) (3,22) (4,8) (4,18) (4,15) (4,33) (4,34) (4,28) (5,20) (5,8) (5,6) (5,30) (5,9) (6,10) (6,17) (6,8) (6,23) (6,18) (6,19) (6,25) (6,33) (6,32) (6,28) (6,14) (6,9) (8,32) (8,12) (8,29) (8,26) (8,30) (8,9) (8,31) (9,19) (9,33) (9,32) (9,12) (10,11) (10,25) (10,28) (10,14) (11,23) (11,12) (11,26) (11,30) (11,31) (12,15) (12,33) (12,30) (12,14) (13,22) (14,19) (14,31) (15,23) (15,28) (15,29) (16,24) (17,20) (18,32) (18,29) (18,26) (19,34) (19,31) (20,26) (21,27) (22,24) (23,32) (23,28) (24,27) (25,34) (25,28) (25,29) (26,34) (26,28) (28,34) (29,31) (30,33) (30,34) (31,32) (32,34) (33,34)\nIs there a path between node 18 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph456-10_6", + "image": "data/connectivity/graph_visual/hard/graph456.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,28) (0,12) (0,19) (1,25) (1,11) (1,20) (1,18) (1,10) (1,31) (1,5) (3,20) (3,15) (3,8) (3,30) (3,18) (4,9) (5,25) (5,11) (5,15) (5,6) (5,18) (5,19) (6,30) (6,12) (7,25) (7,24) (7,28) (7,8) (7,30) (7,18) (7,10) (7,31) (7,14) (8,15) (8,10) (8,31) (9,22) (10,25) (10,15) (10,30) (10,31) (11,20) (12,25) (12,24) (12,28) (13,26) (13,21) (14,24) (14,28) (14,18) (14,19) (15,20) (15,30) (15,19) (16,27) (16,23) (18,24) (18,20) (18,28) (18,30) (20,30) (21,27) (21,26) (21,23) (21,29) (23,27) (23,32) (26,27) (26,32) (26,29) (28,30) (30,31)\nIs there a path between node 10 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph653-13_11", + "image": "data/connectivity/graph_visual/hard/graph653.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,20) (0,13) (0,1) (1,4) (1,12) (1,34) (1,6) (1,28) (3,32) (4,20) (4,12) (4,34) (4,6) (4,28) (4,13) (5,26) (5,23) (5,18) (5,24) (5,30) (5,8) (5,21) (5,10) (5,25) (5,29) (5,22) (5,33) (5,15) (5,11) (6,20) (6,12) (6,28) (6,13) (7,16) (8,9) (8,31) (8,26) (8,23) (8,18) (8,24) (8,19) (8,21) (8,10) (8,25) (8,22) (8,33) (8,11) (8,17) (9,31) (9,26) (9,23) (9,18) (9,24) (9,21) (9,10) (9,25) (9,29) (9,22) (9,33) (9,15) (9,17) (10,31) (10,26) (10,23) (10,18) (10,24) (10,30) (10,19) (10,21) (10,29) (10,33) (10,15) (11,31) (11,23) (11,18) (11,24) (11,30) (11,19) (11,21) (11,25) (11,29) (11,33) (11,15) (11,17) (12,20) (12,34) (12,13) (13,20) (14,16) (15,31) (15,26) (15,18) (15,24) (15,30) (15,19) (15,21) (15,25) (15,22) (15,17) (15,27) (17,31) (17,23) (17,18) (17,24) (17,22) (17,27) (18,31) (18,26) (18,23) (18,24) (18,30) (18,19) (18,21) (18,25) (18,29) (18,22) (18,27) (19,31) (19,26) (19,24) (19,21) (19,25) (19,22) (19,33) (19,27) (20,34) (20,28) (21,31) (21,26) (21,23) (21,25) (21,29) (21,22) (21,33) (21,27) (22,24) (22,25) (22,29) (22,33) (22,27) (23,26) (23,29) (23,27) (24,31) (24,26) (24,30) (24,25) (24,29) (25,26) (25,30) (25,29) (25,33) (25,27) (26,31) (26,30) (26,29) (26,33) (26,27) (27,30) (27,29) (27,33) (28,34) (29,31) (29,33) (30,31) (31,33)\nIs there a path between node 13 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph94-16_23", + "image": "data/connectivity/graph_visual/hard/graph94.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,20) (0,24) (0,3) (0,19) (0,9) (0,21) (1,2) (2,13) (2,6) (3,24) (3,8) (3,12) (4,20) (4,8) (4,19) (4,17) (4,23) (4,21) (5,7) (5,25) (5,18) (6,13) (7,25) (8,20) (8,24) (8,14) (8,11) (8,23) (9,26) (9,15) (9,24) (9,14) (9,11) (9,23) (10,26) (10,15) (10,12) (10,23) (11,26) (11,15) (11,27) (11,12) (11,17) (11,23) (12,20) (12,24) (12,14) (13,22) (14,19) (14,17) (14,21) (15,19) (15,23) (15,21) (16,24) (16,19) (16,21) (17,24) (18,25) (19,26) (19,24) (20,27) (21,24) (21,27) (23,26) (23,24) (24,26)\nIs there a path between node 16 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph323-5_26", + "image": "data/connectivity/graph_visual/hard/graph323.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,16) (0,1) (0,21) (0,27) (0,20) (0,7) (0,25) (0,23) (0,15) (0,17) (0,10) (0,2) (0,6) (0,11) (0,19) (0,4) (0,14) (0,9) (0,30) (0,29) (0,13) (1,16) (1,26) (1,21) (1,12) (1,27) (1,20) (1,7) (1,17) (1,10) (1,2) (1,6) (1,11) (1,4) (1,8) (1,14) (1,29) (1,13) (2,18) (2,16) (2,26) (2,21) (2,24) (2,12) (2,27) (2,20) (2,7) (2,22) (2,23) (2,15) (2,17) (2,11) (2,19) (2,4) (2,8) (2,14) (2,9) (2,29) (2,13) (3,31) (4,18) (4,16) (4,26) (4,21) (4,27) (4,7) (4,25) (4,22) (4,15) (4,10) (4,28) (4,11) (4,19) (4,14) (4,9) (4,30) (4,29) (6,18) (6,16) (6,12) (6,20) (6,25) (6,23) (6,15) (6,17) (6,10) (6,28) (6,11) (6,19) (6,14) (6,9) (6,29) (7,16) (7,26) (7,21) (7,24) (7,12) (7,27) (7,20) (7,25) (7,22) (7,23) (7,15) (7,10) (7,28) (7,11) (7,19) (7,8) (7,9) (7,30) (7,13) (8,16) (8,21) (8,27) (8,20) (8,25) (8,23) (8,15) (8,17) (8,10) (8,11) (8,14) (8,29) (8,13) (9,18) (9,16) (9,21) (9,24) (9,27) (9,22) (9,23) (9,17) (9,10) (9,28) (9,19) (9,14) (9,30) (9,29) (9,13) (10,18) (10,16) (10,26) (10,21) (10,12) (10,27) (10,20) (10,25) (10,22) (10,23) (10,15) (10,11) (10,19) (10,29) (10,13) (11,18) (11,16) (11,26) (11,21) (11,24) (11,12) (11,20) (11,22) (11,23) (11,15) (11,17) (11,30) (11,13) (12,18) (12,16) (12,26) (12,21) (12,24) (12,27) (12,20) (12,25) (12,22) (12,23) (12,17) (12,28) (12,19) (12,30) (12,29) (12,13) (13,18) (13,16) (13,21) (13,24) (13,20) (13,25) (13,22) (13,23) (13,15) (13,17) (13,28) (13,19) (13,30) (13,29) (14,18) (14,16) (14,26) (14,24) (14,27) (14,20) (14,25) (14,23) (14,15) (14,17) (14,28) (14,19) (14,30) (14,29) (15,18) (15,26) (15,21) (15,24) (15,27) (15,20) (15,25) (15,23) (15,28) (15,30) (16,18) (16,26) (16,24) (16,27) (16,20) (16,25) (16,22) (16,23) (16,28) (16,30) (16,29) (17,18) (17,21) (17,24) (17,27) (17,25) (17,23) (17,28) (17,30) (18,26) (18,27) (18,20) (18,23) (18,28) (18,19) (18,30) (18,29) (19,26) (19,24) (19,27) (19,20) (19,25) (19,22) (19,23) (19,28) (19,30) (19,29) (20,26) (20,25) (20,22) (20,23) (20,28) (20,30) (20,29) (21,26) (21,24) (21,23) (21,28) (21,29) (22,26) (22,24) (22,27) (22,25) (22,23) (22,28) (22,30) (22,29) (23,26) (23,27) (23,25) (23,28) (23,30) (24,26) (24,25) (25,26) (25,27) (25,28) (25,29) (26,27) (26,28) (26,30) (26,29) (27,30) (27,29) (28,29)\nIs there a path between node 5 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph589-29_4", + "image": "data/connectivity/graph_visual/hard/graph589.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,11) (0,16) (0,3) (0,26) (0,15) (0,30) (0,20) (0,27) (0,17) (0,18) (0,7) (0,1) (0,23) (0,24) (0,12) (1,8) (1,16) (1,25) (1,10) (1,5) (1,26) (1,15) (1,20) (1,27) (1,18) (1,13) (1,23) (1,2) (1,24) (1,31) (1,33) (1,12) (1,4) (1,6) (2,8) (2,11) (2,21) (2,25) (2,3) (2,10) (2,5) (2,26) (2,15) (2,27) (2,28) (2,14) (2,13) (2,31) (2,33) (2,4) (3,8) (3,9) (3,16) (3,25) (3,5) (3,26) (3,22) (3,30) (3,20) (3,17) (3,7) (3,28) (3,23) (3,24) (3,12) (3,4) (4,8) (4,11) (4,21) (4,25) (4,10) (4,15) (4,22) (4,20) (4,27) (4,18) (4,7) (4,28) (4,14) (4,23) (4,24) (4,31) (4,12) (5,8) (5,11) (5,9) (5,16) (5,21) (5,25) (5,10) (5,26) (5,15) (5,22) (5,30) (5,27) (5,18) (5,7) (5,28) (5,14) (5,13) (5,31) (6,8) (6,21) (6,25) (6,10) (6,26) (6,15) (6,22) (6,30) (6,20) (6,27) (6,28) (6,13) (6,31) (6,33) (7,11) (7,9) (7,16) (7,21) (7,25) (7,10) (7,26) (7,15) (7,22) (7,30) (7,20) (7,27) (7,28) (7,14) (7,13) (7,23) (7,24) (7,31) (7,12) (8,11) (8,9) (8,16) (8,21) (8,25) (8,10) (8,26) (8,30) (8,20) (8,17) (8,18) (8,28) (8,14) (8,23) (8,24) (8,31) (8,12) (9,11) (9,16) (9,21) (9,10) (9,26) (9,15) (9,22) (9,30) (9,27) (9,17) (9,18) (9,28) (9,14) (9,13) (9,24) (9,31) (10,26) (10,30) (10,27) (10,17) (10,18) (10,28) (10,14) (10,13) (10,31) (10,33) (10,12) (11,16) (11,21) (11,25) (11,26) (11,15) (11,22) (11,30) (11,20) (11,27) (11,17) (11,18) (11,28) (11,14) (11,13) (11,24) (11,31) (11,33) (11,12) (12,21) (12,25) (12,26) (12,22) (12,20) (12,17) (12,18) (12,28) (12,14) (12,13) (12,23) (12,31) (12,33) (13,25) (13,26) (13,15) (13,30) (13,20) (13,17) (13,18) (13,14) (13,23) (13,24) (13,31) (13,33) (14,16) (14,21) (14,25) (14,26) (14,22) (14,20) (14,17) (14,18) (14,28) (14,23) (14,31) (14,33) (15,16) (15,22) (15,30) (15,18) (15,28) (15,23) (15,24) (15,31) (15,33) (16,21) (16,25) (16,22) (16,20) (16,27) (16,17) (16,18) (16,28) (16,23) (16,33) (17,25) (17,22) (17,30) (17,20) (17,27) (17,18) (17,28) (17,23) (17,24) (17,33) (18,25) (18,22) (18,30) (18,20) (18,27) (18,23) (18,24) (18,33) (19,29) (19,32) (20,26) (20,22) (20,30) (20,27) (20,28) (20,23) (20,24) (20,31) (20,33) (21,25) (21,26) (21,30) (21,27) (21,28) (21,23) (21,33) (22,26) (22,30) (22,23) (22,33) (23,25) (23,26) (23,27) (23,28) (23,24) (23,31) (23,33) (24,25) (24,26) (24,28) (24,31) (25,26) (25,30) (25,27) (25,28) (25,33) (26,30) (26,27) (26,28) (26,31) (27,30) (27,28) (27,33) (28,31) (28,33) (29,32) (30,33) (31,33)\nIs there a path between node 29 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph50-8_13", + "image": "data/connectivity/graph_visual/hard/graph50.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,14) (0,17) (0,12) (0,9) (0,8) (1,11) (1,24) (1,15) (1,10) (1,13) (2,14) (2,17) (2,8) (2,3) (3,12) (4,15) (4,25) (4,6) (5,17) (5,12) (5,23) (6,11) (6,24) (6,20) (7,24) (7,20) (7,15) (7,18) (7,26) (8,9) (9,12) (10,20) (10,13) (11,24) (11,26) (11,13) (12,16) (13,26) (15,24) (15,20) (15,25) (15,22) (16,19) (16,21) (17,19) (17,23) (22,26) (24,25)\nIs there a path between node 8 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph688-21_22", + "image": "data/connectivity/graph_visual/hard/graph688.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,29) (0,30) (1,19) (1,22) (1,13) (1,28) (1,26) (1,24) (1,3) (1,12) (1,7) (1,16) (1,25) (1,27) (1,11) (2,31) (2,10) (2,18) (2,9) (2,14) (2,23) (2,33) (2,32) (3,19) (3,21) (3,22) (3,28) (3,26) (3,24) (3,12) (3,7) (3,16) (3,25) (3,27) (3,11) (4,17) (5,8) (5,9) (5,23) (5,32) (6,29) (6,15) (7,19) (7,22) (7,28) (7,26) (7,24) (7,12) (7,16) (7,25) (7,27) (8,31) (8,10) (8,18) (8,14) (8,23) (8,33) (8,32) (9,31) (9,10) (9,18) (9,14) (9,23) (9,32) (10,31) (10,18) (10,14) (10,23) (10,33) (10,32) (11,19) (11,21) (11,22) (11,13) (11,28) (11,26) (11,12) (11,16) (11,27) (12,22) (12,13) (12,24) (12,16) (12,25) (12,27) (13,19) (13,22) (13,28) (13,26) (13,24) (13,16) (13,25) (14,31) (14,18) (14,23) (14,33) (14,32) (15,34) (15,30) (16,21) (16,22) (16,25) (16,27) (17,20) (18,31) (18,23) (18,32) (19,21) (19,22) (19,28) (19,26) (19,24) (19,25) (21,22) (21,28) (21,26) (21,24) (21,25) (21,27) (22,28) (22,27) (23,31) (23,33) (23,32) (24,28) (24,26) (24,27) (25,28) (25,26) (25,27) (26,28) (26,27) (30,34) (31,33)\nIs there a path between node 21 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph487-25_16", + "image": "data/connectivity/graph_visual/hard/graph487.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,8) (0,30) (0,9) (0,18) (0,2) (0,4) (0,20) (0,28) (0,1) (0,7) (0,16) (0,5) (0,17) (0,32) (0,26) (0,29) (0,21) (0,25) (0,11) (0,13) (0,31) (0,27) (1,8) (1,9) (1,18) (1,15) (1,4) (1,20) (1,28) (1,7) (1,16) (1,5) (1,32) (1,21) (1,25) (1,22) (1,11) (1,13) (1,31) (1,3) (1,27) (2,18) (2,15) (2,4) (2,20) (2,28) (2,7) (2,16) (2,23) (2,32) (2,26) (2,21) (2,25) (2,22) (2,12) (2,13) (2,31) (2,27) (3,8) (3,9) (3,18) (3,15) (3,4) (3,20) (3,7) (3,16) (3,23) (3,29) (3,21) (3,25) (3,22) (3,11) (3,27) (4,8) (4,30) (4,9) (4,18) (4,15) (4,7) (4,16) (4,5) (4,17) (4,26) (4,21) (4,25) (4,22) (4,12) (4,13) (4,31) (4,27) (5,30) (5,18) (5,15) (5,28) (5,7) (5,32) (5,26) (5,29) (5,21) (5,25) (5,22) (5,12) (5,11) (5,13) (5,31) (5,27) (6,24) (6,10) (6,19) (6,14) (7,9) (7,18) (7,15) (7,28) (7,16) (7,17) (7,23) (7,32) (7,21) (7,25) (7,22) (7,12) (7,31) (8,30) (8,9) (8,15) (8,28) (8,16) (8,17) (8,23) (8,26) (8,29) (8,21) (8,22) (8,11) (8,13) (8,27) (9,28) (9,17) (9,32) (9,26) (9,21) (9,25) (9,11) (9,31) (9,27) (10,24) (10,19) (10,14) (11,18) (11,15) (11,28) (11,16) (11,32) (11,21) (11,22) (11,13) (11,31) (11,27) (12,30) (12,18) (12,15) (12,32) (12,26) (12,21) (12,22) (12,13) (12,31) (13,18) (13,28) (13,17) (13,32) (13,26) (13,29) (13,21) (13,25) (13,22) (13,31) (13,27) (14,24) (14,19) (15,18) (15,20) (15,28) (15,17) (15,23) (15,32) (15,29) (15,25) (15,22) (15,31) (16,30) (16,18) (16,20) (16,28) (16,17) (16,26) (16,21) (16,31) (16,27) (17,30) (17,18) (17,20) (17,23) (17,32) (17,26) (17,29) (17,25) (17,31) (17,27) (18,30) (18,20) (18,28) (18,23) (18,32) (18,26) (18,29) (18,21) (18,25) (18,31) (18,27) (19,24) (20,30) (20,28) (20,32) (20,26) (20,29) (20,31) (20,27) (21,30) (21,23) (21,32) (21,29) (21,25) (21,27) (22,28) (22,26) (22,29) (22,25) (22,31) (22,27) (23,30) (23,32) (23,29) (23,25) (23,31) (23,27) (25,30) (25,28) (25,26) (25,31) (26,30) (26,28) (26,27) (27,30) (27,28) (27,32) (28,29) (28,31) (29,30) (29,32) (29,31) (30,32) (31,32)\nIs there a path between node 25 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph133-14_15", + "image": "data/connectivity/graph_visual/hard/graph133.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,6) (0,2) (0,5) (0,27) (0,8) (0,1) (0,21) (0,24) (0,10) (0,4) (0,11) (0,19) (0,25) (0,7) (0,9) (0,13) (0,18) (1,6) (1,12) (1,27) (1,8) (1,21) (1,10) (1,4) (1,11) (1,19) (1,25) (1,7) (1,26) (1,18) (2,6) (2,12) (2,27) (2,8) (2,21) (2,24) (2,22) (2,10) (2,4) (2,3) (2,19) (2,7) (2,9) (2,13) (2,18) (3,6) (3,5) (3,12) (3,27) (3,8) (3,21) (3,24) (3,22) (3,10) (3,4) (3,11) (3,25) (3,9) (3,13) (3,18) (4,6) (4,5) (4,12) (4,27) (4,21) (4,24) (4,22) (4,10) (4,19) (4,25) (4,7) (4,13) (5,6) (5,27) (5,22) (5,10) (5,11) (5,19) (5,25) (5,7) (5,13) (5,26) (5,18) (6,12) (6,27) (6,8) (6,24) (6,22) (6,10) (6,11) (6,19) (6,25) (6,7) (6,13) (6,26) (7,12) (7,27) (7,8) (7,21) (7,24) (7,22) (7,25) (7,9) (7,13) (7,26) (7,18) (8,12) (8,27) (8,21) (8,24) (8,22) (8,11) (8,19) (8,25) (8,9) (8,13) (8,26) (9,12) (9,21) (9,24) (9,22) (9,11) (9,19) (9,25) (9,13) (9,26) (10,27) (10,21) (10,24) (10,22) (10,19) (10,25) (10,13) (11,12) (11,27) (11,24) (11,22) (11,19) (11,25) (11,13) (11,26) (11,18) (12,21) (12,25) (12,13) (12,26) (12,18) (13,27) (13,24) (13,22) (13,19) (13,25) (13,26) (13,18) (14,15) (14,17) (14,23) (14,16) (14,20) (15,17) (15,23) (15,20) (16,17) (16,20) (18,22) (18,19) (18,26) (19,27) (19,21) (19,26) (20,23) (21,27) (21,24) (21,22) (21,26) (22,27) (22,26) (24,25) (25,26) (26,27)\nIs there a path between node 14 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph369-25_29", + "image": "data/connectivity/graph_visual/hard/graph369.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,16) (0,6) (0,12) (0,29) (0,13) (0,3) (0,21) (0,17) (0,30) (0,27) (0,8) (0,10) (1,9) (1,11) (1,16) (1,6) (1,20) (1,24) (1,13) (1,14) (1,3) (1,21) (1,17) (1,30) (1,25) (1,19) (1,27) (1,8) (1,10) (2,4) (3,26) (3,9) (3,11) (3,7) (3,12) (3,24) (3,13) (3,14) (3,17) (3,30) (3,25) (3,27) (3,8) (3,10) (4,23) (5,28) (5,15) (6,26) (6,9) (6,11) (6,16) (6,7) (6,12) (6,24) (6,14) (6,21) (6,17) (6,25) (6,19) (6,27) (6,10) (7,26) (7,11) (7,16) (7,12) (7,29) (7,24) (7,21) (7,17) (7,30) (7,8) (7,10) (8,9) (8,16) (8,12) (8,20) (8,24) (8,13) (8,14) (8,17) (8,30) (8,19) (8,27) (8,10) (9,11) (9,16) (9,12) (9,20) (9,29) (9,24) (9,14) (9,21) (9,17) (9,30) (9,25) (9,19) (9,27) (10,16) (10,12) (10,20) (10,24) (10,13) (10,14) (10,21) (10,17) (10,30) (10,25) (10,19) (10,27) (11,26) (11,16) (11,24) (11,14) (11,21) (11,30) (11,25) (11,19) (11,27) (12,26) (12,16) (12,20) (12,29) (12,24) (12,13) (12,14) (12,21) (12,17) (12,30) (12,19) (12,27) (13,26) (13,16) (13,20) (13,24) (13,14) (13,21) (13,17) (13,30) (13,19) (13,27) (14,26) (14,16) (14,20) (14,29) (14,30) (14,25) (15,31) (16,26) (16,29) (16,21) (16,17) (16,30) (16,25) (16,27) (17,26) (17,29) (17,21) (17,30) (17,25) (17,19) (17,27) (18,23) (18,22) (19,26) (19,20) (19,21) (19,30) (19,25) (19,27) (20,26) (20,29) (20,24) (20,21) (20,30) (20,25) (20,27) (21,26) (21,29) (21,30) (21,25) (21,27) (22,23) (24,29) (24,30) (25,29) (25,30) (25,27) (26,29) (27,29) (27,30) (29,30)\nIs there a path between node 25 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph36-6_20", + "image": "data/connectivity/graph_visual/hard/graph36.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,19) (0,18) (0,23) (0,22) (0,1) (0,21) (0,24) (0,7) (0,4) (0,3) (0,15) (0,12) (0,5) (1,22) (1,7) (1,4) (1,15) (1,12) (2,17) (2,9) (2,11) (2,25) (2,14) (3,19) (3,22) (3,21) (3,7) (3,4) (3,15) (3,12) (3,5) (4,19) (4,23) (4,7) (4,15) (4,12) (4,5) (5,19) (5,23) (5,22) (5,21) (5,7) (5,12) (6,20) (7,19) (7,23) (7,24) (7,15) (7,12) (8,10) (8,13) (9,17) (9,11) (9,25) (9,16) (10,13) (10,20) (11,17) (11,16) (11,14) (12,18) (12,22) (12,21) (12,15) (13,20) (14,25) (14,16) (15,19) (15,18) (15,23) (15,22) (15,21) (15,24) (16,17) (16,25) (17,25) (18,19) (18,23) (18,22) (18,21) (18,24) (19,23) (19,21) (19,24) (21,23) (21,22) (21,24) (22,24) (23,24)\nIs there a path between node 6 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph385-16_23", + "image": "data/connectivity/graph_visual/hard/graph385.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,25) (0,9) (0,21) (0,29) (0,20) (0,22) (0,10) (0,15) (0,17) (0,23) (0,5) (0,31) (1,4) (1,26) (1,18) (1,6) (1,19) (1,24) (1,27) (1,30) (1,28) (1,13) (1,11) (2,12) (2,4) (2,18) (2,6) (2,24) (2,27) (2,28) (2,13) (2,11) (3,25) (3,21) (3,29) (3,20) (3,22) (3,10) (3,14) (3,8) (3,17) (3,23) (3,7) (4,12) (4,26) (4,18) (4,6) (4,19) (4,30) (4,28) (4,13) (4,11) (5,25) (5,9) (5,21) (5,29) (5,16) (5,20) (5,22) (5,8) (5,15) (5,17) (5,7) (5,31) (6,26) (6,18) (6,19) (6,24) (6,27) (6,28) (6,13) (6,11) (7,25) (7,9) (7,21) (7,29) (7,16) (7,20) (7,22) (7,14) (7,8) (7,15) (7,23) (8,9) (8,21) (8,29) (8,16) (8,22) (8,10) (8,15) (8,17) (8,23) (8,31) (9,25) (9,21) (9,16) (9,20) (9,10) (9,14) (9,17) (9,23) (9,31) (10,21) (10,29) (10,16) (10,20) (10,22) (10,15) (10,23) (11,26) (11,24) (11,27) (11,30) (11,28) (11,13) (12,26) (12,18) (12,24) (12,28) (13,26) (13,18) (13,19) (13,24) (13,27) (13,28) (14,21) (14,29) (14,20) (14,15) (14,23) (14,31) (15,25) (15,21) (15,16) (15,20) (15,22) (15,23) (15,31) (16,21) (16,29) (16,22) (16,17) (16,23) (16,31) (17,21) (17,29) (17,20) (17,22) (17,23) (18,26) (18,19) (18,24) (18,30) (19,26) (19,24) (19,27) (20,21) (20,29) (21,25) (21,22) (21,23) (22,29) (22,23) (22,31) (23,25) (23,31) (24,26) (24,30) (24,28) (25,31) (26,27) (26,30) (26,28) (27,30) (28,30) (29,31)\nIs there a path between node 16 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph654-22_32", + "image": "data/connectivity/graph_visual/hard/graph654.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,25) (0,10) (0,11) (0,18) (0,15) (0,21) (0,24) (0,26) (0,16) (0,31) (1,13) (1,30) (1,6) (1,22) (1,28) (1,23) (1,20) (1,3) (1,14) (1,29) (1,2) (1,32) (1,27) (1,9) (1,17) (2,13) (2,6) (2,12) (2,22) (2,28) (2,23) (2,20) (2,14) (2,29) (2,32) (2,27) (3,13) (3,30) (3,6) (3,22) (3,28) (3,5) (3,23) (3,29) (3,32) (3,27) (3,9) (3,17) (4,33) (4,19) (4,10) (4,11) (4,18) (4,15) (4,21) (4,24) (4,26) (4,16) (4,31) (5,13) (5,30) (5,6) (5,12) (5,22) (5,28) (5,20) (5,14) (5,32) (5,27) (5,9) (6,12) (6,22) (6,28) (6,23) (6,20) (6,14) (6,29) (6,32) (6,27) (6,9) (6,17) (7,8) (7,25) (7,33) (7,19) (7,10) (7,11) (7,15) (7,34) (7,26) (7,16) (7,31) (8,33) (8,19) (8,10) (8,18) (8,24) (8,26) (8,16) (8,31) (9,13) (9,30) (9,12) (9,28) (9,14) (9,29) (9,32) (9,27) (10,33) (10,19) (10,18) (10,15) (10,34) (10,24) (10,26) (10,16) (10,31) (11,25) (11,33) (11,19) (11,18) (11,34) (11,24) (11,26) (11,16) (11,31) (12,13) (12,30) (12,14) (12,29) (12,32) (12,27) (12,17) (13,30) (13,23) (13,20) (13,14) (13,29) (13,27) (13,17) (14,30) (14,23) (14,20) (14,29) (14,27) (14,17) (15,33) (15,19) (15,21) (15,24) (15,26) (15,16) (15,31) (16,25) (16,33) (16,19) (16,18) (16,21) (16,24) (16,26) (16,31) (17,30) (17,22) (17,20) (17,29) (17,32) (17,27) (18,25) (18,33) (18,19) (18,21) (18,34) (18,31) (19,21) (19,34) (19,24) (20,22) (20,28) (20,23) (20,29) (20,32) (20,27) (21,34) (21,24) (21,26) (22,30) (22,29) (22,27) (23,30) (23,29) (23,32) (24,33) (24,26) (24,31) (25,31) (26,34) (26,31) (27,28) (27,29) (27,32) (28,30) (28,29) (28,32) (29,30) (30,32) (31,33) (31,34) (33,34)\nIs there a path between node 22 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph7-24_14", + "image": "data/connectivity/graph_visual/hard/graph7.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,5) (0,1) (0,4) (0,12) (0,23) (0,19) (0,14) (0,21) (0,15) (0,7) (0,22) (1,24) (1,6) (1,20) (1,23) (1,25) (1,3) (1,9) (1,16) (1,7) (2,6) (2,19) (2,14) (2,10) (2,3) (2,8) (2,9) (2,7) (3,5) (3,24) (3,14) (3,25) (3,22) (4,24) (4,19) (4,10) (4,16) (5,24) (5,14) (5,15) (5,9) (6,23) (6,14) (6,15) (7,24) (7,23) (7,14) (7,15) (7,10) (7,22) (8,19) (8,14) (8,21) (8,25) (8,22) (9,23) (10,24) (10,16) (11,18) (11,17) (12,20) (12,14) (12,25) (12,16) (14,24) (14,23) (14,19) (14,15) (15,20) (15,19) (15,21) (15,22) (16,25) (17,18) (19,21) (20,24) (20,23) (20,25) (21,23) (22,23)\nIs there a path between node 24 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph203-14_22", + "image": "data/connectivity/graph_visual/hard/graph203.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,5) (0,11) (0,13) (3,4) (3,21) (5,14) (5,27) (5,6) (5,19) (5,29) (5,25) (5,16) (5,13) (6,8) (6,9) (6,20) (6,29) (6,16) (6,11) (7,8) (7,26) (7,20) (7,12) (8,9) (8,19) (8,20) (8,28) (8,10) (8,22) (9,19) (9,20) (9,25) (9,11) (9,12) (9,22) (10,20) (10,25) (10,24) (10,15) (10,22) (11,26) (11,20) (11,28) (11,16) (11,24) (11,15) (12,25) (12,16) (12,23) (12,22) (13,18) (14,26) (14,24) (15,26) (15,20) (15,28) (16,27) (16,18) (16,26) (16,25) (16,23) (16,22) (18,27) (18,19) (18,20) (18,28) (18,25) (19,26) (19,20) (20,29) (20,25) (20,22) (22,24) (23,27) (23,29) (24,26) (24,28) (24,29) (25,27) (25,26)\nIs there a path between node 14 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph317-21_1", + "image": "data/connectivity/graph_visual/hard/graph317.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,31) (0,12) (0,22) (0,2) (1,18) (1,31) (1,30) (1,10) (1,2) (2,9) (2,31) (2,30) (2,12) (2,17) (2,16) (2,24) (3,20) (3,28) (3,14) (4,27) (4,29) (4,28) (4,7) (4,26) (5,29) (5,28) (6,8) (6,27) (6,15) (6,29) (7,20) (7,19) (7,29) (8,19) (8,11) (8,21) (8,29) (8,28) (9,18) (9,23) (9,16) (9,22) (10,30) (11,25) (11,19) (11,14) (11,26) (12,31) (13,25) (13,27) (13,29) (14,20) (14,28) (14,26) (15,20) (15,27) (15,26) (16,31) (16,30) (17,18) (18,31) (18,30) (18,22) (19,28) (20,21) (20,29) (20,28) (20,26) (21,25) (21,27) (22,24) (23,31) (24,31) (26,29)\nIs there a path between node 21 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph517-22_33", + "image": "data/connectivity/graph_visual/hard/graph517.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,22) (0,28) (0,25) (0,14) (0,29) (1,22) (1,31) (1,7) (1,25) (1,16) (1,14) (2,13) (2,22) (2,21) (2,31) (2,11) (2,4) (2,20) (3,33) (4,17) (4,13) (4,7) (4,8) (4,24) (4,25) (4,16) (4,29) (5,17) (5,13) (5,24) (5,6) (6,21) (6,7) (6,24) (7,28) (7,8) (7,16) (8,20) (9,21) (9,16) (9,20) (10,26) (10,19) (10,12) (10,32) (10,18) (11,21) (11,14) (12,19) (14,28) (14,24) (14,16) (15,30) (16,22) (16,24) (16,25) (17,28) (17,24) (17,29) (17,20) (18,32) (20,31) (20,24) (21,22) (21,29) (22,31) (22,29) (23,26) (23,32) (24,28) (27,32) (28,29) (29,31)\nIs there a path between node 22 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph401-11_21", + "image": "data/connectivity/graph_visual/hard/graph401.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,11) (0,15) (0,31) (0,7) (0,4) (0,28) (0,32) (0,19) (0,16) (0,25) (0,17) (0,12) (0,27) (0,9) (0,23) (0,3) (0,14) (0,1) (0,2) (0,29) (1,30) (1,31) (1,13) (1,7) (1,4) (1,6) (1,32) (1,19) (1,22) (1,26) (1,16) (1,25) (1,17) (1,27) (1,9) (1,24) (1,14) (1,2) (2,15) (2,30) (2,31) (2,13) (2,7) (2,4) (2,6) (2,32) (2,8) (2,19) (2,26) (2,17) (2,12) (2,18) (2,27) (2,9) (2,24) (2,23) (2,5) (2,3) (2,14) (2,29) (3,11) (3,30) (3,31) (3,13) (3,7) (3,4) (3,28) (3,6) (3,32) (3,8) (3,22) (3,26) (3,16) (3,25) (3,17) (3,18) (3,27) (3,23) (3,5) (3,14) (3,29) (4,11) (4,30) (4,31) (4,6) (4,32) (4,19) (4,16) (4,25) (4,17) (4,12) (4,18) (4,27) (4,9) (4,24) (4,5) (4,14) (5,11) (5,31) (5,13) (5,7) (5,28) (5,19) (5,26) (5,25) (5,12) (5,18) (5,24) (5,23) (5,14) (6,11) (6,15) (6,30) (6,31) (6,13) (6,7) (6,28) (6,8) (6,22) (6,26) (6,16) (6,25) (6,17) (6,12) (6,14) (6,29) (7,11) (7,15) (7,30) (7,31) (7,28) (7,32) (7,19) (7,22) (7,17) (7,12) (7,18) (7,27) (7,24) (7,23) (7,29) (8,11) (8,15) (8,30) (8,31) (8,13) (8,28) (8,32) (8,19) (8,26) (8,16) (8,17) (8,12) (8,9) (8,24) (8,23) (8,14) (8,29) (9,11) (9,30) (9,13) (9,32) (9,19) (9,26) (9,16) (9,25) (9,12) (9,18) (9,27) (9,24) (9,29) (10,20) (11,31) (11,13) (11,28) (11,32) (11,19) (11,22) (11,16) (11,25) (11,17) (11,27) (11,24) (11,23) (11,29) (12,15) (12,13) (12,28) (12,32) (12,19) (12,26) (12,25) (12,27) (12,23) (12,29) (13,15) (13,31) (13,28) (13,32) (13,22) (13,26) (13,16) (13,25) (13,18) (13,27) (13,24) (13,23) (13,29) (14,15) (14,30) (14,31) (14,28) (14,32) (14,19) (14,22) (14,26) (14,16) (14,25) (14,17) (14,18) (14,27) (14,24) (14,23) (14,29) (15,31) (15,19) (15,22) (15,17) (15,18) (15,27) (15,24) (15,23) (15,29) (16,30) (16,31) (16,32) (16,19) (16,22) (16,26) (16,27) (16,24) (17,28) (17,32) (17,19) (17,18) (17,27) (18,30) (18,31) (18,28) (18,32) (18,19) (18,22) (18,27) (18,24) (18,23) (19,30) (19,31) (19,28) (19,32) (19,22) (19,25) (19,27) (19,23) (19,29) (20,21) (22,30) (22,26) (22,25) (22,27) (22,29) (23,30) (23,28) (23,32) (23,26) (23,25) (23,27) (23,24) (23,29) (24,30) (24,31) (24,28) (24,32) (24,25) (24,27) (24,29) (25,30) (25,28) (25,32) (25,27) (25,29) (26,30) (26,32) (26,27) (26,29) (27,28) (27,29) (28,29) (29,31) (29,32) (30,32) (31,32)\nIs there a path between node 11 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph454-15_0", + "image": "data/connectivity/graph_visual/hard/graph454.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,7) (0,4) (0,23) (0,21) (0,18) (1,10) (1,19) (1,24) (1,18) (1,5) (2,11) (2,14) (2,22) (2,23) (2,13) (2,15) (2,31) (2,20) (3,11) (3,22) (3,16) (3,30) (3,13) (3,20) (3,18) (4,11) (4,14) (4,6) (4,23) (4,24) (4,31) (4,32) (4,18) (4,5) (5,19) (5,11) (5,7) (5,23) (5,15) (5,31) (6,19) (6,7) (6,13) (6,8) (7,11) (7,22) (7,28) (7,30) (7,21) (7,31) (8,10) (8,12) (8,14) (8,16) (8,30) (8,21) (9,17) (10,12) (10,24) (10,21) (10,32) (10,20) (11,22) (11,23) (11,13) (11,15) (11,18) (12,22) (12,31) (12,18) (13,16) (13,30) (13,23) (13,21) (13,15) (13,32) (14,19) (14,30) (14,23) (14,31) (15,30) (15,31) (15,32) (15,20) (16,30) (16,24) (16,21) (16,32) (17,25) (18,19) (18,28) (18,24) (19,21) (20,22) (20,21) (22,30) (22,23) (22,32) (24,28) (24,31) (24,32) (25,26) (25,27)\nIs there a path between node 15 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph690-30_25", + "image": "data/connectivity/graph_visual/hard/graph690.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,10) (0,7) (0,14) (0,32) (0,24) (0,29) (1,27) (1,31) (1,25) (1,3) (1,18) (1,9) (1,16) (1,33) (1,15) (1,13) (1,19) (1,22) (1,21) (1,30) (2,11) (3,31) (3,25) (3,18) (3,34) (3,20) (3,9) (3,16) (3,33) (3,13) (3,22) (3,21) (3,30) (4,27) (4,31) (4,34) (4,20) (4,9) (4,16) (4,15) (4,13) (4,19) (4,30) (5,17) (5,8) (6,12) (6,10) (6,28) (6,7) (6,14) (6,32) (6,29) (7,26) (7,12) (7,14) (7,32) (7,23) (7,24) (7,29) (8,17) (9,31) (9,18) (9,34) (9,20) (9,16) (9,22) (10,26) (10,12) (10,28) (10,32) (10,24) (12,26) (12,14) (12,24) (12,29) (13,27) (13,31) (13,25) (13,18) (13,34) (13,16) (13,33) (13,19) (13,22) (13,21) (13,30) (14,26) (14,28) (14,32) (15,25) (15,18) (15,34) (15,20) (15,33) (15,19) (15,22) (15,30) (16,27) (16,18) (16,34) (16,20) (16,33) (16,19) (16,22) (16,21) (18,25) (18,34) (18,22) (18,21) (18,30) (19,27) (19,31) (19,25) (19,20) (19,33) (19,22) (19,21) (19,30) (20,27) (20,31) (20,34) (20,33) (20,22) (20,21) (21,31) (21,22) (21,30) (22,27) (22,31) (22,25) (22,34) (22,30) (23,26) (23,28) (23,32) (23,29) (24,28) (24,32) (24,29) (25,27) (25,31) (25,33) (25,30) (26,28) (27,31) (27,34) (27,30) (28,29) (29,32) (30,34) (30,33) (31,34) (31,33)\nIs there a path between node 30 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph443-14_23", + "image": "data/connectivity/graph_visual/hard/graph443.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (1,28) (1,23) (1,20) (1,4) (1,21) (1,13) (2,28) (2,18) (2,27) (2,31) (2,21) (2,32) (3,28) (3,8) (3,20) (3,7) (3,27) (3,29) (3,10) (3,16) (3,4) (3,6) (3,17) (3,32) (4,18) (4,23) (4,8) (4,29) (4,6) (5,28) (5,24) (5,26) (5,23) (5,8) (5,7) (5,10) (5,6) (5,9) (5,11) (6,23) (6,20) (6,10) (6,16) (6,13) (6,11) (6,32) (7,25) (7,27) (7,31) (7,10) (7,17) (7,30) (7,32) (8,26) (8,9) (9,24) (9,19) (9,27) (9,30) (9,32) (10,26) (10,23) (10,29) (10,31) (10,16) (10,21) (11,28) (11,25) (11,24) (11,19) (11,23) (11,20) (11,31) (11,13) (11,17) (12,22) (13,28) (13,25) (13,24) (13,19) (13,26) (13,23) (13,29) (13,31) (13,21) (13,15) (15,25) (15,18) (15,24) (15,21) (15,30) (16,28) (16,19) (16,26) (16,23) (16,29) (16,31) (16,30) (17,23) (17,29) (18,25) (18,19) (18,23) (18,27) (18,21) (19,29) (19,31) (20,28) (20,31) (20,32) (21,26) (21,23) (21,27) (21,29) (21,31) (23,28) (23,27) (23,29) (23,30) (24,29) (24,30) (25,31) (25,30) (26,29) (26,30) (26,32) (27,28) (27,29) (27,31) (28,29) (29,31)\nIs there a path between node 14 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph16-23_2", + "image": "data/connectivity/graph_visual/hard/graph16.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (1,4) (1,11) (2,21) (2,20) (2,24) (3,24) (4,13) (4,15) (4,8) (5,19) (5,24) (6,20) (6,24) (7,25) (7,21) (8,17) (8,15) (8,12) (9,13) (9,12) (10,16) (11,13) (11,18) (11,23) (11,14) (11,12) (13,17) (14,23) (15,18) (15,23) (18,23) (19,25) (19,24) (20,21) (21,25) (24,25)\nIs there a path between node 23 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph203-11_1", + "image": "data/connectivity/graph_visual/hard/graph203.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,5) (0,11) (0,13) (3,4) (3,21) (5,14) (5,27) (5,6) (5,19) (5,29) (5,25) (5,16) (5,13) (6,8) (6,9) (6,20) (6,29) (6,16) (6,11) (7,8) (7,26) (7,20) (7,12) (8,9) (8,19) (8,20) (8,28) (8,10) (8,22) (9,19) (9,20) (9,25) (9,11) (9,12) (9,22) (10,20) (10,25) (10,24) (10,15) (10,22) (11,26) (11,20) (11,28) (11,16) (11,24) (11,15) (12,25) (12,16) (12,23) (12,22) (13,18) (14,26) (14,24) (15,26) (15,20) (15,28) (16,27) (16,18) (16,26) (16,25) (16,23) (16,22) (18,27) (18,19) (18,20) (18,28) (18,25) (19,26) (19,20) (20,29) (20,25) (20,22) (22,24) (23,27) (23,29) (24,26) (24,28) (24,29) (25,27) (25,26)\nIs there a path between node 11 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph162-7_24", + "image": "data/connectivity/graph_visual/hard/graph162.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,6) (0,22) (0,7) (0,3) (1,15) (1,16) (1,10) (2,15) (2,24) (2,16) (3,6) (3,7) (3,27) (3,5) (3,20) (4,11) (4,7) (4,27) (4,21) (5,26) (5,22) (5,19) (5,21) (5,20) (5,9) (6,7) (6,27) (6,21) (6,20) (7,21) (7,20) (8,13) (8,12) (8,16) (8,14) (9,11) (9,26) (9,19) (12,15) (12,16) (13,18) (16,18) (16,25) (17,24) (18,25) (19,22) (21,26)\nIs there a path between node 7 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph23-7_15", + "image": "data/connectivity/graph_visual/hard/graph23.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,21) (0,24) (0,3) (0,23) (0,2) (0,1) (0,22) (1,7) (1,2) (1,8) (1,11) (1,22) (2,23) (2,8) (2,10) (3,19) (3,20) (3,8) (4,9) (5,21) (5,24) (5,17) (5,15) (5,8) (6,14) (7,21) (7,24) (7,13) (7,15) (8,21) (8,16) (8,23) (8,22) (10,17) (10,18) (10,25) (10,22) (11,24) (11,23) (13,24) (13,20) (13,22) (15,20) (15,23) (15,25) (16,19) (16,20) (16,23) (17,21) (17,20) (17,23) (18,24) (18,23) (18,25) (21,22) (22,23) (23,24)\nIs there a path between node 7 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph664-5_25", + "image": "data/connectivity/graph_visual/hard/graph664.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,14) (0,16) (0,33) (0,10) (0,7) (0,25) (1,28) (1,2) (1,12) (1,17) (1,13) (1,18) (1,32) (1,20) (1,16) (1,30) (1,7) (1,25) (1,31) (2,17) (2,18) (2,21) (2,33) (2,8) (2,11) (3,24) (3,6) (3,19) (4,6) (4,23) (4,34) (4,26) (5,24) (5,23) (5,26) (6,23) (6,19) (7,28) (7,13) (7,20) (7,22) (8,17) (8,20) (8,16) (8,22) (9,28) (9,18) (9,32) (9,16) (9,30) (9,11) (10,28) (10,14) (10,22) (10,25) (11,28) (11,12) (11,17) (11,18) (11,22) (11,33) (12,28) (12,15) (12,14) (12,16) (12,29) (12,33) (12,25) (13,30) (14,17) (14,18) (14,16) (14,22) (14,31) (15,18) (15,21) (15,16) (15,30) (16,28) (16,21) (16,20) (16,22) (16,31) (17,28) (17,18) (17,32) (17,20) (18,32) (18,21) (18,22) (18,30) (19,23) (19,34) (20,27) (20,25) (20,31) (21,32) (21,29) (21,33) (21,31) (22,31) (25,28) (25,32) (25,27) (26,34) (27,29) (30,31) (31,32) (31,33) (32,33)\nIs there a path between node 5 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph572-26_4", + "image": "data/connectivity/graph_visual/hard/graph572.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,10) (0,4) (1,15) (1,11) (1,24) (1,5) (2,6) (2,7) (2,9) (2,30) (3,9) (3,20) (3,14) (3,23) (3,18) (4,10) (4,6) (4,29) (4,9) (4,17) (4,8) (4,23) (4,18) (4,30) (5,15) (5,22) (5,24) (6,10) (6,7) (6,14) (6,21) (6,30) (7,28) (7,29) (7,9) (7,27) (7,17) (7,21) (7,30) (8,10) (8,9) (8,27) (8,14) (8,23) (8,21) (9,10) (9,28) (9,27) (9,17) (10,28) (10,29) (10,18) (12,16) (12,31) (12,33) (13,19) (14,27) (14,17) (14,18) (15,24) (16,31) (16,33) (16,24) (17,29) (18,28) (18,30) (19,22) (20,27) (20,21) (21,28) (22,33) (22,24) (24,31) (24,33) (25,26)\nIs there a path between node 26 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph176-20_1", + "image": "data/connectivity/graph_visual/hard/graph176.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,19) (0,13) (0,4) (0,28) (0,3) (0,11) (0,9) (0,18) (1,22) (1,6) (1,20) (1,21) (2,8) (2,15) (2,25) (2,19) (2,23) (2,4) (2,28) (2,24) (2,16) (2,11) (2,9) (2,26) (2,18) (3,25) (3,19) (3,23) (3,24) (3,11) (3,12) (3,9) (3,26) (3,18) (4,8) (4,15) (4,25) (4,13) (4,23) (4,28) (4,16) (4,11) (4,12) (4,9) (4,26) (4,18) (5,14) (5,22) (5,10) (5,6) (5,17) (5,21) (5,27) (5,7) (6,14) (6,10) (6,17) (6,27) (7,14) (7,22) (7,10) (8,15) (8,25) (8,19) (8,23) (8,28) (8,16) (8,9) (8,18) (9,19) (9,28) (9,24) (9,11) (9,12) (10,14) (10,22) (10,17) (10,20) (10,21) (10,27) (11,15) (11,23) (11,24) (11,16) (11,26) (11,18) (12,15) (12,25) (12,19) (12,13) (12,23) (12,24) (12,26) (13,15) (13,19) (13,24) (13,16) (13,18) (14,22) (14,17) (14,20) (14,21) (15,25) (15,19) (15,23) (15,16) (15,18) (16,25) (16,19) (16,28) (16,24) (16,26) (16,18) (17,20) (17,21) (17,27) (18,25) (18,19) (18,23) (18,28) (19,25) (19,23) (19,28) (19,24) (19,26) (20,22) (20,21) (21,22) (21,27) (22,27) (23,28) (23,24) (24,25) (24,26) (25,26) (26,28)\nIs there a path between node 20 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph635-27_11", + "image": "data/connectivity/graph_visual/hard/graph635.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,25) (0,21) (0,13) (0,34) (0,12) (0,32) (0,31) (0,24) (0,15) (0,29) (1,23) (1,31) (1,14) (1,24) (1,15) (2,5) (2,25) (2,13) (2,17) (2,15) (2,29) (2,16) (3,6) (3,10) (4,20) (4,19) (5,7) (5,13) (5,17) (5,12) (5,14) (5,30) (5,26) (6,19) (6,8) (6,18) (6,27) (7,22) (7,21) (7,34) (7,32) (7,14) (7,24) (8,11) (8,19) (8,10) (9,11) (9,19) (9,10) (10,28) (11,19) (11,18) (12,21) (12,34) (12,14) (12,15) (12,30) (13,22) (13,33) (13,32) (14,34) (14,31) (14,24) (14,15) (14,29) (15,22) (15,25) (15,34) (15,31) (15,30) (16,25) (16,21) (17,23) (17,33) (17,32) (17,29) (18,20) (18,28) (20,28) (20,27) (21,25) (21,33) (21,24) (22,23) (22,33) (22,34) (23,29) (26,30) (27,28) (29,33) (30,31) (31,32) (32,33)\nIs there a path between node 27 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph286-13_29", + "image": "data/connectivity/graph_visual/hard/graph286.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,1) (0,20) (0,8) (0,31) (0,22) (1,4) (1,24) (1,19) (1,16) (1,5) (1,2) (1,8) (1,18) (1,27) (2,4) (2,19) (2,12) (2,17) (2,21) (2,31) (2,22) (3,25) (3,20) (3,14) (3,31) (3,22) (3,27) (4,7) (4,21) (4,26) (4,27) (5,11) (5,24) (5,20) (5,19) (5,12) (5,16) (5,17) (5,21) (5,9) (5,22) (6,15) (7,24) (7,20) (7,19) (7,16) (7,29) (7,17) (7,21) (7,14) (7,9) (7,8) (7,18) (7,22) (7,30) (8,20) (8,12) (8,14) (9,20) (9,16) (9,14) (9,18) (9,26) (9,23) (10,15) (11,25) (11,28) (11,20) (11,21) (11,26) (12,28) (12,24) (12,20) (12,29) (12,14) (12,18) (12,26) (12,22) (12,27) (12,23) (14,24) (14,16) (14,18) (14,31) (16,25) (16,26) (16,31) (16,23) (17,31) (17,27) (18,25) (18,28) (18,24) (18,21) (18,26) (18,27) (19,29) (19,21) (19,22) (20,25) (20,21) (20,26) (21,24) (21,29) (21,31) (21,23) (22,29) (22,26) (22,23) (23,25) (23,26) (24,25) (24,26) (24,30) (25,29) (25,31) (26,29) (26,31) (27,28) (27,31) (28,29) (29,31) (29,30) (30,31)\nIs there a path between node 13 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph235-13_26", + "image": "data/connectivity/graph_visual/hard/graph235.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,29) (0,27) (0,23) (0,4) (0,20) (0,17) (0,6) (1,5) (1,22) (1,11) (1,19) (1,24) (1,2) (1,15) (1,8) (1,30) (1,9) (1,28) (1,18) (2,5) (2,22) (2,24) (2,15) (2,8) (2,30) (2,9) (2,28) (2,18) (3,26) (3,13) (4,21) (4,29) (4,23) (4,20) (4,17) (4,6) (5,22) (5,19) (5,24) (5,14) (5,30) (5,28) (5,18) (6,21) (6,29) (6,27) (6,23) (6,20) (6,17) (7,26) (7,10) (7,13) (7,16) (7,12) (8,11) (8,24) (8,14) (8,30) (8,9) (8,28) (8,18) (9,22) (9,11) (9,19) (9,15) (9,28) (10,16) (10,12) (11,15) (11,30) (11,28) (11,18) (12,13) (12,16) (13,26) (13,16) (13,25) (14,22) (14,19) (14,15) (14,30) (15,19) (15,30) (15,28) (15,18) (16,26) (16,25) (17,29) (17,23) (18,19) (18,24) (18,28) (19,30) (19,28) (20,21) (20,27) (21,29) (21,27) (21,23) (22,24) (22,28) (23,27) (24,30) (24,28) (25,26) (28,30)\nIs there a path between node 13 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph180-5_22", + "image": "data/connectivity/graph_visual/hard/graph180.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,6) (0,15) (0,9) (0,19) (0,26) (0,21) (0,13) (0,24) (0,11) (0,2) (0,25) (0,3) (0,12) (0,23) (0,27) (0,4) (1,28) (1,16) (1,7) (1,10) (2,8) (2,6) (2,15) (2,26) (2,17) (2,21) (2,13) (2,11) (2,14) (2,18) (2,5) (2,12) (2,4) (3,8) (3,22) (3,6) (3,15) (3,9) (3,19) (3,17) (3,21) (3,24) (3,11) (3,25) (3,14) (3,23) (3,4) (4,22) (4,15) (4,9) (4,19) (4,17) (4,13) (4,24) (4,25) (4,14) (4,18) (4,5) (4,23) (4,27) (5,8) (5,15) (5,9) (5,26) (5,17) (5,13) (5,24) (5,25) (5,12) (5,23) (5,27) (6,15) (6,19) (6,26) (6,17) (6,21) (6,13) (6,14) (6,12) (6,23) (6,27) (7,16) (7,20) (8,22) (8,9) (8,19) (8,17) (8,13) (8,24) (8,14) (8,18) (8,23) (8,27) (9,22) (9,19) (9,17) (9,21) (9,24) (9,11) (9,25) (9,14) (9,18) (9,12) (9,23) (9,27) (10,28) (10,16) (10,20) (11,22) (11,19) (11,26) (11,21) (11,24) (11,14) (11,18) (11,12) (11,23) (11,27) (12,22) (12,19) (12,26) (12,21) (12,13) (12,24) (12,14) (12,18) (12,27) (13,22) (13,15) (13,26) (13,21) (13,25) (13,14) (13,18) (13,27) (14,22) (14,15) (14,19) (14,26) (14,17) (14,21) (14,24) (14,18) (14,23) (14,27) (15,22) (15,19) (15,17) (15,21) (15,24) (15,25) (15,18) (15,27) (16,28) (17,22) (17,26) (17,21) (17,24) (17,25) (17,23) (17,27) (18,19) (18,26) (18,21) (18,23) (18,27) (19,22) (19,24) (20,28) (21,22) (21,26) (21,23) (21,27) (22,26) (22,24) (22,27) (23,26) (23,24) (23,25) (23,27) (24,25) (24,27) (25,26) (26,27)\nIs there a path between node 5 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph675-34_1", + "image": "data/connectivity/graph_visual/hard/graph675.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (1,28) (1,5) (1,3) (2,15) (2,12) (2,11) (2,18) (2,29) (2,10) (3,24) (3,21) (5,23) (6,16) (6,18) (6,29) (6,9) (6,27) (6,10) (7,25) (7,16) (7,11) (7,18) (7,20) (7,26) (9,15) (9,25) (9,12) (9,20) (9,29) (10,17) (10,30) (10,25) (10,14) (10,16) (10,29) (10,22) (11,16) (11,19) (11,29) (11,27) (12,30) (12,19) (13,32) (13,19) (13,29) (13,27) (13,26) (14,15) (14,19) (14,26) (15,17) (15,25) (15,16) (15,18) (16,19) (16,18) (16,29) (17,30) (17,18) (17,29) (17,26) (18,22) (18,31) (18,26) (19,32) (19,22) (19,31) (20,34) (20,29) (20,27) (22,30) (22,31) (25,27) (27,34) (27,30) (27,32) (27,29) (27,31) (29,32) (29,31) (30,32) (31,34) (32,34)\nIs there a path between node 34 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph209-18_15", + "image": "data/connectivity/graph_visual/hard/graph209.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,22) (1,18) (1,25) (1,8) (1,16) (1,11) (1,6) (1,24) (2,22) (2,18) (2,17) (2,20) (2,11) (2,6) (3,13) (4,22) (4,25) (4,21) (4,17) (4,11) (4,6) (5,27) (5,13) (6,29) (6,24) (7,22) (7,21) (7,17) (7,16) (7,11) (7,24) (7,15) (7,19) (8,18) (8,12) (8,11) (8,24) (9,28) (10,26) (10,23) (11,17) (12,17) (12,20) (12,16) (13,27) (16,22) (16,25) (16,21) (16,29) (16,19) (17,29) (17,20) (19,21) (19,29) (19,20) (20,22) (21,22) (21,25) (21,29) (27,28)\nIs there a path between node 18 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph197-18_29", + "image": "data/connectivity/graph_visual/hard/graph197.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,5) (0,18) (0,28) (0,10) (0,13) (0,8) (0,22) (0,20) (1,3) (1,29) (1,23) (1,26) (1,6) (1,24) (1,15) (2,4) (2,27) (3,25) (3,29) (3,23) (3,26) (3,6) (3,24) (3,14) (3,16) (3,9) (4,27) (5,11) (5,18) (5,7) (5,10) (5,8) (5,22) (5,21) (5,20) (6,25) (6,29) (6,23) (6,12) (6,26) (6,24) (6,16) (6,15) (6,9) (7,11) (7,28) (7,19) (7,10) (7,13) (7,8) (7,22) (7,21) (7,20) (8,11) (8,18) (8,19) (8,10) (8,13) (8,22) (8,21) (8,20) (9,25) (9,29) (9,12) (9,26) (9,24) (9,14) (9,16) (9,15) (10,11) (10,18) (10,28) (10,19) (10,13) (10,22) (10,21) (11,18) (11,28) (11,19) (11,13) (11,22) (11,21) (12,25) (12,29) (12,23) (12,24) (12,14) (12,15) (13,18) (13,28) (13,19) (13,21) (14,25) (14,29) (14,16) (15,29) (15,23) (15,26) (15,24) (15,16) (16,25) (16,23) (16,26) (16,24) (18,28) (18,21) (19,28) (19,22) (19,21) (19,20) (20,28) (20,21) (21,22) (22,28) (23,29) (24,25) (24,29) (24,26) (25,29)\nIs there a path between node 18 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph200-9_12", + "image": "data/connectivity/graph_visual/hard/graph200.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,26) (0,1) (0,17) (0,6) (0,27) (0,11) (0,2) (1,16) (1,26) (1,17) (1,6) (1,27) (1,11) (1,2) (2,17) (2,27) (2,11) (3,5) (3,23) (3,22) (3,4) (4,23) (4,14) (5,23) (5,14) (5,18) (6,16) (6,17) (6,27) (7,8) (7,24) (7,19) (7,10) (7,9) (7,12) (7,21) (7,25) (7,28) (7,15) (8,24) (8,19) (8,10) (8,9) (8,21) (8,13) (8,28) (8,15) (9,24) (9,19) (9,10) (9,20) (9,12) (9,13) (9,29) (9,15) (10,24) (10,19) (10,20) (10,21) (10,25) (10,29) (10,28) (10,15) (11,16) (11,26) (11,27) (12,24) (12,19) (12,20) (12,21) (12,25) (12,29) (12,28) (13,19) (13,20) (13,21) (13,25) (13,28) (13,15) (14,23) (14,18) (15,24) (15,19) (15,25) (15,28) (16,26) (16,17) (16,27) (17,27) (18,22) (19,24) (19,20) (19,29) (19,28) (20,24) (20,29) (20,28) (21,24) (21,25) (21,29) (21,28) (22,23) (24,25) (24,29) (24,28) (25,28) (26,27) (28,29)\nIs there a path between node 9 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph383-27_19", + "image": "data/connectivity/graph_visual/hard/graph383.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,29) (0,28) (0,8) (0,23) (0,6) (0,10) (0,11) (0,31) (0,2) (0,9) (0,21) (0,12) (0,22) (0,14) (0,30) (1,15) (1,26) (1,19) (1,13) (1,20) (2,29) (2,28) (2,8) (2,6) (2,10) (2,11) (2,31) (2,21) (2,12) (2,14) (3,24) (3,26) (3,19) (3,13) (3,4) (4,15) (4,26) (4,19) (5,16) (5,7) (5,17) (6,28) (6,23) (6,10) (6,11) (6,31) (6,9) (6,22) (6,14) (6,30) (7,27) (8,29) (8,28) (8,23) (8,10) (8,11) (8,31) (8,9) (8,25) (8,21) (8,12) (8,14) (9,18) (9,29) (9,23) (9,10) (9,11) (9,31) (9,25) (9,14) (10,18) (10,28) (10,23) (10,11) (10,21) (10,12) (10,14) (10,30) (11,18) (11,28) (11,23) (11,31) (11,25) (11,21) (11,12) (11,22) (11,14) (11,30) (12,18) (12,29) (12,28) (12,31) (12,25) (12,22) (12,14) (13,24) (13,15) (13,26) (13,19) (14,18) (14,23) (14,31) (14,25) (14,21) (14,22) (14,30) (15,19) (15,20) (16,27) (16,17) (17,27) (18,29) (18,23) (18,31) (18,25) (19,24) (19,26) (19,20) (20,26) (21,29) (21,28) (21,23) (21,25) (21,22) (22,29) (22,28) (22,23) (22,31) (22,25) (22,30) (23,29) (23,28) (23,31) (23,25) (25,29) (25,28) (25,31) (25,30) (28,29) (28,31) (28,30) (29,30) (30,31)\nIs there a path between node 27 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph537-14_13", + "image": "data/connectivity/graph_visual/hard/graph537.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,16) (0,17) (0,4) (0,8) (0,12) (0,31) (1,19) (1,21) (1,2) (1,30) (1,26) (1,3) (1,9) (1,22) (1,6) (1,23) (1,18) (2,21) (2,28) (2,26) (2,3) (2,25) (2,20) (2,33) (2,9) (2,22) (2,6) (2,15) (2,7) (2,23) (2,18) (3,19) (3,30) (3,28) (3,26) (3,22) (3,32) (3,6) (3,15) (3,23) (3,18) (4,10) (4,16) (4,17) (4,5) (4,8) (4,12) (5,10) (5,13) (5,24) (5,16) (5,31) (6,19) (6,14) (6,30) (6,26) (6,25) (6,20) (6,11) (6,9) (6,22) (6,27) (6,32) (6,15) (6,29) (7,21) (7,30) (7,28) (7,26) (7,25) (7,33) (7,22) (7,27) (7,32) (7,15) (7,29) (7,23) (7,18) (8,13) (8,24) (8,16) (8,17) (8,31) (9,19) (9,21) (9,30) (9,20) (9,11) (9,22) (9,15) (9,23) (9,18) (10,13) (10,24) (10,16) (10,17) (10,12) (10,31) (11,19) (11,21) (11,14) (11,28) (11,26) (11,25) (11,20) (11,22) (11,32) (11,15) (11,29) (11,23) (11,18) (12,24) (12,17) (13,24) (13,16) (13,17) (14,19) (14,21) (14,30) (14,28) (14,25) (14,20) (14,33) (14,32) (14,15) (14,29) (14,23) (14,18) (15,30) (15,28) (15,26) (15,25) (15,20) (15,33) (15,22) (15,32) (15,29) (15,23) (15,18) (16,24) (16,17) (17,31) (18,19) (18,28) (18,26) (18,20) (18,33) (18,22) (18,27) (18,29) (18,23) (19,21) (19,28) (19,26) (19,20) (19,22) (19,29) (19,23) (20,21) (20,30) (20,26) (20,25) (20,22) (20,32) (20,29) (20,23) (21,28) (21,33) (21,22) (21,27) (21,32) (21,29) (22,30) (22,28) (22,26) (22,25) (22,27) (22,32) (22,23) (23,30) (23,28) (23,26) (23,33) (23,27) (23,32) (23,29) (24,31) (25,30) (25,26) (25,33) (25,27) (25,32) (25,29) (26,28) (26,27) (26,32) (26,29) (27,30) (27,28) (27,32) (27,29) (28,30) (28,33) (28,29) (29,32) (30,32) (32,33)\nIs there a path between node 14 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph185-20_11", + "image": "data/connectivity/graph_visual/hard/graph185.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,3) (0,18) (0,24) (0,5) (0,12) (0,26) (0,14) (0,16) (0,21) (0,9) (0,1) (0,28) (0,25) (1,3) (1,18) (1,24) (1,5) (1,12) (1,26) (1,14) (1,16) (1,21) (1,2) (1,23) (1,20) (1,28) (1,25) (2,3) (2,18) (2,10) (2,24) (2,5) (2,12) (2,26) (2,14) (2,16) (2,9) (2,23) (2,20) (2,28) (2,7) (2,25) (2,22) (2,13) (3,18) (3,24) (3,12) (3,26) (3,16) (3,9) (3,19) (3,7) (3,25) (3,22) (4,11) (4,27) (4,17) (4,15) (4,8) (5,18) (5,24) (5,12) (5,26) (5,14) (5,16) (5,21) (5,9) (5,23) (5,19) (5,20) (5,7) (5,13) (6,11) (6,27) (6,29) (6,15) (6,8) (7,18) (7,10) (7,12) (7,26) (7,14) (7,16) (7,21) (7,9) (7,20) (7,25) (7,22) (7,13) (8,11) (8,27) (8,29) (8,17) (8,15) (9,18) (9,10) (9,24) (9,16) (9,21) (9,19) (9,20) (9,28) (9,25) (9,13) (10,18) (10,24) (10,12) (10,26) (10,14) (10,16) (10,23) (10,20) (10,28) (10,25) (10,22) (10,13) (11,27) (11,29) (12,18) (12,24) (12,16) (12,21) (12,23) (12,20) (12,28) (12,22) (12,13) (13,18) (13,24) (13,26) (13,14) (13,16) (13,21) (13,23) (13,20) (13,28) (13,25) (13,22) (14,26) (14,16) (14,21) (14,23) (14,19) (14,20) (14,28) (14,25) (15,27) (15,17) (16,18) (16,24) (16,26) (16,20) (16,25) (16,22) (17,29) (18,24) (18,26) (18,23) (18,19) (18,20) (18,25) (18,22) (19,21) (19,23) (19,28) (19,25) (20,26) (20,23) (20,28) (20,25) (20,22) (21,26) (21,23) (21,28) (21,22) (22,26) (22,23) (22,25) (23,24) (23,26) (24,26) (24,28) (25,26)\nIs there a path between node 20 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph551-1_23", + "image": "data/connectivity/graph_visual/hard/graph551.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,21) (0,30) (0,19) (0,25) (1,24) (1,18) (1,19) (1,31) (1,25) (1,26) (2,22) (2,23) (3,8) (3,13) (3,10) (5,14) (6,24) (6,8) (6,9) (6,13) (6,10) (6,28) (6,15) (7,11) (8,30) (8,9) (8,13) (8,26) (9,24) (9,16) (9,30) (9,10) (9,27) (10,18) (10,28) (10,15) (11,22) (11,29) (13,18) (13,21) (14,17) (15,18) (15,30) (15,19) (15,33) (15,31) (15,27) (15,26) (16,30) (16,19) (16,27) (18,30) (18,19) (18,28) (18,27) (19,24) (19,33) (19,28) (20,22) (20,29) (21,33) (21,25) (21,27) (23,32) (24,30) (24,28) (24,31) (25,31) (26,30) (26,28) (28,30) (31,33)\nIs there a path between node 1 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph491-32_11", + "image": "data/connectivity/graph_visual/hard/graph491.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (0,15) (0,32) (0,3) (0,13) (0,19) (0,17) (1,14) (1,10) (1,21) (1,5) (1,29) (1,2) (2,14) (2,12) (2,21) (2,22) (2,29) (2,6) (2,4) (3,18) (3,13) (3,11) (3,19) (3,9) (3,17) (4,14) (4,12) (4,21) (4,5) (4,29) (4,6) (5,14) (5,22) (6,14) (6,12) (6,10) (6,21) (6,22) (6,29) (7,23) (7,30) (7,18) (7,32) (7,11) (8,25) (8,31) (8,20) (8,16) (9,23) (9,18) (9,32) (9,13) (9,11) (9,19) (9,17) (10,22) (10,29) (11,23) (11,15) (11,30) (11,18) (11,32) (11,19) (11,17) (12,14) (12,22) (12,29) (13,23) (13,15) (13,18) (13,32) (13,17) (14,22) (15,23) (15,30) (15,32) (15,19) (15,17) (16,25) (16,31) (16,24) (16,20) (16,28) (16,26) (16,27) (17,30) (17,18) (17,32) (17,19) (19,30) (19,32) (20,24) (20,27) (21,22) (21,29) (22,29) (23,32) (24,28) (24,26) (24,27) (25,31) (25,28) (25,27) (26,28) (26,27) (27,31) (27,28) (28,31) (30,32)\nIs there a path between node 32 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph355-10_9", + "image": "data/connectivity/graph_visual/hard/graph355.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,2) (1,16) (1,8) (1,6) (1,13) (1,18) (1,22) (1,10) (1,17) (1,12) (3,5) (3,30) (3,17) (3,12) (4,28) (5,29) (5,6) (5,25) (5,22) (5,10) (5,17) (5,12) (6,15) (6,13) (6,7) (6,30) (6,11) (6,12) (6,26) (7,29) (7,21) (7,25) (7,14) (7,19) (7,17) (7,12) (8,20) (8,21) (8,13) (8,11) (8,25) (8,14) (8,17) (10,15) (10,27) (10,18) (10,26) (11,20) (11,31) (11,13) (11,27) (11,24) (11,17) (12,21) (12,16) (12,31) (12,25) (13,21) (13,31) (13,27) (13,22) (13,19) (14,29) (14,16) (14,24) (14,25) (14,17) (14,26) (15,18) (16,20) (16,30) (16,24) (16,17) (16,26) (17,25) (18,20) (18,21) (18,31) (18,24) (19,27) (19,25) (19,22) (20,29) (20,27) (20,22) (21,30) (21,24) (21,26) (22,30) (24,27) (24,26) (25,26) (26,29) (26,27) (27,29) (27,30)\nIs there a path between node 10 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph589-24_16", + "image": "data/connectivity/graph_visual/hard/graph589.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,11) (0,16) (0,3) (0,26) (0,15) (0,30) (0,20) (0,27) (0,17) (0,18) (0,7) (0,1) (0,23) (0,24) (0,12) (1,8) (1,16) (1,25) (1,10) (1,5) (1,26) (1,15) (1,20) (1,27) (1,18) (1,13) (1,23) (1,2) (1,24) (1,31) (1,33) (1,12) (1,4) (1,6) (2,8) (2,11) (2,21) (2,25) (2,3) (2,10) (2,5) (2,26) (2,15) (2,27) (2,28) (2,14) (2,13) (2,31) (2,33) (2,4) (3,8) (3,9) (3,16) (3,25) (3,5) (3,26) (3,22) (3,30) (3,20) (3,17) (3,7) (3,28) (3,23) (3,24) (3,12) (3,4) (4,8) (4,11) (4,21) (4,25) (4,10) (4,15) (4,22) (4,20) (4,27) (4,18) (4,7) (4,28) (4,14) (4,23) (4,24) (4,31) (4,12) (5,8) (5,11) (5,9) (5,16) (5,21) (5,25) (5,10) (5,26) (5,15) (5,22) (5,30) (5,27) (5,18) (5,7) (5,28) (5,14) (5,13) (5,31) (6,8) (6,21) (6,25) (6,10) (6,26) (6,15) (6,22) (6,30) (6,20) (6,27) (6,28) (6,13) (6,31) (6,33) (7,11) (7,9) (7,16) (7,21) (7,25) (7,10) (7,26) (7,15) (7,22) (7,30) (7,20) (7,27) (7,28) (7,14) (7,13) (7,23) (7,24) (7,31) (7,12) (8,11) (8,9) (8,16) (8,21) (8,25) (8,10) (8,26) (8,30) (8,20) (8,17) (8,18) (8,28) (8,14) (8,23) (8,24) (8,31) (8,12) (9,11) (9,16) (9,21) (9,10) (9,26) (9,15) (9,22) (9,30) (9,27) (9,17) (9,18) (9,28) (9,14) (9,13) (9,24) (9,31) (10,26) (10,30) (10,27) (10,17) (10,18) (10,28) (10,14) (10,13) (10,31) (10,33) (10,12) (11,16) (11,21) (11,25) (11,26) (11,15) (11,22) (11,30) (11,20) (11,27) (11,17) (11,18) (11,28) (11,14) (11,13) (11,24) (11,31) (11,33) (11,12) (12,21) (12,25) (12,26) (12,22) (12,20) (12,17) (12,18) (12,28) (12,14) (12,13) (12,23) (12,31) (12,33) (13,25) (13,26) (13,15) (13,30) (13,20) (13,17) (13,18) (13,14) (13,23) (13,24) (13,31) (13,33) (14,16) (14,21) (14,25) (14,26) (14,22) (14,20) (14,17) (14,18) (14,28) (14,23) (14,31) (14,33) (15,16) (15,22) (15,30) (15,18) (15,28) (15,23) (15,24) (15,31) (15,33) (16,21) (16,25) (16,22) (16,20) (16,27) (16,17) (16,18) (16,28) (16,23) (16,33) (17,25) (17,22) (17,30) (17,20) (17,27) (17,18) (17,28) (17,23) (17,24) (17,33) (18,25) (18,22) (18,30) (18,20) (18,27) (18,23) (18,24) (18,33) (19,29) (19,32) (20,26) (20,22) (20,30) (20,27) (20,28) (20,23) (20,24) (20,31) (20,33) (21,25) (21,26) (21,30) (21,27) (21,28) (21,23) (21,33) (22,26) (22,30) (22,23) (22,33) (23,25) (23,26) (23,27) (23,28) (23,24) (23,31) (23,33) (24,25) (24,26) (24,28) (24,31) (25,26) (25,30) (25,27) (25,28) (25,33) (26,30) (26,27) (26,28) (26,31) (27,30) (27,28) (27,33) (28,31) (28,33) (29,32) (30,33) (31,33)\nIs there a path between node 24 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph147-18_6", + "image": "data/connectivity/graph_visual/hard/graph147.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,8) (0,19) (0,26) (0,7) (0,14) (0,5) (0,21) (0,13) (0,24) (0,17) (0,1) (0,9) (0,3) (0,16) (0,25) (1,8) (1,19) (1,26) (1,2) (1,7) (1,14) (1,5) (1,27) (1,4) (1,28) (1,15) (1,24) (1,17) (1,9) (1,23) (1,11) (1,3) (1,16) (2,12) (2,8) (2,22) (2,19) (2,26) (2,7) (2,18) (2,21) (2,27) (2,13) (2,15) (2,17) (2,9) (2,10) (2,23) (2,3) (2,16) (2,25) (3,12) (3,22) (3,19) (3,26) (3,7) (3,14) (3,18) (3,5) (3,21) (3,27) (3,4) (3,28) (3,13) (3,15) (3,24) (3,17) (3,9) (3,23) (3,11) (3,16) (4,12) (4,8) (4,26) (4,14) (4,18) (4,21) (4,13) (4,15) (4,24) (4,17) (4,23) (4,16) (5,12) (5,8) (5,22) (5,26) (5,14) (5,18) (5,21) (5,27) (5,28) (5,13) (5,15) (5,17) (5,10) (5,11) (5,25) (7,12) (7,8) (7,26) (7,14) (7,18) (7,21) (7,27) (7,13) (7,15) (7,17) (7,9) (7,10) (7,11) (7,16) (7,25) (8,12) (8,19) (8,14) (8,18) (8,21) (8,27) (8,13) (8,24) (8,17) (8,9) (8,10) (8,23) (8,16) (8,25) (9,12) (9,19) (9,14) (9,18) (9,27) (9,28) (9,13) (9,15) (9,17) (9,10) (9,23) (9,11) (9,16) (9,25) (10,12) (10,22) (10,19) (10,14) (10,18) (10,21) (10,27) (10,28) (10,13) (10,24) (10,23) (10,11) (10,25) (11,22) (11,19) (11,27) (11,13) (11,15) (11,23) (11,25) (12,19) (12,14) (12,18) (12,21) (12,27) (12,15) (12,24) (12,17) (12,25) (13,22) (13,19) (13,26) (13,14) (13,18) (13,21) (13,28) (13,15) (13,17) (13,23) (13,16) (13,25) (14,18) (14,21) (14,27) (14,28) (14,17) (14,23) (14,16) (14,25) (15,22) (15,19) (15,18) (15,24) (15,17) (15,23) (15,25) (16,22) (16,19) (16,26) (16,18) (16,21) (16,27) (16,28) (16,24) (16,17) (16,23) (16,25) (17,22) (17,19) (17,18) (17,21) (17,27) (17,24) (17,23) (17,25) (18,22) (18,19) (18,26) (18,21) (18,27) (18,28) (18,24) (18,23) (19,22) (19,26) (19,28) (19,24) (19,23) (19,25) (21,22) (21,26) (21,27) (21,28) (21,25) (22,26) (22,27) (22,24) (22,23) (22,25) (23,26) (23,27) (23,28) (23,24) (23,25) (24,26) (24,28) (24,25) (25,26) (25,27) (25,28) (27,28)\nIs there a path between node 18 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph527-19_27", + "image": "data/connectivity/graph_visual/hard/graph527.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,33) (0,21) (0,2) (0,19) (1,11) (2,17) (3,18) (3,10) (4,12) (4,7) (4,13) (5,14) (5,32) (6,10) (6,14) (7,12) (7,21) (8,14) (8,28) (10,32) (10,28) (12,33) (12,17) (12,19) (13,21) (13,29) (14,18) (14,32) (16,21) (16,19) (17,29) (18,26) (19,33) (19,29) (20,23) (23,31) (24,32) (25,30) (26,32) (26,28)\nIs there a path between node 19 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph28-5_16", + "image": "data/connectivity/graph_visual/hard/graph28.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,1) (0,11) (1,18) (1,17) (1,2) (4,16) (4,18) (4,22) (5,13) (5,24) (5,10) (7,12) (8,16) (8,11) (9,13) (9,14) (10,15) (10,14) (11,18) (13,14) (14,15) (15,24) (16,19) (16,22) (17,18) (18,20) (18,21) (18,25) (19,20) (19,21) (19,22) (20,21) (22,25) (23,24)\nIs there a path between node 5 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph423-7_6", + "image": "data/connectivity/graph_visual/hard/graph423.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,6) (0,15) (0,9) (0,23) (0,10) (0,28) (1,24) (1,13) (1,9) (1,23) (1,28) (2,30) (2,17) (2,31) (2,4) (2,11) (3,18) (4,25) (4,32) (4,22) (4,19) (4,31) (4,8) (5,24) (5,14) (5,23) (6,26) (6,28) (8,30) (8,32) (8,20) (8,11) (9,24) (9,13) (9,23) (9,18) (10,13) (11,25) (11,21) (11,16) (12,25) (12,32) (13,23) (13,28) (14,29) (15,26) (15,28) (16,17) (16,20) (17,25) (17,31) (18,23) (19,25) (20,22) (20,21) (20,31) (21,25) (21,31) (22,25) (23,27) (24,29) (24,26) (24,28) (25,30) (25,32) (26,29) (26,28) (31,32)\nIs there a path between node 7 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph271-16_17", + "image": "data/connectivity/graph_visual/hard/graph271.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,20) (1,3) (1,27) (1,23) (1,9) (1,26) (1,29) (1,15) (1,11) (1,24) (1,22) (1,10) (1,21) (1,18) (1,17) (1,2) (1,5) (1,4) (1,28) (1,7) (1,25) (2,20) (2,19) (2,3) (2,27) (2,23) (2,26) (2,29) (2,11) (2,24) (2,22) (2,21) (2,30) (2,18) (2,5) (2,4) (2,28) (2,7) (2,13) (2,25) (3,20) (3,19) (3,9) (3,26) (3,29) (3,15) (3,11) (3,24) (3,22) (3,10) (3,21) (3,30) (3,8) (3,28) (3,12) (3,7) (3,13) (3,25) (4,20) (4,19) (4,27) (4,26) (4,29) (4,15) (4,11) (4,24) (4,10) (4,30) (4,18) (4,17) (4,12) (4,7) (4,13) (4,25) (5,20) (5,19) (5,27) (5,26) (5,29) (5,24) (5,22) (5,30) (5,18) (5,8) (5,17) (5,6) (5,12) (5,13) (5,25) (6,19) (6,27) (6,23) (6,9) (6,26) (6,29) (6,15) (6,11) (6,22) (6,21) (6,30) (6,17) (6,28) (6,12) (6,7) (6,13) (6,25) (7,19) (7,27) (7,9) (7,26) (7,29) (7,15) (7,11) (7,22) (7,21) (7,30) (7,18) (7,8) (7,17) (7,28) (7,12) (7,13) (7,25) (8,20) (8,19) (8,27) (8,23) (8,9) (8,29) (8,15) (8,24) (8,22) (8,10) (8,30) (8,18) (8,17) (8,28) (8,13) (8,25) (9,20) (9,19) (9,27) (9,23) (9,11) (9,24) (9,22) (9,10) (9,30) (9,17) (9,12) (9,13) (9,25) (10,27) (10,23) (10,29) (10,15) (10,11) (10,24) (10,21) (10,30) (10,17) (10,28) (10,13) (10,25) (11,20) (11,27) (11,23) (11,29) (11,15) (11,24) (11,22) (11,21) (11,30) (11,12) (11,13) (11,25) (12,19) (12,27) (12,23) (12,26) (12,29) (12,15) (12,24) (12,22) (12,30) (12,18) (12,13) (12,25) (13,20) (13,19) (13,27) (13,26) (13,29) (13,24) (13,21) (13,18) (13,28) (14,16) (15,20) (15,19) (15,23) (15,26) (15,29) (15,24) (15,22) (15,21) (15,18) (15,28) (15,25) (17,20) (17,23) (17,24) (17,22) (17,21) (17,30) (17,28) (17,25) (18,20) (18,19) (18,23) (18,26) (18,24) (18,22) (18,30) (18,28) (18,25) (19,27) (19,29) (19,22) (19,21) (19,30) (19,25) (20,27) (20,26) (20,29) (20,24) (20,22) (20,21) (21,27) (21,23) (21,22) (21,30) (21,28) (21,25) (22,27) (22,23) (22,29) (22,24) (22,30) (22,28) (22,25) (23,27) (23,26) (23,29) (23,30) (23,28) (23,25) (24,27) (24,25) (25,26) (25,29) (25,30) (25,28) (26,30) (27,30) (27,28) (29,30)\nIs there a path between node 16 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph46-5_22", + "image": "data/connectivity/graph_visual/hard/graph46.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,12) (0,19) (0,25) (0,2) (0,13) (0,1) (1,17) (1,24) (1,25) (1,11) (2,17) (2,25) (2,16) (2,13) (3,17) (4,23) (4,7) (4,14) (4,8) (5,18) (5,16) (6,18) (6,16) (6,21) (7,14) (7,15) (7,10) (8,23) (8,10) (9,14) (9,10) (10,23) (10,20) (11,17) (11,18) (11,25) (11,16) (11,13) (12,16) (13,17) (13,24) (13,25) (13,21) (14,15) (16,21) (17,19) (17,18) (17,25) (19,25) (19,21) (21,25)\nIs there a path between node 5 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph267-14_18", + "image": "data/connectivity/graph_visual/hard/graph267.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,3) (0,16) (0,21) (0,15) (1,18) (1,11) (1,22) (1,30) (1,12) (2,3) (2,25) (2,7) (3,17) (3,25) (3,19) (4,22) (4,30) (5,28) (7,16) (7,25) (7,14) (7,21) (7,19) (7,27) (8,9) (10,13) (10,30) (10,12) (10,26) (11,18) (11,30) (11,26) (12,29) (12,18) (12,30) (15,17) (15,25) (15,19) (17,25) (18,22) (18,26) (19,27) (20,28) (22,29) (24,26) (26,29)\nIs there a path between node 14 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph692-32_3", + "image": "data/connectivity/graph_visual/hard/graph692.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,15) (0,2) (0,33) (0,4) (0,8) (0,23) (0,34) (0,30) (1,22) (1,28) (1,9) (1,29) (1,24) (1,26) (1,7) (1,27) (1,32) (1,19) (1,16) (1,5) (1,10) (2,12) (2,3) (2,15) (2,33) (2,20) (2,8) (2,23) (3,12) (3,11) (3,33) (3,4) (3,8) (3,23) (4,12) (4,11) (4,33) (4,20) (4,23) (5,22) (5,17) (5,28) (5,29) (5,14) (5,31) (5,25) (5,18) (5,24) (5,26) (5,6) (5,27) (5,32) (5,21) (5,19) (5,16) (6,17) (6,28) (6,13) (6,29) (6,14) (6,31) (6,25) (6,24) (6,27) (6,19) (6,16) (6,10) (7,22) (7,17) (7,9) (7,13) (7,29) (7,25) (7,24) (7,26) (7,27) (7,21) (7,19) (7,16) (7,10) (8,12) (8,11) (8,15) (8,33) (8,30) (9,22) (9,28) (9,13) (9,29) (9,14) (9,31) (9,18) (9,24) (9,26) (9,27) (9,32) (9,21) (9,19) (9,16) (9,10) (10,22) (10,17) (10,28) (10,13) (10,29) (10,14) (10,31) (10,25) (10,18) (10,26) (10,32) (10,21) (10,16) (11,33) (11,20) (11,23) (11,30) (12,33) (12,20) (12,34) (12,30) (13,22) (13,17) (13,28) (13,29) (13,14) (13,31) (13,25) (13,18) (13,24) (13,26) (13,32) (13,21) (13,19) (13,16) (14,22) (14,17) (14,28) (14,29) (14,31) (14,25) (14,18) (14,24) (14,26) (14,27) (14,32) (14,21) (14,19) (14,16) (15,33) (15,20) (15,23) (15,34) (15,30) (16,22) (16,17) (16,28) (16,29) (16,31) (16,18) (16,24) (16,26) (16,27) (16,32) (16,21) (17,28) (17,29) (17,31) (17,18) (17,24) (17,27) (17,32) (17,21) (17,19) (18,22) (18,28) (18,29) (18,31) (18,25) (18,27) (18,21) (19,22) (19,28) (19,29) (19,31) (19,25) (19,27) (19,21) (20,33) (20,23) (20,34) (20,30) (21,28) (21,29) (21,31) (21,25) (21,26) (21,32) (22,28) (22,31) (22,25) (22,24) (22,26) (22,27) (22,32) (23,33) (24,28) (24,29) (24,31) (24,26) (24,32) (25,31) (25,27) (25,32) (26,29) (26,31) (26,27) (27,28) (27,29) (27,31) (27,32) (28,29) (28,32) (29,32) (30,33) (30,34) (31,32) (33,34)\nIs there a path between node 32 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph677-30_16", + "image": "data/connectivity/graph_visual/hard/graph677.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,7) (0,9) (0,11) (0,27) (0,24) (0,29) (0,22) (0,20) (1,4) (1,17) (1,28) (1,12) (1,14) (1,31) (1,24) (1,13) (1,3) (1,22) (1,20) (2,18) (2,4) (2,6) (2,28) (2,12) (2,31) (2,29) (2,22) (2,23) (2,5) (2,19) (3,14) (3,24) (3,20) (3,5) (3,30) (3,19) (4,17) (4,9) (4,27) (4,13) (4,5) (4,30) (4,19) (5,8) (5,18) (5,28) (5,31) (5,9) (5,11) (5,13) (5,22) (5,23) (6,18) (6,28) (6,31) (6,9) (6,20) (7,8) (7,18) (7,9) (8,17) (8,14) (8,31) (8,27) (8,22) (8,20) (8,30) (8,33) (8,19) (9,28) (9,14) (9,31) (10,13) (10,19) (11,18) (11,28) (11,14) (11,31) (11,27) (11,29) (11,22) (11,30) (11,33) (12,18) (12,17) (12,24) (12,23) (13,18) (13,17) (13,28) (13,31) (13,22) (14,18) (14,29) (14,22) (14,30) (14,33) (15,16) (17,27) (17,25) (17,29) (17,22) (17,20) (17,30) (17,33) (18,28) (18,24) (18,22) (18,20) (18,19) (19,27) (19,24) (19,23) (20,29) (20,33) (21,32) (21,34) (22,23) (22,33) (23,24) (23,25) (25,29) (27,30) (27,33) (29,33) (30,31) (31,33) (32,34)\nIs there a path between node 30 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph505-27_4", + "image": "data/connectivity/graph_visual/hard/graph505.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,33) (0,8) (0,16) (0,5) (0,17) (0,23) (1,6) (1,7) (1,27) (1,14) (1,4) (1,13) (1,24) (1,21) (2,32) (2,19) (2,29) (2,12) (2,28) (2,15) (3,32) (3,19) (3,26) (3,12) (3,20) (3,30) (3,28) (3,15) (4,6) (4,9) (4,7) (4,14) (4,10) (4,24) (5,33) (5,8) (5,16) (5,31) (5,17) (5,23) (6,7) (6,27) (6,10) (6,25) (6,13) (7,27) (7,14) (7,10) (7,25) (7,24) (7,21) (8,16) (8,17) (9,27) (9,14) (9,10) (9,24) (9,21) (10,25) (10,21) (11,32) (11,19) (11,26) (11,12) (11,20) (11,30) (11,28) (11,22) (12,19) (12,29) (12,26) (12,20) (12,15) (12,22) (13,27) (13,14) (13,25) (13,24) (13,21) (14,25) (14,24) (14,21) (15,32) (15,19) (15,26) (15,20) (15,30) (15,28) (16,33) (16,18) (16,31) (16,23) (17,33) (17,18) (17,23) (18,33) (18,31) (19,32) (19,29) (19,26) (19,30) (19,28) (19,22) (20,32) (20,30) (20,28) (21,25) (22,32) (22,29) (22,26) (22,30) (22,28) (23,33) (24,27) (24,25) (25,27) (26,29) (26,30) (26,28) (28,30) (29,32) (29,30) (30,32) (31,33)\nIs there a path between node 27 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph447-30_29", + "image": "data/connectivity/graph_visual/hard/graph447.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (1,11) (1,25) (1,27) (1,20) (1,24) (2,14) (3,19) (3,17) (5,18) (5,27) (5,28) (6,7) (6,13) (6,29) (7,8) (7,10) (7,17) (8,31) (8,13) (9,10) (9,13) (10,19) (10,12) (11,25) (11,28) (12,13) (12,29) (13,29) (15,22) (15,25) (15,23) (15,27) (18,22) (18,23) (18,24) (19,31) (19,29) (20,23) (20,28) (20,24) (21,26) (22,25) (22,23) (22,27) (25,28) (27,28)\nIs there a path between node 30 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph297-13_7", + "image": "data/connectivity/graph_visual/hard/graph297.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,11) (0,21) (0,15) (0,12) (0,7) (0,13) (0,10) (0,20) (0,19) (0,6) (0,26) (0,30) (0,1) (0,27) (0,16) (0,5) (0,3) (0,22) (0,14) (0,25) (1,9) (1,11) (1,21) (1,15) (1,12) (1,13) (1,20) (1,19) (1,26) (1,27) (1,16) (1,5) (1,29) (1,3) (1,24) (1,25) (2,18) (2,31) (2,23) (3,9) (3,4) (3,15) (3,7) (3,13) (3,6) (3,30) (3,16) (3,29) (3,28) (3,24) (3,14) (4,11) (4,21) (4,17) (4,12) (4,7) (4,19) (4,6) (4,26) (4,16) (4,5) (4,29) (4,28) (4,22) (4,14) (4,25) (5,9) (5,11) (5,17) (5,15) (5,12) (5,13) (5,10) (5,20) (5,26) (5,27) (5,16) (5,29) (5,22) (5,24) (5,14) (6,9) (6,11) (6,21) (6,17) (6,15) (6,12) (6,7) (6,10) (6,26) (6,16) (6,29) (6,28) (6,22) (6,24) (6,14) (6,25) (7,9) (7,21) (7,10) (7,20) (7,19) (7,26) (7,27) (7,16) (7,29) (7,22) (7,24) (7,25) (8,18) (8,31) (8,23) (9,11) (9,21) (9,17) (9,15) (9,12) (9,13) (9,19) (9,26) (9,30) (9,27) (9,16) (9,29) (9,28) (9,14) (10,11) (10,21) (10,17) (10,12) (10,20) (10,26) (10,27) (10,29) (10,22) (10,24) (10,14) (10,25) (11,21) (11,17) (11,13) (11,20) (11,19) (11,26) (11,27) (11,16) (11,29) (11,22) (11,24) (11,25) (12,17) (12,13) (12,20) (12,19) (12,30) (12,27) (12,16) (12,29) (12,24) (12,14) (13,21) (13,20) (13,19) (13,26) (13,30) (13,16) (13,28) (13,22) (13,25) (14,20) (14,19) (14,30) (14,27) (14,16) (14,29) (14,28) (14,22) (14,25) (15,21) (15,19) (15,30) (15,16) (15,29) (15,24) (15,25) (16,21) (16,17) (16,20) (16,19) (16,30) (16,27) (16,29) (16,28) (16,22) (16,24) (17,21) (17,19) (17,26) (17,30) (17,29) (17,28) (17,22) (17,25) (18,31) (18,23) (19,21) (19,20) (19,26) (19,30) (19,27) (19,29) (19,28) (19,24) (19,25) (20,26) (20,30) (20,27) (20,29) (20,28) (20,24) (20,25) (21,27) (21,29) (21,22) (21,25) (22,26) (22,30) (22,27) (22,28) (22,24) (22,25) (24,26) (24,30) (24,27) (24,28) (25,30) (25,29) (25,28) (26,30) (26,27) (26,29) (27,30) (28,30)\nIs there a path between node 13 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph355-1_24", + "image": "data/connectivity/graph_visual/hard/graph355.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,2) (1,16) (1,8) (1,6) (1,13) (1,18) (1,22) (1,10) (1,17) (1,12) (3,5) (3,30) (3,17) (3,12) (4,28) (5,29) (5,6) (5,25) (5,22) (5,10) (5,17) (5,12) (6,15) (6,13) (6,7) (6,30) (6,11) (6,12) (6,26) (7,29) (7,21) (7,25) (7,14) (7,19) (7,17) (7,12) (8,20) (8,21) (8,13) (8,11) (8,25) (8,14) (8,17) (10,15) (10,27) (10,18) (10,26) (11,20) (11,31) (11,13) (11,27) (11,24) (11,17) (12,21) (12,16) (12,31) (12,25) (13,21) (13,31) (13,27) (13,22) (13,19) (14,29) (14,16) (14,24) (14,25) (14,17) (14,26) (15,18) (16,20) (16,30) (16,24) (16,17) (16,26) (17,25) (18,20) (18,21) (18,31) (18,24) (19,27) (19,25) (19,22) (20,29) (20,27) (20,22) (21,30) (21,24) (21,26) (22,30) (24,27) (24,26) (25,26) (26,29) (26,27) (27,29) (27,30)\nIs there a path between node 1 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph623-24_28", + "image": "data/connectivity/graph_visual/hard/graph623.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,29) (0,9) (0,17) (0,30) (0,16) (1,31) (1,25) (1,5) (1,16) (2,13) (2,15) (2,23) (2,30) (2,25) (2,5) (3,14) (5,13) (5,9) (5,17) (5,15) (5,23) (5,19) (5,30) (5,16) (5,22) (7,20) (7,34) (7,8) (7,17) (7,31) (7,18) (7,16) (7,32) (8,12) (8,34) (8,11) (8,18) (9,12) (9,34) (9,31) (9,18) (9,30) (9,16) (10,26) (10,28) (11,12) (11,20) (11,23) (11,19) (11,18) (11,30) (12,34) (12,13) (12,17) (12,23) (12,19) (12,18) (13,34) (13,15) (13,31) (13,21) (13,24) (13,32) (15,17) (15,23) (15,19) (15,30) (15,25) (15,21) (16,20) (16,17) (16,18) (16,25) (16,24) (16,27) (16,22) (17,20) (17,34) (17,29) (17,30) (17,21) (18,20) (18,27) (19,30) (20,34) (20,23) (20,25) (20,24) (20,27) (21,25) (22,23) (22,25) (23,29) (23,30) (23,27) (24,29) (24,31) (24,32) (25,29) (26,33) (28,33) (29,31) (29,32) (30,31) (31,34)\nIs there a path between node 24 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph701-10_15", + "image": "data/connectivity/graph_visual/hard/graph701.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,12) (0,6) (0,25) (0,9) (0,33) (0,3) (0,2) (0,24) (0,10) (0,28) (0,4) (0,29) (0,31) (0,21) (0,26) (0,13) (0,8) (0,5) (1,20) (1,34) (1,32) (1,19) (1,16) (2,15) (2,12) (2,25) (2,9) (2,33) (2,3) (2,28) (2,4) (2,29) (2,31) (2,26) (2,8) (2,5) (3,15) (3,12) (3,33) (3,28) (3,4) (3,29) (3,31) (3,21) (3,26) (3,8) (4,25) (4,9) (4,28) (4,31) (4,13) (4,8) (5,15) (5,12) (5,25) (5,33) (5,24) (5,10) (5,26) (5,13) (5,8) (6,12) (6,25) (6,9) (6,33) (6,24) (6,10) (6,28) (6,29) (6,31) (6,21) (6,13) (6,8) (7,20) (7,34) (7,32) (7,19) (7,16) (8,12) (8,25) (8,33) (8,10) (8,28) (8,29) (8,21) (8,26) (9,12) (9,33) (9,24) (9,10) (9,28) (9,26) (10,15) (10,12) (10,33) (10,24) (10,29) (10,31) (10,21) (10,26) (10,13) (11,22) (11,23) (11,14) (11,17) (12,28) (12,29) (12,21) (12,26) (12,13) (13,25) (13,33) (13,24) (13,28) (13,29) (13,31) (13,21) (13,26) (14,18) (14,22) (14,23) (14,27) (14,17) (14,30) (15,33) (15,24) (15,28) (15,29) (15,31) (15,21) (15,26) (16,20) (16,34) (16,32) (17,22) (17,23) (17,30) (18,27) (18,30) (19,20) (19,32) (20,34) (20,32) (21,25) (21,24) (21,28) (21,29) (21,26) (22,23) (22,27) (22,30) (23,30) (24,25) (24,28) (24,29) (24,26) (25,33) (25,28) (25,29) (25,31) (26,33) (26,29) (27,30) (28,33) (28,29) (29,33) (29,31) (31,33) (32,34)\nIs there a path between node 10 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph11-11_14", + "image": "data/connectivity/graph_visual/hard/graph11.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,15) (0,2) (0,1) (0,23) (0,8) (0,24) (0,6) (0,22) (0,4) (0,11) (1,15) (1,14) (1,2) (1,8) (1,12) (1,17) (1,19) (2,15) (2,14) (2,23) (2,8) (2,20) (2,6) (2,22) (2,4) (2,17) (2,11) (2,19) (2,7) (3,18) (3,9) (3,10) (3,21) (3,13) (3,16) (4,15) (4,14) (4,5) (4,23) (4,24) (4,12) (4,17) (4,11) (4,19) (4,7) (5,15) (5,14) (5,8) (5,20) (5,6) (5,22) (5,12) (5,17) (5,11) (5,19) (5,7) (6,15) (6,14) (6,23) (6,8) (6,20) (6,22) (6,12) (6,11) (6,19) (7,15) (7,23) (7,22) (7,12) (7,17) (7,19) (8,15) (8,14) (8,23) (8,24) (8,12) (8,17) (9,18) (9,21) (9,13) (9,16) (10,25) (10,16) (11,15) (11,14) (11,23) (11,24) (11,17) (11,19) (12,14) (12,22) (12,19) (13,25) (13,18) (13,21) (13,16) (14,15) (14,23) (14,22) (14,17) (14,19) (15,23) (15,24) (15,20) (15,22) (15,17) (15,19) (16,18) (17,23) (17,24) (17,19) (18,25) (18,21) (19,23) (19,24) (19,20) (20,23) (20,22) (21,25) (23,24)\nIs there a path between node 11 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph15-14_22", + "image": "data/connectivity/graph_visual/hard/graph15.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,14) (0,7) (0,6) (0,23) (0,25) (1,4) (1,3) (1,5) (1,13) (1,10) (1,20) (1,16) (1,22) (1,8) (1,18) (1,15) (2,7) (2,12) (2,6) (2,25) (2,17) (2,9) (3,11) (3,20) (3,16) (3,22) (3,8) (4,11) (4,13) (4,10) (4,16) (4,8) (4,18) (4,15) (5,11) (5,13) (5,16) (5,22) (5,8) (5,18) (6,7) (6,12) (6,23) (6,25) (6,9) (7,14) (7,12) (7,23) (7,25) (7,21) (7,17) (7,9) (8,11) (8,13) (8,10) (8,20) (8,16) (8,22) (8,15) (9,14) (9,25) (9,21) (9,17) (10,11) (10,20) (10,22) (10,15) (11,20) (11,16) (11,22) (11,18) (12,14) (12,23) (12,25) (12,21) (12,17) (13,16) (14,23) (14,21) (14,17) (15,20) (15,22) (15,18) (16,20) (16,22) (16,18) (17,23) (17,21) (18,20) (18,22) (20,22) (23,25)\nIs there a path between node 14 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph327-15_31", + "image": "data/connectivity/graph_visual/hard/graph327.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,3) (0,10) (0,27) (0,1) (0,29) (0,7) (0,14) (0,13) (0,20) (0,6) (1,3) (1,4) (1,10) (1,27) (1,7) (1,16) (1,14) (1,13) (1,20) (1,15) (1,6) (2,30) (2,12) (2,5) (2,11) (2,21) (2,28) (2,22) (2,25) (2,31) (2,19) (3,4) (3,29) (3,16) (3,14) (3,13) (3,20) (3,15) (4,10) (4,7) (4,16) (4,13) (4,15) (4,6) (5,12) (5,23) (5,24) (5,21) (5,28) (5,25) (5,31) (5,19) (6,27) (6,29) (6,7) (6,14) (6,13) (6,20) (6,15) (7,10) (7,27) (7,20) (8,18) (9,26) (9,18) (10,27) (10,29) (10,16) (10,13) (10,15) (11,30) (11,24) (11,21) (11,17) (11,28) (11,25) (12,23) (12,24) (12,21) (12,17) (12,28) (12,22) (12,25) (12,19) (13,27) (13,16) (13,20) (13,15) (14,27) (14,29) (14,16) (14,15) (15,27) (15,29) (15,16) (15,20) (16,27) (16,29) (16,20) (17,30) (17,23) (17,24) (17,21) (17,28) (17,22) (17,25) (17,31) (17,19) (18,26) (19,30) (19,23) (19,24) (19,21) (19,28) (19,25) (19,31) (20,27) (21,30) (21,24) (21,28) (21,22) (21,25) (21,31) (22,30) (22,23) (22,24) (22,28) (22,25) (22,31) (23,30) (23,24) (23,25) (23,31) (24,28) (24,25) (24,31) (25,30) (25,28) (25,31) (27,29) (28,30) (30,31)\nIs there a path between node 15 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph650-8_6", + "image": "data/connectivity/graph_visual/hard/graph650.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,19) (0,29) (0,25) (0,12) (0,30) (0,27) (0,3) (0,15) (0,32) (0,9) (0,7) (0,31) (0,13) (0,2) (0,33) (0,20) (0,17) (0,4) (0,34) (1,21) (1,28) (1,6) (1,5) (1,25) (1,12) (1,30) (1,27) (1,3) (1,32) (1,9) (1,7) (1,31) (1,22) (1,33) (1,20) (1,17) (1,26) (1,4) (1,34) (2,11) (2,18) (2,21) (2,19) (2,28) (2,5) (2,29) (2,25) (2,12) (2,30) (2,27) (2,3) (2,15) (2,7) (2,22) (2,24) (2,33) (2,20) (2,17) (2,26) (2,34) (3,11) (3,18) (3,21) (3,19) (3,28) (3,5) (3,29) (3,25) (3,12) (3,30) (3,27) (3,14) (3,32) (3,7) (3,31) (3,13) (3,22) (3,20) (3,17) (3,4) (4,11) (4,18) (4,19) (4,28) (4,6) (4,5) (4,29) (4,25) (4,12) (4,30) (4,27) (4,14) (4,15) (4,32) (4,9) (4,7) (4,13) (4,24) (4,17) (4,34) (5,11) (5,18) (5,21) (5,6) (5,29) (5,25) (5,27) (5,14) (5,15) (5,9) (5,23) (5,31) (5,22) (5,24) (5,33) (5,20) (5,17) (5,26) (5,34) (6,21) (6,19) (6,28) (6,29) (6,25) (6,12) (6,27) (6,14) (6,15) (6,32) (6,9) (6,23) (6,7) (6,31) (6,22) (6,24) (6,33) (6,20) (6,17) (6,26) (6,34) (7,11) (7,18) (7,19) (7,28) (7,30) (7,27) (7,14) (7,32) (7,23) (7,13) (7,22) (7,24) (7,33) (7,20) (7,17) (7,26) (7,34) (8,16) (9,11) (9,18) (9,21) (9,19) (9,28) (9,29) (9,25) (9,12) (9,30) (9,15) (9,32) (9,23) (9,31) (9,13) (9,22) (9,24) (9,33) (9,20) (9,17) (9,34) (10,16) (11,18) (11,21) (11,19) (11,12) (11,30) (11,27) (11,15) (11,32) (11,23) (11,31) (11,13) (11,22) (11,24) (11,20) (11,17) (11,26) (11,34) (12,18) (12,21) (12,28) (12,29) (12,25) (12,30) (12,27) (12,14) (12,32) (12,13) (12,22) (12,24) (12,33) (12,20) (12,26) (12,34) (13,18) (13,21) (13,19) (13,28) (13,29) (13,25) (13,30) (13,27) (13,32) (13,23) (13,31) (13,22) (13,24) (13,20) (13,17) (13,26) (13,34) (14,18) (14,21) (14,19) (14,28) (14,29) (14,30) (14,27) (14,15) (14,32) (14,23) (14,31) (14,22) (14,33) (14,20) (14,17) (14,26) (15,18) (15,21) (15,29) (15,25) (15,30) (15,23) (15,31) (15,22) (15,33) (15,17) (15,26) (17,18) (17,21) (17,19) (17,28) (17,29) (17,25) (17,30) (17,27) (17,32) (17,23) (17,31) (17,22) (17,24) (17,33) (17,26) (17,34) (18,19) (18,28) (18,23) (18,22) (18,33) (18,20) (19,21) (19,28) (19,25) (19,30) (19,27) (19,31) (19,24) (19,33) (19,26) (19,34) (20,21) (20,28) (20,25) (20,27) (20,32) (20,31) (20,24) (21,28) (21,29) (21,25) (21,30) (21,27) (21,31) (21,22) (21,24) (21,26) (21,34) (22,28) (22,25) (22,27) (22,32) (22,23) (22,24) (22,33) (22,26) (22,34) (23,28) (23,25) (23,30) (23,27) (23,32) (23,31) (23,24) (23,33) (23,26) (23,34) (24,28) (24,29) (24,25) (24,30) (24,31) (24,33) (24,26) (24,34) (25,28) (25,30) (25,27) (25,32) (25,33) (25,26) (25,34) (26,28) (26,27) (26,32) (26,31) (26,33) (27,29) (27,32) (27,33) (27,34) (28,29) (28,30) (28,32) (28,31) (28,34) (29,32) (29,31) (29,34) (30,32) (30,31) (31,32) (31,33) (32,33) (33,34)\nIs there a path between node 8 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph70-21_19", + "image": "data/connectivity/graph_visual/hard/graph70.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,12) (0,19) (0,15) (1,5) (1,20) (1,14) (1,25) (1,10) (2,23) (3,5) (3,11) (3,7) (3,19) (3,18) (4,5) (4,20) (4,25) (4,19) (5,20) (5,25) (5,11) (5,17) (5,19) (5,15) (6,22) (6,25) (6,11) (6,15) (7,20) (7,19) (8,16) (8,26) (9,23) (10,20) (10,17) (10,13) (11,20) (11,17) (11,13) (11,19) (12,14) (12,25) (12,19) (13,14) (14,17) (15,25) (16,21) (16,23) (17,22) (17,20) (17,25) (22,25)\nIs there a path between node 21 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph237-21_25", + "image": "data/connectivity/graph_visual/hard/graph237.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,29) (0,12) (0,18) (0,24) (0,22) (0,2) (0,3) (1,14) (1,20) (1,26) (1,29) (1,12) (1,30) (1,15) (1,19) (1,3) (1,7) (2,17) (2,6) (2,23) (3,28) (3,30) (3,18) (3,19) (3,7) (4,26) (4,29) (4,12) (4,30) (4,18) (4,19) (4,7) (6,8) (6,24) (6,10) (6,19) (7,17) (7,26) (7,30) (7,18) (7,8) (7,13) (7,15) (7,23) (8,16) (8,14) (8,20) (8,26) (8,30) (10,14) (10,20) (10,29) (10,18) (10,13) (10,22) (10,19) (10,11) (11,21) (11,16) (11,14) (11,26) (11,18) (12,16) (12,26) (12,18) (13,17) (13,26) (13,15) (14,28) (14,26) (14,24) (14,23) (15,28) (15,16) (15,29) (15,30) (16,21) (16,20) (16,29) (16,24) (17,28) (17,20) (17,29) (17,30) (17,19) (18,21) (18,28) (18,23) (19,28) (19,20) (19,26) (19,22) (19,23) (20,29) (20,24) (20,22) (21,29) (22,28) (23,28) (23,29) (24,26) (24,29) (25,27) (26,29)\nIs there a path between node 21 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph190-5_15", + "image": "data/connectivity/graph_visual/hard/graph190.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,3) (0,16) (0,26) (0,9) (0,8) (1,28) (1,22) (1,20) (1,26) (1,9) (2,17) (2,28) (2,3) (2,14) (3,15) (3,6) (3,22) (3,26) (3,8) (3,29) (4,12) (4,20) (4,26) (5,7) (5,25) (5,19) (6,22) (6,14) (7,24) (7,23) (7,19) (7,13) (7,10) (8,17) (8,28) (8,18) (8,29) (9,17) (9,15) (9,20) (9,11) (10,24) (11,17) (11,16) (11,26) (12,28) (12,20) (12,26) (12,14) (13,19) (14,17) (15,17) (16,22) (17,20) (17,26) (17,29) (19,25) (20,22) (20,26) (21,27) (22,28) (22,26) (24,25) (25,27) (26,29) (28,29)\nIs there a path between node 5 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph254-27_4", + "image": "data/connectivity/graph_visual/hard/graph254.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,30) (0,16) (0,1) (0,22) (0,25) (1,20) (1,23) (1,2) (1,12) (2,20) (2,23) (2,22) (3,21) (3,7) (4,16) (4,8) (4,22) (4,5) (5,23) (5,12) (6,25) (7,17) (7,28) (7,13) (8,16) (9,26) (11,15) (11,28) (11,14) (12,16) (12,25) (13,21) (13,18) (15,28) (15,18) (16,30) (20,23) (21,28) (23,27) (29,30)\nIs there a path between node 27 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph488-14_26", + "image": "data/connectivity/graph_visual/hard/graph488.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,9) (0,13) (0,24) (1,21) (1,19) (1,15) (1,10) (1,32) (1,4) (1,11) (1,27) (1,22) (1,20) (1,17) (1,5) (1,29) (1,18) (1,7) (1,3) (1,16) (2,21) (2,19) (2,15) (2,28) (2,32) (2,4) (2,27) (2,22) (2,20) (2,17) (2,5) (2,6) (2,29) (2,18) (2,7) (2,14) (2,16) (3,21) (3,15) (3,28) (3,10) (3,32) (3,4) (3,11) (3,27) (3,22) (3,20) (3,6) (3,29) (3,7) (3,23) (3,14) (4,21) (4,19) (4,15) (4,28) (4,10) (4,20) (4,17) (4,14) (5,21) (5,15) (5,10) (5,22) (5,20) (5,17) (5,29) (5,18) (5,7) (5,23) (5,14) (5,16) (6,28) (6,10) (6,32) (6,11) (6,22) (6,20) (6,17) (6,29) (6,18) (6,7) (6,23) (6,16) (7,15) (7,10) (7,32) (7,11) (7,27) (7,17) (7,29) (7,18) (7,16) (8,24) (9,13) (9,25) (9,24) (10,21) (10,15) (10,28) (10,32) (10,27) (10,22) (10,20) (10,17) (10,29) (10,18) (10,23) (10,16) (11,21) (11,28) (11,27) (11,20) (11,17) (11,14) (11,16) (12,30) (12,31) (13,24) (14,21) (14,19) (14,15) (14,32) (14,27) (14,20) (14,17) (14,29) (14,18) (14,23) (14,16) (15,21) (15,19) (15,28) (15,27) (15,22) (15,17) (15,29) (15,18) (16,21) (16,19) (16,32) (16,27) (16,22) (16,20) (16,17) (16,29) (16,23) (17,27) (17,29) (17,18) (17,23) (18,21) (18,19) (18,32) (18,27) (18,22) (18,29) (19,21) (19,28) (19,32) (19,27) (19,22) (19,20) (19,29) (19,23) (20,27) (21,32) (21,27) (21,22) (22,28) (22,27) (22,29) (22,23) (23,28) (23,32) (23,29) (24,25) (26,31) (27,28) (27,29) (28,32) (28,29) (29,32) (30,31)\nIs there a path between node 14 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph438-31_1", + "image": "data/connectivity/graph_visual/hard/graph438.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,27) (0,10) (0,6) (0,24) (0,30) (0,18) (0,19) (0,31) (0,16) (0,12) (1,25) (1,15) (1,17) (1,22) (1,2) (1,7) (1,3) (1,13) (1,9) (2,32) (2,25) (2,15) (2,17) (2,20) (2,29) (2,3) (2,11) (2,13) (2,9) (3,25) (3,15) (3,21) (3,4) (3,17) (3,20) (3,22) (3,29) (3,11) (4,32) (4,25) (4,20) (4,11) (4,13) (4,9) (6,27) (6,10) (6,30) (6,18) (6,31) (6,12) (6,8) (6,26) (6,28) (7,32) (7,25) (7,20) (7,29) (7,11) (7,13) (7,9) (8,27) (8,10) (8,24) (8,30) (8,18) (8,31) (8,12) (8,26) (9,25) (9,21) (9,17) (9,22) (9,29) (9,11) (9,13) (10,30) (10,31) (10,23) (10,12) (10,28) (11,32) (11,25) (11,15) (11,21) (11,17) (11,20) (11,22) (11,29) (11,13) (12,27) (12,24) (12,30) (12,19) (12,16) (12,23) (12,26) (12,28) (13,32) (13,25) (13,15) (13,21) (13,20) (13,29) (15,32) (15,25) (15,21) (15,17) (15,29) (16,24) (16,30) (16,18) (16,19) (16,31) (16,23) (16,26) (16,28) (17,21) (17,22) (17,29) (18,27) (18,24) (18,30) (18,31) (18,23) (19,24) (19,31) (19,23) (19,28) (20,32) (20,25) (20,21) (20,22) (21,32) (21,25) (21,22) (22,25) (23,24) (23,31) (23,28) (24,27) (24,31) (24,26) (24,28) (25,29) (26,30) (27,30) (27,31) (27,28) (28,31) (29,32) (30,31)\nIs there a path between node 31 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph533-10_3", + "image": "data/connectivity/graph_visual/hard/graph533.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,28) (0,18) (0,19) (0,2) (0,15) (0,26) (0,8) (0,1) (0,33) (0,17) (0,16) (1,28) (1,6) (1,19) (1,2) (1,15) (1,26) (1,8) (1,33) (1,5) (1,23) (1,17) (1,16) (1,7) (2,28) (2,6) (2,18) (2,19) (2,15) (2,26) (2,8) (2,33) (2,5) (2,17) (2,16) (2,24) (3,11) (3,21) (3,22) (3,4) (3,12) (4,11) (4,12) (5,28) (5,6) (5,19) (5,15) (5,26) (5,33) (5,23) (5,16) (5,24) (5,7) (6,28) (6,18) (6,19) (6,15) (6,26) (6,8) (6,33) (6,23) (6,17) (6,16) (6,24) (7,18) (7,19) (7,26) (7,23) (7,17) (7,16) (7,24) (8,28) (8,15) (8,33) (8,23) (8,17) (8,16) (8,24) (9,31) (9,27) (9,25) (9,10) (9,32) (9,29) (9,14) (10,20) (10,31) (10,27) (10,13) (10,32) (10,30) (11,21) (11,12) (12,21) (13,20) (13,31) (13,27) (13,32) (13,30) (13,29) (14,20) (14,31) (14,27) (14,25) (14,32) (14,30) (14,29) (15,28) (15,18) (15,33) (15,16) (15,24) (16,18) (16,26) (16,33) (16,23) (16,17) (17,28) (17,18) (17,26) (17,23) (18,28) (18,19) (18,33) (18,23) (18,24) (19,28) (19,33) (19,23) (19,24) (20,31) (20,27) (20,32) (20,30) (20,29) (23,28) (23,26) (23,33) (24,26) (24,33) (25,31) (25,27) (25,29) (26,28) (26,33) (27,31) (27,32) (27,30) (29,32) (29,30) (30,31) (31,32)\nIs there a path between node 10 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph179-4_27", + "image": "data/connectivity/graph_visual/hard/graph179.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,13) (0,25) (0,1) (0,5) (0,20) (0,15) (0,22) (0,7) (0,9) (0,28) (0,17) (0,6) (0,16) (1,5) (1,20) (1,15) (1,22) (1,3) (1,7) (1,9) (1,6) (2,26) (2,18) (2,19) (2,23) (2,12) (2,24) (3,13) (3,5) (3,20) (3,15) (3,22) (3,14) (3,9) (3,28) (3,17) (3,6) (4,26) (4,18) (4,19) (4,11) (4,23) (4,12) (4,21) (4,24) (4,27) (5,13) (5,25) (5,20) (5,15) (5,14) (5,7) (5,9) (5,28) (5,6) (5,16) (6,13) (6,25) (6,20) (6,22) (6,9) (6,17) (6,16) (7,25) (7,20) (7,9) (7,17) (8,19) (8,11) (8,23) (8,12) (8,24) (8,27) (9,13) (9,20) (9,15) (9,22) (9,28) (9,17) (9,16) (11,26) (11,18) (11,19) (11,23) (11,12) (11,21) (12,26) (12,18) (12,19) (12,21) (12,27) (13,25) (13,15) (13,22) (13,17) (14,25) (14,15) (14,28) (14,17) (14,16) (15,25) (15,17) (15,16) (16,25) (16,20) (16,22) (16,28) (16,17) (17,20) (18,26) (18,19) (18,23) (18,27) (19,26) (19,21) (19,24) (19,27) (20,28) (21,26) (21,24) (21,27) (22,25) (22,28) (23,26) (23,27) (24,26) (24,27) (26,27)\nIs there a path between node 4 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph355-24_13", + "image": "data/connectivity/graph_visual/hard/graph355.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,2) (1,16) (1,8) (1,6) (1,13) (1,18) (1,22) (1,10) (1,17) (1,12) (3,5) (3,30) (3,17) (3,12) (4,28) (5,29) (5,6) (5,25) (5,22) (5,10) (5,17) (5,12) (6,15) (6,13) (6,7) (6,30) (6,11) (6,12) (6,26) (7,29) (7,21) (7,25) (7,14) (7,19) (7,17) (7,12) (8,20) (8,21) (8,13) (8,11) (8,25) (8,14) (8,17) (10,15) (10,27) (10,18) (10,26) (11,20) (11,31) (11,13) (11,27) (11,24) (11,17) (12,21) (12,16) (12,31) (12,25) (13,21) (13,31) (13,27) (13,22) (13,19) (14,29) (14,16) (14,24) (14,25) (14,17) (14,26) (15,18) (16,20) (16,30) (16,24) (16,17) (16,26) (17,25) (18,20) (18,21) (18,31) (18,24) (19,27) (19,25) (19,22) (20,29) (20,27) (20,22) (21,30) (21,24) (21,26) (22,30) (24,27) (24,26) (25,26) (26,29) (26,27) (27,29) (27,30)\nIs there a path between node 24 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph625-9_29", + "image": "data/connectivity/graph_visual/hard/graph625.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,30) (0,9) (0,23) (0,3) (2,19) (2,6) (2,31) (2,21) (2,18) (2,11) (3,7) (3,10) (3,34) (3,27) (3,23) (4,16) (4,14) (4,21) (4,18) (4,11) (4,33) (5,17) (6,21) (7,15) (7,13) (7,9) (8,16) (8,31) (8,11) (9,10) (9,15) (9,26) (9,27) (9,23) (10,34) (10,13) (10,28) (11,16) (11,19) (11,31) (12,34) (12,13) (12,30) (12,27) (12,23) (13,26) (13,27) (13,28) (14,31) (14,21) (14,32) (15,27) (15,22) (16,19) (16,25) (17,20) (18,21) (18,33) (18,32) (19,29) (19,21) (19,32) (21,29) (21,25) (21,32) (22,24) (22,28) (23,30) (23,28) (24,34) (24,30) (24,28) (25,31) (26,30) (29,31) (29,33) (29,32) (30,34) (31,33)\nIs there a path between node 9 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph529-6_15", + "image": "data/connectivity/graph_visual/hard/graph529.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,5) (1,21) (2,26) (2,15) (2,14) (2,20) (2,28) (2,12) (3,29) (3,19) (3,22) (3,21) (4,33) (4,32) (4,9) (4,20) (4,28) (4,7) (4,27) (5,23) (5,17) (5,6) (6,25) (7,32) (7,15) (7,9) (7,11) (7,18) (8,19) (8,22) (8,16) (9,28) (9,27) (10,30) (10,33) (10,32) (10,20) (11,13) (11,12) (12,30) (12,13) (12,33) (12,32) (12,15) (12,28) (12,31) (12,27) (12,18) (13,33) (13,32) (13,20) (14,26) (14,20) (15,26) (15,27) (15,18) (16,29) (16,22) (17,23) (17,24) (18,20) (18,28) (18,31) (19,22) (19,21) (20,33) (20,31) (20,27) (23,24) (26,33) (26,31) (26,27) (27,33) (28,33) (28,31) (30,33) (32,33)\nIs there a path between node 6 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph139-14_10", + "image": "data/connectivity/graph_visual/hard/graph139.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,9) (2,8) (2,6) (3,10) (3,16) (3,23) (4,28) (4,8) (5,7) (5,13) (5,18) (5,8) (5,6) (6,7) (6,13) (6,24) (6,18) (6,28) (7,13) (7,11) (8,24) (8,28) (8,22) (9,10) (9,16) (9,15) (10,23) (11,24) (11,18) (12,21) (13,28) (13,22) (14,27) (14,20) (15,27) (15,16) (16,19) (17,19) (19,27) (20,27) (22,28) (23,27) (25,26)\nIs there a path between node 14 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph71-19_20", + "image": "data/connectivity/graph_visual/hard/graph71.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,7) (0,14) (0,16) (0,2) (0,26) (0,17) (0,9) (1,7) (1,14) (1,21) (1,16) (1,20) (1,2) (1,6) (1,8) (1,19) (1,11) (1,17) (2,13) (2,21) (2,22) (2,16) (2,3) (2,24) (2,6) (2,11) (3,13) (3,7) (3,25) (3,20) (3,24) (3,6) (3,23) (4,5) (4,16) (4,24) (4,6) (4,8) (4,19) (5,25) (5,15) (5,19) (6,13) (6,14) (6,21) (6,25) (6,22) (6,16) (6,24) (6,19) (6,23) (6,17) (7,22) (7,16) (7,8) (7,17) (7,9) (8,13) (8,15) (8,11) (8,23) (8,17) (8,9) (9,14) (9,25) (9,22) (9,16) (9,20) (9,15) (9,19) (9,11) (9,26) (10,18) (11,21) (11,16) (11,20) (11,24) (11,23) (11,17) (12,18) (13,22) (13,20) (13,24) (13,23) (14,21) (14,25) (14,22) (14,16) (14,20) (14,15) (14,19) (15,25) (15,19) (15,26) (15,17) (16,25) (16,19) (16,23) (16,26) (16,17) (17,20) (17,23) (17,26) (19,25) (19,20) (19,24) (20,22) (21,22) (22,23) (23,25)\nIs there a path between node 19 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph31-8_10", + "image": "data/connectivity/graph_visual/hard/graph31.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,25) (0,18) (0,8) (0,24) (0,6) (0,12) (0,5) (0,7) (0,16) (0,1) (0,22) (1,25) (1,18) (1,8) (1,4) (1,9) (1,6) (1,12) (1,11) (1,7) (1,13) (1,16) (1,20) (2,8) (2,9) (2,24) (2,6) (2,12) (2,11) (2,15) (2,5) (2,7) (2,16) (2,20) (2,22) (3,19) (3,23) (3,21) (3,14) (4,25) (4,18) (4,8) (4,9) (4,11) (4,15) (4,13) (4,22) (5,25) (5,8) (5,9) (5,24) (5,6) (5,15) (5,7) (5,13) (5,16) (5,20) (5,22) (6,25) (6,8) (6,9) (6,24) (6,12) (6,15) (6,7) (6,16) (7,25) (7,18) (7,24) (7,12) (7,16) (7,22) (8,18) (8,24) (8,12) (8,15) (9,25) (9,18) (9,24) (9,12) (9,11) (9,15) (9,16) (9,20) (9,22) (10,17) (11,24) (11,12) (11,16) (11,20) (12,25) (12,18) (12,24) (12,15) (12,13) (12,16) (12,22) (13,18) (13,20) (13,22) (14,19) (14,23) (14,21) (15,25) (15,18) (15,24) (15,20) (16,25) (16,18) (16,24) (16,20) (16,22) (18,25) (18,20) (18,22) (19,23) (19,21) (20,25) (20,24) (21,23) (22,24)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph543-32_9", + "image": "data/connectivity/graph_visual/hard/graph543.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,15) (0,7) (0,17) (0,2) (0,27) (1,3) (1,32) (1,26) (1,30) (1,19) (1,22) (1,4) (1,18) (1,20) (1,31) (1,25) (1,16) (1,13) (1,14) (1,23) (1,24) (2,15) (2,7) (2,17) (2,8) (2,27) (3,32) (3,26) (3,19) (3,6) (3,4) (3,18) (3,20) (3,31) (3,21) (3,16) (3,13) (3,23) (3,5) (3,29) (4,26) (4,30) (4,19) (4,6) (4,10) (4,18) (4,11) (4,20) (4,25) (4,21) (4,13) (4,14) (4,23) (4,12) (4,24) (4,29) (5,32) (5,9) (5,19) (5,6) (5,28) (5,10) (5,11) (5,20) (5,31) (5,25) (5,33) (5,16) (5,13) (5,14) (5,23) (5,24) (5,29) (6,32) (6,26) (6,30) (6,9) (6,19) (6,28) (6,10) (6,18) (6,11) (6,20) (6,31) (6,25) (6,33) (6,21) (6,16) (6,13) (6,14) (6,23) (6,24) (6,29) (7,15) (8,15) (8,27) (9,32) (9,30) (9,19) (9,28) (9,10) (9,18) (9,11) (9,20) (9,31) (9,25) (9,33) (9,16) (9,14) (9,12) (9,29) (10,32) (10,28) (10,18) (10,20) (10,33) (10,21) (10,16) (10,13) (10,23) (10,12) (10,24) (10,29) (11,32) (11,26) (11,30) (11,19) (11,22) (11,20) (11,31) (11,25) (11,33) (11,21) (11,14) (11,24) (11,29) (12,32) (12,26) (12,30) (12,19) (12,22) (12,18) (12,33) (12,21) (12,14) (12,23) (13,32) (13,26) (13,19) (13,22) (13,28) (13,18) (13,20) (13,31) (13,33) (13,23) (13,24) (13,29) (14,32) (14,26) (14,30) (14,19) (14,22) (14,28) (14,18) (14,20) (14,31) (14,25) (14,21) (14,16) (14,23) (15,17) (16,26) (16,19) (16,22) (16,28) (16,25) (16,33) (16,21) (16,29) (18,26) (18,30) (18,19) (18,22) (18,28) (18,31) (18,25) (18,21) (18,23) (18,29) (19,32) (19,26) (19,30) (19,22) (19,28) (19,25) (19,33) (19,23) (19,24) (19,29) (20,32) (20,26) (20,30) (20,22) (20,25) (20,33) (20,29) (21,26) (21,30) (21,22) (21,28) (21,31) (21,25) (21,33) (21,23) (21,29) (22,32) (22,26) (22,28) (22,31) (23,32) (23,31) (23,25) (23,33) (23,24) (23,29) (24,32) (24,26) (24,30) (24,28) (24,25) (24,33) (25,32) (25,26) (25,30) (25,33) (25,29) (26,33) (26,29) (28,30) (28,31) (28,33) (28,29) (29,32) (29,33) (30,33) (31,32) (32,33)\nIs there a path between node 32 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph349-0_9", + "image": "data/connectivity/graph_visual/hard/graph349.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,11) (0,12) (0,27) (0,20) (0,6) (0,18) (1,11) (1,13) (1,6) (1,26) (1,10) (1,30) (2,5) (2,4) (2,31) (2,19) (2,15) (2,14) (3,25) (3,29) (4,9) (4,15) (4,14) (5,8) (5,15) (5,16) (6,11) (6,27) (6,20) (6,17) (6,29) (6,30) (6,7) (7,27) (7,21) (10,11) (10,27) (10,20) (10,26) (10,18) (10,29) (10,21) (10,30) (10,28) (11,26) (11,25) (11,18) (11,29) (12,20) (12,17) (12,29) (13,20) (13,17) (13,25) (13,29) (15,19) (15,16) (17,20) (17,25) (17,29) (18,26) (18,29) (18,30) (19,31) (20,26) (21,26) (23,31) (24,25) (24,28) (25,26) (27,30) (28,29) (29,30)\nIs there a path between node 0 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph300-31_8", + "image": "data/connectivity/graph_visual/hard/graph300.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,22) (0,19) (0,24) (0,1) (0,2) (0,5) (0,28) (0,29) (0,31) (0,12) (0,23) (0,15) (0,11) (0,10) (1,6) (1,22) (1,19) (1,24) (1,2) (1,5) (1,28) (1,29) (1,31) (1,14) (1,23) (1,15) (1,11) (2,6) (2,22) (2,19) (2,5) (2,28) (2,18) (2,31) (2,14) (2,12) (2,15) (2,11) (2,10) (3,6) (3,19) (3,28) (3,29) (3,18) (3,23) (3,15) (3,10) (4,25) (4,20) (4,17) (4,30) (4,27) (4,9) (4,21) (4,26) (4,13) (4,7) (4,16) (5,6) (5,19) (5,24) (5,28) (5,18) (5,31) (5,14) (5,12) (5,23) (5,15) (5,11) (6,19) (6,24) (6,29) (6,18) (6,31) (6,12) (6,15) (6,10) (7,25) (7,20) (7,17) (7,30) (7,27) (7,9) (7,21) (7,26) (7,13) (7,16) (8,25) (8,9) (9,25) (9,20) (9,17) (9,30) (9,21) (9,26) (9,13) (9,16) (10,22) (10,24) (10,28) (10,29) (10,18) (10,31) (10,14) (10,15) (11,24) (11,28) (11,29) (11,18) (11,14) (11,12) (11,15) (12,29) (12,18) (12,31) (12,15) (13,20) (13,17) (13,30) (13,27) (13,21) (13,26) (13,16) (14,22) (14,19) (14,24) (14,18) (14,31) (14,23) (14,15) (15,22) (15,19) (15,24) (15,28) (15,29) (15,18) (16,20) (16,17) (16,30) (16,21) (16,26) (17,25) (17,20) (17,27) (18,22) (18,19) (18,24) (18,28) (18,29) (18,31) (19,22) (19,24) (19,28) (19,29) (19,23) (20,30) (20,27) (20,21) (20,26) (21,25) (21,30) (21,27) (21,26) (22,24) (22,28) (22,31) (22,23) (23,28) (23,29) (23,31) (24,28) (24,31) (25,30) (26,30) (26,27) (28,29) (28,31) (29,31)\nIs there a path between node 31 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph261-13_23", + "image": "data/connectivity/graph_visual/hard/graph261.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,23) (0,17) (1,9) (2,21) (2,30) (3,9) (3,7) (4,17) (4,20) (5,28) (5,26) (5,24) (6,21) (7,21) (7,9) (7,11) (8,16) (8,18) (9,21) (10,11) (12,28) (12,19) (12,26) (12,17) (12,13) (13,23) (13,24) (14,15) (14,29) (15,16) (16,18) (16,29) (17,23) (19,23) (19,24) (20,28) (20,23) (20,22)\nIs there a path between node 13 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph280-29_12", + "image": "data/connectivity/graph_visual/hard/graph280.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,12) (0,14) (0,16) (0,20) (0,8) (0,13) (0,18) (0,10) (0,29) (0,3) (0,7) (0,9) (1,26) (1,5) (1,11) (1,19) (1,28) (1,24) (1,6) (2,12) (2,14) (2,16) (2,20) (2,8) (2,13) (2,23) (2,18) (2,25) (2,3) (2,7) (2,9) (3,16) (3,8) (3,13) (3,18) (3,25) (3,10) (3,29) (3,7) (4,15) (4,27) (5,28) (5,24) (5,22) (6,26) (6,11) (6,19) (6,28) (6,24) (6,22) (7,14) (7,16) (7,20) (7,13) (7,23) (7,25) (7,10) (7,21) (7,9) (8,14) (8,20) (8,13) (8,23) (8,10) (9,14) (9,16) (9,20) (9,13) (9,18) (9,25) (9,21) (9,29) (10,14) (10,16) (10,20) (10,13) (10,23) (10,25) (10,21) (11,26) (11,17) (11,24) (11,22) (12,14) (12,16) (12,13) (12,23) (12,18) (12,25) (12,21) (12,29) (13,14) (13,16) (13,18) (13,21) (13,29) (14,16) (14,20) (14,23) (14,18) (14,21) (14,29) (15,30) (15,27) (16,20) (16,23) (16,25) (16,21) (16,29) (17,26) (17,19) (17,28) (17,22) (18,23) (18,25) (18,21) (18,29) (19,26) (20,23) (20,25) (20,29) (21,23) (21,25) (21,29) (22,26) (22,28) (22,24) (23,25) (23,29) (24,26) (24,28) (25,29) (26,28)\nIs there a path between node 29 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph663-33_14", + "image": "data/connectivity/graph_visual/hard/graph663.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,15) (0,17) (0,13) (0,5) (0,16) (0,14) (1,23) (1,20) (1,4) (1,34) (1,29) (1,19) (1,28) (2,17) (2,5) (2,16) (2,14) (3,25) (3,22) (4,26) (4,18) (4,29) (4,19) (5,8) (5,15) (5,17) (5,27) (5,31) (6,26) (6,33) (6,30) (6,29) (6,28) (7,26) (7,11) (7,34) (7,18) (7,28) (8,15) (8,16) (8,24) (9,10) (9,18) (10,23) (10,11) (10,18) (10,30) (11,23) (11,18) (11,21) (13,24) (14,15) (14,17) (14,24) (14,32) (15,16) (16,31) (17,32) (18,19) (18,28) (18,21) (19,23) (19,30) (20,23) (21,26) (21,33) (22,25) (23,26) (23,34) (24,27) (24,31) (24,32) (26,33) (27,31) (29,34) (30,33) (30,34)\nIs there a path between node 33 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph364-1_4", + "image": "data/connectivity/graph_visual/hard/graph364.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,15) (0,25) (0,4) (0,27) (0,9) (0,10) (0,1) (0,7) (0,3) (0,31) (0,24) (0,20) (0,23) (1,15) (1,12) (1,25) (1,4) (1,27) (1,9) (1,30) (1,13) (1,8) (1,7) (1,3) (1,2) (1,20) (1,23) (2,15) (2,12) (2,25) (2,26) (2,9) (2,13) (2,8) (2,10) (2,22) (2,7) (2,3) (2,31) (2,19) (2,20) (2,23) (3,4) (3,27) (3,9) (3,13) (3,22) (3,7) (3,16) (3,24) (3,19) (3,20) (3,23) (4,12) (4,25) (4,27) (4,9) (4,13) (4,8) (4,10) (4,22) (4,31) (4,24) (4,23) (5,14) (5,17) (6,18) (6,21) (6,29) (6,28) (7,12) (7,25) (7,26) (7,9) (7,13) (7,8) (7,10) (7,22) (7,31) (7,16) (7,24) (7,19) (7,20) (7,23) (8,15) (8,25) (8,27) (8,30) (8,13) (8,10) (8,24) (8,19) (9,26) (9,27) (9,30) (9,22) (9,16) (9,20) (9,23) (10,12) (10,25) (10,30) (10,13) (10,22) (10,31) (10,24) (10,20) (10,23) (11,18) (11,21) (11,28) (12,25) (12,30) (12,13) (12,31) (12,16) (12,24) (12,20) (13,15) (13,25) (13,26) (13,27) (13,22) (13,24) (13,19) (13,20) (13,23) (14,17) (15,16) (15,19) (16,25) (16,27) (16,30) (16,22) (16,31) (16,19) (16,20) (16,23) (18,29) (19,25) (19,22) (19,31) (19,24) (19,20) (19,23) (20,26) (20,27) (20,30) (20,22) (20,31) (20,24) (20,23) (21,29) (21,28) (22,25) (22,26) (22,27) (22,30) (22,31) (22,24) (22,23) (23,25) (23,27) (23,30) (24,25) (24,26) (24,31) (25,26) (25,27) (25,30) (26,27) (26,30) (27,30) (27,31) (30,31)\nIs there a path between node 1 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph707-25_20", + "image": "data/connectivity/graph_visual/hard/graph707.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,20) (0,7) (0,13) (0,27) (0,34) (0,28) (0,19) (0,3) (0,17) (0,21) (0,6) (0,32) (0,31) (0,25) (0,24) (1,14) (1,29) (1,12) (1,23) (1,33) (1,11) (2,26) (2,18) (2,20) (2,7) (2,34) (2,28) (2,3) (2,15) (2,17) (2,21) (2,6) (2,32) (2,10) (2,31) (2,25) (2,22) (3,26) (3,18) (3,20) (3,7) (3,13) (3,27) (3,6) (3,32) (3,10) (3,9) (3,31) (3,25) (3,24) (4,29) (4,8) (4,5) (4,12) (4,30) (4,16) (5,14) (5,8) (5,12) (5,23) (5,30) (5,16) (5,33) (5,11) (6,7) (6,13) (6,34) (6,28) (6,19) (6,15) (6,17) (6,32) (6,31) (6,25) (6,24) (6,22) (7,18) (7,13) (7,27) (7,32) (7,9) (7,25) (7,24) (7,22) (8,29) (8,12) (8,23) (8,16) (8,33) (9,18) (9,13) (9,27) (9,34) (9,28) (9,19) (9,15) (9,17) (9,21) (9,32) (9,31) (9,25) (9,24) (9,22) (10,26) (10,20) (10,27) (10,34) (10,28) (10,19) (10,17) (10,32) (10,25) (11,29) (11,12) (11,30) (11,16) (12,23) (13,18) (13,20) (13,27) (13,28) (13,15) (13,17) (13,21) (13,32) (13,31) (13,25) (13,22) (14,29) (14,23) (14,16) (14,33) (15,18) (15,27) (15,34) (15,28) (15,19) (15,17) (15,32) (15,31) (15,24) (16,23) (16,30) (16,33) (17,26) (17,20) (17,27) (17,28) (17,19) (17,21) (17,32) (17,31) (17,25) (17,22) (18,20) (18,27) (18,28) (18,19) (18,32) (18,31) (18,25) (19,20) (19,27) (19,34) (19,21) (19,32) (19,31) (19,25) (19,24) (19,22) (20,26) (20,34) (20,21) (20,32) (20,31) (20,24) (21,26) (21,27) (21,32) (21,31) (21,25) (21,22) (22,28) (22,32) (22,31) (22,24) (23,29) (23,30) (23,33) (24,34) (24,28) (24,32) (24,25) (25,26) (25,27) (25,28) (25,32) (25,31) (26,27) (26,34) (26,28) (26,32) (26,31) (27,34) (27,28) (27,32) (27,31) (28,34) (28,32) (28,31) (29,30) (29,33) (30,33) (31,34) (32,34)\nIs there a path between node 25 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph1-13_2", + "image": "data/connectivity/graph_visual/hard/graph1.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,4) (0,8) (0,2) (0,20) (0,16) (0,14) (0,15) (0,7) (1,18) (1,24) (1,22) (1,5) (1,19) (1,11) (1,17) (2,6) (2,4) (2,23) (2,8) (2,20) (2,16) (2,21) (2,14) (2,15) (2,10) (3,6) (3,4) (3,23) (3,8) (3,16) (3,14) (3,25) (3,15) (3,7) (4,6) (4,23) (4,8) (4,20) (4,16) (4,21) (4,14) (4,15) (4,10) (4,7) (5,18) (5,24) (5,22) (5,13) (5,9) (5,11) (5,12) (6,23) (6,8) (6,20) (6,16) (6,14) (6,25) (6,15) (7,23) (7,20) (7,16) (7,21) (7,14) (7,25) (7,15) (7,10) (8,20) (8,16) (8,14) (8,25) (8,15) (9,18) (9,24) (9,22) (9,19) (9,11) (9,17) (9,12) (10,23) (10,20) (10,16) (10,21) (10,14) (10,25) (11,22) (11,19) (11,17) (11,12) (12,18) (12,13) (12,19) (13,18) (13,24) (13,22) (13,17) (14,23) (14,20) (14,16) (14,25) (15,20) (15,16) (15,21) (15,25) (16,23) (16,20) (16,25) (17,18) (17,22) (17,19) (18,24) (18,22) (18,19) (19,24) (19,22) (20,21) (20,25) (21,23) (21,25) (22,24) (23,25)\nIs there a path between node 13 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph705-21_7", + "image": "data/connectivity/graph_visual/hard/graph705.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,17) (0,1) (0,20) (0,5) (0,16) (0,34) (1,17) (1,9) (1,5) (1,16) (1,34) (2,30) (2,26) (2,25) (2,24) (3,18) (3,12) (3,4) (3,32) (3,7) (3,33) (3,22) (3,13) (3,15) (3,6) (3,10) (3,27) (4,12) (4,11) (4,7) (4,22) (4,19) (4,13) (4,15) (4,6) (4,21) (4,27) (5,17) (5,9) (5,20) (5,34) (6,18) (6,32) (6,11) (6,7) (6,33) (6,22) (6,19) (6,15) (6,21) (7,18) (7,11) (7,33) (7,22) (7,19) (7,13) (7,10) (7,27) (8,31) (8,29) (9,17) (9,20) (9,16) (9,34) (10,12) (10,32) (10,19) (10,13) (10,15) (10,27) (11,12) (11,32) (11,33) (11,22) (11,19) (11,13) (11,27) (12,22) (12,19) (12,13) (12,15) (12,27) (13,18) (13,32) (13,33) (13,19) (13,15) (13,21) (13,27) (14,28) (14,30) (14,25) (14,24) (15,18) (15,33) (15,22) (15,19) (15,21) (15,27) (16,20) (17,20) (18,33) (18,19) (18,27) (19,32) (19,33) (19,21) (19,27) (20,34) (21,32) (21,27) (22,32) (22,33) (22,27) (23,31) (23,29) (24,28) (24,25) (25,28) (25,26) (26,28) (26,30) (28,30) (29,31) (32,33)\nIs there a path between node 21 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph96-8_10", + "image": "data/connectivity/graph_visual/hard/graph96.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,20) (0,8) (0,13) (0,11) (0,22) (0,15) (1,24) (2,3) (3,24) (4,18) (5,13) (5,27) (5,11) (5,7) (5,21) (6,11) (6,22) (6,17) (7,25) (7,8) (7,23) (7,11) (7,12) (7,22) (7,17) (8,20) (8,10) (8,12) (8,21) (10,20) (10,25) (10,13) (10,22) (10,16) (10,21) (11,20) (11,25) (11,16) (11,15) (12,23) (12,16) (12,21) (13,20) (13,23) (13,22) (13,17) (13,15) (15,26) (15,25) (15,22) (16,27) (17,26) (17,23) (17,27) (20,26) (20,22) (21,25) (22,25) (23,25) (25,26) (26,27)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph238-15_4", + "image": "data/connectivity/graph_visual/hard/graph238.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,13) (0,4) (0,26) (1,6) (1,15) (1,30) (1,24) (2,3) (2,20) (2,25) (2,26) (3,12) (3,10) (3,25) (4,12) (4,13) (4,10) (4,7) (4,25) (4,26) (5,29) (5,20) (5,11) (5,25) (5,26) (6,14) (6,30) (6,28) (6,17) (7,29) (7,12) (7,13) (7,10) (7,20) (7,25) (7,26) (8,19) (8,27) (8,24) (9,22) (9,11) (9,25) (10,22) (10,29) (10,12) (10,13) (10,25) (10,26) (11,22) (11,23) (11,20) (12,29) (12,23) (14,27) (14,28) (14,24) (15,21) (15,19) (16,30) (16,24) (17,19) (17,28) (17,24) (18,20) (18,25) (20,22) (20,29) (20,25) (21,30) (21,24) (22,23) (22,25) (22,26) (23,29) (25,29) (25,26) (26,29) (28,30)\nIs there a path between node 15 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph564-30_17", + "image": "data/connectivity/graph_visual/hard/graph564.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,16) (1,3) (1,28) (1,21) (1,29) (1,27) (1,26) (3,28) (3,20) (3,26) (4,31) (4,8) (4,23) (4,17) (4,29) (4,33) (4,13) (4,26) (4,18) (4,9) (5,16) (6,11) (7,20) (7,29) (7,9) (7,12) (7,25) (8,30) (8,17) (8,14) (8,13) (8,18) (9,19) (9,21) (9,27) (9,26) (9,12) (12,30) (12,22) (12,19) (12,17) (12,14) (12,33) (13,20) (13,14) (13,27) (14,19) (14,21) (14,33) (14,25) (17,24) (17,21) (17,29) (17,27) (17,33) (17,26) (17,18) (18,31) (18,24) (18,27) (18,33) (18,25) (19,30) (19,23) (20,31) (20,24) (20,29) (20,27) (20,26) (21,31) (21,24) (21,28) (21,29) (22,30) (22,23) (22,28) (22,27) (23,30) (23,24) (23,25) (25,31) (25,27) (25,33) (26,29) (27,31) (27,28) (27,33) (28,31) (28,29) (29,31) (29,30)\nIs there a path between node 30 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph371-8_12", + "image": "data/connectivity/graph_visual/hard/graph371.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,12) (0,24) (0,31) (0,15) (0,27) (1,26) (1,24) (1,31) (1,27) (1,19) (2,25) (2,20) (2,23) (2,8) (2,9) (2,4) (2,29) (2,7) (2,14) (2,5) (2,11) (2,6) (2,3) (2,13) (2,10) (3,25) (3,30) (3,23) (3,9) (3,4) (3,29) (3,21) (3,28) (3,7) (3,14) (3,5) (3,11) (3,6) (3,10) (4,25) (4,20) (4,30) (4,23) (4,18) (4,17) (4,21) (4,16) (4,14) (4,11) (4,6) (4,13) (4,22) (5,25) (5,20) (5,30) (5,23) (5,18) (5,17) (5,8) (5,9) (5,29) (5,28) (5,16) (5,14) (5,11) (5,13) (5,22) (5,10) (6,25) (6,20) (6,23) (6,18) (6,17) (6,9) (6,29) (6,21) (6,7) (6,13) (6,22) (7,25) (7,20) (7,30) (7,23) (7,18) (7,8) (7,9) (7,29) (7,21) (7,28) (7,16) (7,14) (7,11) (7,13) (7,10) (8,20) (8,30) (8,23) (8,18) (8,9) (8,21) (8,28) (8,16) (8,14) (8,11) (8,13) (8,10) (9,20) (9,30) (9,23) (9,18) (9,29) (9,28) (9,11) (9,13) (9,22) (9,10) (10,25) (10,30) (10,23) (10,17) (10,28) (10,16) (10,14) (10,11) (10,13) (10,22) (11,25) (11,20) (11,30) (11,23) (11,18) (11,29) (11,21) (11,28) (11,22) (12,26) (12,24) (12,19) (13,25) (13,23) (13,18) (13,17) (13,29) (13,21) (13,28) (13,16) (13,22) (14,25) (14,20) (14,23) (14,29) (14,21) (14,28) (14,16) (15,26) (15,31) (15,27) (16,25) (16,20) (16,30) (16,17) (16,29) (16,21) (16,28) (16,22) (17,25) (17,30) (17,23) (17,18) (17,29) (17,28) (17,22) (18,25) (18,20) (18,30) (18,23) (18,29) (18,21) (18,22) (19,26) (19,31) (19,27) (20,30) (20,29) (20,21) (20,28) (21,25) (21,30) (21,23) (21,29) (21,22) (22,25) (22,30) (22,23) (22,29) (22,28) (23,25) (23,30) (23,29) (24,26) (25,29) (25,28) (28,30) (28,29) (29,30)\nIs there a path between node 8 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph506-23_18", + "image": "data/connectivity/graph_visual/hard/graph506.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,32) (0,10) (0,4) (0,11) (0,24) (0,14) (0,21) (0,8) (0,18) (0,27) (0,13) (0,1) (0,29) (0,16) (0,28) (0,12) (0,20) (1,32) (1,4) (1,26) (1,11) (1,24) (1,8) (1,18) (1,13) (1,31) (1,29) (1,25) (1,15) (1,28) (1,12) (1,20) (2,6) (2,33) (4,10) (4,18) (4,27) (4,31) (4,22) (4,29) (4,25) (4,16) (4,15) (4,28) (4,12) (5,17) (5,23) (5,30) (5,9) (6,19) (7,19) (8,32) (8,10) (8,26) (8,11) (8,24) (8,14) (8,21) (8,18) (8,22) (8,29) (8,15) (8,20) (9,30) (10,11) (10,24) (10,14) (10,18) (10,27) (10,13) (10,31) (10,22) (10,29) (10,25) (10,28) (10,12) (10,20) (11,32) (11,26) (11,24) (11,14) (11,21) (11,27) (11,13) (11,31) (11,29) (11,16) (11,28) (11,12) (12,32) (12,24) (12,14) (12,18) (12,27) (12,31) (12,16) (12,15) (12,20) (13,32) (13,26) (13,14) (13,18) (13,22) (13,29) (13,25) (13,16) (13,15) (13,28) (13,20) (14,26) (14,24) (14,18) (14,31) (14,22) (14,29) (14,25) (14,16) (14,28) (14,20) (15,26) (15,24) (15,21) (15,18) (15,27) (15,31) (15,22) (15,25) (15,28) (15,20) (16,26) (16,24) (16,21) (16,31) (16,22) (16,25) (16,28) (16,20) (18,24) (18,21) (18,22) (18,28) (19,33) (20,32) (20,26) (20,24) (20,21) (20,31) (20,22) (20,29) (20,25) (20,28) (21,32) (21,24) (21,27) (21,31) (21,22) (21,29) (22,32) (22,26) (22,24) (22,27) (22,31) (22,29) (22,25) (22,28) (23,30) (24,32) (24,27) (24,31) (24,25) (24,28) (25,32) (25,31) (25,28) (26,32) (26,27) (26,31) (26,29) (26,28) (27,32) (27,31) (27,29) (27,28) (31,32)\nIs there a path between node 23 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph549-27_20", + "image": "data/connectivity/graph_visual/hard/graph549.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,20) (1,22) (2,13) (2,7) (2,3) (2,5) (2,32) (2,10) (2,8) (3,17) (3,26) (3,6) (3,21) (4,33) (4,23) (4,16) (4,5) (4,6) (4,15) (4,21) (5,23) (5,19) (5,32) (5,8) (6,17) (6,26) (6,32) (6,8) (7,33) (7,16) (7,15) (7,10) (8,33) (8,17) (8,26) (8,27) (8,18) (9,24) (10,13) (10,16) (10,26) (10,27) (10,18) (10,15) (11,16) (11,27) (11,18) (12,20) (13,25) (13,16) (13,27) (14,22) (14,20) (15,23) (15,21) (16,33) (16,23) (16,32) (16,21) (17,23) (17,27) (17,21) (19,25) (19,32) (21,27) (21,32) (22,28) (23,33) (25,33) (25,27) (25,32) (26,33) (26,27) (28,29)\nIs there a path between node 27 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph48-4_2", + "image": "data/connectivity/graph_visual/hard/graph48.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,1) (0,19) (1,21) (2,8) (2,10) (3,8) (3,10) (4,7) (4,21) (4,18) (4,19) (4,5) (5,16) (6,12) (6,23) (6,13) (6,11) (7,19) (8,14) (8,23) (8,25) (9,20) (9,18) (9,26) (10,23) (10,22) (10,15) (11,14) (11,23) (12,14) (12,24) (12,13) (12,25) (12,22) (13,14) (13,24) (13,15) (14,24) (14,23) (14,15) (16,18) (16,17) (16,26) (17,26) (18,20) (22,24) (23,24) (23,25)\nIs there a path between node 4 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph644-28_0", + "image": "data/connectivity/graph_visual/hard/graph644.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,34) (0,17) (0,18) (0,1) (0,4) (0,28) (0,14) (0,22) (0,12) (1,20) (1,5) (1,26) (1,8) (1,34) (1,17) (1,28) (1,22) (2,9) (2,30) (2,6) (2,21) (2,23) (2,19) (2,25) (2,29) (2,13) (2,15) (2,16) (2,10) (2,27) (3,9) (3,31) (3,6) (3,21) (3,23) (3,19) (3,33) (3,25) (3,13) (3,15) (3,7) (3,16) (3,10) (3,24) (3,32) (3,11) (3,27) (4,5) (4,26) (4,8) (4,34) (4,17) (4,18) (4,28) (4,14) (5,20) (5,26) (5,8) (5,34) (5,17) (5,18) (5,14) (6,30) (6,31) (6,23) (6,33) (6,29) (6,7) (6,16) (6,10) (6,11) (7,9) (7,30) (7,31) (7,21) (7,23) (7,19) (7,29) (7,13) (7,16) (7,10) (7,24) (7,32) (7,11) (7,27) (8,20) (8,17) (8,18) (8,28) (8,14) (8,22) (9,30) (9,31) (9,21) (9,19) (9,33) (9,25) (9,10) (9,32) (9,11) (10,23) (10,19) (10,33) (10,25) (10,13) (10,15) (10,16) (10,24) (10,32) (10,27) (11,30) (11,31) (11,21) (11,23) (11,33) (11,25) (11,29) (11,13) (11,15) (11,16) (11,24) (11,27) (12,20) (12,26) (12,34) (12,18) (12,22) (13,31) (13,21) (13,33) (13,25) (13,15) (13,16) (13,27) (14,20) (14,26) (14,34) (14,17) (14,28) (14,22) (15,30) (15,23) (15,19) (15,25) (15,24) (15,32) (15,27) (16,30) (16,31) (16,21) (16,23) (16,24) (16,32) (17,20) (17,26) (17,34) (17,28) (17,22) (18,20) (18,26) (18,34) (18,22) (19,30) (19,31) (19,23) (19,25) (19,27) (20,34) (21,23) (21,33) (21,25) (21,29) (21,24) (21,27) (22,34) (22,28) (23,31) (23,29) (23,24) (23,32) (24,30) (24,31) (24,33) (24,29) (24,32) (24,27) (25,30) (25,31) (25,33) (25,32) (25,27) (26,34) (27,30) (27,33) (29,30) (29,31) (30,33) (30,32) (31,33) (31,32)\nIs there a path between node 28 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph548-16_20", + "image": "data/connectivity/graph_visual/hard/graph548.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,2) (0,31) (1,4) (1,27) (1,25) (2,31) (2,24) (2,13) (2,10) (3,30) (3,32) (3,27) (3,15) (4,30) (4,6) (4,28) (4,8) (5,22) (6,27) (7,20) (7,11) (7,12) (8,15) (9,14) (10,17) (10,23) (10,13) (11,14) (12,18) (13,23) (14,22) (15,30) (15,27) (15,25) (15,16) (15,28) (17,23) (17,21) (18,22) (18,33) (20,22) (21,31) (23,24) (25,30) (25,27) (25,28) (26,31) (27,30) (27,32) (28,32)\nIs there a path between node 16 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph399-18_0", + "image": "data/connectivity/graph_visual/hard/graph399.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,4) (0,12) (0,11) (0,10) (0,3) (0,17) (0,21) (0,27) (0,15) (0,23) (0,31) (0,29) (0,2) (0,8) (0,9) (0,14) (0,18) (1,5) (1,26) (1,13) (1,20) (1,32) (1,7) (2,19) (2,4) (2,28) (2,22) (2,16) (2,12) (2,10) (2,3) (2,17) (2,21) (2,27) (2,15) (2,23) (2,31) (2,29) (2,8) (2,9) (2,14) (2,18) (3,4) (3,22) (3,16) (3,12) (3,10) (3,17) (3,21) (3,27) (3,23) (3,31) (3,29) (3,6) (3,9) (3,14) (3,18) (4,16) (4,12) (4,11) (4,17) (4,21) (4,15) (4,30) (4,23) (4,29) (4,6) (4,8) (4,9) (4,18) (5,26) (5,13) (5,25) (5,24) (5,32) (5,7) (6,19) (6,22) (6,12) (6,11) (6,10) (6,17) (6,21) (6,27) (6,15) (6,30) (6,23) (6,31) (6,29) (6,9) (6,14) (7,26) (7,25) (7,32) (8,19) (8,28) (8,10) (8,17) (8,27) (8,15) (8,30) (8,23) (9,19) (9,28) (9,22) (9,16) (9,12) (9,10) (9,17) (9,21) (9,15) (9,30) (9,23) (9,29) (9,18) (10,19) (10,28) (10,22) (10,12) (10,11) (10,17) (10,21) (10,27) (10,15) (10,30) (10,23) (10,31) (10,29) (10,14) (10,18) (11,16) (11,12) (11,17) (11,21) (11,27) (11,15) (11,30) (11,31) (11,29) (11,14) (11,18) (12,19) (12,28) (12,22) (12,17) (12,27) (12,15) (12,30) (12,23) (12,31) (12,29) (12,14) (12,18) (13,26) (13,25) (13,20) (13,32) (14,28) (14,16) (14,17) (14,21) (14,27) (14,15) (14,31) (14,29) (14,18) (15,19) (15,22) (15,16) (15,17) (15,21) (15,27) (15,30) (15,23) (15,31) (15,29) (15,18) (16,19) (16,28) (16,22) (16,17) (16,21) (16,27) (16,30) (16,31) (16,18) (17,22) (17,21) (17,30) (17,31) (17,29) (17,18) (18,19) (18,28) (18,22) (18,21) (18,27) (18,29) (19,28) (19,22) (19,21) (19,30) (19,31) (19,29) (20,32) (21,28) (21,22) (21,27) (21,29) (22,28) (22,30) (22,23) (22,31) (22,29) (23,28) (23,27) (23,30) (23,31) (23,29) (24,26) (24,25) (25,26) (25,32) (26,32) (27,28) (27,30) (27,29) (28,30) (28,31) (28,29) (29,30) (29,31)\nIs there a path between node 18 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph697-16_0", + "image": "data/connectivity/graph_visual/hard/graph697.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,18) (0,11) (0,9) (0,15) (0,17) (0,12) (1,33) (1,16) (1,24) (1,32) (1,34) (1,22) (1,26) (1,20) (1,2) (1,19) (1,23) (1,29) (1,7) (2,33) (2,16) (2,32) (2,34) (2,22) (2,20) (2,14) (2,7) (3,27) (3,6) (3,10) (4,8) (4,13) (5,18) (5,11) (5,28) (5,17) (5,12) (6,27) (7,25) (7,16) (7,32) (7,22) (7,21) (7,20) (7,14) (7,19) (7,23) (7,29) (8,30) (9,18) (9,11) (9,28) (9,15) (9,17) (9,12) (10,27) (11,28) (11,17) (12,18) (12,17) (13,30) (13,31) (14,25) (14,16) (14,32) (14,34) (14,26) (14,20) (14,23) (14,29) (15,18) (15,28) (15,17) (16,33) (16,25) (16,24) (16,32) (16,34) (16,22) (16,21) (16,26) (16,20) (16,19) (17,28) (18,28) (19,33) (19,25) (19,24) (19,32) (19,34) (19,22) (19,21) (19,26) (19,20) (19,23) (19,29) (20,25) (20,24) (20,32) (20,21) (20,26) (20,23) (20,29) (21,33) (21,25) (21,24) (21,34) (21,22) (21,26) (21,23) (22,25) (22,24) (22,32) (22,26) (22,23) (23,33) (23,24) (23,34) (23,26) (23,29) (24,25) (24,26) (24,29) (25,33) (25,34) (25,26) (25,29) (26,33) (26,29) (29,33) (30,31) (32,33) (32,34)\nIs there a path between node 16 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph366-20_0", + "image": "data/connectivity/graph_visual/hard/graph366.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,15) (0,2) (0,1) (0,29) (0,21) (0,19) (0,16) (0,18) (0,26) (0,31) (0,17) (0,4) (0,22) (0,10) (0,24) (1,13) (1,15) (1,6) (1,20) (1,25) (1,21) (1,7) (1,18) (1,26) (1,31) (1,17) (1,22) (1,10) (1,24) (2,13) (2,29) (2,20) (2,25) (2,21) (2,16) (2,7) (2,18) (2,26) (2,17) (2,4) (2,22) (2,30) (2,10) (2,5) (2,24) (3,8) (3,23) (3,11) (3,28) (3,14) (3,12) (3,27) (4,13) (4,6) (4,21) (4,19) (4,18) (4,26) (4,31) (4,17) (4,22) (4,30) (4,5) (5,13) (5,29) (5,6) (5,20) (5,21) (5,19) (5,16) (5,7) (5,18) (5,26) (5,31) (5,17) (5,22) (5,30) (5,10) (5,24) (6,13) (6,15) (6,29) (6,25) (6,21) (6,19) (6,7) (6,18) (6,26) (6,31) (6,17) (6,22) (6,30) (6,10) (7,15) (7,29) (7,20) (7,25) (7,21) (7,19) (7,16) (7,31) (7,17) (7,22) (7,30) (7,10) (7,24) (8,23) (8,11) (8,28) (8,12) (8,27) (9,23) (9,14) (9,12) (9,27) (10,15) (10,25) (10,21) (10,16) (10,26) (10,31) (10,17) (10,30) (10,24) (11,23) (11,28) (11,14) (12,23) (12,28) (12,27) (13,29) (13,20) (13,25) (13,21) (13,16) (13,18) (13,26) (13,22) (13,24) (14,28) (14,27) (15,29) (15,20) (15,25) (15,21) (15,19) (15,16) (15,18) (15,31) (15,17) (15,30) (16,20) (16,25) (16,21) (16,19) (16,18) (16,31) (16,30) (16,24) (17,29) (17,20) (17,21) (17,19) (17,18) (17,31) (17,22) (17,30) (17,24) (18,29) (18,20) (18,21) (18,19) (18,26) (18,31) (18,22) (18,30) (18,24) (19,25) (19,21) (19,26) (19,22) (19,24) (20,25) (20,26) (20,31) (20,22) (20,30) (20,24) (21,29) (21,26) (21,31) (21,22) (21,30) (21,24) (22,29) (22,26) (22,30) (23,28) (23,27) (24,29) (24,25) (24,26) (24,31) (25,29) (25,26) (25,31) (25,30) (26,29) (26,31) (26,30) (29,31) (30,31)\nIs there a path between node 20 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph468-19_26", + "image": "data/connectivity/graph_visual/hard/graph468.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,6) (0,2) (0,22) (0,32) (0,27) (0,5) (0,14) (0,3) (0,21) (0,7) (0,25) (0,29) (0,9) (0,18) (0,19) (0,11) (0,31) (0,10) (0,8) (1,6) (1,2) (1,5) (1,3) (1,21) (1,7) (1,29) (1,9) (1,19) (1,10) (1,8) (2,32) (2,5) (2,14) (2,3) (2,7) (2,29) (2,9) (2,18) (2,23) (2,11) (2,10) (2,8) (3,22) (3,27) (3,5) (3,21) (3,7) (3,25) (3,29) (3,19) (3,23) (3,10) (4,20) (4,15) (4,28) (4,12) (4,30) (5,6) (5,22) (5,32) (5,27) (5,14) (5,21) (5,25) (5,29) (5,9) (5,18) (5,19) (5,11) (5,31) (5,10) (5,8) (6,24) (6,32) (6,27) (6,14) (6,21) (6,25) (6,29) (6,9) (6,18) (6,19) (6,23) (6,8) (7,22) (7,24) (7,27) (7,14) (7,21) (7,29) (7,9) (7,23) (7,11) (7,10) (7,8) (8,24) (8,32) (8,27) (8,14) (8,25) (8,29) (8,9) (8,18) (8,19) (8,23) (8,11) (8,31) (9,22) (9,24) (9,32) (9,27) (9,21) (9,29) (9,18) (9,19) (9,23) (9,11) (9,10) (10,22) (10,32) (10,27) (10,14) (10,21) (10,19) (10,23) (10,31) (11,22) (11,24) (11,32) (11,27) (11,14) (11,21) (11,25) (11,29) (11,18) (11,19) (11,31) (12,20) (12,15) (12,28) (12,30) (13,16) (13,17) (14,24) (14,32) (14,21) (14,25) (14,29) (14,19) (14,23) (14,31) (15,20) (15,28) (15,30) (16,17) (16,26) (17,26) (18,32) (18,27) (18,21) (18,25) (18,29) (18,23) (18,31) (19,22) (19,32) (19,27) (19,21) (19,25) (20,28) (20,30) (21,22) (21,24) (21,32) (21,27) (21,29) (21,23) (22,32) (22,25) (22,29) (22,23) (22,31) (23,24) (23,27) (23,31) (24,32) (24,27) (24,25) (24,31) (25,27) (25,29) (27,29) (27,31) (28,30) (29,32) (31,32)\nIs there a path between node 19 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph160-7_19", + "image": "data/connectivity/graph_visual/hard/graph160.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,6) (1,11) (1,2) (1,12) (1,28) (2,22) (2,28) (3,6) (3,8) (3,20) (3,23) (3,19) (4,24) (4,12) (4,28) (5,24) (6,9) (6,21) (7,20) (7,16) (7,13) (8,20) (8,9) (8,23) (8,21) (9,23) (9,13) (10,26) (10,24) (10,12) (10,18) (11,12) (11,18) (11,17) (11,25) (12,18) (13,20) (13,23) (14,27) (15,27) (16,21) (16,19) (17,18) (18,26) (18,22) (19,21) (25,26)\nIs there a path between node 7 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph334-29_26", + "image": "data/connectivity/graph_visual/hard/graph334.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,28) (0,16) (0,30) (0,27) (0,22) (0,18) (1,4) (1,29) (1,2) (1,8) (1,21) (1,6) (1,23) (1,17) (1,11) (1,15) (1,10) (1,12) (1,3) (1,31) (1,25) (1,14) (2,29) (2,8) (2,21) (2,11) (2,15) (2,10) (2,12) (2,3) (2,31) (2,9) (2,19) (3,4) (3,29) (3,8) (3,21) (3,6) (3,17) (3,20) (3,11) (3,12) (3,31) (3,19) (3,14) (4,29) (4,21) (4,23) (4,17) (4,20) (4,11) (4,15) (4,10) (4,12) (4,31) (4,9) (4,19) (4,14) (5,29) (5,8) (5,21) (5,6) (5,23) (5,17) (5,20) (5,11) (5,15) (5,10) (5,12) (5,31) (5,25) (5,19) (5,14) (6,8) (6,21) (6,23) (6,20) (6,11) (6,10) (6,12) (6,31) (6,25) (7,16) (7,30) (7,24) (7,22) (7,18) (8,29) (8,23) (8,17) (8,11) (8,15) (8,10) (8,12) (8,31) (8,25) (8,9) (8,14) (9,29) (9,20) (9,11) (9,15) (9,10) (9,31) (9,19) (9,14) (10,29) (10,23) (10,20) (10,11) (10,15) (10,19) (11,29) (11,23) (11,17) (11,20) (11,12) (11,25) (11,19) (11,14) (12,21) (12,23) (12,17) (12,20) (12,31) (12,19) (12,14) (13,26) (13,28) (13,16) (13,30) (13,18) (14,29) (14,21) (14,23) (14,17) (14,20) (14,15) (14,31) (15,21) (15,20) (15,31) (15,19) (16,30) (16,24) (16,27) (16,22) (16,18) (17,29) (17,21) (17,23) (17,20) (17,31) (17,25) (18,28) (18,24) (18,27) (18,22) (19,29) (19,21) (19,23) (19,20) (19,31) (19,25) (20,23) (20,31) (20,25) (21,29) (22,26) (22,28) (22,30) (22,24) (23,29) (23,31) (24,26) (24,28) (24,27) (25,31) (26,28) (27,30) (28,30) (29,31)\nIs there a path between node 29 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph666-24_34", + "image": "data/connectivity/graph_visual/hard/graph666.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,10) (0,28) (0,12) (0,26) (0,31) (0,13) (0,15) (0,22) (0,8) (0,7) (1,23) (1,27) (1,16) (2,11) (2,17) (2,10) (2,28) (2,3) (2,13) (2,15) (2,22) (2,19) (3,17) (3,10) (3,12) (3,32) (3,24) (4,11) (4,17) (4,29) (4,32) (4,24) (4,7) (5,10) (5,31) (5,32) (5,15) (5,22) (5,33) (6,11) (6,28) (6,26) (6,15) (6,14) (7,21) (7,13) (7,33) (7,24) (8,17) (8,10) (8,32) (8,15) (8,33) (8,34) (8,19) (9,18) (9,16) (10,17) (10,28) (10,22) (10,24) (11,28) (11,31) (11,15) (12,28) (12,29) (12,33) (13,15) (13,14) (14,28) (14,32) (14,22) (15,29) (15,26) (15,32) (15,22) (15,24) (16,20) (16,30) (17,21) (17,22) (17,34) (18,30) (20,23) (20,27) (21,29) (21,33) (21,34) (22,34) (22,24) (24,29) (24,33) (25,30) (25,27) (26,31) (28,32) (28,33) (28,34)\nIs there a path between node 24 and node 34 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph245-17_6", + "image": "data/connectivity/graph_visual/hard/graph245.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,3) (0,14) (0,17) (0,2) (0,25) (0,8) (0,21) (0,10) (0,18) (0,19) (0,26) (0,4) (0,29) (0,20) (0,13) (0,12) (1,3) (1,14) (1,17) (1,25) (1,8) (1,21) (1,16) (1,15) (1,10) (1,19) (1,9) (1,4) (1,5) (1,29) (1,30) (1,27) (1,13) (1,12) (2,3) (2,17) (2,24) (2,8) (2,16) (2,15) (2,26) (2,4) (2,29) (2,30) (2,27) (2,13) (3,14) (3,17) (3,24) (3,25) (3,8) (3,21) (3,16) (3,10) (3,9) (3,26) (3,29) (3,30) (3,27) (3,20) (3,13) (3,12) (4,25) (4,8) (4,21) (4,16) (4,10) (4,18) (4,19) (4,9) (4,5) (4,30) (4,27) (4,20) (5,14) (5,17) (5,24) (5,8) (5,21) (5,16) (5,15) (5,10) (5,18) (5,19) (5,9) (5,26) (5,30) (5,27) (5,20) (6,22) (6,7) (6,23) (8,14) (8,17) (8,25) (8,16) (8,15) (8,18) (8,19) (8,9) (8,26) (8,29) (8,30) (8,27) (8,13) (9,14) (9,17) (9,24) (9,25) (9,16) (9,15) (9,10) (9,26) (9,30) (9,20) (9,13) (10,14) (10,17) (10,24) (10,25) (10,21) (10,18) (10,29) (10,30) (10,27) (10,20) (10,13) (10,12) (11,28) (12,14) (12,25) (12,21) (12,16) (12,18) (12,19) (12,29) (12,27) (13,14) (13,17) (13,24) (13,16) (13,15) (13,19) (13,29) (13,30) (13,27) (14,17) (14,25) (14,21) (14,18) (14,19) (14,26) (14,29) (14,27) (14,20) (15,17) (15,24) (15,25) (15,16) (15,18) (15,19) (15,26) (15,29) (15,30) (15,20) (16,17) (16,24) (16,19) (16,26) (16,29) (16,30) (16,27) (16,20) (17,24) (17,21) (17,19) (17,30) (17,27) (18,24) (18,25) (18,21) (18,19) (18,26) (18,29) (18,30) (18,27) (19,25) (19,26) (19,29) (19,27) (19,20) (20,24) (20,25) (20,26) (20,29) (20,30) (20,27) (21,25) (21,26) (21,29) (21,30) (21,27) (24,25) (24,26) (24,29) (24,27) (25,26) (25,30) (25,27) (26,30) (26,27) (27,29) (29,30)\nIs there a path between node 17 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph468-6_23", + "image": "data/connectivity/graph_visual/hard/graph468.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,6) (0,2) (0,22) (0,32) (0,27) (0,5) (0,14) (0,3) (0,21) (0,7) (0,25) (0,29) (0,9) (0,18) (0,19) (0,11) (0,31) (0,10) (0,8) (1,6) (1,2) (1,5) (1,3) (1,21) (1,7) (1,29) (1,9) (1,19) (1,10) (1,8) (2,32) (2,5) (2,14) (2,3) (2,7) (2,29) (2,9) (2,18) (2,23) (2,11) (2,10) (2,8) (3,22) (3,27) (3,5) (3,21) (3,7) (3,25) (3,29) (3,19) (3,23) (3,10) (4,20) (4,15) (4,28) (4,12) (4,30) (5,6) (5,22) (5,32) (5,27) (5,14) (5,21) (5,25) (5,29) (5,9) (5,18) (5,19) (5,11) (5,31) (5,10) (5,8) (6,24) (6,32) (6,27) (6,14) (6,21) (6,25) (6,29) (6,9) (6,18) (6,19) (6,23) (6,8) (7,22) (7,24) (7,27) (7,14) (7,21) (7,29) (7,9) (7,23) (7,11) (7,10) (7,8) (8,24) (8,32) (8,27) (8,14) (8,25) (8,29) (8,9) (8,18) (8,19) (8,23) (8,11) (8,31) (9,22) (9,24) (9,32) (9,27) (9,21) (9,29) (9,18) (9,19) (9,23) (9,11) (9,10) (10,22) (10,32) (10,27) (10,14) (10,21) (10,19) (10,23) (10,31) (11,22) (11,24) (11,32) (11,27) (11,14) (11,21) (11,25) (11,29) (11,18) (11,19) (11,31) (12,20) (12,15) (12,28) (12,30) (13,16) (13,17) (14,24) (14,32) (14,21) (14,25) (14,29) (14,19) (14,23) (14,31) (15,20) (15,28) (15,30) (16,17) (16,26) (17,26) (18,32) (18,27) (18,21) (18,25) (18,29) (18,23) (18,31) (19,22) (19,32) (19,27) (19,21) (19,25) (20,28) (20,30) (21,22) (21,24) (21,32) (21,27) (21,29) (21,23) (22,32) (22,25) (22,29) (22,23) (22,31) (23,24) (23,27) (23,31) (24,32) (24,27) (24,25) (24,31) (25,27) (25,29) (27,29) (27,31) (28,30) (29,32) (31,32)\nIs there a path between node 6 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph16-23_18", + "image": "data/connectivity/graph_visual/hard/graph16.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (1,4) (1,11) (2,21) (2,20) (2,24) (3,24) (4,13) (4,15) (4,8) (5,19) (5,24) (6,20) (6,24) (7,25) (7,21) (8,17) (8,15) (8,12) (9,13) (9,12) (10,16) (11,13) (11,18) (11,23) (11,14) (11,12) (13,17) (14,23) (15,18) (15,23) (18,23) (19,25) (19,24) (20,21) (21,25) (24,25)\nIs there a path between node 23 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph42-23_25", + "image": "data/connectivity/graph_visual/hard/graph42.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,10) (0,8) (0,19) (0,7) (0,4) (0,21) (0,14) (0,25) (0,1) (0,17) (0,24) (0,9) (0,16) (0,20) (0,5) (0,13) (1,8) (1,19) (1,4) (1,18) (1,25) (1,17) (1,24) (1,9) (1,16) (1,13) (2,6) (2,11) (2,23) (2,3) (3,11) (4,10) (4,19) (4,7) (4,18) (4,25) (4,17) (4,24) (4,9) (4,20) (5,19) (5,21) (5,18) (5,14) (5,25) (5,17) (5,24) (5,16) (5,20) (6,11) (6,23) (7,10) (7,12) (7,8) (7,18) (7,14) (7,17) (7,24) (7,9) (7,16) (7,20) (7,13) (8,10) (8,12) (8,19) (8,18) (8,14) (8,25) (8,17) (8,16) (8,20) (9,10) (9,21) (9,18) (9,14) (9,25) (9,17) (9,24) (9,16) (9,13) (10,12) (10,19) (10,21) (10,14) (10,25) (10,17) (10,24) (10,16) (11,23) (12,19) (12,18) (12,14) (12,17) (12,24) (12,13) (13,19) (13,21) (13,14) (13,25) (13,17) (13,24) (13,20) (14,21) (14,18) (14,25) (14,24) (14,16) (14,20) (16,19) (16,25) (16,17) (16,24) (17,19) (17,21) (17,18) (17,25) (17,20) (18,21) (18,25) (18,24) (18,20) (19,25) (19,24) (19,20) (20,24) (21,25) (21,24)\nIs there a path between node 23 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph660-19_9", + "image": "data/connectivity/graph_visual/hard/graph660.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,31) (0,28) (0,12) (0,20) (0,22) (0,16) (0,7) (1,25) (1,28) (1,27) (1,29) (1,20) (1,16) (1,17) (2,31) (2,18) (2,12) (2,24) (2,29) (2,13) (2,19) (2,26) (2,16) (3,14) (3,28) (3,27) (3,29) (3,19) (3,22) (4,21) (4,31) (4,25) (4,28) (4,18) (4,11) (4,8) (4,10) (5,6) (6,9) (6,33) (7,23) (7,31) (7,24) (7,29) (7,13) (7,20) (8,21) (8,31) (8,14) (8,27) (8,12) (8,29) (8,20) (9,33) (10,23) (10,14) (10,27) (10,29) (10,19) (10,11) (10,26) (11,23) (11,31) (11,14) (11,28) (11,27) (11,18) (11,12) (11,29) (11,20) (11,16) (12,15) (12,28) (12,18) (12,13) (12,20) (13,31) (13,25) (13,15) (13,28) (13,22) (13,26) (13,32) (13,16) (13,17) (14,31) (14,15) (14,28) (14,27) (15,23) (15,25) (15,27) (15,18) (15,30) (15,26) (15,32) (16,25) (16,27) (16,24) (16,29) (16,20) (16,26) (17,23) (17,25) (17,27) (17,30) (17,32) (18,25) (18,28) (18,24) (18,20) (18,30) (18,32) (19,24) (19,29) (19,26) (20,21) (20,31) (20,22) (21,25) (21,29) (22,24) (23,26) (24,31) (24,25) (24,27) (24,32) (27,30) (28,29) (28,32)\nIs there a path between node 19 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph369-18_3", + "image": "data/connectivity/graph_visual/hard/graph369.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,16) (0,6) (0,12) (0,29) (0,13) (0,3) (0,21) (0,17) (0,30) (0,27) (0,8) (0,10) (1,9) (1,11) (1,16) (1,6) (1,20) (1,24) (1,13) (1,14) (1,3) (1,21) (1,17) (1,30) (1,25) (1,19) (1,27) (1,8) (1,10) (2,4) (3,26) (3,9) (3,11) (3,7) (3,12) (3,24) (3,13) (3,14) (3,17) (3,30) (3,25) (3,27) (3,8) (3,10) (4,23) (5,28) (5,15) (6,26) (6,9) (6,11) (6,16) (6,7) (6,12) (6,24) (6,14) (6,21) (6,17) (6,25) (6,19) (6,27) (6,10) (7,26) (7,11) (7,16) (7,12) (7,29) (7,24) (7,21) (7,17) (7,30) (7,8) (7,10) (8,9) (8,16) (8,12) (8,20) (8,24) (8,13) (8,14) (8,17) (8,30) (8,19) (8,27) (8,10) (9,11) (9,16) (9,12) (9,20) (9,29) (9,24) (9,14) (9,21) (9,17) (9,30) (9,25) (9,19) (9,27) (10,16) (10,12) (10,20) (10,24) (10,13) (10,14) (10,21) (10,17) (10,30) (10,25) (10,19) (10,27) (11,26) (11,16) (11,24) (11,14) (11,21) (11,30) (11,25) (11,19) (11,27) (12,26) (12,16) (12,20) (12,29) (12,24) (12,13) (12,14) (12,21) (12,17) (12,30) (12,19) (12,27) (13,26) (13,16) (13,20) (13,24) (13,14) (13,21) (13,17) (13,30) (13,19) (13,27) (14,26) (14,16) (14,20) (14,29) (14,30) (14,25) (15,31) (16,26) (16,29) (16,21) (16,17) (16,30) (16,25) (16,27) (17,26) (17,29) (17,21) (17,30) (17,25) (17,19) (17,27) (18,23) (18,22) (19,26) (19,20) (19,21) (19,30) (19,25) (19,27) (20,26) (20,29) (20,24) (20,21) (20,30) (20,25) (20,27) (21,26) (21,29) (21,30) (21,25) (21,27) (22,23) (24,29) (24,30) (25,29) (25,30) (25,27) (26,29) (27,29) (27,30) (29,30)\nIs there a path between node 18 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph31-20_25", + "image": "data/connectivity/graph_visual/hard/graph31.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,25) (0,18) (0,8) (0,24) (0,6) (0,12) (0,5) (0,7) (0,16) (0,1) (0,22) (1,25) (1,18) (1,8) (1,4) (1,9) (1,6) (1,12) (1,11) (1,7) (1,13) (1,16) (1,20) (2,8) (2,9) (2,24) (2,6) (2,12) (2,11) (2,15) (2,5) (2,7) (2,16) (2,20) (2,22) (3,19) (3,23) (3,21) (3,14) (4,25) (4,18) (4,8) (4,9) (4,11) (4,15) (4,13) (4,22) (5,25) (5,8) (5,9) (5,24) (5,6) (5,15) (5,7) (5,13) (5,16) (5,20) (5,22) (6,25) (6,8) (6,9) (6,24) (6,12) (6,15) (6,7) (6,16) (7,25) (7,18) (7,24) (7,12) (7,16) (7,22) (8,18) (8,24) (8,12) (8,15) (9,25) (9,18) (9,24) (9,12) (9,11) (9,15) (9,16) (9,20) (9,22) (10,17) (11,24) (11,12) (11,16) (11,20) (12,25) (12,18) (12,24) (12,15) (12,13) (12,16) (12,22) (13,18) (13,20) (13,22) (14,19) (14,23) (14,21) (15,25) (15,18) (15,24) (15,20) (16,25) (16,18) (16,24) (16,20) (16,22) (18,25) (18,20) (18,22) (19,23) (19,21) (20,25) (20,24) (21,23) (22,24)\nIs there a path between node 20 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph8-1_21", + "image": "data/connectivity/graph_visual/hard/graph8.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,15) (0,14) (1,20) (2,24) (2,3) (2,13) (4,8) (4,6) (4,11) (4,5) (5,19) (5,21) (5,23) (6,19) (6,20) (7,14) (7,10) (8,21) (9,19) (9,11) (10,15) (10,22) (11,23) (12,18) (13,24) (13,25) (14,22) (15,22) (18,25) (19,20) (21,23)\nIs there a path between node 1 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph37-21_24", + "image": "data/connectivity/graph_visual/hard/graph37.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,20) (1,10) (1,8) (1,16) (1,6) (1,23) (1,24) (1,18) (1,13) (1,17) (1,3) (1,4) (1,25) (1,14) (1,7) (1,22) (2,12) (2,21) (3,5) (3,10) (3,9) (3,11) (3,8) (3,16) (3,6) (3,24) (3,19) (3,17) (3,25) (3,14) (3,7) (3,22) (4,5) (4,11) (4,8) (4,16) (4,6) (4,23) (4,24) (4,18) (4,19) (4,15) (4,17) (4,25) (4,14) (4,7) (5,10) (5,11) (5,8) (5,6) (5,23) (5,24) (5,18) (5,15) (5,17) (5,25) (5,7) (5,22) (6,10) (6,9) (6,11) (6,8) (6,23) (6,24) (6,19) (6,13) (6,17) (6,25) (6,14) (7,10) (7,11) (7,23) (7,19) (7,15) (7,17) (7,25) (7,14) (8,10) (8,9) (8,11) (8,18) (8,19) (8,13) (8,15) (8,17) (8,25) (8,22) (9,10) (9,11) (9,16) (9,23) (9,24) (9,18) (9,19) (9,13) (9,15) (9,17) (9,25) (9,14) (10,11) (10,16) (10,24) (10,18) (10,19) (10,13) (10,15) (10,17) (10,14) (10,22) (11,16) (11,23) (11,24) (11,18) (11,19) (11,13) (11,15) (11,17) (11,25) (11,14) (11,22) (12,21) (13,16) (13,15) (13,17) (13,25) (13,14) (13,22) (14,16) (14,23) (14,24) (14,18) (14,19) (14,17) (14,25) (15,16) (15,23) (15,24) (15,18) (15,19) (15,17) (15,25) (16,23) (16,18) (16,25) (17,23) (17,24) (17,18) (17,19) (17,25) (17,22) (18,23) (18,24) (18,19) (18,25) (19,23) (19,24) (19,25) (22,24) (22,25) (23,24) (23,25)\nIs there a path between node 21 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph349-26_16", + "image": "data/connectivity/graph_visual/hard/graph349.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,11) (0,12) (0,27) (0,20) (0,6) (0,18) (1,11) (1,13) (1,6) (1,26) (1,10) (1,30) (2,5) (2,4) (2,31) (2,19) (2,15) (2,14) (3,25) (3,29) (4,9) (4,15) (4,14) (5,8) (5,15) (5,16) (6,11) (6,27) (6,20) (6,17) (6,29) (6,30) (6,7) (7,27) (7,21) (10,11) (10,27) (10,20) (10,26) (10,18) (10,29) (10,21) (10,30) (10,28) (11,26) (11,25) (11,18) (11,29) (12,20) (12,17) (12,29) (13,20) (13,17) (13,25) (13,29) (15,19) (15,16) (17,20) (17,25) (17,29) (18,26) (18,29) (18,30) (19,31) (20,26) (21,26) (23,31) (24,25) (24,28) (25,26) (27,30) (28,29) (29,30)\nIs there a path between node 26 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph51-22_8", + "image": "data/connectivity/graph_visual/hard/graph51.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,4) (0,11) (0,16) (2,19) (2,4) (2,11) (3,4) (3,11) (5,8) (5,20) (5,25) (6,8) (6,22) (6,7) (6,18) (6,25) (7,22) (8,18) (8,24) (8,20) (8,21) (10,20) (10,26) (10,13) (11,19) (11,23) (13,22) (13,25) (15,24) (15,20) (15,25) (15,21) (16,23) (18,26) (19,23) (21,24) (21,25) (22,25) (22,26) (24,26)\nIs there a path between node 22 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph593-16_3", + "image": "data/connectivity/graph_visual/hard/graph593.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,3) (0,18) (0,13) (0,17) (0,4) (0,15) (0,28) (0,19) (0,14) (0,31) (0,25) (0,29) (0,30) (0,26) (0,2) (0,23) (0,5) (0,8) (1,3) (1,18) (1,13) (1,17) (1,15) (1,28) (1,19) (1,14) (1,25) (1,2) (1,23) (1,5) (1,8) (2,18) (2,13) (2,17) (2,28) (2,14) (2,29) (2,30) (2,23) (2,5) (2,32) (2,8) (3,13) (3,4) (3,15) (3,28) (3,19) (3,14) (3,31) (3,29) (3,10) (3,30) (3,5) (3,32) (4,18) (4,13) (4,17) (4,15) (4,28) (4,31) (4,25) (4,29) (4,10) (4,30) (4,26) (4,5) (4,22) (4,32) (4,8) (5,13) (5,28) (5,19) (5,14) (5,25) (5,29) (5,10) (5,30) (5,26) (5,23) (5,22) (5,8) (6,16) (6,27) (6,9) (6,21) (6,12) (6,11) (6,20) (7,16) (7,27) (7,33) (7,9) (7,21) (7,12) (7,11) (8,13) (8,17) (8,15) (8,14) (8,25) (8,29) (8,10) (8,30) (8,23) (9,16) (9,27) (9,33) (9,21) (9,12) (9,20) (10,13) (10,17) (10,15) (10,28) (10,14) (10,25) (10,23) (10,22) (10,32) (11,16) (11,27) (11,33) (11,20) (12,16) (12,33) (12,24) (13,18) (13,28) (13,31) (13,25) (13,29) (13,30) (13,26) (13,23) (13,22) (14,18) (14,15) (14,19) (14,31) (14,25) (14,29) (14,23) (14,22) (14,32) (15,18) (15,17) (15,28) (15,31) (15,29) (15,30) (15,26) (15,23) (15,22) (15,32) (16,27) (16,33) (17,18) (17,28) (17,19) (17,31) (17,25) (17,29) (17,26) (17,23) (17,22) (17,32) (18,19) (18,29) (18,22) (19,28) (19,31) (19,25) (19,29) (19,30) (19,26) (19,23) (19,22) (19,32) (20,27) (20,21) (20,24) (21,27) (21,24) (22,28) (22,25) (22,29) (22,30) (22,26) (22,23) (22,32) (23,28) (23,29) (23,30) (23,26) (25,31) (25,26) (26,28) (26,29) (26,30) (27,33) (28,30) (28,32) (29,30) (29,32) (30,31) (30,32) (31,32)\nIs there a path between node 16 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph536-6_16", + "image": "data/connectivity/graph_visual/hard/graph536.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,28) (0,24) (0,10) (0,2) (0,16) (0,15) (0,19) (0,23) (0,27) (0,12) (0,20) (0,11) (0,18) (0,3) (0,8) (1,17) (1,26) (1,28) (1,24) (1,10) (1,2) (1,16) (1,33) (1,19) (1,27) (1,12) (1,25) (1,11) (1,18) (2,17) (2,26) (2,28) (2,24) (2,10) (2,13) (2,33) (2,15) (2,19) (2,6) (2,7) (2,23) (2,27) (2,20) (2,25) (2,18) (2,3) (2,8) (3,17) (3,24) (3,16) (3,15) (3,19) (3,23) (3,27) (3,12) (3,25) (3,11) (3,18) (4,31) (4,14) (4,30) (4,32) (4,21) (5,30) (5,9) (5,32) (5,21) (5,29) (6,17) (6,26) (6,10) (6,16) (6,33) (6,19) (6,23) (6,22) (6,27) (6,12) (6,20) (6,25) (6,11) (6,18) (6,8) (7,26) (7,24) (7,10) (7,16) (7,13) (7,33) (7,15) (7,19) (7,27) (7,12) (7,20) (7,25) (7,11) (7,18) (7,8) (8,28) (8,10) (8,13) (8,33) (8,15) (8,19) (8,22) (8,27) (8,12) (8,20) (8,18) (9,31) (9,14) (9,32) (9,21) (9,29) (10,26) (10,16) (10,13) (10,33) (10,19) (10,23) (10,27) (10,11) (11,17) (11,28) (11,24) (11,16) (11,13) (11,33) (11,19) (11,12) (11,20) (11,25) (11,18) (12,17) (12,26) (12,24) (12,16) (12,13) (12,33) (12,15) (12,23) (12,27) (13,17) (13,28) (13,16) (13,33) (13,19) (13,23) (13,22) (13,20) (13,25) (13,18) (14,30) (15,17) (15,26) (15,16) (15,19) (15,27) (15,20) (15,25) (15,18) (16,17) (16,28) (16,33) (16,22) (16,27) (16,20) (16,25) (17,26) (17,24) (17,33) (17,19) (17,23) (17,22) (17,27) (17,25) (18,33) (18,19) (18,25) (19,26) (19,28) (19,33) (19,22) (19,27) (19,20) (20,28) (20,24) (20,33) (20,23) (20,22) (20,27) (21,31) (21,30) (21,32) (21,29) (22,23) (22,27) (23,26) (23,24) (23,33) (23,27) (24,26) (24,28) (24,33) (24,25) (25,28) (25,33) (25,27) (26,33) (27,28) (29,31) (29,30) (29,32) (30,31) (30,32) (31,32)\nIs there a path between node 6 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph395-7_16", + "image": "data/connectivity/graph_visual/hard/graph395.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,24) (0,18) (0,29) (0,9) (0,4) (0,14) (0,3) (0,13) (1,21) (1,24) (1,20) (1,9) (1,3) (2,10) (2,26) (2,28) (3,20) (3,6) (3,8) (3,5) (3,27) (4,21) (4,24) (4,29) (4,6) (4,9) (4,8) (4,17) (4,15) (4,27) (4,32) (4,13) (5,21) (5,16) (5,24) (5,9) (5,27) (6,24) (6,9) (6,17) (6,15) (6,32) (7,31) (8,16) (8,24) (8,11) (8,9) (8,27) (9,21) (9,16) (9,24) (9,11) (9,15) (9,14) (9,13) (11,16) (12,25) (13,16) (13,20) (13,30) (13,27) (14,16) (14,24) (14,18) (14,27) (15,24) (15,18) (15,20) (15,17) (16,21) (16,30) (16,27) (17,21) (17,20) (17,29) (18,20) (18,29) (18,30) (18,27) (19,25) (19,26) (19,22) (20,24) (21,24) (21,29) (22,26) (22,28) (23,25) (24,30) (26,28) (27,32) (29,32)\nIs there a path between node 7 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph634-1_17", + "image": "data/connectivity/graph_visual/hard/graph634.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,6) (0,1) (0,8) (0,13) (0,32) (0,2) (1,33) (1,34) (1,30) (1,8) (1,10) (1,19) (1,31) (1,2) (2,15) (2,34) (2,18) (2,8) (2,3) (2,16) (2,32) (2,4) (3,5) (3,26) (3,15) (3,11) (3,16) (3,4) (3,14) (4,5) (4,26) (4,12) (4,33) (4,34) (4,30) (4,13) (4,19) (5,34) (5,21) (5,6) (5,8) (5,19) (5,32) (5,31) (6,33) (6,15) (6,34) (6,13) (6,31) (7,23) (7,20) (8,33) (8,15) (8,34) (8,21) (8,11) (9,24) (10,33) (10,21) (10,27) (10,13) (10,11) (10,19) (11,26) (11,33) (11,13) (11,32) (12,30) (12,16) (13,33) (13,34) (13,19) (13,14) (15,33) (15,34) (15,27) (16,34) (16,30) (16,27) (16,32) (17,29) (18,27) (18,32) (19,30) (19,21) (19,32) (20,28) (21,27) (21,32) (26,33) (26,30) (26,31) (27,34)\nIs there a path between node 1 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph60-13_18", + "image": "data/connectivity/graph_visual/hard/graph60.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,18) (0,13) (0,22) (1,12) (1,6) (2,20) (2,14) (2,11) (3,5) (3,23) (3,6) (5,17) (6,19) (7,23) (8,13) (8,15) (9,21) (9,18) (12,24) (12,17) (12,19) (13,21) (13,18) (13,25) (13,15) (13,16) (15,16) (16,21) (16,25) (17,23) (17,19) (19,26) (21,22) (22,25)\nIs there a path between node 13 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph89-4_7", + "image": "data/connectivity/graph_visual/hard/graph89.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,7) (0,9) (0,8) (0,19) (0,13) (0,11) (1,15) (1,6) (1,3) (1,12) (1,4) (1,2) (1,23) (1,5) (1,16) (1,22) (1,17) (1,18) (1,21) (1,24) (1,25) (2,15) (2,3) (2,4) (2,20) (2,23) (2,22) (2,27) (2,18) (2,21) (2,24) (3,15) (3,4) (3,26) (3,20) (3,23) (3,5) (3,16) (3,14) (3,22) (3,27) (3,18) (3,21) (3,24) (3,25) (4,15) (4,6) (4,12) (4,26) (4,20) (4,5) (4,22) (4,27) (4,17) (4,21) (4,25) (5,15) (5,6) (5,12) (5,20) (5,16) (5,14) (5,22) (5,27) (5,18) (5,21) (5,25) (6,15) (6,12) (6,27) (6,17) (6,21) (6,24) (6,25) (7,19) (7,13) (8,9) (8,19) (8,13) (9,19) (9,10) (10,19) (10,13) (10,11) (11,13) (12,15) (12,26) (12,20) (12,14) (12,22) (12,21) (12,24) (13,19) (14,15) (14,26) (14,20) (14,16) (14,22) (14,17) (14,21) (14,24) (14,25) (15,26) (15,20) (15,23) (15,16) (15,22) (15,17) (15,18) (15,24) (16,26) (16,27) (16,18) (16,25) (17,26) (17,23) (17,18) (17,21) (17,24) (17,25) (18,26) (18,20) (18,22) (18,27) (18,24) (18,25) (20,26) (20,23) (20,22) (20,27) (20,24) (20,25) (21,22) (21,27) (21,24) (21,25) (22,23) (22,27) (22,24) (22,25) (23,27) (23,25) (24,26) (24,27) (25,26) (25,27) (26,27)\nIs there a path between node 4 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph682-5_11", + "image": "data/connectivity/graph_visual/hard/graph682.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,8) (0,28) (0,29) (0,16) (0,5) (0,6) (0,12) (0,15) (1,28) (1,18) (1,4) (1,3) (1,21) (1,14) (1,12) (2,22) (3,8) (3,29) (3,33) (3,5) (3,21) (3,30) (3,26) (3,14) (3,7) (3,31) (3,24) (3,12) (3,32) (4,17) (4,5) (4,34) (4,12) (4,32) (4,19) (5,18) (5,16) (5,33) (5,21) (5,6) (5,30) (5,20) (5,11) (6,27) (6,17) (6,26) (6,7) (6,24) (6,15) (7,28) (7,18) (7,29) (7,17) (7,21) (7,26) (7,14) (7,11) (7,32) (8,28) (8,18) (8,29) (8,34) (8,10) (8,30) (8,26) (8,23) (8,14) (8,20) (10,21) (10,30) (10,14) (10,24) (10,20) (10,12) (10,11) (11,16) (11,34) (11,30) (11,14) (11,24) (11,20) (12,27) (12,28) (12,29) (12,17) (12,16) (12,20) (12,32) (12,19) (13,27) (13,17) (13,16) (13,33) (13,23) (13,14) (13,24) (14,33) (14,34) (14,21) (14,30) (14,20) (14,32) (14,19) (14,15) (15,18) (15,29) (15,21) (15,30) (15,23) (16,27) (16,18) (16,17) (16,24) (17,28) (17,33) (17,34) (17,31) (17,32) (18,33) (18,34) (18,21) (18,30) (18,23) (18,24) (18,32) (19,29) (19,33) (19,21) (19,26) (19,32) (20,28) (20,29) (20,33) (20,30) (21,29) (21,33) (21,26) (23,33) (24,27) (24,29) (24,33) (24,30) (24,26) (26,28) (26,29) (27,29) (28,31) (28,32) (29,32)\nIs there a path between node 5 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph177-23_17", + "image": "data/connectivity/graph_visual/hard/graph177.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,7) (0,24) (0,22) (0,21) (0,20) (0,3) (1,13) (1,27) (1,23) (1,28) (1,2) (1,10) (1,11) (1,18) (1,14) (1,8) (1,16) (1,12) (2,13) (2,27) (2,23) (2,15) (2,26) (2,10) (2,9) (2,11) (2,14) (2,8) (2,5) (3,24) (3,22) (3,4) (3,21) (3,20) (4,7) (4,24) (4,21) (5,13) (5,23) (5,26) (5,28) (5,17) (5,11) (5,14) (5,8) (5,12) (6,13) (6,27) (6,23) (6,15) (6,26) (6,17) (6,10) (6,9) (6,19) (6,11) (6,14) (6,8) (6,16) (7,24) (7,22) (8,13) (8,27) (8,26) (8,28) (8,17) (8,10) (8,9) (8,19) (8,11) (8,18) (8,16) (9,13) (9,27) (9,15) (9,26) (9,28) (9,17) (9,10) (9,19) (9,11) (9,14) (9,16) (9,12) (10,13) (10,27) (10,23) (10,15) (10,28) (10,17) (10,19) (10,11) (10,18) (10,14) (11,13) (11,27) (11,23) (11,15) (11,28) (11,17) (11,19) (11,18) (11,14) (11,16) (12,23) (12,15) (12,17) (12,19) (12,18) (12,14) (13,27) (13,23) (13,15) (13,26) (13,17) (13,19) (13,18) (13,14) (13,16) (14,23) (14,15) (14,28) (14,17) (14,19) (15,26) (15,28) (15,17) (15,19) (15,16) (16,27) (16,26) (16,28) (16,19) (16,18) (17,27) (17,23) (17,19) (18,26) (18,28) (19,23) (19,26) (19,28) (20,24) (20,21) (21,24) (23,26) (26,28) (27,28)\nIs there a path between node 23 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph217-26_24", + "image": "data/connectivity/graph_visual/hard/graph217.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,17) (0,13) (0,2) (0,27) (0,24) (0,6) (0,28) (0,10) (0,9) (1,25) (1,13) (1,24) (1,21) (1,16) (2,14) (2,16) (2,8) (2,23) (2,9) (3,18) (3,17) (3,25) (3,29) (3,27) (3,12) (3,28) (3,10) (3,8) (3,20) (4,17) (4,13) (4,5) (4,24) (4,21) (4,16) (5,14) (5,27) (5,28) (5,8) (5,20) (6,18) (6,13) (6,12) (7,26) (8,14) (8,17) (8,25) (8,27) (8,21) (8,11) (8,20) (9,14) (9,27) (9,11) (9,28) (9,10) (10,13) (10,29) (10,27) (10,24) (10,21) (10,16) (11,17) (12,21) (13,14) (13,18) (13,17) (13,25) (13,24) (14,18) (14,27) (14,16) (16,28) (16,20) (17,29) (17,21) (17,23) (17,20) (18,23) (20,23) (21,25) (21,28) (23,25) (23,27) (23,24) (23,28) (24,29) (24,27) (25,29) (25,28) (27,28)\nIs there a path between node 26 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph210-26_23", + "image": "data/connectivity/graph_visual/hard/graph210.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,28) (0,26) (0,21) (0,16) (0,2) (0,7) (0,22) (1,28) (1,27) (1,24) (1,10) (1,26) (1,12) (1,14) (1,19) (1,20) (2,24) (2,26) (2,16) (2,22) (2,4) (3,25) (4,5) (4,8) (4,10) (4,14) (4,22) (5,28) (5,8) (5,24) (5,12) (5,7) (5,23) (6,13) (6,26) (6,21) (6,19) (7,28) (7,26) (7,19) (7,22) (7,23) (7,20) (8,27) (8,24) (8,10) (8,26) (8,22) (10,18) (10,12) (11,13) (11,26) (11,22) (11,23) (11,20) (12,13) (12,24) (12,21) (12,29) (13,28) (13,18) (14,24) (14,26) (14,20) (16,28) (16,24) (16,21) (17,27) (17,20) (18,27) (18,19) (20,21) (20,22) (21,29) (24,28) (27,28)\nIs there a path between node 26 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph138-6_10", + "image": "data/connectivity/graph_visual/hard/graph138.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,12) (0,10) (0,25) (0,16) (0,24) (0,4) (0,8) (0,27) (0,19) (1,5) (1,28) (2,15) (3,12) (3,13) (3,21) (3,24) (3,4) (3,8) (4,26) (4,20) (4,21) (4,11) (4,9) (6,13) (6,14) (6,22) (6,21) (6,7) (6,23) (6,11) (7,12) (7,26) (7,20) (7,17) (7,14) (7,10) (7,25) (7,24) (7,8) (7,11) (7,19) (7,9) (8,25) (8,27) (8,11) (9,17) (9,14) (9,21) (9,23) (9,27) (9,11) (10,26) (10,20) (10,14) (10,25) (10,23) (10,24) (11,13) (11,17) (11,21) (11,25) (11,23) (11,19) (12,20) (12,17) (12,24) (13,26) (13,20) (13,17) (13,22) (13,25) (13,24) (13,19) (14,20) (14,16) (15,28) (15,18) (16,26) (16,21) (16,23) (17,26) (17,22) (17,23) (17,27) (18,28) (19,22) (20,23) (20,24) (20,27) (21,26) (21,27) (23,25) (24,25) (24,27) (25,27)\nIs there a path between node 6 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph365-29_17", + "image": "data/connectivity/graph_visual/hard/graph365.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,29) (0,27) (0,31) (0,21) (0,10) (0,5) (0,11) (0,19) (0,18) (0,6) (0,20) (0,26) (1,14) (1,22) (1,23) (1,9) (1,28) (1,25) (1,12) (1,13) (1,2) (1,30) (2,23) (2,9) (2,28) (2,25) (2,12) (2,13) (3,15) (3,7) (3,17) (3,16) (4,29) (4,27) (4,31) (4,10) (4,5) (4,11) (4,20) (4,26) (5,29) (5,27) (5,24) (5,31) (5,19) (5,18) (5,26) (6,29) (6,27) (6,24) (6,31) (6,21) (6,11) (6,19) (6,18) (6,20) (7,15) (7,16) (8,15) (8,17) (8,16) (9,22) (9,23) (9,28) (9,25) (9,12) (9,13) (9,30) (10,29) (10,24) (10,31) (10,11) (10,19) (10,20) (11,29) (11,27) (11,24) (11,31) (11,18) (11,20) (12,14) (12,22) (12,13) (12,30) (13,22) (13,23) (13,28) (13,25) (13,30) (14,22) (14,28) (14,25) (14,30) (16,17) (18,29) (18,27) (18,24) (18,31) (18,19) (19,29) (19,24) (19,31) (19,21) (19,20) (19,26) (20,27) (20,24) (20,31) (20,21) (21,29) (21,27) (21,24) (21,26) (23,25) (24,27) (24,26) (25,30) (26,29) (26,27) (26,31) (27,29) (27,31) (28,30) (29,31)\nIs there a path between node 29 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph654-16_17", + "image": "data/connectivity/graph_visual/hard/graph654.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,25) (0,10) (0,11) (0,18) (0,15) (0,21) (0,24) (0,26) (0,16) (0,31) (1,13) (1,30) (1,6) (1,22) (1,28) (1,23) (1,20) (1,3) (1,14) (1,29) (1,2) (1,32) (1,27) (1,9) (1,17) (2,13) (2,6) (2,12) (2,22) (2,28) (2,23) (2,20) (2,14) (2,29) (2,32) (2,27) (3,13) (3,30) (3,6) (3,22) (3,28) (3,5) (3,23) (3,29) (3,32) (3,27) (3,9) (3,17) (4,33) (4,19) (4,10) (4,11) (4,18) (4,15) (4,21) (4,24) (4,26) (4,16) (4,31) (5,13) (5,30) (5,6) (5,12) (5,22) (5,28) (5,20) (5,14) (5,32) (5,27) (5,9) (6,12) (6,22) (6,28) (6,23) (6,20) (6,14) (6,29) (6,32) (6,27) (6,9) (6,17) (7,8) (7,25) (7,33) (7,19) (7,10) (7,11) (7,15) (7,34) (7,26) (7,16) (7,31) (8,33) (8,19) (8,10) (8,18) (8,24) (8,26) (8,16) (8,31) (9,13) (9,30) (9,12) (9,28) (9,14) (9,29) (9,32) (9,27) (10,33) (10,19) (10,18) (10,15) (10,34) (10,24) (10,26) (10,16) (10,31) (11,25) (11,33) (11,19) (11,18) (11,34) (11,24) (11,26) (11,16) (11,31) (12,13) (12,30) (12,14) (12,29) (12,32) (12,27) (12,17) (13,30) (13,23) (13,20) (13,14) (13,29) (13,27) (13,17) (14,30) (14,23) (14,20) (14,29) (14,27) (14,17) (15,33) (15,19) (15,21) (15,24) (15,26) (15,16) (15,31) (16,25) (16,33) (16,19) (16,18) (16,21) (16,24) (16,26) (16,31) (17,30) (17,22) (17,20) (17,29) (17,32) (17,27) (18,25) (18,33) (18,19) (18,21) (18,34) (18,31) (19,21) (19,34) (19,24) (20,22) (20,28) (20,23) (20,29) (20,32) (20,27) (21,34) (21,24) (21,26) (22,30) (22,29) (22,27) (23,30) (23,29) (23,32) (24,33) (24,26) (24,31) (25,31) (26,34) (26,31) (27,28) (27,29) (27,32) (28,30) (28,29) (28,32) (29,30) (30,32) (31,33) (31,34) (33,34)\nIs there a path between node 16 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph582-2_27", + "image": "data/connectivity/graph_visual/hard/graph582.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,19) (0,10) (0,22) (0,8) (0,12) (0,9) (0,31) (0,16) (0,32) (0,24) (0,26) (0,15) (0,4) (0,21) (0,18) (0,2) (0,28) (0,1) (0,20) (0,27) (0,29) (0,14) (1,19) (1,23) (1,10) (1,22) (1,7) (1,30) (1,12) (1,9) (1,31) (1,16) (1,26) (1,13) (1,4) (1,21) (1,18) (1,2) (1,20) (1,27) (1,17) (1,29) (1,3) (1,11) (2,19) (2,23) (2,10) (2,22) (2,7) (2,8) (2,12) (2,9) (2,32) (2,24) (2,26) (2,15) (2,13) (2,4) (2,21) (2,18) (2,33) (2,28) (2,20) (2,14) (2,3) (2,11) (3,7) (3,8) (3,9) (3,31) (3,16) (3,24) (3,15) (3,4) (3,21) (3,18) (3,33) (3,28) (3,20) (3,27) (3,14) (3,11) (4,19) (4,23) (4,10) (4,22) (4,7) (4,8) (4,30) (4,12) (4,31) (4,16) (4,24) (4,15) (4,21) (4,18) (4,33) (4,28) (4,20) (4,27) (4,17) (4,14) (4,11) (5,25) (6,25) (7,23) (7,10) (7,22) (7,8) (7,31) (7,16) (7,24) (7,26) (7,13) (7,21) (7,18) (7,33) (7,28) (7,20) (7,17) (7,29) (7,14) (7,11) (8,19) (8,10) (8,22) (8,30) (8,31) (8,16) (8,24) (8,26) (8,15) (8,13) (8,21) (8,18) (8,33) (8,20) (8,17) (8,14) (8,11) (9,19) (9,23) (9,10) (9,30) (9,12) (9,16) (9,32) (9,26) (9,15) (9,21) (9,28) (9,20) (9,17) (9,29) (9,14) (9,11) (10,23) (10,12) (10,31) (10,16) (10,32) (10,24) (10,26) (10,21) (10,33) (10,27) (10,17) (10,14) (10,11) (11,19) (11,23) (11,22) (11,30) (11,12) (11,31) (11,16) (11,24) (11,26) (11,13) (11,21) (11,28) (11,20) (11,27) (12,19) (12,23) (12,22) (12,30) (12,16) (12,32) (12,15) (12,13) (12,21) (12,18) (12,33) (12,28) (12,29) (13,19) (13,30) (13,16) (13,32) (13,26) (13,33) (13,28) (13,29) (13,14) (14,19) (14,23) (14,22) (14,30) (14,24) (14,15) (14,33) (14,27) (14,17) (14,29) (15,19) (15,22) (15,30) (15,31) (15,21) (15,18) (15,27) (15,17) (15,29) (16,19) (16,22) (16,30) (16,32) (16,24) (16,33) (16,28) (16,20) (16,27) (16,17) (16,29) (17,19) (17,22) (17,30) (17,31) (17,32) (17,24) (17,26) (17,21) (17,33) (17,28) (17,20) (17,27) (17,29) (18,23) (18,22) (18,30) (18,32) (18,24) (18,21) (18,33) (18,28) (18,20) (18,27) (19,23) (19,22) (19,30) (19,31) (19,32) (19,24) (19,26) (19,21) (19,33) (19,28) (19,27) (19,29) (20,22) (20,30) (20,31) (20,26) (20,21) (20,33) (20,27) (20,29) (21,23) (21,22) (21,30) (21,31) (21,28) (21,27) (21,29) (22,30) (22,31) (22,24) (22,26) (22,33) (22,27) (23,32) (23,26) (23,28) (23,27) (23,29) (24,32) (24,33) (24,28) (24,27) (24,29) (26,30) (26,31) (26,28) (27,31) (27,32) (27,29) (28,30) (28,31) (28,33) (28,29) (29,30) (29,31) (29,32) (31,33)\nIs there a path between node 2 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph692-32_20", + "image": "data/connectivity/graph_visual/hard/graph692.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,15) (0,2) (0,33) (0,4) (0,8) (0,23) (0,34) (0,30) (1,22) (1,28) (1,9) (1,29) (1,24) (1,26) (1,7) (1,27) (1,32) (1,19) (1,16) (1,5) (1,10) (2,12) (2,3) (2,15) (2,33) (2,20) (2,8) (2,23) (3,12) (3,11) (3,33) (3,4) (3,8) (3,23) (4,12) (4,11) (4,33) (4,20) (4,23) (5,22) (5,17) (5,28) (5,29) (5,14) (5,31) (5,25) (5,18) (5,24) (5,26) (5,6) (5,27) (5,32) (5,21) (5,19) (5,16) (6,17) (6,28) (6,13) (6,29) (6,14) (6,31) (6,25) (6,24) (6,27) (6,19) (6,16) (6,10) (7,22) (7,17) (7,9) (7,13) (7,29) (7,25) (7,24) (7,26) (7,27) (7,21) (7,19) (7,16) (7,10) (8,12) (8,11) (8,15) (8,33) (8,30) (9,22) (9,28) (9,13) (9,29) (9,14) (9,31) (9,18) (9,24) (9,26) (9,27) (9,32) (9,21) (9,19) (9,16) (9,10) (10,22) (10,17) (10,28) (10,13) (10,29) (10,14) (10,31) (10,25) (10,18) (10,26) (10,32) (10,21) (10,16) (11,33) (11,20) (11,23) (11,30) (12,33) (12,20) (12,34) (12,30) (13,22) (13,17) (13,28) (13,29) (13,14) (13,31) (13,25) (13,18) (13,24) (13,26) (13,32) (13,21) (13,19) (13,16) (14,22) (14,17) (14,28) (14,29) (14,31) (14,25) (14,18) (14,24) (14,26) (14,27) (14,32) (14,21) (14,19) (14,16) (15,33) (15,20) (15,23) (15,34) (15,30) (16,22) (16,17) (16,28) (16,29) (16,31) (16,18) (16,24) (16,26) (16,27) (16,32) (16,21) (17,28) (17,29) (17,31) (17,18) (17,24) (17,27) (17,32) (17,21) (17,19) (18,22) (18,28) (18,29) (18,31) (18,25) (18,27) (18,21) (19,22) (19,28) (19,29) (19,31) (19,25) (19,27) (19,21) (20,33) (20,23) (20,34) (20,30) (21,28) (21,29) (21,31) (21,25) (21,26) (21,32) (22,28) (22,31) (22,25) (22,24) (22,26) (22,27) (22,32) (23,33) (24,28) (24,29) (24,31) (24,26) (24,32) (25,31) (25,27) (25,32) (26,29) (26,31) (26,27) (27,28) (27,29) (27,31) (27,32) (28,29) (28,32) (29,32) (30,33) (30,34) (31,32) (33,34)\nIs there a path between node 32 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph397-25_5", + "image": "data/connectivity/graph_visual/hard/graph397.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,27) (0,1) (0,32) (0,9) (1,25) (1,20) (1,23) (1,24) (1,8) (2,25) (2,20) (2,23) (2,16) (2,19) (3,24) (3,32) (3,19) (4,13) (5,13) (5,7) (5,26) (5,29) (5,6) (5,22) (6,28) (7,13) (7,21) (7,22) (7,18) (7,28) (8,24) (8,31) (8,10) (8,9) (9,11) (9,10) (9,32) (9,19) (9,14) (10,24) (10,15) (11,25) (11,20) (11,19) (12,30) (12,20) (12,24) (13,21) (13,29) (13,18) (13,28) (14,20) (14,23) (14,24) (14,27) (14,15) (15,16) (16,27) (16,31) (17,28) (18,21) (18,26) (19,24) (20,30) (20,27) (20,32) (21,28) (24,25) (24,27) (24,31) (24,32) (25,27) (25,31) (27,32)\nIs there a path between node 25 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph412-8_26", + "image": "data/connectivity/graph_visual/hard/graph412.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,16) (0,14) (0,20) (1,32) (1,25) (1,21) (1,22) (1,23) (1,26) (2,9) (2,20) (3,32) (3,28) (4,9) (4,5) (4,17) (4,31) (5,13) (5,31) (5,11) (6,32) (6,26) (7,32) (7,27) (7,25) (7,28) (7,22) (7,23) (8,30) (8,31) (8,20) (9,24) (9,12) (9,11) (10,18) (10,29) (10,25) (10,28) (10,26) (11,17) (11,14) (12,14) (12,20) (13,16) (13,17) (14,24) (14,16) (14,20) (15,32) (15,25) (15,28) (15,23) (16,17) (16,20) (17,30) (18,29) (18,21) (18,28) (18,22) (19,28) (19,26) (20,30) (21,25) (21,23) (21,26) (22,25) (22,28) (22,26) (25,27) (25,29) (25,28) (27,28)\nIs there a path between node 8 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph484-25_28", + "image": "data/connectivity/graph_visual/hard/graph484.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,12) (0,29) (0,23) (0,2) (0,20) (0,30) (0,26) (0,3) (0,1) (0,6) (0,4) (0,7) (1,24) (1,2) (1,30) (1,18) (1,26) (1,6) (1,14) (2,12) (2,29) (2,20) (2,13) (2,3) (2,14) (2,7) (3,12) (3,29) (3,23) (3,30) (3,18) (3,26) (3,6) (3,14) (4,12) (4,23) (4,20) (4,13) (4,30) (4,18) (4,26) (4,6) (4,14) (4,7) (5,11) (5,17) (5,8) (5,25) (6,12) (6,29) (6,20) (6,30) (6,18) (6,14) (6,7) (7,12) (7,23) (7,20) (7,13) (7,30) (7,18) (7,14) (8,17) (8,25) (9,15) (9,31) (9,21) (9,28) (9,16) (9,19) (10,22) (11,17) (11,25) (12,29) (12,20) (12,13) (12,30) (12,14) (13,24) (13,29) (13,23) (13,20) (13,30) (13,18) (13,26) (14,29) (14,23) (14,20) (14,30) (14,26) (15,28) (15,32) (15,16) (15,27) (15,19) (16,31) (16,21) (16,28) (17,25) (18,29) (18,26) (19,31) (19,21) (19,32) (19,27) (20,29) (20,23) (20,30) (21,31) (21,32) (23,24) (23,30) (23,26) (24,29) (24,30) (26,29) (26,30) (27,31) (27,28) (27,32) (28,31) (28,32)\nIs there a path between node 25 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph154-12_13", + "image": "data/connectivity/graph_visual/hard/graph154.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,2) (0,23) (0,8) (1,6) (1,26) (1,11) (2,6) (2,11) (3,12) (3,19) (3,20) (4,13) (4,21) (4,17) (4,10) (4,6) (4,23) (4,8) (5,13) (5,7) (5,21) (5,17) (5,28) (5,6) (5,23) (5,8) (5,26) (5,24) (5,11) (6,13) (6,17) (6,10) (6,23) (6,24) (7,17) (7,28) (7,23) (8,21) (8,10) (9,15) (10,13) (10,21) (10,23) (10,11) (11,13) (11,17) (12,19) (12,14) (12,27) (12,15) (12,22) (13,17) (13,16) (14,22) (15,19) (16,17) (16,28) (16,24) (17,24) (18,19) (18,27) (19,27) (21,26) (21,24) (22,25) (23,28) (24,28) (25,27)\nIs there a path between node 12 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph568-1_26", + "image": "data/connectivity/graph_visual/hard/graph568.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,17) (0,26) (0,2) (0,5) (0,4) (0,25) (0,18) (0,29) (1,24) (1,6) (1,21) (2,22) (2,8) (2,30) (2,17) (2,33) (2,26) (2,11) (2,7) (2,5) (2,23) (2,18) (2,29) (3,27) (4,13) (4,9) (4,33) (4,11) (4,5) (4,23) (4,25) (4,29) (5,22) (5,16) (5,30) (5,9) (5,19) (5,10) (5,15) (5,29) (6,24) (6,31) (7,17) (7,23) (7,25) (8,16) (8,32) (8,10) (8,18) (8,29) (9,22) (9,30) (9,23) (10,22) (10,16) (10,19) (11,22) (11,13) (11,30) (11,33) (11,23) (11,18) (12,28) (12,31) (13,30) (13,32) (13,23) (14,17) (14,32) (14,23) (14,25) (14,15) (14,29) (15,16) (15,33) (15,32) (15,18) (16,22) (16,17) (16,32) (16,23) (16,18) (16,29) (17,32) (17,18) (17,29) (18,19) (18,32) (18,23) (19,29) (20,24) (20,21) (21,27) (22,32) (22,25) (25,33) (25,26) (25,29) (26,33) (26,29) (27,28) (28,31) (29,30)\nIs there a path between node 1 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph80-12_26", + "image": "data/connectivity/graph_visual/hard/graph80.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,24) (0,26) (0,15) (0,14) (0,22) (0,25) (1,7) (1,24) (1,26) (1,17) (1,4) (1,15) (1,14) (1,9) (1,25) (2,12) (2,20) (2,6) (2,8) (2,18) (2,11) (2,23) (2,10) (3,7) (3,24) (3,26) (3,4) (3,15) (3,14) (3,19) (3,9) (3,21) (3,22) (3,25) (4,24) (4,26) (4,15) (4,9) (4,21) (4,22) (5,20) (5,6) (5,16) (5,8) (5,18) (5,11) (5,23) (5,10) (6,12) (6,20) (6,8) (6,18) (6,11) (6,23) (6,10) (7,13) (7,24) (7,26) (7,15) (7,14) (7,19) (7,9) (7,21) (7,22) (7,25) (8,20) (8,16) (8,10) (9,13) (9,26) (9,17) (9,15) (9,19) (9,21) (9,22) (9,25) (10,12) (10,16) (10,18) (10,11) (11,12) (11,16) (11,18) (11,23) (12,20) (12,23) (13,24) (13,17) (13,15) (13,19) (13,21) (13,22) (13,25) (14,26) (14,15) (14,19) (14,21) (14,22) (14,25) (15,24) (15,26) (15,17) (15,22) (16,20) (16,23) (17,19) (17,22) (17,25) (18,23) (19,26) (19,21) (19,22) (19,25) (20,23) (21,24) (21,26) (21,22) (21,25) (22,25) (24,26) (24,25)\nIs there a path between node 12 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph528-16_2", + "image": "data/connectivity/graph_visual/hard/graph528.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,32) (0,22) (0,33) (0,19) (0,4) (0,13) (0,31) (0,15) (0,24) (1,23) (1,27) (2,4) (2,31) (2,29) (3,16) (3,23) (3,8) (4,33) (4,12) (4,28) (4,6) (5,26) (5,17) (5,21) (5,8) (6,32) (6,33) (6,31) (6,29) (7,32) (7,22) (7,31) (7,15) (7,29) (8,9) (9,16) (9,21) (9,27) (10,32) (10,25) (10,28) (10,24) (10,29) (11,33) (11,15) (12,22) (12,31) (12,28) (13,22) (13,29) (14,17) (14,18) (14,23) (15,32) (15,19) (15,31) (15,30) (15,24) (15,29) (16,18) (16,20) (16,27) (17,18) (17,23) (18,26) (19,33) (19,25) (19,24) (20,21) (20,23) (21,26) (22,24) (23,26) (23,27) (24,28) (24,30) (25,29) (28,32) (28,30) (30,33)\nIs there a path between node 16 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph261-15_26", + "image": "data/connectivity/graph_visual/hard/graph261.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,23) (0,17) (1,9) (2,21) (2,30) (3,9) (3,7) (4,17) (4,20) (5,28) (5,26) (5,24) (6,21) (7,21) (7,9) (7,11) (8,16) (8,18) (9,21) (10,11) (12,28) (12,19) (12,26) (12,17) (12,13) (13,23) (13,24) (14,15) (14,29) (15,16) (16,18) (16,29) (17,23) (19,23) (19,24) (20,28) (20,23) (20,22)\nIs there a path between node 15 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph451-23_5", + "image": "data/connectivity/graph_visual/hard/graph451.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (2,30) (2,8) (2,22) (2,17) (2,12) (2,18) (3,27) (3,6) (3,20) (3,12) (4,16) (6,30) (6,8) (6,22) (6,26) (6,17) (6,12) (6,28) (7,13) (7,21) (8,9) (8,24) (8,18) (9,27) (9,20) (9,32) (9,24) (10,30) (10,17) (10,20) (10,12) (10,28) (11,23) (12,27) (12,30) (12,20) (12,24) (13,14) (13,29) (13,25) (14,31) (15,23) (17,32) (17,24) (17,18) (18,27) (18,26) (19,21) (20,30) (20,22) (20,26) (21,31) (21,29) (21,25) (22,24) (24,30) (24,32) (24,28) (25,31) (26,30) (27,28) (28,30) (30,32)\nIs there a path between node 23 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph220-2_1", + "image": "data/connectivity/graph_visual/hard/graph220.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,16) (0,5) (0,6) (0,8) (0,4) (0,18) (0,9) (1,14) (1,11) (1,29) (1,26) (1,19) (1,27) (1,13) (1,22) (1,21) (1,15) (2,25) (2,10) (2,12) (2,20) (2,17) (2,7) (3,25) (3,10) (3,24) (3,12) (3,20) (4,28) (4,16) (4,6) (4,8) (4,18) (5,28) (5,16) (5,6) (5,8) (5,18) (5,9) (6,28) (6,16) (6,8) (6,18) (6,9) (7,25) (7,24) (7,12) (7,20) (7,17) (8,28) (8,9) (9,16) (9,18) (10,25) (10,24) (10,12) (10,20) (11,14) (11,29) (11,26) (11,27) (11,13) (11,22) (11,21) (11,15) (12,25) (12,17) (13,14) (13,26) (13,19) (13,27) (13,23) (13,21) (13,15) (14,19) (14,22) (14,21) (14,15) (15,26) (15,27) (15,22) (16,18) (17,25) (17,20) (19,29) (19,26) (19,23) (19,21) (20,25) (20,24) (21,29) (21,26) (21,23) (22,26) (22,27) (22,23) (23,29) (23,27) (24,25) (26,29)\nIs there a path between node 2 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph41-9_22", + "image": "data/connectivity/graph_visual/hard/graph41.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,17) (0,2) (0,25) (0,14) (0,9) (0,15) (0,12) (0,1) (0,7) (0,16) (0,18) (0,11) (0,10) (0,5) (1,17) (1,2) (1,21) (1,14) (1,9) (1,15) (1,12) (1,19) (1,8) (1,7) (1,18) (1,11) (1,10) (1,5) (2,17) (2,21) (2,14) (2,9) (2,13) (2,3) (2,12) (2,6) (2,19) (2,7) (2,18) (2,11) (2,5) (3,17) (3,22) (3,21) (3,9) (3,15) (3,13) (3,6) (3,19) (3,8) (3,7) (3,16) (3,18) (3,11) (4,20) (4,23) (4,24) (5,17) (5,22) (5,21) (5,9) (5,15) (5,12) (5,19) (5,8) (5,16) (5,11) (5,10) (6,22) (6,25) (6,9) (6,15) (6,13) (6,12) (6,19) (6,8) (6,7) (6,16) (7,17) (7,22) (7,25) (7,9) (7,15) (7,13) (7,12) (7,19) (7,8) (7,16) (7,11) (7,10) (8,17) (8,22) (8,14) (8,12) (8,16) (8,18) (8,11) (9,17) (9,22) (9,25) (9,15) (9,13) (9,12) (9,19) (9,16) (9,18) (9,11) (10,17) (10,22) (10,25) (10,13) (10,19) (10,11) (11,17) (11,25) (11,14) (11,15) (11,13) (11,12) (11,19) (12,22) (12,21) (12,14) (12,19) (12,16) (13,22) (13,25) (13,21) (13,14) (13,16) (14,17) (14,21) (14,15) (14,19) (14,16) (14,18) (15,17) (15,25) (15,21) (15,16) (16,22) (16,25) (16,21) (16,19) (16,18) (17,22) (17,25) (17,21) (17,19) (17,18) (18,22) (18,21) (18,19) (19,22) (19,25) (19,21) (20,23) (20,24) (21,22) (21,25) (23,24)\nIs there a path between node 9 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph391-25_10", + "image": "data/connectivity/graph_visual/hard/graph391.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,9) (0,18) (0,31) (0,7) (0,30) (0,1) (0,21) (0,2) (1,13) (1,18) (1,12) (1,26) (1,24) (1,2) (2,14) (2,16) (2,22) (3,27) (4,27) (5,27) (6,7) (6,30) (6,24) (6,23) (7,13) (7,32) (7,23) (8,19) (8,12) (8,26) (8,21) (8,23) (8,16) (8,22) (9,18) (9,24) (9,23) (11,18) (11,12) (11,23) (11,16) (12,13) (12,14) (12,26) (12,24) (12,21) (12,16) (13,19) (13,18) (13,14) (13,24) (13,16) (14,19) (14,18) (14,30) (14,21) (14,16) (14,22) (16,31) (16,24) (16,23) (16,22) (18,26) (18,32) (21,26) (21,23) (21,22) (22,26) (22,24) (25,28) (31,32)\nIs there a path between node 25 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph452-3_14", + "image": "data/connectivity/graph_visual/hard/graph452.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,20) (0,27) (0,5) (0,16) (0,8) (0,30) (0,3) (0,31) (1,7) (1,4) (1,18) (2,17) (2,21) (2,23) (2,26) (2,30) (2,14) (2,11) (2,29) (2,31) (3,19) (3,20) (3,28) (3,16) (3,23) (3,10) (3,26) (3,32) (3,14) (3,6) (3,9) (5,19) (5,20) (5,23) (5,32) (5,29) (6,15) (6,13) (6,26) (6,22) (7,18) (8,15) (8,17) (8,10) (8,26) (8,30) (8,29) (8,31) (9,20) (9,13) (9,23) (9,14) (9,22) (10,15) (10,13) (10,21) (10,25) (10,26) (10,31) (11,15) (11,28) (11,16) (11,17) (11,25) (11,22) (12,24) (13,19) (13,15) (13,27) (13,28) (13,25) (13,26) (14,19) (14,27) (14,32) (14,29) (14,22) (15,27) (15,23) (15,26) (15,32) (16,23) (16,29) (16,22) (16,31) (17,27) (17,21) (19,27) (19,32) (19,31) (21,25) (21,32) (21,29) (21,22) (21,31) (22,23) (22,30) (23,27) (23,28) (25,32) (26,28) (26,29) (28,30) (28,29) (31,32)\nIs there a path between node 3 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph616-8_16", + "image": "data/connectivity/graph_visual/hard/graph616.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,33) (0,24) (0,27) (0,12) (0,16) (0,20) (0,5) (0,14) (0,17) (0,34) (0,29) (0,23) (0,22) (0,10) (0,28) (0,2) (0,15) (0,11) (0,8) (1,3) (1,6) (1,33) (1,27) (1,16) (1,20) (1,5) (1,26) (1,7) (1,19) (1,34) (1,29) (1,23) (1,22) (1,10) (1,28) (1,2) (1,9) (1,15) (1,11) (1,31) (1,8) (2,13) (2,33) (2,27) (2,12) (2,20) (2,7) (2,14) (2,19) (2,34) (2,29) (2,15) (2,11) (2,31) (3,6) (3,33) (3,12) (3,20) (3,5) (3,21) (3,7) (3,14) (3,17) (3,34) (3,29) (3,23) (3,22) (3,10) (3,28) (3,15) (3,11) (3,31) (3,8) (4,32) (4,30) (4,18) (5,13) (5,6) (5,33) (5,24) (5,12) (5,16) (5,20) (5,21) (5,26) (5,7) (5,14) (5,19) (5,17) (5,34) (5,29) (5,23) (5,22) (5,10) (5,28) (5,9) (5,15) (5,11) (6,13) (6,33) (6,27) (6,12) (6,20) (6,21) (6,26) (6,7) (6,14) (6,34) (6,23) (6,22) (6,10) (6,15) (6,31) (6,8) (7,13) (7,33) (7,24) (7,27) (7,16) (7,20) (7,21) (7,14) (7,19) (7,17) (7,29) (7,23) (7,10) (7,28) (7,9) (7,15) (7,11) (7,31) (7,8) (8,33) (8,24) (8,27) (8,26) (8,34) (8,29) (8,23) (8,10) (8,28) (8,9) (8,15) (8,11) (8,31) (9,13) (9,33) (9,24) (9,27) (9,16) (9,20) (9,21) (9,26) (9,14) (9,19) (9,17) (9,34) (9,22) (9,15) (9,11) (9,31) (10,13) (10,33) (10,24) (10,20) (10,14) (10,19) (10,17) (10,34) (10,29) (10,23) (10,28) (10,11) (10,31) (11,13) (11,33) (11,24) (11,27) (11,12) (11,16) (11,20) (11,21) (11,26) (11,19) (11,29) (11,22) (12,13) (12,24) (12,27) (12,16) (12,20) (12,21) (12,26) (12,14) (12,19) (12,34) (12,23) (12,22) (12,28) (12,15) (12,31) (13,24) (13,27) (13,16) (13,20) (13,21) (13,14) (13,19) (13,17) (13,34) (13,23) (13,22) (13,28) (13,15) (13,31) (14,24) (14,27) (14,16) (14,20) (14,26) (14,17) (14,34) (14,22) (14,28) (15,33) (15,24) (15,16) (15,26) (15,17) (15,34) (15,29) (15,22) (15,28) (15,31) (16,33) (16,24) (16,20) (16,21) (16,17) (16,34) (16,29) (16,31) (17,33) (17,24) (17,27) (17,20) (17,26) (17,19) (17,34) (17,29) (17,23) (17,22) (17,28) (17,31) (18,32) (18,25) (19,33) (19,24) (19,20) (19,21) (19,26) (19,29) (19,23) (19,31) (20,33) (20,24) (20,27) (20,21) (20,26) (20,34) (20,29) (20,23) (20,22) (20,28) (20,31) (21,33) (21,24) (21,27) (21,26) (21,23) (21,22) (21,28) (21,31) (22,33) (22,24) (22,27) (22,26) (22,34) (22,29) (22,23) (22,28) (22,31) (23,33) (23,27) (23,26) (23,34) (23,29) (23,28) (23,31) (24,33) (24,27) (24,34) (24,31) (25,32) (25,30) (26,33) (26,27) (26,34) (26,29) (26,28) (26,31) (27,33) (27,28) (27,31) (28,33) (28,34) (29,33) (29,34) (29,31) (30,32) (31,33) (31,34)\nIs there a path between node 8 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph255-4_2", + "image": "data/connectivity/graph_visual/hard/graph255.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,6) (0,2) (0,10) (0,29) (0,19) (0,5) (0,3) (1,30) (1,8) (1,28) (2,3) (3,6) (3,19) (4,14) (5,25) (6,19) (7,13) (7,30) (7,21) (7,8) (7,11) (8,13) (8,16) (8,30) (9,18) (12,19) (13,20) (13,28) (14,24) (14,18) (14,23) (15,30) (16,22) (16,28) (17,29) (17,19) (18,23) (19,25) (20,30) (20,28)\nIs there a path between node 4 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph589-6_29", + "image": "data/connectivity/graph_visual/hard/graph589.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,11) (0,16) (0,3) (0,26) (0,15) (0,30) (0,20) (0,27) (0,17) (0,18) (0,7) (0,1) (0,23) (0,24) (0,12) (1,8) (1,16) (1,25) (1,10) (1,5) (1,26) (1,15) (1,20) (1,27) (1,18) (1,13) (1,23) (1,2) (1,24) (1,31) (1,33) (1,12) (1,4) (1,6) (2,8) (2,11) (2,21) (2,25) (2,3) (2,10) (2,5) (2,26) (2,15) (2,27) (2,28) (2,14) (2,13) (2,31) (2,33) (2,4) (3,8) (3,9) (3,16) (3,25) (3,5) (3,26) (3,22) (3,30) (3,20) (3,17) (3,7) (3,28) (3,23) (3,24) (3,12) (3,4) (4,8) (4,11) (4,21) (4,25) (4,10) (4,15) (4,22) (4,20) (4,27) (4,18) (4,7) (4,28) (4,14) (4,23) (4,24) (4,31) (4,12) (5,8) (5,11) (5,9) (5,16) (5,21) (5,25) (5,10) (5,26) (5,15) (5,22) (5,30) (5,27) (5,18) (5,7) (5,28) (5,14) (5,13) (5,31) (6,8) (6,21) (6,25) (6,10) (6,26) (6,15) (6,22) (6,30) (6,20) (6,27) (6,28) (6,13) (6,31) (6,33) (7,11) (7,9) (7,16) (7,21) (7,25) (7,10) (7,26) (7,15) (7,22) (7,30) (7,20) (7,27) (7,28) (7,14) (7,13) (7,23) (7,24) (7,31) (7,12) (8,11) (8,9) (8,16) (8,21) (8,25) (8,10) (8,26) (8,30) (8,20) (8,17) (8,18) (8,28) (8,14) (8,23) (8,24) (8,31) (8,12) (9,11) (9,16) (9,21) (9,10) (9,26) (9,15) (9,22) (9,30) (9,27) (9,17) (9,18) (9,28) (9,14) (9,13) (9,24) (9,31) (10,26) (10,30) (10,27) (10,17) (10,18) (10,28) (10,14) (10,13) (10,31) (10,33) (10,12) (11,16) (11,21) (11,25) (11,26) (11,15) (11,22) (11,30) (11,20) (11,27) (11,17) (11,18) (11,28) (11,14) (11,13) (11,24) (11,31) (11,33) (11,12) (12,21) (12,25) (12,26) (12,22) (12,20) (12,17) (12,18) (12,28) (12,14) (12,13) (12,23) (12,31) (12,33) (13,25) (13,26) (13,15) (13,30) (13,20) (13,17) (13,18) (13,14) (13,23) (13,24) (13,31) (13,33) (14,16) (14,21) (14,25) (14,26) (14,22) (14,20) (14,17) (14,18) (14,28) (14,23) (14,31) (14,33) (15,16) (15,22) (15,30) (15,18) (15,28) (15,23) (15,24) (15,31) (15,33) (16,21) (16,25) (16,22) (16,20) (16,27) (16,17) (16,18) (16,28) (16,23) (16,33) (17,25) (17,22) (17,30) (17,20) (17,27) (17,18) (17,28) (17,23) (17,24) (17,33) (18,25) (18,22) (18,30) (18,20) (18,27) (18,23) (18,24) (18,33) (19,29) (19,32) (20,26) (20,22) (20,30) (20,27) (20,28) (20,23) (20,24) (20,31) (20,33) (21,25) (21,26) (21,30) (21,27) (21,28) (21,23) (21,33) (22,26) (22,30) (22,23) (22,33) (23,25) (23,26) (23,27) (23,28) (23,24) (23,31) (23,33) (24,25) (24,26) (24,28) (24,31) (25,26) (25,30) (25,27) (25,28) (25,33) (26,30) (26,27) (26,28) (26,31) (27,30) (27,28) (27,33) (28,31) (28,33) (29,32) (30,33) (31,33)\nIs there a path between node 6 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph638-2_22", + "image": "data/connectivity/graph_visual/hard/graph638.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,1) (0,19) (0,15) (0,20) (0,9) (0,21) (0,3) (0,22) (0,32) (0,24) (0,14) (0,11) (0,17) (0,5) (0,34) (0,4) (0,26) (0,10) (0,8) (1,27) (1,23) (1,30) (1,6) (1,19) (1,20) (1,2) (1,9) (1,21) (1,3) (1,22) (1,24) (1,14) (1,11) (1,17) (1,5) (1,4) (1,26) (1,8) (2,27) (2,30) (2,6) (2,19) (2,20) (2,9) (2,21) (2,3) (2,22) (2,32) (2,7) (2,11) (2,17) (2,5) (2,34) (2,4) (2,26) (2,12) (2,10) (3,27) (3,23) (3,30) (3,6) (3,19) (3,15) (3,20) (3,9) (3,22) (3,24) (3,14) (3,34) (3,4) (3,12) (3,10) (3,8) (3,28) (4,27) (4,23) (4,30) (4,19) (4,15) (4,20) (4,9) (4,21) (4,32) (4,24) (4,14) (4,7) (4,11) (4,17) (4,5) (4,26) (4,12) (4,8) (4,28) (5,30) (5,19) (5,9) (5,21) (5,24) (5,7) (5,11) (5,17) (5,34) (5,12) (6,27) (6,23) (6,30) (6,19) (6,20) (6,9) (6,21) (6,22) (6,32) (6,24) (6,14) (6,7) (6,11) (6,17) (6,34) (6,26) (6,8) (6,28) (7,23) (7,30) (7,19) (7,15) (7,20) (7,21) (7,32) (7,24) (7,11) (7,17) (7,34) (7,12) (7,10) (7,8) (7,28) (8,23) (8,15) (8,20) (8,24) (8,14) (8,11) (8,17) (8,34) (8,26) (8,12) (8,10) (8,28) (9,30) (9,19) (9,15) (9,20) (9,22) (9,32) (9,24) (9,11) (9,34) (9,12) (9,10) (9,28) (10,27) (10,23) (10,30) (10,19) (10,21) (10,32) (10,24) (10,26) (10,12) (11,27) (11,30) (11,19) (11,20) (11,21) (11,22) (11,32) (11,24) (11,14) (11,17) (11,34) (11,12) (12,27) (12,30) (12,19) (12,20) (12,22) (12,32) (12,24) (12,14) (12,17) (12,34) (12,28) (14,27) (14,23) (14,30) (14,19) (14,15) (14,21) (14,22) (14,32) (14,17) (14,34) (14,28) (15,19) (15,20) (15,21) (15,22) (15,32) (15,24) (15,34) (15,26) (15,28) (16,33) (16,29) (16,18) (16,31) (17,27) (17,23) (17,30) (17,19) (17,20) (17,21) (17,22) (17,32) (17,24) (17,34) (17,28) (18,33) (18,31) (18,25) (19,27) (19,23) (19,30) (19,20) (19,22) (19,32) (19,34) (19,26) (19,28) (20,23) (20,30) (20,21) (20,22) (20,32) (20,24) (20,34) (20,26) (21,27) (21,23) (21,30) (21,22) (21,32) (21,24) (21,34) (21,26) (21,28) (22,27) (22,23) (22,24) (22,34) (22,26) (22,28) (23,32) (23,26) (23,28) (24,27) (24,32) (24,34) (24,26) (25,33) (26,30) (26,32) (26,34) (27,30) (27,32) (27,28) (28,30) (28,32) (28,34) (29,33) (29,31) (31,33) (32,34)\nIs there a path between node 2 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph615-10_15", + "image": "data/connectivity/graph_visual/hard/graph615.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,29) (0,8) (0,16) (0,1) (0,28) (0,4) (0,33) (0,21) (0,3) (0,18) (0,17) (0,23) (0,14) (0,27) (0,25) (0,30) (0,11) (0,19) (0,7) (0,26) (0,5) (0,12) (1,8) (1,28) (1,33) (1,3) (1,18) (1,17) (1,23) (1,27) (1,25) (1,30) (1,15) (1,32) (1,19) (1,9) (1,5) (1,20) (1,2) (1,12) (1,34) (2,29) (2,24) (2,8) (2,16) (2,4) (2,33) (2,3) (2,18) (2,17) (2,23) (2,27) (2,25) (2,11) (2,15) (2,32) (2,19) (2,9) (2,26) (2,5) (2,12) (2,34) (3,29) (3,24) (3,8) (3,16) (3,28) (3,4) (3,33) (3,18) (3,17) (3,27) (3,30) (3,11) (3,6) (3,32) (3,9) (3,7) (3,12) (4,29) (4,24) (4,16) (4,33) (4,21) (4,18) (4,17) (4,14) (4,27) (4,25) (4,30) (4,11) (4,15) (4,32) (4,31) (4,19) (4,9) (4,7) (4,26) (4,5) (4,12) (5,29) (5,24) (5,8) (5,16) (5,28) (5,33) (5,18) (5,23) (5,14) (5,27) (5,25) (5,30) (5,15) (5,6) (5,31) (5,19) (5,9) (5,7) (5,26) (5,20) (5,12) (6,24) (6,8) (6,16) (6,28) (6,21) (6,17) (6,14) (6,27) (6,11) (6,15) (6,32) (6,19) (6,9) (6,7) (6,26) (6,20) (6,34) (7,24) (7,8) (7,33) (7,21) (7,18) (7,23) (7,14) (7,25) (7,30) (7,11) (7,15) (7,31) (7,9) (7,26) (7,20) (7,12) (7,34) (8,29) (8,24) (8,16) (8,17) (8,23) (8,14) (8,25) (8,30) (8,32) (8,31) (8,9) (8,20) (8,12) (9,29) (9,24) (9,16) (9,28) (9,21) (9,18) (9,17) (9,23) (9,27) (9,25) (9,15) (9,32) (9,31) (9,19) (9,26) (9,20) (9,12) (9,34) (10,13) (11,29) (11,24) (11,28) (11,33) (11,21) (11,18) (11,23) (11,14) (11,27) (11,25) (11,30) (11,32) (11,31) (11,26) (11,12) (11,34) (12,24) (12,16) (12,28) (12,33) (12,21) (12,18) (12,14) (12,27) (12,25) (12,15) (12,32) (12,26) (12,20) (12,34) (14,29) (14,24) (14,16) (14,28) (14,33) (14,21) (14,17) (14,23) (14,27) (14,25) (14,15) (14,31) (14,26) (14,20) (14,34) (15,29) (15,24) (15,28) (15,18) (15,17) (15,23) (15,27) (15,25) (15,30) (15,31) (15,19) (15,26) (15,34) (16,29) (16,24) (16,28) (16,33) (16,17) (16,27) (16,30) (16,31) (16,26) (16,20) (16,34) (17,24) (17,28) (17,33) (17,18) (17,23) (17,27) (17,30) (17,31) (17,19) (17,20) (17,34) (18,29) (18,28) (18,33) (18,21) (18,23) (18,27) (18,25) (18,30) (18,32) (18,31) (18,19) (18,34) (19,33) (19,21) (19,23) (19,27) (19,25) (19,31) (19,26) (19,20) (19,34) (20,21) (20,23) (20,27) (20,25) (20,30) (20,32) (20,26) (20,34) (21,29) (21,24) (21,33) (21,23) (21,31) (23,24) (23,28) (23,27) (23,25) (23,30) (23,32) (23,31) (23,26) (23,34) (24,29) (24,30) (24,32) (24,31) (24,26) (24,34) (25,29) (25,28) (25,33) (25,27) (25,31) (25,34) (26,28) (26,27) (26,32) (26,31) (26,34) (27,29) (27,33) (27,30) (27,32) (27,31) (28,29) (28,33) (28,30) (28,32) (28,31) (28,34) (29,33) (29,30) (29,32) (29,31) (29,34) (30,33) (30,32) (30,31) (30,34) (31,33) (31,34) (32,33) (32,34) (33,34)\nIs there a path between node 10 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph274-6_7", + "image": "data/connectivity/graph_visual/hard/graph274.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,27) (0,3) (0,14) (0,23) (0,10) (0,25) (1,22) (1,28) (1,8) (1,30) (1,2) (1,4) (1,21) (1,29) (1,9) (2,22) (2,28) (2,8) (2,30) (2,4) (2,9) (3,27) (3,6) (3,14) (3,15) (3,7) (3,5) (3,20) (3,10) (3,25) (4,28) (4,30) (4,21) (4,29) (4,9) (4,13) (5,27) (5,6) (5,15) (5,7) (5,23) (5,20) (5,10) (6,27) (6,14) (6,15) (6,23) (6,20) (6,10) (7,27) (7,14) (7,15) (7,10) (7,25) (8,22) (8,30) (8,21) (8,9) (9,22) (9,28) (9,30) (9,29) (9,13) (10,27) (10,23) (10,20) (10,25) (11,24) (11,19) (11,26) (11,18) (11,12) (11,17) (11,16) (12,19) (12,26) (12,18) (12,17) (12,16) (13,22) (13,28) (13,30) (13,21) (13,29) (14,27) (14,15) (14,23) (14,25) (15,27) (15,23) (15,20) (16,24) (16,26) (16,17) (17,24) (17,19) (17,26) (17,18) (18,26) (19,24) (20,27) (20,23) (20,25) (21,22) (21,28) (22,28) (22,30) (22,29) (23,27) (24,26) (25,27) (28,30) (28,29)\nIs there a path between node 6 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph382-5_27", + "image": "data/connectivity/graph_visual/hard/graph382.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,16) (0,4) (0,22) (0,1) (0,23) (0,11) (0,21) (0,2) (0,13) (0,31) (0,19) (0,27) (0,17) (0,14) (0,3) (0,6) (0,12) (1,15) (1,9) (1,16) (1,4) (1,22) (1,23) (1,11) (1,21) (1,30) (1,13) (1,31) (1,19) (1,27) (1,17) (1,14) (1,12) (1,10) (2,9) (2,4) (2,23) (2,21) (2,30) (2,13) (2,31) (2,26) (2,19) (2,14) (2,3) (2,18) (3,15) (3,9) (3,16) (3,4) (3,22) (3,23) (3,11) (3,13) (3,31) (3,19) (3,17) (3,6) (4,15) (4,9) (4,16) (4,11) (4,21) (4,30) (4,13) (4,19) (4,27) (4,17) (4,14) (4,18) (4,12) (5,24) (5,20) (5,29) (5,8) (5,28) (6,15) (6,16) (6,22) (6,23) (6,21) (6,27) (6,14) (6,12) (6,10) (7,25) (8,24) (8,20) (8,28) (9,15) (9,16) (9,23) (9,30) (9,31) (9,26) (9,17) (9,14) (9,12) (9,10) (10,15) (10,16) (10,22) (10,11) (10,21) (10,30) (10,13) (10,31) (10,26) (10,19) (10,27) (10,18) (10,12) (11,16) (11,22) (11,23) (11,21) (11,30) (11,13) (11,31) (11,19) (11,17) (12,16) (12,22) (12,23) (12,30) (12,13) (12,31) (12,26) (12,19) (12,27) (12,17) (12,14) (13,15) (13,16) (13,22) (13,23) (13,30) (13,26) (13,19) (13,27) (13,17) (13,14) (14,16) (14,23) (14,21) (14,30) (14,31) (14,26) (14,19) (14,27) (14,17) (14,18) (15,16) (15,22) (15,23) (15,21) (15,26) (15,19) (15,17) (15,18) (16,22) (16,23) (16,30) (16,31) (16,26) (16,19) (16,27) (16,17) (16,18) (17,23) (17,21) (17,30) (17,31) (17,26) (17,19) (18,22) (18,23) (18,30) (18,26) (18,27) (19,22) (19,23) (19,21) (19,30) (19,26) (20,24) (20,29) (20,28) (21,22) (21,30) (21,27) (22,23) (22,31) (22,27) (23,30) (23,31) (23,26) (23,27) (24,28) (26,30) (26,31) (27,30) (27,31) (28,29) (30,31)\nIs there a path between node 5 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph102-14_9", + "image": "data/connectivity/graph_visual/hard/graph102.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,14) (0,27) (0,17) (0,9) (0,10) (0,2) (0,4) (0,20) (1,22) (1,13) (1,7) (1,21) (1,12) (1,19) (1,6) (1,26) (1,5) (1,16) (1,8) (2,14) (2,24) (2,17) (2,9) (2,15) (2,10) (2,18) (3,14) (3,24) (3,15) (3,10) (3,18) (4,14) (4,27) (4,9) (4,15) (4,10) (4,18) (4,20) (5,13) (5,7) (5,23) (5,25) (5,12) (5,19) (5,6) (5,26) (5,11) (5,16) (6,22) (6,13) (6,7) (6,23) (6,21) (6,12) (6,19) (6,11) (6,16) (6,8) (7,22) (7,13) (7,23) (7,12) (7,19) (7,26) (7,11) (7,16) (7,8) (8,22) (8,13) (8,23) (8,25) (8,21) (8,19) (8,16) (9,14) (9,24) (9,17) (9,10) (9,20) (10,14) (10,24) (10,17) (10,18) (11,22) (11,13) (11,12) (11,19) (11,26) (11,16) (12,22) (12,13) (12,21) (12,19) (12,26) (12,16) (13,22) (13,23) (13,19) (14,24) (14,17) (14,15) (14,18) (14,20) (15,27) (15,17) (15,18) (16,22) (16,23) (16,25) (16,21) (16,26) (17,27) (17,18) (17,20) (18,27) (18,20) (19,22) (19,23) (19,25) (19,21) (20,24) (20,27) (21,22) (21,23) (21,25) (21,26) (22,25) (22,26) (23,26) (24,27) (25,26)\nIs there a path between node 14 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph203-4_2", + "image": "data/connectivity/graph_visual/hard/graph203.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,5) (0,11) (0,13) (3,4) (3,21) (5,14) (5,27) (5,6) (5,19) (5,29) (5,25) (5,16) (5,13) (6,8) (6,9) (6,20) (6,29) (6,16) (6,11) (7,8) (7,26) (7,20) (7,12) (8,9) (8,19) (8,20) (8,28) (8,10) (8,22) (9,19) (9,20) (9,25) (9,11) (9,12) (9,22) (10,20) (10,25) (10,24) (10,15) (10,22) (11,26) (11,20) (11,28) (11,16) (11,24) (11,15) (12,25) (12,16) (12,23) (12,22) (13,18) (14,26) (14,24) (15,26) (15,20) (15,28) (16,27) (16,18) (16,26) (16,25) (16,23) (16,22) (18,27) (18,19) (18,20) (18,28) (18,25) (19,26) (19,20) (20,29) (20,25) (20,22) (22,24) (23,27) (23,29) (24,26) (24,28) (24,29) (25,27) (25,26)\nIs there a path between node 4 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph126-17_18", + "image": "data/connectivity/graph_visual/hard/graph126.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,4) (0,12) (0,27) (0,10) (0,21) (0,22) (0,8) (0,15) (0,19) (0,20) (0,23) (0,25) (0,14) (0,5) (0,18) (1,2) (1,17) (1,3) (2,24) (2,26) (2,3) (3,17) (3,26) (3,16) (4,12) (4,10) (4,7) (4,9) (4,22) (4,8) (4,19) (4,11) (4,14) (4,13) (4,5) (4,18) (5,12) (5,10) (5,21) (5,7) (5,9) (5,22) (5,8) (5,15) (5,19) (5,11) (5,14) (5,18) (6,12) (6,10) (6,21) (6,9) (6,22) (6,8) (6,15) (6,19) (6,20) (6,25) (6,11) (6,13) (6,18) (7,12) (7,21) (7,9) (7,22) (7,8) (7,15) (7,19) (7,20) (7,25) (7,11) (7,14) (7,13) (7,18) (8,10) (8,21) (8,9) (8,22) (8,15) (8,23) (8,25) (8,11) (8,14) (8,13) (8,18) (9,12) (9,10) (9,22) (9,19) (9,20) (9,23) (9,11) (9,14) (10,12) (10,27) (10,19) (10,23) (10,11) (10,14) (10,13) (10,18) (11,27) (11,21) (11,22) (11,20) (11,18) (12,27) (12,22) (12,15) (12,20) (12,13) (12,18) (13,21) (13,22) (13,15) (13,19) (13,20) (13,23) (13,25) (13,18) (14,22) (14,15) (14,19) (14,20) (14,23) (14,25) (14,18) (15,22) (15,19) (15,20) (15,25) (15,18) (16,24) (16,17) (16,26) (17,24) (17,26) (18,21) (18,22) (18,20) (18,23) (19,27) (19,21) (19,22) (19,23) (19,25) (20,21) (20,22) (20,23) (20,25) (21,27) (21,22) (21,23) (22,27) (22,23) (24,26)\nIs there a path between node 17 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph523-19_29", + "image": "data/connectivity/graph_visual/hard/graph523.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,30) (0,1) (0,22) (0,18) (0,3) (1,7) (1,22) (1,14) (1,20) (1,32) (1,17) (1,23) (1,12) (2,7) (2,11) (2,16) (2,31) (2,14) (2,20) (2,17) (3,7) (3,11) (3,33) (3,30) (3,22) (3,9) (3,14) (3,5) (3,6) (3,24) (3,12) (4,30) (4,31) (4,29) (4,5) (4,25) (4,24) (4,28) (4,23) (5,27) (5,7) (5,22) (5,16) (5,20) (5,26) (5,13) (5,23) (6,11) (6,30) (6,16) (6,14) (6,20) (6,25) (7,11) (7,30) (7,29) (7,20) (7,32) (7,28) (8,19) (9,27) (9,29) (9,14) (9,32) (9,28) (9,23) (9,12) (10,19) (11,33) (11,21) (11,16) (11,31) (11,18) (11,26) (11,25) (12,22) (12,18) (12,14) (12,17) (12,25) (12,24) (13,21) (13,22) (13,16) (13,32) (13,17) (13,25) (13,24) (14,33) (14,15) (14,16) (14,28) (15,22) (15,18) (15,26) (15,17) (15,25) (16,21) (16,29) (16,20) (16,32) (16,17) (17,31) (17,25) (17,28) (18,21) (18,25) (18,23) (20,33) (20,22) (20,32) (21,27) (21,30) (22,23) (23,33) (23,29) (23,26) (24,33) (24,30) (24,31) (24,32) (24,28) (25,31) (25,29) (25,26) (26,29) (26,28) (27,29) (27,28) (29,32) (31,32) (32,33)\nIs there a path between node 19 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph55-5_1", + "image": "data/connectivity/graph_visual/hard/graph55.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,11) (0,1) (0,5) (0,24) (0,12) (0,4) (0,2) (0,14) (0,7) (0,25) (0,17) (0,9) (0,20) (1,11) (1,18) (1,5) (1,8) (1,6) (1,24) (1,12) (1,3) (1,4) (1,2) (1,14) (1,7) (1,17) (1,16) (1,9) (2,11) (2,18) (2,8) (2,3) (2,14) (2,7) (2,25) (2,17) (2,9) (2,20) (2,26) (3,11) (3,18) (3,5) (3,8) (3,6) (3,24) (3,12) (3,4) (3,7) (3,25) (3,17) (3,16) (3,9) (3,20) (3,26) (4,11) (4,18) (4,5) (4,8) (4,6) (4,24) (4,12) (4,14) (4,17) (4,23) (4,9) (4,20) (4,22) (4,26) (5,11) (5,18) (5,8) (5,6) (5,24) (5,12) (5,25) (5,23) (5,9) (5,20) (5,22) (5,26) (6,18) (6,8) (6,24) (6,14) (6,7) (6,17) (6,23) (6,9) (6,22) (6,26) (7,11) (7,18) (7,8) (7,24) (7,25) (7,23) (7,16) (7,9) (7,20) (7,22) (7,26) (8,24) (8,14) (8,25) (8,23) (8,16) (8,9) (8,20) (8,22) (8,26) (9,11) (9,18) (9,12) (9,14) (9,25) (9,17) (9,23) (9,20) (9,22) (10,13) (10,15) (10,21) (11,24) (11,12) (11,14) (11,25) (11,23) (11,16) (11,22) (11,26) (12,24) (12,25) (12,23) (12,16) (12,20) (12,22) (12,26) (13,19) (13,15) (13,21) (14,18) (14,24) (14,25) (14,23) (14,22) (14,26) (15,19) (15,21) (16,18) (16,24) (16,17) (16,23) (16,20) (17,18) (17,24) (17,23) (17,20) (17,22) (17,26) (18,23) (18,26) (20,25) (20,23) (20,26) (22,24) (22,25) (22,23) (23,25) (23,26) (24,25) (24,26)\nIs there a path between node 5 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph265-22_17", + "image": "data/connectivity/graph_visual/hard/graph265.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,25) (0,9) (0,15) (0,27) (0,29) (1,25) (1,28) (1,23) (1,15) (1,18) (1,8) (1,13) (1,4) (1,29) (1,26) (2,20) (3,6) (3,28) (3,23) (3,14) (3,8) (3,12) (3,17) (4,5) (4,9) (4,12) (4,26) (5,16) (5,14) (5,12) (6,23) (6,21) (7,23) (7,16) (7,8) (7,12) (8,23) (8,14) (8,27) (8,19) (8,12) (8,17) (9,25) (9,28) (9,22) (9,15) (9,16) (9,14) (9,19) (9,12) (9,26) (11,24) (12,22) (12,15) (12,18) (12,14) (12,19) (12,13) (12,21) (12,26) (13,22) (13,27) (14,16) (15,22) (15,27) (15,17) (15,21) (15,26) (16,25) (16,28) (16,27) (16,19) (17,25) (17,27) (17,26) (18,25) (18,28) (18,21) (18,26) (19,22) (19,29) (20,24) (20,30) (21,26) (23,27) (25,27) (25,29)\nIs there a path between node 22 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph513-5_30", + "image": "data/connectivity/graph_visual/hard/graph513.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,17) (0,8) (0,6) (0,1) (0,22) (0,25) (0,11) (0,2) (1,10) (1,8) (1,22) (1,25) (1,11) (1,32) (1,29) (1,7) (1,3) (2,10) (2,18) (2,25) (2,30) (2,11) (2,15) (2,28) (2,7) (3,33) (3,8) (3,20) (3,30) (3,15) (3,19) (4,14) (4,12) (4,13) (5,33) (5,17) (5,21) (5,18) (5,22) (5,28) (5,7) (6,20) (6,30) (6,32) (6,27) (7,33) (7,21) (7,18) (7,22) (7,30) (7,15) (7,27) (7,28) (7,29) (8,21) (8,25) (8,20) (8,11) (8,27) (10,17) (10,20) (10,32) (10,27) (11,22) (11,25) (11,15) (11,27) (12,31) (12,16) (12,23) (13,16) (13,23) (14,31) (14,26) (15,25) (15,20) (15,27) (17,22) (17,20) (17,32) (17,29) (18,32) (19,25) (19,30) (19,32) (19,27) (20,33) (20,25) (20,30) (20,32) (20,27) (21,22) (21,29) (22,28) (23,31) (23,24) (24,31) (25,29) (26,31) (28,33) (29,30) (32,33)\nIs there a path between node 5 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph251-15_14", + "image": "data/connectivity/graph_visual/hard/graph251.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,17) (1,8) (1,29) (1,10) (1,7) (1,11) (1,25) (1,18) (1,14) (1,30) (1,16) (1,5) (1,26) (1,4) (1,23) (1,27) (2,21) (3,21) (4,17) (4,29) (4,9) (4,10) (4,6) (4,7) (4,11) (4,14) (4,22) (4,26) (4,13) (4,24) (4,23) (4,19) (5,17) (5,29) (5,9) (5,10) (5,6) (5,7) (5,11) (5,18) (5,14) (5,30) (5,16) (5,26) (5,15) (5,13) (5,24) (5,19) (5,27) (6,17) (6,9) (6,10) (6,11) (6,18) (6,14) (6,30) (6,16) (6,22) (6,15) (6,24) (6,19) (6,27) (7,17) (7,8) (7,29) (7,9) (7,10) (7,25) (7,18) (7,30) (7,16) (7,22) (7,24) (7,23) (7,19) (7,27) (8,17) (8,11) (8,25) (8,18) (8,14) (8,30) (8,16) (8,15) (8,13) (8,24) (8,19) (8,27) (9,17) (9,29) (9,10) (9,11) (9,25) (9,14) (9,30) (9,16) (9,22) (9,15) (9,13) (9,24) (9,19) (9,27) (10,17) (10,11) (10,25) (10,18) (10,14) (10,30) (10,16) (10,22) (10,15) (10,13) (10,24) (10,23) (10,27) (11,29) (11,25) (11,14) (11,30) (11,16) (11,26) (11,15) (11,13) (11,24) (11,23) (11,19) (11,27) (12,28) (13,29) (13,18) (13,14) (13,30) (13,16) (13,22) (13,26) (13,15) (13,24) (13,19) (13,27) (14,17) (14,25) (14,18) (14,30) (14,16) (14,22) (14,26) (14,15) (14,19) (14,27) (15,17) (15,25) (15,18) (15,30) (15,16) (15,22) (15,26) (15,24) (15,23) (15,19) (15,27) (16,29) (16,25) (16,30) (16,23) (16,27) (17,29) (17,25) (17,18) (17,30) (17,26) (17,19) (17,27) (18,22) (18,26) (18,24) (18,23) (18,19) (19,29) (19,25) (19,22) (19,26) (19,24) (19,23) (19,27) (22,29) (22,25) (22,26) (22,24) (22,23) (22,27) (23,25) (23,30) (23,24) (24,29) (24,25) (24,26) (24,27) (25,29) (25,30) (25,26) (25,27) (26,29) (26,30) (29,30)\nIs there a path between node 15 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph385-15_21", + "image": "data/connectivity/graph_visual/hard/graph385.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,25) (0,9) (0,21) (0,29) (0,20) (0,22) (0,10) (0,15) (0,17) (0,23) (0,5) (0,31) (1,4) (1,26) (1,18) (1,6) (1,19) (1,24) (1,27) (1,30) (1,28) (1,13) (1,11) (2,12) (2,4) (2,18) (2,6) (2,24) (2,27) (2,28) (2,13) (2,11) (3,25) (3,21) (3,29) (3,20) (3,22) (3,10) (3,14) (3,8) (3,17) (3,23) (3,7) (4,12) (4,26) (4,18) (4,6) (4,19) (4,30) (4,28) (4,13) (4,11) (5,25) (5,9) (5,21) (5,29) (5,16) (5,20) (5,22) (5,8) (5,15) (5,17) (5,7) (5,31) (6,26) (6,18) (6,19) (6,24) (6,27) (6,28) (6,13) (6,11) (7,25) (7,9) (7,21) (7,29) (7,16) (7,20) (7,22) (7,14) (7,8) (7,15) (7,23) (8,9) (8,21) (8,29) (8,16) (8,22) (8,10) (8,15) (8,17) (8,23) (8,31) (9,25) (9,21) (9,16) (9,20) (9,10) (9,14) (9,17) (9,23) (9,31) (10,21) (10,29) (10,16) (10,20) (10,22) (10,15) (10,23) (11,26) (11,24) (11,27) (11,30) (11,28) (11,13) (12,26) (12,18) (12,24) (12,28) (13,26) (13,18) (13,19) (13,24) (13,27) (13,28) (14,21) (14,29) (14,20) (14,15) (14,23) (14,31) (15,25) (15,21) (15,16) (15,20) (15,22) (15,23) (15,31) (16,21) (16,29) (16,22) (16,17) (16,23) (16,31) (17,21) (17,29) (17,20) (17,22) (17,23) (18,26) (18,19) (18,24) (18,30) (19,26) (19,24) (19,27) (20,21) (20,29) (21,25) (21,22) (21,23) (22,29) (22,23) (22,31) (23,25) (23,31) (24,26) (24,30) (24,28) (25,31) (26,27) (26,30) (26,28) (27,30) (28,30) (29,31)\nIs there a path between node 15 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph346-9_17", + "image": "data/connectivity/graph_visual/hard/graph346.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,29) (0,31) (0,26) (0,27) (0,19) (1,28) (2,30) (4,6) (5,29) (5,31) (6,17) (6,30) (7,24) (7,29) (7,31) (8,21) (8,28) (10,11) (10,15) (12,28) (14,15) (14,20) (15,20) (18,29) (18,26) (20,23) (21,28) (24,26) (24,27)\nIs there a path between node 9 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph25-1_20", + "image": "data/connectivity/graph_visual/hard/graph25.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,7) (0,25) (0,15) (0,16) (0,20) (0,4) (1,7) (1,11) (1,20) (2,23) (2,6) (2,5) (3,25) (3,15) (3,14) (3,19) (3,12) (3,4) (4,17) (4,15) (4,11) (4,22) (4,12) (5,6) (6,13) (7,24) (7,14) (7,19) (7,22) (8,18) (8,13) (8,9) (9,23) (9,10) (11,25) (11,15) (11,16) (11,12) (12,24) (12,25) (12,14) (12,20) (12,22) (13,23) (13,18) (14,22) (15,17) (16,24) (16,25) (16,17) (16,20) (17,24) (20,25) (22,25) (24,25)\nIs there a path between node 1 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph599-26_0", + "image": "data/connectivity/graph_visual/hard/graph599.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,25) (0,32) (0,24) (0,10) (0,1) (0,28) (0,17) (0,3) (0,16) (0,7) (0,29) (0,5) (1,6) (1,25) (1,32) (1,24) (1,13) (1,10) (1,11) (1,28) (1,16) (1,7) (1,29) (2,14) (2,15) (2,8) (2,33) (3,18) (3,25) (3,24) (3,13) (3,10) (3,11) (3,28) (3,17) (3,16) (3,7) (3,29) (4,12) (4,27) (4,21) (5,18) (5,6) (5,25) (5,24) (5,13) (5,10) (5,11) (5,17) (5,29) (6,18) (6,25) (6,24) (6,13) (6,10) (6,11) (6,28) (7,18) (7,25) (7,32) (7,24) (7,13) (7,10) (7,28) (7,17) (7,29) (8,19) (8,33) (8,30) (9,22) (9,31) (10,25) (10,32) (10,24) (10,13) (10,28) (10,16) (10,29) (11,25) (11,32) (11,24) (11,13) (11,28) (11,17) (11,29) (12,26) (13,18) (13,25) (13,32) (13,28) (13,16) (14,19) (14,20) (14,15) (14,33) (15,19) (15,20) (15,33) (15,30) (16,32) (16,24) (16,28) (16,17) (16,29) (17,32) (17,24) (17,28) (17,29) (18,32) (18,24) (18,29) (19,20) (19,33) (19,30) (20,33) (20,30) (21,26) (22,31) (22,23) (23,31) (24,25) (24,32) (24,28) (24,29) (25,28) (26,27) (28,32) (28,29) (30,33)\nIs there a path between node 26 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph210-24_29", + "image": "data/connectivity/graph_visual/hard/graph210.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,28) (0,26) (0,21) (0,16) (0,2) (0,7) (0,22) (1,28) (1,27) (1,24) (1,10) (1,26) (1,12) (1,14) (1,19) (1,20) (2,24) (2,26) (2,16) (2,22) (2,4) (3,25) (4,5) (4,8) (4,10) (4,14) (4,22) (5,28) (5,8) (5,24) (5,12) (5,7) (5,23) (6,13) (6,26) (6,21) (6,19) (7,28) (7,26) (7,19) (7,22) (7,23) (7,20) (8,27) (8,24) (8,10) (8,26) (8,22) (10,18) (10,12) (11,13) (11,26) (11,22) (11,23) (11,20) (12,13) (12,24) (12,21) (12,29) (13,28) (13,18) (14,24) (14,26) (14,20) (16,28) (16,24) (16,21) (17,27) (17,20) (18,27) (18,19) (20,21) (20,22) (21,29) (24,28) (27,28)\nIs there a path between node 24 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph676-6_2", + "image": "data/connectivity/graph_visual/hard/graph676.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,10) (0,26) (0,32) (0,20) (0,28) (0,15) (0,17) (0,3) (0,12) (0,9) (1,10) (1,24) (1,26) (1,34) (1,18) (1,25) (1,15) (1,27) (1,21) (1,29) (1,12) (1,9) (2,13) (2,4) (2,17) (3,10) (3,11) (3,33) (3,18) (3,4) (3,27) (3,17) (3,30) (4,18) (4,25) (4,27) (4,29) (4,7) (5,16) (7,11) (7,33) (7,34) (7,18) (7,13) (7,19) (7,28) (7,27) (7,31) (7,12) (7,9) (9,26) (9,32) (9,20) (9,13) (9,14) (9,12) (10,26) (10,34) (10,14) (10,31) (10,30) (11,24) (11,34) (11,18) (11,14) (11,15) (11,27) (12,33) (12,20) (12,28) (12,27) (13,33) (13,18) (13,32) (13,15) (13,22) (13,17) (13,31) (14,33) (14,26) (14,19) (15,33) (15,18) (15,28) (15,25) (15,23) (17,18) (17,32) (17,29) (18,33) (18,24) (18,34) (18,20) (18,25) (18,27) (18,30) (19,28) (19,25) (19,22) (19,21) (20,33) (20,26) (20,32) (20,22) (21,33) (21,24) (21,34) (21,28) (21,25) (21,27) (22,33) (22,26) (22,29) (23,33) (23,34) (23,28) (23,31) (23,29) (24,32) (24,31) (24,30) (25,33) (25,32) (25,27) (26,32) (27,31) (28,33) (30,34) (31,34) (32,33) (33,34)\nIs there a path between node 6 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph460-3_26", + "image": "data/connectivity/graph_visual/hard/graph460.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (0,16) (0,12) (0,2) (0,27) (0,30) (0,19) (0,28) (0,21) (0,13) (0,18) (1,5) (1,7) (1,4) (1,30) (1,24) (1,3) (2,5) (2,6) (2,22) (2,29) (2,19) (2,24) (2,21) (2,3) (3,31) (3,5) (3,16) (3,6) (3,12) (3,22) (3,29) (3,28) (3,24) (3,21) (3,18) (4,31) (4,16) (4,7) (4,23) (5,17) (5,22) (5,13) (6,32) (6,25) (6,19) (6,23) (6,15) (7,31) (7,25) (7,21) (7,13) (7,18) (8,26) (8,11) (10,12) (10,19) (10,13) (10,18) (11,20) (12,16) (12,27) (12,22) (12,30) (12,28) (12,21) (12,13) (12,15) (13,25) (13,27) (13,30) (13,19) (13,24) (13,18) (15,16) (15,22) (15,21) (15,18) (16,31) (16,32) (16,25) (16,22) (16,29) (16,24) (17,32) (17,19) (17,28) (17,21) (17,23) (18,32) (18,22) (18,19) (18,28) (18,21) (19,31) (19,27) (19,22) (19,29) (19,24) (19,21) (20,26) (21,32) (21,24) (22,31) (22,32) (23,31) (23,25) (23,27) (23,29) (24,25) (28,30) (31,32)\nIs there a path between node 3 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph305-18_24", + "image": "data/connectivity/graph_visual/hard/graph305.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,29) (0,19) (0,26) (0,23) (0,7) (0,1) (1,2) (1,18) (1,23) (1,6) (2,10) (2,25) (2,6) (2,24) (3,20) (3,30) (3,4) (4,27) (4,28) (4,12) (5,27) (5,15) (6,10) (6,29) (6,25) (6,22) (6,7) (7,10) (7,29) (7,18) (8,29) (8,25) (8,18) (10,19) (10,25) (10,26) (10,24) (11,27) (11,15) (12,21) (13,28) (14,31) (15,30) (16,17) (17,19) (17,22) (18,25) (18,26) (18,24) (19,25) (19,26) (19,24) (20,21) (22,26) (22,24) (23,26) (24,26) (25,26) (26,29) (27,30)\nIs there a path between node 18 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph439-27_10", + "image": "data/connectivity/graph_visual/hard/graph439.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,12) (0,15) (0,27) (0,11) (0,32) (0,23) (0,17) (0,21) (0,19) (0,14) (0,22) (0,29) (0,16) (0,5) (0,4) (0,2) (0,1) (1,15) (1,27) (1,32) (1,23) (1,21) (1,3) (1,14) (1,20) (1,7) (1,29) (1,16) (1,5) (1,4) (1,2) (1,13) (2,12) (2,15) (2,11) (2,18) (2,32) (2,23) (2,3) (2,19) (2,14) (2,28) (2,22) (2,7) (2,29) (2,16) (2,4) (2,13) (3,27) (3,11) (3,32) (3,23) (3,21) (3,10) (3,19) (3,14) (3,28) (3,7) (3,29) (3,16) (3,4) (4,15) (4,27) (4,11) (4,18) (4,32) (4,23) (4,17) (4,21) (4,10) (4,19) (4,14) (4,20) (4,29) (4,5) (4,8) (4,13) (5,12) (5,15) (5,27) (5,11) (5,18) (5,32) (5,23) (5,17) (5,21) (5,10) (5,28) (5,29) (5,16) (5,8) (6,25) (7,12) (7,15) (7,27) (7,11) (7,18) (7,32) (7,23) (7,17) (7,21) (7,10) (7,19) (7,20) (7,29) (7,16) (7,13) (8,15) (8,11) (8,18) (8,32) (8,23) (8,17) (8,28) (8,22) (8,20) (8,13) (9,31) (9,26) (9,30) (10,27) (10,32) (10,23) (10,17) (10,21) (10,19) (10,14) (10,28) (10,22) (10,20) (10,29) (10,16) (11,12) (11,15) (11,27) (11,18) (11,32) (11,23) (11,21) (11,14) (11,28) (11,22) (11,29) (11,16) (11,13) (12,18) (12,32) (12,23) (12,17) (12,21) (12,19) (12,22) (12,29) (12,13) (13,15) (13,27) (13,18) (13,32) (13,23) (13,14) (13,28) (13,22) (13,20) (13,29) (13,16) (14,15) (14,18) (14,32) (14,17) (14,21) (14,19) (14,22) (14,29) (15,27) (15,18) (15,32) (15,21) (15,28) (15,16) (16,27) (16,18) (16,32) (16,23) (16,17) (16,21) (16,28) (16,29) (17,23) (17,21) (17,19) (17,22) (17,20) (17,29) (18,27) (18,32) (18,23) (18,21) (18,19) (18,28) (18,22) (19,32) (19,23) (19,21) (19,28) (19,20) (19,29) (20,27) (20,21) (20,22) (20,29) (21,27) (21,32) (21,23) (21,28) (21,22) (21,29) (22,27) (22,23) (22,28) (22,29) (23,27) (23,32) (23,28) (24,26) (26,31) (26,30) (27,32) (27,28) (27,29) (28,29) (29,32) (30,31)\nIs there a path between node 27 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph66-15_22", + "image": "data/connectivity/graph_visual/hard/graph66.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,23) (0,10) (0,15) (0,1) (0,24) (1,17) (1,11) (1,23) (1,18) (1,13) (1,6) (1,24) (2,25) (3,21) (3,18) (3,10) (3,13) (3,20) (3,24) (5,21) (5,12) (5,23) (5,15) (5,6) (5,24) (6,7) (6,17) (6,13) (6,19) (6,24) (7,16) (7,15) (7,19) (7,24) (8,25) (8,26) (9,26) (10,13) (11,23) (12,21) (12,18) (13,17) (13,15) (13,22) (13,19) (15,20) (16,22) (17,18) (17,22) (19,20) (19,24) (20,21) (21,22) (23,24)\nIs there a path between node 15 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph402-19_26", + "image": "data/connectivity/graph_visual/hard/graph402.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,32) (0,31) (0,24) (0,30) (0,3) (0,16) (0,5) (0,1) (0,23) (1,14) (1,32) (1,17) (1,20) (1,31) (1,27) (1,24) (1,3) (1,16) (1,7) (1,5) (1,23) (2,8) (2,11) (2,28) (2,19) (2,22) (2,29) (2,26) (2,18) (3,14) (3,32) (3,31) (3,27) (3,24) (3,30) (3,10) (3,16) (3,7) (3,5) (3,23) (4,25) (4,11) (4,28) (4,21) (4,29) (4,18) (4,15) (5,14) (5,17) (5,31) (5,27) (5,30) (5,10) (5,7) (5,23) (6,25) (6,8) (6,11) (6,28) (6,19) (6,21) (6,29) (6,26) (6,15) (7,32) (7,17) (7,30) (7,10) (8,11) (8,28) (8,19) (8,22) (8,21) (8,29) (8,18) (8,15) (9,12) (10,14) (10,32) (10,20) (10,27) (10,24) (10,30) (10,16) (11,25) (11,28) (11,21) (11,26) (11,18) (12,13) (14,32) (14,17) (14,20) (14,31) (14,24) (14,16) (14,23) (15,28) (15,19) (15,22) (15,29) (15,18) (16,20) (16,31) (16,27) (16,24) (16,30) (16,23) (17,32) (17,20) (17,27) (17,24) (17,30) (17,23) (18,25) (18,22) (19,25) (19,28) (19,22) (19,26) (20,27) (20,24) (20,23) (21,28) (21,22) (22,25) (22,28) (22,29) (23,32) (23,27) (23,24) (24,32) (24,31) (24,27) (24,30) (25,28) (25,29) (25,26) (26,28) (27,32) (27,31) (28,29) (30,32) (30,31)\nIs there a path between node 19 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph109-5_3", + "image": "data/connectivity/graph_visual/hard/graph109.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,5) (1,27) (1,3) (1,18) (1,23) (2,14) (2,15) (2,27) (2,13) (2,8) (2,26) (3,12) (3,15) (3,13) (3,18) (3,20) (4,5) (4,15) (4,21) (4,11) (4,22) (4,20) (5,15) (5,8) (7,14) (7,25) (7,27) (7,13) (7,9) (7,20) (8,14) (8,15) (8,21) (8,23) (8,19) (9,12) (9,15) (9,27) (9,21) (9,13) (10,12) (10,21) (10,17) (10,19) (11,25) (11,27) (11,17) (11,26) (11,22) (11,19) (12,21) (12,26) (13,25) (13,21) (13,26) (13,18) (14,25) (14,15) (14,27) (14,17) (14,23) (14,19) (15,17) (15,26) (15,22) (15,18) (15,20) (15,19) (17,26) (17,18) (19,27) (20,25) (20,27) (20,26) (20,22) (20,23) (21,25) (21,27) (21,23) (22,26) (23,25) (25,26) (26,27)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph644-21_15", + "image": "data/connectivity/graph_visual/hard/graph644.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,34) (0,17) (0,18) (0,1) (0,4) (0,28) (0,14) (0,22) (0,12) (1,20) (1,5) (1,26) (1,8) (1,34) (1,17) (1,28) (1,22) (2,9) (2,30) (2,6) (2,21) (2,23) (2,19) (2,25) (2,29) (2,13) (2,15) (2,16) (2,10) (2,27) (3,9) (3,31) (3,6) (3,21) (3,23) (3,19) (3,33) (3,25) (3,13) (3,15) (3,7) (3,16) (3,10) (3,24) (3,32) (3,11) (3,27) (4,5) (4,26) (4,8) (4,34) (4,17) (4,18) (4,28) (4,14) (5,20) (5,26) (5,8) (5,34) (5,17) (5,18) (5,14) (6,30) (6,31) (6,23) (6,33) (6,29) (6,7) (6,16) (6,10) (6,11) (7,9) (7,30) (7,31) (7,21) (7,23) (7,19) (7,29) (7,13) (7,16) (7,10) (7,24) (7,32) (7,11) (7,27) (8,20) (8,17) (8,18) (8,28) (8,14) (8,22) (9,30) (9,31) (9,21) (9,19) (9,33) (9,25) (9,10) (9,32) (9,11) (10,23) (10,19) (10,33) (10,25) (10,13) (10,15) (10,16) (10,24) (10,32) (10,27) (11,30) (11,31) (11,21) (11,23) (11,33) (11,25) (11,29) (11,13) (11,15) (11,16) (11,24) (11,27) (12,20) (12,26) (12,34) (12,18) (12,22) (13,31) (13,21) (13,33) (13,25) (13,15) (13,16) (13,27) (14,20) (14,26) (14,34) (14,17) (14,28) (14,22) (15,30) (15,23) (15,19) (15,25) (15,24) (15,32) (15,27) (16,30) (16,31) (16,21) (16,23) (16,24) (16,32) (17,20) (17,26) (17,34) (17,28) (17,22) (18,20) (18,26) (18,34) (18,22) (19,30) (19,31) (19,23) (19,25) (19,27) (20,34) (21,23) (21,33) (21,25) (21,29) (21,24) (21,27) (22,34) (22,28) (23,31) (23,29) (23,24) (23,32) (24,30) (24,31) (24,33) (24,29) (24,32) (24,27) (25,30) (25,31) (25,33) (25,32) (25,27) (26,34) (27,30) (27,33) (29,30) (29,31) (30,33) (30,32) (31,33) (31,32)\nIs there a path between node 21 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph631-30_13", + "image": "data/connectivity/graph_visual/hard/graph631.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,16) (1,33) (1,17) (1,12) (1,25) (1,7) (1,18) (1,32) (1,11) (1,10) (1,15) (1,9) (1,5) (1,26) (1,4) (2,19) (2,33) (2,18) (2,30) (3,34) (3,31) (3,14) (3,6) (3,17) (3,11) (3,22) (3,29) (3,15) (3,24) (3,30) (4,16) (4,6) (4,12) (4,32) (4,24) (5,31) (5,16) (5,8) (5,23) (5,24) (5,21) (6,19) (6,33) (6,25) (6,11) (6,10) (6,24) (6,30) (7,12) (7,15) (7,9) (7,30) (8,17) (8,12) (8,32) (8,22) (8,29) (8,24) (8,30) (9,16) (9,14) (9,12) (9,25) (9,18) (9,23) (9,26) (10,31) (10,14) (10,19) (10,25) (10,32) (10,22) (10,23) (10,21) (11,34) (11,14) (11,17) (11,27) (11,25) (11,18) (11,26) (14,19) (14,33) (14,25) (14,18) (14,30) (14,26) (14,21) (15,34) (15,31) (15,33) (15,32) (15,24) (15,26) (15,21) (16,34) (16,22) (16,29) (16,24) (16,26) (17,31) (17,18) (17,23) (17,26) (18,22) (18,26) (19,33) (19,27) (19,25) (19,29) (19,26) (21,34) (21,31) (21,33) (21,25) (21,22) (21,24) (21,30) (22,34) (22,29) (22,24) (23,33) (23,27) (23,32) (24,33) (24,27) (24,32) (25,34) (25,31) (26,29) (27,34) (27,33) (29,31) (29,33) (29,30) (30,31) (31,34)\nIs there a path between node 30 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph408-20_28", + "image": "data/connectivity/graph_visual/hard/graph408.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,21) (0,17) (0,7) (0,29) (1,20) (2,32) (2,6) (2,13) (3,22) (3,23) (3,8) (4,30) (4,31) (6,23) (6,16) (6,32) (7,19) (8,14) (8,23) (8,16) (8,32) (8,13) (9,24) (9,17) (9,29) (13,14) (13,32) (14,16) (14,32) (16,20) (16,28) (17,24) (20,28) (21,29) (24,29) (27,30) (30,31)\nIs there a path between node 20 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph145-4_25", + "image": "data/connectivity/graph_visual/hard/graph145.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,3) (0,24) (0,15) (0,16) (0,19) (0,7) (0,25) (0,26) (1,28) (1,23) (3,6) (3,18) (3,11) (3,24) (3,22) (3,4) (3,7) (3,25) (4,27) (4,24) (4,22) (4,12) (4,21) (4,16) (4,19) (5,6) (5,13) (5,22) (5,12) (5,16) (6,11) (6,21) (6,15) (6,25) (6,26) (7,14) (7,25) (8,23) (9,11) (9,13) (10,11) (10,15) (10,19) (11,27) (11,18) (11,22) (11,12) (11,21) (11,19) (11,25) (12,27) (12,14) (13,27) (13,18) (13,14) (13,21) (14,18) (14,24) (14,15) (15,22) (15,16) (15,26) (16,18) (16,22) (17,28) (17,23) (17,20) (18,27) (19,27) (19,24) (21,26) (22,25) (22,26) (23,28) (24,25) (24,26)\nIs there a path between node 4 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph577-4_1", + "image": "data/connectivity/graph_visual/hard/graph577.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,10) (0,13) (0,4) (0,23) (0,22) (0,25) (0,18) (0,17) (0,21) (0,32) (0,1) (0,2) (0,27) (0,3) (1,6) (1,7) (1,23) (1,22) (1,25) (1,18) (1,14) (1,17) (1,21) (1,32) (1,2) (1,27) (1,3) (1,24) (2,6) (2,13) (2,4) (2,16) (2,22) (2,14) (2,32) (2,29) (2,27) (2,3) (2,24) (3,10) (3,23) (3,16) (3,14) (3,17) (3,32) (3,27) (3,24) (4,10) (4,13) (4,7) (4,23) (4,22) (4,18) (4,17) (4,21) (4,32) (4,29) (4,27) (4,24) (5,9) (5,8) (5,28) (5,11) (5,19) (5,33) (5,15) (5,20) (5,12) (5,31) (6,10) (6,13) (6,7) (6,16) (6,22) (6,25) (6,14) (6,21) (6,32) (6,29) (6,27) (7,10) (7,23) (7,16) (7,22) (7,18) (7,21) (7,32) (7,29) (7,24) (8,28) (8,11) (8,19) (8,12) (8,31) (9,26) (9,28) (9,30) (9,19) (9,15) (9,20) (9,12) (9,31) (10,16) (10,25) (10,18) (10,14) (10,17) (10,29) (10,27) (10,24) (11,26) (11,30) (11,19) (11,33) (11,15) (11,20) (11,12) (11,31) (12,28) (12,30) (12,19) (12,33) (12,15) (12,20) (13,16) (13,25) (13,18) (13,17) (13,32) (13,29) (13,27) (13,24) (14,23) (14,16) (14,29) (14,27) (15,26) (15,28) (15,30) (15,33) (15,20) (15,31) (16,22) (16,21) (16,29) (16,27) (16,24) (17,23) (17,18) (17,29) (17,24) (18,23) (18,22) (18,25) (18,21) (18,32) (18,27) (19,26) (19,28) (19,30) (19,20) (19,31) (20,28) (20,30) (20,33) (20,31) (21,25) (21,32) (21,29) (21,27) (21,24) (22,32) (22,24) (23,25) (23,32) (23,29) (23,27) (24,25) (24,32) (24,29) (24,27) (25,32) (25,29) (25,27) (26,30) (26,33) (27,32) (27,29) (28,30) (28,31) (29,32)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph262-18_19", + "image": "data/connectivity/graph_visual/hard/graph262.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,23) (1,19) (1,11) (1,16) (1,28) (2,10) (2,13) (2,16) (2,3) (2,4) (2,27) (2,9) (3,14) (3,19) (3,26) (3,8) (3,11) (3,24) (3,27) (4,21) (4,29) (4,16) (4,27) (4,28) (5,7) (5,6) (5,12) (5,23) (6,30) (6,12) (7,23) (7,15) (8,14) (8,26) (8,10) (8,29) (8,27) (8,28) (9,26) (9,21) (9,13) (10,18) (10,27) (11,14) (11,19) (11,26) (11,21) (12,20) (13,19) (13,26) (13,18) (14,21) (14,25) (15,30) (16,24) (16,28) (18,25) (19,26) (19,21) (19,29) (19,28) (20,23) (21,26) (21,24) (22,30) (24,29) (24,28) (25,27) (26,27)\nIs there a path between node 18 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph706-9_20", + "image": "data/connectivity/graph_visual/hard/graph706.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,21) (0,17) (0,24) (0,27) (0,4) (0,10) (0,7) (1,29) (1,14) (1,5) (1,26) (1,18) (1,23) (1,28) (1,34) (1,8) (1,6) (2,29) (2,16) (2,30) (2,5) (2,26) (2,19) (2,25) (2,11) (2,18) (2,23) (2,28) (2,20) (2,9) (2,8) (2,6) (3,33) (3,32) (4,13) (4,17) (4,22) (4,24) (4,15) (4,27) (4,12) (4,10) (4,7) (5,29) (5,14) (5,26) (5,19) (5,25) (5,11) (5,31) (5,28) (5,34) (5,6) (6,29) (6,14) (6,30) (6,26) (6,19) (6,25) (6,11) (6,18) (6,28) (6,20) (6,9) (6,8) (7,13) (7,21) (7,17) (7,22) (7,24) (7,27) (7,10) (8,16) (8,14) (8,30) (8,26) (8,25) (8,11) (8,31) (8,18) (8,23) (8,20) (8,9) (8,34) (9,29) (9,16) (9,30) (9,26) (9,19) (9,25) (9,11) (9,31) (9,23) (10,13) (10,21) (10,17) (10,24) (10,15) (10,27) (11,29) (11,16) (11,14) (11,30) (11,26) (11,19) (11,25) (11,23) (12,13) (12,17) (12,22) (12,27) (13,21) (13,17) (13,22) (13,24) (13,15) (13,27) (14,29) (14,16) (14,30) (14,26) (14,25) (14,31) (14,18) (14,28) (14,34) (15,22) (15,24) (15,27) (16,29) (16,30) (16,26) (16,25) (16,31) (16,23) (17,21) (17,24) (17,27) (18,29) (18,30) (18,26) (18,19) (18,25) (18,31) (18,23) (18,34) (19,29) (19,30) (19,26) (19,31) (19,23) (19,20) (19,34) (20,29) (20,30) (20,31) (20,23) (20,28) (20,34) (21,22) (21,24) (22,24) (22,27) (23,29) (23,26) (23,34) (24,27) (25,29) (25,30) (25,31) (25,28) (25,34) (26,29) (26,30) (26,31) (26,28) (26,34) (28,29) (28,31) (29,30) (29,31) (29,34) (30,31) (30,34) (31,34)\nIs there a path between node 9 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph316-14_5", + "image": "data/connectivity/graph_visual/hard/graph316.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,19) (0,31) (0,15) (0,18) (1,24) (1,19) (1,31) (1,5) (2,30) (2,23) (2,4) (2,17) (3,30) (3,23) (3,12) (3,17) (5,28) (5,6) (5,14) (5,9) (5,31) (5,18) (6,10) (6,13) (6,19) (6,31) (6,21) (6,18) (7,28) (7,14) (7,25) (7,20) (8,26) (8,23) (8,12) (8,17) (9,22) (9,13) (9,29) (9,31) (9,15) (9,21) (9,18) (10,13) (10,19) (10,14) (10,15) (10,18) (11,12) (11,16) (12,30) (12,17) (13,28) (13,29) (13,15) (13,21) (13,20) (13,18) (14,22) (14,24) (14,29) (15,29) (15,25) (16,26) (17,30) (18,25) (18,20) (19,29) (19,21) (19,20) (20,22) (20,28) (20,29) (20,25) (21,27) (21,31) (22,28) (22,29) (23,30) (23,26) (24,29) (24,31) (27,31)\nIs there a path between node 14 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph550-11_28", + "image": "data/connectivity/graph_visual/hard/graph550.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,28) (0,23) (0,22) (0,32) (1,28) (1,15) (1,12) (1,13) (2,11) (2,19) (2,9) (4,16) (4,21) (4,24) (5,7) (5,8) (5,20) (6,19) (6,24) (6,27) (7,8) (7,20) (9,19) (9,24) (10,28) (10,12) (10,14) (10,32) (11,21) (12,18) (12,26) (12,22) (13,28) (13,15) (13,26) (14,18) (14,17) (14,22) (15,25) (15,26) (15,23) (16,30) (17,28) (17,32) (19,31) (19,21) (19,24) (19,33) (21,30) (21,24) (21,27) (23,28) (23,25) (25,26) (26,32) (30,31) (30,33)\nIs there a path between node 11 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph140-17_20", + "image": "data/connectivity/graph_visual/hard/graph140.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,21) (0,25) (0,12) (0,26) (1,15) (1,23) (1,17) (1,13) (2,27) (2,10) (2,24) (4,9) (4,20) (4,13) (5,28) (5,11) (6,16) (6,23) (6,7) (6,13) (7,15) (7,16) (7,23) (7,17) (7,28) (8,12) (11,17) (11,20) (12,18) (12,14) (12,25) (12,19) (12,26) (13,23) (15,16) (16,23) (17,28) (18,26) (25,26)\nIs there a path between node 17 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph329-4_24", + "image": "data/connectivity/graph_visual/hard/graph329.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,28) (0,2) (0,25) (0,6) (0,27) (0,4) (0,31) (0,9) (0,1) (0,29) (0,10) (0,11) (0,16) (0,21) (1,28) (1,2) (1,25) (1,27) (1,4) (1,31) (1,9) (1,14) (1,11) (1,16) (1,22) (1,20) (2,28) (2,25) (2,6) (2,27) (2,4) (2,9) (2,14) (2,10) (2,19) (2,11) (2,16) (2,20) (2,26) (2,21) (3,24) (3,18) (3,8) (4,28) (4,25) (4,27) (4,31) (4,14) (4,10) (4,19) (4,22) (4,20) (4,26) (4,21) (5,17) (5,12) (5,15) (5,30) (5,13) (6,28) (6,25) (6,27) (6,9) (6,14) (6,29) (6,19) (6,11) (6,16) (6,20) (6,21) (7,24) (7,18) (7,8) (8,24) (9,28) (9,25) (9,31) (9,29) (9,10) (9,19) (9,11) (9,22) (9,20) (9,26) (9,21) (10,25) (10,31) (10,14) (10,11) (10,16) (10,20) (10,26) (10,21) (11,25) (11,27) (11,31) (11,29) (11,19) (11,16) (11,22) (11,26) (12,15) (12,30) (12,13) (13,17) (13,15) (13,30) (14,28) (14,25) (14,27) (14,29) (14,19) (14,16) (14,22) (14,20) (14,26) (14,21) (15,17) (16,28) (16,25) (16,27) (16,31) (16,22) (16,20) (16,21) (19,28) (19,25) (19,27) (19,31) (19,22) (19,20) (19,26) (19,21) (20,28) (20,25) (20,27) (20,31) (20,29) (20,22) (20,26) (20,21) (21,27) (21,29) (21,22) (21,26) (22,28) (22,25) (22,31) (22,29) (22,26) (25,27) (25,31) (25,26) (26,28) (26,27) (27,29) (28,31) (29,31)\nIs there a path between node 4 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph673-27_29", + "image": "data/connectivity/graph_visual/hard/graph673.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,24) (0,27) (0,26) (0,2) (0,33) (2,19) (2,15) (2,7) (2,18) (2,24) (2,32) (2,26) (2,6) (2,16) (2,34) (2,21) (3,29) (4,19) (4,15) (4,7) (4,8) (4,18) (4,5) (4,31) (4,10) (4,13) (4,34) (4,20) (5,15) (5,11) (5,24) (5,27) (5,21) (6,18) (6,27) (6,26) (6,28) (6,23) (6,12) (6,21) (6,22) (7,27) (7,26) (7,34) (7,23) (7,22) (8,14) (8,26) (8,33) (8,22) (10,11) (10,24) (10,27) (10,28) (10,23) (10,12) (10,21) (10,22) (11,15) (11,30) (11,31) (11,26) (11,16) (11,33) (12,14) (12,15) (12,18) (12,24) (12,33) (12,21) (13,24) (13,33) (13,20) (13,21) (13,22) (14,24) (14,27) (14,16) (14,20) (14,21) (14,22) (15,16) (15,23) (15,21) (15,22) (16,24) (16,34) (16,20) (17,29) (18,19) (18,21) (19,24) (19,31) (19,32) (19,26) (19,28) (19,34) (20,31) (20,26) (20,28) (20,21) (20,22) (21,26) (21,28) (21,34) (21,23) (22,30) (22,27) (22,34) (22,33) (23,27) (23,33) (24,30) (24,27) (24,26) (25,29) (26,33) (27,28) (27,33) (32,34)\nIs there a path between node 27 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph174-24_6", + "image": "data/connectivity/graph_visual/hard/graph174.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,1) (0,25) (0,17) (0,8) (0,9) (0,7) (0,10) (0,11) (0,6) (0,15) (0,27) (0,16) (0,24) (1,25) (1,17) (1,8) (1,10) (1,11) (1,15) (1,27) (1,16) (1,24) (2,18) (2,21) (2,23) (2,5) (2,26) (2,3) (3,21) (3,23) (4,22) (4,20) (4,28) (4,12) (4,14) (5,18) (5,19) (6,25) (6,17) (6,8) (6,7) (6,11) (6,16) (6,24) (6,13) (7,8) (7,9) (7,10) (7,27) (7,16) (7,24) (8,25) (8,17) (8,10) (8,27) (8,24) (9,25) (9,17) (9,10) (9,11) (9,15) (9,27) (9,16) (9,24) (9,13) (10,25) (10,16) (10,24) (10,13) (11,25) (11,15) (11,27) (11,16) (11,13) (12,22) (13,25) (13,17) (13,27) (13,16) (13,24) (14,22) (14,20) (14,28) (15,17) (15,27) (15,16) (15,24) (16,25) (16,17) (17,25) (17,27) (18,23) (18,19) (18,26) (19,21) (19,23) (20,22) (21,23) (21,26) (22,28) (24,25) (24,27) (25,27)\nIs there a path between node 24 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph593-13_8", + "image": "data/connectivity/graph_visual/hard/graph593.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,3) (0,18) (0,13) (0,17) (0,4) (0,15) (0,28) (0,19) (0,14) (0,31) (0,25) (0,29) (0,30) (0,26) (0,2) (0,23) (0,5) (0,8) (1,3) (1,18) (1,13) (1,17) (1,15) (1,28) (1,19) (1,14) (1,25) (1,2) (1,23) (1,5) (1,8) (2,18) (2,13) (2,17) (2,28) (2,14) (2,29) (2,30) (2,23) (2,5) (2,32) (2,8) (3,13) (3,4) (3,15) (3,28) (3,19) (3,14) (3,31) (3,29) (3,10) (3,30) (3,5) (3,32) (4,18) (4,13) (4,17) (4,15) (4,28) (4,31) (4,25) (4,29) (4,10) (4,30) (4,26) (4,5) (4,22) (4,32) (4,8) (5,13) (5,28) (5,19) (5,14) (5,25) (5,29) (5,10) (5,30) (5,26) (5,23) (5,22) (5,8) (6,16) (6,27) (6,9) (6,21) (6,12) (6,11) (6,20) (7,16) (7,27) (7,33) (7,9) (7,21) (7,12) (7,11) (8,13) (8,17) (8,15) (8,14) (8,25) (8,29) (8,10) (8,30) (8,23) (9,16) (9,27) (9,33) (9,21) (9,12) (9,20) (10,13) (10,17) (10,15) (10,28) (10,14) (10,25) (10,23) (10,22) (10,32) (11,16) (11,27) (11,33) (11,20) (12,16) (12,33) (12,24) (13,18) (13,28) (13,31) (13,25) (13,29) (13,30) (13,26) (13,23) (13,22) (14,18) (14,15) (14,19) (14,31) (14,25) (14,29) (14,23) (14,22) (14,32) (15,18) (15,17) (15,28) (15,31) (15,29) (15,30) (15,26) (15,23) (15,22) (15,32) (16,27) (16,33) (17,18) (17,28) (17,19) (17,31) (17,25) (17,29) (17,26) (17,23) (17,22) (17,32) (18,19) (18,29) (18,22) (19,28) (19,31) (19,25) (19,29) (19,30) (19,26) (19,23) (19,22) (19,32) (20,27) (20,21) (20,24) (21,27) (21,24) (22,28) (22,25) (22,29) (22,30) (22,26) (22,23) (22,32) (23,28) (23,29) (23,30) (23,26) (25,31) (25,26) (26,28) (26,29) (26,30) (27,33) (28,30) (28,32) (29,30) (29,32) (30,31) (30,32) (31,32)\nIs there a path between node 13 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph466-29_30", + "image": "data/connectivity/graph_visual/hard/graph466.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,17) (0,32) (0,5) (0,31) (0,29) (0,27) (0,1) (0,18) (0,13) (0,2) (0,23) (1,7) (1,17) (1,20) (1,14) (1,13) (1,28) (2,3) (2,26) (2,32) (2,20) (2,31) (2,27) (2,23) (3,17) (3,25) (3,5) (3,19) (3,31) (3,14) (3,29) (3,11) (3,27) (3,18) (3,13) (3,22) (3,9) (4,20) (4,31) (4,14) (4,11) (4,16) (4,27) (4,18) (4,10) (4,9) (5,7) (5,17) (5,25) (5,32) (5,20) (5,18) (6,15) (6,12) (7,20) (7,19) (7,9) (7,23) (8,17) (8,32) (8,19) (8,29) (8,11) (8,22) (8,21) (9,17) (9,25) (9,28) (10,25) (10,20) (10,31) (10,14) (11,26) (11,17) (11,13) (11,22) (11,28) (11,21) (12,30) (13,19) (13,16) (13,28) (13,23) (14,29) (14,16) (14,18) (14,22) (15,30) (15,24) (16,19) (16,27) (16,28) (17,32) (17,20) (17,31) (17,23) (18,25) (18,31) (19,20) (19,28) (19,21) (20,25) (20,32) (20,27) (20,21) (21,23) (22,26) (22,31) (22,23) (23,26) (23,32) (23,29) (24,30) (26,32) (26,29) (26,28) (27,31) (28,32) (29,32) (29,31)\nIs there a path between node 29 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph636-21_18", + "image": "data/connectivity/graph_visual/hard/graph636.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,32) (0,18) (0,25) (1,13) (1,17) (1,28) (1,2) (1,33) (2,17) (2,28) (2,15) (2,26) (2,16) (3,30) (3,26) (5,17) (5,28) (5,27) (6,22) (6,21) (7,34) (7,22) (7,24) (8,19) (10,29) (10,22) (10,31) (10,24) (10,21) (10,11) (11,34) (13,30) (13,15) (13,27) (13,33) (13,26) (13,16) (14,32) (15,28) (15,26) (16,28) (16,26) (17,30) (18,25) (20,28) (20,26) (21,31) (21,24) (22,34) (22,31) (22,24) (23,32) (24,29) (26,33) (28,33) (31,34)\nIs there a path between node 21 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph448-7_21", + "image": "data/connectivity/graph_visual/hard/graph448.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,10) (0,30) (0,14) (0,26) (0,7) (0,8) (0,17) (1,24) (1,21) (1,29) (1,19) (2,11) (2,10) (2,30) (2,23) (2,32) (2,7) (3,29) (3,19) (4,18) (5,11) (5,14) (5,6) (5,22) (5,7) (6,10) (6,14) (6,32) (6,17) (7,30) (8,11) (8,10) (8,27) (8,14) (8,22) (8,32) (9,28) (9,16) (10,11) (10,30) (10,27) (10,14) (10,26) (10,22) (10,17) (11,14) (12,16) (13,28) (13,31) (14,27) (14,20) (14,23) (14,32) (16,31) (17,30) (17,26) (17,23) (18,24) (18,25) (19,29) (19,25) (20,23) (21,24) (21,29) (22,30) (22,26) (23,30) (23,26) (24,29) (25,29) (26,30) (26,27) (27,30) (30,32)\nIs there a path between node 7 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph587-21_8", + "image": "data/connectivity/graph_visual/hard/graph587.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,21) (0,30) (0,33) (0,6) (0,24) (0,25) (0,1) (0,17) (0,11) (0,16) (1,10) (1,30) (1,4) (1,33) (1,6) (1,25) (1,31) (1,5) (1,17) (1,11) (1,16) (2,27) (3,15) (3,28) (3,12) (3,32) (3,14) (3,20) (3,13) (4,21) (4,33) (4,6) (4,24) (4,25) (4,31) (4,5) (4,17) (4,11) (5,10) (5,21) (5,30) (5,33) (5,6) (5,24) (5,25) (5,31) (5,17) (5,11) (6,30) (6,33) (6,24) (6,25) (6,31) (6,17) (6,11) (6,16) (7,19) (7,29) (7,22) (7,18) (7,9) (8,23) (8,15) (8,28) (8,32) (8,14) (8,20) (9,19) (9,29) (9,22) (9,18) (10,30) (10,33) (10,24) (10,25) (10,31) (10,17) (10,11) (11,21) (11,30) (11,33) (11,24) (11,25) (11,17) (11,16) (12,23) (12,15) (12,32) (12,14) (12,13) (13,15) (13,28) (13,32) (13,14) (14,15) (14,28) (14,32) (15,23) (15,28) (15,32) (15,20) (16,30) (16,25) (16,17) (17,33) (17,31) (18,19) (18,29) (18,22) (19,29) (20,28) (20,32) (21,33) (21,24) (21,25) (21,31) (23,32) (24,30) (24,33) (24,25) (24,31) (25,33) (25,31) (26,27) (30,31)\nIs there a path between node 21 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph369-23_24", + "image": "data/connectivity/graph_visual/hard/graph369.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,16) (0,6) (0,12) (0,29) (0,13) (0,3) (0,21) (0,17) (0,30) (0,27) (0,8) (0,10) (1,9) (1,11) (1,16) (1,6) (1,20) (1,24) (1,13) (1,14) (1,3) (1,21) (1,17) (1,30) (1,25) (1,19) (1,27) (1,8) (1,10) (2,4) (3,26) (3,9) (3,11) (3,7) (3,12) (3,24) (3,13) (3,14) (3,17) (3,30) (3,25) (3,27) (3,8) (3,10) (4,23) (5,28) (5,15) (6,26) (6,9) (6,11) (6,16) (6,7) (6,12) (6,24) (6,14) (6,21) (6,17) (6,25) (6,19) (6,27) (6,10) (7,26) (7,11) (7,16) (7,12) (7,29) (7,24) (7,21) (7,17) (7,30) (7,8) (7,10) (8,9) (8,16) (8,12) (8,20) (8,24) (8,13) (8,14) (8,17) (8,30) (8,19) (8,27) (8,10) (9,11) (9,16) (9,12) (9,20) (9,29) (9,24) (9,14) (9,21) (9,17) (9,30) (9,25) (9,19) (9,27) (10,16) (10,12) (10,20) (10,24) (10,13) (10,14) (10,21) (10,17) (10,30) (10,25) (10,19) (10,27) (11,26) (11,16) (11,24) (11,14) (11,21) (11,30) (11,25) (11,19) (11,27) (12,26) (12,16) (12,20) (12,29) (12,24) (12,13) (12,14) (12,21) (12,17) (12,30) (12,19) (12,27) (13,26) (13,16) (13,20) (13,24) (13,14) (13,21) (13,17) (13,30) (13,19) (13,27) (14,26) (14,16) (14,20) (14,29) (14,30) (14,25) (15,31) (16,26) (16,29) (16,21) (16,17) (16,30) (16,25) (16,27) (17,26) (17,29) (17,21) (17,30) (17,25) (17,19) (17,27) (18,23) (18,22) (19,26) (19,20) (19,21) (19,30) (19,25) (19,27) (20,26) (20,29) (20,24) (20,21) (20,30) (20,25) (20,27) (21,26) (21,29) (21,30) (21,25) (21,27) (22,23) (24,29) (24,30) (25,29) (25,30) (25,27) (26,29) (27,29) (27,30) (29,30)\nIs there a path between node 23 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph517-4_5", + "image": "data/connectivity/graph_visual/hard/graph517.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,22) (0,28) (0,25) (0,14) (0,29) (1,22) (1,31) (1,7) (1,25) (1,16) (1,14) (2,13) (2,22) (2,21) (2,31) (2,11) (2,4) (2,20) (3,33) (4,17) (4,13) (4,7) (4,8) (4,24) (4,25) (4,16) (4,29) (5,17) (5,13) (5,24) (5,6) (6,21) (6,7) (6,24) (7,28) (7,8) (7,16) (8,20) (9,21) (9,16) (9,20) (10,26) (10,19) (10,12) (10,32) (10,18) (11,21) (11,14) (12,19) (14,28) (14,24) (14,16) (15,30) (16,22) (16,24) (16,25) (17,28) (17,24) (17,29) (17,20) (18,32) (20,31) (20,24) (21,22) (21,29) (22,31) (22,29) (23,26) (23,32) (24,28) (27,32) (28,29) (29,31)\nIs there a path between node 4 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph629-8_22", + "image": "data/connectivity/graph_visual/hard/graph629.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,1) (0,28) (0,7) (0,32) (0,34) (0,29) (1,16) (1,9) (1,27) (1,4) (1,22) (1,34) (2,16) (2,28) (2,9) (2,5) (2,31) (2,22) (3,13) (3,17) (3,26) (3,12) (4,24) (4,11) (4,7) (4,5) (4,27) (4,22) (5,16) (5,9) (5,31) (5,23) (6,17) (6,12) (7,24) (7,32) (7,31) (7,23) (8,21) (9,28) (9,11) (11,31) (11,19) (11,23) (12,18) (12,17) (13,20) (13,26) (14,24) (14,32) (14,27) (14,19) (14,29) (15,30) (16,24) (16,23) (19,27) (20,33) (21,25) (22,32) (22,29) (23,28) (23,24) (23,27) (24,27) (24,31) (27,32) (27,34) (31,34)\nIs there a path between node 8 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph204-16_24", + "image": "data/connectivity/graph_visual/hard/graph204.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,15) (0,26) (0,23) (0,4) (0,6) (0,3) (0,24) (2,17) (2,6) (2,3) (2,9) (2,11) (3,18) (3,14) (3,9) (3,11) (4,17) (4,15) (4,21) (4,29) (4,23) (4,13) (4,27) (4,9) (4,8) (5,22) (5,10) (5,15) (5,23) (5,9) (5,8) (6,22) (6,10) (6,26) (6,27) (6,24) (6,8) (6,11) (8,10) (8,21) (9,19) (9,17) (9,15) (9,29) (9,25) (9,23) (9,14) (9,27) (10,22) (10,29) (10,25) (10,23) (10,18) (10,13) (10,24) (10,11) (11,22) (11,19) (11,15) (11,29) (11,14) (13,19) (13,17) (13,29) (13,26) (13,23) (13,27) (13,24) (14,17) (14,21) (14,29) (14,23) (14,18) (14,27) (14,28) (15,19) (15,29) (15,25) (17,22) (17,21) (17,26) (17,23) (18,22) (18,29) (18,26) (18,28) (19,22) (19,26) (21,25) (21,28) (22,25) (22,26) (22,23) (22,24) (24,28) (25,28) (26,27) (27,28)\nIs there a path between node 16 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph384-31_3", + "image": "data/connectivity/graph_visual/hard/graph384.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,5) (0,30) (0,29) (0,17) (0,3) (0,22) (0,12) (0,15) (0,27) (1,2) (1,9) (1,31) (1,13) (1,16) (1,20) (1,18) (1,25) (2,9) (2,31) (2,13) (2,21) (2,16) (2,10) (2,20) (3,23) (3,4) (3,5) (3,24) (3,17) (3,7) (3,22) (3,19) (3,15) (3,27) (3,14) (4,23) (4,24) (4,30) (4,29) (4,7) (4,22) (4,26) (4,19) (4,28) (4,15) (4,27) (4,14) (5,23) (5,24) (5,29) (5,7) (5,26) (5,19) (5,12) (5,28) (5,15) (5,27) (6,9) (6,31) (6,13) (6,21) (6,16) (6,10) (6,18) (6,25) (7,23) (7,24) (7,30) (7,29) (7,17) (7,22) (7,28) (7,15) (7,27) (8,11) (9,13) (9,21) (9,16) (9,10) (9,18) (9,25) (10,31) (10,13) (10,21) (10,16) (12,23) (12,30) (12,17) (12,22) (12,26) (12,19) (12,28) (12,27) (13,31) (13,21) (13,25) (14,24) (14,30) (14,29) (14,17) (14,22) (14,19) (14,28) (14,15) (14,27) (15,23) (15,24) (15,17) (15,22) (15,26) (15,28) (15,27) (16,31) (16,18) (16,25) (17,23) (17,24) (17,30) (17,22) (17,28) (18,31) (18,20) (18,25) (19,23) (19,24) (19,29) (19,22) (19,27) (20,31) (21,25) (22,23) (22,30) (22,29) (22,26) (22,28) (22,27) (23,30) (23,29) (23,26) (23,28) (24,30) (24,29) (24,28) (24,27) (25,31) (26,30) (26,29) (26,28) (26,27) (27,28) (28,30) (28,29)\nIs there a path between node 31 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph231-22_5", + "image": "data/connectivity/graph_visual/hard/graph231.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,21) (0,13) (0,14) (0,8) (0,6) (0,3) (0,15) (1,25) (1,27) (1,18) (1,23) (1,19) (1,10) (1,16) (2,20) (2,11) (2,29) (2,4) (2,7) (3,12) (3,17) (3,21) (3,5) (3,13) (3,14) (3,8) (3,24) (3,15) (4,20) (4,28) (4,22) (4,9) (5,26) (5,17) (5,21) (5,13) (5,14) (5,8) (5,6) (5,15) (6,12) (6,26) (6,21) (6,13) (6,14) (6,8) (6,24) (6,15) (7,20) (7,28) (7,11) (7,29) (7,9) (8,12) (8,26) (8,21) (8,14) (8,24) (9,20) (9,28) (9,11) (9,29) (9,22) (10,25) (10,27) (10,18) (10,23) (10,19) (11,20) (11,29) (12,26) (12,17) (12,21) (12,13) (12,24) (12,15) (13,26) (13,17) (13,21) (13,24) (13,15) (14,17) (14,21) (14,24) (14,15) (15,26) (15,21) (15,24) (16,27) (16,18) (16,23) (16,19) (17,26) (17,21) (18,25) (18,27) (18,19) (19,25) (19,27) (19,23) (20,28) (20,29) (20,22) (21,26) (21,24) (22,28) (22,29) (23,25) (23,27) (24,26) (28,29)\nIs there a path between node 22 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph100-13_2", + "image": "data/connectivity/graph_visual/hard/graph100.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,11) (0,20) (1,12) (1,5) (1,2) (1,16) (1,17) (1,25) (1,6) (1,21) (1,7) (1,3) (1,15) (1,23) (1,4) (1,24) (1,9) (1,27) (1,10) (2,8) (2,26) (2,5) (2,19) (2,18) (2,16) (2,6) (2,21) (2,7) (2,3) (2,23) (2,24) (2,9) (2,10) (3,8) (3,26) (3,12) (3,5) (3,22) (3,19) (3,18) (3,17) (3,6) (3,21) (3,7) (3,15) (3,23) (3,4) (3,24) (3,9) (3,27) (3,10) (4,14) (4,26) (4,12) (4,5) (4,22) (4,19) (4,18) (4,16) (4,17) (4,25) (4,6) (4,21) (4,7) (4,15) (4,23) (4,24) (4,9) (4,27) (5,14) (5,26) (5,12) (5,19) (5,16) (5,17) (5,6) (5,21) (5,7) (5,15) (5,23) (5,24) (5,9) (5,27) (6,8) (6,26) (6,12) (6,19) (6,16) (6,17) (6,25) (6,21) (6,7) (6,15) (6,24) (6,9) (6,27) (7,14) (7,26) (7,22) (7,19) (7,18) (7,16) (7,17) (7,25) (7,21) (7,15) (7,23) (7,24) (7,9) (7,27) (8,14) (8,12) (8,22) (8,19) (8,18) (8,16) (8,17) (8,25) (8,21) (8,15) (8,23) (8,24) (8,9) (8,27) (8,10) (9,14) (9,26) (9,12) (9,22) (9,19) (9,18) (9,16) (9,21) (9,15) (9,23) (9,24) (9,27) (9,10) (10,14) (10,26) (10,22) (10,19) (10,18) (10,16) (10,17) (10,25) (10,21) (10,15) (10,23) (10,24) (10,27) (11,20) (11,13) (12,14) (12,26) (12,22) (12,19) (12,18) (12,16) (12,17) (12,25) (12,21) (12,15) (12,23) (13,20) (14,26) (14,22) (14,16) (14,17) (14,15) (14,23) (14,27) (15,26) (15,22) (15,18) (15,16) (15,25) (15,24) (16,26) (16,18) (16,17) (16,23) (16,27) (17,26) (17,19) (17,25) (17,24) (17,27) (18,26) (18,19) (18,25) (18,21) (18,23) (18,24) (18,27) (19,26) (19,25) (19,24) (21,26) (21,22) (21,25) (21,24) (21,27) (22,26) (22,24) (22,27) (23,24) (24,25) (24,27) (25,26) (25,27) (26,27)\nIs there a path between node 13 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph41-4_9", + "image": "data/connectivity/graph_visual/hard/graph41.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,17) (0,2) (0,25) (0,14) (0,9) (0,15) (0,12) (0,1) (0,7) (0,16) (0,18) (0,11) (0,10) (0,5) (1,17) (1,2) (1,21) (1,14) (1,9) (1,15) (1,12) (1,19) (1,8) (1,7) (1,18) (1,11) (1,10) (1,5) (2,17) (2,21) (2,14) (2,9) (2,13) (2,3) (2,12) (2,6) (2,19) (2,7) (2,18) (2,11) (2,5) (3,17) (3,22) (3,21) (3,9) (3,15) (3,13) (3,6) (3,19) (3,8) (3,7) (3,16) (3,18) (3,11) (4,20) (4,23) (4,24) (5,17) (5,22) (5,21) (5,9) (5,15) (5,12) (5,19) (5,8) (5,16) (5,11) (5,10) (6,22) (6,25) (6,9) (6,15) (6,13) (6,12) (6,19) (6,8) (6,7) (6,16) (7,17) (7,22) (7,25) (7,9) (7,15) (7,13) (7,12) (7,19) (7,8) (7,16) (7,11) (7,10) (8,17) (8,22) (8,14) (8,12) (8,16) (8,18) (8,11) (9,17) (9,22) (9,25) (9,15) (9,13) (9,12) (9,19) (9,16) (9,18) (9,11) (10,17) (10,22) (10,25) (10,13) (10,19) (10,11) (11,17) (11,25) (11,14) (11,15) (11,13) (11,12) (11,19) (12,22) (12,21) (12,14) (12,19) (12,16) (13,22) (13,25) (13,21) (13,14) (13,16) (14,17) (14,21) (14,15) (14,19) (14,16) (14,18) (15,17) (15,25) (15,21) (15,16) (16,22) (16,25) (16,21) (16,19) (16,18) (17,22) (17,25) (17,21) (17,19) (17,18) (18,22) (18,21) (18,19) (19,22) (19,25) (19,21) (20,23) (20,24) (21,22) (21,25) (23,24)\nIs there a path between node 4 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph329-22_11", + "image": "data/connectivity/graph_visual/hard/graph329.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,28) (0,2) (0,25) (0,6) (0,27) (0,4) (0,31) (0,9) (0,1) (0,29) (0,10) (0,11) (0,16) (0,21) (1,28) (1,2) (1,25) (1,27) (1,4) (1,31) (1,9) (1,14) (1,11) (1,16) (1,22) (1,20) (2,28) (2,25) (2,6) (2,27) (2,4) (2,9) (2,14) (2,10) (2,19) (2,11) (2,16) (2,20) (2,26) (2,21) (3,24) (3,18) (3,8) (4,28) (4,25) (4,27) (4,31) (4,14) (4,10) (4,19) (4,22) (4,20) (4,26) (4,21) (5,17) (5,12) (5,15) (5,30) (5,13) (6,28) (6,25) (6,27) (6,9) (6,14) (6,29) (6,19) (6,11) (6,16) (6,20) (6,21) (7,24) (7,18) (7,8) (8,24) (9,28) (9,25) (9,31) (9,29) (9,10) (9,19) (9,11) (9,22) (9,20) (9,26) (9,21) (10,25) (10,31) (10,14) (10,11) (10,16) (10,20) (10,26) (10,21) (11,25) (11,27) (11,31) (11,29) (11,19) (11,16) (11,22) (11,26) (12,15) (12,30) (12,13) (13,17) (13,15) (13,30) (14,28) (14,25) (14,27) (14,29) (14,19) (14,16) (14,22) (14,20) (14,26) (14,21) (15,17) (16,28) (16,25) (16,27) (16,31) (16,22) (16,20) (16,21) (19,28) (19,25) (19,27) (19,31) (19,22) (19,20) (19,26) (19,21) (20,28) (20,25) (20,27) (20,31) (20,29) (20,22) (20,26) (20,21) (21,27) (21,29) (21,22) (21,26) (22,28) (22,25) (22,31) (22,29) (22,26) (25,27) (25,31) (25,26) (26,28) (26,27) (27,29) (28,31) (29,31)\nIs there a path between node 22 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph32-22_17", + "image": "data/connectivity/graph_visual/hard/graph32.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,13) (0,12) (0,20) (0,15) (0,4) (0,8) (0,18) (0,24) (0,10) (0,14) (0,9) (0,16) (0,2) (0,7) (0,11) (0,17) (1,20) (1,19) (1,23) (1,5) (1,15) (1,4) (1,18) (1,24) (1,10) (1,14) (1,16) (1,21) (1,7) (1,11) (1,17) (2,13) (2,12) (2,19) (2,5) (2,15) (2,18) (2,24) (2,14) (2,9) (2,21) (2,17) (3,13) (3,20) (3,23) (3,15) (3,4) (3,18) (3,24) (3,14) (3,9) (3,16) (3,21) (3,7) (3,11) (4,13) (4,12) (4,20) (4,19) (4,15) (4,24) (4,10) (4,9) (4,16) (4,7) (4,11) (4,17) (5,12) (5,20) (5,19) (5,23) (5,15) (5,18) (5,24) (5,10) (5,14) (5,9) (5,21) (5,7) (5,17) (6,22) (7,12) (7,20) (7,19) (7,23) (7,15) (7,8) (7,18) (7,24) (7,10) (7,14) (7,9) (7,21) (7,11) (8,13) (8,15) (8,18) (8,24) (8,10) (8,14) (8,16) (8,17) (9,19) (9,23) (9,15) (9,18) (9,24) (9,10) (9,21) (9,17) (10,13) (10,23) (10,15) (10,24) (10,14) (10,21) (10,11) (11,13) (11,12) (11,20) (11,19) (11,23) (11,15) (11,18) (11,14) (11,16) (11,21) (12,13) (12,20) (12,15) (12,24) (12,14) (12,16) (12,21) (12,17) (13,20) (13,19) (13,15) (13,18) (13,21) (13,17) (14,20) (14,19) (14,23) (14,15) (14,18) (14,16) (14,17) (15,20) (15,19) (15,23) (15,18) (15,24) (15,17) (16,19) (16,23) (16,18) (17,20) (17,19) (17,24) (18,20) (18,19) (18,21) (19,20) (19,23) (19,24) (19,21) (20,23) (20,24) (20,21) (21,23) (21,24) (22,25) (23,24)\nIs there a path between node 22 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph568-26_15", + "image": "data/connectivity/graph_visual/hard/graph568.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,17) (0,26) (0,2) (0,5) (0,4) (0,25) (0,18) (0,29) (1,24) (1,6) (1,21) (2,22) (2,8) (2,30) (2,17) (2,33) (2,26) (2,11) (2,7) (2,5) (2,23) (2,18) (2,29) (3,27) (4,13) (4,9) (4,33) (4,11) (4,5) (4,23) (4,25) (4,29) (5,22) (5,16) (5,30) (5,9) (5,19) (5,10) (5,15) (5,29) (6,24) (6,31) (7,17) (7,23) (7,25) (8,16) (8,32) (8,10) (8,18) (8,29) (9,22) (9,30) (9,23) (10,22) (10,16) (10,19) (11,22) (11,13) (11,30) (11,33) (11,23) (11,18) (12,28) (12,31) (13,30) (13,32) (13,23) (14,17) (14,32) (14,23) (14,25) (14,15) (14,29) (15,16) (15,33) (15,32) (15,18) (16,22) (16,17) (16,32) (16,23) (16,18) (16,29) (17,32) (17,18) (17,29) (18,19) (18,32) (18,23) (19,29) (20,24) (20,21) (21,27) (22,32) (22,25) (25,33) (25,26) (25,29) (26,33) (26,29) (27,28) (28,31) (29,30)\nIs there a path between node 26 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph131-26_6", + "image": "data/connectivity/graph_visual/hard/graph131.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,7) (0,18) (0,14) (0,6) (0,13) (1,12) (1,2) (1,11) (1,16) (1,21) (1,20) (1,4) (1,10) (1,27) (2,15) (2,12) (2,11) (2,16) (2,21) (2,17) (2,20) (2,4) (2,10) (3,19) (4,15) (4,16) (4,21) (4,17) (4,20) (4,5) (4,10) (5,15) (5,12) (5,16) (5,21) (5,17) (5,10) (5,27) (6,26) (6,8) (6,23) (6,9) (6,18) (7,26) (7,8) (7,9) (7,25) (8,26) (8,23) (8,18) (8,25) (8,14) (8,13) (9,25) (9,14) (10,15) (10,12) (10,11) (11,12) (11,16) (11,21) (11,17) (11,20) (11,27) (12,15) (12,16) (12,21) (12,20) (12,27) (13,23) (13,18) (13,25) (13,14) (14,26) (14,25) (15,16) (15,21) (15,17) (15,20) (15,27) (16,17) (16,20) (16,27) (17,21) (17,20) (17,27) (18,26) (18,25) (19,22) (20,21) (20,27) (23,26) (23,25) (25,26)\nIs there a path between node 26 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph703-21_16", + "image": "data/connectivity/graph_visual/hard/graph703.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,20) (0,22) (0,9) (0,29) (0,7) (0,8) (1,3) (1,26) (1,2) (1,19) (1,6) (1,27) (1,18) (1,25) (1,17) (1,16) (1,31) (1,12) (1,21) (1,34) (2,23) (2,28) (2,19) (2,6) (2,5) (2,27) (2,24) (2,11) (2,18) (2,17) (2,33) (2,12) (2,4) (2,21) (3,26) (3,19) (3,27) (3,24) (3,11) (3,18) (3,25) (3,17) (3,16) (3,31) (3,12) (3,4) (3,21) (4,28) (4,5) (4,27) (4,24) (4,18) (4,25) (4,17) (4,34) (5,23) (5,28) (5,26) (5,19) (5,6) (5,25) (5,17) (5,16) (5,31) (5,34) (6,28) (6,19) (6,24) (6,11) (6,18) (6,17) (6,31) (6,12) (6,21) (7,32) (7,22) (7,9) (7,29) (8,32) (8,20) (8,9) (9,20) (10,13) (10,15) (10,14) (11,28) (11,19) (11,27) (11,18) (11,17) (11,16) (11,31) (11,12) (12,28) (12,19) (12,27) (12,24) (12,18) (12,25) (12,17) (12,31) (12,34) (13,30) (13,15) (13,14) (14,30) (14,15) (16,23) (16,28) (16,26) (16,24) (16,25) (16,33) (16,31) (16,21) (16,34) (17,23) (17,26) (17,19) (17,27) (17,24) (17,18) (17,25) (17,33) (17,31) (17,21) (17,34) (18,23) (18,28) (18,26) (18,27) (18,24) (18,25) (18,33) (18,34) (19,23) (19,28) (19,27) (19,24) (19,25) (19,33) (19,21) (19,34) (20,29) (21,23) (21,27) (21,25) (21,33) (21,31) (22,32) (22,29) (23,28) (23,26) (23,27) (23,24) (23,25) (23,33) (23,31) (23,34) (24,26) (24,25) (24,33) (24,31) (25,26) (25,34) (26,28) (26,33) (26,31) (26,34) (27,28) (27,33) (27,31) (27,34) (28,33) (28,31) (28,34) (29,32) (33,34)\nIs there a path between node 21 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph325-24_25", + "image": "data/connectivity/graph_visual/hard/graph325.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,23) (0,8) (0,27) (0,12) (0,10) (0,24) (0,7) (1,13) (1,11) (1,26) (1,20) (1,30) (1,16) (1,5) (1,25) (1,14) (1,28) (1,21) (2,19) (2,27) (2,10) (2,24) (3,13) (3,11) (3,26) (3,20) (3,30) (3,25) (3,17) (3,21) (4,13) (4,11) (4,26) (4,20) (4,30) (4,31) (4,5) (4,25) (4,17) (4,14) (4,28) (4,21) (5,13) (5,11) (5,26) (5,20) (5,16) (5,25) (5,17) (5,28) (5,21) (6,18) (6,22) (6,15) (7,9) (7,27) (7,12) (7,24) (8,9) (8,27) (8,12) (8,24) (9,23) (9,19) (9,12) (9,10) (9,24) (10,23) (10,27) (10,12) (10,24) (11,13) (11,26) (11,20) (11,30) (11,31) (11,25) (11,28) (11,21) (12,23) (12,19) (12,24) (13,20) (13,31) (13,25) (13,17) (13,21) (14,26) (14,20) (14,30) (14,25) (14,17) (14,28) (14,21) (15,18) (15,22) (16,26) (16,20) (16,30) (16,31) (16,25) (16,17) (16,21) (17,20) (17,30) (17,31) (17,25) (17,21) (19,23) (19,27) (19,24) (20,26) (20,31) (20,25) (20,21) (21,26) (21,30) (21,31) (21,25) (23,27) (24,27) (25,26) (25,30) (25,28) (26,31) (26,28) (28,30) (30,31)\nIs there a path between node 24 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph67-12_2", + "image": "data/connectivity/graph_visual/hard/graph67.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,2) (0,12) (0,8) (1,23) (1,22) (1,26) (1,24) (1,13) (2,12) (2,20) (3,12) (3,20) (4,15) (4,10) (4,21) (5,11) (6,11) (7,10) (9,13) (10,15) (11,18) (11,19) (13,23) (13,26) (16,23) (16,26) (17,26) (22,26) (23,26) (23,24)\nIs there a path between node 12 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph99-12_14", + "image": "data/connectivity/graph_visual/hard/graph99.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,1) (0,13) (0,22) (0,23) (0,9) (0,18) (0,7) (0,2) (0,15) (0,10) (0,16) (0,21) (0,4) (0,25) (0,27) (1,8) (1,13) (1,14) (1,22) (1,6) (1,24) (1,9) (1,18) (1,7) (1,2) (1,15) (1,26) (1,10) (1,12) (1,16) (1,11) (1,4) (1,5) (2,13) (2,14) (2,23) (2,6) (2,24) (2,9) (2,12) (2,16) (2,21) (2,11) (2,4) (2,25) (3,19) (4,8) (4,13) (4,14) (4,22) (4,6) (4,24) (4,18) (4,7) (4,15) (4,20) (4,16) (4,21) (4,11) (4,17) (4,27) (5,8) (5,13) (5,14) (5,23) (5,6) (5,9) (5,18) (5,7) (5,15) (5,26) (5,20) (5,12) (5,16) (5,21) (6,8) (6,13) (6,14) (6,22) (6,24) (6,9) (6,18) (6,7) (6,15) (6,26) (6,20) (6,10) (6,25) (6,17) (6,27) (7,8) (7,13) (7,14) (7,22) (7,24) (7,9) (7,15) (7,26) (7,10) (7,11) (7,25) (7,17) (8,13) (8,14) (8,22) (8,23) (8,24) (8,9) (8,26) (8,10) (8,12) (8,11) (8,25) (8,17) (9,14) (9,22) (9,23) (9,24) (9,18) (9,15) (9,26) (9,16) (9,21) (9,11) (9,25) (10,23) (10,24) (10,18) (10,15) (10,12) (10,21) (10,25) (10,17) (10,27) (11,14) (11,22) (11,15) (11,26) (11,20) (11,12) (11,21) (11,25) (11,17) (11,27) (12,13) (12,14) (12,22) (12,23) (12,24) (12,18) (12,15) (12,26) (12,16) (12,21) (12,17) (13,14) (13,22) (13,24) (13,26) (13,20) (13,16) (13,25) (13,17) (13,27) (14,22) (14,18) (14,15) (14,26) (14,20) (14,16) (14,25) (15,23) (15,24) (15,18) (15,26) (15,20) (15,16) (15,21) (15,25) (15,17) (15,27) (16,22) (16,26) (16,20) (16,21) (16,25) (16,17) (16,27) (17,22) (17,23) (17,25) (18,22) (18,23) (18,24) (18,26) (18,21) (18,25) (20,26) (20,21) (21,23) (21,26) (21,25) (21,27) (22,23) (22,26) (22,27) (23,24) (23,27) (24,26) (24,27) (25,27) (26,27)\nIs there a path between node 12 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph538-8_21", + "image": "data/connectivity/graph_visual/hard/graph538.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,17) (0,4) (0,11) (0,9) (0,3) (0,13) (0,16) (0,31) (0,23) (0,6) (0,14) (0,30) (0,27) (0,5) (0,2) (0,24) (0,10) (0,28) (0,7) (0,26) (1,15) (1,22) (1,8) (2,17) (2,4) (2,3) (2,13) (2,12) (2,16) (2,18) (2,32) (2,31) (2,6) (2,14) (2,19) (2,24) (2,21) (2,10) (2,28) (2,7) (2,26) (2,25) (2,29) (3,17) (3,11) (3,9) (3,12) (3,18) (3,20) (3,32) (3,31) (3,6) (3,14) (3,19) (3,30) (3,5) (3,21) (3,7) (3,25) (4,11) (4,9) (4,16) (4,18) (4,20) (4,31) (4,23) (4,6) (4,14) (4,19) (4,30) (4,27) (4,5) (4,24) (4,21) (4,28) (4,7) (4,25) (4,29) (5,11) (5,9) (5,13) (5,12) (5,16) (5,18) (5,32) (5,31) (5,14) (5,19) (5,28) (5,7) (5,25) (5,29) (6,11) (6,12) (6,16) (6,20) (6,31) (6,23) (6,14) (6,19) (6,30) (6,24) (6,21) (6,10) (6,28) (6,7) (6,25) (6,29) (7,11) (7,13) (7,18) (7,20) (7,32) (7,31) (7,23) (7,14) (7,19) (7,30) (7,27) (7,24) (7,21) (7,10) (7,25) (7,29) (8,15) (9,17) (9,16) (9,32) (9,31) (9,23) (9,14) (9,19) (9,30) (9,27) (9,21) (9,10) (9,28) (9,26) (10,17) (10,11) (10,12) (10,18) (10,20) (10,32) (10,30) (10,24) (10,28) (10,26) (10,25) (11,17) (11,13) (11,12) (11,18) (11,31) (11,23) (11,19) (11,30) (11,27) (11,24) (11,28) (11,26) (11,25) (11,29) (12,17) (12,13) (12,16) (12,20) (12,32) (12,31) (12,23) (12,19) (12,24) (12,21) (12,28) (12,26) (12,25) (12,29) (13,16) (13,18) (13,20) (13,32) (13,31) (13,14) (13,19) (13,30) (13,24) (13,26) (13,29) (14,17) (14,16) (14,18) (14,20) (14,31) (14,19) (14,30) (14,24) (14,21) (14,26) (14,25) (14,29) (15,22) (16,17) (16,18) (16,20) (16,32) (16,31) (16,23) (16,19) (16,30) (16,21) (16,28) (16,26) (16,29) (17,20) (17,23) (17,19) (17,27) (17,24) (17,21) (17,28) (17,29) (18,27) (18,24) (18,28) (18,26) (19,20) (19,31) (19,23) (19,21) (19,28) (19,26) (19,25) (20,32) (20,23) (20,24) (20,21) (20,28) (20,25) (20,29) (21,32) (21,31) (21,23) (21,30) (21,27) (21,24) (21,28) (21,25) (21,29) (22,33) (23,30) (23,27) (23,24) (23,28) (23,25) (24,32) (24,31) (24,30) (24,27) (24,28) (24,26) (24,29) (25,32) (25,30) (25,26) (25,29) (26,32) (26,31) (26,30) (26,27) (27,32) (27,30) (27,28) (27,29) (28,32) (28,31) (28,30) (28,29) (29,32) (30,32) (30,31) (31,32)\nIs there a path between node 8 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph155-23_18", + "image": "data/connectivity/graph_visual/hard/graph155.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,9) (0,15) (1,5) (1,22) (1,4) (1,20) (1,12) (1,25) (2,5) (2,22) (2,13) (2,12) (2,10) (3,23) (4,19) (4,14) (4,18) (4,28) (4,11) (5,12) (5,24) (5,28) (6,16) (6,17) (7,15) (8,15) (10,19) (10,14) (10,24) (10,28) (11,22) (11,19) (12,13) (12,27) (12,20) (13,19) (13,20) (13,25) (14,26) (14,18) (14,24) (14,25) (17,21) (18,26) (18,27) (18,20) (18,28) (18,25) (19,26) (19,27) (19,24) (19,28) (20,27) (20,24) (24,28) (26,28)\nIs there a path between node 23 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph3-20_7", + "image": "data/connectivity/graph_visual/hard/graph3.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,2) (0,10) (0,6) (0,8) (0,17) (0,25) (2,23) (2,21) (2,24) (2,15) (2,5) (2,22) (2,12) (2,19) (3,23) (3,8) (3,16) (4,14) (4,23) (4,10) (4,6) (4,8) (4,17) (4,16) (5,14) (5,18) (5,15) (5,10) (5,17) (6,22) (8,14) (8,23) (8,21) (8,24) (8,10) (9,18) (9,15) (9,22) (9,17) (10,20) (10,14) (10,23) (11,20) (11,14) (11,23) (11,22) (11,12) (11,17) (12,22) (12,17) (14,24) (15,23) (15,24) (15,25) (16,21) (16,24) (16,18) (17,20) (17,23) (17,21) (17,24) (18,20) (18,19) (19,20) (19,24) (19,22) (19,25) (20,23) (20,21) (22,25) (23,25)\nIs there a path between node 20 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph309-8_30", + "image": "data/connectivity/graph_visual/hard/graph309.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,1) (0,12) (0,20) (0,31) (0,16) (0,24) (0,26) (1,31) (1,8) (1,18) (2,22) (3,10) (3,6) (3,19) (4,27) (5,14) (5,25) (5,11) (6,10) (6,7) (8,12) (8,29) (8,23) (8,15) (9,27) (10,22) (10,17) (11,25) (12,30) (12,23) (12,15) (13,22) (13,19) (14,25) (14,27) (15,16) (15,29) (15,23) (15,28) (16,31) (16,30) (16,24) (17,19) (18,20) (18,26) (18,28) (20,29) (20,26) (23,31) (23,30) (23,26) (23,28) (26,29) (26,28) (28,30)\nIs there a path between node 8 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph517-32_16", + "image": "data/connectivity/graph_visual/hard/graph517.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,22) (0,28) (0,25) (0,14) (0,29) (1,22) (1,31) (1,7) (1,25) (1,16) (1,14) (2,13) (2,22) (2,21) (2,31) (2,11) (2,4) (2,20) (3,33) (4,17) (4,13) (4,7) (4,8) (4,24) (4,25) (4,16) (4,29) (5,17) (5,13) (5,24) (5,6) (6,21) (6,7) (6,24) (7,28) (7,8) (7,16) (8,20) (9,21) (9,16) (9,20) (10,26) (10,19) (10,12) (10,32) (10,18) (11,21) (11,14) (12,19) (14,28) (14,24) (14,16) (15,30) (16,22) (16,24) (16,25) (17,28) (17,24) (17,29) (17,20) (18,32) (20,31) (20,24) (21,22) (21,29) (22,31) (22,29) (23,26) (23,32) (24,28) (27,32) (28,29) (29,31)\nIs there a path between node 32 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph585-31_19", + "image": "data/connectivity/graph_visual/hard/graph585.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,9) (0,27) (0,18) (0,16) (0,5) (0,21) (0,29) (0,24) (1,10) (1,7) (1,15) (2,31) (2,14) (2,25) (2,23) (2,11) (2,20) (3,33) (3,4) (4,33) (4,13) (4,32) (5,9) (5,27) (5,12) (5,26) (5,21) (5,29) (5,24) (6,31) (6,14) (6,19) (6,20) (7,10) (7,8) (8,28) (8,10) (8,15) (9,27) (9,18) (9,12) (9,16) (9,29) (9,24) (10,28) (10,15) (11,25) (11,19) (11,20) (12,16) (12,26) (12,21) (12,24) (13,22) (13,33) (14,31) (14,25) (14,20) (16,26) (16,21) (16,29) (16,24) (17,22) (17,33) (17,32) (18,27) (18,26) (18,21) (18,29) (18,24) (19,31) (19,23) (19,20) (20,31) (20,25) (20,23) (21,26) (21,29) (21,24) (22,30) (22,32) (25,31) (26,27) (26,29) (27,29) (30,33) (30,32) (32,33)\nIs there a path between node 31 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph310-17_29", + "image": "data/connectivity/graph_visual/hard/graph310.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,16) (0,29) (0,2) (0,24) (1,7) (2,23) (2,12) (2,4) (2,8) (2,10) (3,17) (3,26) (3,27) (4,11) (4,12) (4,5) (5,31) (5,16) (5,28) (6,16) (6,11) (6,14) (6,28) (8,31) (8,11) (8,12) (10,11) (10,14) (11,31) (12,16) (12,23) (13,19) (13,20) (13,26) (14,16) (14,29) (15,19) (16,29) (16,23) (18,27) (19,20) (19,27) (19,22) (21,23) (23,28) (25,29)\nIs there a path between node 17 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph537-24_32", + "image": "data/connectivity/graph_visual/hard/graph537.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,16) (0,17) (0,4) (0,8) (0,12) (0,31) (1,19) (1,21) (1,2) (1,30) (1,26) (1,3) (1,9) (1,22) (1,6) (1,23) (1,18) (2,21) (2,28) (2,26) (2,3) (2,25) (2,20) (2,33) (2,9) (2,22) (2,6) (2,15) (2,7) (2,23) (2,18) (3,19) (3,30) (3,28) (3,26) (3,22) (3,32) (3,6) (3,15) (3,23) (3,18) (4,10) (4,16) (4,17) (4,5) (4,8) (4,12) (5,10) (5,13) (5,24) (5,16) (5,31) (6,19) (6,14) (6,30) (6,26) (6,25) (6,20) (6,11) (6,9) (6,22) (6,27) (6,32) (6,15) (6,29) (7,21) (7,30) (7,28) (7,26) (7,25) (7,33) (7,22) (7,27) (7,32) (7,15) (7,29) (7,23) (7,18) (8,13) (8,24) (8,16) (8,17) (8,31) (9,19) (9,21) (9,30) (9,20) (9,11) (9,22) (9,15) (9,23) (9,18) (10,13) (10,24) (10,16) (10,17) (10,12) (10,31) (11,19) (11,21) (11,14) (11,28) (11,26) (11,25) (11,20) (11,22) (11,32) (11,15) (11,29) (11,23) (11,18) (12,24) (12,17) (13,24) (13,16) (13,17) (14,19) (14,21) (14,30) (14,28) (14,25) (14,20) (14,33) (14,32) (14,15) (14,29) (14,23) (14,18) (15,30) (15,28) (15,26) (15,25) (15,20) (15,33) (15,22) (15,32) (15,29) (15,23) (15,18) (16,24) (16,17) (17,31) (18,19) (18,28) (18,26) (18,20) (18,33) (18,22) (18,27) (18,29) (18,23) (19,21) (19,28) (19,26) (19,20) (19,22) (19,29) (19,23) (20,21) (20,30) (20,26) (20,25) (20,22) (20,32) (20,29) (20,23) (21,28) (21,33) (21,22) (21,27) (21,32) (21,29) (22,30) (22,28) (22,26) (22,25) (22,27) (22,32) (22,23) (23,30) (23,28) (23,26) (23,33) (23,27) (23,32) (23,29) (24,31) (25,30) (25,26) (25,33) (25,27) (25,32) (25,29) (26,28) (26,27) (26,32) (26,29) (27,30) (27,28) (27,32) (27,29) (28,30) (28,33) (28,29) (29,32) (30,32) (32,33)\nIs there a path between node 24 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph452-3_5", + "image": "data/connectivity/graph_visual/hard/graph452.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,20) (0,27) (0,5) (0,16) (0,8) (0,30) (0,3) (0,31) (1,7) (1,4) (1,18) (2,17) (2,21) (2,23) (2,26) (2,30) (2,14) (2,11) (2,29) (2,31) (3,19) (3,20) (3,28) (3,16) (3,23) (3,10) (3,26) (3,32) (3,14) (3,6) (3,9) (5,19) (5,20) (5,23) (5,32) (5,29) (6,15) (6,13) (6,26) (6,22) (7,18) (8,15) (8,17) (8,10) (8,26) (8,30) (8,29) (8,31) (9,20) (9,13) (9,23) (9,14) (9,22) (10,15) (10,13) (10,21) (10,25) (10,26) (10,31) (11,15) (11,28) (11,16) (11,17) (11,25) (11,22) (12,24) (13,19) (13,15) (13,27) (13,28) (13,25) (13,26) (14,19) (14,27) (14,32) (14,29) (14,22) (15,27) (15,23) (15,26) (15,32) (16,23) (16,29) (16,22) (16,31) (17,27) (17,21) (19,27) (19,32) (19,31) (21,25) (21,32) (21,29) (21,22) (21,31) (22,23) (22,30) (23,27) (23,28) (25,32) (26,28) (26,29) (28,30) (28,29) (31,32)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph490-25_21", + "image": "data/connectivity/graph_visual/hard/graph490.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (0,8) (0,9) (0,17) (0,14) (0,7) (0,3) (1,8) (1,15) (1,9) (1,16) (1,17) (1,14) (1,19) (1,2) (1,7) (1,3) (2,8) (2,15) (2,25) (2,9) (2,16) (2,17) (2,14) (2,19) (2,3) (3,23) (3,8) (3,15) (3,25) (3,9) (3,7) (4,30) (4,10) (4,32) (4,22) (4,6) (4,18) (4,31) (4,21) (4,24) (4,27) (4,20) (4,28) (4,26) (4,5) (5,30) (5,11) (5,10) (5,6) (5,18) (5,31) (5,21) (5,24) (5,20) (5,28) (5,29) (6,11) (6,32) (6,22) (6,18) (6,31) (6,21) (6,27) (6,13) (6,20) (6,28) (6,26) (6,29) (7,23) (7,8) (7,15) (7,25) (7,16) (7,14) (7,19) (8,23) (8,15) (8,25) (8,16) (8,17) (8,14) (8,19) (9,23) (9,16) (9,17) (9,14) (9,19) (10,30) (10,32) (10,22) (10,18) (10,31) (10,21) (10,24) (10,27) (10,13) (10,20) (10,28) (10,26) (10,29) (11,30) (11,32) (11,22) (11,18) (11,31) (11,21) (11,12) (11,24) (11,20) (11,28) (11,26) (11,29) (12,30) (12,22) (12,31) (12,21) (12,24) (12,13) (12,28) (12,26) (13,30) (13,32) (13,18) (13,21) (13,24) (13,27) (13,20) (13,28) (13,26) (13,29) (14,23) (14,15) (14,25) (14,16) (14,17) (14,19) (15,23) (15,25) (15,16) (15,17) (15,19) (16,23) (16,25) (16,19) (17,23) (17,25) (18,30) (18,32) (18,22) (18,31) (18,21) (18,27) (18,20) (18,28) (18,26) (19,23) (20,32) (20,22) (20,31) (20,21) (20,28) (20,26) (20,29) (21,30) (21,32) (21,24) (21,27) (21,28) (21,29) (22,32) (22,31) (22,24) (22,27) (22,28) (22,26) (24,32) (24,31) (24,28) (24,26) (26,30) (26,32) (26,27) (26,29) (27,30) (27,32) (27,31) (27,28) (27,29) (28,32) (28,31) (28,29) (29,32) (29,31) (30,32) (30,31) (31,32)\nIs there a path between node 25 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph304-13_20", + "image": "data/connectivity/graph_visual/hard/graph304.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,5) (0,17) (0,24) (1,11) (1,9) (1,3) (2,19) (2,29) (2,27) (3,7) (3,20) (4,23) (4,25) (5,17) (6,22) (7,29) (7,27) (7,9) (8,16) (8,30) (8,26) (8,18) (8,31) (9,11) (9,27) (10,13) (10,12) (11,19) (11,27) (12,26) (12,18) (14,28) (15,27) (16,30) (17,23) (18,26) (19,28) (20,29) (21,22) (23,24) (24,25) (27,28) (30,31)\nIs there a path between node 13 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph158-14_20", + "image": "data/connectivity/graph_visual/hard/graph158.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,21) (0,2) (0,13) (0,26) (1,24) (1,22) (1,17) (2,11) (2,15) (2,10) (2,19) (3,4) (3,6) (3,22) (3,17) (3,20) (4,8) (4,24) (5,8) (5,24) (5,20) (6,8) (6,22) (6,20) (6,7) (7,24) (7,22) (7,25) (9,11) (9,12) (9,18) (9,23) (9,14) (9,19) (9,26) (10,19) (10,28) (11,21) (11,14) (11,15) (11,19) (11,16) (11,28) (11,26) (12,26) (13,28) (14,18) (15,21) (15,18) (15,23) (17,27) (17,24) (17,25) (17,20) (19,21) (19,23) (19,26) (20,22) (23,26)\nIs there a path between node 14 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph89-20_24", + "image": "data/connectivity/graph_visual/hard/graph89.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,7) (0,9) (0,8) (0,19) (0,13) (0,11) (1,15) (1,6) (1,3) (1,12) (1,4) (1,2) (1,23) (1,5) (1,16) (1,22) (1,17) (1,18) (1,21) (1,24) (1,25) (2,15) (2,3) (2,4) (2,20) (2,23) (2,22) (2,27) (2,18) (2,21) (2,24) (3,15) (3,4) (3,26) (3,20) (3,23) (3,5) (3,16) (3,14) (3,22) (3,27) (3,18) (3,21) (3,24) (3,25) (4,15) (4,6) (4,12) (4,26) (4,20) (4,5) (4,22) (4,27) (4,17) (4,21) (4,25) (5,15) (5,6) (5,12) (5,20) (5,16) (5,14) (5,22) (5,27) (5,18) (5,21) (5,25) (6,15) (6,12) (6,27) (6,17) (6,21) (6,24) (6,25) (7,19) (7,13) (8,9) (8,19) (8,13) (9,19) (9,10) (10,19) (10,13) (10,11) (11,13) (12,15) (12,26) (12,20) (12,14) (12,22) (12,21) (12,24) (13,19) (14,15) (14,26) (14,20) (14,16) (14,22) (14,17) (14,21) (14,24) (14,25) (15,26) (15,20) (15,23) (15,16) (15,22) (15,17) (15,18) (15,24) (16,26) (16,27) (16,18) (16,25) (17,26) (17,23) (17,18) (17,21) (17,24) (17,25) (18,26) (18,20) (18,22) (18,27) (18,24) (18,25) (20,26) (20,23) (20,22) (20,27) (20,24) (20,25) (21,22) (21,27) (21,24) (21,25) (22,23) (22,27) (22,24) (22,25) (23,27) (23,25) (24,26) (24,27) (25,26) (25,27) (26,27)\nIs there a path between node 20 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph292-5_15", + "image": "data/connectivity/graph_visual/hard/graph292.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,29) (0,7) (0,26) (1,20) (1,21) (1,24) (2,13) (3,17) (3,25) (3,26) (4,20) (4,27) (4,24) (5,9) (5,12) (5,8) (6,9) (6,7) (6,26) (6,22) (7,10) (7,9) (7,12) (7,25) (7,22) (8,9) (8,29) (8,22) (9,17) (9,10) (9,25) (10,17) (10,16) (10,29) (10,18) (10,25) (10,22) (11,13) (12,29) (12,26) (13,23) (13,30) (13,28) (13,27) (14,15) (14,19) (15,31) (16,25) (18,26) (18,22) (19,31) (20,27) (20,21) (21,23) (21,30) (21,27) (23,28) (23,27)\nIs there a path between node 5 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph12-15_17", + "image": "data/connectivity/graph_visual/hard/graph12.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,25) (0,7) (0,15) (0,3) (0,17) (0,23) (0,2) (0,19) (0,16) (0,6) (0,4) (0,22) (0,1) (0,8) (0,13) (0,21) (1,25) (1,11) (1,7) (1,20) (1,5) (1,15) (1,3) (1,23) (1,12) (1,18) (1,2) (1,19) (1,9) (1,16) (1,4) (1,22) (1,13) (1,21) (2,11) (2,5) (2,3) (2,17) (2,23) (2,12) (2,19) (2,9) (2,16) (2,6) (2,22) (2,8) (2,13) (2,21) (3,25) (3,11) (3,5) (3,15) (3,23) (3,12) (3,18) (3,19) (3,9) (3,16) (3,4) (3,22) (3,8) (3,13) (4,11) (4,20) (4,5) (4,15) (4,17) (4,23) (4,12) (4,18) (4,19) (4,9) (4,16) (4,6) (4,22) (5,15) (5,17) (5,18) (5,19) (5,9) (5,16) (5,6) (5,22) (5,13) (5,21) (6,11) (6,7) (6,20) (6,15) (6,23) (6,12) (6,19) (6,9) (6,16) (6,22) (6,8) (6,13) (6,21) (7,11) (7,15) (7,23) (7,12) (7,19) (7,9) (7,16) (7,8) (7,13) (8,25) (8,11) (8,15) (8,17) (8,12) (8,18) (8,19) (8,9) (8,22) (8,13) (8,21) (9,25) (9,11) (9,15) (9,17) (9,23) (9,12) (9,18) (9,19) (9,16) (9,22) (10,24) (10,14) (11,25) (11,20) (11,23) (11,12) (11,18) (11,19) (11,13) (11,21) (12,25) (12,20) (12,15) (12,17) (12,23) (12,18) (12,19) (12,16) (12,21) (13,25) (13,20) (13,15) (13,23) (13,18) (13,16) (13,22) (14,24) (15,20) (15,17) (15,23) (15,18) (15,19) (15,16) (15,22) (15,21) (16,25) (16,20) (16,17) (16,23) (16,18) (16,19) (16,22) (17,25) (17,20) (17,23) (17,19) (17,22) (17,21) (18,25) (18,20) (19,25) (19,20) (19,22) (20,25) (20,21) (21,25) (21,22) (22,25) (23,25)\nIs there a path between node 15 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph267-8_21", + "image": "data/connectivity/graph_visual/hard/graph267.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,3) (0,16) (0,21) (0,15) (1,18) (1,11) (1,22) (1,30) (1,12) (2,3) (2,25) (2,7) (3,17) (3,25) (3,19) (4,22) (4,30) (5,28) (7,16) (7,25) (7,14) (7,21) (7,19) (7,27) (8,9) (10,13) (10,30) (10,12) (10,26) (11,18) (11,30) (11,26) (12,29) (12,18) (12,30) (15,17) (15,25) (15,19) (17,25) (18,22) (18,26) (19,27) (20,28) (22,29) (24,26) (26,29)\nIs there a path between node 8 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph331-29_30", + "image": "data/connectivity/graph_visual/hard/graph331.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,16) (0,12) (0,23) (0,10) (0,31) (0,3) (0,26) (0,22) (0,6) (0,25) (0,14) (0,24) (0,5) (1,29) (1,7) (1,16) (1,27) (1,12) (1,23) (1,31) (1,3) (1,19) (1,15) (1,9) (1,26) (1,6) (1,28) (1,13) (1,14) (1,24) (1,5) (2,20) (2,4) (2,17) (2,21) (2,30) (3,29) (3,7) (3,16) (3,27) (3,23) (3,31) (3,19) (3,15) (3,26) (3,6) (3,25) (3,28) (3,8) (3,13) (3,14) (3,24) (3,5) (4,20) (4,18) (4,30) (5,29) (5,7) (5,27) (5,12) (5,10) (5,9) (5,11) (5,26) (5,6) (5,28) (5,14) (5,24) (6,7) (6,16) (6,27) (6,23) (6,10) (6,15) (6,11) (6,26) (6,22) (6,25) (6,28) (6,13) (6,14) (7,29) (7,12) (7,23) (7,19) (7,15) (7,26) (7,22) (7,13) (7,14) (7,24) (8,29) (8,27) (8,23) (8,10) (8,19) (8,9) (8,11) (8,26) (8,22) (8,25) (8,14) (9,29) (9,12) (9,23) (9,10) (9,31) (9,19) (9,15) (9,22) (9,13) (9,24) (10,27) (10,12) (10,15) (10,11) (10,26) (10,25) (10,28) (10,13) (10,14) (11,29) (11,16) (11,27) (11,12) (11,23) (11,19) (11,15) (11,26) (11,28) (11,14) (11,24) (12,29) (12,23) (12,31) (12,19) (12,26) (12,22) (12,25) (12,28) (12,13) (12,24) (13,29) (13,16) (13,27) (13,31) (13,19) (13,22) (13,28) (13,14) (13,24) (14,29) (14,16) (14,27) (14,23) (14,31) (14,19) (14,26) (14,22) (14,25) (14,28) (14,24) (15,29) (15,16) (15,31) (15,19) (15,26) (15,22) (15,25) (15,28) (15,24) (16,29) (16,31) (16,26) (16,22) (16,25) (16,28) (16,24) (17,20) (17,18) (17,21) (17,30) (18,21) (18,30) (19,29) (19,27) (19,23) (19,22) (19,25) (20,21) (21,30) (22,29) (22,27) (22,23) (22,31) (22,25) (22,28) (22,24) (23,29) (23,27) (23,31) (23,24) (24,29) (24,27) (24,31) (24,26) (24,25) (24,28) (25,29) (25,27) (25,31) (25,28) (26,29) (26,27) (26,31) (27,29) (27,28) (28,29) (29,31)\nIs there a path between node 29 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph601-1_7", + "image": "data/connectivity/graph_visual/hard/graph601.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,25) (0,3) (1,25) (1,29) (2,14) (2,13) (2,20) (2,18) (2,31) (2,9) (2,27) (2,21) (2,12) (2,7) (2,33) (2,11) (2,24) (2,26) (2,30) (3,25) (4,23) (4,22) (4,34) (4,5) (5,23) (5,22) (5,34) (6,14) (6,13) (6,20) (6,18) (6,27) (6,21) (6,12) (6,7) (6,28) (6,24) (6,26) (6,30) (7,14) (7,13) (7,20) (7,31) (7,17) (7,9) (7,27) (7,21) (7,12) (7,10) (7,33) (7,28) (7,30) (8,14) (8,13) (8,31) (8,17) (8,9) (8,27) (8,12) (8,33) (8,11) (8,28) (8,26) (8,30) (9,14) (9,13) (9,20) (9,18) (9,27) (9,21) (9,12) (9,10) (9,33) (9,24) (9,26) (9,19) (9,30) (10,13) (10,20) (10,18) (10,31) (10,17) (10,27) (10,12) (10,33) (10,11) (10,28) (10,24) (11,14) (11,13) (11,20) (11,18) (11,31) (11,12) (11,33) (11,28) (11,24) (11,26) (11,30) (12,14) (12,13) (12,20) (12,18) (12,17) (12,27) (12,21) (12,33) (12,19) (13,14) (13,20) (13,18) (13,31) (13,17) (13,21) (13,28) (13,24) (13,26) (14,18) (14,31) (14,17) (14,27) (14,21) (14,33) (14,26) (15,32) (17,18) (17,31) (17,27) (17,33) (17,28) (17,24) (17,26) (17,19) (17,30) (18,20) (18,31) (18,33) (18,24) (18,26) (18,19) (18,30) (19,31) (19,27) (19,21) (19,33) (19,28) (19,26) (20,31) (20,27) (20,21) (20,33) (20,24) (20,26) (20,30) (21,27) (21,33) (21,28) (21,24) (21,30) (22,23) (22,34) (23,34) (24,33) (24,26) (25,29) (26,31) (26,33) (26,30) (27,31) (27,33) (27,28) (27,30) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nIs there a path between node 1 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph512-28_25", + "image": "data/connectivity/graph_visual/hard/graph512.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,19) (0,11) (0,1) (0,25) (0,28) (0,16) (0,31) (0,2) (0,23) (1,20) (1,26) (1,24) (1,10) (1,31) (1,21) (2,26) (2,19) (2,11) (2,5) (2,15) (2,32) (2,33) (2,8) (2,16) (2,31) (2,21) (2,30) (3,12) (3,4) (4,18) (5,11) (5,24) (6,14) (6,12) (6,9) (6,13) (7,26) (7,25) (7,33) (7,8) (7,21) (8,26) (8,19) (8,32) (8,31) (9,12) (10,19) (10,11) (10,25) (11,33) (11,24) (12,14) (14,18) (15,19) (15,17) (15,32) (15,25) (15,31) (15,21) (16,26) (16,32) (17,20) (17,19) (17,23) (19,24) (19,31) (19,21) (19,30) (21,32) (21,25) (21,24) (21,31) (23,31) (24,28) (25,32) (25,33) (25,28) (26,32) (26,33) (26,28) (26,31) (26,30) (28,33) (28,30) (31,32)\nIs there a path between node 28 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph413-22_32", + "image": "data/connectivity/graph_visual/hard/graph413.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,21) (0,3) (0,26) (0,18) (0,27) (2,20) (2,21) (2,28) (2,27) (3,30) (4,16) (4,15) (6,12) (8,21) (8,14) (8,18) (9,10) (10,12) (10,15) (10,32) (11,20) (11,21) (11,28) (11,25) (12,16) (12,32) (14,20) (14,23) (14,26) (14,27) (14,17) (15,32) (17,30) (17,21) (17,29) (17,27) (18,30) (18,27) (19,22) (20,23) (20,29) (23,25) (23,29) (25,27) (26,27) (27,30) (28,30)\nIs there a path between node 22 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph206-0_10", + "image": "data/connectivity/graph_visual/hard/graph206.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,23) (0,26) (0,24) (0,27) (1,4) (1,16) (1,15) (1,10) (1,29) (1,17) (1,11) (2,9) (2,7) (2,6) (2,27) (3,13) (3,28) (3,16) (3,18) (3,29) (3,21) (4,20) (4,16) (4,5) (4,15) (4,18) (4,14) (4,25) (5,28) (5,16) (5,15) (5,18) (5,14) (5,29) (5,19) (5,17) (5,11) (7,23) (7,26) (7,27) (8,26) (10,29) (10,19) (11,13) (11,28) (11,15) (11,17) (13,20) (13,28) (13,19) (14,16) (14,15) (14,29) (14,19) (14,21) (15,20) (15,28) (15,29) (15,19) (16,28) (16,25) (16,17) (17,19) (18,20) (18,21) (20,21) (21,29) (21,25) (22,28) (23,24) (26,27) (28,29)\nIs there a path between node 0 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph252-8_27", + "image": "data/connectivity/graph_visual/hard/graph252.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,20) (0,13) (0,30) (0,1) (0,4) (0,2) (0,22) (1,30) (1,17) (1,5) (1,4) (1,25) (1,29) (2,3) (2,5) (2,23) (3,28) (3,24) (3,4) (3,6) (3,8) (3,12) (4,15) (4,24) (4,25) (4,7) (4,6) (4,29) (5,21) (5,23) (5,7) (5,12) (6,20) (6,28) (6,23) (7,13) (7,15) (7,16) (7,8) (7,12) (8,20) (8,30) (8,24) (8,17) (8,23) (10,19) (11,19) (11,26) (12,20) (12,16) (12,25) (12,18) (13,28) (13,18) (14,20) (15,28) (15,24) (15,23) (16,20) (16,30) (16,24) (16,29) (17,21) (17,28) (17,25) (18,21) (18,23) (18,29) (20,24) (20,23) (20,22) (20,29) (21,25) (21,23) (21,22) (22,25) (23,24) (23,29) (24,28) (24,29) (25,28) (26,27) (29,30)\nIs there a path between node 8 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph83-24_23", + "image": "data/connectivity/graph_visual/hard/graph83.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,18) (0,14) (0,16) (0,12) (0,2) (0,22) (0,1) (0,21) (1,18) (1,14) (1,16) (1,21) (2,18) (2,14) (2,5) (2,12) (2,22) (2,21) (3,7) (3,9) (3,15) (3,25) (3,23) (3,26) (3,19) (4,7) (4,10) (4,20) (4,13) (4,15) (4,17) (4,25) (4,23) (4,26) (4,6) (4,11) (4,24) (5,18) (5,14) (5,16) (5,22) (5,21) (6,13) (6,8) (6,15) (6,17) (6,25) (6,26) (6,19) (6,24) (7,9) (7,10) (7,20) (7,13) (7,17) (7,25) (7,23) (7,26) (7,19) (7,11) (8,9) (8,10) (8,17) (8,23) (8,26) (8,11) (8,24) (9,10) (9,20) (9,15) (9,17) (9,23) (9,24) (10,15) (10,25) (10,26) (11,20) (11,15) (11,17) (11,25) (11,23) (12,18) (12,16) (12,22) (13,15) (13,17) (13,25) (13,26) (13,19) (13,24) (14,16) (15,20) (15,17) (15,25) (15,23) (15,26) (15,19) (16,18) (16,21) (17,20) (17,23) (17,26) (17,24) (18,22) (18,21) (19,25) (19,23) (19,26) (19,24) (20,25) (20,26) (20,24) (21,22) (23,24) (24,25) (25,26)\nIs there a path between node 24 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph581-20_31", + "image": "data/connectivity/graph_visual/hard/graph581.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,28) (0,6) (0,33) (0,2) (0,27) (0,5) (0,13) (0,17) (0,16) (0,21) (0,29) (0,15) (0,32) (0,8) (1,31) (1,7) (1,26) (1,30) (1,14) (1,11) (1,19) (1,22) (1,9) (1,24) (1,3) (1,4) (1,10) (2,28) (2,6) (2,33) (2,27) (2,5) (2,13) (2,20) (2,16) (2,25) (2,21) (2,29) (2,8) (3,23) (3,31) (3,7) (3,30) (3,12) (3,14) (3,11) (3,19) (3,22) (3,18) (3,9) (3,24) (3,4) (3,10) (4,23) (4,31) (4,26) (4,30) (4,12) (4,14) (4,19) (4,18) (4,9) (5,6) (5,33) (5,27) (5,13) (5,20) (5,16) (5,25) (5,21) (5,29) (5,8) (6,17) (6,16) (6,29) (6,15) (6,32) (6,8) (7,31) (7,26) (7,30) (7,19) (7,22) (7,18) (7,9) (7,24) (7,10) (8,27) (8,17) (8,20) (8,16) (8,25) (8,15) (9,31) (9,26) (9,30) (9,12) (9,14) (9,19) (9,22) (9,24) (9,10) (10,23) (10,31) (10,30) (10,14) (10,11) (10,24) (11,23) (11,26) (11,30) (11,19) (11,24) (12,23) (12,26) (12,30) (12,14) (12,19) (12,22) (12,24) (13,27) (13,17) (13,20) (13,16) (13,25) (13,21) (13,29) (13,32) (14,23) (14,26) (14,30) (14,19) (14,18) (14,24) (15,33) (15,27) (15,17) (15,25) (15,21) (15,29) (15,32) (16,28) (16,33) (16,17) (16,20) (16,25) (16,29) (16,32) (17,27) (17,20) (17,25) (17,21) (17,29) (17,32) (18,23) (18,26) (18,30) (18,22) (19,31) (19,26) (19,30) (19,24) (20,33) (20,25) (20,29) (21,28) (21,27) (21,25) (21,32) (22,31) (22,26) (22,30) (23,26) (23,30) (23,24) (24,26) (24,30) (25,28) (25,33) (25,27) (25,29) (26,30) (27,28) (27,33) (27,29) (28,29) (28,32) (29,33) (30,31)\nIs there a path between node 20 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph460-19_15", + "image": "data/connectivity/graph_visual/hard/graph460.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (0,16) (0,12) (0,2) (0,27) (0,30) (0,19) (0,28) (0,21) (0,13) (0,18) (1,5) (1,7) (1,4) (1,30) (1,24) (1,3) (2,5) (2,6) (2,22) (2,29) (2,19) (2,24) (2,21) (2,3) (3,31) (3,5) (3,16) (3,6) (3,12) (3,22) (3,29) (3,28) (3,24) (3,21) (3,18) (4,31) (4,16) (4,7) (4,23) (5,17) (5,22) (5,13) (6,32) (6,25) (6,19) (6,23) (6,15) (7,31) (7,25) (7,21) (7,13) (7,18) (8,26) (8,11) (10,12) (10,19) (10,13) (10,18) (11,20) (12,16) (12,27) (12,22) (12,30) (12,28) (12,21) (12,13) (12,15) (13,25) (13,27) (13,30) (13,19) (13,24) (13,18) (15,16) (15,22) (15,21) (15,18) (16,31) (16,32) (16,25) (16,22) (16,29) (16,24) (17,32) (17,19) (17,28) (17,21) (17,23) (18,32) (18,22) (18,19) (18,28) (18,21) (19,31) (19,27) (19,22) (19,29) (19,24) (19,21) (20,26) (21,32) (21,24) (22,31) (22,32) (23,31) (23,25) (23,27) (23,29) (24,25) (28,30) (31,32)\nIs there a path between node 19 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph298-23_29", + "image": "data/connectivity/graph_visual/hard/graph298.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,31) (0,27) (0,3) (0,21) (0,19) (0,23) (0,18) (0,29) (0,16) (0,24) (1,25) (1,5) (1,6) (2,12) (2,10) (2,17) (2,13) (3,4) (3,31) (3,27) (3,21) (3,15) (3,23) (3,18) (3,16) (3,24) (4,27) (4,15) (4,23) (4,18) (4,29) (4,22) (4,16) (4,24) (5,25) (5,6) (6,25) (7,20) (7,11) (8,25) (9,12) (9,14) (9,10) (9,17) (9,13) (10,12) (10,14) (10,17) (10,13) (11,26) (11,20) (11,28) (12,17) (13,14) (13,17) (14,17) (15,31) (15,27) (15,21) (15,30) (15,23) (15,29) (15,22) (15,24) (16,27) (16,30) (16,19) (16,23) (16,22) (16,24) (18,31) (18,27) (18,21) (18,30) (18,19) (18,23) (18,22) (19,31) (19,27) (19,21) (19,24) (20,26) (21,27) (21,30) (21,23) (21,29) (21,22) (22,31) (22,27) (22,30) (22,29) (23,31) (23,29) (24,27) (24,29) (26,28) (29,31) (29,30) (30,31)\nIs there a path between node 23 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph249-7_9", + "image": "data/connectivity/graph_visual/hard/graph249.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,22) (0,29) (0,21) (0,1) (0,28) (0,15) (0,7) (0,12) (0,10) (0,19) (0,17) (0,8) (0,6) (1,22) (1,9) (1,21) (1,20) (1,18) (1,7) (1,14) (1,19) (1,17) (1,8) (1,2) (1,23) (2,22) (2,9) (2,29) (2,21) (2,18) (2,30) (2,12) (2,5) (2,19) (2,17) (2,25) (2,8) (2,6) (2,23) (3,4) (3,27) (3,11) (3,26) (4,27) (4,11) (4,26) (5,9) (5,21) (5,18) (5,13) (5,28) (5,30) (5,12) (5,10) (5,19) (5,6) (5,23) (6,29) (6,21) (6,20) (6,18) (6,13) (6,15) (6,7) (6,16) (6,30) (6,12) (6,10) (6,8) (6,23) (7,22) (7,9) (7,29) (7,21) (7,18) (7,28) (7,15) (7,30) (7,10) (7,14) (7,19) (7,17) (7,8) (7,23) (8,22) (8,9) (8,29) (8,21) (8,20) (8,18) (8,13) (8,15) (8,16) (8,30) (8,12) (8,10) (8,14) (8,19) (8,23) (9,22) (9,21) (9,20) (9,18) (9,13) (9,28) (9,30) (9,12) (9,10) (9,14) (9,19) (9,17) (9,25) (10,22) (10,21) (10,20) (10,18) (10,13) (10,28) (10,15) (10,25) (10,23) (11,27) (11,26) (12,22) (12,29) (12,21) (12,28) (12,15) (12,30) (12,19) (12,17) (12,25) (12,23) (13,29) (13,21) (13,20) (13,15) (13,16) (13,14) (13,19) (13,17) (13,25) (13,23) (14,21) (14,28) (14,15) (14,16) (14,30) (14,19) (14,25) (14,23) (15,22) (15,29) (15,20) (15,16) (15,30) (15,19) (15,17) (15,25) (15,23) (16,22) (16,20) (16,18) (16,28) (16,30) (16,19) (16,17) (16,25) (16,23) (17,29) (17,21) (17,18) (17,28) (17,25) (18,22) (18,29) (18,21) (18,20) (18,28) (18,30) (18,19) (18,25) (19,29) (19,20) (19,30) (19,25) (19,23) (20,29) (20,21) (20,28) (20,30) (20,23) (21,22) (21,28) (21,30) (21,25) (21,23) (22,29) (22,28) (22,25) (23,29) (23,28) (25,29) (25,28) (25,30) (26,27) (28,29) (28,30) (29,30)\nIs there a path between node 7 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph552-4_29", + "image": "data/connectivity/graph_visual/hard/graph552.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,27) (0,26) (0,3) (0,13) (0,22) (0,12) (0,31) (0,17) (1,2) (1,20) (1,23) (1,13) (1,4) (1,29) (2,20) (2,5) (2,6) (2,22) (2,16) (2,31) (2,17) (2,29) (3,27) (3,5) (3,23) (3,24) (3,15) (3,13) (3,4) (3,17) (4,7) (4,5) (4,15) (4,13) (4,10) (4,22) (4,16) (4,18) (4,12) (4,21) (5,27) (5,20) (5,14) (5,23) (5,6) (5,15) (5,13) (5,28) (5,12) (5,21) (5,8) (5,25) (6,26) (6,20) (6,23) (6,24) (6,15) (6,9) (6,28) (6,22) (6,16) (6,8) (7,9) (7,19) (7,12) (7,21) (7,25) (8,24) (8,15) (8,32) (8,31) (8,25) (9,23) (9,22) (9,19) (9,12) (9,17) (10,26) (10,14) (10,23) (10,28) (10,29) (11,33) (12,15) (12,28) (12,16) (12,29) (13,14) (13,24) (13,32) (13,18) (13,17) (14,27) (14,26) (14,15) (14,31) (14,17) (14,25) (15,27) (15,26) (15,28) (15,19) (15,25) (16,20) (16,19) (16,18) (16,25) (17,20) (17,24) (17,32) (17,18) (17,25) (18,27) (18,24) (18,22) (18,31) (18,29) (19,26) (19,29) (19,25) (20,27) (20,23) (20,24) (20,22) (20,31) (21,22) (22,32) (22,28) (22,29) (22,25) (23,32) (23,25) (24,31) (26,27) (26,32) (27,29) (28,32) (28,31) (29,31)\nIs there a path between node 4 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph477-10_5", + "image": "data/connectivity/graph_visual/hard/graph477.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,4) (0,16) (0,9) (1,2) (1,10) (1,26) (1,18) (1,3) (1,31) (1,28) (1,12) (1,23) (1,27) (1,7) (1,32) (1,8) (1,21) (1,6) (2,25) (2,11) (2,10) (2,26) (2,18) (2,3) (2,31) (2,28) (2,23) (2,19) (2,27) (2,32) (2,8) (2,6) (3,10) (3,26) (3,18) (3,12) (3,23) (3,19) (3,27) (3,7) (3,32) (3,29) (3,8) (3,21) (3,6) (4,20) (4,24) (4,30) (4,9) (5,15) (6,25) (6,11) (6,10) (6,26) (6,31) (6,28) (6,23) (6,19) (6,32) (6,29) (6,8) (6,21) (7,11) (7,10) (7,26) (7,31) (7,28) (7,12) (7,19) (7,27) (7,29) (8,25) (8,11) (8,10) (8,26) (8,28) (8,12) (8,23) (8,19) (8,27) (8,29) (8,21) (9,20) (9,24) (9,14) (9,17) (9,16) (9,30) (10,25) (10,11) (10,26) (10,18) (10,31) (10,28) (10,23) (10,19) (10,27) (10,29) (10,21) (11,25) (11,31) (11,28) (11,12) (11,19) (11,27) (11,32) (12,25) (12,26) (12,18) (12,31) (12,23) (12,19) (12,27) (12,32) (13,20) (13,22) (13,14) (13,17) (13,16) (13,30) (14,20) (14,22) (14,17) (14,30) (16,20) (16,22) (17,20) (17,22) (18,25) (18,31) (18,28) (18,23) (18,27) (18,32) (19,26) (19,31) (19,23) (19,27) (19,32) (19,29) (19,21) (20,22) (20,24) (20,30) (21,25) (21,23) (21,32) (21,29) (23,25) (23,26) (23,31) (23,27) (24,30) (25,26) (25,28) (25,27) (25,29) (26,31) (26,32) (26,29) (27,31) (27,28) (27,29) (28,32) (28,29) (29,32) (31,32)\nIs there a path between node 10 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph157-28_20", + "image": "data/connectivity/graph_visual/hard/graph157.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,24) (0,7) (1,14) (1,10) (1,28) (1,4) (2,11) (2,24) (2,7) (2,18) (2,27) (2,3) (2,19) (3,12) (3,27) (3,19) (4,16) (4,13) (5,14) (5,22) (5,10) (5,9) (7,11) (7,24) (7,18) (7,27) (7,19) (8,12) (8,19) (9,17) (9,10) (9,15) (10,21) (11,26) (12,24) (12,26) (13,14) (13,28) (14,17) (14,22) (14,21) (14,15) (15,17) (15,22) (16,22) (17,28) (18,25) (18,26) (19,23) (20,23) (21,28) (23,24) (23,27)\nIs there a path between node 28 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph85-5_22", + "image": "data/connectivity/graph_visual/hard/graph85.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,20) (0,15) (0,19) (0,3) (0,5) (1,12) (1,17) (1,6) (1,16) (1,24) (1,13) (1,23) (1,4) (1,11) (1,26) (1,8) (2,17) (2,25) (2,16) (2,10) (2,13) (2,23) (2,21) (2,14) (2,22) (2,26) (2,8) (3,20) (3,19) (4,12) (4,6) (4,25) (4,9) (4,16) (4,24) (4,10) (4,13) (4,21) (4,22) (4,26) (4,8) (5,20) (5,15) (5,19) (5,18) (6,9) (6,10) (6,13) (6,23) (6,14) (6,22) (6,8) (7,12) (7,17) (7,25) (7,9) (7,24) (7,13) (7,21) (7,14) (7,26) (7,8) (8,12) (8,17) (8,25) (8,9) (8,16) (8,24) (8,10) (8,13) (8,23) (8,21) (8,11) (8,22) (8,26) (9,12) (9,17) (9,25) (9,16) (9,24) (9,10) (9,13) (9,23) (9,21) (9,14) (9,22) (9,26) (10,12) (10,17) (10,25) (10,16) (10,24) (10,23) (10,21) (10,22) (10,26) (11,12) (11,17) (11,25) (11,16) (11,23) (11,21) (11,14) (11,22) (12,17) (12,13) (12,23) (12,21) (12,14) (12,22) (13,17) (13,16) (13,21) (13,14) (13,22) (13,26) (14,25) (14,16) (14,23) (14,21) (14,22) (14,26) (15,19) (15,18) (16,17) (16,25) (16,24) (16,23) (16,21) (17,25) (17,23) (17,21) (18,20) (21,25) (21,24) (21,22) (21,26) (22,24) (22,26) (23,26) (24,26)\nIs there a path between node 5 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph129-17_24", + "image": "data/connectivity/graph_visual/hard/graph129.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,6) (0,7) (0,19) (0,18) (0,12) (0,17) (0,13) (0,24) (0,3) (0,1) (0,15) (0,11) (0,27) (0,16) (1,6) (1,8) (1,26) (1,7) (1,10) (1,19) (1,18) (1,24) (1,3) (1,9) (1,15) (1,11) (1,27) (2,20) (2,25) (2,14) (2,21) (3,6) (3,8) (3,26) (3,7) (3,10) (3,19) (3,18) (3,12) (3,17) (3,24) (3,9) (3,15) (3,11) (4,22) (5,23) (5,20) (5,25) (6,8) (6,26) (6,19) (6,18) (6,12) (6,17) (6,13) (6,24) (6,15) (6,11) (6,27) (6,16) (7,10) (7,19) (7,18) (7,17) (7,13) (7,24) (7,9) (7,16) (8,26) (8,19) (8,18) (8,12) (8,17) (8,13) (8,24) (8,9) (8,15) (8,27) (8,16) (9,26) (9,10) (9,18) (9,12) (9,17) (9,13) (9,15) (9,27) (9,16) (10,26) (10,19) (10,17) (10,13) (10,15) (10,16) (11,26) (11,19) (11,18) (11,12) (11,17) (11,15) (12,26) (12,19) (12,18) (12,13) (12,24) (13,18) (13,24) (13,27) (13,16) (14,23) (14,20) (14,21) (15,26) (15,19) (15,18) (15,17) (15,16) (16,26) (16,19) (16,24) (16,27) (17,26) (17,24) (17,27) (18,26) (18,19) (18,27) (19,26) (19,27) (20,25) (21,23) (21,25)\nIs there a path between node 17 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph498-3_11", + "image": "data/connectivity/graph_visual/hard/graph498.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,13) (0,29) (0,24) (0,31) (0,12) (0,10) (1,11) (1,21) (2,23) (2,29) (2,32) (2,24) (2,12) (2,9) (2,6) (2,4) (2,20) (3,33) (3,18) (3,22) (3,31) (3,12) (3,8) (3,9) (3,26) (3,6) (4,18) (4,22) (4,15) (4,8) (4,20) (5,11) (5,28) (5,14) (5,27) (6,33) (6,13) (6,19) (6,18) (6,22) (6,31) (6,26) (6,10) (7,16) (7,25) (8,24) (9,18) (9,22) (10,13) (10,29) (10,18) (10,17) (10,26) (10,20) (11,25) (12,13) (12,29) (12,24) (12,15) (12,20) (13,29) (13,19) (13,18) (13,24) (14,28) (14,16) (14,27) (15,33) (15,23) (15,29) (16,30) (17,29) (17,19) (17,26) (18,33) (18,23) (18,29) (18,24) (18,31) (19,31) (19,26) (20,32) (21,30) (21,27) (22,29) (24,33) (25,28) (25,30) (25,27) (26,32) (29,31) (31,32)\nIs there a path between node 3 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph147-23_6", + "image": "data/connectivity/graph_visual/hard/graph147.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,8) (0,19) (0,26) (0,7) (0,14) (0,5) (0,21) (0,13) (0,24) (0,17) (0,1) (0,9) (0,3) (0,16) (0,25) (1,8) (1,19) (1,26) (1,2) (1,7) (1,14) (1,5) (1,27) (1,4) (1,28) (1,15) (1,24) (1,17) (1,9) (1,23) (1,11) (1,3) (1,16) (2,12) (2,8) (2,22) (2,19) (2,26) (2,7) (2,18) (2,21) (2,27) (2,13) (2,15) (2,17) (2,9) (2,10) (2,23) (2,3) (2,16) (2,25) (3,12) (3,22) (3,19) (3,26) (3,7) (3,14) (3,18) (3,5) (3,21) (3,27) (3,4) (3,28) (3,13) (3,15) (3,24) (3,17) (3,9) (3,23) (3,11) (3,16) (4,12) (4,8) (4,26) (4,14) (4,18) (4,21) (4,13) (4,15) (4,24) (4,17) (4,23) (4,16) (5,12) (5,8) (5,22) (5,26) (5,14) (5,18) (5,21) (5,27) (5,28) (5,13) (5,15) (5,17) (5,10) (5,11) (5,25) (7,12) (7,8) (7,26) (7,14) (7,18) (7,21) (7,27) (7,13) (7,15) (7,17) (7,9) (7,10) (7,11) (7,16) (7,25) (8,12) (8,19) (8,14) (8,18) (8,21) (8,27) (8,13) (8,24) (8,17) (8,9) (8,10) (8,23) (8,16) (8,25) (9,12) (9,19) (9,14) (9,18) (9,27) (9,28) (9,13) (9,15) (9,17) (9,10) (9,23) (9,11) (9,16) (9,25) (10,12) (10,22) (10,19) (10,14) (10,18) (10,21) (10,27) (10,28) (10,13) (10,24) (10,23) (10,11) (10,25) (11,22) (11,19) (11,27) (11,13) (11,15) (11,23) (11,25) (12,19) (12,14) (12,18) (12,21) (12,27) (12,15) (12,24) (12,17) (12,25) (13,22) (13,19) (13,26) (13,14) (13,18) (13,21) (13,28) (13,15) (13,17) (13,23) (13,16) (13,25) (14,18) (14,21) (14,27) (14,28) (14,17) (14,23) (14,16) (14,25) (15,22) (15,19) (15,18) (15,24) (15,17) (15,23) (15,25) (16,22) (16,19) (16,26) (16,18) (16,21) (16,27) (16,28) (16,24) (16,17) (16,23) (16,25) (17,22) (17,19) (17,18) (17,21) (17,27) (17,24) (17,23) (17,25) (18,22) (18,19) (18,26) (18,21) (18,27) (18,28) (18,24) (18,23) (19,22) (19,26) (19,28) (19,24) (19,23) (19,25) (21,22) (21,26) (21,27) (21,28) (21,25) (22,26) (22,27) (22,24) (22,23) (22,25) (23,26) (23,27) (23,28) (23,24) (23,25) (24,26) (24,28) (24,25) (25,26) (25,27) (25,28) (27,28)\nIs there a path between node 23 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph282-30_29", + "image": "data/connectivity/graph_visual/hard/graph282.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,13) (0,28) (0,2) (0,25) (0,9) (0,3) (0,1) (0,19) (0,23) (0,29) (0,16) (0,8) (0,27) (0,14) (0,22) (1,28) (1,2) (1,25) (1,9) (1,11) (1,3) (1,10) (1,20) (1,19) (1,29) (1,16) (1,8) (1,14) (1,26) (1,22) (1,4) (2,28) (2,25) (2,11) (2,10) (2,20) (2,19) (2,23) (2,29) (2,8) (2,21) (2,22) (3,13) (3,25) (3,9) (3,11) (3,20) (3,23) (3,29) (3,27) (3,26) (3,21) (3,22) (3,4) (4,25) (4,9) (4,11) (4,10) (4,20) (4,23) (4,29) (4,16) (4,14) (4,21) (4,22) (5,24) (6,12) (6,15) (6,18) (7,12) (7,18) (8,13) (8,28) (8,25) (8,9) (8,11) (8,10) (8,20) (8,23) (8,29) (8,16) (8,27) (8,26) (9,13) (9,28) (9,25) (9,10) (9,20) (9,19) (9,23) (9,29) (9,16) (9,27) (9,14) (9,26) (9,21) (9,22) (10,13) (10,28) (10,25) (10,11) (10,20) (10,19) (10,23) (10,29) (10,16) (10,27) (10,14) (10,21) (10,22) (11,13) (11,25) (11,20) (11,19) (11,23) (11,29) (11,16) (11,27) (11,14) (11,26) (11,21) (11,22) (12,15) (12,18) (13,28) (13,25) (13,20) (13,19) (13,29) (13,14) (13,26) (13,22) (14,20) (14,19) (14,23) (14,29) (14,27) (14,26) (14,22) (15,18) (16,28) (16,25) (16,20) (16,23) (16,27) (16,26) (16,22) (17,30) (17,24) (19,28) (19,25) (19,23) (19,27) (19,26) (19,21) (19,22) (20,28) (20,25) (20,29) (20,26) (20,21) (20,22) (21,25) (21,23) (21,27) (21,22) (22,28) (22,29) (22,27) (22,26) (23,28) (23,25) (23,29) (23,27) (24,30) (25,28) (25,29) (25,27) (25,26) (26,28) (26,29) (27,28) (27,29) (28,29)\nIs there a path between node 30 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph581-24_16", + "image": "data/connectivity/graph_visual/hard/graph581.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,28) (0,6) (0,33) (0,2) (0,27) (0,5) (0,13) (0,17) (0,16) (0,21) (0,29) (0,15) (0,32) (0,8) (1,31) (1,7) (1,26) (1,30) (1,14) (1,11) (1,19) (1,22) (1,9) (1,24) (1,3) (1,4) (1,10) (2,28) (2,6) (2,33) (2,27) (2,5) (2,13) (2,20) (2,16) (2,25) (2,21) (2,29) (2,8) (3,23) (3,31) (3,7) (3,30) (3,12) (3,14) (3,11) (3,19) (3,22) (3,18) (3,9) (3,24) (3,4) (3,10) (4,23) (4,31) (4,26) (4,30) (4,12) (4,14) (4,19) (4,18) (4,9) (5,6) (5,33) (5,27) (5,13) (5,20) (5,16) (5,25) (5,21) (5,29) (5,8) (6,17) (6,16) (6,29) (6,15) (6,32) (6,8) (7,31) (7,26) (7,30) (7,19) (7,22) (7,18) (7,9) (7,24) (7,10) (8,27) (8,17) (8,20) (8,16) (8,25) (8,15) (9,31) (9,26) (9,30) (9,12) (9,14) (9,19) (9,22) (9,24) (9,10) (10,23) (10,31) (10,30) (10,14) (10,11) (10,24) (11,23) (11,26) (11,30) (11,19) (11,24) (12,23) (12,26) (12,30) (12,14) (12,19) (12,22) (12,24) (13,27) (13,17) (13,20) (13,16) (13,25) (13,21) (13,29) (13,32) (14,23) (14,26) (14,30) (14,19) (14,18) (14,24) (15,33) (15,27) (15,17) (15,25) (15,21) (15,29) (15,32) (16,28) (16,33) (16,17) (16,20) (16,25) (16,29) (16,32) (17,27) (17,20) (17,25) (17,21) (17,29) (17,32) (18,23) (18,26) (18,30) (18,22) (19,31) (19,26) (19,30) (19,24) (20,33) (20,25) (20,29) (21,28) (21,27) (21,25) (21,32) (22,31) (22,26) (22,30) (23,26) (23,30) (23,24) (24,26) (24,30) (25,28) (25,33) (25,27) (25,29) (26,30) (27,28) (27,33) (27,29) (28,29) (28,32) (29,33) (30,31)\nIs there a path between node 24 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph93-17_1", + "image": "data/connectivity/graph_visual/hard/graph93.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,19) (0,18) (0,16) (0,13) (0,4) (0,8) (0,10) (0,22) (1,2) (2,7) (3,19) (3,18) (3,12) (3,20) (3,10) (4,11) (4,14) (4,5) (4,20) (4,8) (5,11) (5,14) (5,18) (5,16) (5,13) (5,12) (6,19) (6,11) (6,12) (6,20) (6,8) (7,26) (8,24) (8,14) (8,18) (8,25) (9,17) (10,15) (10,27) (10,21) (10,18) (10,13) (10,12) (10,20) (11,27) (11,21) (11,13) (11,12) (11,25) (12,24) (12,16) (12,25) (13,24) (13,27) (13,25) (13,20) (13,22) (14,16) (14,22) (15,20) (16,25) (17,26) (17,23) (18,27) (19,25) (19,20) (20,24) (20,25) (20,22) (21,27) (22,25) (23,26) (25,27)\nIs there a path between node 17 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph394-19_31", + "image": "data/connectivity/graph_visual/hard/graph394.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,12) (0,24) (0,5) (0,32) (0,18) (0,23) (0,25) (1,20) (2,21) (2,13) (2,29) (3,12) (3,7) (3,11) (3,23) (3,25) (4,27) (4,12) (4,32) (5,30) (5,14) (7,10) (7,11) (7,23) (7,25) (8,27) (8,18) (8,30) (8,11) (8,25) (9,28) (10,27) (10,24) (10,32) (10,18) (10,23) (11,22) (11,14) (12,27) (12,24) (12,25) (13,15) (13,21) (13,29) (14,27) (14,32) (14,23) (15,21) (19,20) (22,30) (22,23) (23,30) (24,32) (24,30) (24,25) (25,27)\nIs there a path between node 19 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph172-21_7", + "image": "data/connectivity/graph_visual/hard/graph172.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,17) (0,11) (0,6) (0,9) (1,23) (1,21) (1,3) (1,19) (1,15) (1,22) (1,24) (1,5) (1,14) (1,25) (1,27) (1,18) (2,28) (2,13) (2,6) (3,23) (3,21) (3,12) (3,19) (3,15) (3,22) (3,24) (3,10) (3,14) (3,26) (3,25) (3,27) (4,21) (4,12) (4,15) (4,22) (4,24) (4,5) (4,14) (4,26) (4,25) (4,16) (4,27) (5,23) (5,21) (5,19) (5,15) (5,24) (5,10) (5,26) (5,8) (5,27) (6,28) (6,13) (6,17) (6,11) (7,28) (7,13) (7,11) (7,20) (8,21) (8,12) (8,19) (8,15) (8,22) (8,14) (8,26) (8,25) (8,16) (8,27) (9,17) (9,11) (9,20) (10,23) (10,12) (10,15) (10,22) (10,24) (10,14) (10,26) (10,25) (10,16) (10,18) (11,28) (11,13) (11,17) (11,20) (12,23) (12,21) (12,15) (12,22) (12,24) (12,16) (12,18) (13,28) (13,17) (13,20) (14,23) (14,21) (14,19) (14,15) (14,24) (14,25) (14,16) (14,27) (15,23) (15,19) (15,26) (15,25) (15,16) (15,27) (15,18) (16,23) (16,21) (16,19) (16,24) (16,26) (16,27) (16,18) (17,28) (18,23) (18,21) (18,19) (18,22) (18,24) (18,26) (18,25) (19,23) (19,22) (19,24) (19,26) (19,25) (19,27) (20,28) (21,23) (21,22) (21,24) (21,26) (21,25) (21,27) (22,24) (22,25) (23,24) (24,26) (24,25) (24,27)\nIs there a path between node 21 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph602-26_22", + "image": "data/connectivity/graph_visual/hard/graph602.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,7) (0,20) (0,27) (0,29) (0,26) (0,17) (0,3) (0,1) (0,16) (1,6) (1,7) (1,20) (1,19) (1,3) (1,33) (1,4) (2,27) (2,34) (2,26) (2,19) (2,17) (2,3) (2,21) (2,4) (3,6) (3,7) (3,11) (3,28) (3,29) (4,6) (4,28) (4,27) (4,29) (4,26) (4,19) (4,33) (4,23) (5,7) (5,11) (5,28) (5,19) (5,33) (5,16) (6,7) (6,28) (6,27) (6,26) (6,21) (7,34) (8,13) (8,12) (8,22) (8,15) (9,24) (9,12) (9,10) (10,25) (11,16) (11,23) (12,32) (12,18) (12,22) (12,15) (13,14) (14,18) (14,15) (15,30) (15,18) (16,27) (16,17) (16,23) (17,29) (17,19) (17,33) (17,23) (18,31) (18,24) (19,28) (19,27) (19,34) (19,29) (19,33) (19,21) (20,21) (21,26) (21,33) (22,30) (22,25) (25,30) (25,31) (26,28) (26,34) (26,29) (27,28) (30,32) (31,32)\nIs there a path between node 26 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph579-9_15", + "image": "data/connectivity/graph_visual/hard/graph579.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,29) (0,12) (0,5) (0,30) (0,19) (0,21) (0,28) (1,17) (1,31) (1,6) (1,16) (1,2) (1,32) (1,4) (1,3) (1,18) (2,23) (2,17) (2,8) (2,6) (2,24) (2,16) (2,33) (2,13) (2,22) (2,3) (3,23) (3,17) (3,31) (3,8) (3,6) (3,24) (3,16) (3,33) (3,4) (3,18) (4,23) (4,17) (4,31) (4,6) (4,24) (4,33) (4,32) (5,29) (5,12) (5,21) (5,28) (5,11) (6,23) (6,17) (6,31) (6,8) (6,24) (6,16) (6,33) (6,13) (6,22) (6,32) (7,20) (7,26) (7,15) (7,14) (7,27) (7,25) (8,17) (8,31) (8,24) (8,33) (8,13) (8,22) (8,32) (8,18) (9,26) (9,15) (9,10) (9,14) (9,27) (9,25) (10,20) (10,26) (10,27) (10,25) (11,29) (11,12) (11,19) (11,28) (12,29) (12,30) (12,19) (12,21) (12,28) (13,23) (13,17) (13,31) (13,24) (13,16) (13,33) (13,22) (14,20) (14,15) (14,27) (14,25) (15,20) (15,26) (15,27) (15,25) (16,31) (16,33) (16,32) (16,18) (17,33) (18,23) (18,33) (18,22) (18,32) (19,29) (19,30) (19,21) (21,30) (22,31) (22,24) (22,33) (22,32) (23,31) (23,24) (23,33) (24,31) (24,33) (24,32) (25,26) (25,27) (26,27) (28,29) (29,30) (31,33) (31,32)\nIs there a path between node 9 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph705-4_18", + "image": "data/connectivity/graph_visual/hard/graph705.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,17) (0,1) (0,20) (0,5) (0,16) (0,34) (1,17) (1,9) (1,5) (1,16) (1,34) (2,30) (2,26) (2,25) (2,24) (3,18) (3,12) (3,4) (3,32) (3,7) (3,33) (3,22) (3,13) (3,15) (3,6) (3,10) (3,27) (4,12) (4,11) (4,7) (4,22) (4,19) (4,13) (4,15) (4,6) (4,21) (4,27) (5,17) (5,9) (5,20) (5,34) (6,18) (6,32) (6,11) (6,7) (6,33) (6,22) (6,19) (6,15) (6,21) (7,18) (7,11) (7,33) (7,22) (7,19) (7,13) (7,10) (7,27) (8,31) (8,29) (9,17) (9,20) (9,16) (9,34) (10,12) (10,32) (10,19) (10,13) (10,15) (10,27) (11,12) (11,32) (11,33) (11,22) (11,19) (11,13) (11,27) (12,22) (12,19) (12,13) (12,15) (12,27) (13,18) (13,32) (13,33) (13,19) (13,15) (13,21) (13,27) (14,28) (14,30) (14,25) (14,24) (15,18) (15,33) (15,22) (15,19) (15,21) (15,27) (16,20) (17,20) (18,33) (18,19) (18,27) (19,32) (19,33) (19,21) (19,27) (20,34) (21,32) (21,27) (22,32) (22,33) (22,27) (23,31) (23,29) (24,28) (24,25) (25,28) (25,26) (26,28) (26,30) (28,30) (29,31) (32,33)\nIs there a path between node 4 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph467-8_25", + "image": "data/connectivity/graph_visual/hard/graph467.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,29) (0,10) (0,18) (0,21) (0,30) (0,28) (0,15) (1,27) (1,24) (1,22) (1,32) (1,14) (1,5) (2,29) (2,10) (2,18) (2,21) (2,19) (2,30) (2,16) (2,28) (2,15) (3,24) (3,13) (3,22) (3,20) (3,5) (4,17) (4,11) (4,6) (4,26) (4,23) (4,31) (4,25) (5,27) (5,13) (5,22) (5,20) (5,32) (5,14) (6,17) (6,9) (6,23) (6,31) (6,25) (7,29) (7,10) (7,18) (7,19) (7,30) (7,16) (7,15) (8,17) (8,11) (8,26) (8,23) (8,31) (9,17) (9,26) (9,23) (9,31) (9,25) (10,29) (10,18) (10,21) (10,30) (10,28) (10,15) (11,17) (11,26) (11,23) (12,27) (12,24) (12,13) (12,22) (12,32) (13,27) (13,24) (13,22) (13,20) (13,32) (13,14) (14,27) (14,22) (14,32) (15,29) (15,18) (15,21) (15,19) (15,28) (16,29) (16,21) (16,19) (16,28) (17,23) (18,29) (18,21) (18,30) (18,28) (19,29) (19,21) (19,30) (19,28) (20,24) (20,22) (20,32) (21,29) (21,30) (21,28) (22,27) (22,24) (22,32) (23,31) (24,27) (25,26) (26,31) (28,30)\nIs there a path between node 8 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph28-11_24", + "image": "data/connectivity/graph_visual/hard/graph28.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,1) (0,11) (1,18) (1,17) (1,2) (4,16) (4,18) (4,22) (5,13) (5,24) (5,10) (7,12) (8,16) (8,11) (9,13) (9,14) (10,15) (10,14) (11,18) (13,14) (14,15) (15,24) (16,19) (16,22) (17,18) (18,20) (18,21) (18,25) (19,20) (19,21) (19,22) (20,21) (22,25) (23,24)\nIs there a path between node 11 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph219-11_3", + "image": "data/connectivity/graph_visual/hard/graph219.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,23) (0,2) (0,27) (1,16) (1,7) (1,25) (1,22) (1,24) (1,5) (1,13) (1,21) (1,12) (1,17) (1,20) (1,29) (1,28) (1,10) (1,8) (1,18) (1,6) (1,3) (1,9) (2,27) (2,26) (3,14) (3,4) (3,25) (3,22) (3,24) (3,5) (3,12) (3,19) (3,15) (3,20) (3,11) (3,10) (3,8) (3,18) (3,6) (3,9) (4,14) (4,16) (4,7) (4,25) (4,24) (4,5) (4,13) (4,21) (4,12) (4,19) (4,17) (4,20) (4,29) (4,11) (4,10) (4,8) (4,18) (4,6) (4,9) (5,14) (5,16) (5,25) (5,24) (5,13) (5,21) (5,12) (5,19) (5,15) (5,20) (5,29) (5,28) (5,18) (5,9) (6,14) (6,16) (6,7) (6,25) (6,24) (6,13) (6,21) (6,12) (6,15) (6,29) (6,11) (6,28) (6,8) (6,18) (7,14) (7,25) (7,22) (7,24) (7,13) (7,21) (7,12) (7,19) (7,15) (7,17) (7,20) (7,29) (7,11) (7,28) (7,10) (7,8) (7,18) (7,9) (8,21) (8,12) (8,15) (8,17) (8,20) (8,29) (8,28) (8,18) (8,9) (9,16) (9,25) (9,22) (9,19) (9,17) (9,11) (9,28) (9,10) (9,18) (10,16) (10,25) (10,24) (10,21) (10,15) (10,17) (10,20) (10,29) (10,11) (10,18) (11,14) (11,16) (11,25) (11,22) (11,24) (11,21) (11,15) (11,20) (11,29) (11,28) (12,22) (12,24) (12,21) (12,15) (12,20) (13,14) (13,25) (13,24) (13,21) (13,19) (13,15) (13,17) (13,28) (13,18) (14,16) (14,25) (14,22) (14,24) (14,21) (14,19) (14,15) (14,20) (14,29) (14,28) (14,18) (15,16) (15,25) (15,22) (15,24) (15,21) (15,19) (15,17) (15,20) (15,29) (15,28) (15,18) (16,25) (16,19) (16,17) (16,20) (16,18) (17,25) (17,22) (17,24) (17,21) (17,19) (17,28) (17,18) (18,25) (18,24) (18,21) (18,19) (18,29) (18,28) (19,22) (19,24) (19,21) (19,29) (19,28) (20,22) (20,24) (20,21) (20,28) (21,25) (21,24) (21,29) (22,25) (22,24) (22,28) (23,26) (24,29) (24,28) (26,27) (28,29)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph362-11_23", + "image": "data/connectivity/graph_visual/hard/graph362.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,30) (0,28) (0,21) (0,5) (0,20) (0,13) (1,26) (1,17) (2,27) (2,15) (3,19) (3,24) (3,21) (3,14) (3,4) (3,22) (3,12) (3,13) (4,16) (4,31) (4,11) (5,7) (5,23) (5,14) (5,6) (5,12) (6,7) (6,24) (6,16) (6,28) (6,14) (7,25) (7,28) (7,14) (7,20) (7,22) (7,11) (7,12) (8,10) (8,18) (9,27) (9,15) (10,27) (10,15) (10,18) (11,24) (11,21) (12,25) (12,24) (12,20) (12,22) (12,13) (13,29) (13,25) (13,24) (13,31) (14,16) (14,22) (15,26) (15,17) (16,29) (16,21) (16,31) (16,20) (17,26) (18,26) (19,29) (19,23) (19,20) (20,22) (21,25) (21,24) (21,30) (21,22) (22,30) (23,30) (23,31) (24,25) (24,30) (24,31) (26,27) (29,30)\nIs there a path between node 11 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph428-27_26", + "image": "data/connectivity/graph_visual/hard/graph428.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,30) (0,7) (0,26) (0,13) (0,21) (0,22) (0,1) (1,24) (1,7) (1,26) (1,11) (2,32) (2,18) (2,9) (2,8) (2,12) (2,29) (2,14) (2,16) (2,10) (2,3) (2,5) (2,17) (2,28) (3,27) (3,32) (3,18) (3,9) (3,8) (3,12) (3,29) (3,16) (3,4) (3,23) (3,5) (3,31) (3,17) (3,15) (3,28) (4,18) (4,9) (4,29) (4,16) (4,10) (4,23) (4,5) (4,17) (4,15) (5,27) (5,32) (5,18) (5,20) (5,9) (5,16) (5,10) (5,17) (5,15) (5,28) (6,25) (6,19) (7,24) (7,30) (7,13) (7,21) (7,22) (8,27) (8,32) (8,18) (8,20) (8,9) (8,29) (8,14) (8,16) (8,10) (8,23) (8,31) (8,17) (8,15) (8,28) (9,27) (9,32) (9,20) (9,12) (9,14) (9,10) (9,23) (9,17) (9,15) (9,28) (10,32) (10,18) (10,20) (10,12) (10,29) (10,16) (10,31) (10,15) (10,28) (11,24) (11,30) (11,26) (11,22) (12,32) (12,18) (12,14) (12,16) (12,23) (12,31) (12,15) (12,28) (13,24) (13,30) (13,26) (14,27) (14,32) (14,18) (14,20) (14,29) (14,17) (14,28) (15,27) (15,32) (15,20) (15,23) (15,31) (15,17) (15,28) (16,27) (16,32) (16,18) (16,20) (16,23) (16,31) (16,28) (17,32) (17,20) (17,29) (17,23) (17,28) (18,27) (18,32) (18,20) (18,29) (18,31) (20,27) (20,32) (20,29) (20,23) (20,31) (20,28) (21,24) (21,30) (21,26) (21,22) (22,30) (22,26) (23,29) (23,31) (24,26) (26,30) (27,32) (28,29) (28,31) (31,32)\nIs there a path between node 27 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph686-6_13", + "image": "data/connectivity/graph_visual/hard/graph686.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,24) (0,27) (0,32) (0,33) (0,29) (0,9) (0,21) (0,5) (0,31) (0,14) (0,12) (0,26) (0,11) (0,17) (0,16) (0,34) (0,23) (0,30) (0,7) (0,6) (1,24) (1,32) (1,4) (1,20) (1,9) (1,21) (1,22) (1,12) (1,26) (1,25) (1,11) (1,17) (1,34) (1,23) (1,7) (1,6) (1,8) (2,27) (2,4) (2,29) (2,9) (2,21) (2,5) (2,15) (2,31) (2,22) (2,12) (2,26) (2,25) (2,11) (2,17) (2,18) (2,34) (2,23) (2,30) (3,24) (3,27) (3,32) (3,33) (3,4) (3,20) (3,5) (3,15) (3,31) (3,14) (3,22) (3,25) (3,11) (3,17) (3,16) (3,18) (3,34) (3,30) (3,7) (3,28) (3,6) (3,8) (4,24) (4,27) (4,33) (4,29) (4,20) (4,9) (4,21) (4,5) (4,15) (4,31) (4,14) (4,22) (4,12) (4,25) (4,17) (4,16) (4,18) (4,30) (4,28) (4,6) (4,8) (5,27) (5,29) (5,20) (5,21) (5,15) (5,31) (5,14) (5,12) (5,26) (5,25) (5,11) (5,17) (5,16) (5,30) (5,7) (5,28) (5,8) (6,24) (6,32) (6,33) (6,29) (6,20) (6,9) (6,21) (6,15) (6,14) (6,22) (6,12) (6,26) (6,25) (6,11) (6,16) (6,18) (6,7) (6,28) (6,8) (7,24) (7,27) (7,33) (7,9) (7,21) (7,15) (7,31) (7,14) (7,22) (7,12) (7,26) (7,25) (7,18) (7,23) (7,28) (7,8) (8,24) (8,32) (8,20) (8,9) (8,15) (8,31) (8,14) (8,22) (8,12) (8,17) (8,16) (8,34) (8,23) (8,30) (8,28) (9,27) (9,32) (9,33) (9,29) (9,20) (9,21) (9,31) (9,14) (9,12) (9,26) (9,16) (9,34) (9,23) (9,30) (9,28) (10,19) (10,13) (11,24) (11,32) (11,29) (11,20) (11,21) (11,15) (11,14) (11,22) (11,12) (11,26) (11,17) (11,18) (11,34) (11,23) (11,30) (11,28) (12,24) (12,27) (12,32) (12,33) (12,20) (12,21) (12,31) (12,22) (12,26) (12,25) (12,17) (12,16) (12,18) (12,34) (12,30) (12,28) (13,19) (14,32) (14,29) (14,21) (14,31) (14,26) (14,25) (14,17) (14,16) (14,18) (14,23) (14,30) (15,24) (15,27) (15,32) (15,33) (15,20) (15,31) (15,22) (15,26) (15,25) (15,17) (15,16) (15,34) (15,23) (15,30) (16,27) (16,33) (16,29) (16,20) (16,21) (16,31) (16,22) (16,26) (16,25) (16,17) (16,18) (16,34) (16,23) (16,30) (17,24) (17,32) (17,33) (17,29) (17,20) (17,31) (17,22) (17,26) (17,25) (17,34) (17,23) (17,28) (18,24) (18,32) (18,33) (18,20) (18,31) (18,22) (18,26) (18,34) (18,23) (18,28) (20,24) (20,33) (20,29) (20,31) (20,22) (20,26) (20,34) (20,23) (20,30) (20,28) (21,24) (21,32) (21,26) (21,25) (21,34) (21,23) (21,30) (21,28) (22,24) (22,32) (22,33) (22,29) (22,31) (22,26) (22,25) (22,34) (22,28) (23,27) (23,32) (23,33) (23,29) (23,31) (23,34) (23,30) (23,28) (24,27) (24,33) (24,29) (24,31) (24,26) (24,25) (24,34) (24,30) (24,28) (25,27) (25,32) (25,33) (25,29) (25,26) (25,34) (25,30) (25,28) (26,27) (26,32) (26,33) (26,29) (26,31) (26,28) (27,32) (27,33) (27,29) (27,31) (27,30) (28,32) (28,31) (28,34) (28,30) (29,32) (29,33) (29,34) (30,32) (30,31) (30,34) (31,32) (31,33) (32,33) (32,34) (33,34)\nIs there a path between node 6 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph73-7_19", + "image": "data/connectivity/graph_visual/hard/graph73.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,7) (0,16) (0,14) (0,13) (0,25) (0,4) (0,19) (0,9) (0,10) (2,13) (2,15) (2,10) (3,18) (3,14) (3,25) (3,23) (3,15) (3,10) (3,24) (4,16) (4,23) (4,19) (4,15) (4,11) (5,21) (5,8) (5,26) (6,20) (6,19) (6,15) (6,10) (6,24) (7,20) (7,11) (8,21) (9,20) (9,22) (9,25) (9,11) (9,24) (10,17) (10,25) (11,17) (11,13) (11,23) (12,16) (12,14) (12,25) (12,15) (13,17) (13,25) (14,17) (14,16) (14,25) (14,15) (15,17) (15,16) (15,20) (15,24) (16,18) (16,17) (16,20) (16,22) (16,19) (17,23) (18,22) (18,23) (19,22) (19,25) (22,23) (24,25)\nIs there a path between node 7 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph492-30_8", + "image": "data/connectivity/graph_visual/hard/graph492.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,13) (2,25) (2,28) (2,21) (2,5) (2,23) (3,22) (3,8) (3,6) (3,19) (3,21) (3,31) (3,15) (5,20) (5,16) (5,21) (5,23) (6,18) (6,17) (6,23) (7,10) (8,21) (9,24) (12,22) (12,18) (13,30) (13,27) (14,26) (15,16) (15,19) (15,31) (16,22) (16,20) (16,19) (17,20) (17,21) (17,31) (18,22) (18,25) (18,20) (18,21) (18,23) (19,25) (19,28) (20,28) (20,21) (21,25) (22,25) (22,28) (23,28) (27,29) (29,30) (30,32)\nIs there a path between node 30 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph186-11_2", + "image": "data/connectivity/graph_visual/hard/graph186.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,14) (0,10) (0,2) (2,15) (2,20) (2,23) (2,14) (2,17) (2,24) (2,18) (3,21) (4,27) (5,9) (5,22) (6,29) (6,8) (7,29) (7,25) (7,20) (7,17) (7,18) (7,8) (8,23) (8,24) (10,23) (10,18) (11,27) (12,13) (13,21) (14,25) (14,23) (14,17) (14,24) (15,29) (15,25) (15,23) (15,16) (16,29) (16,17) (17,25) (17,23) (17,24) (17,18) (18,29) (20,25) (22,26) (23,25) (24,29) (26,27)\nIs there a path between node 11 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph9-21_19", + "image": "data/connectivity/graph_visual/hard/graph9.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,2) (0,10) (0,13) (0,12) (0,9) (0,18) (0,24) (0,5) (0,20) (0,21) (0,7) (0,3) (0,23) (1,2) (1,13) (1,16) (1,12) (1,18) (1,24) (1,20) (1,4) (1,7) (1,3) (1,19) (1,23) (2,13) (2,16) (2,12) (2,9) (2,11) (2,18) (2,24) (2,5) (2,20) (2,4) (2,21) (2,7) (2,3) (2,23) (3,13) (3,16) (3,12) (3,9) (3,11) (3,24) (3,5) (3,20) (3,21) (3,7) (3,19) (3,23) (4,10) (4,16) (4,12) (4,11) (4,18) (4,24) (4,5) (4,20) (4,21) (4,7) (4,19) (4,23) (5,13) (5,12) (5,11) (5,18) (5,24) (5,20) (5,21) (5,7) (5,23) (6,15) (6,25) (6,22) (6,8) (7,13) (7,12) (7,9) (7,11) (7,18) (7,20) (7,21) (7,19) (8,17) (8,15) (8,22) (8,14) (9,10) (9,13) (9,16) (9,11) (9,18) (9,21) (9,19) (9,23) (10,13) (10,12) (10,11) (10,24) (10,20) (10,21) (10,19) (10,23) (11,13) (11,16) (11,24) (11,20) (11,21) (11,19) (11,23) (12,13) (12,16) (12,18) (12,24) (12,20) (12,21) (12,19) (12,23) (13,16) (13,24) (13,21) (13,23) (14,17) (14,15) (14,22) (15,17) (15,25) (15,22) (16,18) (16,24) (16,21) (16,23) (17,25) (17,22) (18,20) (18,21) (18,19) (18,23) (19,20) (19,23) (20,24) (20,21) (21,23) (22,25) (23,24)\nIs there a path between node 21 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph548-4_20", + "image": "data/connectivity/graph_visual/hard/graph548.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,2) (0,31) (1,4) (1,27) (1,25) (2,31) (2,24) (2,13) (2,10) (3,30) (3,32) (3,27) (3,15) (4,30) (4,6) (4,28) (4,8) (5,22) (6,27) (7,20) (7,11) (7,12) (8,15) (9,14) (10,17) (10,23) (10,13) (11,14) (12,18) (13,23) (14,22) (15,30) (15,27) (15,25) (15,16) (15,28) (17,23) (17,21) (18,22) (18,33) (20,22) (21,31) (23,24) (25,30) (25,27) (25,28) (26,31) (27,30) (27,32) (28,32)\nIs there a path between node 4 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph646-8_32", + "image": "data/connectivity/graph_visual/hard/graph646.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,13) (0,16) (0,5) (0,12) (0,29) (0,33) (0,18) (0,8) (0,15) (0,10) (0,34) (0,14) (0,21) (0,25) (1,11) (1,9) (1,19) (1,20) (1,7) (1,3) (1,28) (1,4) (1,24) (1,32) (1,26) (1,22) (2,6) (2,13) (2,17) (2,5) (2,31) (2,23) (2,27) (2,12) (2,29) (2,33) (2,18) (2,8) (2,15) (2,10) (2,30) (2,21) (2,25) (3,11) (3,9) (3,19) (3,28) (3,4) (3,24) (3,32) (3,26) (4,11) (4,9) (4,19) (4,20) (4,7) (4,28) (4,32) (4,26) (4,22) (5,17) (5,16) (5,23) (5,27) (5,12) (5,29) (5,33) (5,18) (5,8) (5,10) (5,25) (6,13) (6,17) (6,16) (6,31) (6,27) (6,12) (6,29) (6,8) (6,15) (6,10) (6,30) (6,14) (6,25) (7,11) (7,28) (7,24) (7,32) (7,22) (8,13) (8,16) (8,31) (8,27) (8,12) (8,29) (8,33) (8,18) (8,15) (8,10) (8,34) (8,14) (8,25) (9,11) (9,19) (9,20) (9,24) (9,22) (10,13) (10,17) (10,27) (10,12) (10,33) (10,18) (10,30) (10,14) (10,25) (11,19) (11,20) (11,28) (11,32) (11,26) (11,22) (12,13) (12,17) (12,31) (12,23) (12,29) (12,15) (12,30) (12,34) (12,21) (12,25) (13,16) (13,31) (13,29) (13,33) (13,30) (13,34) (13,14) (13,25) (14,17) (14,16) (14,31) (14,27) (14,29) (14,33) (14,18) (14,15) (14,34) (14,25) (15,17) (15,23) (15,27) (15,33) (15,30) (15,34) (15,21) (16,23) (16,27) (16,33) (16,18) (16,34) (17,23) (17,27) (17,33) (17,30) (17,34) (17,21) (17,25) (18,31) (18,27) (18,29) (18,34) (19,20) (19,28) (19,24) (19,32) (19,26) (19,22) (20,28) (20,24) (20,22) (21,31) (21,27) (21,33) (21,30) (21,25) (22,24) (22,32) (23,31) (23,27) (23,29) (23,33) (23,34) (23,25) (24,28) (24,32) (24,26) (25,27) (25,30) (25,34) (27,29) (27,33) (27,30) (28,32) (29,31) (29,33) (29,30) (29,34) (30,31) (30,33) (30,34) (33,34)\nIs there a path between node 8 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph430-3_0", + "image": "data/connectivity/graph_visual/hard/graph430.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,12) (0,17) (0,11) (0,31) (0,25) (0,27) (0,28) (0,8) (0,16) (1,23) (1,3) (1,15) (1,10) (2,18) (2,24) (2,19) (2,4) (2,5) (2,26) (2,6) (2,7) (2,32) (3,23) (3,15) (3,10) (4,18) (4,22) (4,20) (4,6) (4,7) (4,32) (5,18) (5,29) (5,22) (5,24) (5,19) (5,20) (5,13) (5,6) (5,7) (6,24) (6,13) (6,7) (7,18) (7,29) (7,24) (7,32) (8,14) (8,12) (8,21) (8,17) (8,31) (8,25) (8,9) (9,30) (9,14) (9,12) (9,21) (9,17) (9,11) (9,31) (9,27) (9,28) (9,16) (10,23) (10,15) (11,14) (11,21) (11,17) (11,31) (11,25) (11,27) (11,28) (12,30) (12,31) (12,16) (13,18) (13,22) (13,24) (13,19) (13,20) (13,32) (14,30) (14,21) (14,17) (14,27) (14,28) (14,16) (15,23) (16,21) (16,17) (16,31) (16,27) (16,28) (17,21) (17,25) (17,27) (17,28) (18,22) (18,19) (18,20) (18,26) (18,32) (19,22) (19,24) (19,20) (19,26) (19,32) (20,29) (20,24) (20,26) (20,32) (21,31) (21,25) (21,27) (21,28) (22,29) (22,26) (22,32) (24,32) (25,30) (25,27) (25,28) (26,29) (26,32) (27,30) (27,31) (27,28) (28,30) (29,32) (30,31)\nIs there a path between node 3 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph20-3_20", + "image": "data/connectivity/graph_visual/hard/graph20.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,5) (0,14) (0,23) (1,10) (1,6) (1,3) (1,22) (2,16) (2,12) (3,8) (3,14) (3,22) (4,21) (4,25) (6,7) (6,18) (6,14) (6,15) (6,22) (7,18) (7,22) (8,10) (8,23) (11,16) (11,21) (12,17) (12,21) (12,25) (13,20) (14,20) (14,22) (15,18) (16,21) (16,25) (17,21) (19,21) (20,23) (21,25)\nIs there a path between node 3 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph271-14_19", + "image": "data/connectivity/graph_visual/hard/graph271.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,20) (1,3) (1,27) (1,23) (1,9) (1,26) (1,29) (1,15) (1,11) (1,24) (1,22) (1,10) (1,21) (1,18) (1,17) (1,2) (1,5) (1,4) (1,28) (1,7) (1,25) (2,20) (2,19) (2,3) (2,27) (2,23) (2,26) (2,29) (2,11) (2,24) (2,22) (2,21) (2,30) (2,18) (2,5) (2,4) (2,28) (2,7) (2,13) (2,25) (3,20) (3,19) (3,9) (3,26) (3,29) (3,15) (3,11) (3,24) (3,22) (3,10) (3,21) (3,30) (3,8) (3,28) (3,12) (3,7) (3,13) (3,25) (4,20) (4,19) (4,27) (4,26) (4,29) (4,15) (4,11) (4,24) (4,10) (4,30) (4,18) (4,17) (4,12) (4,7) (4,13) (4,25) (5,20) (5,19) (5,27) (5,26) (5,29) (5,24) (5,22) (5,30) (5,18) (5,8) (5,17) (5,6) (5,12) (5,13) (5,25) (6,19) (6,27) (6,23) (6,9) (6,26) (6,29) (6,15) (6,11) (6,22) (6,21) (6,30) (6,17) (6,28) (6,12) (6,7) (6,13) (6,25) (7,19) (7,27) (7,9) (7,26) (7,29) (7,15) (7,11) (7,22) (7,21) (7,30) (7,18) (7,8) (7,17) (7,28) (7,12) (7,13) (7,25) (8,20) (8,19) (8,27) (8,23) (8,9) (8,29) (8,15) (8,24) (8,22) (8,10) (8,30) (8,18) (8,17) (8,28) (8,13) (8,25) (9,20) (9,19) (9,27) (9,23) (9,11) (9,24) (9,22) (9,10) (9,30) (9,17) (9,12) (9,13) (9,25) (10,27) (10,23) (10,29) (10,15) (10,11) (10,24) (10,21) (10,30) (10,17) (10,28) (10,13) (10,25) (11,20) (11,27) (11,23) (11,29) (11,15) (11,24) (11,22) (11,21) (11,30) (11,12) (11,13) (11,25) (12,19) (12,27) (12,23) (12,26) (12,29) (12,15) (12,24) (12,22) (12,30) (12,18) (12,13) (12,25) (13,20) (13,19) (13,27) (13,26) (13,29) (13,24) (13,21) (13,18) (13,28) (14,16) (15,20) (15,19) (15,23) (15,26) (15,29) (15,24) (15,22) (15,21) (15,18) (15,28) (15,25) (17,20) (17,23) (17,24) (17,22) (17,21) (17,30) (17,28) (17,25) (18,20) (18,19) (18,23) (18,26) (18,24) (18,22) (18,30) (18,28) (18,25) (19,27) (19,29) (19,22) (19,21) (19,30) (19,25) (20,27) (20,26) (20,29) (20,24) (20,22) (20,21) (21,27) (21,23) (21,22) (21,30) (21,28) (21,25) (22,27) (22,23) (22,29) (22,24) (22,30) (22,28) (22,25) (23,27) (23,26) (23,29) (23,30) (23,28) (23,25) (24,27) (24,25) (25,26) (25,29) (25,30) (25,28) (26,30) (27,30) (27,28) (29,30)\nIs there a path between node 14 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph225-28_27", + "image": "data/connectivity/graph_visual/hard/graph225.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,28) (0,13) (0,8) (0,1) (0,10) (0,14) (0,22) (0,23) (0,20) (0,6) (0,18) (0,26) (0,29) (0,27) (0,11) (0,21) (1,28) (1,12) (1,24) (1,8) (1,10) (1,14) (1,22) (1,2) (1,20) (1,6) (1,18) (1,26) (1,17) (1,29) (1,27) (1,21) (2,28) (2,24) (2,3) (2,10) (2,22) (2,23) (2,20) (2,7) (2,6) (2,18) (2,27) (2,11) (2,21) (3,28) (3,24) (3,13) (3,10) (3,14) (3,22) (3,23) (3,20) (3,7) (3,29) (3,25) (3,21) (4,9) (4,5) (4,15) (4,19) (5,16) (6,28) (6,12) (6,24) (6,13) (6,8) (6,14) (6,23) (6,20) (6,26) (6,27) (6,11) (6,21) (7,28) (7,12) (7,24) (7,13) (7,10) (7,14) (7,22) (7,26) (7,17) (7,11) (7,21) (8,28) (8,12) (8,10) (8,22) (8,23) (8,20) (8,29) (8,27) (8,25) (8,11) (8,21) (9,16) (9,15) (9,19) (10,28) (10,12) (10,24) (10,13) (10,14) (10,22) (10,20) (10,18) (10,26) (10,27) (10,25) (10,11) (10,21) (11,22) (11,23) (11,20) (11,18) (11,26) (11,29) (11,27) (11,25) (11,21) (12,28) (12,24) (12,14) (12,22) (12,20) (12,18) (12,26) (12,17) (12,29) (12,27) (12,25) (12,21) (13,28) (13,24) (13,14) (13,22) (13,23) (13,20) (13,18) (13,17) (13,25) (13,21) (14,28) (14,24) (14,23) (14,20) (14,18) (14,26) (14,17) (14,29) (15,16) (15,19) (16,19) (17,28) (17,24) (17,23) (17,20) (17,18) (17,25) (17,21) (18,28) (18,24) (18,22) (18,23) (18,29) (18,27) (18,25) (18,21) (20,28) (20,24) (20,23) (20,26) (20,25) (20,21) (21,22) (21,23) (21,26) (21,29) (21,27) (21,25) (22,24) (22,23) (22,26) (22,29) (22,27) (22,25) (23,24) (23,26) (23,29) (23,27) (23,25) (24,28) (24,26) (24,29) (24,27) (24,25) (25,28) (25,26) (25,29) (25,27) (26,27) (27,29) (28,29)\nIs there a path between node 28 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph115-2_7", + "image": "data/connectivity/graph_visual/hard/graph115.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,13) (1,6) (1,12) (1,20) (1,5) (1,27) (1,24) (1,14) (1,16) (2,7) (3,17) (3,21) (3,26) (3,22) (3,10) (3,24) (3,14) (3,16) (4,19) (4,21) (4,6) (4,20) (4,9) (4,5) (4,23) (4,10) (4,14) (4,15) (4,16) (4,8) (5,13) (5,12) (5,27) (6,21) (6,26) (6,16) (6,8) (8,17) (8,26) (8,23) (8,15) (9,27) (9,22) (9,10) (9,24) (10,12) (10,20) (10,27) (10,22) (10,24) (10,15) (10,16) (12,13) (12,24) (12,15) (12,16) (13,22) (13,15) (14,19) (14,20) (14,26) (14,18) (14,23) (14,24) (15,27) (15,23) (15,24) (16,19) (16,21) (16,20) (16,23) (17,20) (17,23) (18,21) (18,23) (19,23) (19,24) (21,22) (21,24) (22,27) (22,23) (23,26) (23,27) (24,27)\nIs there a path between node 2 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph171-26_5", + "image": "data/connectivity/graph_visual/hard/graph171.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,2) (0,24) (0,19) (0,5) (0,8) (0,9) (0,23) (0,22) (0,13) (0,20) (0,7) (1,11) (1,24) (1,6) (1,14) (1,17) (1,8) (1,9) (1,23) (1,22) (1,13) (1,20) (1,26) (2,21) (2,3) (2,11) (2,24) (2,6) (2,14) (2,23) (2,13) (2,28) (2,20) (2,15) (2,18) (3,21) (3,11) (3,24) (3,6) (3,14) (3,17) (3,8) (3,9) (3,23) (3,25) (3,28) (3,15) (3,18) (3,7) (5,21) (5,11) (5,24) (5,6) (5,14) (5,19) (5,8) (5,9) (5,13) (5,28) (5,15) (5,18) (5,7) (6,11) (6,24) (6,14) (6,19) (6,17) (6,23) (6,22) (6,13) (6,25) (6,28) (6,18) (6,7) (6,26) (7,21) (7,24) (7,14) (7,19) (7,17) (7,9) (7,23) (7,13) (7,25) (7,28) (7,20) (7,15) (8,21) (8,14) (8,19) (8,17) (8,9) (8,23) (8,22) (8,13) (8,25) (8,18) (8,26) (9,21) (9,24) (9,14) (9,19) (9,17) (9,23) (9,22) (9,25) (9,15) (9,18) (9,26) (10,16) (10,27) (11,21) (11,24) (11,14) (11,17) (11,23) (11,13) (11,25) (11,28) (11,15) (11,18) (11,26) (13,21) (13,14) (13,17) (13,22) (13,28) (13,20) (13,18) (13,26) (14,21) (14,23) (14,25) (14,20) (14,18) (15,21) (15,24) (15,19) (15,17) (15,23) (15,22) (15,25) (15,18) (15,26) (17,21) (17,24) (17,23) (17,22) (17,25) (17,28) (17,20) (17,18) (18,21) (18,24) (18,19) (18,23) (18,22) (18,25) (18,28) (18,20) (18,26) (19,21) (19,24) (19,23) (19,22) (19,25) (19,28) (19,20) (20,24) (20,23) (20,22) (20,25) (20,28) (20,26) (21,23) (21,22) (21,28) (21,26) (22,24) (22,23) (22,25) (22,26) (23,24) (23,25) (23,28) (23,26) (24,25) (24,26) (25,28) (25,26) (26,28)\nIs there a path between node 26 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph232-13_19", + "image": "data/connectivity/graph_visual/hard/graph232.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,20) (0,9) (0,21) (0,1) (0,19) (0,7) (0,3) (0,27) (0,12) (0,23) (0,17) (1,9) (1,21) (1,10) (1,4) (1,19) (1,3) (1,12) (1,23) (1,17) (2,8) (2,28) (2,16) (2,24) (2,5) (2,11) (2,15) (3,20) (3,9) (3,21) (3,19) (3,27) (3,12) (3,23) (4,20) (4,9) (4,21) (4,19) (4,12) (4,23) (4,17) (5,18) (5,28) (5,16) (5,6) (5,14) (6,18) (6,28) (6,24) (7,20) (7,9) (7,12) (7,17) (8,16) (8,24) (8,15) (9,21) (9,10) (9,27) (9,12) (9,23) (9,17) (10,19) (10,27) (10,12) (10,23) (11,28) (11,16) (11,14) (11,24) (11,15) (12,20) (12,19) (12,27) (12,23) (12,17) (13,25) (13,26) (13,29) (14,28) (14,24) (14,15) (15,18) (15,28) (15,24) (16,18) (16,28) (17,20) (17,21) (17,23) (18,28) (18,24) (19,20) (19,21) (19,23) (20,27) (21,27) (22,25) (22,26) (22,29) (25,29) (26,29)\nIs there a path between node 13 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph103-3_4", + "image": "data/connectivity/graph_visual/hard/graph103.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,20) (0,2) (0,21) (0,26) (0,24) (0,9) (0,18) (0,8) (0,23) (0,5) (0,4) (0,7) (0,14) (0,17) (0,12) (0,10) (0,25) (0,27) (2,20) (2,21) (2,24) (2,9) (2,18) (2,8) (2,6) (2,23) (2,4) (2,11) (2,7) (2,14) (2,17) (2,12) (2,10) (2,25) (2,13) (2,27) (4,20) (4,22) (4,21) (4,24) (4,9) (4,8) (4,6) (4,23) (4,5) (4,11) (4,14) (4,15) (4,12) (4,10) (4,25) (4,13) (4,16) (4,27) (5,22) (5,21) (5,26) (5,6) (5,23) (5,7) (5,14) (5,15) (5,10) (5,13) (6,20) (6,22) (6,24) (6,11) (6,7) (6,17) (6,12) (6,25) (6,13) (6,16) (7,20) (7,22) (7,21) (7,9) (7,23) (7,14) (7,17) (7,10) (7,25) (7,13) (7,16) (8,20) (8,22) (8,26) (8,18) (8,23) (8,11) (8,14) (8,15) (8,17) (8,12) (8,13) (8,16) (9,20) (9,22) (9,21) (9,24) (9,18) (9,23) (9,14) (9,15) (9,17) (9,10) (9,25) (9,13) (9,16) (10,20) (10,21) (10,26) (10,23) (10,11) (10,14) (10,15) (10,17) (10,12) (10,25) (10,13) (10,16) (10,27) (11,21) (11,26) (11,18) (11,23) (11,14) (11,15) (11,17) (11,12) (11,25) (11,13) (11,27) (12,20) (12,21) (12,26) (12,18) (12,23) (12,14) (12,15) (12,25) (12,13) (12,16) (13,20) (13,21) (13,24) (13,18) (13,14) (13,15) (13,17) (13,27) (14,20) (14,22) (14,21) (14,26) (14,24) (14,23) (14,25) (14,27) (15,20) (15,22) (15,21) (15,26) (15,25) (15,16) (15,27) (16,20) (16,22) (16,21) (16,26) (16,24) (16,18) (16,23) (16,17) (17,20) (17,22) (17,21) (17,26) (17,24) (17,18) (17,23) (17,25) (17,27) (18,20) (18,26) (18,24) (18,23) (20,22) (20,21) (20,26) (20,24) (20,25) (20,27) (21,26) (21,24) (21,23) (21,25) (22,26) (22,24) (22,23) (22,25) (23,26) (23,24) (23,25) (23,27) (24,26) (24,25) (24,27)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph18-20_24", + "image": "data/connectivity/graph_visual/hard/graph18.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,11) (1,4) (2,21) (2,14) (2,20) (3,15) (3,17) (3,12) (3,16) (3,23) (4,11) (4,10) (4,7) (5,18) (5,12) (8,18) (8,14) (9,15) (9,17) (9,12) (9,23) (11,25) (12,14) (13,15) (13,21) (13,23) (13,20) (15,17) (15,19) (16,21) (16,23) (16,19) (17,21) (18,21) (19,23) (21,23)\nIs there a path between node 20 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph465-23_18", + "image": "data/connectivity/graph_visual/hard/graph465.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (1,5) (1,31) (1,4) (1,3) (1,30) (1,13) (2,22) (2,5) (2,31) (2,23) (2,3) (2,20) (2,30) (3,22) (3,31) (3,19) (4,22) (4,5) (4,23) (4,20) (5,7) (5,23) (5,19) (5,6) (6,28) (6,23) (6,19) (7,20) (7,13) (8,24) (8,21) (8,15) (8,25) (8,12) (10,26) (10,15) (10,14) (11,32) (11,27) (11,12) (12,29) (12,17) (13,20) (13,19) (14,21) (14,16) (14,17) (15,21) (15,17) (16,24) (16,32) (16,17) (17,24) (17,29) (19,28) (19,20) (19,30) (20,23) (22,30) (24,32) (24,29) (25,29) (27,29) (28,31) (28,30)\nIs there a path between node 23 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph638-31_34", + "image": "data/connectivity/graph_visual/hard/graph638.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,1) (0,19) (0,15) (0,20) (0,9) (0,21) (0,3) (0,22) (0,32) (0,24) (0,14) (0,11) (0,17) (0,5) (0,34) (0,4) (0,26) (0,10) (0,8) (1,27) (1,23) (1,30) (1,6) (1,19) (1,20) (1,2) (1,9) (1,21) (1,3) (1,22) (1,24) (1,14) (1,11) (1,17) (1,5) (1,4) (1,26) (1,8) (2,27) (2,30) (2,6) (2,19) (2,20) (2,9) (2,21) (2,3) (2,22) (2,32) (2,7) (2,11) (2,17) (2,5) (2,34) (2,4) (2,26) (2,12) (2,10) (3,27) (3,23) (3,30) (3,6) (3,19) (3,15) (3,20) (3,9) (3,22) (3,24) (3,14) (3,34) (3,4) (3,12) (3,10) (3,8) (3,28) (4,27) (4,23) (4,30) (4,19) (4,15) (4,20) (4,9) (4,21) (4,32) (4,24) (4,14) (4,7) (4,11) (4,17) (4,5) (4,26) (4,12) (4,8) (4,28) (5,30) (5,19) (5,9) (5,21) (5,24) (5,7) (5,11) (5,17) (5,34) (5,12) (6,27) (6,23) (6,30) (6,19) (6,20) (6,9) (6,21) (6,22) (6,32) (6,24) (6,14) (6,7) (6,11) (6,17) (6,34) (6,26) (6,8) (6,28) (7,23) (7,30) (7,19) (7,15) (7,20) (7,21) (7,32) (7,24) (7,11) (7,17) (7,34) (7,12) (7,10) (7,8) (7,28) (8,23) (8,15) (8,20) (8,24) (8,14) (8,11) (8,17) (8,34) (8,26) (8,12) (8,10) (8,28) (9,30) (9,19) (9,15) (9,20) (9,22) (9,32) (9,24) (9,11) (9,34) (9,12) (9,10) (9,28) (10,27) (10,23) (10,30) (10,19) (10,21) (10,32) (10,24) (10,26) (10,12) (11,27) (11,30) (11,19) (11,20) (11,21) (11,22) (11,32) (11,24) (11,14) (11,17) (11,34) (11,12) (12,27) (12,30) (12,19) (12,20) (12,22) (12,32) (12,24) (12,14) (12,17) (12,34) (12,28) (14,27) (14,23) (14,30) (14,19) (14,15) (14,21) (14,22) (14,32) (14,17) (14,34) (14,28) (15,19) (15,20) (15,21) (15,22) (15,32) (15,24) (15,34) (15,26) (15,28) (16,33) (16,29) (16,18) (16,31) (17,27) (17,23) (17,30) (17,19) (17,20) (17,21) (17,22) (17,32) (17,24) (17,34) (17,28) (18,33) (18,31) (18,25) (19,27) (19,23) (19,30) (19,20) (19,22) (19,32) (19,34) (19,26) (19,28) (20,23) (20,30) (20,21) (20,22) (20,32) (20,24) (20,34) (20,26) (21,27) (21,23) (21,30) (21,22) (21,32) (21,24) (21,34) (21,26) (21,28) (22,27) (22,23) (22,24) (22,34) (22,26) (22,28) (23,32) (23,26) (23,28) (24,27) (24,32) (24,34) (24,26) (25,33) (26,30) (26,32) (26,34) (27,30) (27,32) (27,28) (28,30) (28,32) (28,34) (29,33) (29,31) (31,33) (32,34)\nIs there a path between node 31 and node 34 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph140-17_5", + "image": "data/connectivity/graph_visual/hard/graph140.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,21) (0,25) (0,12) (0,26) (1,15) (1,23) (1,17) (1,13) (2,27) (2,10) (2,24) (4,9) (4,20) (4,13) (5,28) (5,11) (6,16) (6,23) (6,7) (6,13) (7,15) (7,16) (7,23) (7,17) (7,28) (8,12) (11,17) (11,20) (12,18) (12,14) (12,25) (12,19) (12,26) (13,23) (15,16) (16,23) (17,28) (18,26) (25,26)\nIs there a path between node 17 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph277-0_29", + "image": "data/connectivity/graph_visual/hard/graph277.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,8) (0,30) (0,14) (0,1) (0,10) (0,29) (0,12) (0,2) (0,17) (0,23) (0,7) (1,26) (1,3) (1,10) (1,25) (1,27) (1,29) (1,12) (1,20) (1,17) (1,7) (2,26) (2,3) (2,8) (2,30) (2,14) (2,10) (2,25) (2,27) (2,29) (2,12) (2,17) (2,23) (3,26) (3,30) (3,14) (3,10) (3,25) (3,27) (3,12) (3,20) (3,17) (3,23) (4,9) (4,22) (4,19) (4,21) (4,16) (4,6) (5,18) (5,13) (5,15) (6,9) (6,22) (6,21) (6,16) (7,26) (7,8) (7,30) (7,14) (7,10) (7,25) (7,27) (7,29) (7,12) (7,20) (7,17) (7,23) (8,27) (8,29) (8,12) (8,20) (8,23) (9,22) (9,21) (9,16) (9,28) (10,26) (10,14) (10,25) (10,29) (10,17) (11,21) (11,16) (11,28) (12,26) (12,25) (12,27) (12,29) (12,20) (12,17) (13,18) (13,15) (14,30) (14,25) (14,27) (14,29) (14,20) (14,17) (14,23) (16,22) (16,21) (16,28) (17,30) (17,27) (17,20) (17,23) (18,24) (19,22) (20,26) (20,25) (20,27) (20,23) (22,28) (23,26) (23,30) (23,25) (23,27) (23,29) (25,26) (25,27) (25,29) (26,27) (26,29) (27,30) (27,29)\nIs there a path between node 0 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph360-13_30", + "image": "data/connectivity/graph_visual/hard/graph360.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,28) (0,24) (0,31) (0,30) (0,27) (0,20) (1,21) (1,6) (1,19) (1,12) (1,22) (1,4) (1,17) (1,13) (1,30) (2,23) (2,3) (2,14) (3,25) (4,5) (4,17) (4,27) (5,17) (5,31) (5,20) (6,26) (6,16) (6,28) (6,10) (6,19) (6,12) (6,22) (6,13) (7,21) (7,28) (7,19) (7,17) (7,13) (7,18) (7,27) (8,23) (8,11) (8,25) (10,26) (10,28) (10,22) (10,31) (10,18) (11,23) (12,30) (13,21) (13,19) (13,31) (15,26) (15,16) (15,17) (15,18) (15,20) (16,21) (16,28) (16,19) (16,30) (16,27) (16,20) (17,24) (17,22) (17,18) (18,22) (19,22) (19,31) (19,20) (20,28) (21,22) (21,31) (22,30) (24,31) (27,28) (28,31)\nIs there a path between node 13 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph312-24_19", + "image": "data/connectivity/graph_visual/hard/graph312.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,2) (0,19) (1,9) (1,26) (1,15) (1,27) (1,17) (1,4) (2,14) (3,29) (4,24) (4,28) (4,8) (4,27) (4,12) (5,23) (6,24) (6,10) (6,18) (6,17) (6,16) (7,26) (7,10) (7,18) (7,12) (8,15) (8,18) (8,17) (8,12) (8,16) (9,16) (10,20) (10,18) (12,13) (12,20) (12,17) (12,16) (13,24) (13,16) (15,24) (15,26) (15,18) (15,17) (16,28) (16,20) (17,20) (18,28) (18,20) (19,21) (20,24) (22,25) (22,29) (22,30) (27,28) (30,31)\nIs there a path between node 24 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph496-24_8", + "image": "data/connectivity/graph_visual/hard/graph496.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,15) (0,27) (0,3) (1,6) (1,8) (1,12) (1,4) (1,10) (1,19) (2,9) (2,8) (2,26) (2,31) (2,18) (2,4) (3,15) (3,5) (4,6) (4,8) (4,28) (4,18) (4,13) (4,10) (4,23) (5,15) (5,27) (6,31) (6,10) (6,20) (7,25) (8,29) (8,28) (8,18) (9,26) (9,13) (9,10) (9,33) (10,26) (10,13) (11,26) (11,12) (11,22) (11,24) (11,13) (11,20) (12,26) (12,22) (12,24) (12,18) (12,20) (12,23) (12,33) (13,33) (14,17) (14,25) (14,32) (18,29) (18,22) (19,28) (19,24) (19,33) (20,29) (21,25) (21,32) (22,26) (22,23) (22,33) (23,28) (23,31) (23,33) (24,33) (26,28) (26,31) (26,33) (28,29) (29,31) (29,33) (30,32) (31,33)\nIs there a path between node 24 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph346-6_2", + "image": "data/connectivity/graph_visual/hard/graph346.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,29) (0,31) (0,26) (0,27) (0,19) (1,28) (2,30) (4,6) (5,29) (5,31) (6,17) (6,30) (7,24) (7,29) (7,31) (8,21) (8,28) (10,11) (10,15) (12,28) (14,15) (14,20) (15,20) (18,29) (18,26) (20,23) (21,28) (24,26) (24,27)\nIs there a path between node 6 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph522-16_14", + "image": "data/connectivity/graph_visual/hard/graph522.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,11) (0,33) (0,7) (0,13) (1,25) (1,30) (1,27) (2,6) (2,5) (2,13) (3,30) (3,17) (3,15) (3,32) (3,14) (3,21) (3,8) (3,12) (3,4) (3,24) (4,25) (4,17) (4,32) (4,12) (5,9) (7,16) (7,33) (8,28) (8,25) (8,32) (8,26) (8,21) (8,27) (8,20) (9,11) (9,16) (9,13) (10,28) (10,15) (10,26) (10,27) (10,24) (10,18) (11,16) (11,33) (12,28) (12,25) (12,24) (13,33) (14,27) (15,27) (15,29) (15,24) (17,25) (17,21) (18,25) (18,31) (18,21) (18,27) (20,25) (20,32) (20,22) (20,21) (20,27) (20,29) (20,24) (21,28) (21,29) (21,24) (22,24) (24,30) (24,31) (24,26) (25,31) (25,32) (25,26) (25,27) (26,30) (27,31) (28,29) (30,32)\nIs there a path between node 16 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph630-24_10", + "image": "data/connectivity/graph_visual/hard/graph630.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,30) (1,27) (1,11) (2,17) (2,15) (2,32) (3,24) (3,15) (3,10) (3,25) (3,32) (4,21) (4,12) (4,27) (4,8) (5,9) (5,34) (6,30) (6,11) (6,8) (7,29) (7,24) (7,15) (7,14) (8,30) (8,11) (10,19) (10,14) (11,16) (11,31) (11,21) (11,27) (11,23) (12,27) (13,25) (13,20) (14,17) (15,29) (15,24) (15,32) (15,20) (16,31) (17,29) (17,24) (17,19) (17,25) (17,20) (19,24) (19,25) (19,20) (20,32) (21,27) (21,23) (23,31) (24,32) (26,28) (27,30) (29,32)\nIs there a path between node 24 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph544-26_27", + "image": "data/connectivity/graph_visual/hard/graph544.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,11) (0,20) (0,7) (0,4) (0,24) (0,13) (0,18) (0,31) (0,32) (0,1) (0,28) (0,3) (0,29) (0,25) (0,16) (0,19) (1,11) (1,17) (1,20) (1,5) (1,4) (1,13) (1,18) (1,31) (1,32) (1,27) (1,3) (1,16) (1,19) (2,33) (2,12) (3,8) (3,11) (3,17) (3,20) (3,4) (3,24) (3,13) (3,18) (3,31) (3,32) (3,14) (3,28) (3,29) (3,16) (3,19) (4,8) (4,11) (4,15) (4,5) (4,7) (4,24) (4,13) (4,18) (4,31) (4,32) (4,14) (4,28) (4,30) (4,29) (4,25) (4,26) (5,17) (5,20) (5,13) (5,31) (5,14) (5,30) (5,29) (5,25) (5,16) (5,26) (5,19) (6,21) (6,9) (7,8) (7,17) (7,20) (7,15) (7,24) (7,32) (7,14) (7,30) (7,29) (7,26) (8,11) (8,17) (8,20) (8,15) (8,24) (8,18) (8,27) (8,14) (8,28) (8,29) (8,26) (9,23) (9,21) (9,10) (10,23) (10,21) (11,17) (11,20) (11,24) (11,13) (11,31) (11,32) (11,14) (11,28) (11,29) (11,16) (11,26) (13,24) (13,27) (13,14) (13,29) (13,16) (13,26) (13,19) (14,17) (14,20) (14,15) (14,24) (14,18) (14,31) (14,32) (14,27) (14,28) (14,30) (14,29) (14,25) (14,19) (15,17) (15,20) (15,24) (15,18) (15,31) (15,32) (15,27) (15,28) (15,29) (15,25) (15,16) (15,26) (15,19) (16,17) (16,20) (16,24) (16,32) (16,27) (16,28) (16,30) (16,29) (16,25) (16,26) (17,24) (17,18) (17,31) (17,32) (17,28) (17,29) (17,25) (17,26) (17,19) (18,20) (18,31) (18,32) (18,27) (18,28) (18,29) (18,25) (18,26) (18,19) (19,20) (19,24) (19,32) (19,28) (19,29) (19,25) (20,24) (20,31) (20,32) (20,27) (20,28) (20,30) (20,29) (20,26) (21,23) (24,31) (24,32) (24,27) (24,28) (24,30) (24,29) (24,25) (25,31) (25,32) (25,27) (25,29) (25,26) (26,31) (26,32) (26,28) (27,32) (27,28) (28,32) (28,30) (29,32) (29,30) (30,31) (30,32) (31,32)\nIs there a path between node 26 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph340-27_14", + "image": "data/connectivity/graph_visual/hard/graph340.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,14) (0,13) (0,27) (1,21) (1,24) (1,13) (1,5) (2,19) (3,30) (3,26) (3,10) (3,25) (5,15) (5,9) (5,27) (5,19) (6,22) (6,29) (6,16) (7,15) (7,24) (7,9) (7,19) (9,21) (9,15) (9,24) (10,31) (10,11) (10,23) (11,23) (11,26) (11,17) (12,22) (12,29) (12,16) (13,14) (13,24) (14,21) (14,24) (14,27) (15,21) (16,29) (17,23) (17,25) (18,20) (18,29) (20,22) (21,27) (24,27) (25,28)\nIs there a path between node 27 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph112-8_3", + "image": "data/connectivity/graph_visual/hard/graph112.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,22) (0,11) (0,10) (0,23) (0,4) (0,9) (0,19) (1,17) (1,27) (1,15) (1,23) (1,24) (1,5) (1,18) (2,15) (2,10) (2,23) (2,5) (2,6) (2,16) (4,17) (4,27) (4,16) (4,25) (5,27) (5,11) (5,24) (5,7) (5,16) (5,25) (5,21) (5,18) (6,17) (6,13) (6,27) (6,11) (6,10) (6,14) (6,16) (6,8) (6,19) (7,20) (7,15) (7,10) (7,24) (7,16) (7,8) (7,19) (7,25) (7,21) (8,20) (8,17) (8,27) (8,11) (8,24) (8,16) (9,20) (9,27) (9,11) (9,16) (9,25) (10,13) (10,27) (10,15) (10,16) (11,20) (11,13) (11,14) (11,24) (11,21) (13,20) (13,14) (13,16) (14,22) (14,15) (14,23) (14,19) (15,24) (15,19) (15,25) (16,22) (16,17) (16,23) (17,22) (17,23) (17,25) (18,19) (18,21) (19,27) (19,24) (19,25) (21,25) (23,27) (25,27)\nIs there a path between node 8 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph668-10_15", + "image": "data/connectivity/graph_visual/hard/graph668.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,19) (0,18) (0,12) (0,21) (0,23) (0,5) (0,26) (0,11) (0,30) (1,16) (1,19) (1,21) (1,17) (1,5) (1,26) (2,22) (2,18) (2,27) (2,23) (2,28) (2,24) (3,20) (3,14) (3,5) (3,33) (3,26) (3,25) (3,30) (4,16) (4,18) (4,21) (4,23) (4,28) (4,11) (4,25) (4,6) (5,22) (5,7) (5,18) (5,9) (5,17) (5,29) (5,28) (5,24) (5,11) (6,16) (6,20) (6,7) (6,19) (6,18) (6,14) (6,12) (6,9) (6,21) (6,23) (7,31) (7,18) (7,12) (7,9) (7,32) (7,17) (7,29) (7,26) (8,31) (8,10) (8,14) (8,9) (8,21) (8,32) (8,29) (8,33) (8,26) (9,13) (9,27) (9,12) (9,17) (9,29) (9,33) (9,28) (9,11) (9,25) (10,22) (10,31) (10,20) (10,18) (10,12) (10,23) (10,29) (10,28) (11,16) (11,13) (11,14) (11,17) (11,26) (11,30) (12,16) (12,22) (12,20) (12,13) (12,27) (12,21) (12,32) (12,17) (12,25) (13,18) (14,20) (14,32) (14,28) (14,26) (16,19) (16,17) (16,28) (16,24) (16,25) (16,30) (17,19) (17,18) (17,27) (17,25) (18,20) (18,28) (18,26) (19,22) (19,31) (19,27) (19,23) (19,29) (19,33) (20,22) (20,31) (20,23) (20,32) (20,33) (20,26) (20,30) (21,22) (21,29) (21,24) (21,25) (22,31) (22,23) (22,33) (22,26) (23,32) (23,33) (23,24) (23,30) (24,27) (24,25) (25,27) (25,32) (25,28) (25,26) (26,33) (26,30) (27,33) (27,30) (28,31) (28,29) (29,31) (29,32) (30,31) (30,33) (31,33)\nIs there a path between node 10 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph63-25_10", + "image": "data/connectivity/graph_visual/hard/graph63.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (2,26) (3,4) (3,5) (3,6) (3,15) (3,7) (3,18) (3,23) (3,22) (4,6) (4,9) (4,15) (4,7) (4,21) (4,17) (4,8) (4,23) (4,16) (4,24) (5,11) (5,9) (5,15) (5,23) (5,14) (5,24) (5,10) (6,20) (6,7) (6,17) (6,23) (6,14) (6,25) (7,15) (7,18) (7,12) (7,14) (7,25) (8,15) (8,21) (8,22) (8,12) (8,14) (8,25) (9,15) (9,18) (9,23) (9,14) (10,21) (10,17) (10,12) (10,24) (10,25) (11,21) (11,23) (11,22) (11,14) (12,21) (12,14) (12,25) (13,26) (14,17) (14,16) (14,24) (15,21) (15,23) (15,24) (16,20) (17,20) (17,25) (18,21) (20,25) (21,24) (21,25)\nIs there a path between node 25 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph160-17_4", + "image": "data/connectivity/graph_visual/hard/graph160.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,6) (1,11) (1,2) (1,12) (1,28) (2,22) (2,28) (3,6) (3,8) (3,20) (3,23) (3,19) (4,24) (4,12) (4,28) (5,24) (6,9) (6,21) (7,20) (7,16) (7,13) (8,20) (8,9) (8,23) (8,21) (9,23) (9,13) (10,26) (10,24) (10,12) (10,18) (11,12) (11,18) (11,17) (11,25) (12,18) (13,20) (13,23) (14,27) (15,27) (16,21) (16,19) (17,18) (18,26) (18,22) (19,21) (25,26)\nIs there a path between node 17 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph30-20_8", + "image": "data/connectivity/graph_visual/hard/graph30.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,16) (0,14) (0,10) (0,24) (0,2) (0,12) (0,19) (0,3) (0,17) (0,25) (0,23) (0,15) (1,18) (1,11) (1,8) (2,14) (2,10) (2,24) (2,7) (2,3) (2,21) (2,25) (2,23) (2,6) (3,14) (3,24) (3,12) (3,19) (3,17) (3,25) (3,23) (3,6) (3,15) (4,18) (4,8) (5,18) (5,11) (5,8) (6,16) (6,14) (6,10) (6,12) (6,7) (6,19) (6,21) (6,25) (6,23) (6,9) (6,15) (7,16) (7,10) (7,24) (7,12) (7,19) (7,17) (7,25) (7,9) (7,15) (8,18) (8,11) (9,16) (9,14) (9,10) (9,24) (9,12) (9,19) (9,17) (9,21) (9,23) (9,15) (10,16) (10,14) (10,19) (10,21) (10,25) (10,23) (10,15) (11,18) (12,16) (12,14) (12,24) (12,19) (12,17) (12,21) (12,25) (12,23) (12,15) (13,20) (14,16) (14,24) (14,17) (14,21) (14,25) (14,23) (14,15) (15,16) (15,24) (15,23) (16,21) (16,25) (16,23) (17,21) (17,23) (19,21) (19,25) (21,24) (21,25) (21,23) (23,25) (24,25)\nIs there a path between node 20 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph702-31_29", + "image": "data/connectivity/graph_visual/hard/graph702.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,12) (0,4) (0,34) (0,32) (0,13) (0,20) (0,11) (0,14) (0,6) (0,3) (1,12) (1,17) (1,33) (1,20) (1,23) (1,11) (1,6) (1,3) (2,31) (2,30) (2,21) (2,27) (2,7) (2,29) (2,15) (2,19) (2,5) (2,9) (2,16) (2,18) (2,24) (2,26) (3,12) (3,33) (3,4) (3,34) (3,32) (3,20) (3,11) (3,6) (4,33) (4,13) (4,14) (5,25) (5,10) (5,21) (5,27) (5,7) (5,29) (5,8) (5,16) (5,18) (5,22) (5,24) (6,34) (6,13) (6,23) (6,11) (6,14) (7,31) (7,25) (7,30) (7,27) (7,29) (7,9) (7,8) (7,18) (7,22) (7,24) (7,26) (8,25) (8,30) (8,21) (8,27) (8,19) (8,9) (8,16) (8,22) (8,28) (8,24) (9,31) (9,25) (9,30) (9,21) (9,27) (9,29) (9,16) (9,22) (9,28) (9,24) (10,31) (10,25) (10,30) (10,21) (10,29) (10,15) (10,19) (10,16) (10,18) (10,22) (10,26) (11,33) (11,34) (11,32) (11,23) (11,14) (12,17) (12,32) (12,23) (12,14) (13,17) (13,33) (13,34) (13,32) (13,20) (13,23) (13,14) (14,17) (14,34) (14,32) (14,20) (15,25) (15,21) (15,29) (15,19) (15,16) (15,18) (15,28) (15,24) (16,31) (16,25) (16,21) (16,27) (16,29) (16,19) (16,22) (16,28) (16,24) (16,26) (17,33) (17,34) (17,32) (17,20) (18,31) (18,25) (18,30) (18,21) (18,27) (18,29) (18,19) (18,22) (18,28) (18,24) (18,26) (19,31) (19,25) (19,21) (19,28) (19,26) (20,33) (20,34) (20,32) (20,23) (21,31) (21,25) (21,30) (21,27) (21,24) (22,31) (22,25) (22,30) (22,27) (22,29) (22,28) (22,24) (22,26) (23,34) (23,32) (24,31) (24,25) (24,30) (24,29) (24,28) (25,31) (25,30) (25,29) (25,28) (25,26) (26,27) (26,29) (26,28) (27,31) (27,29) (27,28) (28,30) (29,31) (29,30) (30,31) (33,34)\nIs there a path between node 31 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph322-10_31", + "image": "data/connectivity/graph_visual/hard/graph322.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,31) (0,23) (0,26) (0,5) (0,11) (0,19) (0,13) (0,27) (0,16) (0,7) (1,4) (1,6) (1,2) (1,30) (1,29) (1,12) (1,21) (1,10) (2,6) (2,30) (2,28) (2,15) (2,29) (2,12) (2,24) (2,14) (2,10) (3,9) (3,8) (3,31) (3,23) (3,5) (3,11) (3,19) (3,20) (3,16) (3,7) (4,6) (4,30) (4,28) (4,15) (4,29) (4,24) (4,21) (5,23) (5,26) (5,17) (5,11) (5,19) (5,13) (5,20) (5,7) (5,22) (6,18) (6,25) (6,30) (6,29) (6,12) (6,24) (6,21) (6,14) (6,10) (7,9) (7,8) (7,31) (7,26) (7,11) (7,19) (7,27) (7,20) (7,16) (7,22) (8,9) (8,31) (8,26) (8,17) (8,11) (8,13) (8,22) (9,31) (9,26) (9,11) (9,19) (9,13) (9,27) (9,20) (9,22) (10,18) (10,25) (10,28) (10,15) (10,24) (10,21) (11,31) (11,26) (11,17) (11,19) (11,13) (11,20) (12,18) (12,30) (12,29) (12,24) (12,21) (13,31) (13,23) (13,26) (13,17) (13,27) (13,20) (14,18) (14,25) (14,30) (14,15) (14,29) (14,24) (15,18) (15,25) (15,28) (15,29) (15,24) (15,21) (16,31) (16,23) (16,17) (16,27) (16,20) (16,22) (17,27) (17,20) (18,25) (18,28) (18,29) (18,21) (19,31) (19,26) (20,31) (20,23) (20,26) (20,27) (21,25) (21,30) (21,28) (21,29) (21,24) (22,31) (22,26) (23,31) (23,26) (24,30) (24,28) (24,29) (25,30) (25,28) (25,29) (26,31) (27,31) (28,30) (28,29) (29,30)\nIs there a path between node 10 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph583-15_3", + "image": "data/connectivity/graph_visual/hard/graph583.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,19) (0,16) (0,14) (0,22) (0,3) (0,21) (0,28) (0,1) (0,10) (0,8) (0,30) (0,18) (0,4) (0,25) (0,26) (0,23) (0,6) (0,24) (0,20) (0,11) (0,29) (0,33) (1,16) (1,14) (1,3) (1,21) (1,8) (1,30) (1,18) (1,4) (1,26) (1,23) (1,6) (1,24) (1,20) (1,32) (1,11) (1,29) (1,33) (1,12) (2,19) (2,14) (2,22) (2,28) (2,10) (2,8) (2,30) (2,18) (2,4) (2,25) (2,5) (2,26) (2,23) (2,6) (2,24) (2,20) (2,32) (2,29) (2,33) (2,9) (2,12) (3,19) (3,16) (3,10) (3,8) (3,30) (3,18) (3,4) (3,25) (3,5) (3,26) (3,23) (3,6) (3,32) (3,11) (3,29) (4,16) (4,22) (4,21) (4,28) (4,10) (4,18) (4,25) (4,26) (4,20) (4,11) (4,29) (4,33) (4,9) (4,12) (5,19) (5,16) (5,14) (5,22) (5,21) (5,28) (5,10) (5,8) (5,30) (5,18) (5,25) (5,26) (5,6) (5,24) (5,20) (5,32) (5,11) (5,33) (5,9) (5,12) (6,16) (6,14) (6,21) (6,10) (6,30) (6,18) (6,25) (6,24) (6,20) (6,32) (6,11) (6,12) (7,17) (7,13) (8,19) (8,16) (8,22) (8,10) (8,18) (8,23) (8,24) (8,32) (8,11) (8,29) (8,33) (8,9) (9,16) (9,14) (9,28) (9,10) (9,30) (9,18) (9,25) (9,26) (9,11) (9,29) (9,33) (10,19) (10,16) (10,14) (10,22) (10,28) (10,30) (10,18) (10,25) (10,26) (10,32) (10,11) (10,29) (10,12) (11,19) (11,16) (11,22) (11,21) (11,28) (11,18) (11,26) (11,23) (11,24) (11,20) (11,32) (11,29) (11,12) (12,16) (12,14) (12,22) (12,21) (12,28) (12,30) (12,18) (12,25) (12,23) (12,24) (12,32) (12,33) (14,16) (14,22) (14,21) (14,28) (14,18) (14,25) (14,26) (14,20) (14,32) (14,33) (15,31) (15,27) (16,19) (16,22) (16,28) (16,30) (16,18) (16,26) (16,23) (16,24) (16,20) (16,32) (16,33) (18,19) (18,22) (18,21) (18,28) (18,25) (18,26) (18,20) (18,32) (18,33) (19,22) (19,21) (19,28) (19,30) (19,25) (19,26) (19,20) (19,33) (20,22) (20,28) (20,25) (20,26) (20,24) (20,32) (20,33) (21,22) (21,28) (21,30) (21,25) (21,26) (21,24) (21,32) (21,29) (21,33) (22,26) (22,23) (22,24) (22,32) (23,30) (23,25) (23,24) (23,29) (23,33) (24,28) (24,32) (24,29) (25,28) (25,26) (25,33) (26,30) (26,29) (26,33) (27,31) (28,30) (28,32) (28,29) (29,30) (30,32)\nIs there a path between node 15 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph394-3_17", + "image": "data/connectivity/graph_visual/hard/graph394.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,12) (0,24) (0,5) (0,32) (0,18) (0,23) (0,25) (1,20) (2,21) (2,13) (2,29) (3,12) (3,7) (3,11) (3,23) (3,25) (4,27) (4,12) (4,32) (5,30) (5,14) (7,10) (7,11) (7,23) (7,25) (8,27) (8,18) (8,30) (8,11) (8,25) (9,28) (10,27) (10,24) (10,32) (10,18) (10,23) (11,22) (11,14) (12,27) (12,24) (12,25) (13,15) (13,21) (13,29) (14,27) (14,32) (14,23) (15,21) (19,20) (22,30) (22,23) (23,30) (24,32) (24,30) (24,25) (25,27)\nIs there a path between node 3 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph8-11_0", + "image": "data/connectivity/graph_visual/hard/graph8.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,15) (0,14) (1,20) (2,24) (2,3) (2,13) (4,8) (4,6) (4,11) (4,5) (5,19) (5,21) (5,23) (6,19) (6,20) (7,14) (7,10) (8,21) (9,19) (9,11) (10,15) (10,22) (11,23) (12,18) (13,24) (13,25) (14,22) (15,22) (18,25) (19,20) (21,23)\nIs there a path between node 11 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph357-29_1", + "image": "data/connectivity/graph_visual/hard/graph357.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,22) (0,27) (1,18) (1,21) (1,15) (1,6) (1,29) (1,9) (1,4) (1,8) (1,28) (1,17) (2,13) (2,24) (2,14) (2,30) (2,12) (2,17) (2,5) (3,20) (3,14) (3,23) (3,15) (3,26) (3,9) (3,25) (3,8) (3,28) (3,17) (4,20) (4,18) (4,23) (4,15) (4,10) (4,30) (4,6) (4,26) (4,12) (4,16) (5,24) (5,14) (5,15) (5,6) (5,29) (5,12) (5,9) (5,8) (6,18) (6,10) (6,29) (6,28) (6,17) (7,27) (8,18) (8,21) (8,13) (8,23) (8,12) (8,25) (8,19) (8,17) (9,15) (9,30) (9,29) (9,25) (9,19) (9,17) (10,29) (10,26) (10,28) (10,17) (11,18) (11,15) (11,30) (11,26) (11,28) (11,17) (12,20) (12,14) (12,23) (13,18) (13,30) (13,29) (13,26) (13,25) (13,19) (13,28) (13,17) (14,20) (14,19) (15,18) (16,20) (16,26) (16,25) (16,19) (17,30) (17,26) (17,19) (18,21) (18,24) (18,30) (18,25) (18,28) (19,21) (19,23) (20,24) (20,26) (20,28) (21,24) (21,30) (24,30) (24,26) (25,30) (26,29) (26,28)\nIs there a path between node 29 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph123-4_25", + "image": "data/connectivity/graph_visual/hard/graph123.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,13) (0,26) (0,21) (0,20) (0,25) (0,16) (0,22) (0,14) (0,2) (0,27) (0,3) (0,5) (0,4) (0,7) (0,11) (0,24) (0,12) (0,1) (0,6) (0,23) (1,13) (1,26) (1,21) (1,25) (1,16) (1,22) (1,14) (1,2) (1,8) (1,27) (1,3) (1,5) (1,7) (1,11) (1,24) (1,12) (1,6) (1,23) (2,21) (2,25) (2,16) (2,10) (2,14) (2,8) (2,27) (2,3) (2,5) (2,4) (2,7) (2,11) (2,24) (2,12) (3,26) (3,21) (3,25) (3,10) (3,8) (3,4) (3,7) (3,11) (3,24) (3,12) (3,23) (4,13) (4,21) (4,20) (4,16) (4,10) (4,22) (4,8) (4,27) (4,7) (4,11) (4,24) (4,6) (5,21) (5,20) (5,25) (5,10) (5,8) (5,27) (5,11) (5,12) (5,6) (5,23) (6,13) (6,26) (6,21) (6,16) (6,10) (6,22) (6,14) (6,8) (6,11) (6,24) (6,12) (6,23) (7,13) (7,26) (7,21) (7,22) (7,14) (7,8) (7,24) (7,12) (7,23) (8,13) (8,21) (8,20) (8,25) (8,16) (8,22) (8,14) (8,23) (9,17) (9,18) (10,13) (10,26) (10,21) (10,20) (10,16) (10,14) (10,27) (10,11) (10,12) (10,23) (11,26) (11,25) (11,22) (11,27) (11,24) (11,12) (12,13) (12,21) (12,20) (12,16) (12,22) (12,14) (12,27) (12,24) (12,23) (13,26) (13,21) (13,20) (13,16) (13,22) (13,14) (13,27) (13,24) (13,23) (14,26) (14,21) (14,20) (14,25) (14,16) (14,22) (14,27) (14,24) (14,23) (15,18) (15,19) (16,26) (16,21) (16,27) (16,23) (17,18) (17,19) (18,19) (20,26) (20,21) (20,27) (20,24) (20,23) (21,26) (21,22) (21,27) (22,26) (22,25) (22,24) (22,23) (23,25) (23,24) (24,26) (24,25) (24,27)\nIs there a path between node 4 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph386-2_1", + "image": "data/connectivity/graph_visual/hard/graph386.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,16) (0,20) (0,21) (0,24) (0,6) (0,31) (0,26) (0,2) (0,7) (0,14) (0,27) (0,11) (0,1) (1,16) (1,21) (1,24) (1,31) (1,18) (1,25) (1,26) (1,2) (1,7) (1,14) (1,27) (1,11) (1,10) (2,16) (2,20) (2,21) (2,24) (2,6) (2,31) (2,14) (2,27) (2,10) (3,15) (3,29) (3,4) (3,13) (3,8) (3,19) (3,5) (3,22) (4,30) (4,12) (4,17) (4,29) (4,13) (4,5) (4,22) (5,30) (5,12) (5,15) (5,28) (5,29) (5,19) (5,22) (5,23) (6,9) (6,16) (6,24) (6,31) (6,25) (6,7) (6,27) (6,11) (7,16) (7,21) (7,24) (7,18) (7,14) (7,11) (7,10) (8,12) (8,17) (8,15) (8,13) (8,19) (8,22) (8,23) (9,20) (9,21) (9,24) (9,31) (9,18) (9,26) (9,14) (10,21) (10,31) (10,18) (10,25) (10,26) (10,14) (10,27) (10,11) (11,16) (11,20) (11,21) (11,31) (11,18) (11,25) (11,26) (11,14) (12,28) (12,29) (12,13) (12,23) (13,30) (13,17) (13,15) (13,28) (13,19) (13,23) (14,20) (14,21) (14,31) (14,18) (14,25) (14,26) (14,27) (15,17) (15,28) (15,19) (15,23) (16,20) (16,21) (16,24) (16,18) (16,26) (17,30) (17,22) (17,23) (18,21) (18,31) (18,25) (18,27) (19,30) (19,28) (19,22) (19,23) (20,21) (20,31) (20,26) (20,27) (21,24) (21,31) (21,25) (21,26) (21,27) (22,30) (22,29) (23,30) (23,28) (23,29) (24,31) (24,25) (24,26) (25,31) (25,26) (25,27) (26,27) (27,31) (28,30) (28,29)\nIs there a path between node 2 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph483-11_22", + "image": "data/connectivity/graph_visual/hard/graph483.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,6) (0,15) (0,2) (0,10) (0,20) (0,13) (0,30) (0,17) (0,32) (0,22) (0,24) (1,31) (1,8) (1,4) (2,19) (2,15) (2,27) (2,10) (2,11) (2,20) (2,13) (2,17) (2,32) (2,22) (2,7) (3,18) (3,31) (3,8) (3,4) (4,18) (4,8) (5,25) (5,9) (6,19) (6,16) (6,15) (6,11) (6,13) (6,30) (6,17) (6,32) (6,24) (6,7) (7,19) (7,16) (7,15) (7,10) (7,20) (7,13) (7,30) (7,17) (7,32) (7,22) (7,24) (8,18) (8,31) (9,25) (9,23) (9,28) (10,19) (10,16) (10,27) (10,11) (10,20) (10,13) (10,30) (10,32) (10,22) (10,24) (11,19) (11,16) (11,15) (11,27) (11,13) (11,30) (11,17) (11,32) (11,24) (12,18) (13,19) (13,16) (13,27) (13,20) (13,30) (13,17) (13,22) (13,24) (14,29) (14,26) (15,19) (15,16) (15,27) (15,20) (15,30) (15,17) (15,32) (15,24) (16,19) (16,27) (16,20) (16,30) (16,17) (16,32) (16,24) (17,19) (17,20) (17,30) (17,22) (17,24) (18,31) (19,27) (19,20) (19,30) (19,32) (19,24) (20,27) (20,32) (20,22) (20,24) (21,29) (21,26) (22,27) (22,30) (22,32) (22,24) (23,25) (23,28) (24,27) (24,30) (24,32) (26,29) (27,30)\nIs there a path between node 11 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph134-1_6", + "image": "data/connectivity/graph_visual/hard/graph134.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,16) (0,4) (1,27) (1,26) (1,10) (1,13) (1,12) (1,24) (1,19) (1,11) (1,7) (1,6) (1,14) (1,3) (1,18) (1,20) (2,4) (3,9) (3,27) (3,10) (3,21) (3,25) (3,13) (3,24) (3,15) (3,23) (3,19) (3,11) (3,7) (3,6) (3,14) (3,18) (5,9) (5,26) (5,22) (5,10) (5,13) (5,12) (5,15) (5,17) (5,23) (5,19) (5,11) (5,7) (5,6) (5,14) (6,27) (6,26) (6,10) (6,21) (6,25) (6,13) (6,12) (6,8) (6,17) (6,23) (6,19) (6,11) (6,7) (6,14) (6,18) (6,20) (7,9) (7,27) (7,22) (7,10) (7,21) (7,13) (7,12) (7,8) (7,24) (7,15) (7,17) (7,19) (7,11) (7,14) (8,9) (8,27) (8,22) (8,10) (8,21) (8,25) (8,13) (8,12) (8,15) (8,17) (8,23) (8,19) (8,11) (8,14) (8,18) (8,20) (9,27) (9,10) (9,21) (9,13) (9,12) (9,24) (9,15) (9,17) (9,23) (9,19) (9,11) (9,20) (10,27) (10,26) (10,22) (10,21) (10,25) (10,13) (10,24) (10,15) (10,17) (10,19) (10,11) (10,14) (11,27) (11,26) (11,22) (11,25) (11,13) (11,15) (11,17) (11,14) (11,18) (11,20) (12,27) (12,26) (12,22) (12,21) (12,13) (12,15) (12,17) (12,23) (12,19) (12,18) (12,20) (13,22) (13,21) (13,24) (13,15) (13,17) (13,23) (13,19) (13,14) (13,18) (13,20) (14,27) (14,26) (14,24) (14,15) (14,17) (14,23) (14,19) (14,20) (15,27) (15,22) (15,25) (15,24) (15,17) (15,23) (15,20) (17,22) (17,25) (17,23) (17,19) (17,18) (17,20) (18,26) (18,24) (18,23) (18,19) (19,26) (19,21) (19,25) (19,24) (19,23) (19,20) (20,27) (20,26) (20,21) (20,24) (20,23) (21,27) (21,22) (21,25) (21,24) (22,27) (22,26) (23,27) (23,26) (23,24) (25,27) (25,26)\nIs there a path between node 1 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph361-23_4", + "image": "data/connectivity/graph_visual/hard/graph361.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,14) (0,30) (0,15) (0,20) (0,12) (1,28) (1,23) (1,19) (1,27) (2,31) (2,8) (2,14) (2,7) (2,6) (2,12) (3,25) (3,18) (3,13) (3,23) (4,31) (4,24) (4,22) (4,30) (4,12) (5,28) (5,23) (6,31) (6,22) (6,8) (6,10) (6,7) (6,15) (6,20) (6,21) (6,12) (7,22) (7,15) (7,20) (8,10) (8,14) (9,18) (9,13) (9,28) (11,30) (11,15) (11,16) (11,21) (12,22) (12,16) (13,18) (13,28) (14,22) (14,17) (14,30) (15,22) (16,17) (16,21) (17,30) (18,26) (18,29) (18,19) (19,28) (20,21) (21,30) (24,31) (25,26) (25,28) (28,29)\nIs there a path between node 23 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph578-23_21", + "image": "data/connectivity/graph_visual/hard/graph578.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,3) (0,27) (0,22) (0,26) (0,31) (0,21) (0,20) (0,4) (0,17) (0,11) (0,14) (0,28) (0,33) (1,15) (1,23) (1,9) (1,13) (1,29) (1,12) (1,5) (1,25) (1,18) (2,6) (2,24) (2,27) (2,22) (2,26) (2,21) (2,32) (2,4) (2,17) (2,16) (2,11) (2,14) (2,28) (2,33) (3,6) (3,24) (3,8) (3,19) (3,10) (3,27) (3,22) (3,26) (3,31) (3,20) (3,4) (3,17) (3,14) (3,28) (3,33) (4,6) (4,24) (4,19) (4,10) (4,22) (4,26) (4,20) (4,32) (4,17) (4,11) (4,28) (5,15) (5,23) (5,9) (5,13) (5,30) (5,29) (5,12) (5,18) (6,19) (6,27) (6,22) (6,31) (6,20) (6,32) (6,16) (6,14) (6,28) (6,33) (7,24) (7,8) (7,19) (7,27) (7,22) (7,31) (7,21) (7,20) (7,32) (7,16) (7,11) (7,28) (7,33) (8,24) (8,10) (8,27) (8,22) (8,26) (8,31) (8,21) (8,20) (8,17) (8,11) (8,14) (8,28) (9,15) (9,23) (9,30) (9,29) (9,12) (9,25) (9,18) (10,24) (10,19) (10,26) (10,31) (10,21) (10,20) (10,32) (10,16) (10,11) (10,14) (10,28) (10,33) (11,24) (11,19) (11,27) (11,22) (11,26) (11,21) (11,32) (11,17) (11,16) (11,28) (11,33) (12,15) (12,23) (12,13) (12,30) (12,29) (12,25) (12,18) (13,29) (13,25) (14,24) (14,19) (14,27) (14,22) (14,26) (14,31) (14,21) (14,20) (14,17) (14,16) (14,28) (15,29) (15,25) (15,18) (16,24) (16,19) (16,22) (16,26) (16,21) (16,20) (16,32) (16,33) (17,27) (17,22) (17,31) (17,21) (17,20) (17,32) (17,28) (17,33) (18,23) (18,30) (19,24) (19,27) (19,22) (19,26) (19,31) (19,21) (19,20) (19,32) (19,28) (20,24) (20,27) (20,26) (20,21) (20,32) (20,28) (20,33) (21,27) (21,26) (21,32) (21,28) (21,33) (22,24) (22,27) (22,31) (22,32) (22,28) (22,33) (23,30) (23,29) (23,25) (24,26) (24,31) (24,32) (26,27) (26,32) (26,28) (27,31) (27,32) (27,28) (28,33) (29,30) (32,33)\nIs there a path between node 23 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph591-31_1", + "image": "data/connectivity/graph_visual/hard/graph591.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,13) (0,31) (0,32) (0,33) (0,15) (1,5) (1,19) (1,16) (1,18) (1,11) (1,10) (1,9) (1,28) (1,14) (1,3) (1,8) (2,7) (2,5) (2,19) (2,16) (2,29) (2,18) (2,11) (2,25) (2,9) (2,28) (2,14) (2,3) (2,30) (2,8) (2,27) (3,7) (3,5) (3,19) (3,29) (3,18) (3,11) (3,6) (3,10) (3,25) (3,9) (3,28) (3,14) (3,30) (3,8) (4,26) (4,32) (4,17) (4,33) (4,15) (5,7) (5,19) (5,16) (5,18) (5,11) (5,10) (5,14) (5,30) (5,8) (5,27) (6,7) (6,19) (6,16) (6,11) (6,10) (6,25) (6,9) (6,28) (6,14) (6,30) (6,27) (7,16) (7,18) (7,11) (7,10) (7,25) (7,28) (7,14) (7,8) (7,27) (8,19) (8,16) (8,11) (8,10) (8,9) (8,27) (9,19) (9,16) (9,29) (9,11) (9,10) (9,27) (10,29) (10,11) (10,14) (10,30) (10,27) (11,19) (11,18) (11,30) (11,27) (12,24) (12,20) (13,26) (13,32) (13,17) (13,33) (13,15) (14,19) (14,16) (14,29) (14,25) (14,28) (14,30) (14,27) (15,31) (15,26) (15,32) (15,17) (16,19) (16,18) (16,25) (16,27) (17,31) (17,23) (17,26) (17,32) (17,33) (18,19) (18,29) (18,28) (18,30) (18,27) (19,29) (19,25) (19,28) (19,30) (19,27) (20,22) (20,24) (20,21) (21,24) (22,24) (23,31) (23,26) (23,33) (25,29) (25,28) (25,30) (25,27) (26,31) (26,32) (26,33) (27,29) (27,30) (28,29) (28,30) (29,30) (31,32) (32,33)\nIs there a path between node 31 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph146-19_1", + "image": "data/connectivity/graph_visual/hard/graph146.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,14) (0,13) (0,11) (0,21) (0,8) (0,18) (0,3) (0,7) (0,15) (0,20) (0,17) (0,10) (0,22) (0,1) (0,9) (0,6) (0,19) (1,23) (1,14) (1,5) (1,13) (1,11) (1,12) (1,21) (1,8) (1,18) (1,3) (1,25) (1,7) (1,28) (1,15) (1,20) (1,17) (1,10) (1,22) (1,9) (1,6) (1,16) (1,19) (3,27) (3,14) (3,5) (3,13) (3,4) (3,21) (3,18) (3,25) (3,28) (3,15) (3,20) (3,17) (3,22) (3,6) (3,16) (3,19) (4,27) (4,23) (4,5) (4,13) (4,11) (4,12) (4,8) (4,28) (4,15) (4,20) (4,17) (4,10) (4,24) (4,6) (5,27) (5,23) (5,14) (5,13) (5,11) (5,12) (5,21) (5,8) (5,18) (5,25) (5,7) (5,15) (5,10) (5,22) (5,24) (5,9) (5,6) (5,16) (5,19) (6,27) (6,14) (6,11) (6,12) (6,18) (6,25) (6,7) (6,20) (6,17) (6,10) (6,22) (6,24) (6,9) (6,16) (6,19) (7,23) (7,14) (7,13) (7,12) (7,21) (7,8) (7,25) (7,28) (7,20) (7,10) (7,22) (7,16) (7,19) (8,27) (8,13) (8,18) (8,25) (8,15) (8,17) (8,10) (8,22) (8,24) (8,9) (8,16) (8,19) (9,27) (9,23) (9,11) (9,21) (9,25) (9,28) (9,15) (9,20) (9,17) (9,10) (9,22) (9,24) (9,16) (9,19) (10,27) (10,14) (10,11) (10,12) (10,25) (10,28) (10,15) (10,20) (10,17) (10,24) (10,16) (10,19) (11,23) (11,21) (11,18) (11,25) (11,28) (11,15) (11,17) (11,22) (11,24) (11,19) (12,27) (12,23) (12,13) (12,21) (12,18) (12,25) (12,28) (12,15) (12,17) (12,22) (12,24) (12,16) (13,27) (13,14) (13,21) (13,18) (13,28) (13,15) (13,17) (13,24) (13,16) (13,19) (14,27) (14,25) (14,28) (14,15) (14,17) (14,22) (14,24) (14,16) (15,23) (15,21) (15,18) (15,25) (15,20) (15,24) (16,27) (16,23) (16,17) (16,24) (16,19) (17,27) (17,23) (17,18) (17,25) (17,28) (17,20) (17,22) (17,24) (17,19) (18,23) (18,21) (18,25) (18,28) (18,20) (18,22) (18,24) (18,19) (19,27) (19,23) (19,21) (19,25) (19,24) (20,27) (20,23) (20,21) (20,25) (20,24) (21,23) (21,22) (23,27) (23,24) (25,27) (25,28) (27,28)\nIs there a path between node 19 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph306-19_17", + "image": "data/connectivity/graph_visual/hard/graph306.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,8) (0,24) (0,6) (0,14) (0,26) (0,29) (0,10) (0,27) (0,5) (1,15) (2,18) (2,3) (2,6) (2,7) (2,13) (2,17) (2,20) (3,24) (3,22) (3,21) (3,12) (3,7) (3,19) (3,13) (3,25) (5,31) (5,16) (5,22) (5,7) (5,9) (5,14) (5,26) (5,25) (5,29) (5,30) (6,12) (6,14) (6,17) (6,20) (6,29) (6,27) (7,8) (7,18) (7,22) (7,28) (7,14) (7,26) (7,25) (7,30) (8,16) (8,9) (8,14) (8,19) (8,10) (9,31) (9,16) (9,21) (9,12) (9,13) (9,27) (10,31) (10,26) (10,17) (10,25) (10,29) (12,18) (12,26) (12,20) (13,28) (13,26) (13,29) (14,24) (14,21) (14,26) (14,17) (14,29) (15,23) (16,24) (16,31) (16,21) (16,26) (16,20) (16,29) (16,30) (17,31) (17,22) (17,19) (17,20) (17,29) (18,22) (18,21) (18,25) (18,29) (19,31) (19,22) (19,26) (19,20) (19,30) (20,25) (21,25) (22,26) (24,28) (25,28) (25,29) (25,27) (25,30) (27,31) (28,31)\nIs there a path between node 19 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph141-28_15", + "image": "data/connectivity/graph_visual/hard/graph141.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,4) (0,12) (0,17) (0,3) (0,24) (0,10) (1,16) (1,24) (1,7) (1,2) (2,14) (2,11) (2,22) (2,15) (3,11) (3,24) (3,10) (4,17) (4,24) (4,10) (5,27) (5,23) (6,18) (7,22) (7,17) (7,15) (7,24) (9,27) (9,25) (10,14) (10,12) (10,15) (11,14) (11,12) (13,19) (14,16) (14,17) (15,22) (15,16) (16,17) (17,24) (19,26) (21,27) (23,27) (23,25) (25,28)\nIs there a path between node 28 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph16-17_4", + "image": "data/connectivity/graph_visual/hard/graph16.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (1,4) (1,11) (2,21) (2,20) (2,24) (3,24) (4,13) (4,15) (4,8) (5,19) (5,24) (6,20) (6,24) (7,25) (7,21) (8,17) (8,15) (8,12) (9,13) (9,12) (10,16) (11,13) (11,18) (11,23) (11,14) (11,12) (13,17) (14,23) (15,18) (15,23) (18,23) (19,25) (19,24) (20,21) (21,25) (24,25)\nIs there a path between node 17 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph131-15_10", + "image": "data/connectivity/graph_visual/hard/graph131.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,7) (0,18) (0,14) (0,6) (0,13) (1,12) (1,2) (1,11) (1,16) (1,21) (1,20) (1,4) (1,10) (1,27) (2,15) (2,12) (2,11) (2,16) (2,21) (2,17) (2,20) (2,4) (2,10) (3,19) (4,15) (4,16) (4,21) (4,17) (4,20) (4,5) (4,10) (5,15) (5,12) (5,16) (5,21) (5,17) (5,10) (5,27) (6,26) (6,8) (6,23) (6,9) (6,18) (7,26) (7,8) (7,9) (7,25) (8,26) (8,23) (8,18) (8,25) (8,14) (8,13) (9,25) (9,14) (10,15) (10,12) (10,11) (11,12) (11,16) (11,21) (11,17) (11,20) (11,27) (12,15) (12,16) (12,21) (12,20) (12,27) (13,23) (13,18) (13,25) (13,14) (14,26) (14,25) (15,16) (15,21) (15,17) (15,20) (15,27) (16,17) (16,20) (16,27) (17,21) (17,20) (17,27) (18,26) (18,25) (19,22) (20,21) (20,27) (23,26) (23,25) (25,26)\nIs there a path between node 15 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph225-3_15", + "image": "data/connectivity/graph_visual/hard/graph225.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,28) (0,13) (0,8) (0,1) (0,10) (0,14) (0,22) (0,23) (0,20) (0,6) (0,18) (0,26) (0,29) (0,27) (0,11) (0,21) (1,28) (1,12) (1,24) (1,8) (1,10) (1,14) (1,22) (1,2) (1,20) (1,6) (1,18) (1,26) (1,17) (1,29) (1,27) (1,21) (2,28) (2,24) (2,3) (2,10) (2,22) (2,23) (2,20) (2,7) (2,6) (2,18) (2,27) (2,11) (2,21) (3,28) (3,24) (3,13) (3,10) (3,14) (3,22) (3,23) (3,20) (3,7) (3,29) (3,25) (3,21) (4,9) (4,5) (4,15) (4,19) (5,16) (6,28) (6,12) (6,24) (6,13) (6,8) (6,14) (6,23) (6,20) (6,26) (6,27) (6,11) (6,21) (7,28) (7,12) (7,24) (7,13) (7,10) (7,14) (7,22) (7,26) (7,17) (7,11) (7,21) (8,28) (8,12) (8,10) (8,22) (8,23) (8,20) (8,29) (8,27) (8,25) (8,11) (8,21) (9,16) (9,15) (9,19) (10,28) (10,12) (10,24) (10,13) (10,14) (10,22) (10,20) (10,18) (10,26) (10,27) (10,25) (10,11) (10,21) (11,22) (11,23) (11,20) (11,18) (11,26) (11,29) (11,27) (11,25) (11,21) (12,28) (12,24) (12,14) (12,22) (12,20) (12,18) (12,26) (12,17) (12,29) (12,27) (12,25) (12,21) (13,28) (13,24) (13,14) (13,22) (13,23) (13,20) (13,18) (13,17) (13,25) (13,21) (14,28) (14,24) (14,23) (14,20) (14,18) (14,26) (14,17) (14,29) (15,16) (15,19) (16,19) (17,28) (17,24) (17,23) (17,20) (17,18) (17,25) (17,21) (18,28) (18,24) (18,22) (18,23) (18,29) (18,27) (18,25) (18,21) (20,28) (20,24) (20,23) (20,26) (20,25) (20,21) (21,22) (21,23) (21,26) (21,29) (21,27) (21,25) (22,24) (22,23) (22,26) (22,29) (22,27) (22,25) (23,24) (23,26) (23,29) (23,27) (23,25) (24,28) (24,26) (24,29) (24,27) (24,25) (25,28) (25,26) (25,29) (25,27) (26,27) (27,29) (28,29)\nIs there a path between node 3 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph211-6_1", + "image": "data/connectivity/graph_visual/hard/graph211.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,24) (0,29) (0,27) (1,13) (1,20) (1,17) (1,7) (2,28) (2,6) (2,13) (2,17) (2,14) (2,7) (3,6) (3,18) (4,19) (4,12) (4,15) (4,11) (6,13) (7,25) (7,8) (7,18) (7,14) (9,21) (9,27) (12,19) (12,26) (13,18) (13,14) (14,25) (14,20) (17,25) (19,26) (20,28) (21,29) (22,29) (23,24) (23,29) (24,29) (24,27)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph18-3_1", + "image": "data/connectivity/graph_visual/hard/graph18.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,11) (1,4) (2,21) (2,14) (2,20) (3,15) (3,17) (3,12) (3,16) (3,23) (4,11) (4,10) (4,7) (5,18) (5,12) (8,18) (8,14) (9,15) (9,17) (9,12) (9,23) (11,25) (12,14) (13,15) (13,21) (13,23) (13,20) (15,17) (15,19) (16,21) (16,23) (16,19) (17,21) (18,21) (19,23) (21,23)\nIs there a path between node 3 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph561-23_32", + "image": "data/connectivity/graph_visual/hard/graph561.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,23) (0,31) (0,10) (0,14) (0,28) (0,18) (0,8) (0,21) (0,33) (0,22) (0,2) (0,1) (1,12) (1,31) (1,14) (1,28) (1,18) (1,8) (1,21) (1,19) (1,7) (1,5) (2,3) (2,31) (2,16) (2,19) (2,9) (2,22) (2,7) (3,10) (3,29) (3,11) (3,9) (4,23) (4,10) (4,14) (4,16) (4,29) (4,17) (4,8) (4,25) (4,30) (4,15) (5,27) (5,12) (5,23) (5,10) (5,16) (5,18) (5,13) (5,19) (5,9) (6,20) (7,12) (7,14) (7,26) (7,8) (7,30) (8,31) (8,28) (8,29) (8,33) (8,15) (9,12) (9,16) (9,13) (9,19) (9,15) (9,22) (10,27) (10,12) (10,16) (10,28) (11,27) (11,23) (11,31) (11,18) (12,27) (12,13) (12,21) (12,25) (12,19) (13,23) (13,14) (13,28) (13,18) (13,17) (13,33) (13,15) (14,28) (15,27) (15,18) (15,29) (15,25) (15,30) (16,27) (16,28) (16,19) (17,31) (17,28) (17,25) (18,28) (18,25) (19,29) (19,25) (19,22) (21,27) (22,25) (23,29) (23,33) (26,29) (27,28) (27,29) (27,30) (28,31) (29,31) (29,33)\nIs there a path between node 23 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph686-10_26", + "image": "data/connectivity/graph_visual/hard/graph686.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,24) (0,27) (0,32) (0,33) (0,29) (0,9) (0,21) (0,5) (0,31) (0,14) (0,12) (0,26) (0,11) (0,17) (0,16) (0,34) (0,23) (0,30) (0,7) (0,6) (1,24) (1,32) (1,4) (1,20) (1,9) (1,21) (1,22) (1,12) (1,26) (1,25) (1,11) (1,17) (1,34) (1,23) (1,7) (1,6) (1,8) (2,27) (2,4) (2,29) (2,9) (2,21) (2,5) (2,15) (2,31) (2,22) (2,12) (2,26) (2,25) (2,11) (2,17) (2,18) (2,34) (2,23) (2,30) (3,24) (3,27) (3,32) (3,33) (3,4) (3,20) (3,5) (3,15) (3,31) (3,14) (3,22) (3,25) (3,11) (3,17) (3,16) (3,18) (3,34) (3,30) (3,7) (3,28) (3,6) (3,8) (4,24) (4,27) (4,33) (4,29) (4,20) (4,9) (4,21) (4,5) (4,15) (4,31) (4,14) (4,22) (4,12) (4,25) (4,17) (4,16) (4,18) (4,30) (4,28) (4,6) (4,8) (5,27) (5,29) (5,20) (5,21) (5,15) (5,31) (5,14) (5,12) (5,26) (5,25) (5,11) (5,17) (5,16) (5,30) (5,7) (5,28) (5,8) (6,24) (6,32) (6,33) (6,29) (6,20) (6,9) (6,21) (6,15) (6,14) (6,22) (6,12) (6,26) (6,25) (6,11) (6,16) (6,18) (6,7) (6,28) (6,8) (7,24) (7,27) (7,33) (7,9) (7,21) (7,15) (7,31) (7,14) (7,22) (7,12) (7,26) (7,25) (7,18) (7,23) (7,28) (7,8) (8,24) (8,32) (8,20) (8,9) (8,15) (8,31) (8,14) (8,22) (8,12) (8,17) (8,16) (8,34) (8,23) (8,30) (8,28) (9,27) (9,32) (9,33) (9,29) (9,20) (9,21) (9,31) (9,14) (9,12) (9,26) (9,16) (9,34) (9,23) (9,30) (9,28) (10,19) (10,13) (11,24) (11,32) (11,29) (11,20) (11,21) (11,15) (11,14) (11,22) (11,12) (11,26) (11,17) (11,18) (11,34) (11,23) (11,30) (11,28) (12,24) (12,27) (12,32) (12,33) (12,20) (12,21) (12,31) (12,22) (12,26) (12,25) (12,17) (12,16) (12,18) (12,34) (12,30) (12,28) (13,19) (14,32) (14,29) (14,21) (14,31) (14,26) (14,25) (14,17) (14,16) (14,18) (14,23) (14,30) (15,24) (15,27) (15,32) (15,33) (15,20) (15,31) (15,22) (15,26) (15,25) (15,17) (15,16) (15,34) (15,23) (15,30) (16,27) (16,33) (16,29) (16,20) (16,21) (16,31) (16,22) (16,26) (16,25) (16,17) (16,18) (16,34) (16,23) (16,30) (17,24) (17,32) (17,33) (17,29) (17,20) (17,31) (17,22) (17,26) (17,25) (17,34) (17,23) (17,28) (18,24) (18,32) (18,33) (18,20) (18,31) (18,22) (18,26) (18,34) (18,23) (18,28) (20,24) (20,33) (20,29) (20,31) (20,22) (20,26) (20,34) (20,23) (20,30) (20,28) (21,24) (21,32) (21,26) (21,25) (21,34) (21,23) (21,30) (21,28) (22,24) (22,32) (22,33) (22,29) (22,31) (22,26) (22,25) (22,34) (22,28) (23,27) (23,32) (23,33) (23,29) (23,31) (23,34) (23,30) (23,28) (24,27) (24,33) (24,29) (24,31) (24,26) (24,25) (24,34) (24,30) (24,28) (25,27) (25,32) (25,33) (25,29) (25,26) (25,34) (25,30) (25,28) (26,27) (26,32) (26,33) (26,29) (26,31) (26,28) (27,32) (27,33) (27,29) (27,31) (27,30) (28,32) (28,31) (28,34) (28,30) (29,32) (29,33) (29,34) (30,32) (30,31) (30,34) (31,32) (31,33) (32,33) (32,34) (33,34)\nIs there a path between node 10 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph280-14_1", + "image": "data/connectivity/graph_visual/hard/graph280.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,12) (0,14) (0,16) (0,20) (0,8) (0,13) (0,18) (0,10) (0,29) (0,3) (0,7) (0,9) (1,26) (1,5) (1,11) (1,19) (1,28) (1,24) (1,6) (2,12) (2,14) (2,16) (2,20) (2,8) (2,13) (2,23) (2,18) (2,25) (2,3) (2,7) (2,9) (3,16) (3,8) (3,13) (3,18) (3,25) (3,10) (3,29) (3,7) (4,15) (4,27) (5,28) (5,24) (5,22) (6,26) (6,11) (6,19) (6,28) (6,24) (6,22) (7,14) (7,16) (7,20) (7,13) (7,23) (7,25) (7,10) (7,21) (7,9) (8,14) (8,20) (8,13) (8,23) (8,10) (9,14) (9,16) (9,20) (9,13) (9,18) (9,25) (9,21) (9,29) (10,14) (10,16) (10,20) (10,13) (10,23) (10,25) (10,21) (11,26) (11,17) (11,24) (11,22) (12,14) (12,16) (12,13) (12,23) (12,18) (12,25) (12,21) (12,29) (13,14) (13,16) (13,18) (13,21) (13,29) (14,16) (14,20) (14,23) (14,18) (14,21) (14,29) (15,30) (15,27) (16,20) (16,23) (16,25) (16,21) (16,29) (17,26) (17,19) (17,28) (17,22) (18,23) (18,25) (18,21) (18,29) (19,26) (20,23) (20,25) (20,29) (21,23) (21,25) (21,29) (22,26) (22,28) (22,24) (23,25) (23,29) (24,26) (24,28) (25,29) (26,28)\nIs there a path between node 14 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph522-26_7", + "image": "data/connectivity/graph_visual/hard/graph522.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,11) (0,33) (0,7) (0,13) (1,25) (1,30) (1,27) (2,6) (2,5) (2,13) (3,30) (3,17) (3,15) (3,32) (3,14) (3,21) (3,8) (3,12) (3,4) (3,24) (4,25) (4,17) (4,32) (4,12) (5,9) (7,16) (7,33) (8,28) (8,25) (8,32) (8,26) (8,21) (8,27) (8,20) (9,11) (9,16) (9,13) (10,28) (10,15) (10,26) (10,27) (10,24) (10,18) (11,16) (11,33) (12,28) (12,25) (12,24) (13,33) (14,27) (15,27) (15,29) (15,24) (17,25) (17,21) (18,25) (18,31) (18,21) (18,27) (20,25) (20,32) (20,22) (20,21) (20,27) (20,29) (20,24) (21,28) (21,29) (21,24) (22,24) (24,30) (24,31) (24,26) (25,31) (25,32) (25,26) (25,27) (26,30) (27,31) (28,29) (30,32)\nIs there a path between node 26 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph610-0_13", + "image": "data/connectivity/graph_visual/hard/graph610.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,31) (0,11) (0,18) (0,1) (1,28) (1,31) (1,13) (1,8) (1,5) (1,32) (1,34) (2,17) (3,14) (3,15) (3,24) (4,32) (4,34) (5,8) (5,9) (6,25) (6,10) (6,15) (6,7) (6,19) (7,14) (7,10) (7,16) (7,12) (7,21) (8,18) (9,31) (9,11) (9,34) (10,23) (10,29) (10,33) (10,16) (10,30) (11,20) (11,18) (12,23) (12,14) (12,25) (12,19) (12,24) (13,34) (14,25) (15,23) (15,25) (15,24) (16,23) (16,25) (16,29) (16,33) (16,17) (17,30) (17,21) (17,24) (18,22) (18,20) (19,24) (20,28) (20,32) (20,34) (22,26) (22,34) (23,25) (23,30) (24,33) (24,30) (25,29) (25,33) (26,27) (27,32) (28,32) (28,34) (29,30) (30,33) (31,32)\nIs there a path between node 0 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph152-26_15", + "image": "data/connectivity/graph_visual/hard/graph152.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,20) (0,21) (0,25) (0,8) (0,28) (0,7) (0,27) (0,9) (0,13) (0,6) (0,1) (0,22) (0,26) (0,3) (1,20) (1,21) (1,25) (1,8) (1,28) (1,7) (1,27) (1,12) (1,9) (1,13) (1,6) (1,3) (2,20) (2,21) (2,8) (2,11) (2,28) (2,27) (2,9) (2,4) (2,13) (2,22) (2,26) (2,3) (3,20) (3,21) (3,25) (3,11) (3,28) (3,12) (3,4) (3,6) (3,22) (3,26) (4,20) (4,21) (4,8) (4,11) (4,27) (4,9) (4,6) (4,22) (5,14) (5,10) (5,24) (5,16) (5,23) (5,19) (5,18) (5,15) (5,17) (6,21) (6,25) (6,8) (6,28) (6,27) (6,9) (6,26) (7,20) (7,21) (7,8) (7,11) (7,28) (7,12) (7,9) (7,13) (7,22) (7,26) (8,20) (8,21) (8,11) (8,28) (8,27) (8,12) (8,13) (8,22) (8,26) (9,20) (9,21) (9,25) (9,28) (9,12) (9,13) (9,22) (10,14) (10,24) (10,16) (10,23) (10,18) (10,15) (10,17) (11,20) (11,28) (11,27) (11,12) (11,13) (11,22) (11,26) (12,20) (12,21) (12,25) (12,28) (12,27) (12,13) (12,22) (13,20) (13,28) (13,27) (13,26) (14,24) (14,16) (14,18) (15,24) (15,19) (16,23) (16,19) (16,18) (16,17) (17,24) (17,19) (17,18) (18,24) (18,23) (18,19) (19,24) (20,21) (20,28) (21,25) (21,28) (21,27) (22,25) (22,26) (25,28) (25,27) (25,26) (26,28) (27,28)\nIs there a path between node 26 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph462-2_15", + "image": "data/connectivity/graph_visual/hard/graph462.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,8) (0,25) (0,23) (0,24) (1,19) (1,11) (1,3) (2,13) (2,18) (2,4) (2,29) (3,17) (3,6) (3,12) (3,31) (3,20) (3,15) (4,16) (4,13) (4,25) (4,29) (4,23) (4,24) (5,6) (5,31) (5,20) (5,30) (6,7) (6,14) (6,22) (6,9) (6,21) (6,15) (7,10) (7,28) (7,11) (7,22) (8,13) (8,26) (8,29) (9,19) (9,28) (9,11) (9,12) (9,22) (9,21) (9,15) (10,17) (10,11) (10,21) (11,19) (12,19) (13,25) (13,24) (14,28) (14,27) (15,19) (15,21) (15,27) (15,30) (16,25) (16,29) (16,24) (17,19) (17,31) (17,21) (17,30) (18,23) (18,24) (19,28) (19,20) (19,21) (20,28) (20,22) (21,22) (24,25) (25,26) (28,31)\nIs there a path between node 2 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph397-3_18", + "image": "data/connectivity/graph_visual/hard/graph397.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,27) (0,1) (0,32) (0,9) (1,25) (1,20) (1,23) (1,24) (1,8) (2,25) (2,20) (2,23) (2,16) (2,19) (3,24) (3,32) (3,19) (4,13) (5,13) (5,7) (5,26) (5,29) (5,6) (5,22) (6,28) (7,13) (7,21) (7,22) (7,18) (7,28) (8,24) (8,31) (8,10) (8,9) (9,11) (9,10) (9,32) (9,19) (9,14) (10,24) (10,15) (11,25) (11,20) (11,19) (12,30) (12,20) (12,24) (13,21) (13,29) (13,18) (13,28) (14,20) (14,23) (14,24) (14,27) (14,15) (15,16) (16,27) (16,31) (17,28) (18,21) (18,26) (19,24) (20,30) (20,27) (20,32) (21,28) (24,25) (24,27) (24,31) (24,32) (25,27) (25,31) (27,32)\nIs there a path between node 3 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph475-28_18", + "image": "data/connectivity/graph_visual/hard/graph475.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,11) (0,23) (0,8) (0,30) (0,7) (0,14) (0,22) (0,1) (0,6) (0,17) (0,24) (0,4) (0,16) (0,13) (0,19) (0,26) (0,31) (0,2) (0,18) (0,5) (1,11) (1,12) (1,23) (1,8) (1,30) (1,7) (1,14) (1,27) (1,6) (1,17) (1,24) (1,4) (1,16) (1,29) (1,13) (1,19) (1,20) (1,26) (1,2) (1,18) (1,5) (2,12) (2,23) (2,8) (2,30) (2,7) (2,14) (2,22) (2,6) (2,17) (2,24) (2,4) (2,16) (2,29) (2,13) (2,19) (2,26) (2,18) (2,5) (3,28) (3,10) (3,15) (3,9) (4,11) (4,23) (4,8) (4,30) (4,7) (4,14) (4,27) (4,24) (4,16) (4,13) (4,19) (4,20) (4,31) (4,18) (4,5) (5,11) (5,12) (5,23) (5,8) (5,30) (5,7) (5,14) (5,27) (5,22) (5,17) (5,24) (5,29) (5,19) (5,20) (5,26) (5,31) (5,18) (6,11) (6,12) (6,23) (6,8) (6,30) (6,7) (6,14) (6,22) (6,17) (6,13) (6,19) (6,20) (6,26) (6,31) (6,18) (7,11) (7,23) (7,8) (7,30) (7,14) (7,27) (7,22) (7,24) (7,29) (7,13) (7,19) (7,20) (8,23) (8,30) (8,14) (8,22) (8,24) (8,16) (8,20) (8,26) (8,31) (8,18) (9,21) (9,25) (9,28) (10,21) (10,32) (10,25) (10,28) (10,15) (11,12) (11,30) (11,14) (11,27) (11,22) (11,17) (11,24) (11,16) (11,29) (11,13) (11,20) (11,26) (11,31) (11,18) (12,23) (12,30) (12,27) (12,22) (12,24) (12,29) (12,13) (12,20) (12,26) (12,31) (12,18) (13,23) (13,30) (13,14) (13,22) (13,17) (13,24) (13,19) (13,20) (13,26) (13,31) (13,18) (14,30) (14,27) (14,22) (14,24) (14,16) (14,29) (14,19) (14,20) (14,26) (14,31) (14,18) (15,21) (15,32) (15,25) (15,28) (16,23) (16,30) (16,22) (16,24) (16,29) (16,20) (16,26) (16,31) (16,18) (17,23) (17,30) (17,27) (17,22) (17,24) (17,29) (17,19) (17,26) (17,18) (18,23) (18,27) (18,24) (18,19) (18,20) (18,26) (19,30) (19,27) (19,29) (19,20) (19,26) (19,31) (20,30) (20,22) (20,24) (20,29) (20,26) (22,23) (22,27) (22,29) (22,31) (23,30) (23,26) (24,30) (24,27) (24,29) (24,26) (25,32) (25,28) (26,30) (26,27) (26,29) (27,30) (27,29) (28,32) (29,30) (29,31) (30,31)\nIs there a path between node 28 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph31-18_16", + "image": "data/connectivity/graph_visual/hard/graph31.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,25) (0,18) (0,8) (0,24) (0,6) (0,12) (0,5) (0,7) (0,16) (0,1) (0,22) (1,25) (1,18) (1,8) (1,4) (1,9) (1,6) (1,12) (1,11) (1,7) (1,13) (1,16) (1,20) (2,8) (2,9) (2,24) (2,6) (2,12) (2,11) (2,15) (2,5) (2,7) (2,16) (2,20) (2,22) (3,19) (3,23) (3,21) (3,14) (4,25) (4,18) (4,8) (4,9) (4,11) (4,15) (4,13) (4,22) (5,25) (5,8) (5,9) (5,24) (5,6) (5,15) (5,7) (5,13) (5,16) (5,20) (5,22) (6,25) (6,8) (6,9) (6,24) (6,12) (6,15) (6,7) (6,16) (7,25) (7,18) (7,24) (7,12) (7,16) (7,22) (8,18) (8,24) (8,12) (8,15) (9,25) (9,18) (9,24) (9,12) (9,11) (9,15) (9,16) (9,20) (9,22) (10,17) (11,24) (11,12) (11,16) (11,20) (12,25) (12,18) (12,24) (12,15) (12,13) (12,16) (12,22) (13,18) (13,20) (13,22) (14,19) (14,23) (14,21) (15,25) (15,18) (15,24) (15,20) (16,25) (16,18) (16,24) (16,20) (16,22) (18,25) (18,20) (18,22) (19,23) (19,21) (20,25) (20,24) (21,23) (22,24)\nIs there a path between node 18 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph422-3_8", + "image": "data/connectivity/graph_visual/hard/graph422.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,21) (0,6) (0,13) (0,26) (1,27) (1,28) (1,6) (1,17) (1,13) (1,24) (1,10) (1,15) (2,9) (2,31) (2,19) (2,17) (2,29) (3,16) (3,9) (3,18) (3,26) (3,29) (4,20) (4,16) (4,9) (4,17) (4,18) (4,24) (6,27) (6,20) (6,9) (6,14) (6,13) (6,26) (6,24) (7,28) (7,9) (7,31) (7,30) (7,19) (7,17) (7,22) (7,29) (8,32) (9,16) (9,21) (9,30) (9,17) (9,22) (9,18) (10,20) (10,16) (10,14) (10,21) (10,18) (10,15) (13,20) (13,17) (13,26) (13,29) (14,28) (14,21) (14,19) (14,18) (15,17) (15,18) (15,29) (16,20) (16,31) (16,17) (16,18) (16,29) (17,27) (17,28) (17,20) (17,18) (17,26) (18,31) (19,21) (19,30) (19,22) (20,27) (20,28) (21,27) (21,31) (21,30) (22,30) (24,28) (24,29) (26,27) (26,29) (27,31) (27,30) (29,31) (29,30)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph699-6_5", + "image": "data/connectivity/graph_visual/hard/graph699.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,22) (0,23) (0,24) (0,19) (0,4) (0,7) (0,10) (0,3) (0,20) (0,28) (0,2) (0,26) (0,29) (0,21) (1,17) (1,5) (1,14) (1,30) (1,16) (2,13) (2,27) (2,23) (2,24) (2,34) (2,32) (2,10) (2,33) (2,20) (2,26) (2,9) (3,13) (3,27) (3,6) (3,23) (3,24) (3,19) (3,34) (3,10) (3,33) (3,20) (3,28) (3,26) (3,9) (3,29) (3,21) (4,13) (4,27) (4,22) (4,24) (4,19) (4,7) (4,10) (4,33) (4,20) (4,28) (4,26) (4,9) (4,29) (4,21) (5,17) (5,14) (5,15) (5,12) (5,30) (5,18) (5,16) (6,13) (6,22) (6,23) (6,34) (6,32) (6,10) (6,20) (6,26) (6,9) (6,8) (7,13) (7,23) (7,24) (7,19) (7,34) (7,10) (7,33) (7,20) (7,28) (7,8) (7,29) (7,21) (8,27) (8,23) (8,24) (8,34) (8,10) (8,28) (8,9) (8,29) (8,21) (9,13) (9,27) (9,22) (9,23) (9,34) (9,32) (9,10) (9,20) (9,28) (9,26) (9,21) (10,13) (10,27) (10,22) (10,24) (10,19) (10,34) (10,32) (10,33) (10,20) (10,26) (10,29) (10,21) (11,17) (11,31) (11,14) (11,15) (11,18) (11,16) (12,31) (12,15) (12,30) (12,18) (13,27) (13,22) (13,24) (13,32) (13,33) (13,20) (13,28) (13,26) (13,21) (14,17) (14,31) (14,15) (14,30) (14,18) (14,16) (15,17) (15,30) (15,18) (15,16) (16,17) (16,31) (16,30) (16,18) (17,31) (17,18) (18,31) (18,30) (19,22) (19,23) (19,24) (19,34) (19,32) (19,33) (19,20) (19,28) (19,26) (19,29) (19,21) (20,22) (20,23) (20,34) (20,21) (21,27) (21,22) (21,23) (21,34) (21,32) (21,33) (21,28) (21,26) (21,29) (22,27) (22,24) (22,33) (22,28) (22,26) (22,29) (23,27) (23,32) (23,33) (23,26) (23,29) (24,27) (24,34) (24,33) (24,28) (24,26) (24,29) (26,27) (26,34) (26,32) (26,29) (27,34) (27,32) (27,33) (27,28) (27,29) (28,32) (28,33) (28,29) (29,34) (29,32) (32,34) (32,33)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph131-23_25", + "image": "data/connectivity/graph_visual/hard/graph131.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,7) (0,18) (0,14) (0,6) (0,13) (1,12) (1,2) (1,11) (1,16) (1,21) (1,20) (1,4) (1,10) (1,27) (2,15) (2,12) (2,11) (2,16) (2,21) (2,17) (2,20) (2,4) (2,10) (3,19) (4,15) (4,16) (4,21) (4,17) (4,20) (4,5) (4,10) (5,15) (5,12) (5,16) (5,21) (5,17) (5,10) (5,27) (6,26) (6,8) (6,23) (6,9) (6,18) (7,26) (7,8) (7,9) (7,25) (8,26) (8,23) (8,18) (8,25) (8,14) (8,13) (9,25) (9,14) (10,15) (10,12) (10,11) (11,12) (11,16) (11,21) (11,17) (11,20) (11,27) (12,15) (12,16) (12,21) (12,20) (12,27) (13,23) (13,18) (13,25) (13,14) (14,26) (14,25) (15,16) (15,21) (15,17) (15,20) (15,27) (16,17) (16,20) (16,27) (17,21) (17,20) (17,27) (18,26) (18,25) (19,22) (20,21) (20,27) (23,26) (23,25) (25,26)\nIs there a path between node 23 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph684-10_23", + "image": "data/connectivity/graph_visual/hard/graph684.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,24) (0,29) (0,23) (0,13) (0,14) (0,33) (0,21) (0,20) (0,19) (0,28) (0,31) (0,27) (0,22) (0,34) (1,11) (1,32) (1,8) (1,7) (1,3) (1,2) (1,9) (2,11) (2,17) (2,32) (2,5) (2,8) (2,7) (2,16) (2,3) (2,9) (2,6) (3,11) (3,17) (3,32) (3,8) (3,16) (3,9) (4,24) (4,10) (4,29) (4,23) (4,13) (4,25) (4,14) (4,33) (4,20) (4,19) (4,31) (4,18) (4,27) (4,22) (4,15) (4,34) (4,26) (4,30) (4,12) (5,17) (5,32) (5,8) (5,7) (5,16) (5,9) (6,11) (6,17) (6,8) (6,7) (6,16) (7,11) (7,32) (7,8) (7,9) (8,11) (8,17) (8,32) (8,16) (8,9) (9,17) (9,32) (9,16) (10,24) (10,13) (10,25) (10,14) (10,33) (10,21) (10,20) (10,19) (10,28) (10,31) (10,27) (10,22) (10,34) (10,26) (11,17) (11,32) (11,16) (12,29) (12,13) (12,14) (12,33) (12,20) (12,28) (12,31) (12,18) (12,27) (12,22) (12,15) (12,34) (12,26) (13,24) (13,29) (13,14) (13,33) (13,21) (13,20) (13,19) (13,28) (13,18) (13,22) (13,26) (13,30) (14,24) (14,25) (14,33) (14,21) (14,20) (14,19) (14,28) (14,31) (14,27) (14,22) (14,15) (14,34) (14,26) (15,24) (15,29) (15,23) (15,21) (15,20) (15,19) (15,28) (15,31) (15,18) (15,27) (15,22) (15,26) (16,17) (17,32) (18,24) (18,29) (18,25) (18,33) (18,21) (18,19) (18,28) (18,31) (18,22) (18,34) (18,26) (18,30) (19,24) (19,23) (19,33) (19,20) (19,28) (19,31) (19,27) (19,34) (19,30) (20,29) (20,23) (20,25) (20,21) (20,28) (20,31) (20,27) (20,22) (20,34) (20,30) (21,29) (21,33) (21,28) (21,27) (21,22) (21,26) (21,30) (22,24) (22,29) (22,23) (22,25) (22,33) (22,28) (22,27) (22,34) (22,26) (23,29) (23,33) (23,27) (23,34) (23,26) (23,30) (24,29) (24,33) (24,28) (24,27) (24,34) (24,30) (25,29) (25,31) (25,27) (25,34) (25,26) (25,30) (26,29) (26,33) (26,31) (26,34) (26,30) (27,33) (27,28) (27,31) (27,34) (28,29) (28,33) (28,31) (28,30) (29,33) (29,31) (29,30) (30,31) (30,34) (31,34) (33,34)\nIs there a path between node 10 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph606-16_34", + "image": "data/connectivity/graph_visual/hard/graph606.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,31) (0,3) (0,23) (0,7) (0,4) (1,10) (1,28) (1,8) (1,24) (2,5) (2,21) (2,6) (2,29) (3,32) (3,31) (3,30) (3,29) (4,5) (4,31) (4,11) (4,30) (5,14) (5,30) (5,7) (5,20) (6,14) (6,21) (6,29) (6,20) (7,16) (7,14) (7,31) (7,30) (8,15) (8,10) (8,28) (8,19) (9,22) (9,26) (9,28) (9,25) (10,34) (10,33) (10,18) (10,24) (10,19) (11,16) (11,14) (11,13) (11,23) (12,17) (13,14) (13,27) (13,29) (14,16) (14,32) (15,25) (15,18) (15,24) (16,32) (16,21) (16,30) (16,29) (16,20) (19,34) (19,26) (19,25) (19,24) (20,31) (20,30) (20,29) (21,30) (21,27) (22,34) (22,33) (23,30) (23,29) (24,26) (25,33) (26,28) (27,32) (28,34) (29,31)\nIs there a path between node 16 and node 34 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph171-5_21", + "image": "data/connectivity/graph_visual/hard/graph171.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,2) (0,24) (0,19) (0,5) (0,8) (0,9) (0,23) (0,22) (0,13) (0,20) (0,7) (1,11) (1,24) (1,6) (1,14) (1,17) (1,8) (1,9) (1,23) (1,22) (1,13) (1,20) (1,26) (2,21) (2,3) (2,11) (2,24) (2,6) (2,14) (2,23) (2,13) (2,28) (2,20) (2,15) (2,18) (3,21) (3,11) (3,24) (3,6) (3,14) (3,17) (3,8) (3,9) (3,23) (3,25) (3,28) (3,15) (3,18) (3,7) (5,21) (5,11) (5,24) (5,6) (5,14) (5,19) (5,8) (5,9) (5,13) (5,28) (5,15) (5,18) (5,7) (6,11) (6,24) (6,14) (6,19) (6,17) (6,23) (6,22) (6,13) (6,25) (6,28) (6,18) (6,7) (6,26) (7,21) (7,24) (7,14) (7,19) (7,17) (7,9) (7,23) (7,13) (7,25) (7,28) (7,20) (7,15) (8,21) (8,14) (8,19) (8,17) (8,9) (8,23) (8,22) (8,13) (8,25) (8,18) (8,26) (9,21) (9,24) (9,14) (9,19) (9,17) (9,23) (9,22) (9,25) (9,15) (9,18) (9,26) (10,16) (10,27) (11,21) (11,24) (11,14) (11,17) (11,23) (11,13) (11,25) (11,28) (11,15) (11,18) (11,26) (13,21) (13,14) (13,17) (13,22) (13,28) (13,20) (13,18) (13,26) (14,21) (14,23) (14,25) (14,20) (14,18) (15,21) (15,24) (15,19) (15,17) (15,23) (15,22) (15,25) (15,18) (15,26) (17,21) (17,24) (17,23) (17,22) (17,25) (17,28) (17,20) (17,18) (18,21) (18,24) (18,19) (18,23) (18,22) (18,25) (18,28) (18,20) (18,26) (19,21) (19,24) (19,23) (19,22) (19,25) (19,28) (19,20) (20,24) (20,23) (20,22) (20,25) (20,28) (20,26) (21,23) (21,22) (21,28) (21,26) (22,24) (22,23) (22,25) (22,26) (23,24) (23,25) (23,28) (23,26) (24,25) (24,26) (25,28) (25,26) (26,28)\nIs there a path between node 5 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph102-23_13", + "image": "data/connectivity/graph_visual/hard/graph102.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,14) (0,27) (0,17) (0,9) (0,10) (0,2) (0,4) (0,20) (1,22) (1,13) (1,7) (1,21) (1,12) (1,19) (1,6) (1,26) (1,5) (1,16) (1,8) (2,14) (2,24) (2,17) (2,9) (2,15) (2,10) (2,18) (3,14) (3,24) (3,15) (3,10) (3,18) (4,14) (4,27) (4,9) (4,15) (4,10) (4,18) (4,20) (5,13) (5,7) (5,23) (5,25) (5,12) (5,19) (5,6) (5,26) (5,11) (5,16) (6,22) (6,13) (6,7) (6,23) (6,21) (6,12) (6,19) (6,11) (6,16) (6,8) (7,22) (7,13) (7,23) (7,12) (7,19) (7,26) (7,11) (7,16) (7,8) (8,22) (8,13) (8,23) (8,25) (8,21) (8,19) (8,16) (9,14) (9,24) (9,17) (9,10) (9,20) (10,14) (10,24) (10,17) (10,18) (11,22) (11,13) (11,12) (11,19) (11,26) (11,16) (12,22) (12,13) (12,21) (12,19) (12,26) (12,16) (13,22) (13,23) (13,19) (14,24) (14,17) (14,15) (14,18) (14,20) (15,27) (15,17) (15,18) (16,22) (16,23) (16,25) (16,21) (16,26) (17,27) (17,18) (17,20) (18,27) (18,20) (19,22) (19,23) (19,25) (19,21) (20,24) (20,27) (21,22) (21,23) (21,25) (21,26) (22,25) (22,26) (23,26) (24,27) (25,26)\nIs there a path between node 23 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph222-14_28", + "image": "data/connectivity/graph_visual/hard/graph222.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,2) (0,11) (1,20) (1,26) (1,8) (1,14) (1,16) (1,5) (1,18) (1,15) (1,17) (1,10) (1,22) (1,27) (1,24) (1,28) (1,29) (2,11) (3,9) (3,21) (3,12) (3,13) (4,25) (4,26) (4,8) (4,14) (4,6) (4,23) (4,16) (4,5) (4,18) (4,15) (4,17) (4,19) (4,10) (4,27) (4,24) (4,7) (5,20) (5,26) (5,14) (5,6) (5,23) (5,16) (5,15) (5,17) (5,19) (5,22) (5,24) (5,28) (5,29) (6,26) (6,8) (6,14) (6,23) (6,18) (6,15) (6,19) (6,10) (6,22) (6,27) (6,28) (6,29) (6,7) (7,25) (7,26) (7,14) (7,16) (7,18) (7,22) (7,27) (7,28) (8,25) (8,20) (8,26) (8,14) (8,23) (8,16) (8,18) (8,17) (8,10) (8,27) (8,24) (8,28) (8,29) (9,21) (9,12) (9,13) (10,25) (10,20) (10,26) (10,14) (10,23) (10,18) (10,15) (10,17) (10,19) (10,22) (10,24) (10,28) (10,29) (12,21) (12,13) (13,21) (14,25) (14,23) (14,16) (14,18) (14,15) (14,17) (14,22) (14,27) (14,24) (14,28) (15,25) (15,20) (15,26) (15,16) (15,18) (15,22) (15,27) (15,28) (15,29) (16,25) (16,20) (16,26) (16,23) (16,18) (16,19) (16,22) (16,27) (16,24) (17,25) (17,26) (17,18) (17,24) (18,25) (18,20) (18,26) (18,23) (18,22) (18,27) (18,28) (18,29) (19,25) (19,20) (19,23) (19,22) (19,27) (19,24) (19,28) (19,29) (20,25) (20,22) (20,27) (20,28) (22,25) (22,26) (22,23) (22,27) (22,28) (22,29) (23,27) (23,28) (23,29) (24,26) (24,29) (25,26) (25,27) (25,28) (26,27) (26,28) (26,29) (27,28) (27,29) (28,29)\nIs there a path between node 14 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph362-19_24", + "image": "data/connectivity/graph_visual/hard/graph362.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,30) (0,28) (0,21) (0,5) (0,20) (0,13) (1,26) (1,17) (2,27) (2,15) (3,19) (3,24) (3,21) (3,14) (3,4) (3,22) (3,12) (3,13) (4,16) (4,31) (4,11) (5,7) (5,23) (5,14) (5,6) (5,12) (6,7) (6,24) (6,16) (6,28) (6,14) (7,25) (7,28) (7,14) (7,20) (7,22) (7,11) (7,12) (8,10) (8,18) (9,27) (9,15) (10,27) (10,15) (10,18) (11,24) (11,21) (12,25) (12,24) (12,20) (12,22) (12,13) (13,29) (13,25) (13,24) (13,31) (14,16) (14,22) (15,26) (15,17) (16,29) (16,21) (16,31) (16,20) (17,26) (18,26) (19,29) (19,23) (19,20) (20,22) (21,25) (21,24) (21,30) (21,22) (22,30) (23,30) (23,31) (24,25) (24,30) (24,31) (26,27) (29,30)\nIs there a path between node 19 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph169-7_3", + "image": "data/connectivity/graph_visual/hard/graph169.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,27) (0,13) (0,10) (0,15) (0,2) (0,17) (1,5) (1,22) (1,8) (1,19) (1,26) (1,24) (1,18) (1,16) (1,14) (1,12) (1,4) (1,9) (2,7) (2,27) (2,13) (2,3) (2,6) (2,10) (2,11) (2,17) (3,7) (3,27) (3,20) (3,6) (3,10) (3,15) (3,21) (3,17) (4,5) (4,8) (4,19) (4,26) (4,25) (4,18) (4,14) (4,12) (5,8) (5,26) (5,18) (5,16) (5,14) (5,12) (6,7) (6,13) (6,10) (6,21) (7,20) (7,13) (7,10) (7,15) (7,11) (8,19) (8,26) (8,18) (8,16) (8,14) (8,9) (9,22) (9,19) (9,26) (9,25) (9,16) (9,14) (9,12) (10,13) (10,21) (10,17) (11,27) (11,13) (11,15) (11,21) (11,17) (12,22) (12,19) (12,26) (12,24) (12,25) (12,16) (12,14) (13,27) (13,15) (14,22) (14,19) (14,26) (15,27) (15,20) (15,21) (15,17) (16,22) (16,19) (16,24) (16,25) (16,18) (17,27) (17,20) (17,21) (18,22) (18,19) (18,26) (18,24) (19,26) (19,25) (20,27) (20,21) (21,27) (22,26) (22,24) (24,26)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph406-10_14", + "image": "data/connectivity/graph_visual/hard/graph406.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,21) (0,25) (0,3) (0,16) (0,15) (0,5) (0,1) (0,28) (1,25) (1,3) (1,5) (1,28) (2,22) (2,13) (2,24) (2,31) (2,26) (2,32) (2,17) (2,19) (2,30) (3,21) (3,25) (3,15) (3,5) (4,22) (4,13) (4,7) (4,31) (4,26) (4,32) (4,17) (4,30) (5,21) (5,16) (5,15) (6,18) (6,14) (6,9) (6,23) (6,20) (7,22) (7,24) (7,32) (7,17) (7,19) (7,12) (7,30) (9,18) (9,23) (9,20) (9,10) (9,29) (9,27) (10,18) (10,14) (10,11) (10,23) (10,20) (10,29) (10,27) (11,18) (11,23) (11,20) (11,29) (11,27) (12,22) (12,24) (12,31) (12,26) (12,32) (12,17) (12,19) (12,30) (13,22) (13,24) (13,31) (13,26) (13,32) (13,17) (13,30) (14,20) (14,27) (15,16) (15,28) (16,21) (17,24) (17,31) (17,26) (17,32) (17,19) (17,30) (18,23) (18,27) (19,22) (19,31) (19,26) (19,32) (20,23) (20,29) (20,27) (21,25) (22,31) (22,26) (22,32) (23,27) (24,31) (24,26) (24,32) (25,28) (26,31) (26,32) (27,29) (31,32)\nIs there a path between node 10 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph141-12_11", + "image": "data/connectivity/graph_visual/hard/graph141.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,4) (0,12) (0,17) (0,3) (0,24) (0,10) (1,16) (1,24) (1,7) (1,2) (2,14) (2,11) (2,22) (2,15) (3,11) (3,24) (3,10) (4,17) (4,24) (4,10) (5,27) (5,23) (6,18) (7,22) (7,17) (7,15) (7,24) (9,27) (9,25) (10,14) (10,12) (10,15) (11,14) (11,12) (13,19) (14,16) (14,17) (15,22) (15,16) (16,17) (17,24) (19,26) (21,27) (23,27) (23,25) (25,28)\nIs there a path between node 12 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph639-18_21", + "image": "data/connectivity/graph_visual/hard/graph639.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,25) (0,17) (0,1) (0,33) (0,7) (0,3) (0,18) (0,13) (0,22) (0,19) (0,24) (0,21) (0,11) (1,4) (1,10) (1,25) (1,17) (1,32) (1,33) (1,7) (1,3) (1,13) (1,22) (1,31) (1,6) (1,24) (1,21) (1,5) (1,27) (3,4) (3,10) (3,7) (3,18) (3,13) (3,22) (3,19) (3,31) (3,6) (3,24) (3,21) (3,5) (3,11) (3,27) (4,15) (4,17) (4,33) (4,7) (4,13) (4,19) (4,31) (4,6) (4,24) (4,21) (4,5) (4,27) (5,10) (5,25) (5,17) (5,33) (5,7) (5,18) (5,13) (5,22) (5,31) (5,21) (5,11) (6,15) (6,25) (6,17) (6,32) (6,33) (6,22) (6,19) (6,31) (6,21) (6,11) (6,27) (7,15) (7,17) (7,18) (7,31) (7,24) (7,21) (7,27) (8,9) (8,12) (8,16) (8,30) (8,28) (8,20) (8,14) (8,34) (8,29) (8,23) (8,26) (9,12) (9,16) (9,30) (9,28) (9,20) (9,14) (9,34) (9,29) (9,23) (10,15) (10,25) (10,17) (10,32) (10,33) (10,18) (10,13) (10,22) (10,19) (10,24) (10,11) (11,15) (11,17) (11,32) (11,33) (11,13) (11,22) (11,31) (11,21) (11,27) (12,16) (12,30) (12,28) (12,20) (12,14) (12,34) (12,29) (12,23) (13,15) (13,25) (13,32) (13,18) (13,22) (13,31) (13,24) (13,21) (13,27) (14,16) (14,28) (14,20) (14,34) (14,29) (14,23) (14,26) (15,25) (15,32) (15,33) (15,18) (15,22) (15,19) (15,24) (15,27) (16,28) (16,20) (16,29) (16,23) (17,25) (17,33) (17,18) (17,22) (17,31) (17,24) (17,21) (17,27) (18,33) (18,31) (18,24) (18,21) (18,27) (19,25) (19,32) (19,22) (19,31) (19,21) (19,27) (20,30) (20,29) (20,23) (20,26) (21,25) (21,33) (21,22) (21,31) (21,24) (21,27) (22,25) (22,32) (22,33) (22,31) (22,24) (23,30) (23,28) (23,34) (24,31) (24,27) (25,32) (25,33) (25,31) (26,28) (26,29) (27,32) (27,31) (28,30) (29,34) (30,34) (31,33)\nIs there a path between node 18 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph71-8_10", + "image": "data/connectivity/graph_visual/hard/graph71.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,7) (0,14) (0,16) (0,2) (0,26) (0,17) (0,9) (1,7) (1,14) (1,21) (1,16) (1,20) (1,2) (1,6) (1,8) (1,19) (1,11) (1,17) (2,13) (2,21) (2,22) (2,16) (2,3) (2,24) (2,6) (2,11) (3,13) (3,7) (3,25) (3,20) (3,24) (3,6) (3,23) (4,5) (4,16) (4,24) (4,6) (4,8) (4,19) (5,25) (5,15) (5,19) (6,13) (6,14) (6,21) (6,25) (6,22) (6,16) (6,24) (6,19) (6,23) (6,17) (7,22) (7,16) (7,8) (7,17) (7,9) (8,13) (8,15) (8,11) (8,23) (8,17) (8,9) (9,14) (9,25) (9,22) (9,16) (9,20) (9,15) (9,19) (9,11) (9,26) (10,18) (11,21) (11,16) (11,20) (11,24) (11,23) (11,17) (12,18) (13,22) (13,20) (13,24) (13,23) (14,21) (14,25) (14,22) (14,16) (14,20) (14,15) (14,19) (15,25) (15,19) (15,26) (15,17) (16,25) (16,19) (16,23) (16,26) (16,17) (17,20) (17,23) (17,26) (19,25) (19,20) (19,24) (20,22) (21,22) (22,23) (23,25)\nIs there a path between node 8 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph244-25_14", + "image": "data/connectivity/graph_visual/hard/graph244.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,29) (0,4) (0,16) (0,21) (0,1) (0,25) (0,14) (0,9) (0,5) (0,6) (0,12) (0,17) (0,24) (0,23) (1,29) (1,4) (1,27) (1,16) (1,21) (1,14) (1,9) (1,6) (1,24) (1,23) (2,26) (2,10) (2,22) (2,15) (2,28) (2,8) (2,30) (2,19) (3,26) (3,10) (3,11) (3,22) (3,15) (3,28) (3,8) (3,30) (3,19) (3,20) (4,29) (4,27) (4,16) (4,21) (4,14) (4,9) (4,5) (4,6) (4,12) (4,24) (5,29) (5,27) (5,21) (5,7) (5,14) (5,12) (5,17) (5,24) (5,23) (6,29) (6,27) (6,7) (6,25) (6,14) (6,9) (6,12) (6,24) (6,23) (7,25) (7,14) (7,9) (7,12) (7,17) (7,23) (8,26) (8,10) (8,11) (8,13) (8,30) (8,19) (9,29) (9,27) (9,16) (9,14) (9,12) (9,24) (9,23) (10,26) (10,13) (10,15) (10,28) (10,19) (10,20) (11,26) (11,13) (11,15) (11,28) (11,30) (11,19) (11,20) (12,29) (12,27) (12,16) (12,21) (12,25) (12,17) (12,24) (12,23) (13,26) (13,28) (13,30) (14,29) (14,16) (14,21) (14,25) (14,17) (14,24) (14,23) (15,26) (15,28) (15,30) (15,20) (16,27) (16,21) (16,17) (16,24) (16,23) (17,29) (17,27) (17,21) (17,25) (17,24) (19,26) (19,22) (19,30) (19,20) (20,26) (20,22) (20,28) (21,29) (21,27) (21,25) (21,24) (21,23) (22,26) (22,28) (22,30) (23,29) (23,27) (23,25) (24,29) (24,27) (24,25) (25,29) (26,28) (28,30)\nIs there a path between node 25 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph601-17_14", + "image": "data/connectivity/graph_visual/hard/graph601.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,25) (0,3) (1,25) (1,29) (2,14) (2,13) (2,20) (2,18) (2,31) (2,9) (2,27) (2,21) (2,12) (2,7) (2,33) (2,11) (2,24) (2,26) (2,30) (3,25) (4,23) (4,22) (4,34) (4,5) (5,23) (5,22) (5,34) (6,14) (6,13) (6,20) (6,18) (6,27) (6,21) (6,12) (6,7) (6,28) (6,24) (6,26) (6,30) (7,14) (7,13) (7,20) (7,31) (7,17) (7,9) (7,27) (7,21) (7,12) (7,10) (7,33) (7,28) (7,30) (8,14) (8,13) (8,31) (8,17) (8,9) (8,27) (8,12) (8,33) (8,11) (8,28) (8,26) (8,30) (9,14) (9,13) (9,20) (9,18) (9,27) (9,21) (9,12) (9,10) (9,33) (9,24) (9,26) (9,19) (9,30) (10,13) (10,20) (10,18) (10,31) (10,17) (10,27) (10,12) (10,33) (10,11) (10,28) (10,24) (11,14) (11,13) (11,20) (11,18) (11,31) (11,12) (11,33) (11,28) (11,24) (11,26) (11,30) (12,14) (12,13) (12,20) (12,18) (12,17) (12,27) (12,21) (12,33) (12,19) (13,14) (13,20) (13,18) (13,31) (13,17) (13,21) (13,28) (13,24) (13,26) (14,18) (14,31) (14,17) (14,27) (14,21) (14,33) (14,26) (15,32) (17,18) (17,31) (17,27) (17,33) (17,28) (17,24) (17,26) (17,19) (17,30) (18,20) (18,31) (18,33) (18,24) (18,26) (18,19) (18,30) (19,31) (19,27) (19,21) (19,33) (19,28) (19,26) (20,31) (20,27) (20,21) (20,33) (20,24) (20,26) (20,30) (21,27) (21,33) (21,28) (21,24) (21,30) (22,23) (22,34) (23,34) (24,33) (24,26) (25,29) (26,31) (26,33) (26,30) (27,31) (27,33) (27,28) (27,30) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nIs there a path between node 17 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph486-28_14", + "image": "data/connectivity/graph_visual/hard/graph486.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,26) (0,9) (0,24) (0,21) (0,11) (0,22) (1,7) (1,27) (1,29) (1,8) (1,3) (1,15) (1,17) (1,10) (2,7) (2,5) (2,18) (2,29) (2,6) (2,3) (2,15) (2,17) (2,10) (3,7) (3,5) (3,27) (3,18) (3,29) (3,28) (3,8) (4,20) (4,13) (4,23) (4,25) (4,16) (4,12) (4,32) (4,30) (5,7) (5,18) (5,29) (5,28) (5,8) (5,15) (5,17) (5,10) (6,7) (6,27) (6,29) (6,28) (6,8) (6,15) (6,17) (6,10) (7,18) (7,29) (7,28) (7,8) (7,15) (7,17) (7,10) (8,27) (8,18) (8,28) (8,15) (8,17) (9,14) (9,31) (9,26) (9,24) (9,21) (9,22) (10,18) (10,28) (10,17) (11,14) (11,19) (11,31) (11,26) (11,21) (12,20) (12,13) (12,23) (12,25) (12,16) (12,32) (12,30) (13,20) (13,23) (13,16) (13,32) (13,30) (14,19) (14,31) (14,24) (14,21) (15,27) (15,29) (15,28) (16,20) (16,23) (16,25) (16,32) (16,30) (17,27) (17,18) (17,29) (17,28) (18,29) (18,28) (19,31) (19,26) (19,24) (19,21) (19,22) (20,23) (20,25) (20,32) (21,26) (21,24) (21,22) (22,26) (22,24) (23,25) (23,32) (23,30) (24,26) (26,31) (27,29) (27,28) (28,29) (30,32)\nIs there a path between node 28 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph680-25_33", + "image": "data/connectivity/graph_visual/hard/graph680.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,21) (0,4) (0,30) (0,19) (0,26) (1,27) (1,21) (1,32) (1,8) (1,34) (1,3) (2,27) (2,11) (2,7) (2,30) (2,9) (2,13) (2,26) (3,32) (3,4) (3,18) (3,8) (3,30) (3,31) (3,33) (3,26) (4,11) (4,21) (4,32) (4,8) (4,30) (4,9) (4,13) (5,29) (5,23) (5,17) (6,25) (6,29) (6,23) (6,22) (7,28) (7,8) (7,31) (7,26) (8,15) (8,28) (8,18) (8,33) (8,26) (9,27) (9,21) (9,24) (9,19) (9,33) (10,14) (11,31) (11,13) (11,20) (12,14) (12,23) (13,16) (13,34) (13,31) (14,25) (14,29) (14,23) (15,28) (15,30) (16,21) (16,32) (16,18) (16,34) (16,33) (17,25) (18,21) (18,32) (18,30) (18,19) (19,28) (19,31) (20,27) (20,30) (20,34) (20,31) (20,33) (21,27) (21,30) (21,31) (21,33) (24,28) (26,32) (26,34) (26,31) (27,28) (27,30) (27,33) (28,30) (28,34) (28,33) (31,33) (32,34) (32,33) (33,34)\nIs there a path between node 25 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph7-25_0", + "image": "data/connectivity/graph_visual/hard/graph7.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,5) (0,1) (0,4) (0,12) (0,23) (0,19) (0,14) (0,21) (0,15) (0,7) (0,22) (1,24) (1,6) (1,20) (1,23) (1,25) (1,3) (1,9) (1,16) (1,7) (2,6) (2,19) (2,14) (2,10) (2,3) (2,8) (2,9) (2,7) (3,5) (3,24) (3,14) (3,25) (3,22) (4,24) (4,19) (4,10) (4,16) (5,24) (5,14) (5,15) (5,9) (6,23) (6,14) (6,15) (7,24) (7,23) (7,14) (7,15) (7,10) (7,22) (8,19) (8,14) (8,21) (8,25) (8,22) (9,23) (10,24) (10,16) (11,18) (11,17) (12,20) (12,14) (12,25) (12,16) (14,24) (14,23) (14,19) (14,15) (15,20) (15,19) (15,21) (15,22) (16,25) (17,18) (19,21) (20,24) (20,23) (20,25) (21,23) (22,23)\nIs there a path between node 25 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph695-29_27", + "image": "data/connectivity/graph_visual/hard/graph695.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,21) (0,22) (0,25) (0,23) (0,10) (0,16) (0,3) (0,4) (0,7) (0,34) (0,27) (0,28) (0,19) (0,1) (0,20) (1,14) (1,6) (1,12) (1,25) (1,8) (1,16) (1,4) (1,7) (1,34) (1,27) (1,28) (1,26) (2,5) (2,17) (2,18) (2,15) (2,11) (3,14) (3,13) (3,6) (3,21) (3,12) (3,25) (3,33) (3,8) (3,10) (3,4) (3,7) (3,34) (3,28) (3,19) (3,26) (4,13) (4,6) (4,21) (4,22) (4,12) (4,8) (4,23) (4,10) (4,16) (4,34) (4,29) (4,28) (4,20) (5,30) (5,24) (5,9) (5,31) (5,15) (5,11) (6,14) (6,13) (6,21) (6,25) (6,23) (6,16) (6,7) (6,34) (6,27) (6,29) (6,28) (6,19) (7,14) (7,22) (7,12) (7,33) (7,23) (7,10) (7,16) (7,28) (7,19) (7,26) (7,20) (8,14) (8,13) (8,22) (8,12) (8,25) (8,33) (8,23) (8,10) (8,16) (8,34) (8,27) (8,19) (8,26) (8,20) (9,30) (9,24) (9,18) (9,31) (9,32) (10,14) (10,21) (10,22) (10,12) (10,23) (10,34) (10,27) (10,28) (10,19) (10,26) (11,30) (11,24) (11,17) (11,18) (11,31) (11,15) (11,32) (12,14) (12,13) (12,22) (12,25) (12,33) (12,23) (12,34) (12,27) (12,29) (12,28) (12,19) (12,26) (13,21) (13,22) (13,25) (13,33) (13,23) (13,16) (13,34) (13,27) (13,26) (13,20) (14,21) (14,33) (14,16) (14,34) (14,27) (14,29) (14,26) (14,20) (15,30) (15,24) (15,31) (16,25) (16,33) (16,23) (16,27) (16,19) (16,26) (16,20) (18,30) (18,24) (18,31) (18,32) (19,25) (19,33) (19,23) (19,34) (19,27) (19,29) (19,26) (19,20) (20,22) (20,25) (20,33) (20,23) (20,34) (20,27) (20,28) (20,26) (21,33) (21,23) (21,34) (21,27) (21,29) (22,33) (22,23) (22,27) (22,28) (23,25) (23,33) (23,34) (23,29) (23,28) (23,26) (24,31) (25,33) (25,34) (25,27) (25,28) (25,26) (26,33) (26,34) (26,27) (26,28) (27,33) (27,34) (27,29) (27,28) (28,33) (28,34) (29,33) (29,34) (30,32)\nIs there a path between node 29 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph277-3_2", + "image": "data/connectivity/graph_visual/hard/graph277.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,8) (0,30) (0,14) (0,1) (0,10) (0,29) (0,12) (0,2) (0,17) (0,23) (0,7) (1,26) (1,3) (1,10) (1,25) (1,27) (1,29) (1,12) (1,20) (1,17) (1,7) (2,26) (2,3) (2,8) (2,30) (2,14) (2,10) (2,25) (2,27) (2,29) (2,12) (2,17) (2,23) (3,26) (3,30) (3,14) (3,10) (3,25) (3,27) (3,12) (3,20) (3,17) (3,23) (4,9) (4,22) (4,19) (4,21) (4,16) (4,6) (5,18) (5,13) (5,15) (6,9) (6,22) (6,21) (6,16) (7,26) (7,8) (7,30) (7,14) (7,10) (7,25) (7,27) (7,29) (7,12) (7,20) (7,17) (7,23) (8,27) (8,29) (8,12) (8,20) (8,23) (9,22) (9,21) (9,16) (9,28) (10,26) (10,14) (10,25) (10,29) (10,17) (11,21) (11,16) (11,28) (12,26) (12,25) (12,27) (12,29) (12,20) (12,17) (13,18) (13,15) (14,30) (14,25) (14,27) (14,29) (14,20) (14,17) (14,23) (16,22) (16,21) (16,28) (17,30) (17,27) (17,20) (17,23) (18,24) (19,22) (20,26) (20,25) (20,27) (20,23) (22,28) (23,26) (23,30) (23,25) (23,27) (23,29) (25,26) (25,27) (25,29) (26,27) (26,29) (27,30) (27,29)\nIs there a path between node 3 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph30-14_18", + "image": "data/connectivity/graph_visual/hard/graph30.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,16) (0,14) (0,10) (0,24) (0,2) (0,12) (0,19) (0,3) (0,17) (0,25) (0,23) (0,15) (1,18) (1,11) (1,8) (2,14) (2,10) (2,24) (2,7) (2,3) (2,21) (2,25) (2,23) (2,6) (3,14) (3,24) (3,12) (3,19) (3,17) (3,25) (3,23) (3,6) (3,15) (4,18) (4,8) (5,18) (5,11) (5,8) (6,16) (6,14) (6,10) (6,12) (6,7) (6,19) (6,21) (6,25) (6,23) (6,9) (6,15) (7,16) (7,10) (7,24) (7,12) (7,19) (7,17) (7,25) (7,9) (7,15) (8,18) (8,11) (9,16) (9,14) (9,10) (9,24) (9,12) (9,19) (9,17) (9,21) (9,23) (9,15) (10,16) (10,14) (10,19) (10,21) (10,25) (10,23) (10,15) (11,18) (12,16) (12,14) (12,24) (12,19) (12,17) (12,21) (12,25) (12,23) (12,15) (13,20) (14,16) (14,24) (14,17) (14,21) (14,25) (14,23) (14,15) (15,16) (15,24) (15,23) (16,21) (16,25) (16,23) (17,21) (17,23) (19,21) (19,25) (21,24) (21,25) (21,23) (23,25) (24,25)\nIs there a path between node 14 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph211-9_29", + "image": "data/connectivity/graph_visual/hard/graph211.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,24) (0,29) (0,27) (1,13) (1,20) (1,17) (1,7) (2,28) (2,6) (2,13) (2,17) (2,14) (2,7) (3,6) (3,18) (4,19) (4,12) (4,15) (4,11) (6,13) (7,25) (7,8) (7,18) (7,14) (9,21) (9,27) (12,19) (12,26) (13,18) (13,14) (14,25) (14,20) (17,25) (19,26) (20,28) (21,29) (22,29) (23,24) (23,29) (24,29) (24,27)\nIs there a path between node 9 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph246-24_23", + "image": "data/connectivity/graph_visual/hard/graph246.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,3) (0,15) (0,14) (0,1) (0,10) (0,29) (0,20) (0,26) (0,22) (0,18) (0,7) (0,4) (0,2) (1,27) (1,14) (1,10) (1,12) (1,20) (1,26) (1,22) (1,18) (1,11) (1,7) (1,4) (1,2) (2,3) (2,27) (2,15) (2,10) (2,12) (2,20) (2,26) (2,22) (2,18) (2,11) (2,7) (2,4) (2,25) (2,21) (2,19) (3,27) (3,15) (3,14) (3,10) (3,29) (3,20) (3,22) (3,18) (3,11) (3,4) (3,25) (3,21) (3,19) (4,15) (4,14) (4,10) (4,29) (4,12) (4,20) (4,26) (4,18) (4,25) (4,21) (4,19) (5,17) (5,6) (5,30) (5,16) (5,13) (5,24) (5,9) (6,23) (6,30) (6,16) (6,13) (6,8) (6,24) (6,9) (7,27) (7,15) (7,10) (7,29) (7,12) (7,20) (7,26) (7,22) (7,11) (7,25) (7,19) (8,17) (8,28) (8,23) (8,30) (8,16) (8,13) (8,24) (8,9) (9,28) (9,23) (9,30) (9,16) (10,15) (10,14) (10,12) (10,20) (10,26) (10,22) (10,18) (10,11) (10,25) (10,19) (11,27) (11,15) (11,14) (11,12) (11,20) (11,26) (11,22) (11,18) (11,25) (11,21) (12,27) (12,15) (12,14) (12,20) (12,26) (12,22) (12,21) (13,17) (13,28) (13,23) (13,30) (13,16) (14,27) (14,15) (14,20) (14,26) (14,22) (14,18) (14,25) (14,21) (14,19) (15,20) (15,26) (15,22) (15,18) (15,21) (16,17) (16,28) (16,23) (16,24) (17,28) (17,23) (17,30) (18,27) (18,29) (18,20) (18,21) (18,19) (19,29) (19,20) (19,25) (19,21) (20,27) (20,26) (20,22) (20,25) (20,21) (21,29) (21,26) (21,22) (21,25) (22,29) (22,25) (23,28) (23,30) (24,28) (26,27) (26,29) (27,29)\nIs there a path between node 24 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph286-19_26", + "image": "data/connectivity/graph_visual/hard/graph286.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,1) (0,20) (0,8) (0,31) (0,22) (1,4) (1,24) (1,19) (1,16) (1,5) (1,2) (1,8) (1,18) (1,27) (2,4) (2,19) (2,12) (2,17) (2,21) (2,31) (2,22) (3,25) (3,20) (3,14) (3,31) (3,22) (3,27) (4,7) (4,21) (4,26) (4,27) (5,11) (5,24) (5,20) (5,19) (5,12) (5,16) (5,17) (5,21) (5,9) (5,22) (6,15) (7,24) (7,20) (7,19) (7,16) (7,29) (7,17) (7,21) (7,14) (7,9) (7,8) (7,18) (7,22) (7,30) (8,20) (8,12) (8,14) (9,20) (9,16) (9,14) (9,18) (9,26) (9,23) (10,15) (11,25) (11,28) (11,20) (11,21) (11,26) (12,28) (12,24) (12,20) (12,29) (12,14) (12,18) (12,26) (12,22) (12,27) (12,23) (14,24) (14,16) (14,18) (14,31) (16,25) (16,26) (16,31) (16,23) (17,31) (17,27) (18,25) (18,28) (18,24) (18,21) (18,26) (18,27) (19,29) (19,21) (19,22) (20,25) (20,21) (20,26) (21,24) (21,29) (21,31) (21,23) (22,29) (22,26) (22,23) (23,25) (23,26) (24,25) (24,26) (24,30) (25,29) (25,31) (26,29) (26,31) (27,28) (27,31) (28,29) (29,31) (29,30) (30,31)\nIs there a path between node 19 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph314-16_24", + "image": "data/connectivity/graph_visual/hard/graph314.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,7) (1,5) (1,10) (1,23) (1,20) (2,30) (2,24) (2,18) (2,12) (2,16) (2,3) (2,11) (3,30) (3,4) (3,12) (3,10) (3,22) (3,19) (3,20) (4,30) (4,28) (4,18) (4,12) (4,10) (4,23) (4,22) (4,19) (5,28) (5,18) (5,12) (5,10) (5,19) (5,11) (6,8) (6,21) (6,13) (6,29) (7,8) (7,21) (7,13) (7,17) (7,29) (8,17) (8,15) (9,26) (9,23) (9,22) (9,19) (9,25) (9,20) (10,18) (10,16) (10,26) (10,22) (10,11) (11,30) (11,12) (11,22) (12,28) (12,16) (12,23) (13,17) (13,29) (14,31) (15,31) (15,29) (16,24) (16,28) (16,19) (16,20) (17,27) (17,21) (18,26) (18,19) (19,23) (20,24) (20,23) (22,28) (22,23) (22,25) (23,26) (24,28) (24,25) (25,30)\nIs there a path between node 16 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph241-30_15", + "image": "data/connectivity/graph_visual/hard/graph241.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,22) (0,15) (0,7) (0,13) (0,8) (1,2) (1,11) (1,29) (1,15) (1,20) (1,17) (1,23) (1,6) (2,12) (2,11) (2,5) (2,29) (2,10) (2,16) (2,28) (2,13) (2,8) (4,22) (4,9) (4,15) (4,16) (4,19) (4,20) (5,11) (5,22) (5,16) (5,19) (5,18) (5,23) (5,13) (6,22) (6,27) (6,10) (6,18) (6,17) (6,7) (7,27) (7,10) (7,9) (7,15) (7,14) (7,23) (7,8) (8,26) (8,27) (8,29) (8,14) (8,16) (8,28) (8,17) (9,12) (9,11) (9,26) (9,29) (9,16) (9,18) (9,24) (9,23) (9,13) (10,12) (10,11) (10,27) (10,15) (10,28) (10,18) (10,24) (11,27) (11,20) (11,25) (12,29) (12,19) (12,18) (12,25) (12,17) (12,24) (13,15) (13,16) (13,25) (13,24) (14,18) (14,25) (14,23) (15,29) (15,16) (15,28) (15,19) (15,24) (15,23) (16,24) (16,23) (17,29) (17,19) (18,27) (18,19) (19,20) (19,25) (20,27) (20,24) (22,29) (23,26) (23,24) (24,26) (24,27) (26,27) (26,29) (27,28) (28,29)\nIs there a path between node 30 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph668-24_22", + "image": "data/connectivity/graph_visual/hard/graph668.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,19) (0,18) (0,12) (0,21) (0,23) (0,5) (0,26) (0,11) (0,30) (1,16) (1,19) (1,21) (1,17) (1,5) (1,26) (2,22) (2,18) (2,27) (2,23) (2,28) (2,24) (3,20) (3,14) (3,5) (3,33) (3,26) (3,25) (3,30) (4,16) (4,18) (4,21) (4,23) (4,28) (4,11) (4,25) (4,6) (5,22) (5,7) (5,18) (5,9) (5,17) (5,29) (5,28) (5,24) (5,11) (6,16) (6,20) (6,7) (6,19) (6,18) (6,14) (6,12) (6,9) (6,21) (6,23) (7,31) (7,18) (7,12) (7,9) (7,32) (7,17) (7,29) (7,26) (8,31) (8,10) (8,14) (8,9) (8,21) (8,32) (8,29) (8,33) (8,26) (9,13) (9,27) (9,12) (9,17) (9,29) (9,33) (9,28) (9,11) (9,25) (10,22) (10,31) (10,20) (10,18) (10,12) (10,23) (10,29) (10,28) (11,16) (11,13) (11,14) (11,17) (11,26) (11,30) (12,16) (12,22) (12,20) (12,13) (12,27) (12,21) (12,32) (12,17) (12,25) (13,18) (14,20) (14,32) (14,28) (14,26) (16,19) (16,17) (16,28) (16,24) (16,25) (16,30) (17,19) (17,18) (17,27) (17,25) (18,20) (18,28) (18,26) (19,22) (19,31) (19,27) (19,23) (19,29) (19,33) (20,22) (20,31) (20,23) (20,32) (20,33) (20,26) (20,30) (21,22) (21,29) (21,24) (21,25) (22,31) (22,23) (22,33) (22,26) (23,32) (23,33) (23,24) (23,30) (24,27) (24,25) (25,27) (25,32) (25,28) (25,26) (26,33) (26,30) (27,33) (27,30) (28,31) (28,29) (29,31) (29,32) (30,31) (30,33) (31,33)\nIs there a path between node 24 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph112-13_0", + "image": "data/connectivity/graph_visual/hard/graph112.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,22) (0,11) (0,10) (0,23) (0,4) (0,9) (0,19) (1,17) (1,27) (1,15) (1,23) (1,24) (1,5) (1,18) (2,15) (2,10) (2,23) (2,5) (2,6) (2,16) (4,17) (4,27) (4,16) (4,25) (5,27) (5,11) (5,24) (5,7) (5,16) (5,25) (5,21) (5,18) (6,17) (6,13) (6,27) (6,11) (6,10) (6,14) (6,16) (6,8) (6,19) (7,20) (7,15) (7,10) (7,24) (7,16) (7,8) (7,19) (7,25) (7,21) (8,20) (8,17) (8,27) (8,11) (8,24) (8,16) (9,20) (9,27) (9,11) (9,16) (9,25) (10,13) (10,27) (10,15) (10,16) (11,20) (11,13) (11,14) (11,24) (11,21) (13,20) (13,14) (13,16) (14,22) (14,15) (14,23) (14,19) (15,24) (15,19) (15,25) (16,22) (16,17) (16,23) (17,22) (17,23) (17,25) (18,19) (18,21) (19,27) (19,24) (19,25) (21,25) (23,27) (25,27)\nIs there a path between node 13 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph92-4_13", + "image": "data/connectivity/graph_visual/hard/graph92.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,11) (0,1) (0,5) (0,24) (0,22) (0,12) (0,19) (0,25) (0,26) (1,3) (1,24) (1,22) (1,20) (1,26) (2,3) (2,14) (2,9) (2,25) (3,15) (3,12) (3,19) (3,20) (3,16) (4,21) (4,8) (5,27) (5,19) (5,16) (6,24) (6,9) (6,20) (6,16) (7,8) (7,23) (8,13) (8,18) (9,27) (9,11) (9,15) (9,22) (10,24) (10,12) (10,16) (11,12) (11,25) (11,16) (12,25) (12,16) (12,26) (13,21) (14,27) (14,24) (14,22) (14,25) (14,16) (14,26) (15,16) (16,27) (16,25) (16,26) (17,18) (18,21) (18,23) (19,27) (19,26) (20,27) (20,22) (24,27) (24,25) (25,27) (25,26)\nIs there a path between node 4 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph491-27_14", + "image": "data/connectivity/graph_visual/hard/graph491.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (0,15) (0,32) (0,3) (0,13) (0,19) (0,17) (1,14) (1,10) (1,21) (1,5) (1,29) (1,2) (2,14) (2,12) (2,21) (2,22) (2,29) (2,6) (2,4) (3,18) (3,13) (3,11) (3,19) (3,9) (3,17) (4,14) (4,12) (4,21) (4,5) (4,29) (4,6) (5,14) (5,22) (6,14) (6,12) (6,10) (6,21) (6,22) (6,29) (7,23) (7,30) (7,18) (7,32) (7,11) (8,25) (8,31) (8,20) (8,16) (9,23) (9,18) (9,32) (9,13) (9,11) (9,19) (9,17) (10,22) (10,29) (11,23) (11,15) (11,30) (11,18) (11,32) (11,19) (11,17) (12,14) (12,22) (12,29) (13,23) (13,15) (13,18) (13,32) (13,17) (14,22) (15,23) (15,30) (15,32) (15,19) (15,17) (16,25) (16,31) (16,24) (16,20) (16,28) (16,26) (16,27) (17,30) (17,18) (17,32) (17,19) (19,30) (19,32) (20,24) (20,27) (21,22) (21,29) (22,29) (23,32) (24,28) (24,26) (24,27) (25,31) (25,28) (25,27) (26,28) (26,27) (27,31) (27,28) (28,31) (30,32)\nIs there a path between node 27 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph136-21_24", + "image": "data/connectivity/graph_visual/hard/graph136.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,4) (0,18) (0,17) (0,10) (1,7) (1,24) (1,27) (2,4) (2,8) (2,13) (2,19) (2,27) (3,16) (3,28) (3,9) (4,18) (4,6) (4,10) (4,11) (4,27) (6,20) (6,8) (6,7) (6,27) (7,8) (7,18) (7,17) (7,23) (7,24) (7,10) (7,13) (7,19) (7,11) (7,14) (8,17) (8,22) (8,24) (8,10) (8,11) (10,18) (10,17) (10,12) (10,11) (10,27) (11,17) (11,12) (12,20) (12,18) (12,17) (12,14) (13,20) (13,18) (13,24) (13,27) (13,26) (14,18) (15,28) (15,25) (16,25) (17,20) (17,18) (17,26) (18,22) (18,23) (18,19) (18,27) (19,23) (19,27) (19,26) (20,24) (22,23) (22,24) (22,26) (26,27)\nIs there a path between node 21 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph685-6_34", + "image": "data/connectivity/graph_visual/hard/graph685.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,1) (0,2) (0,11) (0,31) (0,24) (0,20) (0,26) (0,7) (0,23) (1,21) (1,2) (1,11) (1,31) (1,14) (1,24) (1,26) (1,19) (1,23) (1,15) (2,32) (2,21) (2,11) (2,8) (2,31) (2,14) (2,24) (2,20) (2,26) (2,19) (2,15) (3,16) (3,29) (3,17) (3,6) (3,13) (3,33) (3,18) (3,27) (3,25) (3,34) (3,9) (4,22) (4,5) (5,30) (5,22) (6,16) (6,12) (6,13) (6,33) (6,18) (6,25) (6,34) (6,9) (7,32) (7,11) (7,8) (7,14) (7,19) (7,23) (8,32) (8,11) (8,14) (8,24) (8,15) (9,29) (9,12) (9,17) (9,33) (9,18) (9,25) (9,10) (9,34) (10,29) (10,13) (10,33) (10,27) (10,25) (10,28) (11,21) (11,31) (11,14) (11,24) (11,26) (11,19) (11,23) (11,15) (12,16) (12,29) (12,13) (12,18) (12,27) (12,25) (12,34) (12,28) (13,16) (13,29) (13,17) (13,33) (13,28) (14,32) (14,21) (14,31) (14,24) (14,20) (14,26) (14,19) (14,23) (15,21) (15,31) (15,24) (15,20) (15,26) (15,23) (16,17) (16,33) (16,18) (16,27) (16,25) (16,34) (16,28) (17,33) (17,27) (17,34) (17,28) (18,29) (18,27) (18,25) (18,34) (18,28) (19,21) (19,24) (19,20) (20,32) (20,21) (20,31) (20,26) (20,23) (21,32) (21,31) (21,24) (21,26) (21,23) (22,30) (23,24) (23,26) (24,32) (24,31) (24,26) (25,33) (25,34) (25,28) (26,32) (27,28) (28,33) (28,34) (29,33) (31,32) (33,34)\nIs there a path between node 6 and node 34 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph75-26_3", + "image": "data/connectivity/graph_visual/hard/graph75.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,18) (0,16) (0,11) (0,20) (0,22) (0,14) (0,23) (0,25) (0,4) (0,5) (0,2) (1,19) (1,17) (1,21) (1,9) (1,3) (2,10) (2,16) (2,7) (2,20) (2,22) (2,6) (2,8) (2,23) (2,25) (3,19) (3,12) (3,21) (3,9) (4,10) (4,18) (4,16) (4,11) (4,20) (4,22) (4,14) (4,8) (4,13) (4,23) (4,25) (4,5) (5,11) (5,7) (5,20) (5,22) (5,14) (5,8) (5,25) (6,10) (6,18) (6,16) (6,11) (6,7) (6,14) (6,8) (6,13) (6,23) (6,25) (7,10) (7,18) (7,11) (7,20) (7,14) (7,8) (7,13) (7,23) (7,25) (8,10) (8,16) (8,11) (8,20) (8,22) (8,14) (8,13) (8,23) (8,25) (9,15) (9,19) (9,17) (9,21) (10,18) (10,16) (10,11) (10,20) (10,14) (10,13) (10,23) (10,25) (11,18) (11,16) (11,22) (11,13) (12,15) (12,26) (12,21) (13,16) (13,20) (13,22) (13,14) (13,23) (14,18) (14,16) (14,20) (14,22) (14,23) (14,25) (15,26) (15,19) (15,17) (15,21) (16,18) (16,20) (16,22) (16,23) (16,25) (17,19) (18,20) (18,22) (18,23) (19,26) (20,22) (20,23) (21,26) (22,25) (23,25)\nIs there a path between node 26 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph417-25_18", + "image": "data/connectivity/graph_visual/hard/graph417.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,27) (1,2) (1,17) (2,10) (2,29) (2,31) (2,17) (2,24) (2,32) (3,27) (3,29) (3,32) (4,22) (4,23) (4,18) (4,12) (4,13) (4,6) (4,26) (5,15) (5,9) (5,13) (6,23) (6,20) (6,18) (6,9) (6,26) (7,10) (7,25) (7,21) (7,31) (8,27) (8,31) (8,30) (8,24) (8,11) (9,22) (9,20) (9,18) (9,15) (9,12) (9,26) (10,29) (11,31) (11,30) (11,32) (12,23) (12,20) (12,19) (13,28) (13,22) (13,20) (13,15) (13,26) (14,20) (14,18) (15,22) (15,19) (15,26) (16,24) (17,29) (17,21) (17,30) (17,32) (18,22) (18,19) (19,26) (20,28) (20,22) (21,25) (21,31) (21,24) (22,23) (24,27) (24,32) (26,28)\nIs there a path between node 25 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph165-28_3", + "image": "data/connectivity/graph_visual/hard/graph165.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,9) (1,22) (1,11) (1,25) (2,9) (2,8) (2,12) (2,20) (2,26) (2,13) (2,11) (2,6) (2,27) (2,25) (3,7) (5,15) (5,28) (5,22) (5,19) (5,17) (5,24) (5,13) (5,21) (5,14) (5,25) (6,18) (6,8) (6,20) (6,11) (6,14) (6,25) (8,15) (8,28) (8,9) (8,17) (8,20) (8,23) (8,26) (8,11) (9,18) (9,15) (9,28) (9,17) (9,24) (9,11) (9,14) (9,27) (10,18) (10,12) (11,18) (11,22) (11,19) (11,17) (11,23) (11,24) (11,26) (12,28) (12,24) (13,15) (13,19) (13,17) (13,23) (13,26) (13,25) (14,15) (14,28) (15,25) (17,28) (17,24) (17,25) (18,22) (18,25) (19,28) (19,22) (19,26) (19,27) (20,23) (20,25) (21,23) (21,26) (22,24) (22,25) (23,28) (25,28) (27,28)\nIs there a path between node 28 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph501-2_15", + "image": "data/connectivity/graph_visual/hard/graph501.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,22) (0,2) (0,17) (0,14) (0,6) (0,28) (0,23) (0,21) (1,22) (1,8) (1,17) (1,14) (1,19) (1,6) (1,10) (1,23) (1,16) (2,22) (2,4) (2,8) (2,18) (2,32) (2,27) (2,16) (3,4) (3,17) (3,14) (3,33) (3,18) (4,7) (4,19) (4,9) (4,18) (4,28) (4,21) (5,25) (5,13) (6,22) (6,14) (6,9) (6,18) (6,10) (6,12) (6,32) (7,17) (7,33) (7,9) (7,32) (8,22) (8,26) (8,9) (8,28) (8,10) (8,31) (8,16) (9,14) (9,18) (9,28) (9,10) (9,12) (9,31) (9,11) (9,27) (9,16) (10,22) (10,26) (10,29) (10,19) (10,23) (10,21) (11,26) (11,18) (11,12) (11,23) (11,32) (11,27) (11,16) (12,22) (12,14) (12,18) (12,31) (12,23) (12,27) (13,24) (14,22) (14,26) (14,29) (14,19) (14,28) (14,32) (14,16) (15,20) (15,24) (16,22) (16,19) (16,32) (17,33) (17,18) (17,28) (17,23) (18,22) (18,27) (19,32) (20,24) (20,30) (22,26) (22,31) (23,32) (24,30) (25,30) (26,29) (26,33) (27,33) (27,28) (27,31) (29,33) (29,32)\nIs there a path between node 2 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph700-28_29", + "image": "data/connectivity/graph_visual/hard/graph700.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,16) (0,22) (0,34) (0,1) (0,7) (0,31) (0,30) (0,18) (0,15) (0,4) (0,23) (0,14) (0,21) (0,17) (1,16) (1,22) (1,34) (1,20) (1,29) (1,7) (1,3) (1,30) (1,8) (1,9) (1,19) (1,25) (1,15) (1,24) (1,4) (1,14) (1,17) (1,26) (1,28) (1,12) (2,16) (2,34) (2,29) (2,31) (2,30) (2,13) (2,33) (2,19) (2,25) (2,5) (2,18) (2,15) (2,4) (2,23) (2,6) (2,14) (2,21) (2,26) (2,27) (2,28) (2,12) (3,16) (3,22) (3,20) (3,29) (3,7) (3,31) (3,30) (3,13) (3,9) (3,33) (3,19) (3,25) (3,18) (3,15) (3,24) (3,4) (3,23) (3,6) (3,14) (3,21) (3,17) (3,26) (3,28) (4,16) (4,22) (4,20) (4,29) (4,7) (4,31) (4,8) (4,9) (4,33) (4,5) (4,18) (4,15) (4,24) (4,23) (4,6) (4,14) (4,21) (4,17) (4,26) (4,27) (4,12) (5,22) (5,34) (5,20) (5,7) (5,8) (5,9) (5,19) (5,25) (5,18) (5,15) (5,23) (5,6) (5,17) (5,27) (5,28) (6,16) (6,22) (6,34) (6,29) (6,7) (6,31) (6,30) (6,33) (6,19) (6,25) (6,18) (6,15) (6,24) (6,14) (6,21) (6,17) (6,26) (6,27) (6,28) (6,12) (7,22) (7,34) (7,20) (7,29) (7,31) (7,30) (7,13) (7,33) (7,18) (7,14) (7,17) (7,26) (7,28) (7,12) (8,16) (8,22) (8,34) (8,29) (8,31) (8,30) (8,33) (8,19) (8,25) (8,18) (8,15) (8,14) (8,17) (8,27) (8,28) (9,16) (9,22) (9,34) (9,20) (9,29) (9,31) (9,33) (9,19) (9,25) (9,18) (9,15) (9,24) (9,21) (9,17) (9,26) (9,27) (9,12) (10,11) (10,32) (11,32) (12,16) (12,22) (12,34) (12,29) (12,30) (12,13) (12,33) (12,19) (12,25) (12,15) (12,24) (12,14) (12,21) (12,28) (13,16) (13,22) (13,34) (13,31) (13,30) (13,33) (13,19) (13,18) (13,15) (13,24) (13,23) (13,14) (13,26) (13,27) (13,28) (14,16) (14,20) (14,29) (14,33) (14,25) (14,18) (14,15) (14,21) (14,28) (15,16) (15,22) (15,34) (15,20) (15,29) (15,31) (15,30) (15,18) (15,24) (15,23) (15,21) (15,27) (16,22) (16,34) (16,20) (16,29) (16,30) (16,19) (16,25) (16,24) (16,21) (16,17) (16,26) (16,28) (17,22) (17,31) (17,30) (17,33) (17,19) (17,25) (17,18) (17,23) (17,21) (17,26) (17,27) (17,28) (18,30) (18,33) (18,19) (18,25) (18,23) (18,27) (19,22) (19,31) (19,30) (19,33) (19,25) (19,24) (19,23) (19,21) (19,27) (19,28) (20,22) (20,34) (20,31) (20,30) (20,33) (20,25) (20,23) (20,26) (20,28) (21,22) (21,34) (21,29) (21,31) (21,30) (21,33) (21,25) (21,24) (21,23) (21,26) (21,27) (21,28) (22,34) (22,29) (22,31) (22,30) (22,25) (22,28) (23,34) (23,29) (23,31) (23,30) (23,33) (23,25) (23,26) (23,27) (23,28) (24,34) (24,29) (24,31) (24,30) (24,33) (24,25) (24,26) (24,27) (25,34) (25,31) (25,33) (25,26) (25,27) (26,29) (26,31) (26,30) (26,27) (27,34) (27,31) (27,30) (28,29) (28,31) (28,30) (28,33) (29,34) (29,31) (29,30) (30,34) (30,33) (31,34) (31,33) (33,34)\nIs there a path between node 28 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph503-16_15", + "image": "data/connectivity/graph_visual/hard/graph503.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,29) (0,30) (0,27) (0,33) (0,11) (0,5) (0,12) (0,20) (0,7) (0,28) (0,17) (0,6) (0,4) (0,32) (0,13) (0,3) (0,22) (0,31) (1,25) (1,29) (1,30) (1,27) (1,33) (1,2) (1,5) (1,12) (1,20) (1,28) (1,18) (1,16) (1,24) (1,6) (1,13) (1,3) (1,22) (1,31) (2,25) (2,23) (2,29) (2,30) (2,27) (2,33) (2,11) (2,5) (2,12) (2,7) (2,18) (2,16) (2,17) (2,24) (2,13) (2,22) (2,15) (3,25) (3,23) (3,29) (3,30) (3,12) (3,7) (3,18) (3,16) (3,24) (3,4) (3,13) (3,22) (3,31) (4,23) (4,29) (4,27) (4,33) (4,11) (4,5) (4,7) (4,18) (4,24) (4,32) (4,15) (4,31) (5,25) (5,23) (5,30) (5,27) (5,33) (5,11) (5,12) (5,20) (5,7) (5,28) (5,24) (5,6) (5,32) (5,13) (5,22) (5,15) (5,31) (6,25) (6,23) (6,30) (6,27) (6,33) (6,12) (6,20) (6,7) (6,18) (6,24) (6,32) (6,13) (7,25) (7,30) (7,27) (7,33) (7,20) (7,28) (7,18) (7,24) (7,32) (7,13) (7,22) (7,15) (7,31) (8,14) (8,26) (8,19) (9,14) (9,26) (9,19) (9,21) (9,10) (10,14) (10,26) (10,19) (11,23) (11,29) (11,30) (11,27) (11,33) (11,20) (11,18) (11,16) (11,17) (11,32) (11,13) (11,22) (11,15) (11,31) (12,25) (12,23) (12,29) (12,27) (12,33) (12,28) (12,16) (12,24) (12,13) (12,22) (12,15) (12,31) (13,25) (13,23) (13,29) (13,27) (13,33) (13,20) (13,28) (13,18) (13,16) (13,17) (13,24) (13,32) (13,15) (13,31) (14,26) (15,25) (15,23) (15,29) (15,30) (15,33) (15,16) (15,17) (15,24) (15,22) (15,31) (16,25) (16,23) (16,29) (16,30) (16,27) (16,28) (16,17) (16,24) (16,32) (16,22) (17,25) (17,23) (17,29) (17,33) (17,20) (17,18) (17,24) (17,31) (18,25) (18,29) (18,30) (18,33) (18,28) (18,24) (18,31) (20,25) (20,23) (20,30) (20,24) (20,32) (20,22) (20,31) (21,26) (22,25) (22,29) (22,30) (22,28) (22,24) (23,25) (23,29) (23,27) (23,28) (23,24) (23,32) (24,25) (24,29) (24,27) (24,33) (24,28) (24,31) (25,29) (25,30) (25,27) (25,28) (25,32) (25,31) (27,29) (27,30) (27,33) (27,28) (28,29) (28,30) (28,33) (28,32) (28,31) (29,30) (29,33) (29,32) (29,31) (30,33) (30,32) (30,31) (31,33) (31,32) (32,33)\nIs there a path between node 16 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph647-4_23", + "image": "data/connectivity/graph_visual/hard/graph647.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,12) (0,21) (0,10) (0,22) (0,23) (0,29) (0,17) (0,28) (0,9) (0,14) (1,4) (1,26) (1,5) (1,8) (1,15) (1,30) (2,19) (2,18) (2,16) (2,11) (2,7) (2,6) (2,34) (3,12) (3,21) (3,10) (3,24) (3,22) (3,23) (3,29) (3,17) (3,32) (3,28) (3,9) (3,27) (4,26) (4,15) (4,30) (5,26) (5,15) (6,13) (6,31) (6,18) (6,16) (6,34) (7,13) (7,31) (7,19) (7,18) (7,11) (7,34) (8,15) (8,30) (9,12) (9,10) (9,22) (9,23) (9,29) (9,32) (9,33) (9,28) (9,27) (9,14) (10,12) (10,21) (10,22) (10,23) (10,29) (10,17) (10,32) (10,33) (10,28) (10,20) (10,27) (10,14) (11,13) (11,31) (11,19) (11,25) (11,18) (11,16) (12,21) (12,24) (12,29) (12,17) (12,32) (12,33) (12,28) (12,20) (12,27) (12,14) (13,31) (13,19) (13,18) (13,16) (13,34) (14,21) (14,22) (14,23) (14,17) (14,32) (14,28) (14,20) (14,27) (15,26) (15,30) (16,31) (16,19) (16,25) (16,34) (17,24) (17,22) (17,23) (17,29) (17,32) (17,20) (18,31) (18,25) (18,34) (19,31) (19,25) (19,34) (20,24) (20,33) (20,28) (20,27) (21,23) (21,32) (21,33) (22,24) (22,23) (22,29) (22,33) (22,27) (23,33) (23,28) (23,27) (24,29) (24,32) (24,33) (24,27) (25,31) (25,34) (26,30) (27,32) (27,28) (28,29) (28,32) (28,33) (29,32)\nIs there a path between node 4 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph57-19_8", + "image": "data/connectivity/graph_visual/hard/graph57.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,19) (0,15) (0,8) (0,10) (0,6) (0,16) (0,21) (0,22) (0,11) (0,2) (0,5) (0,7) (0,24) (0,18) (0,26) (0,14) (0,4) (1,12) (1,19) (1,3) (1,15) (1,8) (1,10) (1,6) (1,16) (1,21) (1,22) (1,11) (1,2) (1,5) (1,20) (1,7) (1,24) (1,26) (1,14) (2,12) (2,19) (2,15) (2,10) (2,6) (2,21) (2,22) (2,11) (2,5) (2,20) (2,7) (2,24) (2,18) (2,26) (2,14) (2,4) (3,12) (3,19) (3,15) (3,8) (3,10) (3,6) (3,16) (3,21) (3,11) (3,5) (3,20) (3,7) (3,24) (3,18) (3,26) (3,4) (4,25) (4,19) (4,15) (4,10) (4,6) (4,16) (4,22) (4,11) (4,20) (4,7) (4,18) (5,25) (5,19) (5,15) (5,8) (5,6) (5,16) (5,21) (5,22) (5,11) (5,24) (5,18) (5,26) (5,14) (6,25) (6,19) (6,8) (6,16) (6,21) (6,22) (6,20) (6,7) (6,24) (6,18) (6,14) (7,12) (7,19) (7,15) (7,10) (7,16) (7,21) (7,11) (7,20) (7,18) (7,26) (7,14) (8,12) (8,25) (8,15) (8,10) (8,16) (8,21) (8,11) (8,20) (8,18) (8,26) (9,17) (9,13) (9,23) (10,12) (10,25) (10,19) (10,15) (10,16) (10,22) (10,11) (10,18) (10,26) (10,14) (11,12) (11,25) (11,19) (11,16) (11,22) (11,20) (11,24) (11,18) (11,26) (11,14) (12,19) (12,15) (12,16) (12,21) (12,20) (12,26) (13,17) (13,23) (14,19) (14,16) (14,21) (14,20) (14,24) (14,18) (14,26) (15,25) (15,19) (15,22) (15,24) (15,18) (15,26) (16,21) (16,22) (16,18) (17,23) (18,25) (18,19) (18,21) (18,22) (18,20) (18,24) (18,26) (19,25) (19,21) (19,20) (19,24) (19,26) (20,25) (20,24) (21,22) (21,24) (21,26) (22,24) (22,26) (24,25) (24,26) (25,26)\nIs there a path between node 19 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph261-28_27", + "image": "data/connectivity/graph_visual/hard/graph261.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,23) (0,17) (1,9) (2,21) (2,30) (3,9) (3,7) (4,17) (4,20) (5,28) (5,26) (5,24) (6,21) (7,21) (7,9) (7,11) (8,16) (8,18) (9,21) (10,11) (12,28) (12,19) (12,26) (12,17) (12,13) (13,23) (13,24) (14,15) (14,29) (15,16) (16,18) (16,29) (17,23) (19,23) (19,24) (20,28) (20,23) (20,22)\nIs there a path between node 28 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph54-1_20", + "image": "data/connectivity/graph_visual/hard/graph54.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,14) (0,25) (0,10) (0,26) (0,16) (0,1) (0,5) (0,22) (0,21) (0,15) (0,2) (0,24) (0,13) (0,7) (1,14) (1,25) (1,10) (1,16) (1,5) (1,22) (1,17) (1,2) (1,24) (1,19) (1,12) (2,25) (2,16) (2,23) (2,22) (2,17) (2,21) (2,8) (2,24) (2,13) (2,7) (2,12) (3,18) (3,9) (4,25) (4,10) (4,26) (4,16) (4,5) (4,22) (4,21) (4,15) (4,8) (4,24) (4,12) (5,14) (5,25) (5,26) (5,16) (5,23) (5,22) (5,17) (5,21) (5,15) (5,13) (5,19) (5,7) (5,12) (7,14) (7,25) (7,10) (7,16) (7,22) (7,21) (7,8) (7,13) (7,19) (7,12) (8,14) (8,25) (8,26) (8,16) (8,23) (8,22) (8,17) (8,15) (8,19) (8,12) (9,11) (9,18) (9,20) (10,25) (10,26) (10,16) (10,23) (10,22) (10,17) (10,21) (10,24) (10,13) (10,19) (10,12) (11,18) (11,20) (12,14) (12,25) (12,26) (12,16) (12,23) (12,22) (12,24) (12,13) (13,14) (13,26) (13,23) (13,17) (13,21) (13,15) (14,26) (14,16) (14,23) (14,22) (14,17) (14,21) (14,15) (14,24) (14,19) (15,25) (15,26) (15,23) (15,17) (15,21) (15,24) (15,19) (16,25) (16,26) (16,23) (16,21) (16,19) (17,25) (17,23) (17,22) (17,21) (17,24) (17,19) (19,25) (19,26) (19,23) (19,22) (19,21) (19,24) (21,25) (21,26) (22,25) (22,26) (22,23) (22,24) (23,25) (23,26) (23,24) (24,25) (25,26)\nIs there a path between node 1 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph458-26_31", + "image": "data/connectivity/graph_visual/hard/graph458.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,32) (0,6) (0,21) (1,7) (2,18) (3,17) (3,23) (4,27) (4,7) (4,18) (5,27) (6,12) (7,27) (8,28) (8,26) (9,29) (9,31) (10,30) (10,16) (10,25) (10,12) (13,18) (14,30) (14,32) (14,15) (15,19) (15,32) (15,25) (16,19) (16,30) (16,25) (16,21) (17,28) (17,29) (21,30) (21,25) (23,28) (23,29) (26,29) (26,31) (30,32)\nIs there a path between node 26 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph541-22_25", + "image": "data/connectivity/graph_visual/hard/graph541.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,13) (0,30) (0,32) (0,15) (0,8) (0,17) (0,21) (0,19) (0,14) (0,26) (0,3) (0,4) (0,18) (0,11) (0,10) (0,7) (0,28) (0,31) (1,13) (1,30) (1,32) (1,23) (1,15) (1,8) (1,17) (1,21) (1,19) (1,33) (1,26) (1,9) (1,4) (1,11) (1,7) (2,20) (2,13) (2,30) (2,32) (2,23) (2,17) (2,22) (2,19) (2,33) (2,14) (2,26) (2,3) (2,18) (2,11) (2,7) (2,28) (2,31) (3,20) (3,13) (3,30) (3,32) (3,23) (3,15) (3,8) (3,17) (3,21) (3,14) (3,26) (3,9) (3,18) (3,11) (3,28) (3,31) (4,20) (4,13) (4,30) (4,32) (4,23) (4,15) (4,33) (4,26) (4,18) (4,11) (4,10) (4,7) (4,28) (4,31) (5,12) (5,27) (6,29) (6,24) (6,12) (6,27) (7,20) (7,13) (7,30) (7,23) (7,15) (7,8) (7,17) (7,22) (7,19) (7,14) (7,26) (7,18) (7,10) (7,28) (7,31) (8,20) (8,30) (8,15) (8,17) (8,22) (8,21) (8,19) (8,33) (8,14) (8,26) (8,9) (8,18) (8,10) (9,13) (9,30) (9,32) (9,23) (9,22) (9,21) (9,33) (9,14) (9,26) (9,18) (9,11) (9,10) (9,28) (9,31) (10,13) (10,30) (10,32) (10,15) (10,22) (10,21) (10,19) (10,33) (10,26) (10,18) (10,11) (10,28) (11,20) (11,13) (11,30) (11,32) (11,23) (11,15) (11,17) (11,22) (11,21) (11,19) (11,26) (11,28) (11,31) (12,29) (12,24) (12,16) (12,27) (13,20) (13,32) (13,15) (13,17) (13,22) (13,21) (13,33) (13,14) (13,28) (13,31) (14,20) (14,32) (14,15) (14,17) (14,22) (14,18) (14,28) (14,31) (15,20) (15,30) (15,32) (15,17) (15,22) (15,21) (15,19) (15,33) (15,26) (15,18) (15,31) (16,29) (16,27) (17,20) (17,30) (17,22) (17,21) (17,19) (17,33) (17,26) (17,18) (17,28) (17,31) (18,20) (18,30) (18,23) (18,22) (18,21) (18,28) (18,31) (19,20) (19,32) (19,21) (19,26) (19,28) (20,30) (20,32) (20,23) (20,22) (20,21) (20,28) (21,30) (21,32) (21,23) (21,22) (21,33) (21,26) (21,31) (22,32) (22,28) (22,31) (23,30) (23,32) (23,33) (23,26) (23,31) (24,29) (24,27) (26,30) (26,32) (26,33) (26,28) (27,29) (28,31) (30,32) (30,33) (30,31) (31,32) (32,33)\nIs there a path between node 22 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph519-3_29", + "image": "data/connectivity/graph_visual/hard/graph519.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,24) (0,8) (0,19) (0,17) (0,22) (1,24) (1,12) (1,29) (1,11) (1,25) (1,10) (2,31) (2,8) (2,12) (2,6) (2,16) (2,23) (3,15) (4,32) (4,8) (4,12) (4,19) (4,11) (4,6) (4,7) (4,16) (4,18) (4,13) (4,22) (5,32) (5,31) (5,27) (5,29) (5,6) (5,16) (5,13) (5,22) (6,7) (6,16) (6,21) (6,18) (6,13) (7,9) (7,8) (7,30) (7,16) (7,33) (7,17) (7,10) (8,31) (8,11) (8,16) (8,33) (8,17) (9,20) (9,32) (9,24) (9,18) (9,23) (9,10) (10,32) (10,19) (10,29) (10,21) (10,13) (11,32) (11,24) (11,12) (11,29) (11,33) (11,13) (11,23) (12,13) (12,22) (13,20) (13,16) (13,22) (14,26) (15,26) (16,24) (16,18) (16,25) (16,22) (17,31) (17,29) (17,23) (18,31) (18,24) (18,19) (18,25) (19,20) (19,27) (20,32) (20,31) (20,27) (20,29) (20,25) (21,32) (21,30) (21,29) (21,25) (21,23) (22,24) (22,29) (22,33) (23,24) (23,27) (23,33) (23,25) (24,31) (24,30) (25,32) (26,28) (27,30) (29,31) (29,30) (29,33) (31,33) (32,33)\nIs there a path between node 3 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph509-10_22", + "image": "data/connectivity/graph_visual/hard/graph509.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,14) (0,15) (0,9) (0,19) (0,5) (0,31) (0,10) (0,3) (0,1) (0,6) (0,12) (0,27) (0,8) (0,25) (0,20) (0,23) (0,13) (0,18) (0,17) (0,33) (1,15) (1,9) (1,5) (1,24) (1,31) (1,10) (1,3) (1,4) (1,12) (1,27) (1,16) (1,26) (1,8) (1,25) (1,20) (1,28) (1,23) (1,29) (1,18) (1,17) (1,33) (2,14) (2,9) (2,5) (2,24) (2,31) (2,3) (2,4) (2,12) (2,8) (2,23) (2,13) (2,29) (2,18) (2,17) (2,33) (3,14) (3,15) (3,9) (3,19) (3,5) (3,24) (3,31) (3,10) (3,4) (3,30) (3,6) (3,12) (3,27) (3,16) (3,26) (3,28) (3,29) (3,18) (3,17) (3,33) (4,14) (4,15) (4,5) (4,31) (4,10) (4,30) (4,12) (4,27) (4,8) (4,25) (4,21) (4,20) (4,23) (4,13) (4,29) (4,18) (4,33) (5,15) (5,9) (5,24) (5,10) (5,30) (5,6) (5,12) (5,27) (5,16) (5,26) (5,8) (5,21) (5,20) (5,28) (5,23) (5,13) (5,29) (5,18) (5,17) (5,33) (6,14) (6,9) (6,19) (6,30) (6,27) (6,16) (6,26) (6,8) (6,25) (6,21) (6,28) (6,23) (6,18) (6,17) (6,33) (8,14) (8,15) (8,9) (8,10) (8,30) (8,12) (8,27) (8,16) (8,25) (8,21) (8,23) (8,13) (8,29) (8,17) (8,33) (9,14) (9,15) (9,19) (9,31) (9,10) (9,12) (9,27) (9,16) (9,25) (9,21) (9,20) (9,23) (9,13) (9,29) (9,18) (10,15) (10,19) (10,31) (10,30) (10,12) (10,27) (10,16) (10,26) (10,21) (10,20) (10,28) (10,23) (10,13) (10,29) (10,18) (10,17) (10,33) (11,32) (11,22) (12,19) (12,24) (12,31) (12,27) (12,16) (12,25) (12,21) (12,28) (12,23) (12,13) (12,18) (12,17) (12,33) (13,15) (13,24) (13,31) (13,27) (13,26) (13,21) (13,28) (13,23) (13,18) (13,17) (14,15) (14,19) (14,24) (14,16) (14,25) (14,21) (14,28) (14,29) (14,33) (15,19) (15,24) (15,31) (15,30) (15,27) (15,26) (15,21) (15,20) (15,28) (15,23) (15,18) (15,17) (15,33) (16,19) (16,31) (16,30) (16,27) (16,26) (16,20) (16,28) (16,23) (16,29) (16,18) (16,33) (17,19) (17,24) (17,31) (17,26) (17,25) (17,21) (17,20) (17,29) (17,33) (18,19) (18,24) (18,27) (18,25) (18,20) (18,23) (18,29) (18,33) (19,24) (19,31) (19,27) (19,26) (19,25) (19,21) (19,20) (19,23) (19,29) (19,33) (20,24) (20,31) (20,30) (20,27) (20,26) (20,25) (20,28) (20,33) (21,24) (21,31) (21,30) (21,27) (21,26) (21,25) (21,28) (21,23) (21,29) (21,33) (22,32) (23,31) (23,30) (23,27) (23,26) (23,25) (23,28) (23,29) (23,33) (24,31) (24,27) (24,26) (24,25) (24,29) (24,33) (25,30) (25,26) (25,29) (25,33) (26,30) (26,27) (26,28) (26,29) (26,33) (27,30) (27,33) (28,29) (28,33) (29,31) (29,30) (29,33) (30,31) (30,33) (31,33)\nIs there a path between node 10 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph709-21_18", + "image": "data/connectivity/graph_visual/hard/graph709.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,10) (0,2) (0,34) (0,21) (1,18) (1,31) (1,3) (1,4) (1,8) (1,20) (1,23) (1,14) (1,26) (1,16) (1,5) (1,17) (1,27) (1,9) (1,19) (1,15) (1,33) (2,10) (3,31) (3,29) (3,22) (3,12) (3,7) (3,4) (3,28) (3,8) (3,6) (3,20) (3,23) (3,14) (3,16) (3,13) (3,17) (3,24) (3,27) (3,15) (4,29) (4,22) (4,12) (4,11) (4,28) (4,20) (4,23) (4,14) (4,26) (4,16) (4,5) (4,13) (4,24) (4,27) (4,19) (4,33) (5,18) (5,31) (5,29) (5,12) (5,11) (5,7) (5,28) (5,8) (5,6) (5,20) (5,32) (5,23) (5,26) (5,16) (5,13) (5,17) (5,24) (5,9) (5,15) (5,33) (6,18) (6,31) (6,22) (6,12) (6,11) (6,7) (6,20) (6,23) (6,14) (6,16) (6,17) (6,27) (6,9) (6,19) (6,15) (7,18) (7,22) (7,12) (7,11) (7,8) (7,20) (7,14) (7,26) (7,16) (7,13) (7,17) (7,24) (7,9) (7,15) (7,33) (8,18) (8,29) (8,12) (8,11) (8,28) (8,20) (8,32) (8,23) (8,26) (8,17) (8,24) (8,27) (8,9) (8,19) (8,15) (8,33) (9,31) (9,22) (9,12) (9,28) (9,20) (9,32) (9,23) (9,14) (9,16) (9,13) (9,17) (9,24) (9,15) (10,30) (10,25) (10,34) (11,18) (11,31) (11,22) (11,12) (11,28) (11,20) (11,32) (11,23) (11,26) (11,13) (11,17) (11,24) (11,27) (11,19) (11,15) (12,18) (12,31) (12,29) (12,22) (12,20) (12,23) (12,14) (12,26) (12,17) (12,27) (12,19) (12,15) (12,33) (13,18) (13,29) (13,28) (13,20) (13,32) (13,23) (13,26) (13,16) (13,24) (13,15) (14,29) (14,22) (14,20) (14,32) (14,23) (14,16) (14,17) (14,27) (14,19) (15,18) (15,31) (15,29) (15,22) (15,28) (15,32) (15,23) (15,26) (15,16) (15,17) (15,24) (15,19) (15,33) (16,18) (16,31) (16,22) (16,28) (16,26) (16,27) (16,33) (17,28) (17,32) (17,23) (17,24) (17,27) (17,19) (18,31) (18,29) (18,22) (18,32) (18,26) (18,24) (18,19) (18,33) (19,31) (19,28) (19,20) (19,23) (19,33) (20,31) (20,32) (20,26) (21,25) (21,34) (22,29) (22,28) (22,32) (22,23) (22,27) (22,33) (23,31) (23,29) (23,28) (23,32) (23,26) (23,24) (23,27) (24,28) (24,26) (24,27) (24,33) (25,30) (26,31) (26,29) (26,28) (26,33) (27,31) (27,28) (27,32) (27,33) (28,29) (28,32) (29,32) (29,33) (31,33) (32,33)\nIs there a path between node 21 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph34-22_23", + "image": "data/connectivity/graph_visual/hard/graph34.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,6) (0,8) (0,5) (0,13) (0,16) (0,19) (0,1) (0,21) (0,14) (1,25) (1,17) (1,5) (1,10) (1,16) (1,9) (1,19) (1,21) (1,14) (2,23) (2,22) (2,4) (2,3) (2,20) (2,24) (2,12) (2,7) (2,11) (3,22) (3,4) (3,20) (3,24) (3,15) (4,23) (4,22) (4,20) (4,24) (4,15) (4,7) (4,11) (5,6) (5,8) (5,25) (5,13) (5,10) (5,9) (5,19) (5,21) (5,14) (6,8) (6,17) (6,13) (6,10) (6,16) (6,9) (6,19) (6,21) (6,14) (7,22) (7,24) (7,15) (7,12) (7,11) (8,25) (8,13) (8,10) (8,9) (8,19) (8,14) (9,25) (9,13) (9,10) (9,19) (9,21) (10,25) (10,17) (10,13) (10,16) (10,19) (11,23) (11,22) (11,24) (11,15) (11,12) (12,23) (12,20) (12,24) (12,15) (13,17) (13,16) (13,14) (14,25) (14,17) (14,16) (14,19) (15,23) (15,20) (15,24) (16,17) (16,21) (17,21) (19,21) (20,23) (21,25) (23,24)\nIs there a path between node 22 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph94-12_16", + "image": "data/connectivity/graph_visual/hard/graph94.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,20) (0,24) (0,3) (0,19) (0,9) (0,21) (1,2) (2,13) (2,6) (3,24) (3,8) (3,12) (4,20) (4,8) (4,19) (4,17) (4,23) (4,21) (5,7) (5,25) (5,18) (6,13) (7,25) (8,20) (8,24) (8,14) (8,11) (8,23) (9,26) (9,15) (9,24) (9,14) (9,11) (9,23) (10,26) (10,15) (10,12) (10,23) (11,26) (11,15) (11,27) (11,12) (11,17) (11,23) (12,20) (12,24) (12,14) (13,22) (14,19) (14,17) (14,21) (15,19) (15,23) (15,21) (16,24) (16,19) (16,21) (17,24) (18,25) (19,26) (19,24) (20,27) (21,24) (21,27) (23,26) (23,24) (24,26)\nIs there a path between node 12 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph240-18_29", + "image": "data/connectivity/graph_visual/hard/graph240.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,13) (0,2) (0,9) (1,5) (1,13) (1,19) (1,16) (1,18) (1,9) (1,7) (1,3) (1,6) (2,30) (2,16) (2,18) (2,4) (2,9) (2,7) (2,14) (3,19) (3,24) (3,17) (3,7) (3,6) (3,23) (4,30) (4,16) (4,6) (5,26) (5,17) (5,14) (6,19) (6,29) (6,16) (6,7) (7,16) (7,24) (8,28) (9,26) (9,13) (9,19) (9,29) (9,25) (9,14) (10,22) (10,11) (10,20) (10,27) (11,27) (11,28) (12,20) (12,21) (13,26) (13,30) (13,29) (13,18) (13,14) (14,29) (14,16) (16,26) (16,17) (16,23) (17,18) (17,23) (18,30) (18,25) (19,29) (19,25) (20,27) (21,22) (21,28) (23,26) (23,30) (24,29) (24,25) (25,30) (26,29) (27,28)\nIs there a path between node 18 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph35-13_12", + "image": "data/connectivity/graph_visual/hard/graph35.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,23) (0,12) (0,6) (0,24) (0,18) (0,21) (0,17) (0,14) (0,9) (0,19) (0,10) (0,11) (0,1) (0,8) (0,15) (0,4) (1,12) (1,6) (1,25) (1,24) (1,20) (1,18) (1,21) (1,17) (1,14) (1,9) (1,10) (1,11) (1,15) (1,4) (1,16) (2,22) (2,3) (2,7) (3,13) (4,23) (4,6) (4,25) (4,24) (4,20) (4,14) (4,9) (4,19) (4,10) (4,5) (4,11) (4,15) (5,23) (5,12) (5,25) (5,24) (5,20) (5,21) (5,14) (5,19) (5,10) (5,11) (5,8) (5,15) (5,16) (6,23) (6,25) (6,24) (6,18) (6,17) (6,9) (6,19) (6,10) (6,11) (6,8) (6,16) (7,22) (7,13) (8,12) (8,25) (8,24) (8,20) (8,18) (8,17) (8,14) (8,19) (8,10) (8,11) (8,15) (8,16) (9,23) (9,25) (9,20) (9,18) (9,19) (9,11) (9,15) (10,23) (10,12) (10,25) (10,18) (10,21) (10,17) (10,19) (10,15) (10,16) (11,25) (11,24) (11,14) (12,25) (12,24) (12,20) (12,18) (12,21) (12,17) (12,14) (12,19) (14,24) (14,20) (14,18) (14,21) (14,17) (14,19) (14,16) (15,23) (15,25) (15,24) (15,20) (15,21) (15,17) (15,19) (15,16) (16,24) (16,20) (16,17) (16,19) (17,23) (17,25) (17,20) (17,21) (18,25) (18,24) (18,20) (18,21) (18,19) (19,23) (19,24) (19,20) (19,21) (20,23) (20,25) (20,24) (20,21) (21,25) (21,24) (23,25)\nIs there a path between node 13 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph80-15_11", + "image": "data/connectivity/graph_visual/hard/graph80.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,24) (0,26) (0,15) (0,14) (0,22) (0,25) (1,7) (1,24) (1,26) (1,17) (1,4) (1,15) (1,14) (1,9) (1,25) (2,12) (2,20) (2,6) (2,8) (2,18) (2,11) (2,23) (2,10) (3,7) (3,24) (3,26) (3,4) (3,15) (3,14) (3,19) (3,9) (3,21) (3,22) (3,25) (4,24) (4,26) (4,15) (4,9) (4,21) (4,22) (5,20) (5,6) (5,16) (5,8) (5,18) (5,11) (5,23) (5,10) (6,12) (6,20) (6,8) (6,18) (6,11) (6,23) (6,10) (7,13) (7,24) (7,26) (7,15) (7,14) (7,19) (7,9) (7,21) (7,22) (7,25) (8,20) (8,16) (8,10) (9,13) (9,26) (9,17) (9,15) (9,19) (9,21) (9,22) (9,25) (10,12) (10,16) (10,18) (10,11) (11,12) (11,16) (11,18) (11,23) (12,20) (12,23) (13,24) (13,17) (13,15) (13,19) (13,21) (13,22) (13,25) (14,26) (14,15) (14,19) (14,21) (14,22) (14,25) (15,24) (15,26) (15,17) (15,22) (16,20) (16,23) (17,19) (17,22) (17,25) (18,23) (19,26) (19,21) (19,22) (19,25) (20,23) (21,24) (21,26) (21,22) (21,25) (22,25) (24,26) (24,25)\nIs there a path between node 15 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph253-16_25", + "image": "data/connectivity/graph_visual/hard/graph253.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,29) (1,11) (1,5) (1,4) (1,12) (1,10) (2,17) (2,14) (2,20) (2,16) (2,8) (2,13) (3,18) (3,17) (3,14) (3,6) (3,13) (4,11) (4,27) (4,5) (4,29) (4,10) (5,9) (5,30) (5,11) (5,27) (5,21) (5,12) (6,19) (6,16) (7,11) (7,24) (7,29) (7,26) (8,19) (8,13) (9,30) (9,21) (9,29) (9,10) (10,23) (10,22) (10,15) (10,28) (11,27) (11,24) (11,29) (11,28) (12,30) (12,22) (12,21) (13,20) (14,25) (14,16) (15,23) (15,27) (15,24) (15,22) (15,26) (16,19) (16,20) (17,18) (18,19) (19,25) (21,30) (21,23) (21,29) (21,28) (22,24) (22,29) (22,26) (22,28) (23,29) (23,26) (24,30) (27,28)\nIs there a path between node 16 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph465-15_24", + "image": "data/connectivity/graph_visual/hard/graph465.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (1,5) (1,31) (1,4) (1,3) (1,30) (1,13) (2,22) (2,5) (2,31) (2,23) (2,3) (2,20) (2,30) (3,22) (3,31) (3,19) (4,22) (4,5) (4,23) (4,20) (5,7) (5,23) (5,19) (5,6) (6,28) (6,23) (6,19) (7,20) (7,13) (8,24) (8,21) (8,15) (8,25) (8,12) (10,26) (10,15) (10,14) (11,32) (11,27) (11,12) (12,29) (12,17) (13,20) (13,19) (14,21) (14,16) (14,17) (15,21) (15,17) (16,24) (16,32) (16,17) (17,24) (17,29) (19,28) (19,20) (19,30) (20,23) (22,30) (24,32) (24,29) (25,29) (27,29) (28,31) (28,30)\nIs there a path between node 15 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph38-10_16", + "image": "data/connectivity/graph_visual/hard/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,7) (0,4) (0,24) (0,15) (1,2) (1,19) (1,6) (1,23) (1,13) (1,5) (1,20) (1,16) (1,25) (1,9) (1,21) (2,3) (2,6) (2,12) (2,23) (2,13) (2,5) (2,20) (2,16) (2,25) (2,9) (2,21) (2,8) (3,10) (3,22) (3,19) (3,6) (3,12) (3,14) (3,23) (3,13) (3,5) (3,20) (3,25) (3,9) (3,8) (4,11) (4,15) (5,6) (5,12) (5,23) (5,20) (5,17) (5,8) (6,22) (6,19) (6,14) (6,23) (6,13) (6,25) (6,17) (6,9) (7,15) (8,10) (8,22) (8,12) (8,13) (8,20) (8,16) (8,25) (8,9) (8,21) (9,22) (9,19) (9,12) (9,14) (9,23) (9,16) (9,25) (9,21) (10,12) (10,14) (10,20) (10,16) (10,25) (11,24) (11,15) (12,22) (12,16) (12,25) (12,17) (12,21) (13,22) (13,19) (13,14) (13,23) (13,20) (13,16) (13,17) (14,22) (14,19) (14,23) (14,25) (14,21) (15,18) (16,22) (16,23) (16,20) (16,25) (17,22) (17,19) (17,23) (17,20) (18,24) (19,22) (19,21) (20,23) (20,25) (21,22) (21,25) (22,25) (23,25)\nIs there a path between node 10 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph658-9_15", + "image": "data/connectivity/graph_visual/hard/graph658.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,1) (0,13) (0,27) (0,17) (0,25) (0,30) (0,26) (0,21) (0,7) (1,8) (1,28) (1,30) (1,19) (1,6) (1,23) (2,3) (4,18) (4,15) (4,13) (4,31) (4,9) (4,26) (4,6) (4,11) (5,8) (5,24) (5,13) (5,31) (5,16) (5,23) (6,8) (6,14) (6,20) (6,16) (6,22) (6,25) (6,9) (6,7) (7,32) (7,15) (7,20) (7,25) (7,29) (7,19) (7,23) (8,28) (8,17) (8,11) (8,23) (9,34) (9,24) (9,17) (9,31) (9,22) (9,19) (9,11) (10,12) (11,34) (11,18) (11,27) (11,17) (11,31) (11,25) (11,29) (11,21) (13,24) (13,15) (13,17) (13,29) (13,21) (13,23) (14,18) (14,31) (14,16) (14,25) (14,29) (14,21) (15,34) (15,32) (15,16) (15,22) (15,19) (16,34) (16,32) (16,20) (16,31) (16,25) (16,30) (16,23) (17,18) (17,32) (17,20) (17,29) (17,21) (17,23) (18,27) (18,22) (18,25) (18,30) (18,29) (18,21) (19,24) (19,27) (19,20) (20,32) (20,27) (20,22) (20,26) (20,21) (21,34) (21,24) (21,32) (21,28) (21,22) (21,25) (21,30) (21,29) (21,23) (22,28) (22,31) (22,25) (22,30) (22,26) (23,24) (23,25) (23,29) (24,34) (24,26) (25,32) (25,31) (25,30) (25,29) (26,31) (26,29) (27,32) (28,34) (28,30) (28,29) (30,32) (33,34)\nIs there a path between node 9 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph414-30_18", + "image": "data/connectivity/graph_visual/hard/graph414.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,2) (0,26) (0,21) (0,6) (0,12) (0,28) (0,15) (0,7) (1,21) (1,14) (1,25) (1,8) (1,18) (1,15) (1,27) (1,7) (2,26) (2,21) (2,14) (2,8) (2,24) (2,16) (2,13) (2,19) (2,28) (2,15) (2,27) (2,7) (3,26) (3,13) (3,18) (3,12) (3,9) (3,15) (3,27) (3,7) (3,4) (4,17) (4,8) (4,16) (4,12) (4,20) (5,14) (5,25) (5,13) (5,18) (5,28) (5,27) (5,32) (6,17) (6,25) (6,16) (6,9) (6,32) (6,11) (7,21) (7,24) (7,18) (7,12) (7,28) (7,15) (7,31) (8,25) (8,24) (8,9) (8,15) (8,31) (8,27) (8,32) (9,17) (9,16) (9,19) (9,12) (9,28) (9,15) (9,27) (10,22) (11,13) (11,18) (11,19) (11,12) (11,31) (11,27) (12,21) (12,25) (12,24) (12,16) (12,15) (12,32) (13,17) (13,14) (13,24) (13,18) (13,15) (13,20) (13,32) (14,24) (14,19) (14,28) (14,15) (14,20) (14,32) (15,28) (16,24) (16,18) (17,25) (17,28) (17,27) (18,21) (19,25) (19,28) (20,24) (20,32) (21,26) (21,25) (22,30) (23,30) (23,29) (24,25) (25,26) (25,28) (25,32) (26,31) (27,28) (27,31) (28,31) (28,32)\nIs there a path between node 30 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph0-0_16", + "image": "data/connectivity/graph_visual/hard/graph0.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,9) (1,18) (1,8) (1,4) (2,15) (2,18) (2,11) (2,23) (2,4) (3,12) (3,5) (4,23) (4,25) (5,12) (5,17) (6,22) (6,13) (7,18) (7,23) (7,8) (9,17) (10,19) (10,17) (11,15) (12,24) (14,20) (14,22) (15,18) (16,20) (16,22) (20,22) (21,22) (23,25)\nIs there a path between node 0 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph530-23_0", + "image": "data/connectivity/graph_visual/hard/graph530.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,19) (0,4) (1,23) (1,7) (1,18) (1,24) (1,32) (1,31) (1,21) (1,27) (1,11) (1,6) (1,29) (1,17) (1,20) (2,23) (2,7) (2,18) (2,33) (2,24) (2,31) (2,21) (2,8) (2,27) (2,11) (2,29) (2,17) (2,26) (3,9) (3,22) (3,13) (3,5) (3,30) (3,28) (3,16) (3,14) (3,15) (4,19) (4,10) (5,9) (5,22) (5,13) (5,28) (5,16) (5,14) (6,18) (6,32) (6,25) (6,21) (6,8) (6,11) (6,17) (6,20) (6,26) (7,18) (7,33) (7,24) (7,32) (7,25) (7,31) (7,21) (7,17) (7,20) (7,26) (8,18) (8,33) (8,32) (8,25) (8,31) (8,27) (8,11) (8,29) (8,20) (8,26) (9,22) (9,13) (9,30) (9,28) (9,14) (9,15) (10,19) (10,12) (11,18) (11,33) (11,24) (11,25) (11,31) (11,27) (11,29) (11,26) (12,19) (13,28) (13,15) (14,30) (14,28) (14,16) (14,15) (15,22) (15,30) (15,16) (16,22) (17,23) (17,18) (17,33) (17,25) (17,31) (17,21) (17,27) (17,29) (17,20) (17,26) (18,23) (18,32) (18,25) (18,21) (18,29) (18,20) (18,26) (20,23) (20,33) (20,32) (20,25) (20,31) (20,21) (20,27) (20,29) (20,26) (21,23) (21,33) (21,24) (21,25) (21,29) (23,33) (23,24) (23,25) (23,31) (23,27) (23,29) (23,26) (24,33) (24,32) (24,25) (24,27) (24,29) (24,26) (25,32) (25,31) (25,27) (25,29) (25,26) (26,33) (26,31) (26,27) (27,31) (27,29) (28,30) (31,32) (32,33)\nIs there a path between node 23 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph316-1_21", + "image": "data/connectivity/graph_visual/hard/graph316.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,19) (0,31) (0,15) (0,18) (1,24) (1,19) (1,31) (1,5) (2,30) (2,23) (2,4) (2,17) (3,30) (3,23) (3,12) (3,17) (5,28) (5,6) (5,14) (5,9) (5,31) (5,18) (6,10) (6,13) (6,19) (6,31) (6,21) (6,18) (7,28) (7,14) (7,25) (7,20) (8,26) (8,23) (8,12) (8,17) (9,22) (9,13) (9,29) (9,31) (9,15) (9,21) (9,18) (10,13) (10,19) (10,14) (10,15) (10,18) (11,12) (11,16) (12,30) (12,17) (13,28) (13,29) (13,15) (13,21) (13,20) (13,18) (14,22) (14,24) (14,29) (15,29) (15,25) (16,26) (17,30) (18,25) (18,20) (19,29) (19,21) (19,20) (20,22) (20,28) (20,29) (20,25) (21,27) (21,31) (22,28) (22,29) (23,30) (23,26) (24,29) (24,31) (27,31)\nIs there a path between node 1 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph454-1_27", + "image": "data/connectivity/graph_visual/hard/graph454.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,7) (0,4) (0,23) (0,21) (0,18) (1,10) (1,19) (1,24) (1,18) (1,5) (2,11) (2,14) (2,22) (2,23) (2,13) (2,15) (2,31) (2,20) (3,11) (3,22) (3,16) (3,30) (3,13) (3,20) (3,18) (4,11) (4,14) (4,6) (4,23) (4,24) (4,31) (4,32) (4,18) (4,5) (5,19) (5,11) (5,7) (5,23) (5,15) (5,31) (6,19) (6,7) (6,13) (6,8) (7,11) (7,22) (7,28) (7,30) (7,21) (7,31) (8,10) (8,12) (8,14) (8,16) (8,30) (8,21) (9,17) (10,12) (10,24) (10,21) (10,32) (10,20) (11,22) (11,23) (11,13) (11,15) (11,18) (12,22) (12,31) (12,18) (13,16) (13,30) (13,23) (13,21) (13,15) (13,32) (14,19) (14,30) (14,23) (14,31) (15,30) (15,31) (15,32) (15,20) (16,30) (16,24) (16,21) (16,32) (17,25) (18,19) (18,28) (18,24) (19,21) (20,22) (20,21) (22,30) (22,23) (22,32) (24,28) (24,31) (24,32) (25,26) (25,27)\nIs there a path between node 1 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph203-12_16", + "image": "data/connectivity/graph_visual/hard/graph203.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,5) (0,11) (0,13) (3,4) (3,21) (5,14) (5,27) (5,6) (5,19) (5,29) (5,25) (5,16) (5,13) (6,8) (6,9) (6,20) (6,29) (6,16) (6,11) (7,8) (7,26) (7,20) (7,12) (8,9) (8,19) (8,20) (8,28) (8,10) (8,22) (9,19) (9,20) (9,25) (9,11) (9,12) (9,22) (10,20) (10,25) (10,24) (10,15) (10,22) (11,26) (11,20) (11,28) (11,16) (11,24) (11,15) (12,25) (12,16) (12,23) (12,22) (13,18) (14,26) (14,24) (15,26) (15,20) (15,28) (16,27) (16,18) (16,26) (16,25) (16,23) (16,22) (18,27) (18,19) (18,20) (18,28) (18,25) (19,26) (19,20) (20,29) (20,25) (20,22) (22,24) (23,27) (23,29) (24,26) (24,28) (24,29) (25,27) (25,26)\nIs there a path between node 12 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph11-19_1", + "image": "data/connectivity/graph_visual/hard/graph11.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,15) (0,2) (0,1) (0,23) (0,8) (0,24) (0,6) (0,22) (0,4) (0,11) (1,15) (1,14) (1,2) (1,8) (1,12) (1,17) (1,19) (2,15) (2,14) (2,23) (2,8) (2,20) (2,6) (2,22) (2,4) (2,17) (2,11) (2,19) (2,7) (3,18) (3,9) (3,10) (3,21) (3,13) (3,16) (4,15) (4,14) (4,5) (4,23) (4,24) (4,12) (4,17) (4,11) (4,19) (4,7) (5,15) (5,14) (5,8) (5,20) (5,6) (5,22) (5,12) (5,17) (5,11) (5,19) (5,7) (6,15) (6,14) (6,23) (6,8) (6,20) (6,22) (6,12) (6,11) (6,19) (7,15) (7,23) (7,22) (7,12) (7,17) (7,19) (8,15) (8,14) (8,23) (8,24) (8,12) (8,17) (9,18) (9,21) (9,13) (9,16) (10,25) (10,16) (11,15) (11,14) (11,23) (11,24) (11,17) (11,19) (12,14) (12,22) (12,19) (13,25) (13,18) (13,21) (13,16) (14,15) (14,23) (14,22) (14,17) (14,19) (15,23) (15,24) (15,20) (15,22) (15,17) (15,19) (16,18) (17,23) (17,24) (17,19) (18,25) (18,21) (19,23) (19,24) (19,20) (20,23) (20,22) (21,25) (23,24)\nIs there a path between node 19 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph451-23_14", + "image": "data/connectivity/graph_visual/hard/graph451.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (2,30) (2,8) (2,22) (2,17) (2,12) (2,18) (3,27) (3,6) (3,20) (3,12) (4,16) (6,30) (6,8) (6,22) (6,26) (6,17) (6,12) (6,28) (7,13) (7,21) (8,9) (8,24) (8,18) (9,27) (9,20) (9,32) (9,24) (10,30) (10,17) (10,20) (10,12) (10,28) (11,23) (12,27) (12,30) (12,20) (12,24) (13,14) (13,29) (13,25) (14,31) (15,23) (17,32) (17,24) (17,18) (18,27) (18,26) (19,21) (20,30) (20,22) (20,26) (21,31) (21,29) (21,25) (22,24) (24,30) (24,32) (24,28) (25,31) (26,30) (27,28) (28,30) (30,32)\nIs there a path between node 23 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph19-8_20", + "image": "data/connectivity/graph_visual/hard/graph19.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,21) (0,9) (0,6) (0,8) (1,21) (1,19) (1,13) (1,9) (1,3) (2,17) (3,21) (3,16) (3,19) (3,13) (3,8) (4,12) (4,13) (4,6) (4,7) (6,12) (6,16) (6,20) (6,13) (6,18) (6,11) (6,7) (7,20) (7,9) (8,12) (8,16) (8,20) (8,18) (8,11) (9,21) (10,25) (10,24) (11,20) (12,19) (12,13) (13,21) (13,19) (15,23) (18,21) (18,20) (19,20) (23,24)\nIs there a path between node 8 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph264-26_7", + "image": "data/connectivity/graph_visual/hard/graph264.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,14) (0,8) (0,20) (0,23) (0,29) (0,15) (0,25) (0,24) (0,18) (1,2) (2,21) (3,8) (3,17) (3,20) (3,12) (3,10) (3,5) (4,26) (4,14) (4,22) (4,8) (4,12) (4,7) (4,10) (4,5) (5,22) (5,13) (5,8) (5,19) (5,17) (5,12) (5,6) (5,7) (5,24) (6,26) (6,22) (6,29) (6,24) (7,26) (7,11) (7,17) (7,20) (7,23) (7,15) (7,10) (7,24) (8,11) (8,13) (8,19) (8,17) (8,29) (8,15) (8,10) (8,25) (9,21) (10,26) (10,28) (10,17) (10,15) (10,25) (10,18) (11,22) (11,28) (11,20) (11,12) (11,29) (11,18) (12,14) (12,13) (12,28) (12,15) (12,25) (13,19) (13,25) (13,18) (14,20) (14,15) (14,25) (15,25) (16,30) (16,21) (17,19) (17,23) (17,29) (17,24) (17,18) (18,22) (18,23) (18,29) (18,25) (18,24) (19,24) (20,22) (20,23) (20,25) (22,26) (22,28) (23,24) (24,26) (25,29) (26,29)\nIs there a path between node 26 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph686-22_15", + "image": "data/connectivity/graph_visual/hard/graph686.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,24) (0,27) (0,32) (0,33) (0,29) (0,9) (0,21) (0,5) (0,31) (0,14) (0,12) (0,26) (0,11) (0,17) (0,16) (0,34) (0,23) (0,30) (0,7) (0,6) (1,24) (1,32) (1,4) (1,20) (1,9) (1,21) (1,22) (1,12) (1,26) (1,25) (1,11) (1,17) (1,34) (1,23) (1,7) (1,6) (1,8) (2,27) (2,4) (2,29) (2,9) (2,21) (2,5) (2,15) (2,31) (2,22) (2,12) (2,26) (2,25) (2,11) (2,17) (2,18) (2,34) (2,23) (2,30) (3,24) (3,27) (3,32) (3,33) (3,4) (3,20) (3,5) (3,15) (3,31) (3,14) (3,22) (3,25) (3,11) (3,17) (3,16) (3,18) (3,34) (3,30) (3,7) (3,28) (3,6) (3,8) (4,24) (4,27) (4,33) (4,29) (4,20) (4,9) (4,21) (4,5) (4,15) (4,31) (4,14) (4,22) (4,12) (4,25) (4,17) (4,16) (4,18) (4,30) (4,28) (4,6) (4,8) (5,27) (5,29) (5,20) (5,21) (5,15) (5,31) (5,14) (5,12) (5,26) (5,25) (5,11) (5,17) (5,16) (5,30) (5,7) (5,28) (5,8) (6,24) (6,32) (6,33) (6,29) (6,20) (6,9) (6,21) (6,15) (6,14) (6,22) (6,12) (6,26) (6,25) (6,11) (6,16) (6,18) (6,7) (6,28) (6,8) (7,24) (7,27) (7,33) (7,9) (7,21) (7,15) (7,31) (7,14) (7,22) (7,12) (7,26) (7,25) (7,18) (7,23) (7,28) (7,8) (8,24) (8,32) (8,20) (8,9) (8,15) (8,31) (8,14) (8,22) (8,12) (8,17) (8,16) (8,34) (8,23) (8,30) (8,28) (9,27) (9,32) (9,33) (9,29) (9,20) (9,21) (9,31) (9,14) (9,12) (9,26) (9,16) (9,34) (9,23) (9,30) (9,28) (10,19) (10,13) (11,24) (11,32) (11,29) (11,20) (11,21) (11,15) (11,14) (11,22) (11,12) (11,26) (11,17) (11,18) (11,34) (11,23) (11,30) (11,28) (12,24) (12,27) (12,32) (12,33) (12,20) (12,21) (12,31) (12,22) (12,26) (12,25) (12,17) (12,16) (12,18) (12,34) (12,30) (12,28) (13,19) (14,32) (14,29) (14,21) (14,31) (14,26) (14,25) (14,17) (14,16) (14,18) (14,23) (14,30) (15,24) (15,27) (15,32) (15,33) (15,20) (15,31) (15,22) (15,26) (15,25) (15,17) (15,16) (15,34) (15,23) (15,30) (16,27) (16,33) (16,29) (16,20) (16,21) (16,31) (16,22) (16,26) (16,25) (16,17) (16,18) (16,34) (16,23) (16,30) (17,24) (17,32) (17,33) (17,29) (17,20) (17,31) (17,22) (17,26) (17,25) (17,34) (17,23) (17,28) (18,24) (18,32) (18,33) (18,20) (18,31) (18,22) (18,26) (18,34) (18,23) (18,28) (20,24) (20,33) (20,29) (20,31) (20,22) (20,26) (20,34) (20,23) (20,30) (20,28) (21,24) (21,32) (21,26) (21,25) (21,34) (21,23) (21,30) (21,28) (22,24) (22,32) (22,33) (22,29) (22,31) (22,26) (22,25) (22,34) (22,28) (23,27) (23,32) (23,33) (23,29) (23,31) (23,34) (23,30) (23,28) (24,27) (24,33) (24,29) (24,31) (24,26) (24,25) (24,34) (24,30) (24,28) (25,27) (25,32) (25,33) (25,29) (25,26) (25,34) (25,30) (25,28) (26,27) (26,32) (26,33) (26,29) (26,31) (26,28) (27,32) (27,33) (27,29) (27,31) (27,30) (28,32) (28,31) (28,34) (28,30) (29,32) (29,33) (29,34) (30,32) (30,31) (30,34) (31,32) (31,33) (32,33) (32,34) (33,34)\nIs there a path between node 22 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph568-0_7", + "image": "data/connectivity/graph_visual/hard/graph568.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,17) (0,26) (0,2) (0,5) (0,4) (0,25) (0,18) (0,29) (1,24) (1,6) (1,21) (2,22) (2,8) (2,30) (2,17) (2,33) (2,26) (2,11) (2,7) (2,5) (2,23) (2,18) (2,29) (3,27) (4,13) (4,9) (4,33) (4,11) (4,5) (4,23) (4,25) (4,29) (5,22) (5,16) (5,30) (5,9) (5,19) (5,10) (5,15) (5,29) (6,24) (6,31) (7,17) (7,23) (7,25) (8,16) (8,32) (8,10) (8,18) (8,29) (9,22) (9,30) (9,23) (10,22) (10,16) (10,19) (11,22) (11,13) (11,30) (11,33) (11,23) (11,18) (12,28) (12,31) (13,30) (13,32) (13,23) (14,17) (14,32) (14,23) (14,25) (14,15) (14,29) (15,16) (15,33) (15,32) (15,18) (16,22) (16,17) (16,32) (16,23) (16,18) (16,29) (17,32) (17,18) (17,29) (18,19) (18,32) (18,23) (19,29) (20,24) (20,21) (21,27) (22,32) (22,25) (25,33) (25,26) (25,29) (26,33) (26,29) (27,28) (28,31) (29,30)\nIs there a path between node 0 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph495-7_15", + "image": "data/connectivity/graph_visual/hard/graph495.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,31) (0,22) (0,13) (0,7) (0,1) (0,30) (0,6) (0,15) (0,14) (0,12) (1,13) (1,4) (1,33) (1,24) (1,30) (1,27) (1,28) (1,25) (1,15) (1,21) (1,18) (1,5) (1,12) (3,31) (3,23) (3,27) (3,28) (3,25) (3,15) (4,33) (4,24) (4,25) (4,8) (5,33) (5,30) (5,27) (5,6) (5,15) (6,22) (6,11) (6,19) (6,33) (6,8) (7,31) (7,22) (7,19) (7,33) (7,24) (7,30) (7,18) (8,24) (8,18) (9,29) (11,15) (11,14) (11,18) (12,31) (12,13) (12,24) (12,27) (12,25) (13,24) (13,15) (14,22) (14,30) (14,21) (14,18) (15,31) (15,25) (16,20) (18,33) (19,23) (19,28) (19,21) (19,32) (20,26) (21,27) (21,32) (22,28) (22,25) (22,32) (23,30) (23,25) (23,32) (24,30) (24,28) (24,32) (25,31) (25,33) (27,33) (27,30) (27,28) (28,32) (30,31) (31,32)\nIs there a path between node 7 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph625-8_29", + "image": "data/connectivity/graph_visual/hard/graph625.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,30) (0,9) (0,23) (0,3) (2,19) (2,6) (2,31) (2,21) (2,18) (2,11) (3,7) (3,10) (3,34) (3,27) (3,23) (4,16) (4,14) (4,21) (4,18) (4,11) (4,33) (5,17) (6,21) (7,15) (7,13) (7,9) (8,16) (8,31) (8,11) (9,10) (9,15) (9,26) (9,27) (9,23) (10,34) (10,13) (10,28) (11,16) (11,19) (11,31) (12,34) (12,13) (12,30) (12,27) (12,23) (13,26) (13,27) (13,28) (14,31) (14,21) (14,32) (15,27) (15,22) (16,19) (16,25) (17,20) (18,21) (18,33) (18,32) (19,29) (19,21) (19,32) (21,29) (21,25) (21,32) (22,24) (22,28) (23,30) (23,28) (24,34) (24,30) (24,28) (25,31) (26,30) (29,31) (29,33) (29,32) (30,34) (31,33)\nIs there a path between node 8 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph163-6_5", + "image": "data/connectivity/graph_visual/hard/graph163.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,8) (0,11) (0,14) (0,13) (0,3) (1,28) (1,10) (1,21) (1,18) (1,14) (1,13) (2,28) (2,8) (2,27) (2,23) (2,7) (2,4) (2,25) (2,20) (2,26) (2,9) (3,28) (3,6) (3,11) (3,23) (3,21) (3,14) (4,19) (4,23) (4,18) (4,20) (4,9) (5,15) (6,28) (6,8) (6,23) (6,21) (6,25) (6,20) (6,26) (7,27) (7,25) (7,20) (7,13) (7,24) (7,26) (8,28) (8,19) (8,14) (8,26) (8,12) (9,19) (9,21) (9,14) (9,26) (10,14) (10,13) (10,12) (11,28) (11,16) (11,27) (11,14) (11,20) (11,13) (11,24) (11,26) (11,12) (12,20) (13,16) (13,21) (13,18) (14,28) (14,19) (14,23) (14,21) (14,25) (14,24) (15,17) (16,23) (16,24) (18,28) (18,27) (18,26) (19,27) (19,24) (19,26) (20,28) (20,27) (20,23) (21,23) (21,25) (21,26) (23,26) (26,27)\nIs there a path between node 6 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph546-1_7", + "image": "data/connectivity/graph_visual/hard/graph546.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,8) (2,3) (2,28) (2,27) (2,22) (2,11) (2,21) (2,9) (2,26) (2,6) (2,14) (2,7) (2,5) (2,13) (2,10) (3,30) (3,28) (3,27) (3,22) (3,11) (3,4) (3,9) (3,7) (3,12) (3,16) (3,13) (3,10) (4,30) (4,28) (4,27) (4,22) (4,11) (4,21) (4,9) (4,26) (4,6) (4,14) (4,12) (4,5) (4,13) (5,30) (5,27) (5,21) (5,9) (5,26) (5,6) (5,14) (5,16) (5,13) (5,10) (6,30) (6,28) (6,27) (6,22) (6,21) (6,9) (6,12) (6,16) (6,13) (6,10) (7,27) (7,11) (7,9) (7,26) (7,14) (7,16) (7,10) (9,30) (9,28) (9,27) (9,22) (9,21) (9,26) (9,14) (9,13) (10,30) (10,28) (10,27) (10,22) (10,11) (10,21) (10,26) (10,12) (10,16) (10,13) (11,30) (11,28) (11,22) (11,21) (11,14) (11,16) (11,13) (12,30) (12,28) (12,27) (12,21) (12,26) (12,16) (12,13) (13,28) (13,27) (13,22) (13,26) (14,30) (14,28) (14,21) (14,16) (15,18) (15,20) (15,25) (15,31) (15,32) (15,19) (15,33) (16,30) (16,28) (16,27) (16,21) (17,18) (17,24) (17,20) (17,25) (17,31) (17,32) (17,23) (17,19) (17,33) (18,24) (18,20) (18,31) (18,32) (18,23) (18,19) (19,29) (19,20) (19,25) (19,31) (19,32) (19,33) (20,29) (20,24) (20,25) (20,31) (20,32) (20,33) (21,22) (21,26) (22,30) (22,27) (22,26) (23,24) (23,25) (23,31) (23,33) (24,29) (24,25) (24,33) (25,29) (25,32) (26,30) (26,28) (26,27) (27,30) (27,28) (28,30) (29,31) (29,32) (29,33) (31,32) (31,33)\nIs there a path between node 1 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph623-17_1", + "image": "data/connectivity/graph_visual/hard/graph623.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,29) (0,9) (0,17) (0,30) (0,16) (1,31) (1,25) (1,5) (1,16) (2,13) (2,15) (2,23) (2,30) (2,25) (2,5) (3,14) (5,13) (5,9) (5,17) (5,15) (5,23) (5,19) (5,30) (5,16) (5,22) (7,20) (7,34) (7,8) (7,17) (7,31) (7,18) (7,16) (7,32) (8,12) (8,34) (8,11) (8,18) (9,12) (9,34) (9,31) (9,18) (9,30) (9,16) (10,26) (10,28) (11,12) (11,20) (11,23) (11,19) (11,18) (11,30) (12,34) (12,13) (12,17) (12,23) (12,19) (12,18) (13,34) (13,15) (13,31) (13,21) (13,24) (13,32) (15,17) (15,23) (15,19) (15,30) (15,25) (15,21) (16,20) (16,17) (16,18) (16,25) (16,24) (16,27) (16,22) (17,20) (17,34) (17,29) (17,30) (17,21) (18,20) (18,27) (19,30) (20,34) (20,23) (20,25) (20,24) (20,27) (21,25) (22,23) (22,25) (23,29) (23,30) (23,27) (24,29) (24,31) (24,32) (25,29) (26,33) (28,33) (29,31) (29,32) (30,31) (31,34)\nIs there a path between node 17 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph145-0_23", + "image": "data/connectivity/graph_visual/hard/graph145.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,3) (0,24) (0,15) (0,16) (0,19) (0,7) (0,25) (0,26) (1,28) (1,23) (3,6) (3,18) (3,11) (3,24) (3,22) (3,4) (3,7) (3,25) (4,27) (4,24) (4,22) (4,12) (4,21) (4,16) (4,19) (5,6) (5,13) (5,22) (5,12) (5,16) (6,11) (6,21) (6,15) (6,25) (6,26) (7,14) (7,25) (8,23) (9,11) (9,13) (10,11) (10,15) (10,19) (11,27) (11,18) (11,22) (11,12) (11,21) (11,19) (11,25) (12,27) (12,14) (13,27) (13,18) (13,14) (13,21) (14,18) (14,24) (14,15) (15,22) (15,16) (15,26) (16,18) (16,22) (17,28) (17,23) (17,20) (18,27) (19,27) (19,24) (21,26) (22,25) (22,26) (23,28) (24,25) (24,26)\nIs there a path between node 0 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph672-22_12", + "image": "data/connectivity/graph_visual/hard/graph672.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,15) (1,5) (1,31) (1,30) (1,18) (2,17) (2,25) (2,15) (2,7) (2,23) (2,24) (2,5) (2,13) (3,34) (3,8) (4,16) (4,12) (4,9) (4,33) (5,17) (5,7) (5,23) (5,20) (5,31) (5,13) (6,26) (6,11) (6,22) (6,9) (6,21) (7,14) (7,25) (7,20) (7,13) (8,26) (8,29) (8,11) (8,21) (9,26) (9,29) (9,21) (9,33) (10,26) (10,29) (10,22) (10,12) (12,22) (12,21) (13,28) (13,31) (13,19) (14,17) (14,15) (14,19) (15,17) (15,25) (15,28) (15,30) (15,19) (16,26) (17,28) (17,31) (17,19) (18,28) (18,20) (19,27) (19,20) (19,32) (20,30) (20,32) (21,34) (21,33) (24,31) (26,29) (26,34) (27,30) (28,31) (28,30) (29,34) (30,32)\nIs there a path between node 22 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph344-4_9", + "image": "data/connectivity/graph_visual/hard/graph344.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,19) (0,22) (0,8) (0,14) (1,9) (1,11) (1,21) (1,16) (1,28) (1,25) (1,6) (1,10) (2,12) (2,18) (2,25) (2,20) (2,10) (3,18) (3,23) (3,5) (4,24) (5,26) (5,21) (5,29) (5,25) (5,20) (5,31) (6,12) (6,18) (6,17) (7,15) (7,14) (8,30) (8,19) (8,13) (9,21) (9,28) (9,25) (9,17) (10,26) (10,11) (10,25) (10,17) (11,18) (11,23) (11,25) (11,20) (12,21) (12,18) (12,23) (13,24) (13,19) (13,15) (13,14) (14,27) (14,22) (15,24) (15,22) (16,23) (16,17) (18,26) (18,28) (18,23) (18,20) (19,24) (19,30) (20,21) (20,28) (21,26) (21,25) (23,26) (24,30) (25,31) (26,28) (26,31) (28,31)\nIs there a path between node 4 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph76-13_1", + "image": "data/connectivity/graph_visual/hard/graph76.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,25) (0,17) (0,1) (0,22) (0,5) (0,26) (0,12) (0,6) (0,11) (0,2) (0,10) (0,9) (0,3) (0,14) (0,4) (0,23) (0,21) (1,17) (1,22) (1,5) (1,26) (1,24) (1,8) (1,16) (1,10) (1,9) (1,3) (1,14) (1,4) (1,23) (2,17) (2,18) (2,24) (2,12) (2,6) (2,11) (2,16) (2,10) (2,15) (2,9) (2,3) (2,14) (2,23) (3,25) (3,22) (3,5) (3,26) (3,24) (3,12) (3,6) (3,8) (3,11) (3,16) (3,10) (3,15) (3,14) (3,4) (3,23) (3,21) (4,25) (4,22) (4,18) (4,26) (4,8) (4,11) (4,16) (4,10) (4,15) (4,14) (4,21) (5,25) (5,22) (5,18) (5,24) (5,12) (5,6) (5,8) (5,11) (5,16) (5,10) (5,15) (5,9) (5,14) (5,23) (5,21) (6,25) (6,17) (6,18) (6,24) (6,8) (6,11) (6,16) (6,15) (6,9) (6,14) (7,13) (7,19) (7,20) (8,22) (8,26) (8,24) (8,12) (8,11) (8,15) (8,9) (9,25) (9,17) (9,22) (9,18) (9,26) (9,24) (9,10) (9,15) (9,14) (9,23) (9,21) (10,25) (10,18) (10,26) (10,11) (10,14) (10,23) (10,21) (11,25) (11,17) (11,22) (11,24) (11,16) (11,15) (11,14) (11,21) (12,18) (12,24) (12,23) (13,20) (14,25) (14,18) (14,26) (14,24) (14,15) (14,23) (14,21) (15,25) (15,17) (15,22) (15,18) (15,24) (15,16) (15,23) (16,17) (16,22) (16,18) (16,26) (17,22) (17,18) (17,24) (17,23) (18,25) (18,22) (18,24) (18,21) (19,20) (21,25) (21,26) (21,24) (21,23) (22,25) (22,23) (23,24) (24,25) (24,26)\nIs there a path between node 13 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph554-29_2", + "image": "data/connectivity/graph_visual/hard/graph554.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,3) (0,14) (0,1) (0,17) (1,23) (1,3) (1,13) (1,14) (2,30) (2,20) (2,31) (3,25) (3,14) (3,6) (3,7) (3,10) (3,33) (4,27) (4,8) (4,5) (4,20) (5,27) (5,22) (5,15) (5,8) (5,29) (6,11) (6,19) (6,18) (6,13) (6,7) (6,17) (7,13) (7,33) (8,26) (8,12) (8,29) (8,24) (9,19) (9,33) (10,11) (10,23) (10,19) (11,23) (11,19) (11,13) (11,21) (12,30) (12,22) (12,31) (13,23) (13,19) (13,14) (14,28) (15,30) (15,16) (15,32) (15,31) (15,24) (16,32) (16,20) (17,18) (17,33) (18,25) (18,21) (19,25) (19,21) (20,30) (20,31) (20,24) (22,24) (23,25) (23,28) (24,27) (24,30) (24,31) (25,33) (26,29) (29,32) (31,32)\nIs there a path between node 29 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph148-18_7", + "image": "data/connectivity/graph_visual/hard/graph148.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,10) (0,6) (1,10) (2,21) (2,9) (2,13) (2,25) (2,22) (2,27) (2,11) (2,7) (2,15) (2,8) (2,12) (2,23) (2,3) (2,28) (2,14) (2,19) (3,21) (3,9) (3,13) (3,5) (3,22) (3,27) (3,11) (3,17) (3,7) (3,20) (3,15) (3,8) (3,12) (3,18) (3,24) (4,21) (4,9) (4,26) (4,13) (4,25) (4,5) (4,22) (4,27) (4,17) (4,7) (4,15) (4,16) (4,8) (4,12) (4,18) (4,24) (4,23) (4,28) (4,14) (4,19) (5,21) (5,9) (5,26) (5,13) (5,22) (5,27) (5,11) (5,17) (5,20) (5,15) (5,16) (5,8) (5,18) (5,23) (5,28) (6,10) (7,9) (7,13) (7,25) (7,22) (7,27) (7,11) (7,17) (7,20) (7,15) (7,16) (7,12) (7,18) (7,24) (7,23) (7,14) (8,21) (8,13) (8,25) (8,27) (8,11) (8,17) (8,20) (8,15) (8,16) (8,23) (8,14) (8,19) (9,25) (9,27) (9,11) (9,17) (9,20) (9,16) (9,12) (9,24) (9,28) (11,26) (11,13) (11,25) (11,22) (11,27) (11,17) (11,20) (11,15) (11,16) (11,12) (11,24) (11,28) (11,14) (12,21) (12,26) (12,13) (12,25) (12,27) (12,17) (12,20) (12,15) (12,18) (12,24) (12,23) (12,28) (12,19) (13,21) (13,26) (13,25) (13,22) (13,27) (13,17) (13,20) (13,15) (13,16) (13,18) (13,24) (13,23) (13,28) (13,14) (13,19) (14,25) (14,22) (14,27) (14,17) (14,20) (14,15) (14,16) (14,18) (14,24) (14,28) (15,26) (15,27) (15,20) (15,18) (15,24) (15,28) (16,21) (16,26) (16,25) (16,27) (16,20) (16,18) (16,24) (16,23) (16,28) (16,19) (17,21) (17,25) (17,22) (17,27) (17,20) (17,23) (17,28) (17,19) (18,26) (18,25) (18,27) (18,20) (18,24) (18,28) (19,26) (19,25) (19,22) (19,27) (19,20) (19,24) (19,23) (19,28) (20,26) (20,25) (20,27) (20,24) (20,23) (20,28) (21,26) (21,22) (21,28) (22,25) (22,27) (22,28) (23,27) (23,24) (23,28) (24,25) (24,27) (24,28) (25,26) (25,28) (26,28) (27,28)\nIs there a path between node 18 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph563-22_0", + "image": "data/connectivity/graph_visual/hard/graph563.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,24) (0,25) (0,5) (0,19) (0,33) (0,29) (0,4) (1,24) (1,17) (1,10) (1,16) (2,8) (3,28) (3,12) (3,15) (3,23) (3,20) (3,13) (4,7) (4,29) (5,17) (5,7) (5,25) (5,33) (6,8) (6,18) (7,24) (7,17) (7,25) (7,19) (8,22) (9,12) (9,14) (9,23) (10,24) (10,16) (10,33) (11,31) (12,14) (12,23) (12,20) (13,20) (14,28) (14,32) (14,20) (15,20) (16,19) (17,33) (18,22) (19,24) (19,26) (21,23) (22,27) (23,30) (24,25) (25,26) (25,29) (26,33) (29,33)\nIs there a path between node 22 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph585-30_21", + "image": "data/connectivity/graph_visual/hard/graph585.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,9) (0,27) (0,18) (0,16) (0,5) (0,21) (0,29) (0,24) (1,10) (1,7) (1,15) (2,31) (2,14) (2,25) (2,23) (2,11) (2,20) (3,33) (3,4) (4,33) (4,13) (4,32) (5,9) (5,27) (5,12) (5,26) (5,21) (5,29) (5,24) (6,31) (6,14) (6,19) (6,20) (7,10) (7,8) (8,28) (8,10) (8,15) (9,27) (9,18) (9,12) (9,16) (9,29) (9,24) (10,28) (10,15) (11,25) (11,19) (11,20) (12,16) (12,26) (12,21) (12,24) (13,22) (13,33) (14,31) (14,25) (14,20) (16,26) (16,21) (16,29) (16,24) (17,22) (17,33) (17,32) (18,27) (18,26) (18,21) (18,29) (18,24) (19,31) (19,23) (19,20) (20,31) (20,25) (20,23) (21,26) (21,29) (21,24) (22,30) (22,32) (25,31) (26,27) (26,29) (27,29) (30,33) (30,32) (32,33)\nIs there a path between node 30 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph369-30_1", + "image": "data/connectivity/graph_visual/hard/graph369.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,16) (0,6) (0,12) (0,29) (0,13) (0,3) (0,21) (0,17) (0,30) (0,27) (0,8) (0,10) (1,9) (1,11) (1,16) (1,6) (1,20) (1,24) (1,13) (1,14) (1,3) (1,21) (1,17) (1,30) (1,25) (1,19) (1,27) (1,8) (1,10) (2,4) (3,26) (3,9) (3,11) (3,7) (3,12) (3,24) (3,13) (3,14) (3,17) (3,30) (3,25) (3,27) (3,8) (3,10) (4,23) (5,28) (5,15) (6,26) (6,9) (6,11) (6,16) (6,7) (6,12) (6,24) (6,14) (6,21) (6,17) (6,25) (6,19) (6,27) (6,10) (7,26) (7,11) (7,16) (7,12) (7,29) (7,24) (7,21) (7,17) (7,30) (7,8) (7,10) (8,9) (8,16) (8,12) (8,20) (8,24) (8,13) (8,14) (8,17) (8,30) (8,19) (8,27) (8,10) (9,11) (9,16) (9,12) (9,20) (9,29) (9,24) (9,14) (9,21) (9,17) (9,30) (9,25) (9,19) (9,27) (10,16) (10,12) (10,20) (10,24) (10,13) (10,14) (10,21) (10,17) (10,30) (10,25) (10,19) (10,27) (11,26) (11,16) (11,24) (11,14) (11,21) (11,30) (11,25) (11,19) (11,27) (12,26) (12,16) (12,20) (12,29) (12,24) (12,13) (12,14) (12,21) (12,17) (12,30) (12,19) (12,27) (13,26) (13,16) (13,20) (13,24) (13,14) (13,21) (13,17) (13,30) (13,19) (13,27) (14,26) (14,16) (14,20) (14,29) (14,30) (14,25) (15,31) (16,26) (16,29) (16,21) (16,17) (16,30) (16,25) (16,27) (17,26) (17,29) (17,21) (17,30) (17,25) (17,19) (17,27) (18,23) (18,22) (19,26) (19,20) (19,21) (19,30) (19,25) (19,27) (20,26) (20,29) (20,24) (20,21) (20,30) (20,25) (20,27) (21,26) (21,29) (21,30) (21,25) (21,27) (22,23) (24,29) (24,30) (25,29) (25,30) (25,27) (26,29) (27,29) (27,30) (29,30)\nIs there a path between node 30 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph613-3_14", + "image": "data/connectivity/graph_visual/hard/graph613.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,13) (0,19) (0,6) (0,21) (0,10) (0,31) (0,16) (0,7) (0,20) (0,8) (0,17) (0,12) (0,3) (0,11) (0,23) (0,2) (0,22) (0,1) (0,18) (1,33) (1,32) (1,13) (1,19) (1,29) (1,26) (1,27) (1,6) (1,21) (1,10) (1,31) (1,16) (1,28) (1,7) (1,20) (1,8) (1,17) (1,12) (1,3) (1,2) (1,14) (1,22) (1,18) (1,5) (2,33) (2,13) (2,19) (2,29) (2,26) (2,27) (2,6) (2,10) (2,31) (2,16) (2,28) (2,7) (2,20) (2,24) (2,8) (2,17) (2,12) (2,22) (2,18) (3,32) (3,29) (3,27) (3,6) (3,21) (3,31) (3,16) (3,28) (3,7) (3,20) (3,8) (3,12) (3,23) (3,14) (3,22) (3,18) (3,5) (4,25) (4,34) (5,33) (5,32) (5,13) (5,19) (5,29) (5,26) (5,27) (5,6) (5,21) (5,10) (5,31) (5,16) (5,28) (5,20) (5,8) (5,12) (5,11) (5,23) (5,14) (5,22) (5,18) (6,32) (6,13) (6,19) (6,26) (6,27) (6,21) (6,10) (6,16) (6,28) (6,7) (6,20) (6,17) (6,12) (6,11) (6,23) (6,14) (6,22) (6,18) (7,32) (7,13) (7,29) (7,27) (7,21) (7,10) (7,16) (7,28) (7,20) (7,24) (7,17) (7,12) (7,11) (7,23) (7,14) (7,22) (7,18) (8,33) (8,32) (8,13) (8,19) (8,29) (8,26) (8,21) (8,10) (8,31) (8,16) (8,28) (8,20) (8,24) (8,17) (8,12) (8,11) (8,23) (8,14) (8,22) (8,18) (9,25) (9,34) (9,15) (9,30) (10,33) (10,32) (10,13) (10,19) (10,29) (10,26) (10,27) (10,16) (10,28) (10,12) (10,11) (10,14) (10,22) (11,33) (11,32) (11,13) (11,19) (11,29) (11,21) (11,28) (11,20) (11,24) (11,17) (11,12) (11,23) (11,14) (11,22) (11,18) (12,33) (12,32) (12,13) (12,19) (12,29) (12,26) (12,31) (12,16) (12,28) (12,20) (12,23) (12,18) (13,33) (13,32) (13,19) (13,29) (13,26) (13,27) (13,21) (13,31) (13,16) (13,28) (13,20) (13,17) (13,23) (13,14) (13,18) (14,33) (14,32) (14,19) (14,29) (14,26) (14,27) (14,21) (14,31) (14,16) (14,28) (14,20) (14,17) (14,22) (15,25) (15,30) (16,33) (16,32) (16,19) (16,29) (16,26) (16,27) (16,21) (16,31) (16,28) (16,20) (16,24) (16,17) (16,23) (16,22) (17,33) (17,32) (17,19) (17,29) (17,21) (17,28) (17,20) (17,24) (17,23) (17,22) (17,18) (18,32) (18,19) (18,29) (18,26) (18,27) (18,21) (18,31) (18,28) (18,24) (18,23) (18,22) (19,29) (19,27) (19,21) (19,31) (19,28) (19,20) (19,23) (20,33) (20,29) (20,26) (20,31) (20,28) (20,22) (21,33) (21,32) (21,29) (21,31) (21,24) (21,23) (22,29) (22,31) (22,24) (23,29) (23,26) (23,27) (23,31) (23,28) (23,24) (24,32) (24,26) (24,27) (24,31) (25,34) (26,32) (26,29) (26,27) (26,31) (26,28) (27,33) (27,29) (27,31) (28,33) (28,31) (29,33) (29,32) (30,34) (31,33) (31,32) (32,33)\nIs there a path between node 3 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph309-28_8", + "image": "data/connectivity/graph_visual/hard/graph309.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,1) (0,12) (0,20) (0,31) (0,16) (0,24) (0,26) (1,31) (1,8) (1,18) (2,22) (3,10) (3,6) (3,19) (4,27) (5,14) (5,25) (5,11) (6,10) (6,7) (8,12) (8,29) (8,23) (8,15) (9,27) (10,22) (10,17) (11,25) (12,30) (12,23) (12,15) (13,22) (13,19) (14,25) (14,27) (15,16) (15,29) (15,23) (15,28) (16,31) (16,30) (16,24) (17,19) (18,20) (18,26) (18,28) (20,29) (20,26) (23,31) (23,30) (23,26) (23,28) (26,29) (26,28) (28,30)\nIs there a path between node 28 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph479-27_14", + "image": "data/connectivity/graph_visual/hard/graph479.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,8) (0,20) (0,5) (0,9) (0,28) (0,16) (0,15) (0,24) (0,13) (0,18) (0,12) (0,17) (0,29) (0,22) (0,23) (0,27) (1,8) (1,7) (1,20) (1,5) (1,26) (1,28) (1,16) (1,15) (1,2) (1,13) (1,18) (1,12) (1,17) (1,23) (2,8) (2,7) (2,20) (2,26) (2,9) (2,28) (2,16) (2,15) (2,24) (2,17) (2,32) (2,22) (2,23) (2,27) (3,5) (3,6) (3,21) (3,9) (3,16) (3,15) (3,24) (3,13) (3,18) (3,12) (3,29) (3,22) (3,23) (4,19) (4,25) (4,10) (4,11) (4,30) (4,14) (5,8) (5,20) (5,21) (5,9) (5,28) (5,16) (5,15) (5,24) (5,12) (5,17) (5,29) (5,32) (5,22) (5,27) (6,8) (6,21) (6,28) (6,15) (6,24) (6,18) (6,12) (6,22) (6,23) (6,27) (7,8) (7,20) (7,21) (7,9) (7,16) (7,15) (7,13) (7,12) (7,17) (7,29) (7,32) (7,22) (7,23) (7,27) (8,21) (8,26) (8,16) (8,15) (8,24) (8,13) (8,18) (8,12) (8,17) (8,29) (8,32) (8,23) (8,27) (9,20) (9,21) (9,26) (9,28) (9,16) (9,13) (9,29) (9,32) (9,23) (10,31) (10,30) (11,19) (11,25) (11,30) (11,14) (12,21) (12,16) (12,15) (12,24) (12,13) (12,18) (12,17) (12,29) (12,32) (12,27) (13,28) (13,16) (13,15) (13,24) (13,17) (13,32) (13,23) (14,25) (14,30) (15,20) (15,21) (15,26) (15,28) (15,16) (15,24) (15,18) (15,17) (15,32) (15,22) (15,27) (16,21) (16,26) (16,24) (16,18) (16,17) (16,29) (16,32) (16,23) (17,20) (17,28) (17,24) (17,32) (17,22) (17,27) (18,21) (18,26) (18,28) (18,24) (18,29) (18,32) (18,22) (18,27) (19,25) (19,31) (19,30) (20,26) (20,32) (21,26) (21,28) (21,24) (21,29) (21,22) (21,27) (22,26) (22,28) (22,24) (22,29) (22,32) (22,23) (22,27) (23,26) (23,28) (23,24) (23,29) (23,27) (24,26) (24,28) (25,30) (26,28) (26,29) (26,32) (26,27) (27,28) (27,29) (27,32) (28,29) (28,32) (29,32) (30,31)\nIs there a path between node 27 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph599-30_22", + "image": "data/connectivity/graph_visual/hard/graph599.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,25) (0,32) (0,24) (0,10) (0,1) (0,28) (0,17) (0,3) (0,16) (0,7) (0,29) (0,5) (1,6) (1,25) (1,32) (1,24) (1,13) (1,10) (1,11) (1,28) (1,16) (1,7) (1,29) (2,14) (2,15) (2,8) (2,33) (3,18) (3,25) (3,24) (3,13) (3,10) (3,11) (3,28) (3,17) (3,16) (3,7) (3,29) (4,12) (4,27) (4,21) (5,18) (5,6) (5,25) (5,24) (5,13) (5,10) (5,11) (5,17) (5,29) (6,18) (6,25) (6,24) (6,13) (6,10) (6,11) (6,28) (7,18) (7,25) (7,32) (7,24) (7,13) (7,10) (7,28) (7,17) (7,29) (8,19) (8,33) (8,30) (9,22) (9,31) (10,25) (10,32) (10,24) (10,13) (10,28) (10,16) (10,29) (11,25) (11,32) (11,24) (11,13) (11,28) (11,17) (11,29) (12,26) (13,18) (13,25) (13,32) (13,28) (13,16) (14,19) (14,20) (14,15) (14,33) (15,19) (15,20) (15,33) (15,30) (16,32) (16,24) (16,28) (16,17) (16,29) (17,32) (17,24) (17,28) (17,29) (18,32) (18,24) (18,29) (19,20) (19,33) (19,30) (20,33) (20,30) (21,26) (22,31) (22,23) (23,31) (24,25) (24,32) (24,28) (24,29) (25,28) (26,27) (28,32) (28,29) (30,33)\nIs there a path between node 30 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph349-9_19", + "image": "data/connectivity/graph_visual/hard/graph349.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,11) (0,12) (0,27) (0,20) (0,6) (0,18) (1,11) (1,13) (1,6) (1,26) (1,10) (1,30) (2,5) (2,4) (2,31) (2,19) (2,15) (2,14) (3,25) (3,29) (4,9) (4,15) (4,14) (5,8) (5,15) (5,16) (6,11) (6,27) (6,20) (6,17) (6,29) (6,30) (6,7) (7,27) (7,21) (10,11) (10,27) (10,20) (10,26) (10,18) (10,29) (10,21) (10,30) (10,28) (11,26) (11,25) (11,18) (11,29) (12,20) (12,17) (12,29) (13,20) (13,17) (13,25) (13,29) (15,19) (15,16) (17,20) (17,25) (17,29) (18,26) (18,29) (18,30) (19,31) (20,26) (21,26) (23,31) (24,25) (24,28) (25,26) (27,30) (28,29) (29,30)\nIs there a path between node 9 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph277-0_9", + "image": "data/connectivity/graph_visual/hard/graph277.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,8) (0,30) (0,14) (0,1) (0,10) (0,29) (0,12) (0,2) (0,17) (0,23) (0,7) (1,26) (1,3) (1,10) (1,25) (1,27) (1,29) (1,12) (1,20) (1,17) (1,7) (2,26) (2,3) (2,8) (2,30) (2,14) (2,10) (2,25) (2,27) (2,29) (2,12) (2,17) (2,23) (3,26) (3,30) (3,14) (3,10) (3,25) (3,27) (3,12) (3,20) (3,17) (3,23) (4,9) (4,22) (4,19) (4,21) (4,16) (4,6) (5,18) (5,13) (5,15) (6,9) (6,22) (6,21) (6,16) (7,26) (7,8) (7,30) (7,14) (7,10) (7,25) (7,27) (7,29) (7,12) (7,20) (7,17) (7,23) (8,27) (8,29) (8,12) (8,20) (8,23) (9,22) (9,21) (9,16) (9,28) (10,26) (10,14) (10,25) (10,29) (10,17) (11,21) (11,16) (11,28) (12,26) (12,25) (12,27) (12,29) (12,20) (12,17) (13,18) (13,15) (14,30) (14,25) (14,27) (14,29) (14,20) (14,17) (14,23) (16,22) (16,21) (16,28) (17,30) (17,27) (17,20) (17,23) (18,24) (19,22) (20,26) (20,25) (20,27) (20,23) (22,28) (23,26) (23,30) (23,25) (23,27) (23,29) (25,26) (25,27) (25,29) (26,27) (26,29) (27,30) (27,29)\nIs there a path between node 0 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph60-4_19", + "image": "data/connectivity/graph_visual/hard/graph60.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,18) (0,13) (0,22) (1,12) (1,6) (2,20) (2,14) (2,11) (3,5) (3,23) (3,6) (5,17) (6,19) (7,23) (8,13) (8,15) (9,21) (9,18) (12,24) (12,17) (12,19) (13,21) (13,18) (13,25) (13,15) (13,16) (15,16) (16,21) (16,25) (17,23) (17,19) (19,26) (21,22) (22,25)\nIs there a path between node 4 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph455-2_20", + "image": "data/connectivity/graph_visual/hard/graph455.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,27) (0,29) (0,23) (0,28) (1,8) (1,9) (1,2) (1,20) (1,26) (1,23) (2,24) (2,8) (2,27) (2,20) (2,23) (3,11) (3,15) (3,16) (3,6) (3,12) (4,10) (4,9) (4,27) (4,20) (4,17) (4,32) (5,11) (5,22) (5,19) (5,6) (5,25) (5,18) (5,12) (6,22) (6,16) (6,25) (6,18) (7,24) (7,20) (7,29) (8,24) (8,17) (8,26) (8,32) (9,26) (9,21) (10,24) (10,30) (10,29) (11,25) (11,13) (13,15) (13,16) (13,14) (14,22) (14,19) (15,22) (15,25) (16,31) (16,19) (16,25) (17,24) (17,23) (17,28) (17,21) (18,22) (19,31) (20,26) (20,32) (21,30) (21,23) (22,25) (23,30) (24,30) (24,29) (26,27) (26,32) (28,32) (30,32)\nIs there a path between node 2 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph448-9_16", + "image": "data/connectivity/graph_visual/hard/graph448.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,10) (0,30) (0,14) (0,26) (0,7) (0,8) (0,17) (1,24) (1,21) (1,29) (1,19) (2,11) (2,10) (2,30) (2,23) (2,32) (2,7) (3,29) (3,19) (4,18) (5,11) (5,14) (5,6) (5,22) (5,7) (6,10) (6,14) (6,32) (6,17) (7,30) (8,11) (8,10) (8,27) (8,14) (8,22) (8,32) (9,28) (9,16) (10,11) (10,30) (10,27) (10,14) (10,26) (10,22) (10,17) (11,14) (12,16) (13,28) (13,31) (14,27) (14,20) (14,23) (14,32) (16,31) (17,30) (17,26) (17,23) (18,24) (18,25) (19,29) (19,25) (20,23) (21,24) (21,29) (22,30) (22,26) (23,30) (23,26) (24,29) (25,29) (26,30) (26,27) (27,30) (30,32)\nIs there a path between node 9 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph29-4_14", + "image": "data/connectivity/graph_visual/hard/graph29.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,19) (0,23) (0,18) (0,8) (0,11) (1,13) (1,18) (1,9) (1,24) (1,25) (2,10) (2,19) (2,6) (2,18) (2,5) (2,25) (2,7) (3,19) (3,21) (3,15) (3,25) (3,16) (5,23) (5,8) (5,15) (5,25) (6,13) (6,23) (6,22) (6,24) (6,7) (7,10) (7,18) (7,8) (7,22) (7,15) (7,16) (8,13) (8,10) (8,19) (8,22) (8,11) (8,9) (8,24) (9,13) (9,22) (9,16) (10,12) (11,13) (11,19) (11,15) (11,12) (11,16) (12,20) (12,22) (12,15) (13,23) (13,21) (13,15) (15,18) (15,21) (15,24) (16,21) (16,24) (16,25) (18,23) (18,22) (19,24) (20,23) (20,22) (20,25) (22,23) (22,25) (23,24)\nIs there a path between node 4 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph355-18_1", + "image": "data/connectivity/graph_visual/hard/graph355.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,2) (1,16) (1,8) (1,6) (1,13) (1,18) (1,22) (1,10) (1,17) (1,12) (3,5) (3,30) (3,17) (3,12) (4,28) (5,29) (5,6) (5,25) (5,22) (5,10) (5,17) (5,12) (6,15) (6,13) (6,7) (6,30) (6,11) (6,12) (6,26) (7,29) (7,21) (7,25) (7,14) (7,19) (7,17) (7,12) (8,20) (8,21) (8,13) (8,11) (8,25) (8,14) (8,17) (10,15) (10,27) (10,18) (10,26) (11,20) (11,31) (11,13) (11,27) (11,24) (11,17) (12,21) (12,16) (12,31) (12,25) (13,21) (13,31) (13,27) (13,22) (13,19) (14,29) (14,16) (14,24) (14,25) (14,17) (14,26) (15,18) (16,20) (16,30) (16,24) (16,17) (16,26) (17,25) (18,20) (18,21) (18,31) (18,24) (19,27) (19,25) (19,22) (20,29) (20,27) (20,22) (21,30) (21,24) (21,26) (22,30) (24,27) (24,26) (25,26) (26,29) (26,27) (27,29) (27,30)\nIs there a path between node 18 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph453-23_31", + "image": "data/connectivity/graph_visual/hard/graph453.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,18) (0,26) (0,7) (0,3) (0,13) (0,11) (0,19) (1,8) (1,12) (1,23) (1,24) (1,15) (1,6) (2,4) (2,15) (2,6) (3,28) (3,11) (3,19) (4,8) (4,5) (4,15) (4,6) (5,32) (5,8) (5,30) (5,27) (5,12) (5,23) (6,32) (6,23) (7,31) (7,19) (8,23) (8,15) (9,22) (10,25) (10,13) (10,11) (11,14) (11,26) (12,29) (13,28) (13,31) (13,19) (14,18) (15,29) (15,27) (15,24) (16,18) (18,28) (19,26) (23,30) (24,27) (25,28) (26,28)\nIs there a path between node 23 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph491-29_20", + "image": "data/connectivity/graph_visual/hard/graph491.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (0,15) (0,32) (0,3) (0,13) (0,19) (0,17) (1,14) (1,10) (1,21) (1,5) (1,29) (1,2) (2,14) (2,12) (2,21) (2,22) (2,29) (2,6) (2,4) (3,18) (3,13) (3,11) (3,19) (3,9) (3,17) (4,14) (4,12) (4,21) (4,5) (4,29) (4,6) (5,14) (5,22) (6,14) (6,12) (6,10) (6,21) (6,22) (6,29) (7,23) (7,30) (7,18) (7,32) (7,11) (8,25) (8,31) (8,20) (8,16) (9,23) (9,18) (9,32) (9,13) (9,11) (9,19) (9,17) (10,22) (10,29) (11,23) (11,15) (11,30) (11,18) (11,32) (11,19) (11,17) (12,14) (12,22) (12,29) (13,23) (13,15) (13,18) (13,32) (13,17) (14,22) (15,23) (15,30) (15,32) (15,19) (15,17) (16,25) (16,31) (16,24) (16,20) (16,28) (16,26) (16,27) (17,30) (17,18) (17,32) (17,19) (19,30) (19,32) (20,24) (20,27) (21,22) (21,29) (22,29) (23,32) (24,28) (24,26) (24,27) (25,31) (25,28) (25,27) (26,28) (26,27) (27,31) (27,28) (28,31) (30,32)\nIs there a path between node 29 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph80-0_15", + "image": "data/connectivity/graph_visual/hard/graph80.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,24) (0,26) (0,15) (0,14) (0,22) (0,25) (1,7) (1,24) (1,26) (1,17) (1,4) (1,15) (1,14) (1,9) (1,25) (2,12) (2,20) (2,6) (2,8) (2,18) (2,11) (2,23) (2,10) (3,7) (3,24) (3,26) (3,4) (3,15) (3,14) (3,19) (3,9) (3,21) (3,22) (3,25) (4,24) (4,26) (4,15) (4,9) (4,21) (4,22) (5,20) (5,6) (5,16) (5,8) (5,18) (5,11) (5,23) (5,10) (6,12) (6,20) (6,8) (6,18) (6,11) (6,23) (6,10) (7,13) (7,24) (7,26) (7,15) (7,14) (7,19) (7,9) (7,21) (7,22) (7,25) (8,20) (8,16) (8,10) (9,13) (9,26) (9,17) (9,15) (9,19) (9,21) (9,22) (9,25) (10,12) (10,16) (10,18) (10,11) (11,12) (11,16) (11,18) (11,23) (12,20) (12,23) (13,24) (13,17) (13,15) (13,19) (13,21) (13,22) (13,25) (14,26) (14,15) (14,19) (14,21) (14,22) (14,25) (15,24) (15,26) (15,17) (15,22) (16,20) (16,23) (17,19) (17,22) (17,25) (18,23) (19,26) (19,21) (19,22) (19,25) (20,23) (21,24) (21,26) (21,22) (21,25) (22,25) (24,26) (24,25)\nIs there a path between node 0 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph70-3_11", + "image": "data/connectivity/graph_visual/hard/graph70.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,12) (0,19) (0,15) (1,5) (1,20) (1,14) (1,25) (1,10) (2,23) (3,5) (3,11) (3,7) (3,19) (3,18) (4,5) (4,20) (4,25) (4,19) (5,20) (5,25) (5,11) (5,17) (5,19) (5,15) (6,22) (6,25) (6,11) (6,15) (7,20) (7,19) (8,16) (8,26) (9,23) (10,20) (10,17) (10,13) (11,20) (11,17) (11,13) (11,19) (12,14) (12,25) (12,19) (13,14) (14,17) (15,25) (16,21) (16,23) (17,22) (17,20) (17,25) (22,25)\nIs there a path between node 3 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph346-14_21", + "image": "data/connectivity/graph_visual/hard/graph346.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,29) (0,31) (0,26) (0,27) (0,19) (1,28) (2,30) (4,6) (5,29) (5,31) (6,17) (6,30) (7,24) (7,29) (7,31) (8,21) (8,28) (10,11) (10,15) (12,28) (14,15) (14,20) (15,20) (18,29) (18,26) (20,23) (21,28) (24,26) (24,27)\nIs there a path between node 14 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph371-5_19", + "image": "data/connectivity/graph_visual/hard/graph371.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,12) (0,24) (0,31) (0,15) (0,27) (1,26) (1,24) (1,31) (1,27) (1,19) (2,25) (2,20) (2,23) (2,8) (2,9) (2,4) (2,29) (2,7) (2,14) (2,5) (2,11) (2,6) (2,3) (2,13) (2,10) (3,25) (3,30) (3,23) (3,9) (3,4) (3,29) (3,21) (3,28) (3,7) (3,14) (3,5) (3,11) (3,6) (3,10) (4,25) (4,20) (4,30) (4,23) (4,18) (4,17) (4,21) (4,16) (4,14) (4,11) (4,6) (4,13) (4,22) (5,25) (5,20) (5,30) (5,23) (5,18) (5,17) (5,8) (5,9) (5,29) (5,28) (5,16) (5,14) (5,11) (5,13) (5,22) (5,10) (6,25) (6,20) (6,23) (6,18) (6,17) (6,9) (6,29) (6,21) (6,7) (6,13) (6,22) (7,25) (7,20) (7,30) (7,23) (7,18) (7,8) (7,9) (7,29) (7,21) (7,28) (7,16) (7,14) (7,11) (7,13) (7,10) (8,20) (8,30) (8,23) (8,18) (8,9) (8,21) (8,28) (8,16) (8,14) (8,11) (8,13) (8,10) (9,20) (9,30) (9,23) (9,18) (9,29) (9,28) (9,11) (9,13) (9,22) (9,10) (10,25) (10,30) (10,23) (10,17) (10,28) (10,16) (10,14) (10,11) (10,13) (10,22) (11,25) (11,20) (11,30) (11,23) (11,18) (11,29) (11,21) (11,28) (11,22) (12,26) (12,24) (12,19) (13,25) (13,23) (13,18) (13,17) (13,29) (13,21) (13,28) (13,16) (13,22) (14,25) (14,20) (14,23) (14,29) (14,21) (14,28) (14,16) (15,26) (15,31) (15,27) (16,25) (16,20) (16,30) (16,17) (16,29) (16,21) (16,28) (16,22) (17,25) (17,30) (17,23) (17,18) (17,29) (17,28) (17,22) (18,25) (18,20) (18,30) (18,23) (18,29) (18,21) (18,22) (19,26) (19,31) (19,27) (20,30) (20,29) (20,21) (20,28) (21,25) (21,30) (21,23) (21,29) (21,22) (22,25) (22,30) (22,23) (22,29) (22,28) (23,25) (23,30) (23,29) (24,26) (25,29) (25,28) (28,30) (28,29) (29,30)\nIs there a path between node 5 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph653-32_30", + "image": "data/connectivity/graph_visual/hard/graph653.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,20) (0,13) (0,1) (1,4) (1,12) (1,34) (1,6) (1,28) (3,32) (4,20) (4,12) (4,34) (4,6) (4,28) (4,13) (5,26) (5,23) (5,18) (5,24) (5,30) (5,8) (5,21) (5,10) (5,25) (5,29) (5,22) (5,33) (5,15) (5,11) (6,20) (6,12) (6,28) (6,13) (7,16) (8,9) (8,31) (8,26) (8,23) (8,18) (8,24) (8,19) (8,21) (8,10) (8,25) (8,22) (8,33) (8,11) (8,17) (9,31) (9,26) (9,23) (9,18) (9,24) (9,21) (9,10) (9,25) (9,29) (9,22) (9,33) (9,15) (9,17) (10,31) (10,26) (10,23) (10,18) (10,24) (10,30) (10,19) (10,21) (10,29) (10,33) (10,15) (11,31) (11,23) (11,18) (11,24) (11,30) (11,19) (11,21) (11,25) (11,29) (11,33) (11,15) (11,17) (12,20) (12,34) (12,13) (13,20) (14,16) (15,31) (15,26) (15,18) (15,24) (15,30) (15,19) (15,21) (15,25) (15,22) (15,17) (15,27) (17,31) (17,23) (17,18) (17,24) (17,22) (17,27) (18,31) (18,26) (18,23) (18,24) (18,30) (18,19) (18,21) (18,25) (18,29) (18,22) (18,27) (19,31) (19,26) (19,24) (19,21) (19,25) (19,22) (19,33) (19,27) (20,34) (20,28) (21,31) (21,26) (21,23) (21,25) (21,29) (21,22) (21,33) (21,27) (22,24) (22,25) (22,29) (22,33) (22,27) (23,26) (23,29) (23,27) (24,31) (24,26) (24,30) (24,25) (24,29) (25,26) (25,30) (25,29) (25,33) (25,27) (26,31) (26,30) (26,29) (26,33) (26,27) (27,30) (27,29) (27,33) (28,34) (29,31) (29,33) (30,31) (31,33)\nIs there a path between node 32 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph57-9_23", + "image": "data/connectivity/graph_visual/hard/graph57.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,19) (0,15) (0,8) (0,10) (0,6) (0,16) (0,21) (0,22) (0,11) (0,2) (0,5) (0,7) (0,24) (0,18) (0,26) (0,14) (0,4) (1,12) (1,19) (1,3) (1,15) (1,8) (1,10) (1,6) (1,16) (1,21) (1,22) (1,11) (1,2) (1,5) (1,20) (1,7) (1,24) (1,26) (1,14) (2,12) (2,19) (2,15) (2,10) (2,6) (2,21) (2,22) (2,11) (2,5) (2,20) (2,7) (2,24) (2,18) (2,26) (2,14) (2,4) (3,12) (3,19) (3,15) (3,8) (3,10) (3,6) (3,16) (3,21) (3,11) (3,5) (3,20) (3,7) (3,24) (3,18) (3,26) (3,4) (4,25) (4,19) (4,15) (4,10) (4,6) (4,16) (4,22) (4,11) (4,20) (4,7) (4,18) (5,25) (5,19) (5,15) (5,8) (5,6) (5,16) (5,21) (5,22) (5,11) (5,24) (5,18) (5,26) (5,14) (6,25) (6,19) (6,8) (6,16) (6,21) (6,22) (6,20) (6,7) (6,24) (6,18) (6,14) (7,12) (7,19) (7,15) (7,10) (7,16) (7,21) (7,11) (7,20) (7,18) (7,26) (7,14) (8,12) (8,25) (8,15) (8,10) (8,16) (8,21) (8,11) (8,20) (8,18) (8,26) (9,17) (9,13) (9,23) (10,12) (10,25) (10,19) (10,15) (10,16) (10,22) (10,11) (10,18) (10,26) (10,14) (11,12) (11,25) (11,19) (11,16) (11,22) (11,20) (11,24) (11,18) (11,26) (11,14) (12,19) (12,15) (12,16) (12,21) (12,20) (12,26) (13,17) (13,23) (14,19) (14,16) (14,21) (14,20) (14,24) (14,18) (14,26) (15,25) (15,19) (15,22) (15,24) (15,18) (15,26) (16,21) (16,22) (16,18) (17,23) (18,25) (18,19) (18,21) (18,22) (18,20) (18,24) (18,26) (19,25) (19,21) (19,20) (19,24) (19,26) (20,25) (20,24) (21,22) (21,24) (21,26) (22,24) (22,26) (24,25) (24,26) (25,26)\nIs there a path between node 9 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph625-20_21", + "image": "data/connectivity/graph_visual/hard/graph625.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,30) (0,9) (0,23) (0,3) (2,19) (2,6) (2,31) (2,21) (2,18) (2,11) (3,7) (3,10) (3,34) (3,27) (3,23) (4,16) (4,14) (4,21) (4,18) (4,11) (4,33) (5,17) (6,21) (7,15) (7,13) (7,9) (8,16) (8,31) (8,11) (9,10) (9,15) (9,26) (9,27) (9,23) (10,34) (10,13) (10,28) (11,16) (11,19) (11,31) (12,34) (12,13) (12,30) (12,27) (12,23) (13,26) (13,27) (13,28) (14,31) (14,21) (14,32) (15,27) (15,22) (16,19) (16,25) (17,20) (18,21) (18,33) (18,32) (19,29) (19,21) (19,32) (21,29) (21,25) (21,32) (22,24) (22,28) (23,30) (23,28) (24,34) (24,30) (24,28) (25,31) (26,30) (29,31) (29,33) (29,32) (30,34) (31,33)\nIs there a path between node 20 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph97-24_17", + "image": "data/connectivity/graph_visual/hard/graph97.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,2) (0,8) (0,4) (0,9) (0,16) (0,21) (0,12) (0,23) (0,7) (0,11) (1,25) (1,22) (2,8) (2,26) (2,16) (2,20) (3,10) (3,16) (3,13) (3,14) (3,11) (4,26) (4,21) (4,12) (4,14) (5,10) (5,21) (5,13) (5,23) (5,7) (5,14) (5,15) (6,10) (6,9) (6,13) (6,12) (6,23) (6,14) (6,20) (6,15) (7,9) (7,16) (7,18) (7,23) (7,14) (7,15) (7,17) (8,10) (8,9) (8,16) (8,15) (8,11) (9,10) (9,26) (9,14) (9,17) (10,16) (12,18) (12,13) (13,18) (13,15) (14,21) (14,15) (15,26) (15,20) (16,18) (16,20) (17,20) (19,24) (19,22) (20,26) (20,21) (22,27)\nIs there a path between node 24 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph662-4_13", + "image": "data/connectivity/graph_visual/hard/graph662.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,7) (0,11) (0,16) (0,3) (0,12) (0,4) (0,34) (0,26) (1,7) (1,10) (1,14) (1,11) (1,30) (1,8) (1,16) (1,29) (2,33) (2,21) (2,10) (2,14) (2,15) (2,3) (2,12) (2,23) (3,31) (3,22) (3,11) (3,32) (3,12) (3,4) (3,34) (3,26) (4,24) (4,5) (4,33) (4,7) (4,11) (4,19) (4,15) (4,30) (4,25) (4,12) (4,9) (4,23) (5,33) (5,22) (5,15) (5,9) (5,23) (6,18) (7,33) (7,31) (7,22) (7,14) (7,30) (7,12) (7,34) (8,33) (8,31) (8,30) (8,25) (8,16) (8,23) (8,29) (9,21) (9,31) (9,22) (9,30) (9,32) (9,26) (10,21) (10,32) (10,23) (11,29) (12,25) (14,24) (14,31) (14,22) (14,16) (14,34) (15,21) (15,31) (15,19) (15,32) (16,24) (16,19) (16,23) (16,26) (18,28) (19,24) (19,21) (19,31) (19,25) (19,23) (21,22) (21,30) (22,24) (22,25) (22,29) (23,31) (23,34) (24,31) (24,34) (25,31) (25,34) (26,33) (26,31) (26,30) (27,28) (29,30) (29,32) (30,33) (30,31)\nIs there a path between node 4 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph409-21_7", + "image": "data/connectivity/graph_visual/hard/graph409.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (0,19) (0,13) (0,15) (0,24) (0,12) (0,8) (1,3) (1,14) (1,21) (1,25) (1,17) (1,4) (1,13) (1,18) (2,14) (2,21) (2,17) (2,29) (2,13) (2,24) (3,17) (3,4) (4,32) (4,21) (4,19) (4,29) (4,15) (4,24) (4,8) (5,22) (5,23) (5,7) (5,28) (6,22) (6,27) (6,30) (7,31) (7,23) (8,14) (8,29) (8,13) (8,10) (10,14) (10,21) (10,25) (10,24) (11,16) (12,29) (12,24) (13,17) (13,19) (13,29) (14,32) (14,25) (14,19) (14,29) (14,18) (15,32) (15,21) (15,19) (15,29) (16,23) (16,28) (17,29) (17,20) (18,29) (19,24) (20,25) (22,26) (22,31) (22,28) (24,32) (26,27)\nIs there a path between node 21 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph180-6_7", + "image": "data/connectivity/graph_visual/hard/graph180.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,6) (0,15) (0,9) (0,19) (0,26) (0,21) (0,13) (0,24) (0,11) (0,2) (0,25) (0,3) (0,12) (0,23) (0,27) (0,4) (1,28) (1,16) (1,7) (1,10) (2,8) (2,6) (2,15) (2,26) (2,17) (2,21) (2,13) (2,11) (2,14) (2,18) (2,5) (2,12) (2,4) (3,8) (3,22) (3,6) (3,15) (3,9) (3,19) (3,17) (3,21) (3,24) (3,11) (3,25) (3,14) (3,23) (3,4) (4,22) (4,15) (4,9) (4,19) (4,17) (4,13) (4,24) (4,25) (4,14) (4,18) (4,5) (4,23) (4,27) (5,8) (5,15) (5,9) (5,26) (5,17) (5,13) (5,24) (5,25) (5,12) (5,23) (5,27) (6,15) (6,19) (6,26) (6,17) (6,21) (6,13) (6,14) (6,12) (6,23) (6,27) (7,16) (7,20) (8,22) (8,9) (8,19) (8,17) (8,13) (8,24) (8,14) (8,18) (8,23) (8,27) (9,22) (9,19) (9,17) (9,21) (9,24) (9,11) (9,25) (9,14) (9,18) (9,12) (9,23) (9,27) (10,28) (10,16) (10,20) (11,22) (11,19) (11,26) (11,21) (11,24) (11,14) (11,18) (11,12) (11,23) (11,27) (12,22) (12,19) (12,26) (12,21) (12,13) (12,24) (12,14) (12,18) (12,27) (13,22) (13,15) (13,26) (13,21) (13,25) (13,14) (13,18) (13,27) (14,22) (14,15) (14,19) (14,26) (14,17) (14,21) (14,24) (14,18) (14,23) (14,27) (15,22) (15,19) (15,17) (15,21) (15,24) (15,25) (15,18) (15,27) (16,28) (17,22) (17,26) (17,21) (17,24) (17,25) (17,23) (17,27) (18,19) (18,26) (18,21) (18,23) (18,27) (19,22) (19,24) (20,28) (21,22) (21,26) (21,23) (21,27) (22,26) (22,24) (22,27) (23,26) (23,24) (23,25) (23,27) (24,25) (24,27) (25,26) (26,27)\nIs there a path between node 6 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph406-20_9", + "image": "data/connectivity/graph_visual/hard/graph406.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,21) (0,25) (0,3) (0,16) (0,15) (0,5) (0,1) (0,28) (1,25) (1,3) (1,5) (1,28) (2,22) (2,13) (2,24) (2,31) (2,26) (2,32) (2,17) (2,19) (2,30) (3,21) (3,25) (3,15) (3,5) (4,22) (4,13) (4,7) (4,31) (4,26) (4,32) (4,17) (4,30) (5,21) (5,16) (5,15) (6,18) (6,14) (6,9) (6,23) (6,20) (7,22) (7,24) (7,32) (7,17) (7,19) (7,12) (7,30) (9,18) (9,23) (9,20) (9,10) (9,29) (9,27) (10,18) (10,14) (10,11) (10,23) (10,20) (10,29) (10,27) (11,18) (11,23) (11,20) (11,29) (11,27) (12,22) (12,24) (12,31) (12,26) (12,32) (12,17) (12,19) (12,30) (13,22) (13,24) (13,31) (13,26) (13,32) (13,17) (13,30) (14,20) (14,27) (15,16) (15,28) (16,21) (17,24) (17,31) (17,26) (17,32) (17,19) (17,30) (18,23) (18,27) (19,22) (19,31) (19,26) (19,32) (20,23) (20,29) (20,27) (21,25) (22,31) (22,26) (22,32) (23,27) (24,31) (24,26) (24,32) (25,28) (26,31) (26,32) (27,29) (31,32)\nIs there a path between node 20 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph99-3_13", + "image": "data/connectivity/graph_visual/hard/graph99.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,1) (0,13) (0,22) (0,23) (0,9) (0,18) (0,7) (0,2) (0,15) (0,10) (0,16) (0,21) (0,4) (0,25) (0,27) (1,8) (1,13) (1,14) (1,22) (1,6) (1,24) (1,9) (1,18) (1,7) (1,2) (1,15) (1,26) (1,10) (1,12) (1,16) (1,11) (1,4) (1,5) (2,13) (2,14) (2,23) (2,6) (2,24) (2,9) (2,12) (2,16) (2,21) (2,11) (2,4) (2,25) (3,19) (4,8) (4,13) (4,14) (4,22) (4,6) (4,24) (4,18) (4,7) (4,15) (4,20) (4,16) (4,21) (4,11) (4,17) (4,27) (5,8) (5,13) (5,14) (5,23) (5,6) (5,9) (5,18) (5,7) (5,15) (5,26) (5,20) (5,12) (5,16) (5,21) (6,8) (6,13) (6,14) (6,22) (6,24) (6,9) (6,18) (6,7) (6,15) (6,26) (6,20) (6,10) (6,25) (6,17) (6,27) (7,8) (7,13) (7,14) (7,22) (7,24) (7,9) (7,15) (7,26) (7,10) (7,11) (7,25) (7,17) (8,13) (8,14) (8,22) (8,23) (8,24) (8,9) (8,26) (8,10) (8,12) (8,11) (8,25) (8,17) (9,14) (9,22) (9,23) (9,24) (9,18) (9,15) (9,26) (9,16) (9,21) (9,11) (9,25) (10,23) (10,24) (10,18) (10,15) (10,12) (10,21) (10,25) (10,17) (10,27) (11,14) (11,22) (11,15) (11,26) (11,20) (11,12) (11,21) (11,25) (11,17) (11,27) (12,13) (12,14) (12,22) (12,23) (12,24) (12,18) (12,15) (12,26) (12,16) (12,21) (12,17) (13,14) (13,22) (13,24) (13,26) (13,20) (13,16) (13,25) (13,17) (13,27) (14,22) (14,18) (14,15) (14,26) (14,20) (14,16) (14,25) (15,23) (15,24) (15,18) (15,26) (15,20) (15,16) (15,21) (15,25) (15,17) (15,27) (16,22) (16,26) (16,20) (16,21) (16,25) (16,17) (16,27) (17,22) (17,23) (17,25) (18,22) (18,23) (18,24) (18,26) (18,21) (18,25) (20,26) (20,21) (21,23) (21,26) (21,25) (21,27) (22,23) (22,26) (22,27) (23,24) (23,27) (24,26) (24,27) (25,27) (26,27)\nIs there a path between node 3 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph9-21_13", + "image": "data/connectivity/graph_visual/hard/graph9.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,2) (0,10) (0,13) (0,12) (0,9) (0,18) (0,24) (0,5) (0,20) (0,21) (0,7) (0,3) (0,23) (1,2) (1,13) (1,16) (1,12) (1,18) (1,24) (1,20) (1,4) (1,7) (1,3) (1,19) (1,23) (2,13) (2,16) (2,12) (2,9) (2,11) (2,18) (2,24) (2,5) (2,20) (2,4) (2,21) (2,7) (2,3) (2,23) (3,13) (3,16) (3,12) (3,9) (3,11) (3,24) (3,5) (3,20) (3,21) (3,7) (3,19) (3,23) (4,10) (4,16) (4,12) (4,11) (4,18) (4,24) (4,5) (4,20) (4,21) (4,7) (4,19) (4,23) (5,13) (5,12) (5,11) (5,18) (5,24) (5,20) (5,21) (5,7) (5,23) (6,15) (6,25) (6,22) (6,8) (7,13) (7,12) (7,9) (7,11) (7,18) (7,20) (7,21) (7,19) (8,17) (8,15) (8,22) (8,14) (9,10) (9,13) (9,16) (9,11) (9,18) (9,21) (9,19) (9,23) (10,13) (10,12) (10,11) (10,24) (10,20) (10,21) (10,19) (10,23) (11,13) (11,16) (11,24) (11,20) (11,21) (11,19) (11,23) (12,13) (12,16) (12,18) (12,24) (12,20) (12,21) (12,19) (12,23) (13,16) (13,24) (13,21) (13,23) (14,17) (14,15) (14,22) (15,17) (15,25) (15,22) (16,18) (16,24) (16,21) (16,23) (17,25) (17,22) (18,20) (18,21) (18,19) (18,23) (19,20) (19,23) (20,24) (20,21) (21,23) (22,25) (23,24)\nIs there a path between node 21 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph132-11_15", + "image": "data/connectivity/graph_visual/hard/graph132.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,23) (0,17) (0,27) (0,18) (0,13) (0,9) (0,19) (0,8) (0,16) (0,22) (0,25) (0,3) (1,4) (1,12) (1,7) (1,20) (1,26) (2,23) (2,27) (2,13) (2,9) (2,24) (2,14) (2,19) (2,16) (2,22) (2,3) (3,21) (3,23) (3,15) (3,27) (3,18) (3,9) (3,24) (3,14) (3,8) (3,16) (3,22) (3,25) (4,12) (4,11) (4,20) (4,26) (4,5) (5,12) (5,7) (5,11) (5,20) (5,26) (6,10) (7,12) (7,20) (8,21) (8,17) (8,15) (8,27) (8,9) (8,24) (8,14) (8,19) (8,16) (8,22) (9,17) (9,27) (9,24) (11,12) (11,20) (12,26) (13,21) (13,23) (13,17) (13,15) (13,18) (13,14) (13,19) (13,22) (13,25) (14,21) (14,23) (14,17) (14,27) (14,18) (14,24) (14,19) (14,22) (14,25) (15,21) (15,23) (15,17) (15,27) (15,18) (15,24) (15,19) (15,16) (15,22) (15,25) (16,21) (16,23) (16,27) (16,18) (16,24) (16,22) (16,25) (17,23) (17,27) (18,21) (18,27) (18,24) (18,19) (18,22) (18,25) (19,23) (19,27) (19,22) (19,25) (20,26) (21,23) (21,27) (22,27) (23,27) (24,27) (24,25) (25,27)\nIs there a path between node 11 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph270-29_3", + "image": "data/connectivity/graph_visual/hard/graph270.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,20) (0,14) (0,18) (0,16) (1,27) (1,28) (1,9) (1,22) (1,21) (1,19) (1,10) (1,23) (1,7) (1,2) (2,26) (2,25) (2,6) (2,9) (2,22) (2,21) (2,10) (2,23) (2,7) (2,30) (2,12) (3,5) (3,15) (3,11) (3,29) (3,4) (4,5) (4,15) (4,11) (5,15) (5,24) (5,29) (5,8) (6,25) (6,22) (6,17) (6,21) (6,19) (6,10) (6,23) (6,7) (6,30) (7,26) (7,25) (7,9) (7,22) (7,17) (7,21) (7,19) (7,10) (7,23) (7,12) (8,24) (9,27) (9,26) (9,22) (9,21) (9,19) (9,23) (9,30) (9,12) (10,28) (10,26) (10,22) (10,17) (10,21) (10,23) (10,30) (10,12) (11,15) (11,24) (11,29) (12,27) (12,28) (12,26) (12,25) (12,17) (12,21) (12,19) (12,23) (12,30) (13,14) (13,16) (14,18) (14,16) (15,24) (15,29) (16,20) (16,18) (17,27) (17,26) (17,22) (17,19) (17,30) (18,20) (19,27) (19,26) (19,22) (19,23) (19,30) (21,28) (21,26) (21,25) (21,22) (21,23) (21,30) (22,27) (22,28) (22,25) (22,23) (22,30) (23,27) (23,28) (23,26) (23,25) (23,30) (24,29) (25,26) (26,27) (26,28) (26,30) (27,28) (27,30) (28,30)\nIs there a path between node 29 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph682-25_6", + "image": "data/connectivity/graph_visual/hard/graph682.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,8) (0,28) (0,29) (0,16) (0,5) (0,6) (0,12) (0,15) (1,28) (1,18) (1,4) (1,3) (1,21) (1,14) (1,12) (2,22) (3,8) (3,29) (3,33) (3,5) (3,21) (3,30) (3,26) (3,14) (3,7) (3,31) (3,24) (3,12) (3,32) (4,17) (4,5) (4,34) (4,12) (4,32) (4,19) (5,18) (5,16) (5,33) (5,21) (5,6) (5,30) (5,20) (5,11) (6,27) (6,17) (6,26) (6,7) (6,24) (6,15) (7,28) (7,18) (7,29) (7,17) (7,21) (7,26) (7,14) (7,11) (7,32) (8,28) (8,18) (8,29) (8,34) (8,10) (8,30) (8,26) (8,23) (8,14) (8,20) (10,21) (10,30) (10,14) (10,24) (10,20) (10,12) (10,11) (11,16) (11,34) (11,30) (11,14) (11,24) (11,20) (12,27) (12,28) (12,29) (12,17) (12,16) (12,20) (12,32) (12,19) (13,27) (13,17) (13,16) (13,33) (13,23) (13,14) (13,24) (14,33) (14,34) (14,21) (14,30) (14,20) (14,32) (14,19) (14,15) (15,18) (15,29) (15,21) (15,30) (15,23) (16,27) (16,18) (16,17) (16,24) (17,28) (17,33) (17,34) (17,31) (17,32) (18,33) (18,34) (18,21) (18,30) (18,23) (18,24) (18,32) (19,29) (19,33) (19,21) (19,26) (19,32) (20,28) (20,29) (20,33) (20,30) (21,29) (21,33) (21,26) (23,33) (24,27) (24,29) (24,33) (24,30) (24,26) (26,28) (26,29) (27,29) (28,31) (28,32) (29,32)\nIs there a path between node 25 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph685-6_31", + "image": "data/connectivity/graph_visual/hard/graph685.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,1) (0,2) (0,11) (0,31) (0,24) (0,20) (0,26) (0,7) (0,23) (1,21) (1,2) (1,11) (1,31) (1,14) (1,24) (1,26) (1,19) (1,23) (1,15) (2,32) (2,21) (2,11) (2,8) (2,31) (2,14) (2,24) (2,20) (2,26) (2,19) (2,15) (3,16) (3,29) (3,17) (3,6) (3,13) (3,33) (3,18) (3,27) (3,25) (3,34) (3,9) (4,22) (4,5) (5,30) (5,22) (6,16) (6,12) (6,13) (6,33) (6,18) (6,25) (6,34) (6,9) (7,32) (7,11) (7,8) (7,14) (7,19) (7,23) (8,32) (8,11) (8,14) (8,24) (8,15) (9,29) (9,12) (9,17) (9,33) (9,18) (9,25) (9,10) (9,34) (10,29) (10,13) (10,33) (10,27) (10,25) (10,28) (11,21) (11,31) (11,14) (11,24) (11,26) (11,19) (11,23) (11,15) (12,16) (12,29) (12,13) (12,18) (12,27) (12,25) (12,34) (12,28) (13,16) (13,29) (13,17) (13,33) (13,28) (14,32) (14,21) (14,31) (14,24) (14,20) (14,26) (14,19) (14,23) (15,21) (15,31) (15,24) (15,20) (15,26) (15,23) (16,17) (16,33) (16,18) (16,27) (16,25) (16,34) (16,28) (17,33) (17,27) (17,34) (17,28) (18,29) (18,27) (18,25) (18,34) (18,28) (19,21) (19,24) (19,20) (20,32) (20,21) (20,31) (20,26) (20,23) (21,32) (21,31) (21,24) (21,26) (21,23) (22,30) (23,24) (23,26) (24,32) (24,31) (24,26) (25,33) (25,34) (25,28) (26,32) (27,28) (28,33) (28,34) (29,33) (31,32) (33,34)\nIs there a path between node 6 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph139-16_20", + "image": "data/connectivity/graph_visual/hard/graph139.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,9) (2,8) (2,6) (3,10) (3,16) (3,23) (4,28) (4,8) (5,7) (5,13) (5,18) (5,8) (5,6) (6,7) (6,13) (6,24) (6,18) (6,28) (7,13) (7,11) (8,24) (8,28) (8,22) (9,10) (9,16) (9,15) (10,23) (11,24) (11,18) (12,21) (13,28) (13,22) (14,27) (14,20) (15,27) (15,16) (16,19) (17,19) (19,27) (20,27) (22,28) (23,27) (25,26)\nIs there a path between node 16 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph114-27_24", + "image": "data/connectivity/graph_visual/hard/graph114.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,11) (0,16) (1,13) (2,27) (2,10) (2,5) (2,25) (2,16) (2,4) (3,10) (3,21) (3,7) (4,5) (4,22) (4,25) (4,21) (4,16) (4,6) (4,14) (5,10) (5,22) (5,25) (5,21) (5,11) (5,16) (5,19) (6,21) (6,19) (7,10) (7,21) (7,14) (7,19) (8,15) (9,13) (9,20) (9,23) (10,22) (10,11) (10,16) (10,19) (11,25) (12,15) (13,20) (14,16) (14,19) (15,24) (15,20) (16,27) (16,22) (16,25) (17,27) (17,22) (17,25) (19,27) (19,26) (20,23) (21,25) (21,26) (25,27) (26,27)\nIs there a path between node 27 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph154-11_10", + "image": "data/connectivity/graph_visual/hard/graph154.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,2) (0,23) (0,8) (1,6) (1,26) (1,11) (2,6) (2,11) (3,12) (3,19) (3,20) (4,13) (4,21) (4,17) (4,10) (4,6) (4,23) (4,8) (5,13) (5,7) (5,21) (5,17) (5,28) (5,6) (5,23) (5,8) (5,26) (5,24) (5,11) (6,13) (6,17) (6,10) (6,23) (6,24) (7,17) (7,28) (7,23) (8,21) (8,10) (9,15) (10,13) (10,21) (10,23) (10,11) (11,13) (11,17) (12,19) (12,14) (12,27) (12,15) (12,22) (13,17) (13,16) (14,22) (15,19) (16,17) (16,28) (16,24) (17,24) (18,19) (18,27) (19,27) (21,26) (21,24) (22,25) (23,28) (24,28) (25,27)\nIs there a path between node 11 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph599-22_9", + "image": "data/connectivity/graph_visual/hard/graph599.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,25) (0,32) (0,24) (0,10) (0,1) (0,28) (0,17) (0,3) (0,16) (0,7) (0,29) (0,5) (1,6) (1,25) (1,32) (1,24) (1,13) (1,10) (1,11) (1,28) (1,16) (1,7) (1,29) (2,14) (2,15) (2,8) (2,33) (3,18) (3,25) (3,24) (3,13) (3,10) (3,11) (3,28) (3,17) (3,16) (3,7) (3,29) (4,12) (4,27) (4,21) (5,18) (5,6) (5,25) (5,24) (5,13) (5,10) (5,11) (5,17) (5,29) (6,18) (6,25) (6,24) (6,13) (6,10) (6,11) (6,28) (7,18) (7,25) (7,32) (7,24) (7,13) (7,10) (7,28) (7,17) (7,29) (8,19) (8,33) (8,30) (9,22) (9,31) (10,25) (10,32) (10,24) (10,13) (10,28) (10,16) (10,29) (11,25) (11,32) (11,24) (11,13) (11,28) (11,17) (11,29) (12,26) (13,18) (13,25) (13,32) (13,28) (13,16) (14,19) (14,20) (14,15) (14,33) (15,19) (15,20) (15,33) (15,30) (16,32) (16,24) (16,28) (16,17) (16,29) (17,32) (17,24) (17,28) (17,29) (18,32) (18,24) (18,29) (19,20) (19,33) (19,30) (20,33) (20,30) (21,26) (22,31) (22,23) (23,31) (24,25) (24,32) (24,28) (24,29) (25,28) (26,27) (28,32) (28,29) (30,33)\nIs there a path between node 22 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph284-8_13", + "image": "data/connectivity/graph_visual/hard/graph284.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,31) (0,11) (0,27) (0,18) (1,4) (1,12) (1,31) (1,7) (1,25) (1,8) (1,18) (2,17) (2,14) (2,6) (2,10) (2,19) (3,17) (3,22) (3,9) (4,12) (4,30) (4,31) (4,13) (4,27) (4,18) (5,29) (5,16) (5,22) (5,21) (5,20) (5,28) (5,19) (6,29) (6,9) (6,10) (6,28) (7,11) (7,27) (7,15) (7,18) (8,30) (8,23) (8,11) (9,14) (9,21) (9,10) (11,23) (11,18) (12,30) (12,31) (12,27) (12,25) (12,15) (12,18) (13,23) (13,25) (13,15) (14,29) (14,17) (16,24) (16,17) (16,20) (17,29) (18,30) (18,26) (20,29) (21,24) (22,24) (23,27) (23,25) (25,26) (25,27) (26,31) (27,31) (28,29)\nIs there a path between node 8 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph206-21_8", + "image": "data/connectivity/graph_visual/hard/graph206.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,23) (0,26) (0,24) (0,27) (1,4) (1,16) (1,15) (1,10) (1,29) (1,17) (1,11) (2,9) (2,7) (2,6) (2,27) (3,13) (3,28) (3,16) (3,18) (3,29) (3,21) (4,20) (4,16) (4,5) (4,15) (4,18) (4,14) (4,25) (5,28) (5,16) (5,15) (5,18) (5,14) (5,29) (5,19) (5,17) (5,11) (7,23) (7,26) (7,27) (8,26) (10,29) (10,19) (11,13) (11,28) (11,15) (11,17) (13,20) (13,28) (13,19) (14,16) (14,15) (14,29) (14,19) (14,21) (15,20) (15,28) (15,29) (15,19) (16,28) (16,25) (16,17) (17,19) (18,20) (18,21) (20,21) (21,29) (21,25) (22,28) (23,24) (26,27) (28,29)\nIs there a path between node 21 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph501-7_24", + "image": "data/connectivity/graph_visual/hard/graph501.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,22) (0,2) (0,17) (0,14) (0,6) (0,28) (0,23) (0,21) (1,22) (1,8) (1,17) (1,14) (1,19) (1,6) (1,10) (1,23) (1,16) (2,22) (2,4) (2,8) (2,18) (2,32) (2,27) (2,16) (3,4) (3,17) (3,14) (3,33) (3,18) (4,7) (4,19) (4,9) (4,18) (4,28) (4,21) (5,25) (5,13) (6,22) (6,14) (6,9) (6,18) (6,10) (6,12) (6,32) (7,17) (7,33) (7,9) (7,32) (8,22) (8,26) (8,9) (8,28) (8,10) (8,31) (8,16) (9,14) (9,18) (9,28) (9,10) (9,12) (9,31) (9,11) (9,27) (9,16) (10,22) (10,26) (10,29) (10,19) (10,23) (10,21) (11,26) (11,18) (11,12) (11,23) (11,32) (11,27) (11,16) (12,22) (12,14) (12,18) (12,31) (12,23) (12,27) (13,24) (14,22) (14,26) (14,29) (14,19) (14,28) (14,32) (14,16) (15,20) (15,24) (16,22) (16,19) (16,32) (17,33) (17,18) (17,28) (17,23) (18,22) (18,27) (19,32) (20,24) (20,30) (22,26) (22,31) (23,32) (24,30) (25,30) (26,29) (26,33) (27,33) (27,28) (27,31) (29,33) (29,32)\nIs there a path between node 7 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph308-30_20", + "image": "data/connectivity/graph_visual/hard/graph308.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,23) (0,26) (1,11) (2,28) (2,12) (3,5) (3,18) (3,31) (4,7) (4,18) (4,24) (4,9) (4,11) (4,19) (5,16) (5,24) (5,11) (5,25) (6,23) (6,13) (6,29) (6,20) (6,14) (8,26) (8,22) (9,17) (9,11) (9,19) (10,27) (10,21) (10,24) (11,16) (11,24) (11,25) (12,29) (13,15) (14,15) (14,30) (14,28) (15,23) (15,30) (15,28) (15,20) (16,17) (16,24) (17,19) (18,21) (18,19) (19,25) (20,26) (20,30) (20,28) (21,31) (24,27) (27,31) (28,29)\nIs there a path between node 30 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph166-4_9", + "image": "data/connectivity/graph_visual/hard/graph166.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,5) (0,17) (0,26) (0,24) (0,25) (1,6) (1,19) (1,16) (1,2) (1,22) (1,11) (1,13) (2,6) (2,19) (2,15) (3,21) (3,19) (3,27) (3,23) (3,8) (4,5) (5,7) (6,27) (6,22) (6,20) (7,12) (7,25) (8,27) (8,22) (8,23) (8,20) (8,13) (9,28) (10,11) (10,14) (11,19) (11,16) (11,27) (11,23) (11,20) (12,26) (12,28) (12,24) (13,27) (13,22) (13,14) (14,27) (14,23) (15,23) (16,27) (16,22) (16,23) (17,24) (17,25) (18,25) (19,27) (19,22) (19,23) (20,21) (20,22) (20,23) (24,28) (25,26)\nIs there a path between node 4 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph402-2_15", + "image": "data/connectivity/graph_visual/hard/graph402.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,32) (0,31) (0,24) (0,30) (0,3) (0,16) (0,5) (0,1) (0,23) (1,14) (1,32) (1,17) (1,20) (1,31) (1,27) (1,24) (1,3) (1,16) (1,7) (1,5) (1,23) (2,8) (2,11) (2,28) (2,19) (2,22) (2,29) (2,26) (2,18) (3,14) (3,32) (3,31) (3,27) (3,24) (3,30) (3,10) (3,16) (3,7) (3,5) (3,23) (4,25) (4,11) (4,28) (4,21) (4,29) (4,18) (4,15) (5,14) (5,17) (5,31) (5,27) (5,30) (5,10) (5,7) (5,23) (6,25) (6,8) (6,11) (6,28) (6,19) (6,21) (6,29) (6,26) (6,15) (7,32) (7,17) (7,30) (7,10) (8,11) (8,28) (8,19) (8,22) (8,21) (8,29) (8,18) (8,15) (9,12) (10,14) (10,32) (10,20) (10,27) (10,24) (10,30) (10,16) (11,25) (11,28) (11,21) (11,26) (11,18) (12,13) (14,32) (14,17) (14,20) (14,31) (14,24) (14,16) (14,23) (15,28) (15,19) (15,22) (15,29) (15,18) (16,20) (16,31) (16,27) (16,24) (16,30) (16,23) (17,32) (17,20) (17,27) (17,24) (17,30) (17,23) (18,25) (18,22) (19,25) (19,28) (19,22) (19,26) (20,27) (20,24) (20,23) (21,28) (21,22) (22,25) (22,28) (22,29) (23,32) (23,27) (23,24) (24,32) (24,31) (24,27) (24,30) (25,28) (25,29) (25,26) (26,28) (27,32) (27,31) (28,29) (30,32) (30,31)\nIs there a path between node 2 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph556-23_33", + "image": "data/connectivity/graph_visual/hard/graph556.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,2) (0,20) (0,30) (0,26) (0,15) (0,32) (0,13) (1,25) (2,31) (2,3) (2,30) (2,12) (2,11) (2,23) (2,27) (2,15) (2,6) (2,21) (3,31) (3,14) (3,33) (3,18) (3,11) (3,26) (3,23) (3,27) (3,16) (3,32) (3,29) (4,7) (4,25) (5,33) (5,12) (5,29) (5,6) (5,8) (6,33) (6,22) (6,18) (6,19) (6,16) (7,10) (8,22) (8,19) (8,11) (8,15) (8,32) (9,33) (9,19) (9,15) (9,29) (9,13) (11,27) (11,15) (11,32) (11,29) (13,33) (13,22) (13,23) (13,28) (13,21) (14,31) (14,33) (14,22) (14,18) (14,26) (14,15) (14,16) (14,21) (15,33) (15,19) (15,21) (16,20) (16,33) (16,27) (18,22) (18,30) (18,19) (18,32) (18,29) (19,26) (19,23) (19,21) (20,31) (20,30) (20,23) (20,28) (21,31) (21,26) (21,32) (22,26) (22,32) (22,29) (22,28) (23,33) (23,30) (23,27) (26,32) (28,31) (28,30) (28,29) (29,31) (29,32) (30,32) (31,33)\nIs there a path between node 23 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph148-6_27", + "image": "data/connectivity/graph_visual/hard/graph148.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,10) (0,6) (1,10) (2,21) (2,9) (2,13) (2,25) (2,22) (2,27) (2,11) (2,7) (2,15) (2,8) (2,12) (2,23) (2,3) (2,28) (2,14) (2,19) (3,21) (3,9) (3,13) (3,5) (3,22) (3,27) (3,11) (3,17) (3,7) (3,20) (3,15) (3,8) (3,12) (3,18) (3,24) (4,21) (4,9) (4,26) (4,13) (4,25) (4,5) (4,22) (4,27) (4,17) (4,7) (4,15) (4,16) (4,8) (4,12) (4,18) (4,24) (4,23) (4,28) (4,14) (4,19) (5,21) (5,9) (5,26) (5,13) (5,22) (5,27) (5,11) (5,17) (5,20) (5,15) (5,16) (5,8) (5,18) (5,23) (5,28) (6,10) (7,9) (7,13) (7,25) (7,22) (7,27) (7,11) (7,17) (7,20) (7,15) (7,16) (7,12) (7,18) (7,24) (7,23) (7,14) (8,21) (8,13) (8,25) (8,27) (8,11) (8,17) (8,20) (8,15) (8,16) (8,23) (8,14) (8,19) (9,25) (9,27) (9,11) (9,17) (9,20) (9,16) (9,12) (9,24) (9,28) (11,26) (11,13) (11,25) (11,22) (11,27) (11,17) (11,20) (11,15) (11,16) (11,12) (11,24) (11,28) (11,14) (12,21) (12,26) (12,13) (12,25) (12,27) (12,17) (12,20) (12,15) (12,18) (12,24) (12,23) (12,28) (12,19) (13,21) (13,26) (13,25) (13,22) (13,27) (13,17) (13,20) (13,15) (13,16) (13,18) (13,24) (13,23) (13,28) (13,14) (13,19) (14,25) (14,22) (14,27) (14,17) (14,20) (14,15) (14,16) (14,18) (14,24) (14,28) (15,26) (15,27) (15,20) (15,18) (15,24) (15,28) (16,21) (16,26) (16,25) (16,27) (16,20) (16,18) (16,24) (16,23) (16,28) (16,19) (17,21) (17,25) (17,22) (17,27) (17,20) (17,23) (17,28) (17,19) (18,26) (18,25) (18,27) (18,20) (18,24) (18,28) (19,26) (19,25) (19,22) (19,27) (19,20) (19,24) (19,23) (19,28) (20,26) (20,25) (20,27) (20,24) (20,23) (20,28) (21,26) (21,22) (21,28) (22,25) (22,27) (22,28) (23,27) (23,24) (23,28) (24,25) (24,27) (24,28) (25,26) (25,28) (26,28) (27,28)\nIs there a path between node 6 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph659-16_24", + "image": "data/connectivity/graph_visual/hard/graph659.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,14) (0,7) (0,19) (0,24) (0,30) (0,33) (0,5) (0,3) (0,6) (0,25) (0,13) (0,22) (0,29) (1,27) (1,9) (2,26) (2,13) (3,30) (3,33) (3,17) (3,6) (3,26) (3,21) (3,13) (3,4) (3,18) (3,12) (4,30) (4,34) (4,17) (4,5) (4,6) (4,21) (4,13) (5,7) (5,24) (5,30) (5,17) (5,25) (5,32) (5,18) (6,19) (6,30) (6,26) (6,28) (6,21) (6,25) (6,23) (6,13) (6,12) (7,19) (7,24) (7,10) (7,33) (7,17) (7,21) (7,13) (8,16) (8,20) (8,9) (9,27) (9,31) (10,30) (10,34) (10,18) (10,12) (11,20) (12,24) (12,30) (12,17) (12,15) (12,23) (12,22) (12,29) (12,18) (13,30) (13,28) (13,22) (13,18) (14,17) (14,15) (14,29) (14,18) (15,30) (15,33) (15,28) (15,25) (15,29) (16,20) (17,24) (17,33) (17,25) (17,23) (17,22) (17,18) (18,19) (18,21) (18,23) (18,32) (18,29) (19,24) (19,30) (19,34) (19,33) (19,28) (19,21) (19,25) (19,32) (20,27) (21,30) (21,33) (21,26) (21,28) (21,25) (21,32) (22,24) (22,30) (22,34) (23,30) (23,33) (23,32) (24,30) (24,33) (24,29) (25,30) (25,34) (25,26) (25,28) (25,29) (26,30) (26,33) (26,28) (28,33) (29,34) (33,34)\nIs there a path between node 16 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph237-27_7", + "image": "data/connectivity/graph_visual/hard/graph237.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,29) (0,12) (0,18) (0,24) (0,22) (0,2) (0,3) (1,14) (1,20) (1,26) (1,29) (1,12) (1,30) (1,15) (1,19) (1,3) (1,7) (2,17) (2,6) (2,23) (3,28) (3,30) (3,18) (3,19) (3,7) (4,26) (4,29) (4,12) (4,30) (4,18) (4,19) (4,7) (6,8) (6,24) (6,10) (6,19) (7,17) (7,26) (7,30) (7,18) (7,8) (7,13) (7,15) (7,23) (8,16) (8,14) (8,20) (8,26) (8,30) (10,14) (10,20) (10,29) (10,18) (10,13) (10,22) (10,19) (10,11) (11,21) (11,16) (11,14) (11,26) (11,18) (12,16) (12,26) (12,18) (13,17) (13,26) (13,15) (14,28) (14,26) (14,24) (14,23) (15,28) (15,16) (15,29) (15,30) (16,21) (16,20) (16,29) (16,24) (17,28) (17,20) (17,29) (17,30) (17,19) (18,21) (18,28) (18,23) (19,28) (19,20) (19,26) (19,22) (19,23) (20,29) (20,24) (20,22) (21,29) (22,28) (23,28) (23,29) (24,26) (24,29) (25,27) (26,29)\nIs there a path between node 27 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph378-25_18", + "image": "data/connectivity/graph_visual/hard/graph378.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,25) (0,4) (0,14) (0,12) (0,9) (0,30) (0,20) (0,2) (0,24) (0,13) (0,10) (0,27) (1,11) (1,8) (1,17) (1,28) (1,26) (1,19) (1,15) (2,25) (2,29) (2,4) (2,14) (2,12) (2,9) (2,30) (2,20) (2,6) (2,10) (2,31) (2,27) (3,11) (3,8) (3,17) (3,28) (3,19) (3,15) (3,23) (4,25) (4,14) (4,12) (4,30) (4,24) (4,13) (4,6) (4,21) (4,16) (5,11) (5,8) (5,18) (5,17) (5,26) (5,15) (5,23) (6,14) (6,12) (6,9) (6,30) (6,20) (6,13) (6,21) (6,7) (6,16) (6,10) (6,27) (7,25) (7,29) (7,14) (7,12) (7,9) (7,30) (7,20) (7,13) (7,10) (7,27) (8,11) (8,17) (8,28) (8,26) (8,19) (8,15) (8,23) (9,25) (9,29) (9,14) (9,12) (9,30) (9,24) (9,13) (9,21) (9,10) (9,31) (10,25) (10,14) (10,12) (10,30) (10,13) (10,21) (10,16) (10,31) (10,27) (11,18) (11,17) (11,28) (11,26) (11,15) (11,23) (11,22) (12,25) (12,29) (12,20) (12,24) (12,13) (12,21) (12,16) (12,31) (12,27) (13,25) (13,29) (13,30) (13,20) (13,24) (13,21) (14,25) (14,29) (14,30) (14,20) (14,21) (14,16) (14,31) (15,17) (15,28) (15,23) (15,22) (16,25) (16,29) (16,30) (16,20) (16,24) (16,21) (16,31) (16,27) (17,18) (17,19) (17,23) (18,28) (18,23) (19,28) (19,26) (19,23) (19,22) (20,29) (20,30) (20,24) (20,21) (20,31) (20,27) (21,25) (21,29) (21,30) (21,31) (21,27) (22,28) (22,26) (23,28) (23,26) (24,30) (24,27) (25,29) (25,30) (26,28) (27,29) (27,30) (27,31) (29,30) (29,31) (30,31)\nIs there a path between node 25 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph691-25_6", + "image": "data/connectivity/graph_visual/hard/graph691.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,17) (0,8) (0,34) (0,14) (0,16) (0,5) (0,22) (0,9) (0,25) (0,3) (0,32) (1,10) (2,21) (2,33) (2,30) (2,20) (3,6) (3,17) (3,26) (3,8) (3,14) (3,23) (3,16) (3,5) (3,22) (3,25) (4,11) (4,28) (4,15) (4,13) (4,19) (4,12) (5,6) (5,26) (5,8) (5,14) (5,23) (5,16) (5,27) (5,25) (6,26) (6,34) (6,16) (6,27) (6,22) (6,9) (6,25) (6,32) (7,33) (7,18) (7,29) (7,30) (7,20) (8,26) (8,34) (8,23) (8,16) (8,27) (8,9) (8,25) (8,32) (9,17) (9,26) (9,34) (9,16) (9,25) (9,32) (11,28) (11,15) (11,13) (11,19) (11,12) (12,28) (12,24) (12,15) (12,19) (13,28) (13,24) (13,19) (14,17) (14,26) (14,34) (14,16) (14,27) (14,25) (14,32) (15,24) (15,19) (16,17) (16,34) (16,23) (16,27) (16,25) (16,32) (17,26) (17,23) (17,27) (17,22) (17,25) (18,21) (18,33) (18,30) (18,20) (19,28) (19,24) (20,21) (20,33) (21,33) (21,29) (21,30) (21,31) (22,26) (22,34) (22,27) (23,26) (23,34) (23,27) (23,32) (24,28) (25,26) (25,34) (25,32) (26,27) (26,32) (27,32) (29,33) (29,31) (30,33) (30,31) (32,34)\nIs there a path between node 25 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph371-24_6", + "image": "data/connectivity/graph_visual/hard/graph371.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,12) (0,24) (0,31) (0,15) (0,27) (1,26) (1,24) (1,31) (1,27) (1,19) (2,25) (2,20) (2,23) (2,8) (2,9) (2,4) (2,29) (2,7) (2,14) (2,5) (2,11) (2,6) (2,3) (2,13) (2,10) (3,25) (3,30) (3,23) (3,9) (3,4) (3,29) (3,21) (3,28) (3,7) (3,14) (3,5) (3,11) (3,6) (3,10) (4,25) (4,20) (4,30) (4,23) (4,18) (4,17) (4,21) (4,16) (4,14) (4,11) (4,6) (4,13) (4,22) (5,25) (5,20) (5,30) (5,23) (5,18) (5,17) (5,8) (5,9) (5,29) (5,28) (5,16) (5,14) (5,11) (5,13) (5,22) (5,10) (6,25) (6,20) (6,23) (6,18) (6,17) (6,9) (6,29) (6,21) (6,7) (6,13) (6,22) (7,25) (7,20) (7,30) (7,23) (7,18) (7,8) (7,9) (7,29) (7,21) (7,28) (7,16) (7,14) (7,11) (7,13) (7,10) (8,20) (8,30) (8,23) (8,18) (8,9) (8,21) (8,28) (8,16) (8,14) (8,11) (8,13) (8,10) (9,20) (9,30) (9,23) (9,18) (9,29) (9,28) (9,11) (9,13) (9,22) (9,10) (10,25) (10,30) (10,23) (10,17) (10,28) (10,16) (10,14) (10,11) (10,13) (10,22) (11,25) (11,20) (11,30) (11,23) (11,18) (11,29) (11,21) (11,28) (11,22) (12,26) (12,24) (12,19) (13,25) (13,23) (13,18) (13,17) (13,29) (13,21) (13,28) (13,16) (13,22) (14,25) (14,20) (14,23) (14,29) (14,21) (14,28) (14,16) (15,26) (15,31) (15,27) (16,25) (16,20) (16,30) (16,17) (16,29) (16,21) (16,28) (16,22) (17,25) (17,30) (17,23) (17,18) (17,29) (17,28) (17,22) (18,25) (18,20) (18,30) (18,23) (18,29) (18,21) (18,22) (19,26) (19,31) (19,27) (20,30) (20,29) (20,21) (20,28) (21,25) (21,30) (21,23) (21,29) (21,22) (22,25) (22,30) (22,23) (22,29) (22,28) (23,25) (23,30) (23,29) (24,26) (25,29) (25,28) (28,30) (28,29) (29,30)\nIs there a path between node 24 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph215-23_18", + "image": "data/connectivity/graph_visual/hard/graph215.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,11) (0,27) (0,29) (1,16) (1,11) (1,20) (1,14) (2,8) (2,18) (2,15) (2,11) (2,27) (2,19) (2,25) (2,29) (3,5) (4,8) (4,24) (4,23) (4,26) (4,13) (4,7) (4,28) (4,6) (4,20) (4,19) (6,15) (6,27) (6,25) (7,22) (7,24) (7,23) (7,26) (7,13) (7,28) (7,29) (8,18) (8,26) (8,12) (9,17) (11,22) (11,24) (11,28) (11,20) (12,22) (12,15) (12,28) (12,27) (12,20) (12,29) (13,16) (13,23) (13,28) (13,27) (13,20) (13,19) (14,19) (15,28) (15,25) (16,26) (16,25) (18,20) (18,29) (19,23) (19,20) (20,24) (20,26) (20,28) (20,27) (20,25) (22,23) (22,28) (22,29) (23,24) (23,26) (23,29) (24,27) (25,27) (26,29) (27,28)\nIs there a path between node 23 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph396-15_13", + "image": "data/connectivity/graph_visual/hard/graph396.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,21) (1,22) (1,4) (1,27) (1,2) (1,32) (1,9) (2,20) (2,4) (2,14) (2,13) (3,28) (3,14) (3,13) (3,9) (4,24) (4,30) (4,32) (5,8) (5,11) (5,16) (5,29) (6,21) (6,26) (6,10) (6,25) (7,15) (8,29) (8,31) (9,20) (9,23) (9,28) (9,14) (9,13) (11,18) (11,31) (13,24) (13,23) (13,14) (14,22) (14,23) (14,30) (14,32) (15,18) (15,16) (15,31) (16,19) (17,26) (18,19) (20,28) (20,30) (23,24) (23,30) (23,32) (24,28) (24,32) (25,26) (27,32) (28,30)\nIs there a path between node 15 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph181-12_26", + "image": "data/connectivity/graph_visual/hard/graph181.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,18) (1,25) (1,22) (1,15) (1,20) (1,19) (1,11) (1,2) (1,23) (1,24) (2,25) (2,22) (2,15) (2,3) (2,11) (2,7) (2,6) (2,14) (2,24) (3,22) (3,16) (3,15) (3,19) (3,7) (3,23) (3,6) (3,14) (4,21) (4,9) (4,28) (4,8) (4,26) (4,17) (5,9) (5,12) (5,27) (5,26) (5,17) (6,25) (6,16) (6,15) (6,20) (6,19) (6,7) (6,14) (6,24) (7,25) (7,22) (7,16) (7,20) (7,19) (7,11) (7,23) (7,24) (8,21) (8,9) (8,12) (8,26) (8,17) (9,21) (9,10) (9,28) (9,12) (9,27) (9,26) (9,17) (10,21) (10,28) (10,12) (10,26) (10,17) (11,22) (11,16) (11,15) (11,20) (11,19) (11,23) (11,14) (11,24) (12,27) (12,26) (12,17) (13,18) (14,16) (14,15) (14,20) (14,24) (15,22) (15,16) (15,20) (15,23) (15,24) (16,25) (16,22) (16,20) (16,19) (16,23) (16,24) (17,21) (17,27) (17,26) (19,25) (19,22) (19,23) (19,24) (20,22) (20,23) (20,24) (21,28) (21,27) (21,26) (22,25) (23,25) (23,24) (24,25) (26,27)\nIs there a path between node 12 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph67-4_7", + "image": "data/connectivity/graph_visual/hard/graph67.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,2) (0,12) (0,8) (1,23) (1,22) (1,26) (1,24) (1,13) (2,12) (2,20) (3,12) (3,20) (4,15) (4,10) (4,21) (5,11) (6,11) (7,10) (9,13) (10,15) (11,18) (11,19) (13,23) (13,26) (16,23) (16,26) (17,26) (22,26) (23,26) (23,24)\nIs there a path between node 4 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph13-14_10", + "image": "data/connectivity/graph_visual/hard/graph13.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,8) (0,5) (0,19) (1,8) (1,5) (1,19) (2,12) (2,15) (2,16) (2,24) (2,17) (2,3) (2,20) (2,9) (2,21) (2,23) (2,25) (2,11) (2,14) (2,22) (3,10) (3,15) (3,16) (3,24) (3,20) (3,4) (3,21) (3,23) (3,25) (3,14) (3,6) (3,22) (4,10) (4,13) (4,15) (4,16) (4,24) (4,20) (4,21) (4,23) (4,25) (4,14) (4,6) (4,22) (5,18) (5,7) (5,19) (6,12) (6,13) (6,24) (6,17) (6,20) (6,9) (6,23) (6,14) (6,22) (7,8) (8,18) (9,10) (9,12) (9,15) (9,16) (9,24) (9,17) (9,23) (9,25) (9,11) (9,14) (9,22) (10,12) (10,13) (10,16) (10,24) (10,17) (10,21) (10,23) (10,25) (10,11) (10,14) (10,22) (11,13) (11,16) (11,20) (11,21) (11,23) (11,25) (11,22) (12,24) (12,17) (12,20) (12,23) (12,22) (13,15) (13,24) (13,17) (13,20) (13,21) (13,25) (13,22) (14,15) (14,16) (14,24) (14,17) (14,20) (14,21) (14,23) (14,25) (15,24) (15,17) (15,20) (15,23) (15,25) (16,24) (16,17) (16,20) (16,21) (16,23) (16,25) (16,22) (17,24) (17,20) (17,23) (17,22) (18,19) (20,24) (20,21) (20,22) (21,24) (21,25) (21,22) (22,23) (22,25) (23,24) (23,25) (24,25)\nIs there a path between node 14 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph603-20_3", + "image": "data/connectivity/graph_visual/hard/graph603.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,27) (0,22) (0,15) (1,32) (1,29) (1,16) (1,17) (1,4) (1,11) (2,26) (2,25) (2,14) (3,26) (3,19) (3,14) (4,24) (4,16) (4,9) (4,8) (5,10) (5,16) (5,17) (5,33) (5,9) (5,6) (5,23) (6,24) (6,31) (6,9) (6,21) (6,23) (6,11) (7,20) (7,22) (7,28) (7,30) (8,32) (8,29) (8,16) (8,17) (8,31) (8,9) (9,29) (9,17) (9,21) (9,11) (10,24) (10,31) (10,33) (10,21) (11,24) (11,29) (11,16) (11,31) (12,27) (13,18) (13,15) (14,19) (15,20) (15,28) (15,30) (16,21) (17,33) (17,21) (18,20) (18,34) (18,28) (20,22) (21,32) (21,29) (21,33) (23,29) (24,31) (25,26) (27,34) (29,33) (31,33)\nIs there a path between node 20 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph699-30_6", + "image": "data/connectivity/graph_visual/hard/graph699.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,22) (0,23) (0,24) (0,19) (0,4) (0,7) (0,10) (0,3) (0,20) (0,28) (0,2) (0,26) (0,29) (0,21) (1,17) (1,5) (1,14) (1,30) (1,16) (2,13) (2,27) (2,23) (2,24) (2,34) (2,32) (2,10) (2,33) (2,20) (2,26) (2,9) (3,13) (3,27) (3,6) (3,23) (3,24) (3,19) (3,34) (3,10) (3,33) (3,20) (3,28) (3,26) (3,9) (3,29) (3,21) (4,13) (4,27) (4,22) (4,24) (4,19) (4,7) (4,10) (4,33) (4,20) (4,28) (4,26) (4,9) (4,29) (4,21) (5,17) (5,14) (5,15) (5,12) (5,30) (5,18) (5,16) (6,13) (6,22) (6,23) (6,34) (6,32) (6,10) (6,20) (6,26) (6,9) (6,8) (7,13) (7,23) (7,24) (7,19) (7,34) (7,10) (7,33) (7,20) (7,28) (7,8) (7,29) (7,21) (8,27) (8,23) (8,24) (8,34) (8,10) (8,28) (8,9) (8,29) (8,21) (9,13) (9,27) (9,22) (9,23) (9,34) (9,32) (9,10) (9,20) (9,28) (9,26) (9,21) (10,13) (10,27) (10,22) (10,24) (10,19) (10,34) (10,32) (10,33) (10,20) (10,26) (10,29) (10,21) (11,17) (11,31) (11,14) (11,15) (11,18) (11,16) (12,31) (12,15) (12,30) (12,18) (13,27) (13,22) (13,24) (13,32) (13,33) (13,20) (13,28) (13,26) (13,21) (14,17) (14,31) (14,15) (14,30) (14,18) (14,16) (15,17) (15,30) (15,18) (15,16) (16,17) (16,31) (16,30) (16,18) (17,31) (17,18) (18,31) (18,30) (19,22) (19,23) (19,24) (19,34) (19,32) (19,33) (19,20) (19,28) (19,26) (19,29) (19,21) (20,22) (20,23) (20,34) (20,21) (21,27) (21,22) (21,23) (21,34) (21,32) (21,33) (21,28) (21,26) (21,29) (22,27) (22,24) (22,33) (22,28) (22,26) (22,29) (23,27) (23,32) (23,33) (23,26) (23,29) (24,27) (24,34) (24,33) (24,28) (24,26) (24,29) (26,27) (26,34) (26,32) (26,29) (27,34) (27,32) (27,33) (27,28) (27,29) (28,32) (28,33) (28,29) (29,34) (29,32) (32,34) (32,33)\nIs there a path between node 30 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph340-12_28", + "image": "data/connectivity/graph_visual/hard/graph340.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,14) (0,13) (0,27) (1,21) (1,24) (1,13) (1,5) (2,19) (3,30) (3,26) (3,10) (3,25) (5,15) (5,9) (5,27) (5,19) (6,22) (6,29) (6,16) (7,15) (7,24) (7,9) (7,19) (9,21) (9,15) (9,24) (10,31) (10,11) (10,23) (11,23) (11,26) (11,17) (12,22) (12,29) (12,16) (13,14) (13,24) (14,21) (14,24) (14,27) (15,21) (16,29) (17,23) (17,25) (18,20) (18,29) (20,22) (21,27) (24,27) (25,28)\nIs there a path between node 12 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph182-7_26", + "image": "data/connectivity/graph_visual/hard/graph182.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,20) (0,27) (0,23) (0,28) (0,10) (0,16) (0,22) (0,2) (0,6) (0,14) (0,25) (0,26) (0,4) (0,21) (1,20) (1,27) (1,23) (1,28) (1,16) (1,22) (1,17) (1,2) (1,12) (1,14) (1,25) (1,26) (1,15) (1,4) (1,21) (1,9) (1,5) (2,20) (2,27) (2,23) (2,10) (2,7) (2,16) (2,22) (2,17) (2,6) (2,14) (2,26) (2,15) (2,4) (2,21) (2,9) (2,5) (3,8) (3,19) (3,24) (4,20) (4,27) (4,23) (4,10) (4,16) (4,22) (4,17) (4,12) (4,6) (4,14) (4,25) (4,26) (4,15) (4,21) (4,5) (5,20) (5,27) (5,23) (5,28) (5,10) (5,16) (5,22) (5,17) (5,12) (5,6) (5,26) (5,15) (5,21) (6,20) (6,27) (6,23) (6,28) (6,10) (6,7) (6,16) (6,22) (6,17) (6,12) (6,14) (6,25) (6,26) (6,15) (6,9) (7,20) (7,23) (7,28) (7,10) (7,16) (7,22) (7,17) (7,15) (7,21) (7,9) (8,19) (8,24) (8,11) (8,13) (8,18) (9,28) (9,10) (9,22) (9,17) (9,26) (9,15) (10,20) (10,27) (10,23) (10,28) (10,16) (10,22) (10,17) (10,12) (10,14) (10,25) (10,26) (10,15) (10,21) (11,19) (11,18) (12,20) (12,27) (12,23) (12,28) (12,17) (12,26) (12,15) (12,21) (13,19) (13,24) (13,18) (14,20) (14,23) (14,16) (14,22) (14,25) (14,26) (14,15) (14,21) (15,20) (15,27) (15,22) (15,17) (15,25) (15,26) (16,20) (16,27) (16,17) (16,25) (16,26) (17,27) (17,23) (17,28) (17,22) (17,25) (17,26) (17,21) (18,24) (19,24) (20,28) (20,22) (20,25) (20,26) (21,23) (21,25) (21,26) (22,28) (22,26) (23,26) (25,27) (25,28) (25,26) (26,27) (26,28) (27,28)\nIs there a path between node 7 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph425-13_10", + "image": "data/connectivity/graph_visual/hard/graph425.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,7) (0,12) (0,32) (0,22) (0,9) (0,20) (0,2) (0,5) (0,14) (0,4) (0,26) (0,21) (1,11) (1,8) (1,24) (1,3) (1,31) (1,28) (1,6) (2,16) (2,7) (2,32) (2,22) (2,9) (2,20) (2,14) (2,4) (2,21) (3,11) (3,8) (3,24) (3,31) (3,28) (4,16) (4,32) (4,22) (4,9) (4,20) (4,5) (4,14) (4,26) (5,16) (5,7) (5,12) (5,32) (5,22) (5,9) (5,20) (5,14) (5,26) (5,21) (6,8) (6,24) (6,31) (6,28) (7,12) (7,32) (7,22) (7,9) (7,14) (7,26) (7,21) (8,24) (8,31) (8,28) (9,16) (9,12) (9,32) (9,20) (9,26) (9,21) (10,23) (10,13) (10,29) (10,19) (10,25) (10,18) (12,32) (12,22) (12,20) (12,26) (12,21) (13,30) (13,27) (13,29) (13,19) (13,25) (13,18) (14,16) (14,32) (14,22) (14,20) (14,26) (15,30) (15,29) (15,25) (15,18) (16,32) (16,22) (16,20) (16,26) (16,21) (17,30) (17,27) (18,30) (18,29) (19,30) (19,23) (19,27) (19,25) (20,32) (20,22) (20,26) (21,32) (21,26) (22,32) (22,26) (23,30) (23,29) (23,25) (24,28) (26,32) (27,30) (27,29) (28,31) (29,30)\nIs there a path between node 13 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph605-34_10", + "image": "data/connectivity/graph_visual/hard/graph605.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,3) (0,18) (0,9) (1,3) (1,31) (1,23) (2,22) (2,5) (3,27) (3,20) (4,12) (4,22) (4,33) (4,10) (4,26) (5,22) (5,17) (5,33) (5,14) (6,32) (6,29) (7,26) (8,28) (8,25) (8,17) (9,34) (9,13) (10,28) (10,17) (10,16) (11,18) (11,13) (11,19) (12,24) (12,22) (12,17) (12,16) (13,31) (13,20) (14,28) (14,30) (14,17) (15,25) (15,30) (15,17) (16,30) (16,26) (18,27) (18,20) (20,23) (22,25) (22,30) (22,33) (22,26) (23,27) (25,28) (26,28) (28,33)\nIs there a path between node 34 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph111-21_4", + "image": "data/connectivity/graph_visual/hard/graph111.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,16) (0,20) (0,1) (0,19) (0,18) (0,7) (0,17) (0,11) (0,13) (0,5) (0,3) (1,16) (1,9) (1,27) (1,19) (1,18) (1,2) (2,20) (2,10) (2,24) (2,23) (3,10) (3,13) (3,12) (4,9) (4,8) (4,14) (4,19) (4,18) (4,7) (4,17) (4,13) (4,5) (4,12) (4,23) (5,16) (5,6) (5,8) (5,19) (5,24) (5,17) (5,26) (6,20) (6,10) (6,18) (6,7) (6,11) (6,25) (7,8) (7,18) (7,17) (8,19) (8,24) (8,11) (8,13) (9,19) (9,11) (9,25) (10,27) (10,19) (10,18) (10,17) (11,14) (11,18) (11,25) (12,16) (12,14) (13,24) (13,25) (14,25) (15,22) (16,19) (16,24) (16,25) (17,19) (17,25) (18,19) (19,20) (24,27)\nIs there a path between node 21 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph387-19_15", + "image": "data/connectivity/graph_visual/hard/graph387.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,27) (0,28) (0,29) (0,22) (0,23) (0,8) (0,19) (0,6) (0,16) (0,7) (0,15) (0,26) (0,1) (1,3) (1,27) (1,20) (1,22) (1,23) (1,8) (1,19) (1,18) (1,6) (1,5) (1,16) (1,10) (1,7) (1,26) (2,31) (2,21) (2,11) (2,17) (2,12) (3,22) (3,8) (3,19) (3,6) (3,16) (3,10) (3,7) (3,15) (4,31) (4,14) (4,11) (4,17) (4,25) (4,24) (4,13) (4,12) (4,30) (5,28) (5,29) (5,23) (5,19) (5,18) (5,10) (5,15) (5,26) (6,27) (6,29) (6,20) (6,23) (6,8) (6,18) (6,16) (6,10) (6,15) (6,26) (7,27) (7,28) (7,20) (7,22) (7,23) (7,8) (7,19) (7,18) (7,16) (7,15) (7,26) (8,27) (8,28) (8,29) (8,20) (8,22) (8,23) (8,18) (8,16) (9,31) (9,21) (9,11) (9,17) (9,25) (9,24) (9,12) (10,27) (10,28) (10,29) (10,20) (10,22) (10,23) (10,19) (10,16) (10,15) (10,26) (11,31) (11,21) (11,25) (11,24) (11,12) (12,31) (12,21) (12,14) (12,17) (12,25) (12,24) (12,30) (13,21) (13,25) (13,24) (13,30) (14,31) (14,17) (14,25) (14,24) (14,30) (15,29) (15,20) (15,22) (15,23) (15,19) (15,18) (15,26) (16,27) (16,28) (16,29) (16,20) (16,22) (16,18) (16,26) (17,31) (17,21) (17,25) (17,24) (17,30) (18,28) (18,29) (18,20) (18,22) (18,19) (19,27) (19,28) (19,29) (19,20) (19,22) (19,23) (19,26) (20,27) (20,28) (20,29) (20,22) (20,23) (21,25) (22,27) (22,28) (22,29) (23,28) (24,25) (24,30) (25,31) (25,30) (26,27) (26,28) (26,29) (27,28) (27,29) (28,29) (30,31)\nIs there a path between node 19 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph213-11_20", + "image": "data/connectivity/graph_visual/hard/graph213.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,26) (0,1) (0,27) (0,11) (1,27) (1,17) (1,8) (1,20) (1,28) (1,11) (1,18) (1,12) (1,22) (2,24) (2,13) (2,3) (2,7) (3,13) (3,10) (3,4) (3,14) (4,15) (4,21) (4,24) (4,13) (4,10) (5,15) (5,21) (5,24) (5,7) (6,27) (6,29) (6,8) (6,20) (6,9) (6,28) (6,18) (6,25) (7,13) (7,16) (8,27) (8,28) (8,18) (9,17) (9,28) (9,25) (10,16) (11,28) (11,18) (11,25) (12,27) (12,17) (12,28) (12,19) (13,15) (14,15) (14,24) (14,23) (15,16) (15,23) (17,19) (18,25) (18,19) (19,20) (19,28) (19,25) (20,27) (23,24) (25,29) (25,28) (26,29) (28,29)\nIs there a path between node 11 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph215-3_9", + "image": "data/connectivity/graph_visual/hard/graph215.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,11) (0,27) (0,29) (1,16) (1,11) (1,20) (1,14) (2,8) (2,18) (2,15) (2,11) (2,27) (2,19) (2,25) (2,29) (3,5) (4,8) (4,24) (4,23) (4,26) (4,13) (4,7) (4,28) (4,6) (4,20) (4,19) (6,15) (6,27) (6,25) (7,22) (7,24) (7,23) (7,26) (7,13) (7,28) (7,29) (8,18) (8,26) (8,12) (9,17) (11,22) (11,24) (11,28) (11,20) (12,22) (12,15) (12,28) (12,27) (12,20) (12,29) (13,16) (13,23) (13,28) (13,27) (13,20) (13,19) (14,19) (15,28) (15,25) (16,26) (16,25) (18,20) (18,29) (19,23) (19,20) (20,24) (20,26) (20,28) (20,27) (20,25) (22,23) (22,28) (22,29) (23,24) (23,26) (23,29) (24,27) (25,27) (26,29) (27,28)\nIs there a path between node 3 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph414-11_29", + "image": "data/connectivity/graph_visual/hard/graph414.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,2) (0,26) (0,21) (0,6) (0,12) (0,28) (0,15) (0,7) (1,21) (1,14) (1,25) (1,8) (1,18) (1,15) (1,27) (1,7) (2,26) (2,21) (2,14) (2,8) (2,24) (2,16) (2,13) (2,19) (2,28) (2,15) (2,27) (2,7) (3,26) (3,13) (3,18) (3,12) (3,9) (3,15) (3,27) (3,7) (3,4) (4,17) (4,8) (4,16) (4,12) (4,20) (5,14) (5,25) (5,13) (5,18) (5,28) (5,27) (5,32) (6,17) (6,25) (6,16) (6,9) (6,32) (6,11) (7,21) (7,24) (7,18) (7,12) (7,28) (7,15) (7,31) (8,25) (8,24) (8,9) (8,15) (8,31) (8,27) (8,32) (9,17) (9,16) (9,19) (9,12) (9,28) (9,15) (9,27) (10,22) (11,13) (11,18) (11,19) (11,12) (11,31) (11,27) (12,21) (12,25) (12,24) (12,16) (12,15) (12,32) (13,17) (13,14) (13,24) (13,18) (13,15) (13,20) (13,32) (14,24) (14,19) (14,28) (14,15) (14,20) (14,32) (15,28) (16,24) (16,18) (17,25) (17,28) (17,27) (18,21) (19,25) (19,28) (20,24) (20,32) (21,26) (21,25) (22,30) (23,30) (23,29) (24,25) (25,26) (25,28) (25,32) (26,31) (27,28) (27,31) (28,31) (28,32)\nIs there a path between node 11 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph652-7_9", + "image": "data/connectivity/graph_visual/hard/graph652.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,33) (0,8) (0,17) (0,12) (0,13) (0,3) (0,6) (0,27) (0,15) (0,11) (0,29) (0,7) (0,19) (0,1) (0,25) (1,33) (1,8) (1,4) (1,13) (1,3) (1,6) (1,27) (1,15) (1,11) (1,10) (1,25) (1,31) (2,24) (2,21) (2,23) (3,8) (3,17) (3,12) (3,4) (3,13) (3,6) (3,27) (3,11) (3,29) (3,7) (3,19) (3,10) (3,31) (4,13) (4,6) (4,27) (4,7) (4,19) (4,10) (4,25) (5,30) (5,22) (5,18) (5,14) (6,33) (6,17) (6,12) (6,13) (6,27) (6,15) (6,11) (6,29) (6,7) (6,10) (6,25) (6,31) (7,8) (7,17) (7,15) (7,11) (7,29) (7,19) (7,31) (8,33) (8,12) (8,13) (8,15) (8,19) (8,25) (8,31) (9,16) (9,26) (9,32) (9,28) (9,20) (10,33) (10,17) (10,12) (10,13) (10,27) (10,15) (10,29) (10,19) (10,25) (11,33) (11,17) (11,13) (11,15) (11,29) (11,19) (11,25) (11,31) (12,33) (12,17) (12,13) (12,27) (12,15) (12,29) (12,19) (12,25) (12,31) (13,33) (13,27) (13,15) (13,19) (13,31) (14,30) (14,22) (14,18) (15,33) (15,27) (15,29) (15,19) (15,25) (15,31) (16,26) (16,32) (17,29) (18,22) (19,33) (19,27) (19,31) (20,26) (20,32) (20,28) (20,34) (21,24) (21,23) (22,30) (23,24) (25,27) (25,31) (26,32) (26,34) (27,33) (27,29) (27,31) (28,34) (29,33) (31,33) (32,34)\nIs there a path between node 7 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph628-27_29", + "image": "data/connectivity/graph_visual/hard/graph628.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,33) (1,28) (1,34) (2,27) (2,4) (2,15) (2,23) (2,12) (3,33) (3,30) (3,26) (4,27) (4,15) (4,8) (5,26) (6,17) (6,22) (6,23) (6,11) (7,12) (7,32) (8,27) (8,10) (8,15) (8,9) (8,14) (8,20) (9,21) (9,11) (10,23) (10,32) (11,27) (11,15) (11,12) (11,32) (11,20) (12,17) (12,22) (12,32) (14,27) (14,19) (14,20) (15,27) (15,32) (15,21) (16,19) (16,32) (17,32) (18,28) (19,20) (20,22) (21,27) (22,27) (22,29) (22,23) (22,32) (23,27) (24,30) (24,26) (25,33) (27,29) (28,31) (29,32) (30,33)\nIs there a path between node 27 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph609-5_24", + "image": "data/connectivity/graph_visual/hard/graph609.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,29) (0,26) (0,2) (0,25) (0,17) (1,26) (1,30) (2,29) (2,7) (2,25) (2,30) (2,28) (3,21) (3,34) (3,11) (3,4) (4,21) (4,19) (4,34) (4,31) (5,20) (6,7) (6,26) (6,32) (6,30) (7,23) (8,15) (9,10) (9,14) (10,13) (11,21) (11,22) (11,15) (11,27) (12,32) (12,17) (12,28) (13,14) (14,16) (14,20) (15,19) (15,27) (16,24) (17,29) (17,26) (17,32) (18,32) (18,23) (18,28) (19,21) (19,34) (19,27) (19,31) (21,34) (21,31) (22,34) (23,29) (23,26) (25,32) (26,29) (26,32) (30,32) (31,34)\nIs there a path between node 5 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph233-24_18", + "image": "data/connectivity/graph_visual/hard/graph233.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,8) (0,16) (0,2) (0,21) (0,12) (0,22) (0,14) (0,1) (0,5) (0,27) (0,10) (0,23) (0,20) (1,8) (1,18) (1,26) (1,21) (1,22) (1,14) (1,6) (1,27) (1,3) (1,15) (1,10) (1,7) (1,23) (1,20) (2,18) (2,26) (2,21) (2,22) (2,14) (2,6) (2,3) (2,15) (2,10) (2,13) (2,7) (2,23) (2,20) (3,21) (3,14) (3,6) (3,15) (3,13) (3,7) (3,23) (4,11) (4,17) (4,9) (4,19) (5,8) (5,16) (5,21) (5,12) (5,14) (5,6) (5,15) (5,10) (5,13) (5,7) (6,16) (6,26) (6,21) (6,12) (6,27) (6,13) (6,7) (6,23) (7,8) (7,16) (7,18) (7,12) (7,22) (7,14) (7,27) (7,15) (7,10) (7,13) (7,23) (7,20) (8,16) (8,18) (8,26) (8,21) (8,22) (8,14) (8,27) (8,15) (8,13) (8,23) (8,20) (9,17) (10,16) (10,18) (10,26) (10,21) (10,12) (10,22) (10,14) (10,23) (10,20) (11,17) (11,28) (11,25) (11,19) (11,29) (12,16) (12,21) (12,22) (12,14) (12,27) (12,15) (12,13) (12,20) (13,16) (13,26) (13,21) (13,22) (13,14) (13,15) (13,23) (13,20) (14,16) (14,26) (14,21) (14,27) (14,15) (15,16) (15,18) (15,26) (15,21) (15,27) (15,23) (16,18) (16,26) (16,21) (16,22) (16,27) (16,20) (17,28) (17,25) (17,19) (17,29) (18,23) (19,28) (19,25) (20,26) (20,21) (20,27) (20,23) (21,26) (21,23) (22,26) (22,27) (23,26) (25,28) (25,29) (26,27) (28,29)\nIs there a path between node 24 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph676-30_29", + "image": "data/connectivity/graph_visual/hard/graph676.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,10) (0,26) (0,32) (0,20) (0,28) (0,15) (0,17) (0,3) (0,12) (0,9) (1,10) (1,24) (1,26) (1,34) (1,18) (1,25) (1,15) (1,27) (1,21) (1,29) (1,12) (1,9) (2,13) (2,4) (2,17) (3,10) (3,11) (3,33) (3,18) (3,4) (3,27) (3,17) (3,30) (4,18) (4,25) (4,27) (4,29) (4,7) (5,16) (7,11) (7,33) (7,34) (7,18) (7,13) (7,19) (7,28) (7,27) (7,31) (7,12) (7,9) (9,26) (9,32) (9,20) (9,13) (9,14) (9,12) (10,26) (10,34) (10,14) (10,31) (10,30) (11,24) (11,34) (11,18) (11,14) (11,15) (11,27) (12,33) (12,20) (12,28) (12,27) (13,33) (13,18) (13,32) (13,15) (13,22) (13,17) (13,31) (14,33) (14,26) (14,19) (15,33) (15,18) (15,28) (15,25) (15,23) (17,18) (17,32) (17,29) (18,33) (18,24) (18,34) (18,20) (18,25) (18,27) (18,30) (19,28) (19,25) (19,22) (19,21) (20,33) (20,26) (20,32) (20,22) (21,33) (21,24) (21,34) (21,28) (21,25) (21,27) (22,33) (22,26) (22,29) (23,33) (23,34) (23,28) (23,31) (23,29) (24,32) (24,31) (24,30) (25,33) (25,32) (25,27) (26,32) (27,31) (28,33) (30,34) (31,34) (32,33) (33,34)\nIs there a path between node 30 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph282-21_30", + "image": "data/connectivity/graph_visual/hard/graph282.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,13) (0,28) (0,2) (0,25) (0,9) (0,3) (0,1) (0,19) (0,23) (0,29) (0,16) (0,8) (0,27) (0,14) (0,22) (1,28) (1,2) (1,25) (1,9) (1,11) (1,3) (1,10) (1,20) (1,19) (1,29) (1,16) (1,8) (1,14) (1,26) (1,22) (1,4) (2,28) (2,25) (2,11) (2,10) (2,20) (2,19) (2,23) (2,29) (2,8) (2,21) (2,22) (3,13) (3,25) (3,9) (3,11) (3,20) (3,23) (3,29) (3,27) (3,26) (3,21) (3,22) (3,4) (4,25) (4,9) (4,11) (4,10) (4,20) (4,23) (4,29) (4,16) (4,14) (4,21) (4,22) (5,24) (6,12) (6,15) (6,18) (7,12) (7,18) (8,13) (8,28) (8,25) (8,9) (8,11) (8,10) (8,20) (8,23) (8,29) (8,16) (8,27) (8,26) (9,13) (9,28) (9,25) (9,10) (9,20) (9,19) (9,23) (9,29) (9,16) (9,27) (9,14) (9,26) (9,21) (9,22) (10,13) (10,28) (10,25) (10,11) (10,20) (10,19) (10,23) (10,29) (10,16) (10,27) (10,14) (10,21) (10,22) (11,13) (11,25) (11,20) (11,19) (11,23) (11,29) (11,16) (11,27) (11,14) (11,26) (11,21) (11,22) (12,15) (12,18) (13,28) (13,25) (13,20) (13,19) (13,29) (13,14) (13,26) (13,22) (14,20) (14,19) (14,23) (14,29) (14,27) (14,26) (14,22) (15,18) (16,28) (16,25) (16,20) (16,23) (16,27) (16,26) (16,22) (17,30) (17,24) (19,28) (19,25) (19,23) (19,27) (19,26) (19,21) (19,22) (20,28) (20,25) (20,29) (20,26) (20,21) (20,22) (21,25) (21,23) (21,27) (21,22) (22,28) (22,29) (22,27) (22,26) (23,28) (23,25) (23,29) (23,27) (24,30) (25,28) (25,29) (25,27) (25,26) (26,28) (26,29) (27,28) (27,29) (28,29)\nIs there a path between node 21 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph351-28_24", + "image": "data/connectivity/graph_visual/hard/graph351.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,31) (0,26) (0,30) (0,17) (0,9) (0,11) (0,2) (0,12) (1,10) (1,31) (1,26) (1,17) (1,28) (1,3) (1,21) (2,20) (2,17) (2,3) (2,18) (2,21) (3,20) (3,19) (3,31) (3,26) (3,28) (4,29) (4,19) (4,26) (4,11) (4,28) (4,18) (4,12) (4,27) (5,19) (5,11) (5,28) (5,21) (5,27) (6,20) (6,19) (6,14) (6,16) (6,25) (6,26) (6,30) (7,10) (7,20) (7,14) (7,31) (7,30) (7,17) (7,28) (7,21) (7,27) (9,10) (9,16) (9,25) (9,17) (9,12) (10,20) (10,16) (10,30) (10,22) (10,11) (10,27) (11,29) (11,30) (12,29) (12,16) (12,22) (13,20) (13,14) (13,31) (13,27) (14,30) (14,17) (16,20) (16,19) (16,31) (17,29) (17,20) (17,26) (18,19) (18,31) (18,30) (18,28) (19,29) (19,22) (20,30) (20,22) (21,30) (21,27) (22,28) (25,28) (26,29) (27,28) (28,31) (28,30) (29,30) (30,31)\nIs there a path between node 28 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph310-4_10", + "image": "data/connectivity/graph_visual/hard/graph310.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,16) (0,29) (0,2) (0,24) (1,7) (2,23) (2,12) (2,4) (2,8) (2,10) (3,17) (3,26) (3,27) (4,11) (4,12) (4,5) (5,31) (5,16) (5,28) (6,16) (6,11) (6,14) (6,28) (8,31) (8,11) (8,12) (10,11) (10,14) (11,31) (12,16) (12,23) (13,19) (13,20) (13,26) (14,16) (14,29) (15,19) (16,29) (16,23) (18,27) (19,20) (19,27) (19,22) (21,23) (23,28) (25,29)\nIs there a path between node 4 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph590-23_11", + "image": "data/connectivity/graph_visual/hard/graph590.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,7) (0,19) (0,33) (0,32) (0,27) (0,10) (0,9) (0,16) (0,8) (0,25) (0,17) (0,3) (0,13) (0,18) (0,15) (0,2) (0,4) (1,22) (1,30) (1,7) (1,20) (1,6) (1,23) (1,33) (1,32) (1,27) (1,10) (1,9) (1,16) (1,17) (1,21) (1,5) (1,14) (1,2) (1,28) (1,12) (1,4) (2,22) (2,30) (2,7) (2,20) (2,6) (2,19) (2,23) (2,26) (2,27) (2,10) (2,8) (2,25) (2,17) (2,21) (2,13) (2,18) (2,5) (2,14) (2,12) (2,4) (3,7) (3,20) (3,19) (3,23) (3,26) (3,33) (3,24) (3,27) (3,10) (3,16) (3,25) (3,17) (3,21) (3,13) (3,18) (3,29) (3,5) (3,14) (3,15) (3,28) (3,12) (4,22) (4,30) (4,7) (4,20) (4,6) (4,19) (4,23) (4,33) (4,32) (4,24) (4,10) (4,9) (4,16) (4,25) (4,17) (4,21) (4,13) (4,18) (4,29) (4,5) (5,30) (5,7) (5,6) (5,19) (5,23) (5,33) (5,24) (5,9) (5,16) (5,8) (5,13) (5,18) (5,29) (5,14) (5,28) (6,22) (6,7) (6,20) (6,26) (6,32) (6,24) (6,10) (6,8) (6,25) (6,29) (6,14) (6,15) (7,22) (7,30) (7,19) (7,26) (7,32) (7,24) (7,27) (7,10) (7,16) (7,8) (7,25) (7,21) (7,13) (7,18) (7,29) (7,14) (7,12) (8,30) (8,20) (8,23) (8,26) (8,33) (8,32) (8,27) (8,10) (8,9) (8,16) (8,17) (8,21) (8,13) (8,18) (8,29) (8,14) (8,15) (8,28) (8,12) (9,30) (9,20) (9,19) (9,23) (9,26) (9,33) (9,32) (9,24) (9,27) (9,16) (9,25) (9,17) (9,13) (9,29) (9,14) (10,30) (10,20) (10,23) (10,26) (10,32) (10,24) (10,27) (10,16) (10,21) (10,13) (10,18) (10,14) (10,15) (10,12) (12,30) (12,19) (12,23) (12,33) (12,32) (12,16) (12,25) (12,17) (12,21) (12,29) (12,14) (12,15) (12,28) (13,22) (13,20) (13,19) (13,23) (13,26) (13,33) (13,32) (13,24) (13,27) (13,16) (13,17) (13,21) (13,29) (13,14) (13,15) (14,19) (14,23) (14,26) (14,33) (14,32) (14,24) (14,27) (14,16) (14,25) (14,17) (14,21) (14,18) (14,29) (14,15) (15,22) (15,30) (15,20) (15,23) (15,33) (15,24) (15,25) (15,17) (15,21) (16,30) (16,20) (16,19) (16,23) (16,33) (16,27) (16,21) (16,28) (17,22) (17,30) (17,20) (17,19) (17,23) (17,33) (17,32) (17,24) (17,25) (17,21) (17,29) (17,28) (18,22) (18,30) (18,23) (18,26) (18,32) (18,24) (18,27) (18,25) (18,21) (18,28) (19,20) (19,23) (19,33) (19,32) (19,25) (19,21) (19,29) (20,22) (20,30) (20,26) (20,33) (20,32) (20,24) (20,27) (20,25) (20,21) (20,29) (20,28) (21,22) (21,30) (21,26) (21,33) (21,32) (21,24) (21,27) (21,29) (21,28) (22,23) (22,26) (22,33) (22,32) (22,24) (22,27) (22,25) (22,29) (22,28) (23,26) (23,33) (23,27) (23,25) (23,29) (24,30) (24,26) (24,33) (24,32) (24,27) (24,25) (24,29) (25,30) (25,26) (25,33) (25,32) (25,27) (25,29) (25,28) (26,30) (26,33) (26,27) (26,28) (27,30) (27,32) (27,28) (28,30) (28,33) (28,32) (28,29) (29,30) (29,33) (30,33) (30,32)\nIs there a path between node 23 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph46-7_18", + "image": "data/connectivity/graph_visual/hard/graph46.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,12) (0,19) (0,25) (0,2) (0,13) (0,1) (1,17) (1,24) (1,25) (1,11) (2,17) (2,25) (2,16) (2,13) (3,17) (4,23) (4,7) (4,14) (4,8) (5,18) (5,16) (6,18) (6,16) (6,21) (7,14) (7,15) (7,10) (8,23) (8,10) (9,14) (9,10) (10,23) (10,20) (11,17) (11,18) (11,25) (11,16) (11,13) (12,16) (13,17) (13,24) (13,25) (13,21) (14,15) (16,21) (17,19) (17,18) (17,25) (19,25) (19,21) (21,25)\nIs there a path between node 7 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph220-16_12", + "image": "data/connectivity/graph_visual/hard/graph220.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,16) (0,5) (0,6) (0,8) (0,4) (0,18) (0,9) (1,14) (1,11) (1,29) (1,26) (1,19) (1,27) (1,13) (1,22) (1,21) (1,15) (2,25) (2,10) (2,12) (2,20) (2,17) (2,7) (3,25) (3,10) (3,24) (3,12) (3,20) (4,28) (4,16) (4,6) (4,8) (4,18) (5,28) (5,16) (5,6) (5,8) (5,18) (5,9) (6,28) (6,16) (6,8) (6,18) (6,9) (7,25) (7,24) (7,12) (7,20) (7,17) (8,28) (8,9) (9,16) (9,18) (10,25) (10,24) (10,12) (10,20) (11,14) (11,29) (11,26) (11,27) (11,13) (11,22) (11,21) (11,15) (12,25) (12,17) (13,14) (13,26) (13,19) (13,27) (13,23) (13,21) (13,15) (14,19) (14,22) (14,21) (14,15) (15,26) (15,27) (15,22) (16,18) (17,25) (17,20) (19,29) (19,26) (19,23) (19,21) (20,25) (20,24) (21,29) (21,26) (21,23) (22,26) (22,27) (22,23) (23,29) (23,27) (24,25) (26,29)\nIs there a path between node 16 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph647-15_33", + "image": "data/connectivity/graph_visual/hard/graph647.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,12) (0,21) (0,10) (0,22) (0,23) (0,29) (0,17) (0,28) (0,9) (0,14) (1,4) (1,26) (1,5) (1,8) (1,15) (1,30) (2,19) (2,18) (2,16) (2,11) (2,7) (2,6) (2,34) (3,12) (3,21) (3,10) (3,24) (3,22) (3,23) (3,29) (3,17) (3,32) (3,28) (3,9) (3,27) (4,26) (4,15) (4,30) (5,26) (5,15) (6,13) (6,31) (6,18) (6,16) (6,34) (7,13) (7,31) (7,19) (7,18) (7,11) (7,34) (8,15) (8,30) (9,12) (9,10) (9,22) (9,23) (9,29) (9,32) (9,33) (9,28) (9,27) (9,14) (10,12) (10,21) (10,22) (10,23) (10,29) (10,17) (10,32) (10,33) (10,28) (10,20) (10,27) (10,14) (11,13) (11,31) (11,19) (11,25) (11,18) (11,16) (12,21) (12,24) (12,29) (12,17) (12,32) (12,33) (12,28) (12,20) (12,27) (12,14) (13,31) (13,19) (13,18) (13,16) (13,34) (14,21) (14,22) (14,23) (14,17) (14,32) (14,28) (14,20) (14,27) (15,26) (15,30) (16,31) (16,19) (16,25) (16,34) (17,24) (17,22) (17,23) (17,29) (17,32) (17,20) (18,31) (18,25) (18,34) (19,31) (19,25) (19,34) (20,24) (20,33) (20,28) (20,27) (21,23) (21,32) (21,33) (22,24) (22,23) (22,29) (22,33) (22,27) (23,33) (23,28) (23,27) (24,29) (24,32) (24,33) (24,27) (25,31) (25,34) (26,30) (27,32) (27,28) (28,29) (28,32) (28,33) (29,32)\nIs there a path between node 15 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph251-26_30", + "image": "data/connectivity/graph_visual/hard/graph251.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,17) (1,8) (1,29) (1,10) (1,7) (1,11) (1,25) (1,18) (1,14) (1,30) (1,16) (1,5) (1,26) (1,4) (1,23) (1,27) (2,21) (3,21) (4,17) (4,29) (4,9) (4,10) (4,6) (4,7) (4,11) (4,14) (4,22) (4,26) (4,13) (4,24) (4,23) (4,19) (5,17) (5,29) (5,9) (5,10) (5,6) (5,7) (5,11) (5,18) (5,14) (5,30) (5,16) (5,26) (5,15) (5,13) (5,24) (5,19) (5,27) (6,17) (6,9) (6,10) (6,11) (6,18) (6,14) (6,30) (6,16) (6,22) (6,15) (6,24) (6,19) (6,27) (7,17) (7,8) (7,29) (7,9) (7,10) (7,25) (7,18) (7,30) (7,16) (7,22) (7,24) (7,23) (7,19) (7,27) (8,17) (8,11) (8,25) (8,18) (8,14) (8,30) (8,16) (8,15) (8,13) (8,24) (8,19) (8,27) (9,17) (9,29) (9,10) (9,11) (9,25) (9,14) (9,30) (9,16) (9,22) (9,15) (9,13) (9,24) (9,19) (9,27) (10,17) (10,11) (10,25) (10,18) (10,14) (10,30) (10,16) (10,22) (10,15) (10,13) (10,24) (10,23) (10,27) (11,29) (11,25) (11,14) (11,30) (11,16) (11,26) (11,15) (11,13) (11,24) (11,23) (11,19) (11,27) (12,28) (13,29) (13,18) (13,14) (13,30) (13,16) (13,22) (13,26) (13,15) (13,24) (13,19) (13,27) (14,17) (14,25) (14,18) (14,30) (14,16) (14,22) (14,26) (14,15) (14,19) (14,27) (15,17) (15,25) (15,18) (15,30) (15,16) (15,22) (15,26) (15,24) (15,23) (15,19) (15,27) (16,29) (16,25) (16,30) (16,23) (16,27) (17,29) (17,25) (17,18) (17,30) (17,26) (17,19) (17,27) (18,22) (18,26) (18,24) (18,23) (18,19) (19,29) (19,25) (19,22) (19,26) (19,24) (19,23) (19,27) (22,29) (22,25) (22,26) (22,24) (22,23) (22,27) (23,25) (23,30) (23,24) (24,29) (24,25) (24,26) (24,27) (25,29) (25,30) (25,26) (25,27) (26,29) (26,30) (29,30)\nIs there a path between node 26 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph232-23_4", + "image": "data/connectivity/graph_visual/hard/graph232.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,20) (0,9) (0,21) (0,1) (0,19) (0,7) (0,3) (0,27) (0,12) (0,23) (0,17) (1,9) (1,21) (1,10) (1,4) (1,19) (1,3) (1,12) (1,23) (1,17) (2,8) (2,28) (2,16) (2,24) (2,5) (2,11) (2,15) (3,20) (3,9) (3,21) (3,19) (3,27) (3,12) (3,23) (4,20) (4,9) (4,21) (4,19) (4,12) (4,23) (4,17) (5,18) (5,28) (5,16) (5,6) (5,14) (6,18) (6,28) (6,24) (7,20) (7,9) (7,12) (7,17) (8,16) (8,24) (8,15) (9,21) (9,10) (9,27) (9,12) (9,23) (9,17) (10,19) (10,27) (10,12) (10,23) (11,28) (11,16) (11,14) (11,24) (11,15) (12,20) (12,19) (12,27) (12,23) (12,17) (13,25) (13,26) (13,29) (14,28) (14,24) (14,15) (15,18) (15,28) (15,24) (16,18) (16,28) (17,20) (17,21) (17,23) (18,28) (18,24) (19,20) (19,21) (19,23) (20,27) (21,27) (22,25) (22,26) (22,29) (25,29) (26,29)\nIs there a path between node 23 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph91-19_9", + "image": "data/connectivity/graph_visual/hard/graph91.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,5) (0,3) (0,13) (1,26) (2,19) (3,22) (3,19) (4,9) (4,27) (4,6) (4,23) (5,7) (6,12) (6,27) (6,16) (6,8) (6,11) (7,19) (8,25) (8,24) (8,16) (8,11) (9,27) (9,21) (9,23) (11,25) (11,14) (11,24) (11,12) (11,23) (12,24) (12,27) (15,24) (15,20) (16,21) (16,23) (18,26) (20,25) (20,21) (21,27) (23,25)\nIs there a path between node 19 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph182-4_25", + "image": "data/connectivity/graph_visual/hard/graph182.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,20) (0,27) (0,23) (0,28) (0,10) (0,16) (0,22) (0,2) (0,6) (0,14) (0,25) (0,26) (0,4) (0,21) (1,20) (1,27) (1,23) (1,28) (1,16) (1,22) (1,17) (1,2) (1,12) (1,14) (1,25) (1,26) (1,15) (1,4) (1,21) (1,9) (1,5) (2,20) (2,27) (2,23) (2,10) (2,7) (2,16) (2,22) (2,17) (2,6) (2,14) (2,26) (2,15) (2,4) (2,21) (2,9) (2,5) (3,8) (3,19) (3,24) (4,20) (4,27) (4,23) (4,10) (4,16) (4,22) (4,17) (4,12) (4,6) (4,14) (4,25) (4,26) (4,15) (4,21) (4,5) (5,20) (5,27) (5,23) (5,28) (5,10) (5,16) (5,22) (5,17) (5,12) (5,6) (5,26) (5,15) (5,21) (6,20) (6,27) (6,23) (6,28) (6,10) (6,7) (6,16) (6,22) (6,17) (6,12) (6,14) (6,25) (6,26) (6,15) (6,9) (7,20) (7,23) (7,28) (7,10) (7,16) (7,22) (7,17) (7,15) (7,21) (7,9) (8,19) (8,24) (8,11) (8,13) (8,18) (9,28) (9,10) (9,22) (9,17) (9,26) (9,15) (10,20) (10,27) (10,23) (10,28) (10,16) (10,22) (10,17) (10,12) (10,14) (10,25) (10,26) (10,15) (10,21) (11,19) (11,18) (12,20) (12,27) (12,23) (12,28) (12,17) (12,26) (12,15) (12,21) (13,19) (13,24) (13,18) (14,20) (14,23) (14,16) (14,22) (14,25) (14,26) (14,15) (14,21) (15,20) (15,27) (15,22) (15,17) (15,25) (15,26) (16,20) (16,27) (16,17) (16,25) (16,26) (17,27) (17,23) (17,28) (17,22) (17,25) (17,26) (17,21) (18,24) (19,24) (20,28) (20,22) (20,25) (20,26) (21,23) (21,25) (21,26) (22,28) (22,26) (23,26) (25,27) (25,28) (25,26) (26,27) (26,28) (27,28)\nIs there a path between node 4 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph424-19_18", + "image": "data/connectivity/graph_visual/hard/graph424.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,16) (0,10) (0,29) (0,2) (0,12) (0,18) (0,26) (0,8) (1,19) (1,16) (1,24) (1,18) (2,19) (2,17) (2,7) (2,32) (2,24) (2,18) (3,15) (3,14) (4,9) (4,25) (5,30) (5,25) (5,6) (6,9) (6,30) (6,25) (7,19) (7,16) (7,26) (8,27) (8,16) (8,12) (8,32) (8,18) (10,27) (10,19) (10,16) (10,12) (10,32) (11,18) (11,26) (12,27) (12,19) (12,17) (12,28) (12,24) (12,18) (12,26) (13,23) (16,31) (16,29) (17,24) (18,31) (19,28) (19,24) (20,28) (20,24) (21,28) (21,26) (26,28) (27,31) (28,31) (28,29) (31,32)\nIs there a path between node 19 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph367-16_26", + "image": "data/connectivity/graph_visual/hard/graph367.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,5) (0,11) (0,22) (0,20) (0,17) (0,13) (0,6) (0,8) (0,23) (0,18) (0,29) (0,10) (0,2) (0,21) (0,9) (0,25) (1,22) (1,20) (1,17) (1,13) (1,6) (1,12) (1,23) (1,19) (1,18) (1,14) (1,29) (1,10) (1,2) (1,21) (1,30) (1,3) (1,26) (1,25) (2,20) (2,15) (2,13) (2,6) (2,23) (2,29) (2,10) (2,3) (2,26) (2,25) (3,5) (3,11) (3,22) (3,20) (3,15) (3,6) (3,19) (3,18) (3,14) (3,21) (3,30) (3,9) (3,26) (4,28) (4,7) (4,16) (5,11) (5,20) (5,17) (5,13) (5,6) (5,8) (5,18) (5,14) (5,10) (5,21) (5,26) (5,25) (6,11) (6,22) (6,15) (6,17) (6,8) (6,23) (6,19) (6,18) (6,14) (6,29) (6,10) (6,21) (6,9) (6,25) (7,31) (7,28) (7,27) (8,22) (8,15) (8,17) (8,13) (8,23) (8,19) (8,18) (8,29) (8,10) (8,21) (8,30) (8,9) (8,26) (9,11) (9,22) (9,15) (9,17) (9,12) (9,14) (9,29) (9,21) (9,25) (10,22) (10,20) (10,15) (10,17) (10,12) (10,23) (10,19) (10,18) (10,14) (10,29) (10,21) (10,26) (10,25) (11,22) (11,15) (11,12) (11,19) (11,18) (11,14) (11,29) (11,21) (11,30) (11,26) (12,22) (12,20) (12,15) (12,17) (12,13) (12,23) (12,19) (12,18) (12,29) (12,30) (12,26) (12,25) (13,22) (13,20) (13,15) (13,17) (13,23) (13,14) (13,29) (13,21) (13,30) (13,26) (13,25) (14,20) (14,15) (14,17) (14,19) (14,29) (14,30) (14,26) (14,25) (15,22) (15,20) (15,23) (15,19) (15,29) (15,21) (15,30) (16,24) (16,28) (17,22) (17,20) (17,23) (17,19) (17,18) (17,29) (17,30) (18,20) (18,23) (18,19) (18,21) (18,26) (19,20) (19,23) (19,29) (19,21) (19,26) (19,25) (20,22) (20,23) (20,21) (20,30) (20,26) (20,25) (21,22) (21,25) (22,30) (22,26) (22,25) (23,29) (23,26) (24,31) (24,28) (24,27) (25,29) (26,29) (27,28) (29,30)\nIs there a path between node 16 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph559-25_2", + "image": "data/connectivity/graph_visual/hard/graph559.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,1) (0,29) (0,8) (0,19) (0,26) (0,7) (0,10) (0,24) (1,8) (1,5) (1,19) (2,11) (2,29) (2,8) (2,6) (2,5) (2,19) (2,26) (2,7) (2,27) (2,14) (2,24) (3,33) (3,32) (4,18) (5,29) (5,10) (6,8) (6,10) (7,29) (7,10) (7,14) (8,26) (9,33) (9,17) (9,30) (9,20) (10,27) (11,24) (12,18) (12,16) (12,20) (13,22) (13,31) (13,15) (14,26) (15,31) (16,17) (16,32) (16,30) (16,20) (17,32) (19,24) (20,33) (21,32) (21,30) (22,23) (23,25) (27,29) (28,31)\nIs there a path between node 25 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph273-20_27", + "image": "data/connectivity/graph_visual/hard/graph273.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,21) (0,13) (0,15) (0,6) (0,18) (0,26) (0,20) (0,23) (0,10) (0,30) (0,8) (1,24) (2,3) (2,6) (2,18) (2,30) (2,25) (2,8) (3,21) (3,15) (3,6) (3,18) (3,26) (3,10) (3,14) (3,25) (3,7) (4,12) (4,19) (4,29) (4,16) (4,11) (4,22) (5,12) (5,17) (5,29) (5,16) (5,11) (6,21) (6,13) (6,28) (6,15) (6,18) (6,26) (6,20) (6,10) (6,30) (6,25) (6,7) (7,13) (7,15) (7,18) (7,26) (7,20) (7,23) (7,10) (7,14) (7,25) (7,8) (8,21) (8,13) (8,28) (8,15) (8,26) (8,23) (8,30) (9,24) (10,21) (10,13) (10,28) (10,15) (10,26) (10,20) (10,23) (10,14) (10,30) (11,12) (11,27) (11,19) (11,16) (12,29) (12,22) (13,21) (13,15) (13,18) (13,26) (13,20) (13,14) (14,28) (14,15) (14,18) (14,26) (14,20) (14,23) (14,30) (14,25) (15,28) (15,18) (15,26) (15,20) (15,25) (16,17) (16,22) (17,27) (17,19) (17,29) (17,22) (18,21) (18,28) (18,26) (18,20) (18,23) (18,30) (18,25) (19,29) (19,22) (20,21) (20,28) (20,30) (20,25) (21,28) (21,23) (22,29) (23,26) (23,30) (23,25) (25,28) (25,30) (26,28) (26,30) (27,29)\nIs there a path between node 20 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph427-7_26", + "image": "data/connectivity/graph_visual/hard/graph427.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,4) (0,30) (0,24) (0,13) (0,20) (0,16) (0,15) (0,25) (0,3) (1,5) (1,17) (1,6) (2,12) (2,22) (2,8) (2,11) (2,9) (2,14) (2,32) (2,21) (2,27) (3,20) (3,15) (4,30) (4,24) (4,13) (4,20) (4,16) (4,15) (4,25) (5,26) (5,17) (5,31) (5,7) (5,6) (6,26) (6,18) (6,31) (6,7) (7,26) (7,18) (7,31) (8,12) (8,22) (8,11) (8,21) (8,28) (8,27) (9,22) (9,14) (9,32) (9,10) (9,28) (10,22) (10,11) (10,19) (10,14) (10,32) (10,21) (10,28) (10,27) (11,12) (11,22) (11,14) (11,32) (11,21) (11,27) (12,22) (12,32) (12,21) (12,28) (12,27) (13,30) (13,24) (13,20) (13,15) (13,25) (14,19) (14,32) (14,21) (15,20) (15,25) (16,24) (16,20) (16,25) (17,18) (17,31) (18,26) (18,31) (19,21) (19,28) (20,24) (20,25) (21,22) (21,32) (21,28) (21,27) (22,32) (22,28) (22,27) (24,25) (25,30) (26,31) (27,28) (28,32)\nIs there a path between node 7 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph259-1_12", + "image": "data/connectivity/graph_visual/hard/graph259.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,21) (1,27) (1,29) (1,22) (1,26) (1,7) (1,28) (1,16) (1,12) (1,3) (2,17) (2,22) (2,15) (2,10) (2,8) (3,22) (3,24) (3,15) (3,10) (3,12) (5,17) (5,29) (5,20) (5,26) (5,7) (5,10) (5,28) (6,9) (6,18) (6,25) (6,21) (6,23) (7,11) (7,12) (7,8) (8,16) (9,18) (9,25) (9,30) (9,21) (10,17) (10,20) (10,15) (10,11) (10,12) (11,27) (11,20) (11,22) (11,24) (12,22) (12,24) (14,19) (14,30) (14,21) (14,23) (15,20) (16,17) (16,28) (17,22) (19,21) (19,23) (21,25) (22,26) (22,28) (23,25) (24,27) (24,28) (26,27) (26,28) (28,29)\nIs there a path between node 1 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph396-24_17", + "image": "data/connectivity/graph_visual/hard/graph396.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,21) (1,22) (1,4) (1,27) (1,2) (1,32) (1,9) (2,20) (2,4) (2,14) (2,13) (3,28) (3,14) (3,13) (3,9) (4,24) (4,30) (4,32) (5,8) (5,11) (5,16) (5,29) (6,21) (6,26) (6,10) (6,25) (7,15) (8,29) (8,31) (9,20) (9,23) (9,28) (9,14) (9,13) (11,18) (11,31) (13,24) (13,23) (13,14) (14,22) (14,23) (14,30) (14,32) (15,18) (15,16) (15,31) (16,19) (17,26) (18,19) (20,28) (20,30) (23,24) (23,30) (23,32) (24,28) (24,32) (25,26) (27,32) (28,30)\nIs there a path between node 24 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph205-8_9", + "image": "data/connectivity/graph_visual/hard/graph205.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,21) (0,12) (0,22) (0,29) (0,26) (0,4) (0,28) (1,22) (1,16) (1,19) (1,23) (1,25) (2,12) (2,22) (2,29) (2,5) (2,8) (3,15) (3,10) (3,18) (3,21) (3,12) (3,22) (3,26) (3,14) (3,27) (3,28) (3,8) (4,10) (4,20) (4,16) (4,26) (4,27) (4,28) (4,5) (5,15) (5,10) (5,12) (5,20) (5,16) (5,7) (5,14) (5,27) (5,17) (7,29) (7,16) (7,23) (7,28) (8,15) (8,23) (8,26) (8,11) (8,17) (10,18) (10,13) (10,22) (10,16) (11,21) (11,12) (11,29) (11,16) (11,14) (12,21) (12,20) (12,23) (12,17) (13,29) (13,20) (14,18) (14,21) (14,23) (14,26) (14,27) (14,17) (15,29) (15,19) (15,23) (15,26) (15,25) (16,18) (16,21) (16,29) (16,27) (16,25) (16,28) (16,17) (17,26) (18,21) (18,20) (18,19) (18,23) (19,26) (20,23) (20,25) (21,22) (22,23) (22,27) (22,28) (23,29) (23,26) (23,27) (23,28) (25,29) (25,27)\nIs there a path between node 8 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph682-29_2", + "image": "data/connectivity/graph_visual/hard/graph682.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,8) (0,28) (0,29) (0,16) (0,5) (0,6) (0,12) (0,15) (1,28) (1,18) (1,4) (1,3) (1,21) (1,14) (1,12) (2,22) (3,8) (3,29) (3,33) (3,5) (3,21) (3,30) (3,26) (3,14) (3,7) (3,31) (3,24) (3,12) (3,32) (4,17) (4,5) (4,34) (4,12) (4,32) (4,19) (5,18) (5,16) (5,33) (5,21) (5,6) (5,30) (5,20) (5,11) (6,27) (6,17) (6,26) (6,7) (6,24) (6,15) (7,28) (7,18) (7,29) (7,17) (7,21) (7,26) (7,14) (7,11) (7,32) (8,28) (8,18) (8,29) (8,34) (8,10) (8,30) (8,26) (8,23) (8,14) (8,20) (10,21) (10,30) (10,14) (10,24) (10,20) (10,12) (10,11) (11,16) (11,34) (11,30) (11,14) (11,24) (11,20) (12,27) (12,28) (12,29) (12,17) (12,16) (12,20) (12,32) (12,19) (13,27) (13,17) (13,16) (13,33) (13,23) (13,14) (13,24) (14,33) (14,34) (14,21) (14,30) (14,20) (14,32) (14,19) (14,15) (15,18) (15,29) (15,21) (15,30) (15,23) (16,27) (16,18) (16,17) (16,24) (17,28) (17,33) (17,34) (17,31) (17,32) (18,33) (18,34) (18,21) (18,30) (18,23) (18,24) (18,32) (19,29) (19,33) (19,21) (19,26) (19,32) (20,28) (20,29) (20,33) (20,30) (21,29) (21,33) (21,26) (23,33) (24,27) (24,29) (24,33) (24,30) (24,26) (26,28) (26,29) (27,29) (28,31) (28,32) (29,32)\nIs there a path between node 29 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph473-5_14", + "image": "data/connectivity/graph_visual/hard/graph473.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,17) (1,2) (1,14) (1,9) (1,18) (1,5) (1,25) (1,28) (1,13) (1,10) (2,31) (2,14) (2,4) (2,18) (2,5) (2,28) (2,13) (2,19) (2,22) (2,10) (2,15) (3,27) (4,21) (4,9) (4,18) (4,25) (4,28) (4,13) (4,22) (4,7) (4,16) (5,21) (5,31) (5,9) (5,18) (5,25) (5,28) (5,13) (5,19) (5,22) (5,16) (5,10) (5,15) (6,17) (6,32) (7,31) (7,14) (7,9) (7,18) (7,25) (7,28) (7,13) (7,19) (7,16) (7,10) (8,11) (8,23) (8,30) (8,12) (8,29) (9,21) (9,31) (9,18) (9,25) (9,13) (9,10) (10,31) (10,18) (10,28) (10,19) (10,22) (10,16) (10,15) (11,24) (11,30) (11,26) (12,24) (12,23) (12,20) (12,26) (12,29) (13,14) (13,18) (13,28) (13,19) (13,22) (13,16) (14,31) (14,18) (14,16) (14,15) (15,31) (15,18) (15,19) (15,22) (15,16) (16,21) (16,31) (16,18) (16,28) (16,19) (18,21) (18,31) (18,25) (18,28) (18,22) (19,31) (19,25) (19,28) (19,22) (20,24) (20,23) (20,30) (20,29) (21,31) (21,28) (21,22) (22,25) (22,28) (23,30) (23,26) (23,29) (24,30) (25,31) (25,28) (26,30) (28,31) (29,30)\nIs there a path between node 5 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph85-20_24", + "image": "data/connectivity/graph_visual/hard/graph85.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,20) (0,15) (0,19) (0,3) (0,5) (1,12) (1,17) (1,6) (1,16) (1,24) (1,13) (1,23) (1,4) (1,11) (1,26) (1,8) (2,17) (2,25) (2,16) (2,10) (2,13) (2,23) (2,21) (2,14) (2,22) (2,26) (2,8) (3,20) (3,19) (4,12) (4,6) (4,25) (4,9) (4,16) (4,24) (4,10) (4,13) (4,21) (4,22) (4,26) (4,8) (5,20) (5,15) (5,19) (5,18) (6,9) (6,10) (6,13) (6,23) (6,14) (6,22) (6,8) (7,12) (7,17) (7,25) (7,9) (7,24) (7,13) (7,21) (7,14) (7,26) (7,8) (8,12) (8,17) (8,25) (8,9) (8,16) (8,24) (8,10) (8,13) (8,23) (8,21) (8,11) (8,22) (8,26) (9,12) (9,17) (9,25) (9,16) (9,24) (9,10) (9,13) (9,23) (9,21) (9,14) (9,22) (9,26) (10,12) (10,17) (10,25) (10,16) (10,24) (10,23) (10,21) (10,22) (10,26) (11,12) (11,17) (11,25) (11,16) (11,23) (11,21) (11,14) (11,22) (12,17) (12,13) (12,23) (12,21) (12,14) (12,22) (13,17) (13,16) (13,21) (13,14) (13,22) (13,26) (14,25) (14,16) (14,23) (14,21) (14,22) (14,26) (15,19) (15,18) (16,17) (16,25) (16,24) (16,23) (16,21) (17,25) (17,23) (17,21) (18,20) (21,25) (21,24) (21,22) (21,26) (22,24) (22,26) (23,26) (24,26)\nIs there a path between node 20 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph475-8_5", + "image": "data/connectivity/graph_visual/hard/graph475.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,11) (0,23) (0,8) (0,30) (0,7) (0,14) (0,22) (0,1) (0,6) (0,17) (0,24) (0,4) (0,16) (0,13) (0,19) (0,26) (0,31) (0,2) (0,18) (0,5) (1,11) (1,12) (1,23) (1,8) (1,30) (1,7) (1,14) (1,27) (1,6) (1,17) (1,24) (1,4) (1,16) (1,29) (1,13) (1,19) (1,20) (1,26) (1,2) (1,18) (1,5) (2,12) (2,23) (2,8) (2,30) (2,7) (2,14) (2,22) (2,6) (2,17) (2,24) (2,4) (2,16) (2,29) (2,13) (2,19) (2,26) (2,18) (2,5) (3,28) (3,10) (3,15) (3,9) (4,11) (4,23) (4,8) (4,30) (4,7) (4,14) (4,27) (4,24) (4,16) (4,13) (4,19) (4,20) (4,31) (4,18) (4,5) (5,11) (5,12) (5,23) (5,8) (5,30) (5,7) (5,14) (5,27) (5,22) (5,17) (5,24) (5,29) (5,19) (5,20) (5,26) (5,31) (5,18) (6,11) (6,12) (6,23) (6,8) (6,30) (6,7) (6,14) (6,22) (6,17) (6,13) (6,19) (6,20) (6,26) (6,31) (6,18) (7,11) (7,23) (7,8) (7,30) (7,14) (7,27) (7,22) (7,24) (7,29) (7,13) (7,19) (7,20) (8,23) (8,30) (8,14) (8,22) (8,24) (8,16) (8,20) (8,26) (8,31) (8,18) (9,21) (9,25) (9,28) (10,21) (10,32) (10,25) (10,28) (10,15) (11,12) (11,30) (11,14) (11,27) (11,22) (11,17) (11,24) (11,16) (11,29) (11,13) (11,20) (11,26) (11,31) (11,18) (12,23) (12,30) (12,27) (12,22) (12,24) (12,29) (12,13) (12,20) (12,26) (12,31) (12,18) (13,23) (13,30) (13,14) (13,22) (13,17) (13,24) (13,19) (13,20) (13,26) (13,31) (13,18) (14,30) (14,27) (14,22) (14,24) (14,16) (14,29) (14,19) (14,20) (14,26) (14,31) (14,18) (15,21) (15,32) (15,25) (15,28) (16,23) (16,30) (16,22) (16,24) (16,29) (16,20) (16,26) (16,31) (16,18) (17,23) (17,30) (17,27) (17,22) (17,24) (17,29) (17,19) (17,26) (17,18) (18,23) (18,27) (18,24) (18,19) (18,20) (18,26) (19,30) (19,27) (19,29) (19,20) (19,26) (19,31) (20,30) (20,22) (20,24) (20,29) (20,26) (22,23) (22,27) (22,29) (22,31) (23,30) (23,26) (24,30) (24,27) (24,29) (24,26) (25,32) (25,28) (26,30) (26,27) (26,29) (27,30) (27,29) (28,32) (29,30) (29,31) (30,31)\nIs there a path between node 8 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph468-10_17", + "image": "data/connectivity/graph_visual/hard/graph468.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,6) (0,2) (0,22) (0,32) (0,27) (0,5) (0,14) (0,3) (0,21) (0,7) (0,25) (0,29) (0,9) (0,18) (0,19) (0,11) (0,31) (0,10) (0,8) (1,6) (1,2) (1,5) (1,3) (1,21) (1,7) (1,29) (1,9) (1,19) (1,10) (1,8) (2,32) (2,5) (2,14) (2,3) (2,7) (2,29) (2,9) (2,18) (2,23) (2,11) (2,10) (2,8) (3,22) (3,27) (3,5) (3,21) (3,7) (3,25) (3,29) (3,19) (3,23) (3,10) (4,20) (4,15) (4,28) (4,12) (4,30) (5,6) (5,22) (5,32) (5,27) (5,14) (5,21) (5,25) (5,29) (5,9) (5,18) (5,19) (5,11) (5,31) (5,10) (5,8) (6,24) (6,32) (6,27) (6,14) (6,21) (6,25) (6,29) (6,9) (6,18) (6,19) (6,23) (6,8) (7,22) (7,24) (7,27) (7,14) (7,21) (7,29) (7,9) (7,23) (7,11) (7,10) (7,8) (8,24) (8,32) (8,27) (8,14) (8,25) (8,29) (8,9) (8,18) (8,19) (8,23) (8,11) (8,31) (9,22) (9,24) (9,32) (9,27) (9,21) (9,29) (9,18) (9,19) (9,23) (9,11) (9,10) (10,22) (10,32) (10,27) (10,14) (10,21) (10,19) (10,23) (10,31) (11,22) (11,24) (11,32) (11,27) (11,14) (11,21) (11,25) (11,29) (11,18) (11,19) (11,31) (12,20) (12,15) (12,28) (12,30) (13,16) (13,17) (14,24) (14,32) (14,21) (14,25) (14,29) (14,19) (14,23) (14,31) (15,20) (15,28) (15,30) (16,17) (16,26) (17,26) (18,32) (18,27) (18,21) (18,25) (18,29) (18,23) (18,31) (19,22) (19,32) (19,27) (19,21) (19,25) (20,28) (20,30) (21,22) (21,24) (21,32) (21,27) (21,29) (21,23) (22,32) (22,25) (22,29) (22,23) (22,31) (23,24) (23,27) (23,31) (24,32) (24,27) (24,25) (24,31) (25,27) (25,29) (27,29) (27,31) (28,30) (29,32) (31,32)\nIs there a path between node 10 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph604-12_7", + "image": "data/connectivity/graph_visual/hard/graph604.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,16) (0,5) (0,18) (1,6) (1,12) (1,2) (1,34) (2,19) (2,11) (2,26) (2,7) (2,12) (2,33) (2,20) (3,15) (4,18) (5,18) (6,19) (6,26) (6,10) (6,23) (6,33) (6,21) (6,20) (7,11) (8,28) (9,14) (10,23) (11,22) (11,27) (11,31) (12,25) (12,33) (12,21) (13,15) (14,15) (14,32) (14,24) (15,29) (16,17) (17,18) (18,30) (19,22) (19,23) (19,21) (19,34) (19,20) (20,22) (20,33) (20,34) (21,26) (21,22) (21,34) (22,27) (22,31) (23,33) (24,32) (24,28) (25,27) (25,33) (27,34) (31,34) (33,34)\nIs there a path between node 12 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph230-13_19", + "image": "data/connectivity/graph_visual/hard/graph230.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,16) (0,8) (0,24) (0,3) (0,6) (0,21) (0,15) (0,29) (0,14) (0,1) (0,17) (0,12) (0,26) (1,16) (1,24) (1,3) (1,6) (1,21) (1,15) (1,20) (1,25) (1,29) (1,17) (1,12) (1,26) (2,22) (2,28) (2,4) (2,5) (2,19) (2,18) (2,9) (3,16) (3,24) (3,6) (3,21) (3,29) (3,11) (3,17) (3,12) (3,26) (4,22) (4,5) (4,19) (4,18) (4,23) (4,10) (4,13) (4,27) (5,22) (5,28) (5,18) (5,23) (5,9) (5,13) (5,27) (6,16) (6,8) (6,24) (6,21) (6,20) (6,11) (6,14) (6,17) (6,12) (6,26) (7,22) (7,28) (7,19) (7,18) (7,23) (7,9) (7,13) (7,27) (8,16) (8,24) (8,21) (8,20) (8,29) (8,11) (8,14) (8,12) (8,26) (9,23) (9,10) (9,13) (9,27) (10,22) (10,18) (10,23) (10,27) (11,16) (11,24) (11,21) (11,15) (11,20) (11,25) (11,14) (11,17) (11,12) (11,26) (12,16) (12,21) (12,15) (12,20) (12,25) (12,14) (12,17) (12,26) (13,19) (13,18) (14,16) (14,24) (14,21) (14,20) (14,25) (14,29) (14,17) (15,16) (15,24) (15,21) (15,20) (15,17) (15,26) (16,24) (16,20) (16,29) (16,17) (17,24) (17,21) (17,25) (17,29) (18,22) (18,28) (18,19) (18,23) (18,27) (19,22) (19,28) (19,23) (19,27) (20,21) (20,25) (20,29) (21,24) (21,25) (21,29) (21,26) (22,28) (22,23) (23,28) (23,27) (24,25) (24,29) (24,26) (25,29) (27,28)\nIs there a path between node 13 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph267-17_19", + "image": "data/connectivity/graph_visual/hard/graph267.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,3) (0,16) (0,21) (0,15) (1,18) (1,11) (1,22) (1,30) (1,12) (2,3) (2,25) (2,7) (3,17) (3,25) (3,19) (4,22) (4,30) (5,28) (7,16) (7,25) (7,14) (7,21) (7,19) (7,27) (8,9) (10,13) (10,30) (10,12) (10,26) (11,18) (11,30) (11,26) (12,29) (12,18) (12,30) (15,17) (15,25) (15,19) (17,25) (18,22) (18,26) (19,27) (20,28) (22,29) (24,26) (26,29)\nIs there a path between node 17 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph20-7_1", + "image": "data/connectivity/graph_visual/hard/graph20.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,5) (0,14) (0,23) (1,10) (1,6) (1,3) (1,22) (2,16) (2,12) (3,8) (3,14) (3,22) (4,21) (4,25) (6,7) (6,18) (6,14) (6,15) (6,22) (7,18) (7,22) (8,10) (8,23) (11,16) (11,21) (12,17) (12,21) (12,25) (13,20) (14,20) (14,22) (15,18) (16,21) (16,25) (17,21) (19,21) (20,23) (21,25)\nIs there a path between node 7 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph130-18_16", + "image": "data/connectivity/graph_visual/hard/graph130.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,27) (0,16) (0,21) (0,4) (0,6) (0,15) (0,5) (0,23) (0,26) (0,10) (0,14) (0,20) (0,19) (0,25) (0,13) (0,24) (1,16) (1,21) (1,4) (1,23) (1,26) (1,2) (1,14) (1,20) (1,19) (1,25) (1,22) (2,16) (2,3) (2,21) (2,4) (2,6) (2,15) (2,23) (2,26) (2,8) (2,10) (2,20) (2,19) (2,25) (2,22) (2,13) (2,24) (3,27) (3,16) (3,21) (3,15) (3,5) (3,23) (3,8) (3,14) (3,19) (3,25) (3,22) (3,13) (3,24) (4,27) (4,16) (4,21) (4,6) (4,5) (4,23) (4,26) (4,8) (4,20) (4,25) (4,13) (5,27) (5,16) (5,21) (5,6) (5,23) (5,8) (5,10) (5,14) (5,20) (5,19) (5,25) (5,22) (5,13) (5,24) (6,16) (6,21) (6,15) (6,23) (6,26) (6,10) (6,14) (6,20) (6,22) (6,13) (7,17) (7,9) (7,18) (7,12) (8,16) (8,21) (8,23) (8,26) (8,10) (8,14) (8,19) (8,25) (8,22) (8,24) (9,17) (9,12) (10,27) (10,16) (10,15) (10,26) (10,19) (10,25) (10,22) (10,13) (10,24) (11,17) (11,18) (11,12) (12,17) (12,18) (13,27) (13,16) (13,21) (13,15) (13,23) (13,14) (13,19) (13,22) (14,16) (14,21) (14,15) (14,23) (14,26) (14,19) (14,22) (15,27) (15,16) (15,21) (15,23) (15,26) (15,25) (15,22) (16,21) (16,23) (16,20) (16,19) (16,25) (16,22) (16,24) (17,18) (19,21) (19,23) (19,24) (20,27) (20,23) (20,26) (20,25) (20,22) (21,27) (21,23) (21,25) (21,22) (22,27) (22,23) (22,26) (22,25) (22,24) (23,27) (23,26) (23,24) (24,25) (25,26) (26,27)\nIs there a path between node 18 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph672-24_9", + "image": "data/connectivity/graph_visual/hard/graph672.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,15) (1,5) (1,31) (1,30) (1,18) (2,17) (2,25) (2,15) (2,7) (2,23) (2,24) (2,5) (2,13) (3,34) (3,8) (4,16) (4,12) (4,9) (4,33) (5,17) (5,7) (5,23) (5,20) (5,31) (5,13) (6,26) (6,11) (6,22) (6,9) (6,21) (7,14) (7,25) (7,20) (7,13) (8,26) (8,29) (8,11) (8,21) (9,26) (9,29) (9,21) (9,33) (10,26) (10,29) (10,22) (10,12) (12,22) (12,21) (13,28) (13,31) (13,19) (14,17) (14,15) (14,19) (15,17) (15,25) (15,28) (15,30) (15,19) (16,26) (17,28) (17,31) (17,19) (18,28) (18,20) (19,27) (19,20) (19,32) (20,30) (20,32) (21,34) (21,33) (24,31) (26,29) (26,34) (27,30) (28,31) (28,30) (29,34) (30,32)\nIs there a path between node 24 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph487-24_18", + "image": "data/connectivity/graph_visual/hard/graph487.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,8) (0,30) (0,9) (0,18) (0,2) (0,4) (0,20) (0,28) (0,1) (0,7) (0,16) (0,5) (0,17) (0,32) (0,26) (0,29) (0,21) (0,25) (0,11) (0,13) (0,31) (0,27) (1,8) (1,9) (1,18) (1,15) (1,4) (1,20) (1,28) (1,7) (1,16) (1,5) (1,32) (1,21) (1,25) (1,22) (1,11) (1,13) (1,31) (1,3) (1,27) (2,18) (2,15) (2,4) (2,20) (2,28) (2,7) (2,16) (2,23) (2,32) (2,26) (2,21) (2,25) (2,22) (2,12) (2,13) (2,31) (2,27) (3,8) (3,9) (3,18) (3,15) (3,4) (3,20) (3,7) (3,16) (3,23) (3,29) (3,21) (3,25) (3,22) (3,11) (3,27) (4,8) (4,30) (4,9) (4,18) (4,15) (4,7) (4,16) (4,5) (4,17) (4,26) (4,21) (4,25) (4,22) (4,12) (4,13) (4,31) (4,27) (5,30) (5,18) (5,15) (5,28) (5,7) (5,32) (5,26) (5,29) (5,21) (5,25) (5,22) (5,12) (5,11) (5,13) (5,31) (5,27) (6,24) (6,10) (6,19) (6,14) (7,9) (7,18) (7,15) (7,28) (7,16) (7,17) (7,23) (7,32) (7,21) (7,25) (7,22) (7,12) (7,31) (8,30) (8,9) (8,15) (8,28) (8,16) (8,17) (8,23) (8,26) (8,29) (8,21) (8,22) (8,11) (8,13) (8,27) (9,28) (9,17) (9,32) (9,26) (9,21) (9,25) (9,11) (9,31) (9,27) (10,24) (10,19) (10,14) (11,18) (11,15) (11,28) (11,16) (11,32) (11,21) (11,22) (11,13) (11,31) (11,27) (12,30) (12,18) (12,15) (12,32) (12,26) (12,21) (12,22) (12,13) (12,31) (13,18) (13,28) (13,17) (13,32) (13,26) (13,29) (13,21) (13,25) (13,22) (13,31) (13,27) (14,24) (14,19) (15,18) (15,20) (15,28) (15,17) (15,23) (15,32) (15,29) (15,25) (15,22) (15,31) (16,30) (16,18) (16,20) (16,28) (16,17) (16,26) (16,21) (16,31) (16,27) (17,30) (17,18) (17,20) (17,23) (17,32) (17,26) (17,29) (17,25) (17,31) (17,27) (18,30) (18,20) (18,28) (18,23) (18,32) (18,26) (18,29) (18,21) (18,25) (18,31) (18,27) (19,24) (20,30) (20,28) (20,32) (20,26) (20,29) (20,31) (20,27) (21,30) (21,23) (21,32) (21,29) (21,25) (21,27) (22,28) (22,26) (22,29) (22,25) (22,31) (22,27) (23,30) (23,32) (23,29) (23,25) (23,31) (23,27) (25,30) (25,28) (25,26) (25,31) (26,30) (26,28) (26,27) (27,30) (27,28) (27,32) (28,29) (28,31) (29,30) (29,32) (29,31) (30,32) (31,32)\nIs there a path between node 24 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph703-32_16", + "image": "data/connectivity/graph_visual/hard/graph703.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,20) (0,22) (0,9) (0,29) (0,7) (0,8) (1,3) (1,26) (1,2) (1,19) (1,6) (1,27) (1,18) (1,25) (1,17) (1,16) (1,31) (1,12) (1,21) (1,34) (2,23) (2,28) (2,19) (2,6) (2,5) (2,27) (2,24) (2,11) (2,18) (2,17) (2,33) (2,12) (2,4) (2,21) (3,26) (3,19) (3,27) (3,24) (3,11) (3,18) (3,25) (3,17) (3,16) (3,31) (3,12) (3,4) (3,21) (4,28) (4,5) (4,27) (4,24) (4,18) (4,25) (4,17) (4,34) (5,23) (5,28) (5,26) (5,19) (5,6) (5,25) (5,17) (5,16) (5,31) (5,34) (6,28) (6,19) (6,24) (6,11) (6,18) (6,17) (6,31) (6,12) (6,21) (7,32) (7,22) (7,9) (7,29) (8,32) (8,20) (8,9) (9,20) (10,13) (10,15) (10,14) (11,28) (11,19) (11,27) (11,18) (11,17) (11,16) (11,31) (11,12) (12,28) (12,19) (12,27) (12,24) (12,18) (12,25) (12,17) (12,31) (12,34) (13,30) (13,15) (13,14) (14,30) (14,15) (16,23) (16,28) (16,26) (16,24) (16,25) (16,33) (16,31) (16,21) (16,34) (17,23) (17,26) (17,19) (17,27) (17,24) (17,18) (17,25) (17,33) (17,31) (17,21) (17,34) (18,23) (18,28) (18,26) (18,27) (18,24) (18,25) (18,33) (18,34) (19,23) (19,28) (19,27) (19,24) (19,25) (19,33) (19,21) (19,34) (20,29) (21,23) (21,27) (21,25) (21,33) (21,31) (22,32) (22,29) (23,28) (23,26) (23,27) (23,24) (23,25) (23,33) (23,31) (23,34) (24,26) (24,25) (24,33) (24,31) (25,26) (25,34) (26,28) (26,33) (26,31) (26,34) (27,28) (27,33) (27,31) (27,34) (28,33) (28,31) (28,34) (29,32) (33,34)\nIs there a path between node 32 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph175-22_0", + "image": "data/connectivity/graph_visual/hard/graph175.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,5) (0,7) (0,6) (0,26) (0,24) (0,15) (0,22) (0,18) (1,2) (1,28) (1,3) (1,13) (1,9) (1,8) (1,4) (2,27) (2,11) (2,14) (2,17) (2,16) (2,28) (2,3) (2,9) (2,4) (3,27) (3,11) (3,25) (3,28) (3,13) (3,9) (3,8) (3,23) (3,12) (4,10) (4,11) (4,25) (4,14) (4,17) (4,16) (4,28) (4,13) (4,23) (5,21) (5,6) (5,26) (5,20) (5,19) (5,15) (5,22) (5,18) (6,7) (6,24) (6,20) (6,19) (6,22) (6,18) (7,21) (7,26) (7,20) (7,15) (8,27) (8,10) (8,11) (8,25) (8,14) (8,16) (8,23) (8,12) (9,27) (9,16) (9,28) (9,13) (9,23) (9,12) (10,27) (10,11) (10,25) (10,14) (10,17) (10,28) (10,13) (10,23) (10,12) (11,14) (11,16) (11,13) (11,12) (12,27) (12,14) (12,17) (12,28) (12,13) (13,27) (13,25) (13,14) (13,17) (13,16) (13,28) (13,23) (14,27) (14,17) (14,16) (14,28) (14,23) (15,21) (15,26) (15,24) (15,20) (15,22) (16,27) (16,25) (16,17) (16,28) (16,23) (17,27) (17,28) (18,21) (18,26) (18,20) (18,19) (19,26) (20,21) (20,26) (20,24) (21,26) (21,24) (22,26) (22,24) (23,27) (23,25) (25,28) (27,28)\nIs there a path between node 22 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph571-20_12", + "image": "data/connectivity/graph_visual/hard/graph571.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,7) (0,31) (0,5) (0,13) (0,33) (0,4) (0,8) (0,16) (1,18) (1,29) (1,2) (2,29) (2,28) (3,20) (3,26) (3,25) (4,7) (4,11) (4,10) (4,31) (4,22) (4,24) (4,16) (5,11) (5,13) (5,17) (6,26) (6,29) (7,10) (7,32) (7,33) (7,8) (7,24) (8,14) (8,10) (8,13) (8,33) (9,12) (9,21) (10,11) (10,24) (10,17) (11,31) (11,13) (11,16) (11,17) (12,30) (13,14) (13,32) (14,31) (14,15) (15,32) (15,24) (18,26) (18,29) (18,28) (20,27) (20,28) (21,23) (22,31) (22,33) (25,29) (26,27) (27,29) (27,28) (28,29) (31,32) (31,33) (32,33)\nIs there a path between node 20 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph559-6_13", + "image": "data/connectivity/graph_visual/hard/graph559.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,1) (0,29) (0,8) (0,19) (0,26) (0,7) (0,10) (0,24) (1,8) (1,5) (1,19) (2,11) (2,29) (2,8) (2,6) (2,5) (2,19) (2,26) (2,7) (2,27) (2,14) (2,24) (3,33) (3,32) (4,18) (5,29) (5,10) (6,8) (6,10) (7,29) (7,10) (7,14) (8,26) (9,33) (9,17) (9,30) (9,20) (10,27) (11,24) (12,18) (12,16) (12,20) (13,22) (13,31) (13,15) (14,26) (15,31) (16,17) (16,32) (16,30) (16,20) (17,32) (19,24) (20,33) (21,32) (21,30) (22,23) (23,25) (27,29) (28,31)\nIs there a path between node 6 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph144-6_1", + "image": "data/connectivity/graph_visual/hard/graph144.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,17) (0,2) (0,12) (0,1) (0,8) (0,10) (0,28) (1,3) (1,7) (1,18) (1,6) (1,15) (1,23) (2,3) (2,10) (2,18) (2,5) (2,28) (2,9) (3,16) (3,12) (3,7) (3,8) (3,19) (3,21) (3,24) (3,6) (3,20) (5,16) (5,17) (5,8) (5,14) (5,24) (5,6) (5,15) (5,9) (6,12) (6,25) (6,10) (6,21) (6,24) (6,23) (7,16) (7,17) (7,12) (7,25) (7,26) (7,10) (7,21) (7,24) (8,17) (8,27) (8,25) (8,10) (8,19) (8,21) (8,23) (9,17) (9,27) (9,12) (9,19) (9,18) (9,24) (9,20) (9,28) (9,15) (10,16) (10,27) (10,18) (10,13) (10,23) (12,17) (12,25) (12,26) (12,19) (12,20) (13,16) (13,27) (13,26) (13,21) (13,18) (13,24) (14,26) (15,18) (16,18) (16,24) (16,28) (17,26) (17,21) (17,18) (17,23) (18,26) (18,21) (18,24) (18,20) (19,26) (19,24) (19,20) (20,21) (20,24) (20,28) (20,23) (21,25) (23,25) (23,24) (24,27) (24,28) (25,26) (26,28)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph581-22_15", + "image": "data/connectivity/graph_visual/hard/graph581.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,28) (0,6) (0,33) (0,2) (0,27) (0,5) (0,13) (0,17) (0,16) (0,21) (0,29) (0,15) (0,32) (0,8) (1,31) (1,7) (1,26) (1,30) (1,14) (1,11) (1,19) (1,22) (1,9) (1,24) (1,3) (1,4) (1,10) (2,28) (2,6) (2,33) (2,27) (2,5) (2,13) (2,20) (2,16) (2,25) (2,21) (2,29) (2,8) (3,23) (3,31) (3,7) (3,30) (3,12) (3,14) (3,11) (3,19) (3,22) (3,18) (3,9) (3,24) (3,4) (3,10) (4,23) (4,31) (4,26) (4,30) (4,12) (4,14) (4,19) (4,18) (4,9) (5,6) (5,33) (5,27) (5,13) (5,20) (5,16) (5,25) (5,21) (5,29) (5,8) (6,17) (6,16) (6,29) (6,15) (6,32) (6,8) (7,31) (7,26) (7,30) (7,19) (7,22) (7,18) (7,9) (7,24) (7,10) (8,27) (8,17) (8,20) (8,16) (8,25) (8,15) (9,31) (9,26) (9,30) (9,12) (9,14) (9,19) (9,22) (9,24) (9,10) (10,23) (10,31) (10,30) (10,14) (10,11) (10,24) (11,23) (11,26) (11,30) (11,19) (11,24) (12,23) (12,26) (12,30) (12,14) (12,19) (12,22) (12,24) (13,27) (13,17) (13,20) (13,16) (13,25) (13,21) (13,29) (13,32) (14,23) (14,26) (14,30) (14,19) (14,18) (14,24) (15,33) (15,27) (15,17) (15,25) (15,21) (15,29) (15,32) (16,28) (16,33) (16,17) (16,20) (16,25) (16,29) (16,32) (17,27) (17,20) (17,25) (17,21) (17,29) (17,32) (18,23) (18,26) (18,30) (18,22) (19,31) (19,26) (19,30) (19,24) (20,33) (20,25) (20,29) (21,28) (21,27) (21,25) (21,32) (22,31) (22,26) (22,30) (23,26) (23,30) (23,24) (24,26) (24,30) (25,28) (25,33) (25,27) (25,29) (26,30) (27,28) (27,33) (27,29) (28,29) (28,32) (29,33) (30,31)\nIs there a path between node 22 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph20-4_7", + "image": "data/connectivity/graph_visual/hard/graph20.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,5) (0,14) (0,23) (1,10) (1,6) (1,3) (1,22) (2,16) (2,12) (3,8) (3,14) (3,22) (4,21) (4,25) (6,7) (6,18) (6,14) (6,15) (6,22) (7,18) (7,22) (8,10) (8,23) (11,16) (11,21) (12,17) (12,21) (12,25) (13,20) (14,20) (14,22) (15,18) (16,21) (16,25) (17,21) (19,21) (20,23) (21,25)\nIs there a path between node 4 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph125-19_24", + "image": "data/connectivity/graph_visual/hard/graph125.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,4) (0,8) (0,14) (0,20) (0,23) (0,16) (0,3) (0,11) (0,12) (0,15) (0,13) (0,25) (1,22) (1,6) (1,10) (1,7) (2,26) (2,19) (2,9) (2,24) (3,4) (3,18) (3,8) (3,20) (3,11) (3,15) (3,25) (4,18) (4,8) (4,20) (4,23) (4,16) (4,11) (4,15) (4,25) (5,22) (6,22) (6,17) (6,7) (7,22) (7,10) (8,18) (8,14) (8,20) (8,23) (8,16) (8,12) (8,15) (8,13) (8,25) (9,21) (9,27) (9,26) (9,24) (11,20) (11,15) (11,25) (12,14) (12,20) (12,23) (12,15) (12,13) (12,25) (13,18) (13,14) (13,20) (13,23) (13,16) (13,25) (14,18) (14,20) (14,16) (14,15) (14,25) (15,18) (15,20) (15,23) (15,25) (16,20) (16,23) (17,22) (18,20) (18,25) (19,21) (19,27) (19,26) (19,24) (20,23) (20,25) (21,27) (21,24) (24,27) (24,26)\nIs there a path between node 19 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph1-18_23", + "image": "data/connectivity/graph_visual/hard/graph1.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,4) (0,8) (0,2) (0,20) (0,16) (0,14) (0,15) (0,7) (1,18) (1,24) (1,22) (1,5) (1,19) (1,11) (1,17) (2,6) (2,4) (2,23) (2,8) (2,20) (2,16) (2,21) (2,14) (2,15) (2,10) (3,6) (3,4) (3,23) (3,8) (3,16) (3,14) (3,25) (3,15) (3,7) (4,6) (4,23) (4,8) (4,20) (4,16) (4,21) (4,14) (4,15) (4,10) (4,7) (5,18) (5,24) (5,22) (5,13) (5,9) (5,11) (5,12) (6,23) (6,8) (6,20) (6,16) (6,14) (6,25) (6,15) (7,23) (7,20) (7,16) (7,21) (7,14) (7,25) (7,15) (7,10) (8,20) (8,16) (8,14) (8,25) (8,15) (9,18) (9,24) (9,22) (9,19) (9,11) (9,17) (9,12) (10,23) (10,20) (10,16) (10,21) (10,14) (10,25) (11,22) (11,19) (11,17) (11,12) (12,18) (12,13) (12,19) (13,18) (13,24) (13,22) (13,17) (14,23) (14,20) (14,16) (14,25) (15,20) (15,16) (15,21) (15,25) (16,23) (16,20) (16,25) (17,18) (17,22) (17,19) (18,24) (18,22) (18,19) (19,24) (19,22) (20,21) (20,25) (21,23) (21,25) (22,24) (23,25)\nIs there a path between node 18 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph686-3_10", + "image": "data/connectivity/graph_visual/hard/graph686.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,24) (0,27) (0,32) (0,33) (0,29) (0,9) (0,21) (0,5) (0,31) (0,14) (0,12) (0,26) (0,11) (0,17) (0,16) (0,34) (0,23) (0,30) (0,7) (0,6) (1,24) (1,32) (1,4) (1,20) (1,9) (1,21) (1,22) (1,12) (1,26) (1,25) (1,11) (1,17) (1,34) (1,23) (1,7) (1,6) (1,8) (2,27) (2,4) (2,29) (2,9) (2,21) (2,5) (2,15) (2,31) (2,22) (2,12) (2,26) (2,25) (2,11) (2,17) (2,18) (2,34) (2,23) (2,30) (3,24) (3,27) (3,32) (3,33) (3,4) (3,20) (3,5) (3,15) (3,31) (3,14) (3,22) (3,25) (3,11) (3,17) (3,16) (3,18) (3,34) (3,30) (3,7) (3,28) (3,6) (3,8) (4,24) (4,27) (4,33) (4,29) (4,20) (4,9) (4,21) (4,5) (4,15) (4,31) (4,14) (4,22) (4,12) (4,25) (4,17) (4,16) (4,18) (4,30) (4,28) (4,6) (4,8) (5,27) (5,29) (5,20) (5,21) (5,15) (5,31) (5,14) (5,12) (5,26) (5,25) (5,11) (5,17) (5,16) (5,30) (5,7) (5,28) (5,8) (6,24) (6,32) (6,33) (6,29) (6,20) (6,9) (6,21) (6,15) (6,14) (6,22) (6,12) (6,26) (6,25) (6,11) (6,16) (6,18) (6,7) (6,28) (6,8) (7,24) (7,27) (7,33) (7,9) (7,21) (7,15) (7,31) (7,14) (7,22) (7,12) (7,26) (7,25) (7,18) (7,23) (7,28) (7,8) (8,24) (8,32) (8,20) (8,9) (8,15) (8,31) (8,14) (8,22) (8,12) (8,17) (8,16) (8,34) (8,23) (8,30) (8,28) (9,27) (9,32) (9,33) (9,29) (9,20) (9,21) (9,31) (9,14) (9,12) (9,26) (9,16) (9,34) (9,23) (9,30) (9,28) (10,19) (10,13) (11,24) (11,32) (11,29) (11,20) (11,21) (11,15) (11,14) (11,22) (11,12) (11,26) (11,17) (11,18) (11,34) (11,23) (11,30) (11,28) (12,24) (12,27) (12,32) (12,33) (12,20) (12,21) (12,31) (12,22) (12,26) (12,25) (12,17) (12,16) (12,18) (12,34) (12,30) (12,28) (13,19) (14,32) (14,29) (14,21) (14,31) (14,26) (14,25) (14,17) (14,16) (14,18) (14,23) (14,30) (15,24) (15,27) (15,32) (15,33) (15,20) (15,31) (15,22) (15,26) (15,25) (15,17) (15,16) (15,34) (15,23) (15,30) (16,27) (16,33) (16,29) (16,20) (16,21) (16,31) (16,22) (16,26) (16,25) (16,17) (16,18) (16,34) (16,23) (16,30) (17,24) (17,32) (17,33) (17,29) (17,20) (17,31) (17,22) (17,26) (17,25) (17,34) (17,23) (17,28) (18,24) (18,32) (18,33) (18,20) (18,31) (18,22) (18,26) (18,34) (18,23) (18,28) (20,24) (20,33) (20,29) (20,31) (20,22) (20,26) (20,34) (20,23) (20,30) (20,28) (21,24) (21,32) (21,26) (21,25) (21,34) (21,23) (21,30) (21,28) (22,24) (22,32) (22,33) (22,29) (22,31) (22,26) (22,25) (22,34) (22,28) (23,27) (23,32) (23,33) (23,29) (23,31) (23,34) (23,30) (23,28) (24,27) (24,33) (24,29) (24,31) (24,26) (24,25) (24,34) (24,30) (24,28) (25,27) (25,32) (25,33) (25,29) (25,26) (25,34) (25,30) (25,28) (26,27) (26,32) (26,33) (26,29) (26,31) (26,28) (27,32) (27,33) (27,29) (27,31) (27,30) (28,32) (28,31) (28,34) (28,30) (29,32) (29,33) (29,34) (30,32) (30,31) (30,34) (31,32) (31,33) (32,33) (32,34) (33,34)\nIs there a path between node 3 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph99-3_27", + "image": "data/connectivity/graph_visual/hard/graph99.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,1) (0,13) (0,22) (0,23) (0,9) (0,18) (0,7) (0,2) (0,15) (0,10) (0,16) (0,21) (0,4) (0,25) (0,27) (1,8) (1,13) (1,14) (1,22) (1,6) (1,24) (1,9) (1,18) (1,7) (1,2) (1,15) (1,26) (1,10) (1,12) (1,16) (1,11) (1,4) (1,5) (2,13) (2,14) (2,23) (2,6) (2,24) (2,9) (2,12) (2,16) (2,21) (2,11) (2,4) (2,25) (3,19) (4,8) (4,13) (4,14) (4,22) (4,6) (4,24) (4,18) (4,7) (4,15) (4,20) (4,16) (4,21) (4,11) (4,17) (4,27) (5,8) (5,13) (5,14) (5,23) (5,6) (5,9) (5,18) (5,7) (5,15) (5,26) (5,20) (5,12) (5,16) (5,21) (6,8) (6,13) (6,14) (6,22) (6,24) (6,9) (6,18) (6,7) (6,15) (6,26) (6,20) (6,10) (6,25) (6,17) (6,27) (7,8) (7,13) (7,14) (7,22) (7,24) (7,9) (7,15) (7,26) (7,10) (7,11) (7,25) (7,17) (8,13) (8,14) (8,22) (8,23) (8,24) (8,9) (8,26) (8,10) (8,12) (8,11) (8,25) (8,17) (9,14) (9,22) (9,23) (9,24) (9,18) (9,15) (9,26) (9,16) (9,21) (9,11) (9,25) (10,23) (10,24) (10,18) (10,15) (10,12) (10,21) (10,25) (10,17) (10,27) (11,14) (11,22) (11,15) (11,26) (11,20) (11,12) (11,21) (11,25) (11,17) (11,27) (12,13) (12,14) (12,22) (12,23) (12,24) (12,18) (12,15) (12,26) (12,16) (12,21) (12,17) (13,14) (13,22) (13,24) (13,26) (13,20) (13,16) (13,25) (13,17) (13,27) (14,22) (14,18) (14,15) (14,26) (14,20) (14,16) (14,25) (15,23) (15,24) (15,18) (15,26) (15,20) (15,16) (15,21) (15,25) (15,17) (15,27) (16,22) (16,26) (16,20) (16,21) (16,25) (16,17) (16,27) (17,22) (17,23) (17,25) (18,22) (18,23) (18,24) (18,26) (18,21) (18,25) (20,26) (20,21) (21,23) (21,26) (21,25) (21,27) (22,23) (22,26) (22,27) (23,24) (23,27) (24,26) (24,27) (25,27) (26,27)\nIs there a path between node 3 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph205-8_25", + "image": "data/connectivity/graph_visual/hard/graph205.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,21) (0,12) (0,22) (0,29) (0,26) (0,4) (0,28) (1,22) (1,16) (1,19) (1,23) (1,25) (2,12) (2,22) (2,29) (2,5) (2,8) (3,15) (3,10) (3,18) (3,21) (3,12) (3,22) (3,26) (3,14) (3,27) (3,28) (3,8) (4,10) (4,20) (4,16) (4,26) (4,27) (4,28) (4,5) (5,15) (5,10) (5,12) (5,20) (5,16) (5,7) (5,14) (5,27) (5,17) (7,29) (7,16) (7,23) (7,28) (8,15) (8,23) (8,26) (8,11) (8,17) (10,18) (10,13) (10,22) (10,16) (11,21) (11,12) (11,29) (11,16) (11,14) (12,21) (12,20) (12,23) (12,17) (13,29) (13,20) (14,18) (14,21) (14,23) (14,26) (14,27) (14,17) (15,29) (15,19) (15,23) (15,26) (15,25) (16,18) (16,21) (16,29) (16,27) (16,25) (16,28) (16,17) (17,26) (18,21) (18,20) (18,19) (18,23) (19,26) (20,23) (20,25) (21,22) (22,23) (22,27) (22,28) (23,29) (23,26) (23,27) (23,28) (25,29) (25,27)\nIs there a path between node 8 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph649-11_3", + "image": "data/connectivity/graph_visual/hard/graph649.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,2) (0,15) (0,11) (0,22) (0,25) (0,10) (0,3) (0,6) (0,34) (0,12) (0,33) (0,27) (0,26) (0,31) (0,7) (0,19) (0,23) (0,5) (0,9) (0,28) (0,24) (1,17) (1,13) (1,4) (2,8) (2,15) (2,11) (2,22) (2,25) (2,3) (2,34) (2,33) (2,27) (2,26) (2,31) (2,7) (2,19) (2,23) (2,5) (2,32) (2,20) (2,28) (2,24) (3,8) (3,22) (3,25) (3,10) (3,6) (3,34) (3,33) (3,14) (3,26) (3,31) (3,7) (3,19) (3,23) (3,32) (3,16) (3,9) (3,30) (3,29) (3,24) (4,17) (4,13) (5,8) (5,15) (5,11) (5,22) (5,25) (5,6) (5,34) (5,33) (5,14) (5,18) (5,19) (5,23) (5,21) (5,32) (5,16) (5,20) (5,9) (5,30) (5,29) (6,8) (6,11) (6,22) (6,10) (6,34) (6,33) (6,27) (6,14) (6,31) (6,7) (6,21) (6,32) (6,16) (6,20) (6,29) (6,28) (6,24) (7,8) (7,11) (7,22) (7,10) (7,33) (7,27) (7,14) (7,18) (7,31) (7,19) (7,23) (7,21) (7,16) (7,9) (7,30) (7,29) (7,28) (7,24) (8,11) (8,22) (8,25) (8,10) (8,34) (8,33) (8,27) (8,14) (8,26) (8,31) (8,19) (8,32) (8,16) (8,20) (8,30) (8,29) (9,15) (9,22) (9,25) (9,34) (9,33) (9,27) (9,14) (9,18) (9,26) (9,31) (9,19) (9,23) (9,32) (9,16) (9,30) (9,29) (9,28) (9,24) (10,15) (10,11) (10,22) (10,34) (10,27) (10,14) (10,18) (10,19) (10,21) (10,32) (10,16) (10,20) (10,30) (10,29) (10,28) (11,15) (11,22) (11,12) (11,33) (11,27) (11,14) (11,18) (11,26) (11,19) (11,32) (11,16) (11,20) (11,29) (11,24) (12,25) (12,33) (12,27) (12,14) (12,18) (12,23) (12,21) (12,32) (12,16) (12,20) (12,29) (12,28) (12,24) (14,22) (14,34) (14,33) (14,27) (14,18) (14,26) (14,31) (14,19) (14,21) (14,32) (14,16) (14,28) (14,24) (15,22) (15,34) (15,33) (15,27) (15,26) (15,19) (15,23) (15,21) (15,32) (15,20) (15,30) (15,24) (16,22) (16,34) (16,33) (16,27) (16,31) (16,19) (16,23) (16,32) (16,30) (16,28) (16,24) (18,22) (18,25) (18,27) (18,26) (18,19) (18,23) (18,21) (18,32) (18,29) (18,28) (18,24) (19,25) (19,34) (19,33) (19,27) (19,26) (19,21) (19,32) (19,20) (19,30) (19,29) (19,28) (19,24) (20,25) (20,34) (20,33) (20,27) (20,31) (20,32) (20,30) (20,29) (20,28) (21,22) (21,25) (21,33) (21,27) (21,31) (21,23) (21,32) (21,30) (21,28) (22,25) (22,34) (22,33) (22,27) (22,23) (22,32) (22,29) (22,24) (23,25) (23,33) (23,26) (23,31) (23,30) (23,28) (24,25) (24,34) (24,33) (24,26) (24,32) (24,30) (24,29) (24,28) (25,34) (25,27) (25,26) (25,32) (25,29) (26,34) (26,33) (26,27) (26,31) (26,32) (26,30) (26,29) (27,34) (27,33) (27,31) (27,32) (27,29) (28,34) (28,32) (28,29) (29,33) (29,31) (29,32) (30,34) (30,32) (31,34) (31,32) (32,33) (33,34)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph402-29_11", + "image": "data/connectivity/graph_visual/hard/graph402.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,32) (0,31) (0,24) (0,30) (0,3) (0,16) (0,5) (0,1) (0,23) (1,14) (1,32) (1,17) (1,20) (1,31) (1,27) (1,24) (1,3) (1,16) (1,7) (1,5) (1,23) (2,8) (2,11) (2,28) (2,19) (2,22) (2,29) (2,26) (2,18) (3,14) (3,32) (3,31) (3,27) (3,24) (3,30) (3,10) (3,16) (3,7) (3,5) (3,23) (4,25) (4,11) (4,28) (4,21) (4,29) (4,18) (4,15) (5,14) (5,17) (5,31) (5,27) (5,30) (5,10) (5,7) (5,23) (6,25) (6,8) (6,11) (6,28) (6,19) (6,21) (6,29) (6,26) (6,15) (7,32) (7,17) (7,30) (7,10) (8,11) (8,28) (8,19) (8,22) (8,21) (8,29) (8,18) (8,15) (9,12) (10,14) (10,32) (10,20) (10,27) (10,24) (10,30) (10,16) (11,25) (11,28) (11,21) (11,26) (11,18) (12,13) (14,32) (14,17) (14,20) (14,31) (14,24) (14,16) (14,23) (15,28) (15,19) (15,22) (15,29) (15,18) (16,20) (16,31) (16,27) (16,24) (16,30) (16,23) (17,32) (17,20) (17,27) (17,24) (17,30) (17,23) (18,25) (18,22) (19,25) (19,28) (19,22) (19,26) (20,27) (20,24) (20,23) (21,28) (21,22) (22,25) (22,28) (22,29) (23,32) (23,27) (23,24) (24,32) (24,31) (24,27) (24,30) (25,28) (25,29) (25,26) (26,28) (27,32) (27,31) (28,29) (30,32) (30,31)\nIs there a path between node 29 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph274-27_21", + "image": "data/connectivity/graph_visual/hard/graph274.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,27) (0,3) (0,14) (0,23) (0,10) (0,25) (1,22) (1,28) (1,8) (1,30) (1,2) (1,4) (1,21) (1,29) (1,9) (2,22) (2,28) (2,8) (2,30) (2,4) (2,9) (3,27) (3,6) (3,14) (3,15) (3,7) (3,5) (3,20) (3,10) (3,25) (4,28) (4,30) (4,21) (4,29) (4,9) (4,13) (5,27) (5,6) (5,15) (5,7) (5,23) (5,20) (5,10) (6,27) (6,14) (6,15) (6,23) (6,20) (6,10) (7,27) (7,14) (7,15) (7,10) (7,25) (8,22) (8,30) (8,21) (8,9) (9,22) (9,28) (9,30) (9,29) (9,13) (10,27) (10,23) (10,20) (10,25) (11,24) (11,19) (11,26) (11,18) (11,12) (11,17) (11,16) (12,19) (12,26) (12,18) (12,17) (12,16) (13,22) (13,28) (13,30) (13,21) (13,29) (14,27) (14,15) (14,23) (14,25) (15,27) (15,23) (15,20) (16,24) (16,26) (16,17) (17,24) (17,19) (17,26) (17,18) (18,26) (19,24) (20,27) (20,23) (20,25) (21,22) (21,28) (22,28) (22,30) (22,29) (23,27) (24,26) (25,27) (28,30) (28,29)\nIs there a path between node 27 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph530-16_5", + "image": "data/connectivity/graph_visual/hard/graph530.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,19) (0,4) (1,23) (1,7) (1,18) (1,24) (1,32) (1,31) (1,21) (1,27) (1,11) (1,6) (1,29) (1,17) (1,20) (2,23) (2,7) (2,18) (2,33) (2,24) (2,31) (2,21) (2,8) (2,27) (2,11) (2,29) (2,17) (2,26) (3,9) (3,22) (3,13) (3,5) (3,30) (3,28) (3,16) (3,14) (3,15) (4,19) (4,10) (5,9) (5,22) (5,13) (5,28) (5,16) (5,14) (6,18) (6,32) (6,25) (6,21) (6,8) (6,11) (6,17) (6,20) (6,26) (7,18) (7,33) (7,24) (7,32) (7,25) (7,31) (7,21) (7,17) (7,20) (7,26) (8,18) (8,33) (8,32) (8,25) (8,31) (8,27) (8,11) (8,29) (8,20) (8,26) (9,22) (9,13) (9,30) (9,28) (9,14) (9,15) (10,19) (10,12) (11,18) (11,33) (11,24) (11,25) (11,31) (11,27) (11,29) (11,26) (12,19) (13,28) (13,15) (14,30) (14,28) (14,16) (14,15) (15,22) (15,30) (15,16) (16,22) (17,23) (17,18) (17,33) (17,25) (17,31) (17,21) (17,27) (17,29) (17,20) (17,26) (18,23) (18,32) (18,25) (18,21) (18,29) (18,20) (18,26) (20,23) (20,33) (20,32) (20,25) (20,31) (20,21) (20,27) (20,29) (20,26) (21,23) (21,33) (21,24) (21,25) (21,29) (23,33) (23,24) (23,25) (23,31) (23,27) (23,29) (23,26) (24,33) (24,32) (24,25) (24,27) (24,29) (24,26) (25,32) (25,31) (25,27) (25,29) (25,26) (26,33) (26,31) (26,27) (27,31) (27,29) (28,30) (31,32) (32,33)\nIs there a path between node 16 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph618-6_21", + "image": "data/connectivity/graph_visual/hard/graph618.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,34) (0,19) (0,17) (0,16) (0,31) (0,2) (0,7) (0,25) (0,22) (0,14) (1,28) (1,19) (1,16) (1,31) (1,8) (1,2) (1,7) (1,25) (1,14) (1,15) (2,28) (2,19) (2,17) (2,3) (2,31) (2,8) (2,7) (2,25) (2,20) (2,22) (2,14) (3,34) (3,19) (3,17) (3,16) (3,31) (3,7) (3,25) (3,22) (3,14) (4,18) (4,10) (4,24) (4,11) (4,6) (4,12) (4,26) (4,27) (4,13) (4,30) (4,21) (4,29) (5,18) (5,9) (5,11) (5,6) (5,26) (5,27) (5,30) (5,29) (6,18) (6,9) (6,24) (6,33) (6,12) (6,23) (6,27) (6,30) (7,34) (7,19) (7,16) (7,31) (7,8) (7,20) (7,14) (7,15) (8,28) (8,17) (8,16) (8,31) (8,25) (8,15) (9,18) (9,10) (9,24) (9,11) (9,33) (9,12) (9,32) (9,23) (9,13) (9,30) (9,29) (10,18) (10,24) (10,11) (10,33) (10,12) (10,32) (10,13) (10,30) (10,21) (10,29) (11,18) (11,12) (11,32) (11,23) (11,26) (11,27) (11,13) (11,30) (11,21) (12,18) (12,24) (12,33) (12,32) (12,23) (12,26) (12,27) (12,13) (12,21) (12,29) (13,18) (13,24) (13,33) (13,32) (13,23) (13,26) (13,27) (13,29) (14,34) (14,28) (14,19) (14,25) (14,22) (14,15) (15,34) (15,28) (15,19) (15,17) (15,16) (15,25) (15,20) (16,28) (16,31) (16,25) (16,22) (17,28) (17,19) (17,31) (17,25) (17,20) (17,22) (18,33) (18,32) (18,23) (18,26) (18,27) (19,34) (19,31) (19,22) (20,34) (20,31) (20,25) (20,22) (21,24) (21,33) (21,32) (21,27) (21,30) (21,29) (22,28) (22,31) (22,25) (23,24) (23,33) (23,32) (23,26) (23,27) (23,30) (24,32) (24,27) (24,30) (24,29) (25,28) (26,32) (26,27) (26,29) (28,34) (28,31) (29,32) (29,30) (30,33) (30,32) (31,34) (32,33)\nIs there a path between node 6 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph22-0_21", + "image": "data/connectivity/graph_visual/hard/graph22.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,19) (0,16) (1,3) (1,4) (1,19) (1,16) (1,10) (2,17) (2,7) (2,9) (2,23) (2,5) (2,18) (3,19) (3,6) (4,14) (5,24) (5,15) (8,13) (8,20) (8,25) (8,23) (8,15) (8,12) (9,17) (9,22) (9,23) (9,21) (11,13) (11,24) (11,22) (11,25) (11,15) (12,13) (12,17) (12,22) (12,18) (13,24) (15,24) (15,17) (15,22) (15,20) (15,18) (15,21) (17,22) (18,22) (20,22) (21,23) (22,24) (24,25)\nIs there a path between node 0 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph453-16_4", + "image": "data/connectivity/graph_visual/hard/graph453.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,18) (0,26) (0,7) (0,3) (0,13) (0,11) (0,19) (1,8) (1,12) (1,23) (1,24) (1,15) (1,6) (2,4) (2,15) (2,6) (3,28) (3,11) (3,19) (4,8) (4,5) (4,15) (4,6) (5,32) (5,8) (5,30) (5,27) (5,12) (5,23) (6,32) (6,23) (7,31) (7,19) (8,23) (8,15) (9,22) (10,25) (10,13) (10,11) (11,14) (11,26) (12,29) (13,28) (13,31) (13,19) (14,18) (15,29) (15,27) (15,24) (16,18) (18,28) (19,26) (23,30) (24,27) (25,28) (26,28)\nIs there a path between node 16 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph181-11_0", + "image": "data/connectivity/graph_visual/hard/graph181.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,18) (1,25) (1,22) (1,15) (1,20) (1,19) (1,11) (1,2) (1,23) (1,24) (2,25) (2,22) (2,15) (2,3) (2,11) (2,7) (2,6) (2,14) (2,24) (3,22) (3,16) (3,15) (3,19) (3,7) (3,23) (3,6) (3,14) (4,21) (4,9) (4,28) (4,8) (4,26) (4,17) (5,9) (5,12) (5,27) (5,26) (5,17) (6,25) (6,16) (6,15) (6,20) (6,19) (6,7) (6,14) (6,24) (7,25) (7,22) (7,16) (7,20) (7,19) (7,11) (7,23) (7,24) (8,21) (8,9) (8,12) (8,26) (8,17) (9,21) (9,10) (9,28) (9,12) (9,27) (9,26) (9,17) (10,21) (10,28) (10,12) (10,26) (10,17) (11,22) (11,16) (11,15) (11,20) (11,19) (11,23) (11,14) (11,24) (12,27) (12,26) (12,17) (13,18) (14,16) (14,15) (14,20) (14,24) (15,22) (15,16) (15,20) (15,23) (15,24) (16,25) (16,22) (16,20) (16,19) (16,23) (16,24) (17,21) (17,27) (17,26) (19,25) (19,22) (19,23) (19,24) (20,22) (20,23) (20,24) (21,28) (21,27) (21,26) (22,25) (23,25) (23,24) (24,25) (26,27)\nIs there a path between node 11 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph517-17_14", + "image": "data/connectivity/graph_visual/hard/graph517.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,22) (0,28) (0,25) (0,14) (0,29) (1,22) (1,31) (1,7) (1,25) (1,16) (1,14) (2,13) (2,22) (2,21) (2,31) (2,11) (2,4) (2,20) (3,33) (4,17) (4,13) (4,7) (4,8) (4,24) (4,25) (4,16) (4,29) (5,17) (5,13) (5,24) (5,6) (6,21) (6,7) (6,24) (7,28) (7,8) (7,16) (8,20) (9,21) (9,16) (9,20) (10,26) (10,19) (10,12) (10,32) (10,18) (11,21) (11,14) (12,19) (14,28) (14,24) (14,16) (15,30) (16,22) (16,24) (16,25) (17,28) (17,24) (17,29) (17,20) (18,32) (20,31) (20,24) (21,22) (21,29) (22,31) (22,29) (23,26) (23,32) (24,28) (27,32) (28,29) (29,31)\nIs there a path between node 17 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph428-28_14", + "image": "data/connectivity/graph_visual/hard/graph428.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,30) (0,7) (0,26) (0,13) (0,21) (0,22) (0,1) (1,24) (1,7) (1,26) (1,11) (2,32) (2,18) (2,9) (2,8) (2,12) (2,29) (2,14) (2,16) (2,10) (2,3) (2,5) (2,17) (2,28) (3,27) (3,32) (3,18) (3,9) (3,8) (3,12) (3,29) (3,16) (3,4) (3,23) (3,5) (3,31) (3,17) (3,15) (3,28) (4,18) (4,9) (4,29) (4,16) (4,10) (4,23) (4,5) (4,17) (4,15) (5,27) (5,32) (5,18) (5,20) (5,9) (5,16) (5,10) (5,17) (5,15) (5,28) (6,25) (6,19) (7,24) (7,30) (7,13) (7,21) (7,22) (8,27) (8,32) (8,18) (8,20) (8,9) (8,29) (8,14) (8,16) (8,10) (8,23) (8,31) (8,17) (8,15) (8,28) (9,27) (9,32) (9,20) (9,12) (9,14) (9,10) (9,23) (9,17) (9,15) (9,28) (10,32) (10,18) (10,20) (10,12) (10,29) (10,16) (10,31) (10,15) (10,28) (11,24) (11,30) (11,26) (11,22) (12,32) (12,18) (12,14) (12,16) (12,23) (12,31) (12,15) (12,28) (13,24) (13,30) (13,26) (14,27) (14,32) (14,18) (14,20) (14,29) (14,17) (14,28) (15,27) (15,32) (15,20) (15,23) (15,31) (15,17) (15,28) (16,27) (16,32) (16,18) (16,20) (16,23) (16,31) (16,28) (17,32) (17,20) (17,29) (17,23) (17,28) (18,27) (18,32) (18,20) (18,29) (18,31) (20,27) (20,32) (20,29) (20,23) (20,31) (20,28) (21,24) (21,30) (21,26) (21,22) (22,30) (22,26) (23,29) (23,31) (24,26) (26,30) (27,32) (28,29) (28,31) (31,32)\nIs there a path between node 28 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph621-18_3", + "image": "data/connectivity/graph_visual/hard/graph621.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,9) (0,26) (0,24) (0,27) (0,11) (1,3) (1,2) (1,20) (1,6) (1,31) (2,3) (2,33) (2,30) (2,32) (2,19) (2,7) (3,31) (3,5) (4,33) (4,9) (4,30) (4,16) (4,25) (4,24) (5,30) (5,26) (5,27) (5,15) (6,33) (6,20) (6,24) (6,27) (6,11) (6,7) (7,33) (7,23) (7,30) (9,26) (9,29) (9,24) (9,31) (9,15) (10,28) (10,13) (10,22) (10,21) (11,16) (11,24) (12,15) (13,14) (13,17) (15,23) (15,20) (15,31) (16,20) (16,24) (16,19) (17,21) (19,33) (19,23) (19,25) (19,32) (20,33) (20,23) (20,32) (20,24) (20,27) (21,28) (23,33) (23,32) (24,30) (24,32) (24,29) (25,30) (25,32) (25,29) (25,27) (26,30) (26,32) (26,29) (27,33) (27,30) (29,30) (29,31) (30,32) (31,32)\nIs there a path between node 18 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph109-3_12", + "image": "data/connectivity/graph_visual/hard/graph109.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,5) (1,27) (1,3) (1,18) (1,23) (2,14) (2,15) (2,27) (2,13) (2,8) (2,26) (3,12) (3,15) (3,13) (3,18) (3,20) (4,5) (4,15) (4,21) (4,11) (4,22) (4,20) (5,15) (5,8) (7,14) (7,25) (7,27) (7,13) (7,9) (7,20) (8,14) (8,15) (8,21) (8,23) (8,19) (9,12) (9,15) (9,27) (9,21) (9,13) (10,12) (10,21) (10,17) (10,19) (11,25) (11,27) (11,17) (11,26) (11,22) (11,19) (12,21) (12,26) (13,25) (13,21) (13,26) (13,18) (14,25) (14,15) (14,27) (14,17) (14,23) (14,19) (15,17) (15,26) (15,22) (15,18) (15,20) (15,19) (17,26) (17,18) (19,27) (20,25) (20,27) (20,26) (20,22) (20,23) (21,25) (21,27) (21,23) (22,26) (23,25) (25,26) (26,27)\nIs there a path between node 3 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph576-16_25", + "image": "data/connectivity/graph_visual/hard/graph576.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,21) (0,19) (0,9) (0,2) (0,10) (0,23) (0,18) (0,7) (0,20) (0,27) (0,24) (0,12) (0,6) (0,8) (0,25) (0,3) (0,14) (0,33) (0,31) (0,22) (0,26) (1,21) (1,19) (1,10) (1,23) (1,7) (1,29) (1,5) (1,24) (1,12) (1,6) (1,4) (1,8) (1,25) (1,3) (1,14) (1,13) (1,33) (1,31) (1,28) (1,26) (2,21) (2,19) (2,9) (2,16) (2,10) (2,23) (2,18) (2,7) (2,20) (2,5) (2,27) (2,24) (2,12) (2,4) (2,8) (2,11) (2,3) (2,14) (2,17) (2,33) (2,28) (2,22) (2,26) (3,16) (3,10) (3,18) (3,7) (3,29) (3,5) (3,24) (3,12) (3,6) (3,8) (3,25) (3,33) (3,31) (3,28) (3,22) (3,26) (4,21) (4,19) (4,16) (4,23) (4,18) (4,7) (4,5) (4,24) (4,11) (4,17) (4,13) (4,33) (4,31) (4,28) (4,22) (5,21) (5,9) (5,16) (5,10) (5,7) (5,29) (5,20) (5,24) (5,12) (5,8) (5,11) (5,14) (5,17) (5,13) (5,22) (5,26) (6,21) (6,19) (6,16) (6,23) (6,18) (6,7) (6,29) (6,27) (6,12) (6,25) (6,14) (6,17) (6,33) (6,28) (6,22) (6,26) (7,21) (7,19) (7,9) (7,10) (7,23) (7,18) (7,29) (7,20) (7,27) (7,24) (7,12) (7,8) (7,25) (7,11) (7,14) (7,17) (7,13) (7,33) (7,22) (7,26) (8,21) (8,19) (8,10) (8,23) (8,29) (8,20) (8,27) (8,24) (8,12) (8,25) (8,14) (8,17) (8,31) (8,28) (9,21) (9,23) (9,18) (9,20) (9,27) (9,24) (9,12) (9,25) (9,11) (9,14) (9,17) (9,28) (9,22) (9,26) (10,21) (10,23) (10,18) (10,29) (10,20) (10,27) (10,24) (10,12) (10,11) (10,13) (10,28) (10,22) (10,26) (11,19) (11,16) (11,23) (11,18) (11,29) (11,27) (11,24) (11,12) (11,25) (11,17) (11,13) (11,33) (11,31) (11,28) (11,22) (11,26) (12,19) (12,23) (12,18) (12,20) (12,27) (12,24) (12,14) (12,13) (12,31) (12,28) (12,22) (12,26) (13,16) (13,23) (13,29) (13,20) (13,27) (13,24) (13,25) (13,14) (13,17) (13,33) (13,31) (13,28) (13,22) (14,21) (14,19) (14,16) (14,23) (14,18) (14,29) (14,20) (14,27) (14,24) (14,25) (14,17) (14,33) (14,28) (14,26) (15,30) (15,32) (16,19) (16,23) (16,29) (16,20) (16,27) (16,25) (16,17) (16,33) (16,31) (16,22) (17,19) (17,18) (17,29) (17,24) (17,33) (17,22) (17,26) (18,21) (18,19) (18,23) (18,29) (18,20) (18,27) (18,25) (18,33) (18,28) (18,22) (18,26) (19,29) (19,20) (19,24) (19,25) (19,31) (19,28) (19,22) (19,26) (20,21) (20,29) (20,27) (20,24) (20,22) (21,23) (21,29) (21,24) (21,31) (21,22) (22,23) (22,29) (22,24) (22,25) (22,31) (22,28) (22,26) (23,29) (23,27) (23,24) (23,31) (24,27) (24,25) (24,33) (24,31) (24,28) (25,29) (25,27) (25,33) (25,31) (25,28) (25,26) (26,29) (26,27) (26,33) (26,31) (26,28) (27,31) (27,28) (28,29) (28,33) (29,33)\nIs there a path between node 16 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph561-12_5", + "image": "data/connectivity/graph_visual/hard/graph561.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,23) (0,31) (0,10) (0,14) (0,28) (0,18) (0,8) (0,21) (0,33) (0,22) (0,2) (0,1) (1,12) (1,31) (1,14) (1,28) (1,18) (1,8) (1,21) (1,19) (1,7) (1,5) (2,3) (2,31) (2,16) (2,19) (2,9) (2,22) (2,7) (3,10) (3,29) (3,11) (3,9) (4,23) (4,10) (4,14) (4,16) (4,29) (4,17) (4,8) (4,25) (4,30) (4,15) (5,27) (5,12) (5,23) (5,10) (5,16) (5,18) (5,13) (5,19) (5,9) (6,20) (7,12) (7,14) (7,26) (7,8) (7,30) (8,31) (8,28) (8,29) (8,33) (8,15) (9,12) (9,16) (9,13) (9,19) (9,15) (9,22) (10,27) (10,12) (10,16) (10,28) (11,27) (11,23) (11,31) (11,18) (12,27) (12,13) (12,21) (12,25) (12,19) (13,23) (13,14) (13,28) (13,18) (13,17) (13,33) (13,15) (14,28) (15,27) (15,18) (15,29) (15,25) (15,30) (16,27) (16,28) (16,19) (17,31) (17,28) (17,25) (18,28) (18,25) (19,29) (19,25) (19,22) (21,27) (22,25) (23,29) (23,33) (26,29) (27,28) (27,29) (27,30) (28,31) (29,31) (29,33)\nIs there a path between node 12 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph166-12_9", + "image": "data/connectivity/graph_visual/hard/graph166.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,5) (0,17) (0,26) (0,24) (0,25) (1,6) (1,19) (1,16) (1,2) (1,22) (1,11) (1,13) (2,6) (2,19) (2,15) (3,21) (3,19) (3,27) (3,23) (3,8) (4,5) (5,7) (6,27) (6,22) (6,20) (7,12) (7,25) (8,27) (8,22) (8,23) (8,20) (8,13) (9,28) (10,11) (10,14) (11,19) (11,16) (11,27) (11,23) (11,20) (12,26) (12,28) (12,24) (13,27) (13,22) (13,14) (14,27) (14,23) (15,23) (16,27) (16,22) (16,23) (17,24) (17,25) (18,25) (19,27) (19,22) (19,23) (20,21) (20,22) (20,23) (24,28) (25,26)\nIs there a path between node 12 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph671-28_25", + "image": "data/connectivity/graph_visual/hard/graph671.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,17) (0,6) (0,19) (0,28) (0,14) (1,27) (1,3) (2,10) (2,23) (2,4) (2,29) (2,26) (2,9) (3,22) (4,8) (4,18) (4,15) (4,33) (4,34) (4,28) (5,20) (5,8) (5,6) (5,30) (5,9) (6,10) (6,17) (6,8) (6,23) (6,18) (6,19) (6,25) (6,33) (6,32) (6,28) (6,14) (6,9) (8,32) (8,12) (8,29) (8,26) (8,30) (8,9) (8,31) (9,19) (9,33) (9,32) (9,12) (10,11) (10,25) (10,28) (10,14) (11,23) (11,12) (11,26) (11,30) (11,31) (12,15) (12,33) (12,30) (12,14) (13,22) (14,19) (14,31) (15,23) (15,28) (15,29) (16,24) (17,20) (18,32) (18,29) (18,26) (19,34) (19,31) (20,26) (21,27) (22,24) (23,32) (23,28) (24,27) (25,34) (25,28) (25,29) (26,34) (26,28) (28,34) (29,31) (30,33) (30,34) (31,32) (32,34) (33,34)\nIs there a path between node 28 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph33-15_11", + "image": "data/connectivity/graph_visual/hard/graph33.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,22) (0,7) (0,18) (0,14) (0,20) (0,13) (0,24) (0,17) (1,25) (1,9) (1,21) (1,15) (1,23) (1,19) (1,16) (1,8) (2,9) (2,21) (2,23) (2,19) (2,6) (2,3) (2,8) (2,5) (3,25) (3,21) (3,15) (3,23) (3,4) (3,19) (4,25) (4,10) (4,9) (4,21) (4,23) (4,19) (4,6) (4,5) (5,25) (5,10) (5,9) (5,23) (5,16) (5,8) (6,9) (6,21) (6,15) (6,19) (6,16) (7,22) (7,14) (7,13) (7,24) (7,17) (8,25) (8,10) (8,9) (8,21) (8,15) (8,23) (8,19) (8,16) (9,10) (9,15) (9,19) (9,16) (10,23) (10,16) (11,22) (11,18) (11,14) (11,20) (11,12) (11,13) (11,24) (11,17) (12,22) (12,18) (12,20) (12,24) (12,17) (13,18) (13,14) (13,20) (13,24) (13,17) (14,22) (14,18) (14,20) (14,24) (14,17) (15,25) (15,21) (15,19) (15,16) (16,25) (16,21) (16,23) (17,18) (17,20) (17,24) (18,22) (18,20) (18,24) (19,25) (19,21) (20,22) (20,24) (21,25) (21,23) (23,25)\nIs there a path between node 15 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph606-10_22", + "image": "data/connectivity/graph_visual/hard/graph606.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,31) (0,3) (0,23) (0,7) (0,4) (1,10) (1,28) (1,8) (1,24) (2,5) (2,21) (2,6) (2,29) (3,32) (3,31) (3,30) (3,29) (4,5) (4,31) (4,11) (4,30) (5,14) (5,30) (5,7) (5,20) (6,14) (6,21) (6,29) (6,20) (7,16) (7,14) (7,31) (7,30) (8,15) (8,10) (8,28) (8,19) (9,22) (9,26) (9,28) (9,25) (10,34) (10,33) (10,18) (10,24) (10,19) (11,16) (11,14) (11,13) (11,23) (12,17) (13,14) (13,27) (13,29) (14,16) (14,32) (15,25) (15,18) (15,24) (16,32) (16,21) (16,30) (16,29) (16,20) (19,34) (19,26) (19,25) (19,24) (20,31) (20,30) (20,29) (21,30) (21,27) (22,34) (22,33) (23,30) (23,29) (24,26) (25,33) (26,28) (27,32) (28,34) (29,31)\nIs there a path between node 10 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph288-28_16", + "image": "data/connectivity/graph_visual/hard/graph288.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,23) (1,9) (1,11) (1,25) (1,30) (1,15) (1,21) (1,26) (2,16) (2,5) (2,19) (2,25) (2,24) (3,8) (4,27) (4,19) (4,30) (4,15) (4,20) (4,21) (5,27) (5,16) (5,18) (5,19) (5,15) (5,14) (5,31) (6,13) (7,10) (7,23) (8,12) (8,9) (8,28) (8,20) (9,11) (9,20) (9,21) (9,14) (10,29) (11,12) (11,30) (11,20) (11,21) (11,26) (12,19) (12,20) (12,14) (12,26) (13,17) (13,29) (14,28) (14,21) (14,26) (14,24) (15,27) (15,18) (15,21) (16,22) (16,25) (16,26) (16,24) (18,25) (18,31) (19,27) (19,28) (19,21) (20,28) (20,25) (20,30) (20,24) (21,28) (21,30) (21,26) (21,31) (22,27) (22,28) (22,31) (23,29) (24,28) (24,26) (24,31) (25,31) (26,27) (26,31) (27,31) (30,31)\nIs there a path between node 28 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph410-7_26", + "image": "data/connectivity/graph_visual/hard/graph410.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,2) (0,8) (1,11) (1,10) (1,31) (1,4) (2,7) (2,28) (2,29) (2,6) (3,28) (3,21) (4,13) (4,9) (4,18) (4,26) (4,24) (4,25) (4,15) (4,22) (4,23) (5,11) (5,18) (5,14) (5,17) (5,31) (5,23) (6,28) (6,20) (6,19) (7,19) (7,21) (7,27) (8,20) (8,19) (9,11) (9,18) (9,26) (9,12) (9,24) (9,17) (10,31) (11,13) (11,17) (11,25) (11,31) (11,15) (11,22) (12,31) (12,22) (12,23) (13,18) (13,26) (13,14) (13,16) (13,24) (13,17) (13,15) (13,22) (13,23) (14,32) (14,17) (14,23) (15,24) (15,31) (16,24) (16,17) (16,31) (17,32) (17,25) (18,24) (18,23) (19,28) (19,30) (19,21) (19,27) (20,30) (20,29) (21,28) (21,30) (21,29) (22,25) (23,32) (24,32) (25,32) (26,32) (26,31) (27,29) (28,29) (29,30)\nIs there a path between node 7 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph48-18_24", + "image": "data/connectivity/graph_visual/hard/graph48.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,1) (0,19) (1,21) (2,8) (2,10) (3,8) (3,10) (4,7) (4,21) (4,18) (4,19) (4,5) (5,16) (6,12) (6,23) (6,13) (6,11) (7,19) (8,14) (8,23) (8,25) (9,20) (9,18) (9,26) (10,23) (10,22) (10,15) (11,14) (11,23) (12,14) (12,24) (12,13) (12,25) (12,22) (13,14) (13,24) (13,15) (14,24) (14,23) (14,15) (16,18) (16,17) (16,26) (17,26) (18,20) (22,24) (23,24) (23,25)\nIs there a path between node 18 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph694-26_15", + "image": "data/connectivity/graph_visual/hard/graph694.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,29) (0,33) (0,25) (0,14) (0,16) (0,4) (0,26) (0,5) (0,27) (0,20) (0,1) (0,7) (0,30) (0,2) (0,9) (0,13) (0,23) (1,29) (1,33) (1,25) (1,14) (1,26) (1,5) (1,20) (1,7) (1,31) (1,30) (1,9) (1,13) (1,23) (2,29) (2,33) (2,25) (2,14) (2,16) (2,4) (2,26) (2,5) (2,27) (2,20) (2,7) (2,31) (2,12) (2,9) (2,23) (3,32) (3,10) (3,6) (3,19) (3,8) (3,15) (3,17) (3,22) (3,21) (3,28) (4,29) (4,33) (4,25) (4,16) (4,26) (4,5) (4,27) (4,31) (4,30) (4,12) (4,13) (4,34) (4,23) (5,29) (5,25) (5,26) (5,27) (5,20) (5,7) (5,31) (5,30) (5,12) (5,9) (5,13) (5,34) (5,23) (6,11) (6,32) (6,19) (6,8) (6,24) (6,18) (6,17) (6,22) (6,21) (6,28) (7,29) (7,33) (7,25) (7,14) (7,16) (7,26) (7,31) (7,30) (7,12) (7,9) (7,13) (7,34) (7,23) (8,11) (8,10) (8,19) (8,15) (8,24) (8,17) (8,22) (8,21) (9,33) (9,25) (9,14) (9,16) (9,26) (9,20) (9,31) (9,12) (9,34) (9,23) (10,11) (10,32) (10,24) (10,18) (10,28) (11,32) (11,19) (11,15) (11,24) (11,18) (11,17) (11,21) (12,29) (12,33) (12,25) (12,16) (12,26) (12,27) (12,31) (12,30) (12,13) (12,34) (13,33) (13,25) (13,27) (13,20) (13,31) (13,30) (13,34) (14,29) (14,33) (14,25) (14,16) (14,27) (14,31) (14,34) (14,23) (15,32) (15,19) (15,22) (15,21) (15,28) (16,33) (16,25) (16,26) (16,27) (16,30) (17,32) (17,24) (17,18) (17,22) (17,28) (18,32) (18,19) (18,24) (18,22) (18,21) (18,28) (19,32) (19,24) (19,22) (19,21) (20,25) (20,26) (20,27) (20,31) (20,30) (20,23) (21,24) (21,22) (21,28) (22,24) (22,28) (23,29) (23,33) (23,26) (23,31) (23,34) (24,32) (24,28) (25,29) (25,33) (25,27) (25,31) (25,30) (25,34) (26,33) (26,27) (26,30) (26,34) (27,29) (27,31) (27,30) (27,34) (28,32) (29,33) (29,30) (29,34) (30,33) (30,31) (30,34) (31,33) (31,34) (33,34)\nIs there a path between node 26 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph118-2_18", + "image": "data/connectivity/graph_visual/hard/graph118.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,9) (0,22) (0,15) (0,19) (0,17) (1,12) (2,21) (3,7) (3,18) (3,16) (3,22) (3,24) (3,4) (3,17) (4,7) (4,6) (4,18) (4,13) (4,16) (4,19) (4,14) (4,5) (5,9) (5,7) (5,10) (5,13) (5,20) (5,26) (5,24) (5,17) (6,16) (6,22) (6,15) (6,19) (6,17) (7,10) (7,18) (7,20) (7,16) (7,26) (7,19) (7,14) (8,9) (8,10) (8,16) (8,23) (8,15) (8,19) (8,24) (8,17) (9,10) (9,16) (9,22) (9,17) (10,18) (10,22) (10,19) (10,17) (11,22) (11,26) (11,15) (11,17) (12,27) (13,18) (13,20) (13,25) (13,14) (14,16) (14,26) (14,25) (14,17) (15,18) (15,20) (15,26) (15,17) (16,18) (16,20) (16,26) (17,25) (19,23) (20,22) (22,26) (23,24)\nIs there a path between node 2 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph223-8_25", + "image": "data/connectivity/graph_visual/hard/graph223.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,3) (0,29) (0,1) (0,20) (0,7) (0,5) (0,9) (0,8) (0,26) (0,25) (1,21) (1,12) (1,3) (1,4) (1,29) (1,19) (1,11) (1,20) (1,7) (1,5) (1,9) (1,23) (1,8) (1,26) (1,25) (2,21) (2,3) (2,4) (2,29) (2,19) (2,7) (2,5) (2,9) (2,17) (2,25) (3,29) (3,10) (3,19) (3,11) (3,20) (3,7) (3,5) (3,9) (3,8) (3,17) (4,21) (4,29) (4,20) (4,7) (4,9) (4,23) (4,8) (4,17) (4,26) (4,25) (5,12) (5,10) (5,8) (5,17) (5,26) (5,25) (6,16) (6,18) (7,21) (7,29) (7,10) (7,19) (7,20) (7,9) (7,8) (7,17) (7,26) (7,25) (8,21) (8,29) (8,10) (8,19) (8,9) (8,23) (8,17) (8,26) (8,25) (9,21) (9,12) (9,10) (9,11) (9,20) (9,23) (9,17) (9,26) (10,29) (10,19) (10,11) (10,20) (10,25) (11,12) (11,29) (11,19) (11,20) (11,23) (11,17) (11,26) (11,25) (12,21) (12,29) (12,19) (12,23) (12,17) (12,26) (12,25) (13,22) (13,15) (14,18) (15,28) (15,27) (15,22) (15,24) (16,18) (17,21) (17,20) (17,23) (17,25) (19,29) (19,20) (19,26) (19,25) (20,21) (20,23) (20,26) (20,25) (21,25) (22,28) (22,24) (23,29) (23,26) (23,25) (24,27) (25,29) (25,26) (27,28)\nIs there a path between node 8 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph55-14_2", + "image": "data/connectivity/graph_visual/hard/graph55.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,11) (0,1) (0,5) (0,24) (0,12) (0,4) (0,2) (0,14) (0,7) (0,25) (0,17) (0,9) (0,20) (1,11) (1,18) (1,5) (1,8) (1,6) (1,24) (1,12) (1,3) (1,4) (1,2) (1,14) (1,7) (1,17) (1,16) (1,9) (2,11) (2,18) (2,8) (2,3) (2,14) (2,7) (2,25) (2,17) (2,9) (2,20) (2,26) (3,11) (3,18) (3,5) (3,8) (3,6) (3,24) (3,12) (3,4) (3,7) (3,25) (3,17) (3,16) (3,9) (3,20) (3,26) (4,11) (4,18) (4,5) (4,8) (4,6) (4,24) (4,12) (4,14) (4,17) (4,23) (4,9) (4,20) (4,22) (4,26) (5,11) (5,18) (5,8) (5,6) (5,24) (5,12) (5,25) (5,23) (5,9) (5,20) (5,22) (5,26) (6,18) (6,8) (6,24) (6,14) (6,7) (6,17) (6,23) (6,9) (6,22) (6,26) (7,11) (7,18) (7,8) (7,24) (7,25) (7,23) (7,16) (7,9) (7,20) (7,22) (7,26) (8,24) (8,14) (8,25) (8,23) (8,16) (8,9) (8,20) (8,22) (8,26) (9,11) (9,18) (9,12) (9,14) (9,25) (9,17) (9,23) (9,20) (9,22) (10,13) (10,15) (10,21) (11,24) (11,12) (11,14) (11,25) (11,23) (11,16) (11,22) (11,26) (12,24) (12,25) (12,23) (12,16) (12,20) (12,22) (12,26) (13,19) (13,15) (13,21) (14,18) (14,24) (14,25) (14,23) (14,22) (14,26) (15,19) (15,21) (16,18) (16,24) (16,17) (16,23) (16,20) (17,18) (17,24) (17,23) (17,20) (17,22) (17,26) (18,23) (18,26) (20,25) (20,23) (20,26) (22,24) (22,25) (22,23) (23,25) (23,26) (24,25) (24,26)\nIs there a path between node 14 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph232-9_20", + "image": "data/connectivity/graph_visual/hard/graph232.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,20) (0,9) (0,21) (0,1) (0,19) (0,7) (0,3) (0,27) (0,12) (0,23) (0,17) (1,9) (1,21) (1,10) (1,4) (1,19) (1,3) (1,12) (1,23) (1,17) (2,8) (2,28) (2,16) (2,24) (2,5) (2,11) (2,15) (3,20) (3,9) (3,21) (3,19) (3,27) (3,12) (3,23) (4,20) (4,9) (4,21) (4,19) (4,12) (4,23) (4,17) (5,18) (5,28) (5,16) (5,6) (5,14) (6,18) (6,28) (6,24) (7,20) (7,9) (7,12) (7,17) (8,16) (8,24) (8,15) (9,21) (9,10) (9,27) (9,12) (9,23) (9,17) (10,19) (10,27) (10,12) (10,23) (11,28) (11,16) (11,14) (11,24) (11,15) (12,20) (12,19) (12,27) (12,23) (12,17) (13,25) (13,26) (13,29) (14,28) (14,24) (14,15) (15,18) (15,28) (15,24) (16,18) (16,28) (17,20) (17,21) (17,23) (18,28) (18,24) (19,20) (19,21) (19,23) (20,27) (21,27) (22,25) (22,26) (22,29) (25,29) (26,29)\nIs there a path between node 9 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph471-11_27", + "image": "data/connectivity/graph_visual/hard/graph471.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,28) (0,30) (0,13) (0,15) (0,2) (0,1) (0,9) (0,21) (1,25) (1,13) (1,3) (1,29) (1,23) (1,14) (1,12) (2,20) (2,25) (2,30) (2,13) (2,3) (2,29) (2,23) (2,18) (2,9) (2,21) (3,20) (3,25) (3,13) (3,29) (3,18) (3,15) (3,9) (3,12) (3,21) (4,7) (5,6) (5,10) (5,8) (5,19) (5,16) (5,27) (5,26) (5,31) (5,11) (6,10) (6,8) (6,19) (6,27) (6,26) (6,31) (6,22) (6,11) (7,17) (8,32) (8,19) (8,16) (8,27) (8,26) (8,31) (8,22) (8,11) (9,28) (9,20) (9,29) (9,23) (9,15) (9,14) (9,21) (10,32) (10,24) (10,31) (10,22) (10,11) (11,32) (11,19) (11,24) (11,27) (11,31) (11,22) (12,25) (12,30) (12,29) (12,18) (12,15) (12,14) (12,21) (13,20) (13,25) (13,30) (13,23) (13,18) (13,14) (14,28) (14,25) (14,23) (14,15) (14,21) (15,20) (15,25) (15,30) (15,29) (15,23) (15,18) (15,21) (16,19) (16,27) (16,26) (16,22) (18,28) (18,20) (18,25) (18,30) (18,29) (18,23) (18,21) (19,32) (19,27) (19,31) (20,30) (20,29) (20,23) (21,28) (21,25) (21,29) (21,23) (22,32) (22,24) (22,27) (22,26) (22,31) (23,25) (23,30) (24,32) (24,27) (24,26) (25,28) (25,29) (26,32) (27,32) (28,30) (28,29) (31,32)\nIs there a path between node 11 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph473-31_28", + "image": "data/connectivity/graph_visual/hard/graph473.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,17) (1,2) (1,14) (1,9) (1,18) (1,5) (1,25) (1,28) (1,13) (1,10) (2,31) (2,14) (2,4) (2,18) (2,5) (2,28) (2,13) (2,19) (2,22) (2,10) (2,15) (3,27) (4,21) (4,9) (4,18) (4,25) (4,28) (4,13) (4,22) (4,7) (4,16) (5,21) (5,31) (5,9) (5,18) (5,25) (5,28) (5,13) (5,19) (5,22) (5,16) (5,10) (5,15) (6,17) (6,32) (7,31) (7,14) (7,9) (7,18) (7,25) (7,28) (7,13) (7,19) (7,16) (7,10) (8,11) (8,23) (8,30) (8,12) (8,29) (9,21) (9,31) (9,18) (9,25) (9,13) (9,10) (10,31) (10,18) (10,28) (10,19) (10,22) (10,16) (10,15) (11,24) (11,30) (11,26) (12,24) (12,23) (12,20) (12,26) (12,29) (13,14) (13,18) (13,28) (13,19) (13,22) (13,16) (14,31) (14,18) (14,16) (14,15) (15,31) (15,18) (15,19) (15,22) (15,16) (16,21) (16,31) (16,18) (16,28) (16,19) (18,21) (18,31) (18,25) (18,28) (18,22) (19,31) (19,25) (19,28) (19,22) (20,24) (20,23) (20,30) (20,29) (21,31) (21,28) (21,22) (22,25) (22,28) (23,30) (23,26) (23,29) (24,30) (25,31) (25,28) (26,30) (28,31) (29,30)\nIs there a path between node 31 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph370-5_20", + "image": "data/connectivity/graph_visual/hard/graph370.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,20) (0,26) (0,29) (0,27) (0,5) (0,30) (0,6) (0,1) (0,21) (0,10) (0,11) (0,16) (0,23) (1,24) (1,20) (1,13) (1,26) (1,29) (1,9) (1,27) (1,5) (1,30) (1,21) (1,16) (1,23) (1,22) (2,3) (2,28) (3,28) (4,24) (4,20) (4,26) (4,9) (4,27) (4,15) (4,5) (4,30) (4,16) (4,12) (4,22) (5,24) (5,26) (5,9) (5,27) (5,15) (5,30) (5,21) (5,10) (5,16) (5,12) (5,23) (6,24) (6,20) (6,9) (6,27) (6,30) (6,10) (6,11) (6,12) (6,23) (7,18) (7,25) (7,8) (7,14) (7,17) (8,18) (8,14) (8,17) (9,24) (9,20) (9,29) (9,27) (9,15) (9,21) (9,16) (9,12) (9,23) (9,22) (10,24) (10,13) (10,27) (10,15) (10,30) (10,21) (10,11) (10,16) (10,23) (10,22) (11,20) (11,13) (11,26) (11,29) (11,15) (11,30) (11,12) (11,23) (11,22) (12,20) (12,13) (12,29) (12,27) (12,15) (12,30) (12,21) (12,16) (12,23) (13,24) (13,20) (13,26) (13,30) (13,16) (14,18) (14,25) (15,20) (15,26) (15,29) (15,27) (15,30) (15,21) (15,22) (16,24) (16,20) (16,29) (16,27) (16,23) (17,18) (19,31) (19,28) (20,24) (20,27) (20,30) (20,21) (20,22) (21,26) (21,29) (21,30) (21,22) (22,24) (22,29) (22,27) (22,30) (23,26) (23,30) (24,26) (24,29) (24,27) (24,30) (26,29) (26,27) (26,30) (27,29) (27,30) (28,31) (29,30)\nIs there a path between node 5 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph43-1_17", + "image": "data/connectivity/graph_visual/hard/graph43.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,15) (0,20) (0,23) (0,5) (0,11) (0,9) (0,21) (0,13) (1,18) (1,22) (1,16) (1,25) (1,17) (1,24) (1,2) (1,14) (1,12) (2,18) (2,19) (2,22) (2,16) (2,25) (2,24) (2,14) (2,12) (2,6) (3,15) (3,20) (3,4) (3,7) (3,5) (3,11) (3,13) (4,15) (4,7) (4,23) (4,11) (4,9) (4,21) (4,13) (5,15) (5,7) (5,23) (5,9) (5,21) (5,13) (6,18) (6,19) (6,10) (6,25) (6,24) (6,8) (6,14) (7,15) (7,11) (7,21) (7,13) (8,18) (8,19) (8,22) (8,10) (8,17) (8,24) (8,14) (8,12) (9,15) (9,20) (9,11) (9,21) (10,18) (10,19) (10,16) (10,25) (10,17) (10,24) (10,12) (11,15) (11,23) (11,13) (12,18) (12,22) (12,16) (12,25) (12,24) (12,14) (13,23) (13,21) (14,18) (14,22) (14,16) (14,25) (14,17) (14,24) (15,20) (15,23) (15,21) (16,18) (16,19) (16,25) (16,17) (16,24) (17,19) (17,22) (18,19) (18,22) (18,24) (19,22) (19,25) (19,24) (20,23) (20,21) (21,23) (22,24) (24,25)\nIs there a path between node 1 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph591-0_7", + "image": "data/connectivity/graph_visual/hard/graph591.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,13) (0,31) (0,32) (0,33) (0,15) (1,5) (1,19) (1,16) (1,18) (1,11) (1,10) (1,9) (1,28) (1,14) (1,3) (1,8) (2,7) (2,5) (2,19) (2,16) (2,29) (2,18) (2,11) (2,25) (2,9) (2,28) (2,14) (2,3) (2,30) (2,8) (2,27) (3,7) (3,5) (3,19) (3,29) (3,18) (3,11) (3,6) (3,10) (3,25) (3,9) (3,28) (3,14) (3,30) (3,8) (4,26) (4,32) (4,17) (4,33) (4,15) (5,7) (5,19) (5,16) (5,18) (5,11) (5,10) (5,14) (5,30) (5,8) (5,27) (6,7) (6,19) (6,16) (6,11) (6,10) (6,25) (6,9) (6,28) (6,14) (6,30) (6,27) (7,16) (7,18) (7,11) (7,10) (7,25) (7,28) (7,14) (7,8) (7,27) (8,19) (8,16) (8,11) (8,10) (8,9) (8,27) (9,19) (9,16) (9,29) (9,11) (9,10) (9,27) (10,29) (10,11) (10,14) (10,30) (10,27) (11,19) (11,18) (11,30) (11,27) (12,24) (12,20) (13,26) (13,32) (13,17) (13,33) (13,15) (14,19) (14,16) (14,29) (14,25) (14,28) (14,30) (14,27) (15,31) (15,26) (15,32) (15,17) (16,19) (16,18) (16,25) (16,27) (17,31) (17,23) (17,26) (17,32) (17,33) (18,19) (18,29) (18,28) (18,30) (18,27) (19,29) (19,25) (19,28) (19,30) (19,27) (20,22) (20,24) (20,21) (21,24) (22,24) (23,31) (23,26) (23,33) (25,29) (25,28) (25,30) (25,27) (26,31) (26,32) (26,33) (27,29) (27,30) (28,29) (28,30) (29,30) (31,32) (32,33)\nIs there a path between node 0 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph304-28_27", + "image": "data/connectivity/graph_visual/hard/graph304.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,5) (0,17) (0,24) (1,11) (1,9) (1,3) (2,19) (2,29) (2,27) (3,7) (3,20) (4,23) (4,25) (5,17) (6,22) (7,29) (7,27) (7,9) (8,16) (8,30) (8,26) (8,18) (8,31) (9,11) (9,27) (10,13) (10,12) (11,19) (11,27) (12,26) (12,18) (14,28) (15,27) (16,30) (17,23) (18,26) (19,28) (20,29) (21,22) (23,24) (24,25) (27,28) (30,31)\nIs there a path between node 28 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph400-0_15", + "image": "data/connectivity/graph_visual/hard/graph400.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,2) (0,31) (0,22) (0,30) (0,29) (0,8) (0,21) (0,13) (0,24) (0,3) (0,23) (0,11) (0,4) (0,14) (0,32) (0,27) (1,16) (1,9) (1,12) (1,19) (1,28) (1,20) (1,10) (2,31) (2,22) (2,26) (2,8) (2,6) (2,18) (2,24) (2,5) (2,3) (2,23) (2,11) (2,4) (2,14) (2,17) (2,27) (3,31) (3,22) (3,26) (3,30) (3,8) (3,13) (3,7) (3,18) (3,5) (3,23) (3,14) (3,17) (3,32) (3,27) (4,29) (4,8) (4,21) (4,6) (4,13) (4,7) (4,11) (4,14) (4,17) (4,32) (4,27) (5,22) (5,29) (5,8) (5,21) (5,13) (5,7) (5,18) (5,24) (5,23) (5,11) (5,17) (5,32) (6,31) (6,30) (6,8) (6,21) (6,13) (6,7) (6,18) (6,24) (6,11) (6,32) (6,27) (7,31) (7,26) (7,30) (7,29) (7,8) (7,21) (7,13) (7,24) (7,11) (7,32) (7,27) (8,31) (8,22) (8,26) (8,30) (8,29) (8,13) (8,18) (8,24) (8,23) (8,14) (8,17) (8,32) (8,27) (9,16) (9,12) (9,19) (9,28) (9,15) (9,20) (9,10) (10,16) (10,25) (10,12) (10,19) (11,31) (11,22) (11,26) (11,29) (11,21) (11,13) (11,18) (11,24) (11,23) (11,14) (11,17) (11,32) (12,25) (12,19) (12,15) (12,20) (13,22) (13,30) (13,29) (13,18) (13,24) (13,23) (13,14) (13,17) (13,32) (14,31) (14,22) (14,26) (14,30) (14,21) (14,18) (14,24) (14,17) (14,32) (14,27) (15,16) (15,25) (15,28) (15,20) (16,19) (17,30) (17,29) (17,21) (17,18) (17,23) (17,32) (17,27) (18,31) (18,22) (18,26) (18,29) (18,21) (18,24) (18,32) (18,27) (19,28) (19,20) (20,25) (20,28) (21,31) (21,30) (21,29) (21,24) (21,23) (22,31) (22,26) (22,24) (22,23) (23,26) (23,30) (23,32) (23,27) (24,31) (24,26) (24,30) (24,29) (24,32) (24,27) (26,29) (26,32) (27,31) (27,30) (27,32) (29,31) (29,30) (30,31) (30,32) (31,32)\nIs there a path between node 0 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph144-23_11", + "image": "data/connectivity/graph_visual/hard/graph144.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,17) (0,2) (0,12) (0,1) (0,8) (0,10) (0,28) (1,3) (1,7) (1,18) (1,6) (1,15) (1,23) (2,3) (2,10) (2,18) (2,5) (2,28) (2,9) (3,16) (3,12) (3,7) (3,8) (3,19) (3,21) (3,24) (3,6) (3,20) (5,16) (5,17) (5,8) (5,14) (5,24) (5,6) (5,15) (5,9) (6,12) (6,25) (6,10) (6,21) (6,24) (6,23) (7,16) (7,17) (7,12) (7,25) (7,26) (7,10) (7,21) (7,24) (8,17) (8,27) (8,25) (8,10) (8,19) (8,21) (8,23) (9,17) (9,27) (9,12) (9,19) (9,18) (9,24) (9,20) (9,28) (9,15) (10,16) (10,27) (10,18) (10,13) (10,23) (12,17) (12,25) (12,26) (12,19) (12,20) (13,16) (13,27) (13,26) (13,21) (13,18) (13,24) (14,26) (15,18) (16,18) (16,24) (16,28) (17,26) (17,21) (17,18) (17,23) (18,26) (18,21) (18,24) (18,20) (19,26) (19,24) (19,20) (20,21) (20,24) (20,28) (20,23) (21,25) (23,25) (23,24) (24,27) (24,28) (25,26) (26,28)\nIs there a path between node 23 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph275-29_27", + "image": "data/connectivity/graph_visual/hard/graph275.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,21) (0,7) (0,14) (0,5) (0,10) (0,4) (0,22) (0,1) (0,26) (0,9) (0,23) (0,30) (0,17) (0,15) (0,8) (0,25) (0,3) (1,27) (1,21) (1,11) (1,16) (1,7) (1,14) (1,13) (1,5) (1,4) (1,22) (1,26) (1,9) (1,2) (1,17) (1,8) (1,25) (1,3) (2,27) (2,21) (2,11) (2,16) (2,14) (2,5) (2,19) (2,4) (2,22) (2,26) (2,9) (2,23) (2,17) (2,15) (2,8) (2,25) (2,3) (3,27) (3,21) (3,11) (3,14) (3,13) (3,5) (3,10) (3,19) (3,4) (3,22) (3,24) (3,23) (3,30) (3,8) (4,27) (4,11) (4,16) (4,13) (4,5) (4,10) (4,19) (4,22) (4,26) (4,24) (4,9) (4,17) (4,15) (4,8) (5,27) (5,11) (5,16) (5,7) (5,14) (5,13) (5,10) (5,22) (5,26) (5,9) (5,23) (5,30) (5,15) (5,8) (5,25) (6,28) (6,29) (6,20) (7,27) (7,21) (7,11) (7,16) (7,10) (7,22) (7,26) (7,9) (7,23) (7,30) (7,17) (7,25) (8,21) (8,11) (8,16) (8,14) (8,13) (8,10) (8,19) (8,22) (8,26) (8,24) (8,9) (8,23) (8,30) (8,17) (9,27) (9,21) (9,11) (9,13) (9,22) (9,26) (9,24) (9,23) (9,30) (9,17) (9,15) (9,25) (10,27) (10,21) (10,11) (10,14) (10,13) (10,22) (10,26) (10,23) (10,30) (10,15) (11,27) (11,21) (11,16) (11,13) (11,19) (11,22) (11,23) (11,30) (11,15) (12,28) (12,29) (12,20) (13,27) (13,21) (13,16) (13,14) (13,24) (13,23) (13,17) (13,15) (13,25) (14,27) (14,21) (14,19) (14,22) (14,26) (14,24) (14,23) (14,30) (14,17) (14,15) (14,25) (15,27) (15,21) (15,22) (15,26) (15,24) (15,30) (15,17) (16,27) (16,21) (16,19) (16,22) (16,24) (16,23) (16,25) (17,27) (17,19) (17,23) (17,30) (17,25) (19,27) (19,21) (19,22) (19,26) (19,23) (19,25) (20,28) (20,29) (21,27) (21,26) (21,23) (21,30) (21,25) (22,27) (22,23) (22,30) (22,25) (23,27) (23,26) (23,25) (24,30) (24,25) (25,26) (25,30) (26,27) (26,30) (28,29)\nIs there a path between node 29 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph184-5_21", + "image": "data/connectivity/graph_visual/hard/graph184.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,3) (0,4) (0,11) (0,13) (1,8) (1,21) (1,10) (1,7) (1,2) (2,24) (2,8) (2,9) (2,10) (2,22) (3,5) (3,11) (3,13) (4,15) (4,6) (4,16) (4,11) (5,12) (5,15) (5,19) (5,18) (5,27) (6,19) (6,11) (7,26) (7,23) (7,9) (8,23) (8,9) (8,10) (8,22) (9,25) (9,14) (10,25) (10,17) (10,23) (11,20) (11,27) (12,15) (12,16) (12,18) (14,22) (15,19) (15,27) (16,19) (17,26) (17,24) (17,28) (17,23) (17,22) (19,20) (19,27) (21,26) (21,25) (21,29) (21,22) (22,29) (23,24) (23,29) (26,28)\nIs there a path between node 5 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph70-1_23", + "image": "data/connectivity/graph_visual/hard/graph70.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,12) (0,19) (0,15) (1,5) (1,20) (1,14) (1,25) (1,10) (2,23) (3,5) (3,11) (3,7) (3,19) (3,18) (4,5) (4,20) (4,25) (4,19) (5,20) (5,25) (5,11) (5,17) (5,19) (5,15) (6,22) (6,25) (6,11) (6,15) (7,20) (7,19) (8,16) (8,26) (9,23) (10,20) (10,17) (10,13) (11,20) (11,17) (11,13) (11,19) (12,14) (12,25) (12,19) (13,14) (14,17) (15,25) (16,21) (16,23) (17,22) (17,20) (17,25) (22,25)\nIs there a path between node 1 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph129-6_24", + "image": "data/connectivity/graph_visual/hard/graph129.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,6) (0,7) (0,19) (0,18) (0,12) (0,17) (0,13) (0,24) (0,3) (0,1) (0,15) (0,11) (0,27) (0,16) (1,6) (1,8) (1,26) (1,7) (1,10) (1,19) (1,18) (1,24) (1,3) (1,9) (1,15) (1,11) (1,27) (2,20) (2,25) (2,14) (2,21) (3,6) (3,8) (3,26) (3,7) (3,10) (3,19) (3,18) (3,12) (3,17) (3,24) (3,9) (3,15) (3,11) (4,22) (5,23) (5,20) (5,25) (6,8) (6,26) (6,19) (6,18) (6,12) (6,17) (6,13) (6,24) (6,15) (6,11) (6,27) (6,16) (7,10) (7,19) (7,18) (7,17) (7,13) (7,24) (7,9) (7,16) (8,26) (8,19) (8,18) (8,12) (8,17) (8,13) (8,24) (8,9) (8,15) (8,27) (8,16) (9,26) (9,10) (9,18) (9,12) (9,17) (9,13) (9,15) (9,27) (9,16) (10,26) (10,19) (10,17) (10,13) (10,15) (10,16) (11,26) (11,19) (11,18) (11,12) (11,17) (11,15) (12,26) (12,19) (12,18) (12,13) (12,24) (13,18) (13,24) (13,27) (13,16) (14,23) (14,20) (14,21) (15,26) (15,19) (15,18) (15,17) (15,16) (16,26) (16,19) (16,24) (16,27) (17,26) (17,24) (17,27) (18,26) (18,19) (18,27) (19,26) (19,27) (20,25) (21,23) (21,25)\nIs there a path between node 6 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph622-34_26", + "image": "data/connectivity/graph_visual/hard/graph622.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,25) (0,13) (1,16) (1,27) (1,32) (1,4) (1,31) (1,34) (2,16) (2,27) (2,32) (2,6) (2,19) (2,9) (3,25) (3,28) (3,7) (3,18) (3,21) (4,29) (4,33) (4,23) (4,12) (4,9) (4,34) (5,27) (5,11) (5,19) (5,9) (6,33) (6,27) (6,34) (7,25) (7,18) (8,10) (9,16) (9,19) (9,34) (10,30) (11,29) (11,16) (11,19) (11,31) (11,14) (11,12) (12,33) (12,26) (12,19) (12,34) (13,25) (13,28) (14,32) (15,30) (16,29) (16,27) (16,32) (18,21) (20,24) (21,25) (22,25) (22,28) (23,27) (26,33) (26,27) (26,34) (27,29) (27,33) (27,34) (29,33)\nIs there a path between node 34 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph505-31_3", + "image": "data/connectivity/graph_visual/hard/graph505.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,33) (0,8) (0,16) (0,5) (0,17) (0,23) (1,6) (1,7) (1,27) (1,14) (1,4) (1,13) (1,24) (1,21) (2,32) (2,19) (2,29) (2,12) (2,28) (2,15) (3,32) (3,19) (3,26) (3,12) (3,20) (3,30) (3,28) (3,15) (4,6) (4,9) (4,7) (4,14) (4,10) (4,24) (5,33) (5,8) (5,16) (5,31) (5,17) (5,23) (6,7) (6,27) (6,10) (6,25) (6,13) (7,27) (7,14) (7,10) (7,25) (7,24) (7,21) (8,16) (8,17) (9,27) (9,14) (9,10) (9,24) (9,21) (10,25) (10,21) (11,32) (11,19) (11,26) (11,12) (11,20) (11,30) (11,28) (11,22) (12,19) (12,29) (12,26) (12,20) (12,15) (12,22) (13,27) (13,14) (13,25) (13,24) (13,21) (14,25) (14,24) (14,21) (15,32) (15,19) (15,26) (15,20) (15,30) (15,28) (16,33) (16,18) (16,31) (16,23) (17,33) (17,18) (17,23) (18,33) (18,31) (19,32) (19,29) (19,26) (19,30) (19,28) (19,22) (20,32) (20,30) (20,28) (21,25) (22,32) (22,29) (22,26) (22,30) (22,28) (23,33) (24,27) (24,25) (25,27) (26,29) (26,30) (26,28) (28,30) (29,32) (29,30) (30,32) (31,33)\nIs there a path between node 31 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph692-15_30", + "image": "data/connectivity/graph_visual/hard/graph692.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,15) (0,2) (0,33) (0,4) (0,8) (0,23) (0,34) (0,30) (1,22) (1,28) (1,9) (1,29) (1,24) (1,26) (1,7) (1,27) (1,32) (1,19) (1,16) (1,5) (1,10) (2,12) (2,3) (2,15) (2,33) (2,20) (2,8) (2,23) (3,12) (3,11) (3,33) (3,4) (3,8) (3,23) (4,12) (4,11) (4,33) (4,20) (4,23) (5,22) (5,17) (5,28) (5,29) (5,14) (5,31) (5,25) (5,18) (5,24) (5,26) (5,6) (5,27) (5,32) (5,21) (5,19) (5,16) (6,17) (6,28) (6,13) (6,29) (6,14) (6,31) (6,25) (6,24) (6,27) (6,19) (6,16) (6,10) (7,22) (7,17) (7,9) (7,13) (7,29) (7,25) (7,24) (7,26) (7,27) (7,21) (7,19) (7,16) (7,10) (8,12) (8,11) (8,15) (8,33) (8,30) (9,22) (9,28) (9,13) (9,29) (9,14) (9,31) (9,18) (9,24) (9,26) (9,27) (9,32) (9,21) (9,19) (9,16) (9,10) (10,22) (10,17) (10,28) (10,13) (10,29) (10,14) (10,31) (10,25) (10,18) (10,26) (10,32) (10,21) (10,16) (11,33) (11,20) (11,23) (11,30) (12,33) (12,20) (12,34) (12,30) (13,22) (13,17) (13,28) (13,29) (13,14) (13,31) (13,25) (13,18) (13,24) (13,26) (13,32) (13,21) (13,19) (13,16) (14,22) (14,17) (14,28) (14,29) (14,31) (14,25) (14,18) (14,24) (14,26) (14,27) (14,32) (14,21) (14,19) (14,16) (15,33) (15,20) (15,23) (15,34) (15,30) (16,22) (16,17) (16,28) (16,29) (16,31) (16,18) (16,24) (16,26) (16,27) (16,32) (16,21) (17,28) (17,29) (17,31) (17,18) (17,24) (17,27) (17,32) (17,21) (17,19) (18,22) (18,28) (18,29) (18,31) (18,25) (18,27) (18,21) (19,22) (19,28) (19,29) (19,31) (19,25) (19,27) (19,21) (20,33) (20,23) (20,34) (20,30) (21,28) (21,29) (21,31) (21,25) (21,26) (21,32) (22,28) (22,31) (22,25) (22,24) (22,26) (22,27) (22,32) (23,33) (24,28) (24,29) (24,31) (24,26) (24,32) (25,31) (25,27) (25,32) (26,29) (26,31) (26,27) (27,28) (27,29) (27,31) (27,32) (28,29) (28,32) (29,32) (30,33) (30,34) (31,32) (33,34)\nIs there a path between node 15 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph369-26_11", + "image": "data/connectivity/graph_visual/hard/graph369.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,16) (0,6) (0,12) (0,29) (0,13) (0,3) (0,21) (0,17) (0,30) (0,27) (0,8) (0,10) (1,9) (1,11) (1,16) (1,6) (1,20) (1,24) (1,13) (1,14) (1,3) (1,21) (1,17) (1,30) (1,25) (1,19) (1,27) (1,8) (1,10) (2,4) (3,26) (3,9) (3,11) (3,7) (3,12) (3,24) (3,13) (3,14) (3,17) (3,30) (3,25) (3,27) (3,8) (3,10) (4,23) (5,28) (5,15) (6,26) (6,9) (6,11) (6,16) (6,7) (6,12) (6,24) (6,14) (6,21) (6,17) (6,25) (6,19) (6,27) (6,10) (7,26) (7,11) (7,16) (7,12) (7,29) (7,24) (7,21) (7,17) (7,30) (7,8) (7,10) (8,9) (8,16) (8,12) (8,20) (8,24) (8,13) (8,14) (8,17) (8,30) (8,19) (8,27) (8,10) (9,11) (9,16) (9,12) (9,20) (9,29) (9,24) (9,14) (9,21) (9,17) (9,30) (9,25) (9,19) (9,27) (10,16) (10,12) (10,20) (10,24) (10,13) (10,14) (10,21) (10,17) (10,30) (10,25) (10,19) (10,27) (11,26) (11,16) (11,24) (11,14) (11,21) (11,30) (11,25) (11,19) (11,27) (12,26) (12,16) (12,20) (12,29) (12,24) (12,13) (12,14) (12,21) (12,17) (12,30) (12,19) (12,27) (13,26) (13,16) (13,20) (13,24) (13,14) (13,21) (13,17) (13,30) (13,19) (13,27) (14,26) (14,16) (14,20) (14,29) (14,30) (14,25) (15,31) (16,26) (16,29) (16,21) (16,17) (16,30) (16,25) (16,27) (17,26) (17,29) (17,21) (17,30) (17,25) (17,19) (17,27) (18,23) (18,22) (19,26) (19,20) (19,21) (19,30) (19,25) (19,27) (20,26) (20,29) (20,24) (20,21) (20,30) (20,25) (20,27) (21,26) (21,29) (21,30) (21,25) (21,27) (22,23) (24,29) (24,30) (25,29) (25,30) (25,27) (26,29) (27,29) (27,30) (29,30)\nIs there a path between node 26 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph516-18_28", + "image": "data/connectivity/graph_visual/hard/graph516.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,4) (1,33) (1,21) (1,17) (2,10) (2,30) (2,23) (3,10) (3,16) (3,30) (3,23) (5,26) (6,22) (6,25) (6,10) (6,13) (6,30) (6,11) (6,15) (6,29) (6,20) (7,8) (7,13) (7,33) (7,27) (7,14) (7,29) (8,10) (8,33) (8,15) (9,10) (9,12) (9,11) (9,15) (9,17) (10,22) (10,31) (10,16) (10,33) (10,27) (10,20) (11,25) (11,31) (11,12) (11,27) (11,14) (12,22) (12,31) (12,30) (12,33) (12,21) (12,27) (12,17) (12,14) (13,25) (13,31) (13,29) (14,33) (14,23) (14,20) (15,33) (15,20) (16,25) (16,33) (16,21) (16,17) (16,20) (17,29) (19,24) (20,25) (20,31) (20,30) (21,29) (22,25) (23,25) (23,33) (25,27) (27,29) (29,31) (31,33)\nIs there a path between node 18 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph441-30_28", + "image": "data/connectivity/graph_visual/hard/graph441.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,18) (0,25) (0,20) (0,19) (0,9) (0,5) (0,30) (0,4) (0,7) (0,6) (0,21) (0,24) (0,22) (0,31) (0,23) (0,8) (0,17) (0,3) (0,32) (0,15) (0,26) (0,12) (1,2) (1,29) (1,27) (1,28) (2,27) (2,28) (3,18) (3,16) (3,25) (3,20) (3,10) (3,13) (3,9) (3,30) (3,7) (3,21) (3,22) (3,31) (3,11) (3,8) (3,17) (3,32) (3,15) (3,26) (4,18) (4,16) (4,25) (4,20) (4,10) (4,19) (4,13) (4,9) (4,5) (4,30) (4,7) (4,6) (4,21) (4,22) (4,31) (4,11) (4,23) (4,8) (4,17) (4,15) (5,18) (5,16) (5,25) (5,20) (5,10) (5,19) (5,13) (5,9) (5,30) (5,7) (5,21) (5,24) (5,11) (5,23) (5,8) (5,17) (5,32) (5,15) (5,26) (6,16) (6,25) (6,10) (6,19) (6,13) (6,9) (6,7) (6,21) (6,8) (6,17) (6,32) (6,26) (6,12) (7,16) (7,25) (7,10) (7,19) (7,13) (7,30) (7,21) (7,24) (7,31) (7,11) (7,8) (7,32) (7,12) (8,18) (8,16) (8,25) (8,20) (8,10) (8,19) (8,13) (8,9) (8,21) (8,22) (8,31) (8,17) (8,12) (9,18) (9,25) (9,10) (9,19) (9,13) (9,22) (9,11) (9,23) (9,17) (9,32) (9,15) (9,26) (9,12) (10,25) (10,20) (10,19) (10,13) (10,21) (10,24) (10,22) (10,31) (10,32) (10,26) (11,18) (11,16) (11,24) (11,22) (11,31) (11,23) (11,17) (11,32) (11,15) (11,12) (12,25) (12,19) (12,13) (12,21) (12,24) (12,22) (12,23) (12,17) (12,32) (12,15) (12,26) (13,16) (13,20) (13,19) (13,21) (13,24) (13,22) (13,23) (13,17) (13,32) (13,15) (13,26) (15,16) (15,25) (15,20) (15,19) (15,30) (15,21) (15,22) (15,31) (15,23) (15,17) (15,32) (15,26) (16,18) (16,20) (16,19) (16,30) (16,21) (16,22) (16,23) (16,26) (17,18) (17,25) (17,19) (17,24) (17,31) (17,32) (17,26) (18,20) (18,19) (18,30) (18,21) (18,24) (18,22) (18,31) (18,23) (18,32) (18,26) (19,25) (19,30) (19,21) (19,24) (19,22) (19,31) (19,23) (19,26) (20,30) (20,21) (20,24) (20,31) (20,23) (20,32) (20,26) (21,25) (21,22) (21,31) (21,23) (21,32) (21,26) (22,25) (22,30) (22,24) (22,31) (22,23) (22,26) (23,30) (23,31) (23,32) (23,26) (24,32) (24,26) (25,30) (25,32) (26,31) (26,32) (27,29) (27,28) (31,32)\nIs there a path between node 30 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph438-31_23", + "image": "data/connectivity/graph_visual/hard/graph438.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,27) (0,10) (0,6) (0,24) (0,30) (0,18) (0,19) (0,31) (0,16) (0,12) (1,25) (1,15) (1,17) (1,22) (1,2) (1,7) (1,3) (1,13) (1,9) (2,32) (2,25) (2,15) (2,17) (2,20) (2,29) (2,3) (2,11) (2,13) (2,9) (3,25) (3,15) (3,21) (3,4) (3,17) (3,20) (3,22) (3,29) (3,11) (4,32) (4,25) (4,20) (4,11) (4,13) (4,9) (6,27) (6,10) (6,30) (6,18) (6,31) (6,12) (6,8) (6,26) (6,28) (7,32) (7,25) (7,20) (7,29) (7,11) (7,13) (7,9) (8,27) (8,10) (8,24) (8,30) (8,18) (8,31) (8,12) (8,26) (9,25) (9,21) (9,17) (9,22) (9,29) (9,11) (9,13) (10,30) (10,31) (10,23) (10,12) (10,28) (11,32) (11,25) (11,15) (11,21) (11,17) (11,20) (11,22) (11,29) (11,13) (12,27) (12,24) (12,30) (12,19) (12,16) (12,23) (12,26) (12,28) (13,32) (13,25) (13,15) (13,21) (13,20) (13,29) (15,32) (15,25) (15,21) (15,17) (15,29) (16,24) (16,30) (16,18) (16,19) (16,31) (16,23) (16,26) (16,28) (17,21) (17,22) (17,29) (18,27) (18,24) (18,30) (18,31) (18,23) (19,24) (19,31) (19,23) (19,28) (20,32) (20,25) (20,21) (20,22) (21,32) (21,25) (21,22) (22,25) (23,24) (23,31) (23,28) (24,27) (24,31) (24,26) (24,28) (25,29) (26,30) (27,30) (27,31) (27,28) (28,31) (29,32) (30,31)\nIs there a path between node 31 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph226-11_29", + "image": "data/connectivity/graph_visual/hard/graph226.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,17) (0,29) (0,18) (0,24) (0,27) (0,12) (0,14) (0,21) (0,7) (0,15) (0,6) (1,25) (1,9) (1,5) (1,8) (1,2) (1,13) (1,10) (1,23) (2,19) (2,3) (2,25) (2,9) (2,5) (2,16) (2,8) (2,13) (2,10) (2,23) (3,19) (3,28) (3,25) (3,5) (3,13) (3,10) (4,17) (4,18) (4,24) (4,27) (4,12) (4,14) (4,20) (4,7) (4,15) (4,6) (4,11) (4,26) (5,19) (5,28) (5,25) (5,9) (5,16) (5,8) (5,10) (5,23) (6,22) (6,17) (6,29) (6,18) (6,24) (6,27) (6,14) (6,21) (6,7) (7,22) (7,17) (7,29) (7,18) (7,24) (7,14) (7,21) (7,20) (7,15) (7,11) (7,26) (8,19) (8,28) (8,9) (8,16) (8,13) (8,10) (8,23) (9,19) (9,28) (9,25) (9,16) (9,13) (9,10) (9,23) (10,28) (10,16) (10,13) (10,23) (11,22) (11,17) (11,24) (11,27) (11,12) (11,14) (11,21) (11,26) (12,22) (12,18) (12,24) (12,15) (12,26) (13,19) (13,28) (13,25) (13,23) (14,22) (14,17) (14,29) (14,18) (14,24) (14,27) (14,21) (14,20) (14,15) (14,26) (15,22) (15,17) (15,29) (15,18) (15,24) (15,27) (15,21) (15,20) (15,26) (16,19) (16,25) (17,22) (17,29) (17,18) (17,27) (17,21) (17,20) (17,26) (18,22) (18,26) (19,28) (19,23) (20,22) (20,24) (20,27) (21,24) (21,27) (21,26) (22,29) (22,24) (22,26) (23,25) (24,29) (25,28) (26,29) (26,27) (27,29)\nIs there a path between node 11 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph323-5_2", + "image": "data/connectivity/graph_visual/hard/graph323.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,16) (0,1) (0,21) (0,27) (0,20) (0,7) (0,25) (0,23) (0,15) (0,17) (0,10) (0,2) (0,6) (0,11) (0,19) (0,4) (0,14) (0,9) (0,30) (0,29) (0,13) (1,16) (1,26) (1,21) (1,12) (1,27) (1,20) (1,7) (1,17) (1,10) (1,2) (1,6) (1,11) (1,4) (1,8) (1,14) (1,29) (1,13) (2,18) (2,16) (2,26) (2,21) (2,24) (2,12) (2,27) (2,20) (2,7) (2,22) (2,23) (2,15) (2,17) (2,11) (2,19) (2,4) (2,8) (2,14) (2,9) (2,29) (2,13) (3,31) (4,18) (4,16) (4,26) (4,21) (4,27) (4,7) (4,25) (4,22) (4,15) (4,10) (4,28) (4,11) (4,19) (4,14) (4,9) (4,30) (4,29) (6,18) (6,16) (6,12) (6,20) (6,25) (6,23) (6,15) (6,17) (6,10) (6,28) (6,11) (6,19) (6,14) (6,9) (6,29) (7,16) (7,26) (7,21) (7,24) (7,12) (7,27) (7,20) (7,25) (7,22) (7,23) (7,15) (7,10) (7,28) (7,11) (7,19) (7,8) (7,9) (7,30) (7,13) (8,16) (8,21) (8,27) (8,20) (8,25) (8,23) (8,15) (8,17) (8,10) (8,11) (8,14) (8,29) (8,13) (9,18) (9,16) (9,21) (9,24) (9,27) (9,22) (9,23) (9,17) (9,10) (9,28) (9,19) (9,14) (9,30) (9,29) (9,13) (10,18) (10,16) (10,26) (10,21) (10,12) (10,27) (10,20) (10,25) (10,22) (10,23) (10,15) (10,11) (10,19) (10,29) (10,13) (11,18) (11,16) (11,26) (11,21) (11,24) (11,12) (11,20) (11,22) (11,23) (11,15) (11,17) (11,30) (11,13) (12,18) (12,16) (12,26) (12,21) (12,24) (12,27) (12,20) (12,25) (12,22) (12,23) (12,17) (12,28) (12,19) (12,30) (12,29) (12,13) (13,18) (13,16) (13,21) (13,24) (13,20) (13,25) (13,22) (13,23) (13,15) (13,17) (13,28) (13,19) (13,30) (13,29) (14,18) (14,16) (14,26) (14,24) (14,27) (14,20) (14,25) (14,23) (14,15) (14,17) (14,28) (14,19) (14,30) (14,29) (15,18) (15,26) (15,21) (15,24) (15,27) (15,20) (15,25) (15,23) (15,28) (15,30) (16,18) (16,26) (16,24) (16,27) (16,20) (16,25) (16,22) (16,23) (16,28) (16,30) (16,29) (17,18) (17,21) (17,24) (17,27) (17,25) (17,23) (17,28) (17,30) (18,26) (18,27) (18,20) (18,23) (18,28) (18,19) (18,30) (18,29) (19,26) (19,24) (19,27) (19,20) (19,25) (19,22) (19,23) (19,28) (19,30) (19,29) (20,26) (20,25) (20,22) (20,23) (20,28) (20,30) (20,29) (21,26) (21,24) (21,23) (21,28) (21,29) (22,26) (22,24) (22,27) (22,25) (22,23) (22,28) (22,30) (22,29) (23,26) (23,27) (23,25) (23,28) (23,30) (24,26) (24,25) (25,26) (25,27) (25,28) (25,29) (26,27) (26,28) (26,30) (26,29) (27,30) (27,29) (28,29)\nIs there a path between node 5 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph605-30_14", + "image": "data/connectivity/graph_visual/hard/graph605.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,3) (0,18) (0,9) (1,3) (1,31) (1,23) (2,22) (2,5) (3,27) (3,20) (4,12) (4,22) (4,33) (4,10) (4,26) (5,22) (5,17) (5,33) (5,14) (6,32) (6,29) (7,26) (8,28) (8,25) (8,17) (9,34) (9,13) (10,28) (10,17) (10,16) (11,18) (11,13) (11,19) (12,24) (12,22) (12,17) (12,16) (13,31) (13,20) (14,28) (14,30) (14,17) (15,25) (15,30) (15,17) (16,30) (16,26) (18,27) (18,20) (20,23) (22,25) (22,30) (22,33) (22,26) (23,27) (25,28) (26,28) (28,33)\nIs there a path between node 30 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph608-16_15", + "image": "data/connectivity/graph_visual/hard/graph608.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,16) (0,32) (0,6) (0,11) (0,34) (1,26) (1,18) (2,13) (2,8) (2,34) (2,20) (3,30) (3,8) (3,11) (4,10) (5,7) (5,29) (6,32) (6,13) (6,28) (6,20) (7,22) (7,12) (7,23) (7,33) (8,16) (8,32) (8,13) (8,28) (8,20) (9,31) (10,19) (11,34) (13,34) (13,28) (13,20) (14,21) (16,32) (16,30) (16,28) (17,34) (17,28) (19,21) (20,32) (21,25) (22,26) (25,27) (28,30) (30,32)\nIs there a path between node 16 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph474-27_12", + "image": "data/connectivity/graph_visual/hard/graph474.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (0,2) (0,21) (0,11) (0,16) (0,30) (0,29) (0,24) (0,14) (0,3) (0,15) (0,17) (0,7) (0,18) (0,8) (0,23) (0,5) (1,21) (1,11) (1,12) (1,26) (1,30) (1,20) (1,29) (1,31) (1,24) (1,14) (1,15) (1,17) (1,7) (1,18) (1,22) (1,23) (1,5) (2,21) (2,11) (2,12) (2,26) (2,30) (2,20) (2,29) (2,31) (2,24) (2,4) (2,3) (2,15) (2,7) (2,13) (2,22) (2,8) (2,23) (3,28) (3,21) (3,11) (3,12) (3,16) (3,30) (3,20) (3,29) (3,31) (3,14) (3,4) (3,17) (3,7) (3,13) (3,8) (3,23) (3,5) (4,28) (4,11) (4,12) (4,16) (4,6) (4,30) (4,29) (4,31) (4,25) (4,14) (4,15) (4,7) (4,22) (4,23) (4,5) (5,28) (5,11) (5,16) (5,26) (5,30) (5,31) (5,25) (5,14) (5,15) (5,17) (5,7) (5,18) (5,22) (5,8) (5,23) (6,28) (6,21) (6,26) (6,30) (6,20) (6,31) (6,25) (6,14) (6,15) (6,17) (6,7) (6,13) (6,18) (6,22) (6,23) (7,28) (7,11) (7,12) (7,16) (7,26) (7,20) (7,24) (7,25) (7,14) (7,23) (8,21) (8,11) (8,12) (8,16) (8,30) (8,20) (8,31) (8,24) (8,25) (8,17) (8,13) (8,18) (10,19) (11,28) (11,21) (11,12) (11,16) (11,26) (11,20) (11,29) (11,31) (11,14) (11,15) (11,17) (11,13) (11,18) (11,23) (12,21) (12,16) (12,26) (12,30) (12,29) (12,25) (12,15) (12,13) (12,18) (12,22) (13,28) (13,21) (13,16) (13,26) (13,30) (13,20) (13,29) (13,31) (13,24) (13,25) (13,14) (13,15) (13,17) (13,18) (13,23) (14,28) (14,21) (14,16) (14,26) (14,30) (14,29) (14,15) (14,17) (14,18) (14,22) (15,28) (15,21) (15,16) (15,30) (15,20) (15,31) (15,24) (15,17) (15,18) (15,23) (16,28) (16,21) (16,26) (16,20) (16,29) (16,31) (16,24) (16,25) (16,17) (16,18) (16,22) (16,23) (17,28) (17,30) (17,20) (17,29) (17,31) (17,24) (17,25) (17,18) (17,22) (18,28) (18,21) (18,26) (18,30) (18,23) (19,32) (20,21) (20,26) (20,30) (20,29) (20,31) (20,24) (20,25) (20,22) (20,23) (21,30) (21,29) (21,31) (21,25) (21,22) (21,23) (22,28) (22,30) (22,29) (22,25) (23,26) (23,30) (23,29) (23,31) (24,26) (24,29) (24,25) (25,26) (26,30) (26,29) (28,30) (28,29) (28,31) (29,30) (30,31)\nIs there a path between node 27 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph214-9_6", + "image": "data/connectivity/graph_visual/hard/graph214.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,5) (0,4) (0,22) (0,15) (2,28) (4,9) (4,15) (5,20) (5,22) (5,18) (6,25) (6,12) (7,10) (7,11) (8,21) (8,20) (8,15) (9,22) (9,18) (10,11) (11,24) (11,17) (11,27) (12,19) (12,13) (12,25) (13,25) (14,17) (15,20) (16,28) (18,21) (19,26) (21,22) (24,27) (25,29) (26,29)\nIs there a path between node 9 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph32-13_23", + "image": "data/connectivity/graph_visual/hard/graph32.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,13) (0,12) (0,20) (0,15) (0,4) (0,8) (0,18) (0,24) (0,10) (0,14) (0,9) (0,16) (0,2) (0,7) (0,11) (0,17) (1,20) (1,19) (1,23) (1,5) (1,15) (1,4) (1,18) (1,24) (1,10) (1,14) (1,16) (1,21) (1,7) (1,11) (1,17) (2,13) (2,12) (2,19) (2,5) (2,15) (2,18) (2,24) (2,14) (2,9) (2,21) (2,17) (3,13) (3,20) (3,23) (3,15) (3,4) (3,18) (3,24) (3,14) (3,9) (3,16) (3,21) (3,7) (3,11) (4,13) (4,12) (4,20) (4,19) (4,15) (4,24) (4,10) (4,9) (4,16) (4,7) (4,11) (4,17) (5,12) (5,20) (5,19) (5,23) (5,15) (5,18) (5,24) (5,10) (5,14) (5,9) (5,21) (5,7) (5,17) (6,22) (7,12) (7,20) (7,19) (7,23) (7,15) (7,8) (7,18) (7,24) (7,10) (7,14) (7,9) (7,21) (7,11) (8,13) (8,15) (8,18) (8,24) (8,10) (8,14) (8,16) (8,17) (9,19) (9,23) (9,15) (9,18) (9,24) (9,10) (9,21) (9,17) (10,13) (10,23) (10,15) (10,24) (10,14) (10,21) (10,11) (11,13) (11,12) (11,20) (11,19) (11,23) (11,15) (11,18) (11,14) (11,16) (11,21) (12,13) (12,20) (12,15) (12,24) (12,14) (12,16) (12,21) (12,17) (13,20) (13,19) (13,15) (13,18) (13,21) (13,17) (14,20) (14,19) (14,23) (14,15) (14,18) (14,16) (14,17) (15,20) (15,19) (15,23) (15,18) (15,24) (15,17) (16,19) (16,23) (16,18) (17,20) (17,19) (17,24) (18,20) (18,19) (18,21) (19,20) (19,23) (19,24) (19,21) (20,23) (20,24) (20,21) (21,23) (21,24) (22,25) (23,24)\nIs there a path between node 13 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph466-12_28", + "image": "data/connectivity/graph_visual/hard/graph466.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,17) (0,32) (0,5) (0,31) (0,29) (0,27) (0,1) (0,18) (0,13) (0,2) (0,23) (1,7) (1,17) (1,20) (1,14) (1,13) (1,28) (2,3) (2,26) (2,32) (2,20) (2,31) (2,27) (2,23) (3,17) (3,25) (3,5) (3,19) (3,31) (3,14) (3,29) (3,11) (3,27) (3,18) (3,13) (3,22) (3,9) (4,20) (4,31) (4,14) (4,11) (4,16) (4,27) (4,18) (4,10) (4,9) (5,7) (5,17) (5,25) (5,32) (5,20) (5,18) (6,15) (6,12) (7,20) (7,19) (7,9) (7,23) (8,17) (8,32) (8,19) (8,29) (8,11) (8,22) (8,21) (9,17) (9,25) (9,28) (10,25) (10,20) (10,31) (10,14) (11,26) (11,17) (11,13) (11,22) (11,28) (11,21) (12,30) (13,19) (13,16) (13,28) (13,23) (14,29) (14,16) (14,18) (14,22) (15,30) (15,24) (16,19) (16,27) (16,28) (17,32) (17,20) (17,31) (17,23) (18,25) (18,31) (19,20) (19,28) (19,21) (20,25) (20,32) (20,27) (20,21) (21,23) (22,26) (22,31) (22,23) (23,26) (23,32) (23,29) (24,30) (26,32) (26,29) (26,28) (27,31) (28,32) (29,32) (29,31)\nIs there a path between node 12 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph38-2_10", + "image": "data/connectivity/graph_visual/hard/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,7) (0,4) (0,24) (0,15) (1,2) (1,19) (1,6) (1,23) (1,13) (1,5) (1,20) (1,16) (1,25) (1,9) (1,21) (2,3) (2,6) (2,12) (2,23) (2,13) (2,5) (2,20) (2,16) (2,25) (2,9) (2,21) (2,8) (3,10) (3,22) (3,19) (3,6) (3,12) (3,14) (3,23) (3,13) (3,5) (3,20) (3,25) (3,9) (3,8) (4,11) (4,15) (5,6) (5,12) (5,23) (5,20) (5,17) (5,8) (6,22) (6,19) (6,14) (6,23) (6,13) (6,25) (6,17) (6,9) (7,15) (8,10) (8,22) (8,12) (8,13) (8,20) (8,16) (8,25) (8,9) (8,21) (9,22) (9,19) (9,12) (9,14) (9,23) (9,16) (9,25) (9,21) (10,12) (10,14) (10,20) (10,16) (10,25) (11,24) (11,15) (12,22) (12,16) (12,25) (12,17) (12,21) (13,22) (13,19) (13,14) (13,23) (13,20) (13,16) (13,17) (14,22) (14,19) (14,23) (14,25) (14,21) (15,18) (16,22) (16,23) (16,20) (16,25) (17,22) (17,19) (17,23) (17,20) (18,24) (19,22) (19,21) (20,23) (20,25) (21,22) (21,25) (22,25) (23,25)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph582-16_4", + "image": "data/connectivity/graph_visual/hard/graph582.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,19) (0,10) (0,22) (0,8) (0,12) (0,9) (0,31) (0,16) (0,32) (0,24) (0,26) (0,15) (0,4) (0,21) (0,18) (0,2) (0,28) (0,1) (0,20) (0,27) (0,29) (0,14) (1,19) (1,23) (1,10) (1,22) (1,7) (1,30) (1,12) (1,9) (1,31) (1,16) (1,26) (1,13) (1,4) (1,21) (1,18) (1,2) (1,20) (1,27) (1,17) (1,29) (1,3) (1,11) (2,19) (2,23) (2,10) (2,22) (2,7) (2,8) (2,12) (2,9) (2,32) (2,24) (2,26) (2,15) (2,13) (2,4) (2,21) (2,18) (2,33) (2,28) (2,20) (2,14) (2,3) (2,11) (3,7) (3,8) (3,9) (3,31) (3,16) (3,24) (3,15) (3,4) (3,21) (3,18) (3,33) (3,28) (3,20) (3,27) (3,14) (3,11) (4,19) (4,23) (4,10) (4,22) (4,7) (4,8) (4,30) (4,12) (4,31) (4,16) (4,24) (4,15) (4,21) (4,18) (4,33) (4,28) (4,20) (4,27) (4,17) (4,14) (4,11) (5,25) (6,25) (7,23) (7,10) (7,22) (7,8) (7,31) (7,16) (7,24) (7,26) (7,13) (7,21) (7,18) (7,33) (7,28) (7,20) (7,17) (7,29) (7,14) (7,11) (8,19) (8,10) (8,22) (8,30) (8,31) (8,16) (8,24) (8,26) (8,15) (8,13) (8,21) (8,18) (8,33) (8,20) (8,17) (8,14) (8,11) (9,19) (9,23) (9,10) (9,30) (9,12) (9,16) (9,32) (9,26) (9,15) (9,21) (9,28) (9,20) (9,17) (9,29) (9,14) (9,11) (10,23) (10,12) (10,31) (10,16) (10,32) (10,24) (10,26) (10,21) (10,33) (10,27) (10,17) (10,14) (10,11) (11,19) (11,23) (11,22) (11,30) (11,12) (11,31) (11,16) (11,24) (11,26) (11,13) (11,21) (11,28) (11,20) (11,27) (12,19) (12,23) (12,22) (12,30) (12,16) (12,32) (12,15) (12,13) (12,21) (12,18) (12,33) (12,28) (12,29) (13,19) (13,30) (13,16) (13,32) (13,26) (13,33) (13,28) (13,29) (13,14) (14,19) (14,23) (14,22) (14,30) (14,24) (14,15) (14,33) (14,27) (14,17) (14,29) (15,19) (15,22) (15,30) (15,31) (15,21) (15,18) (15,27) (15,17) (15,29) (16,19) (16,22) (16,30) (16,32) (16,24) (16,33) (16,28) (16,20) (16,27) (16,17) (16,29) (17,19) (17,22) (17,30) (17,31) (17,32) (17,24) (17,26) (17,21) (17,33) (17,28) (17,20) (17,27) (17,29) (18,23) (18,22) (18,30) (18,32) (18,24) (18,21) (18,33) (18,28) (18,20) (18,27) (19,23) (19,22) (19,30) (19,31) (19,32) (19,24) (19,26) (19,21) (19,33) (19,28) (19,27) (19,29) (20,22) (20,30) (20,31) (20,26) (20,21) (20,33) (20,27) (20,29) (21,23) (21,22) (21,30) (21,31) (21,28) (21,27) (21,29) (22,30) (22,31) (22,24) (22,26) (22,33) (22,27) (23,32) (23,26) (23,28) (23,27) (23,29) (24,32) (24,33) (24,28) (24,27) (24,29) (26,30) (26,31) (26,28) (27,31) (27,32) (27,29) (28,30) (28,31) (28,33) (28,29) (29,30) (29,31) (29,32) (31,33)\nIs there a path between node 16 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph158-7_21", + "image": "data/connectivity/graph_visual/hard/graph158.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,21) (0,2) (0,13) (0,26) (1,24) (1,22) (1,17) (2,11) (2,15) (2,10) (2,19) (3,4) (3,6) (3,22) (3,17) (3,20) (4,8) (4,24) (5,8) (5,24) (5,20) (6,8) (6,22) (6,20) (6,7) (7,24) (7,22) (7,25) (9,11) (9,12) (9,18) (9,23) (9,14) (9,19) (9,26) (10,19) (10,28) (11,21) (11,14) (11,15) (11,19) (11,16) (11,28) (11,26) (12,26) (13,28) (14,18) (15,21) (15,18) (15,23) (17,27) (17,24) (17,25) (17,20) (19,21) (19,23) (19,26) (20,22) (23,26)\nIs there a path between node 7 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph340-25_13", + "image": "data/connectivity/graph_visual/hard/graph340.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,14) (0,13) (0,27) (1,21) (1,24) (1,13) (1,5) (2,19) (3,30) (3,26) (3,10) (3,25) (5,15) (5,9) (5,27) (5,19) (6,22) (6,29) (6,16) (7,15) (7,24) (7,9) (7,19) (9,21) (9,15) (9,24) (10,31) (10,11) (10,23) (11,23) (11,26) (11,17) (12,22) (12,29) (12,16) (13,14) (13,24) (14,21) (14,24) (14,27) (15,21) (16,29) (17,23) (17,25) (18,20) (18,29) (20,22) (21,27) (24,27) (25,28)\nIs there a path between node 25 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph474-27_19", + "image": "data/connectivity/graph_visual/hard/graph474.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (0,2) (0,21) (0,11) (0,16) (0,30) (0,29) (0,24) (0,14) (0,3) (0,15) (0,17) (0,7) (0,18) (0,8) (0,23) (0,5) (1,21) (1,11) (1,12) (1,26) (1,30) (1,20) (1,29) (1,31) (1,24) (1,14) (1,15) (1,17) (1,7) (1,18) (1,22) (1,23) (1,5) (2,21) (2,11) (2,12) (2,26) (2,30) (2,20) (2,29) (2,31) (2,24) (2,4) (2,3) (2,15) (2,7) (2,13) (2,22) (2,8) (2,23) (3,28) (3,21) (3,11) (3,12) (3,16) (3,30) (3,20) (3,29) (3,31) (3,14) (3,4) (3,17) (3,7) (3,13) (3,8) (3,23) (3,5) (4,28) (4,11) (4,12) (4,16) (4,6) (4,30) (4,29) (4,31) (4,25) (4,14) (4,15) (4,7) (4,22) (4,23) (4,5) (5,28) (5,11) (5,16) (5,26) (5,30) (5,31) (5,25) (5,14) (5,15) (5,17) (5,7) (5,18) (5,22) (5,8) (5,23) (6,28) (6,21) (6,26) (6,30) (6,20) (6,31) (6,25) (6,14) (6,15) (6,17) (6,7) (6,13) (6,18) (6,22) (6,23) (7,28) (7,11) (7,12) (7,16) (7,26) (7,20) (7,24) (7,25) (7,14) (7,23) (8,21) (8,11) (8,12) (8,16) (8,30) (8,20) (8,31) (8,24) (8,25) (8,17) (8,13) (8,18) (10,19) (11,28) (11,21) (11,12) (11,16) (11,26) (11,20) (11,29) (11,31) (11,14) (11,15) (11,17) (11,13) (11,18) (11,23) (12,21) (12,16) (12,26) (12,30) (12,29) (12,25) (12,15) (12,13) (12,18) (12,22) (13,28) (13,21) (13,16) (13,26) (13,30) (13,20) (13,29) (13,31) (13,24) (13,25) (13,14) (13,15) (13,17) (13,18) (13,23) (14,28) (14,21) (14,16) (14,26) (14,30) (14,29) (14,15) (14,17) (14,18) (14,22) (15,28) (15,21) (15,16) (15,30) (15,20) (15,31) (15,24) (15,17) (15,18) (15,23) (16,28) (16,21) (16,26) (16,20) (16,29) (16,31) (16,24) (16,25) (16,17) (16,18) (16,22) (16,23) (17,28) (17,30) (17,20) (17,29) (17,31) (17,24) (17,25) (17,18) (17,22) (18,28) (18,21) (18,26) (18,30) (18,23) (19,32) (20,21) (20,26) (20,30) (20,29) (20,31) (20,24) (20,25) (20,22) (20,23) (21,30) (21,29) (21,31) (21,25) (21,22) (21,23) (22,28) (22,30) (22,29) (22,25) (23,26) (23,30) (23,29) (23,31) (24,26) (24,29) (24,25) (25,26) (26,30) (26,29) (28,30) (28,29) (28,31) (29,30) (30,31)\nIs there a path between node 27 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph562-0_20", + "image": "data/connectivity/graph_visual/hard/graph562.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,27) (0,10) (0,8) (0,23) (1,2) (1,21) (1,17) (1,31) (2,6) (2,33) (2,9) (2,3) (2,21) (2,7) (2,16) (3,17) (3,24) (3,5) (4,32) (4,22) (4,12) (5,33) (5,28) (6,24) (6,26) (6,19) (6,16) (6,28) (7,33) (7,24) (7,13) (8,27) (9,31) (9,16) (9,13) (10,27) (10,29) (10,20) (10,12) (11,32) (12,29) (12,22) (13,15) (13,21) (13,26) (13,19) (13,18) (15,21) (16,24) (16,26) (16,18) (17,21) (17,28) (18,33) (18,21) (18,26) (19,21) (19,28) (20,25) (20,22) (21,26) (21,28) (22,30) (22,29) (22,23) (23,29) (23,25) (24,33) (25,29) (26,28) (28,33) (28,31) (29,32) (30,32)\nIs there a path between node 0 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph360-15_18", + "image": "data/connectivity/graph_visual/hard/graph360.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,28) (0,24) (0,31) (0,30) (0,27) (0,20) (1,21) (1,6) (1,19) (1,12) (1,22) (1,4) (1,17) (1,13) (1,30) (2,23) (2,3) (2,14) (3,25) (4,5) (4,17) (4,27) (5,17) (5,31) (5,20) (6,26) (6,16) (6,28) (6,10) (6,19) (6,12) (6,22) (6,13) (7,21) (7,28) (7,19) (7,17) (7,13) (7,18) (7,27) (8,23) (8,11) (8,25) (10,26) (10,28) (10,22) (10,31) (10,18) (11,23) (12,30) (13,21) (13,19) (13,31) (15,26) (15,16) (15,17) (15,18) (15,20) (16,21) (16,28) (16,19) (16,30) (16,27) (16,20) (17,24) (17,22) (17,18) (18,22) (19,22) (19,31) (19,20) (20,28) (21,22) (21,31) (22,30) (24,31) (27,28) (28,31)\nIs there a path between node 15 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph51-21_12", + "image": "data/connectivity/graph_visual/hard/graph51.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,4) (0,11) (0,16) (2,19) (2,4) (2,11) (3,4) (3,11) (5,8) (5,20) (5,25) (6,8) (6,22) (6,7) (6,18) (6,25) (7,22) (8,18) (8,24) (8,20) (8,21) (10,20) (10,26) (10,13) (11,19) (11,23) (13,22) (13,25) (15,24) (15,20) (15,25) (15,21) (16,23) (18,26) (19,23) (21,24) (21,25) (22,25) (22,26) (24,26)\nIs there a path between node 21 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph227-8_12", + "image": "data/connectivity/graph_visual/hard/graph227.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,27) (0,4) (0,11) (0,1) (0,17) (0,15) (0,3) (0,25) (0,18) (1,4) (1,11) (1,22) (1,17) (1,20) (1,15) (1,7) (1,25) (1,18) (1,26) (2,9) (2,23) (2,29) (2,21) (2,28) (2,6) (2,8) (3,4) (3,11) (3,13) (3,22) (3,17) (3,19) (3,15) (3,7) (3,25) (3,18) (3,16) (3,26) (4,27) (4,11) (4,13) (4,22) (4,17) (4,7) (4,25) (4,18) (4,26) (6,24) (6,10) (6,23) (6,21) (6,28) (6,8) (7,11) (7,13) (7,17) (7,25) (7,18) (7,26) (8,9) (8,24) (8,10) (8,23) (8,21) (8,28) (9,24) (9,10) (9,23) (9,29) (9,21) (9,28) (10,24) (10,23) (10,29) (10,21) (10,28) (11,27) (11,13) (11,22) (11,17) (11,20) (11,19) (11,25) (11,18) (11,16) (11,26) (12,14) (13,27) (13,22) (13,17) (13,19) (13,15) (13,25) (13,18) (13,16) (13,26) (15,27) (15,22) (15,17) (15,20) (15,25) (15,16) (15,26) (16,20) (16,25) (16,18) (16,26) (17,22) (17,20) (17,19) (17,25) (17,18) (17,26) (18,27) (18,22) (18,19) (18,25) (18,26) (19,27) (19,22) (19,20) (19,25) (19,26) (20,27) (20,25) (20,26) (21,24) (21,29) (22,27) (22,25) (22,26) (24,28) (25,27) (25,26) (26,27) (28,29)\nIs there a path between node 8 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph331-8_14", + "image": "data/connectivity/graph_visual/hard/graph331.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,16) (0,12) (0,23) (0,10) (0,31) (0,3) (0,26) (0,22) (0,6) (0,25) (0,14) (0,24) (0,5) (1,29) (1,7) (1,16) (1,27) (1,12) (1,23) (1,31) (1,3) (1,19) (1,15) (1,9) (1,26) (1,6) (1,28) (1,13) (1,14) (1,24) (1,5) (2,20) (2,4) (2,17) (2,21) (2,30) (3,29) (3,7) (3,16) (3,27) (3,23) (3,31) (3,19) (3,15) (3,26) (3,6) (3,25) (3,28) (3,8) (3,13) (3,14) (3,24) (3,5) (4,20) (4,18) (4,30) (5,29) (5,7) (5,27) (5,12) (5,10) (5,9) (5,11) (5,26) (5,6) (5,28) (5,14) (5,24) (6,7) (6,16) (6,27) (6,23) (6,10) (6,15) (6,11) (6,26) (6,22) (6,25) (6,28) (6,13) (6,14) (7,29) (7,12) (7,23) (7,19) (7,15) (7,26) (7,22) (7,13) (7,14) (7,24) (8,29) (8,27) (8,23) (8,10) (8,19) (8,9) (8,11) (8,26) (8,22) (8,25) (8,14) (9,29) (9,12) (9,23) (9,10) (9,31) (9,19) (9,15) (9,22) (9,13) (9,24) (10,27) (10,12) (10,15) (10,11) (10,26) (10,25) (10,28) (10,13) (10,14) (11,29) (11,16) (11,27) (11,12) (11,23) (11,19) (11,15) (11,26) (11,28) (11,14) (11,24) (12,29) (12,23) (12,31) (12,19) (12,26) (12,22) (12,25) (12,28) (12,13) (12,24) (13,29) (13,16) (13,27) (13,31) (13,19) (13,22) (13,28) (13,14) (13,24) (14,29) (14,16) (14,27) (14,23) (14,31) (14,19) (14,26) (14,22) (14,25) (14,28) (14,24) (15,29) (15,16) (15,31) (15,19) (15,26) (15,22) (15,25) (15,28) (15,24) (16,29) (16,31) (16,26) (16,22) (16,25) (16,28) (16,24) (17,20) (17,18) (17,21) (17,30) (18,21) (18,30) (19,29) (19,27) (19,23) (19,22) (19,25) (20,21) (21,30) (22,29) (22,27) (22,23) (22,31) (22,25) (22,28) (22,24) (23,29) (23,27) (23,31) (23,24) (24,29) (24,27) (24,31) (24,26) (24,25) (24,28) (25,29) (25,27) (25,31) (25,28) (26,29) (26,27) (26,31) (27,29) (27,28) (28,29) (29,31)\nIs there a path between node 8 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph158-25_6", + "image": "data/connectivity/graph_visual/hard/graph158.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,21) (0,2) (0,13) (0,26) (1,24) (1,22) (1,17) (2,11) (2,15) (2,10) (2,19) (3,4) (3,6) (3,22) (3,17) (3,20) (4,8) (4,24) (5,8) (5,24) (5,20) (6,8) (6,22) (6,20) (6,7) (7,24) (7,22) (7,25) (9,11) (9,12) (9,18) (9,23) (9,14) (9,19) (9,26) (10,19) (10,28) (11,21) (11,14) (11,15) (11,19) (11,16) (11,28) (11,26) (12,26) (13,28) (14,18) (15,21) (15,18) (15,23) (17,27) (17,24) (17,25) (17,20) (19,21) (19,23) (19,26) (20,22) (23,26)\nIs there a path between node 25 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph533-27_32", + "image": "data/connectivity/graph_visual/hard/graph533.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,28) (0,18) (0,19) (0,2) (0,15) (0,26) (0,8) (0,1) (0,33) (0,17) (0,16) (1,28) (1,6) (1,19) (1,2) (1,15) (1,26) (1,8) (1,33) (1,5) (1,23) (1,17) (1,16) (1,7) (2,28) (2,6) (2,18) (2,19) (2,15) (2,26) (2,8) (2,33) (2,5) (2,17) (2,16) (2,24) (3,11) (3,21) (3,22) (3,4) (3,12) (4,11) (4,12) (5,28) (5,6) (5,19) (5,15) (5,26) (5,33) (5,23) (5,16) (5,24) (5,7) (6,28) (6,18) (6,19) (6,15) (6,26) (6,8) (6,33) (6,23) (6,17) (6,16) (6,24) (7,18) (7,19) (7,26) (7,23) (7,17) (7,16) (7,24) (8,28) (8,15) (8,33) (8,23) (8,17) (8,16) (8,24) (9,31) (9,27) (9,25) (9,10) (9,32) (9,29) (9,14) (10,20) (10,31) (10,27) (10,13) (10,32) (10,30) (11,21) (11,12) (12,21) (13,20) (13,31) (13,27) (13,32) (13,30) (13,29) (14,20) (14,31) (14,27) (14,25) (14,32) (14,30) (14,29) (15,28) (15,18) (15,33) (15,16) (15,24) (16,18) (16,26) (16,33) (16,23) (16,17) (17,28) (17,18) (17,26) (17,23) (18,28) (18,19) (18,33) (18,23) (18,24) (19,28) (19,33) (19,23) (19,24) (20,31) (20,27) (20,32) (20,30) (20,29) (23,28) (23,26) (23,33) (24,26) (24,33) (25,31) (25,27) (25,29) (26,28) (26,33) (27,31) (27,32) (27,30) (29,32) (29,30) (30,31) (31,32)\nIs there a path between node 27 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph105-23_20", + "image": "data/connectivity/graph_visual/hard/graph105.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,7) (0,2) (0,24) (0,25) (0,12) (0,3) (0,1) (0,14) (0,26) (0,11) (0,10) (0,6) (0,16) (0,22) (0,9) (1,18) (1,7) (1,2) (1,21) (1,15) (1,24) (1,4) (1,12) (1,26) (1,11) (1,10) (1,16) (1,9) (2,7) (2,21) (2,23) (2,25) (2,12) (2,3) (2,26) (2,11) (2,6) (3,18) (3,7) (3,21) (3,19) (3,24) (3,4) (3,14) (3,26) (3,11) (3,20) (3,6) (3,16) (3,22) (3,9) (4,7) (4,17) (4,19) (4,15) (4,25) (4,14) (4,26) (4,20) (4,10) (4,6) (4,16) (4,9) (5,8) (6,7) (6,21) (6,19) (6,15) (6,23) (6,25) (6,12) (6,14) (6,26) (6,11) (6,20) (6,10) (6,16) (6,22) (6,9) (7,17) (7,21) (7,19) (7,15) (7,24) (7,25) (7,12) (7,14) (7,26) (7,10) (7,22) (8,13) (9,18) (9,17) (9,19) (9,23) (9,24) (9,25) (9,12) (9,14) (9,26) (9,11) (9,20) (9,22) (10,18) (10,17) (10,21) (10,19) (10,24) (10,25) (10,11) (10,22) (11,17) (11,21) (11,15) (11,23) (11,24) (11,25) (11,14) (11,20) (11,16) (11,22) (12,18) (12,17) (12,21) (12,15) (12,23) (12,14) (12,26) (12,20) (12,16) (12,22) (14,18) (14,17) (14,21) (14,19) (14,24) (14,25) (14,26) (14,20) (15,18) (15,17) (15,21) (15,23) (15,24) (15,25) (15,20) (15,16) (15,22) (16,17) (16,21) (16,23) (16,24) (16,25) (16,26) (16,20) (16,22) (17,18) (17,21) (17,19) (17,23) (17,24) (17,25) (17,26) (17,20) (18,19) (18,23) (18,24) (18,25) (18,26) (18,20) (18,22) (19,23) (19,25) (19,26) (20,23) (20,24) (20,26) (20,22) (21,25) (21,26) (21,22) (22,23) (22,24) (22,26) (23,24) (23,26) (24,25) (24,26)\nIs there a path between node 23 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph612-21_33", + "image": "data/connectivity/graph_visual/hard/graph612.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,21) (0,26) (0,9) (0,3) (0,4) (0,30) (0,16) (0,22) (0,12) (0,5) (0,28) (0,29) (0,19) (0,31) (0,27) (0,8) (0,32) (0,15) (0,23) (0,25) (1,34) (2,21) (2,26) (2,20) (2,3) (2,6) (2,30) (2,16) (2,22) (2,12) (2,13) (2,5) (2,33) (2,28) (2,24) (2,29) (2,19) (2,31) (2,17) (2,27) (2,8) (2,32) (2,15) (2,23) (3,21) (3,26) (3,9) (3,20) (3,6) (3,30) (3,7) (3,22) (3,12) (3,13) (3,5) (3,33) (3,28) (3,24) (3,29) (3,19) (3,31) (3,27) (3,8) (3,32) (3,15) (3,18) (3,23) (3,25) (4,21) (4,26) (4,9) (4,20) (4,6) (4,30) (4,7) (4,12) (4,13) (4,5) (4,33) (4,28) (4,29) (4,19) (4,27) (4,8) (4,32) (4,18) (5,21) (5,6) (5,7) (5,13) (5,33) (5,24) (5,31) (5,17) (5,27) (5,32) (5,15) (5,18) (5,25) (6,26) (6,9) (6,20) (6,30) (6,7) (6,22) (6,13) (6,28) (6,24) (6,29) (6,19) (6,31) (6,27) (6,8) (6,32) (6,18) (6,23) (6,25) (7,21) (7,26) (7,9) (7,20) (7,30) (7,22) (7,12) (7,13) (7,28) (7,29) (7,19) (7,31) (7,17) (7,27) (7,32) (7,15) (7,18) (7,23) (7,25) (8,21) (8,9) (8,20) (8,30) (8,16) (8,22) (8,12) (8,13) (8,33) (8,28) (8,31) (8,17) (8,15) (8,18) (8,23) (8,25) (9,21) (9,26) (9,20) (9,30) (9,22) (9,33) (9,28) (9,24) (9,29) (9,19) (9,31) (9,27) (9,32) (9,15) (9,23) (9,25) (10,34) (10,14) (11,34) (11,14) (12,21) (12,26) (12,20) (12,30) (12,22) (12,13) (12,28) (12,24) (12,32) (12,18) (12,25) (13,21) (13,26) (13,20) (13,30) (13,16) (13,22) (13,33) (13,24) (13,29) (13,19) (13,17) (13,27) (13,32) (13,15) (13,18) (13,25) (14,34) (15,21) (15,20) (15,22) (15,33) (15,28) (15,24) (15,29) (15,19) (15,31) (15,17) (15,27) (15,18) (15,23) (16,21) (16,26) (16,30) (16,22) (16,33) (16,28) (16,24) (16,29) (16,27) (16,32) (16,23) (17,21) (17,30) (17,22) (17,33) (17,28) (17,24) (17,29) (17,19) (17,31) (17,27) (17,32) (17,23) (17,25) (18,20) (18,30) (18,33) (18,29) (18,19) (18,31) (18,27) (18,32) (18,23) (18,25) (19,26) (19,20) (19,30) (19,22) (19,33) (19,28) (19,29) (19,32) (19,23) (19,25) (20,30) (20,22) (20,33) (20,28) (20,31) (20,27) (20,32) (20,23) (20,25) (21,22) (21,33) (21,24) (21,29) (21,31) (21,32) (22,26) (22,30) (22,33) (22,28) (22,29) (22,31) (22,27) (22,32) (22,25) (23,26) (23,30) (23,33) (23,28) (23,24) (23,29) (23,31) (23,27) (24,26) (24,30) (24,31) (24,32) (25,26) (25,28) (25,29) (25,32) (26,33) (26,28) (26,27) (27,28) (27,29) (27,31) (27,32) (28,33) (28,29) (28,31) (28,32) (29,30) (29,33) (29,31) (29,32) (30,33) (30,31) (30,32) (31,32) (32,33)\nIs there a path between node 21 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph30-14_16", + "image": "data/connectivity/graph_visual/hard/graph30.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,16) (0,14) (0,10) (0,24) (0,2) (0,12) (0,19) (0,3) (0,17) (0,25) (0,23) (0,15) (1,18) (1,11) (1,8) (2,14) (2,10) (2,24) (2,7) (2,3) (2,21) (2,25) (2,23) (2,6) (3,14) (3,24) (3,12) (3,19) (3,17) (3,25) (3,23) (3,6) (3,15) (4,18) (4,8) (5,18) (5,11) (5,8) (6,16) (6,14) (6,10) (6,12) (6,7) (6,19) (6,21) (6,25) (6,23) (6,9) (6,15) (7,16) (7,10) (7,24) (7,12) (7,19) (7,17) (7,25) (7,9) (7,15) (8,18) (8,11) (9,16) (9,14) (9,10) (9,24) (9,12) (9,19) (9,17) (9,21) (9,23) (9,15) (10,16) (10,14) (10,19) (10,21) (10,25) (10,23) (10,15) (11,18) (12,16) (12,14) (12,24) (12,19) (12,17) (12,21) (12,25) (12,23) (12,15) (13,20) (14,16) (14,24) (14,17) (14,21) (14,25) (14,23) (14,15) (15,16) (15,24) (15,23) (16,21) (16,25) (16,23) (17,21) (17,23) (19,21) (19,25) (21,24) (21,25) (21,23) (23,25) (24,25)\nIs there a path between node 14 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph170-7_26", + "image": "data/connectivity/graph_visual/hard/graph170.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,26) (0,12) (0,7) (0,13) (0,3) (0,8) (0,21) (0,18) (0,22) (0,6) (0,28) (0,11) (0,24) (0,4) (0,5) (0,15) (0,20) (0,19) (1,26) (1,12) (1,13) (1,21) (1,18) (1,22) (1,6) (1,17) (1,23) (1,14) (1,11) (1,27) (1,24) (1,4) (1,5) (1,20) (2,25) (2,9) (2,16) (3,7) (3,13) (3,8) (3,18) (3,22) (3,17) (3,23) (3,14) (3,11) (3,27) (3,24) (3,15) (3,20) (3,19) (4,26) (4,12) (4,13) (4,8) (4,21) (4,6) (4,17) (4,23) (4,28) (4,27) (4,24) (4,5) (4,20) (5,12) (5,7) (5,13) (5,8) (5,21) (5,18) (5,22) (5,17) (5,28) (5,27) (5,15) (5,20) (5,19) (6,12) (6,7) (6,13) (6,8) (6,21) (6,22) (6,17) (6,14) (6,28) (6,27) (6,15) (6,20) (6,19) (7,26) (7,12) (7,13) (7,8) (7,21) (7,22) (7,17) (7,23) (7,28) (7,11) (7,24) (7,15) (8,26) (8,13) (8,22) (8,17) (8,11) (8,27) (8,24) (9,25) (9,16) (11,12) (11,13) (11,21) (11,22) (11,17) (11,23) (11,28) (11,27) (11,24) (11,15) (11,20) (11,19) (12,26) (12,18) (12,22) (12,17) (12,14) (12,28) (12,24) (12,15) (12,20) (12,19) (13,26) (13,18) (13,17) (13,23) (13,14) (13,28) (13,15) (13,20) (13,19) (14,22) (14,17) (14,23) (14,28) (14,24) (14,15) (14,19) (15,26) (15,21) (15,17) (15,28) (15,24) (15,20) (16,25) (17,26) (17,21) (17,18) (17,22) (17,27) (17,24) (17,20) (17,19) (18,21) (18,28) (18,27) (18,24) (19,21) (19,22) (19,28) (19,27) (19,24) (19,20) (20,26) (20,22) (20,24) (21,26) (21,22) (21,28) (21,27) (21,24) (22,23) (22,28) (22,27) (22,24) (23,26) (23,27) (23,24) (24,27) (26,27) (27,28)\nIs there a path between node 7 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph270-15_4", + "image": "data/connectivity/graph_visual/hard/graph270.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,20) (0,14) (0,18) (0,16) (1,27) (1,28) (1,9) (1,22) (1,21) (1,19) (1,10) (1,23) (1,7) (1,2) (2,26) (2,25) (2,6) (2,9) (2,22) (2,21) (2,10) (2,23) (2,7) (2,30) (2,12) (3,5) (3,15) (3,11) (3,29) (3,4) (4,5) (4,15) (4,11) (5,15) (5,24) (5,29) (5,8) (6,25) (6,22) (6,17) (6,21) (6,19) (6,10) (6,23) (6,7) (6,30) (7,26) (7,25) (7,9) (7,22) (7,17) (7,21) (7,19) (7,10) (7,23) (7,12) (8,24) (9,27) (9,26) (9,22) (9,21) (9,19) (9,23) (9,30) (9,12) (10,28) (10,26) (10,22) (10,17) (10,21) (10,23) (10,30) (10,12) (11,15) (11,24) (11,29) (12,27) (12,28) (12,26) (12,25) (12,17) (12,21) (12,19) (12,23) (12,30) (13,14) (13,16) (14,18) (14,16) (15,24) (15,29) (16,20) (16,18) (17,27) (17,26) (17,22) (17,19) (17,30) (18,20) (19,27) (19,26) (19,22) (19,23) (19,30) (21,28) (21,26) (21,25) (21,22) (21,23) (21,30) (22,27) (22,28) (22,25) (22,23) (22,30) (23,27) (23,28) (23,26) (23,25) (23,30) (24,29) (25,26) (26,27) (26,28) (26,30) (27,28) (27,30) (28,30)\nIs there a path between node 15 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph131-18_20", + "image": "data/connectivity/graph_visual/hard/graph131.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,7) (0,18) (0,14) (0,6) (0,13) (1,12) (1,2) (1,11) (1,16) (1,21) (1,20) (1,4) (1,10) (1,27) (2,15) (2,12) (2,11) (2,16) (2,21) (2,17) (2,20) (2,4) (2,10) (3,19) (4,15) (4,16) (4,21) (4,17) (4,20) (4,5) (4,10) (5,15) (5,12) (5,16) (5,21) (5,17) (5,10) (5,27) (6,26) (6,8) (6,23) (6,9) (6,18) (7,26) (7,8) (7,9) (7,25) (8,26) (8,23) (8,18) (8,25) (8,14) (8,13) (9,25) (9,14) (10,15) (10,12) (10,11) (11,12) (11,16) (11,21) (11,17) (11,20) (11,27) (12,15) (12,16) (12,21) (12,20) (12,27) (13,23) (13,18) (13,25) (13,14) (14,26) (14,25) (15,16) (15,21) (15,17) (15,20) (15,27) (16,17) (16,20) (16,27) (17,21) (17,20) (17,27) (18,26) (18,25) (19,22) (20,21) (20,27) (23,26) (23,25) (25,26)\nIs there a path between node 18 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph180-22_2", + "image": "data/connectivity/graph_visual/hard/graph180.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,6) (0,15) (0,9) (0,19) (0,26) (0,21) (0,13) (0,24) (0,11) (0,2) (0,25) (0,3) (0,12) (0,23) (0,27) (0,4) (1,28) (1,16) (1,7) (1,10) (2,8) (2,6) (2,15) (2,26) (2,17) (2,21) (2,13) (2,11) (2,14) (2,18) (2,5) (2,12) (2,4) (3,8) (3,22) (3,6) (3,15) (3,9) (3,19) (3,17) (3,21) (3,24) (3,11) (3,25) (3,14) (3,23) (3,4) (4,22) (4,15) (4,9) (4,19) (4,17) (4,13) (4,24) (4,25) (4,14) (4,18) (4,5) (4,23) (4,27) (5,8) (5,15) (5,9) (5,26) (5,17) (5,13) (5,24) (5,25) (5,12) (5,23) (5,27) (6,15) (6,19) (6,26) (6,17) (6,21) (6,13) (6,14) (6,12) (6,23) (6,27) (7,16) (7,20) (8,22) (8,9) (8,19) (8,17) (8,13) (8,24) (8,14) (8,18) (8,23) (8,27) (9,22) (9,19) (9,17) (9,21) (9,24) (9,11) (9,25) (9,14) (9,18) (9,12) (9,23) (9,27) (10,28) (10,16) (10,20) (11,22) (11,19) (11,26) (11,21) (11,24) (11,14) (11,18) (11,12) (11,23) (11,27) (12,22) (12,19) (12,26) (12,21) (12,13) (12,24) (12,14) (12,18) (12,27) (13,22) (13,15) (13,26) (13,21) (13,25) (13,14) (13,18) (13,27) (14,22) (14,15) (14,19) (14,26) (14,17) (14,21) (14,24) (14,18) (14,23) (14,27) (15,22) (15,19) (15,17) (15,21) (15,24) (15,25) (15,18) (15,27) (16,28) (17,22) (17,26) (17,21) (17,24) (17,25) (17,23) (17,27) (18,19) (18,26) (18,21) (18,23) (18,27) (19,22) (19,24) (20,28) (21,22) (21,26) (21,23) (21,27) (22,26) (22,24) (22,27) (23,26) (23,24) (23,25) (23,27) (24,25) (24,27) (25,26) (26,27)\nIs there a path between node 22 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph144-22_24", + "image": "data/connectivity/graph_visual/hard/graph144.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,17) (0,2) (0,12) (0,1) (0,8) (0,10) (0,28) (1,3) (1,7) (1,18) (1,6) (1,15) (1,23) (2,3) (2,10) (2,18) (2,5) (2,28) (2,9) (3,16) (3,12) (3,7) (3,8) (3,19) (3,21) (3,24) (3,6) (3,20) (5,16) (5,17) (5,8) (5,14) (5,24) (5,6) (5,15) (5,9) (6,12) (6,25) (6,10) (6,21) (6,24) (6,23) (7,16) (7,17) (7,12) (7,25) (7,26) (7,10) (7,21) (7,24) (8,17) (8,27) (8,25) (8,10) (8,19) (8,21) (8,23) (9,17) (9,27) (9,12) (9,19) (9,18) (9,24) (9,20) (9,28) (9,15) (10,16) (10,27) (10,18) (10,13) (10,23) (12,17) (12,25) (12,26) (12,19) (12,20) (13,16) (13,27) (13,26) (13,21) (13,18) (13,24) (14,26) (15,18) (16,18) (16,24) (16,28) (17,26) (17,21) (17,18) (17,23) (18,26) (18,21) (18,24) (18,20) (19,26) (19,24) (19,20) (20,21) (20,24) (20,28) (20,23) (21,25) (23,25) (23,24) (24,27) (24,28) (25,26) (26,28)\nIs there a path between node 22 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph312-15_29", + "image": "data/connectivity/graph_visual/hard/graph312.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,2) (0,19) (1,9) (1,26) (1,15) (1,27) (1,17) (1,4) (2,14) (3,29) (4,24) (4,28) (4,8) (4,27) (4,12) (5,23) (6,24) (6,10) (6,18) (6,17) (6,16) (7,26) (7,10) (7,18) (7,12) (8,15) (8,18) (8,17) (8,12) (8,16) (9,16) (10,20) (10,18) (12,13) (12,20) (12,17) (12,16) (13,24) (13,16) (15,24) (15,26) (15,18) (15,17) (16,28) (16,20) (17,20) (18,28) (18,20) (19,21) (20,24) (22,25) (22,29) (22,30) (27,28) (30,31)\nIs there a path between node 15 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph475-25_10", + "image": "data/connectivity/graph_visual/hard/graph475.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,11) (0,23) (0,8) (0,30) (0,7) (0,14) (0,22) (0,1) (0,6) (0,17) (0,24) (0,4) (0,16) (0,13) (0,19) (0,26) (0,31) (0,2) (0,18) (0,5) (1,11) (1,12) (1,23) (1,8) (1,30) (1,7) (1,14) (1,27) (1,6) (1,17) (1,24) (1,4) (1,16) (1,29) (1,13) (1,19) (1,20) (1,26) (1,2) (1,18) (1,5) (2,12) (2,23) (2,8) (2,30) (2,7) (2,14) (2,22) (2,6) (2,17) (2,24) (2,4) (2,16) (2,29) (2,13) (2,19) (2,26) (2,18) (2,5) (3,28) (3,10) (3,15) (3,9) (4,11) (4,23) (4,8) (4,30) (4,7) (4,14) (4,27) (4,24) (4,16) (4,13) (4,19) (4,20) (4,31) (4,18) (4,5) (5,11) (5,12) (5,23) (5,8) (5,30) (5,7) (5,14) (5,27) (5,22) (5,17) (5,24) (5,29) (5,19) (5,20) (5,26) (5,31) (5,18) (6,11) (6,12) (6,23) (6,8) (6,30) (6,7) (6,14) (6,22) (6,17) (6,13) (6,19) (6,20) (6,26) (6,31) (6,18) (7,11) (7,23) (7,8) (7,30) (7,14) (7,27) (7,22) (7,24) (7,29) (7,13) (7,19) (7,20) (8,23) (8,30) (8,14) (8,22) (8,24) (8,16) (8,20) (8,26) (8,31) (8,18) (9,21) (9,25) (9,28) (10,21) (10,32) (10,25) (10,28) (10,15) (11,12) (11,30) (11,14) (11,27) (11,22) (11,17) (11,24) (11,16) (11,29) (11,13) (11,20) (11,26) (11,31) (11,18) (12,23) (12,30) (12,27) (12,22) (12,24) (12,29) (12,13) (12,20) (12,26) (12,31) (12,18) (13,23) (13,30) (13,14) (13,22) (13,17) (13,24) (13,19) (13,20) (13,26) (13,31) (13,18) (14,30) (14,27) (14,22) (14,24) (14,16) (14,29) (14,19) (14,20) (14,26) (14,31) (14,18) (15,21) (15,32) (15,25) (15,28) (16,23) (16,30) (16,22) (16,24) (16,29) (16,20) (16,26) (16,31) (16,18) (17,23) (17,30) (17,27) (17,22) (17,24) (17,29) (17,19) (17,26) (17,18) (18,23) (18,27) (18,24) (18,19) (18,20) (18,26) (19,30) (19,27) (19,29) (19,20) (19,26) (19,31) (20,30) (20,22) (20,24) (20,29) (20,26) (22,23) (22,27) (22,29) (22,31) (23,30) (23,26) (24,30) (24,27) (24,29) (24,26) (25,32) (25,28) (26,30) (26,27) (26,29) (27,30) (27,29) (28,32) (29,30) (29,31) (30,31)\nIs there a path between node 25 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph564-6_0", + "image": "data/connectivity/graph_visual/hard/graph564.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,16) (1,3) (1,28) (1,21) (1,29) (1,27) (1,26) (3,28) (3,20) (3,26) (4,31) (4,8) (4,23) (4,17) (4,29) (4,33) (4,13) (4,26) (4,18) (4,9) (5,16) (6,11) (7,20) (7,29) (7,9) (7,12) (7,25) (8,30) (8,17) (8,14) (8,13) (8,18) (9,19) (9,21) (9,27) (9,26) (9,12) (12,30) (12,22) (12,19) (12,17) (12,14) (12,33) (13,20) (13,14) (13,27) (14,19) (14,21) (14,33) (14,25) (17,24) (17,21) (17,29) (17,27) (17,33) (17,26) (17,18) (18,31) (18,24) (18,27) (18,33) (18,25) (19,30) (19,23) (20,31) (20,24) (20,29) (20,27) (20,26) (21,31) (21,24) (21,28) (21,29) (22,30) (22,23) (22,28) (22,27) (23,30) (23,24) (23,25) (25,31) (25,27) (25,33) (26,29) (27,31) (27,28) (27,33) (28,31) (28,29) (29,31) (29,30)\nIs there a path between node 6 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph237-9_18", + "image": "data/connectivity/graph_visual/hard/graph237.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,29) (0,12) (0,18) (0,24) (0,22) (0,2) (0,3) (1,14) (1,20) (1,26) (1,29) (1,12) (1,30) (1,15) (1,19) (1,3) (1,7) (2,17) (2,6) (2,23) (3,28) (3,30) (3,18) (3,19) (3,7) (4,26) (4,29) (4,12) (4,30) (4,18) (4,19) (4,7) (6,8) (6,24) (6,10) (6,19) (7,17) (7,26) (7,30) (7,18) (7,8) (7,13) (7,15) (7,23) (8,16) (8,14) (8,20) (8,26) (8,30) (10,14) (10,20) (10,29) (10,18) (10,13) (10,22) (10,19) (10,11) (11,21) (11,16) (11,14) (11,26) (11,18) (12,16) (12,26) (12,18) (13,17) (13,26) (13,15) (14,28) (14,26) (14,24) (14,23) (15,28) (15,16) (15,29) (15,30) (16,21) (16,20) (16,29) (16,24) (17,28) (17,20) (17,29) (17,30) (17,19) (18,21) (18,28) (18,23) (19,28) (19,20) (19,26) (19,22) (19,23) (20,29) (20,24) (20,22) (21,29) (22,28) (23,28) (23,29) (24,26) (24,29) (25,27) (26,29)\nIs there a path between node 9 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph280-9_18", + "image": "data/connectivity/graph_visual/hard/graph280.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,12) (0,14) (0,16) (0,20) (0,8) (0,13) (0,18) (0,10) (0,29) (0,3) (0,7) (0,9) (1,26) (1,5) (1,11) (1,19) (1,28) (1,24) (1,6) (2,12) (2,14) (2,16) (2,20) (2,8) (2,13) (2,23) (2,18) (2,25) (2,3) (2,7) (2,9) (3,16) (3,8) (3,13) (3,18) (3,25) (3,10) (3,29) (3,7) (4,15) (4,27) (5,28) (5,24) (5,22) (6,26) (6,11) (6,19) (6,28) (6,24) (6,22) (7,14) (7,16) (7,20) (7,13) (7,23) (7,25) (7,10) (7,21) (7,9) (8,14) (8,20) (8,13) (8,23) (8,10) (9,14) (9,16) (9,20) (9,13) (9,18) (9,25) (9,21) (9,29) (10,14) (10,16) (10,20) (10,13) (10,23) (10,25) (10,21) (11,26) (11,17) (11,24) (11,22) (12,14) (12,16) (12,13) (12,23) (12,18) (12,25) (12,21) (12,29) (13,14) (13,16) (13,18) (13,21) (13,29) (14,16) (14,20) (14,23) (14,18) (14,21) (14,29) (15,30) (15,27) (16,20) (16,23) (16,25) (16,21) (16,29) (17,26) (17,19) (17,28) (17,22) (18,23) (18,25) (18,21) (18,29) (19,26) (20,23) (20,25) (20,29) (21,23) (21,25) (21,29) (22,26) (22,28) (22,24) (23,25) (23,29) (24,26) (24,28) (25,29) (26,28)\nIs there a path between node 9 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph8-15_4", + "image": "data/connectivity/graph_visual/hard/graph8.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,15) (0,14) (1,20) (2,24) (2,3) (2,13) (4,8) (4,6) (4,11) (4,5) (5,19) (5,21) (5,23) (6,19) (6,20) (7,14) (7,10) (8,21) (9,19) (9,11) (10,15) (10,22) (11,23) (12,18) (13,24) (13,25) (14,22) (15,22) (18,25) (19,20) (21,23)\nIs there a path between node 15 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph256-7_11", + "image": "data/connectivity/graph_visual/hard/graph256.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,16) (0,13) (0,1) (0,18) (0,12) (0,23) (1,20) (1,30) (1,16) (1,27) (1,15) (1,7) (1,18) (1,11) (1,23) (2,3) (3,28) (4,27) (4,15) (4,8) (4,11) (4,25) (5,26) (5,6) (5,21) (5,25) (6,9) (6,26) (6,30) (6,24) (6,13) (6,15) (6,7) (7,18) (7,23) (8,26) (8,15) (8,14) (8,22) (8,12) (9,26) (9,30) (9,16) (9,17) (9,15) (9,14) (9,12) (9,23) (11,30) (11,16) (11,17) (11,27) (11,15) (11,14) (11,22) (11,12) (12,16) (12,15) (12,18) (12,22) (12,19) (12,25) (12,23) (13,16) (13,27) (13,14) (13,18) (13,23) (14,30) (14,16) (14,27) (14,22) (15,30) (15,17) (15,18) (15,19) (15,23) (16,21) (17,24) (17,25) (18,22) (19,30) (19,27) (19,23) (20,26) (21,24) (21,27) (21,25) (21,23) (22,27) (23,25) (24,26) (24,25) (25,30) (28,29)\nIs there a path between node 7 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph78-9_2", + "image": "data/connectivity/graph_visual/hard/graph78.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,7) (0,24) (0,8) (1,10) (1,22) (1,4) (1,5) (1,11) (1,13) (1,12) (1,14) (1,18) (1,20) (1,25) (1,6) (1,15) (1,26) (1,3) (2,10) (2,22) (2,4) (2,5) (2,11) (2,21) (2,12) (2,14) (2,18) (2,20) (2,25) (2,23) (2,6) (2,15) (2,26) (2,3) (3,19) (3,16) (3,22) (3,4) (3,5) (3,11) (3,25) (3,23) (3,15) (3,26) (4,19) (4,16) (4,22) (4,5) (4,11) (4,13) (4,12) (4,14) (4,15) (4,26) (5,19) (5,10) (5,16) (5,21) (5,13) (5,14) (5,18) (5,20) (5,25) (5,23) (5,6) (6,19) (6,10) (6,16) (6,22) (6,18) (6,20) (6,25) (6,23) (6,15) (7,17) (7,9) (7,24) (7,8) (8,17) (8,9) (9,17) (9,24) (10,19) (10,16) (10,22) (10,11) (10,21) (10,13) (10,12) (10,18) (10,20) (10,23) (10,15) (11,19) (11,16) (11,13) (11,12) (11,14) (11,18) (11,20) (11,25) (11,23) (12,19) (12,16) (12,21) (12,13) (12,14) (12,20) (12,25) (12,23) (13,19) (13,16) (13,22) (13,18) (13,20) (13,15) (13,26) (14,19) (14,22) (14,21) (14,18) (14,20) (14,15) (15,16) (15,22) (15,21) (15,20) (15,23) (15,26) (16,19) (16,21) (16,18) (16,20) (16,25) (16,23) (16,26) (17,24) (18,19) (18,22) (18,21) (18,20) (18,23) (19,22) (19,21) (19,20) (19,25) (19,23) (20,22) (20,21) (20,25) (20,23) (20,26) (21,22) (21,23) (22,25) (22,23) (22,26) (23,26) (25,26)\nIs there a path between node 9 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph240-22_30", + "image": "data/connectivity/graph_visual/hard/graph240.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,13) (0,2) (0,9) (1,5) (1,13) (1,19) (1,16) (1,18) (1,9) (1,7) (1,3) (1,6) (2,30) (2,16) (2,18) (2,4) (2,9) (2,7) (2,14) (3,19) (3,24) (3,17) (3,7) (3,6) (3,23) (4,30) (4,16) (4,6) (5,26) (5,17) (5,14) (6,19) (6,29) (6,16) (6,7) (7,16) (7,24) (8,28) (9,26) (9,13) (9,19) (9,29) (9,25) (9,14) (10,22) (10,11) (10,20) (10,27) (11,27) (11,28) (12,20) (12,21) (13,26) (13,30) (13,29) (13,18) (13,14) (14,29) (14,16) (16,26) (16,17) (16,23) (17,18) (17,23) (18,30) (18,25) (19,29) (19,25) (20,27) (21,22) (21,28) (23,26) (23,30) (24,29) (24,25) (25,30) (26,29) (27,28)\nIs there a path between node 22 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph543-12_17", + "image": "data/connectivity/graph_visual/hard/graph543.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,15) (0,7) (0,17) (0,2) (0,27) (1,3) (1,32) (1,26) (1,30) (1,19) (1,22) (1,4) (1,18) (1,20) (1,31) (1,25) (1,16) (1,13) (1,14) (1,23) (1,24) (2,15) (2,7) (2,17) (2,8) (2,27) (3,32) (3,26) (3,19) (3,6) (3,4) (3,18) (3,20) (3,31) (3,21) (3,16) (3,13) (3,23) (3,5) (3,29) (4,26) (4,30) (4,19) (4,6) (4,10) (4,18) (4,11) (4,20) (4,25) (4,21) (4,13) (4,14) (4,23) (4,12) (4,24) (4,29) (5,32) (5,9) (5,19) (5,6) (5,28) (5,10) (5,11) (5,20) (5,31) (5,25) (5,33) (5,16) (5,13) (5,14) (5,23) (5,24) (5,29) (6,32) (6,26) (6,30) (6,9) (6,19) (6,28) (6,10) (6,18) (6,11) (6,20) (6,31) (6,25) (6,33) (6,21) (6,16) (6,13) (6,14) (6,23) (6,24) (6,29) (7,15) (8,15) (8,27) (9,32) (9,30) (9,19) (9,28) (9,10) (9,18) (9,11) (9,20) (9,31) (9,25) (9,33) (9,16) (9,14) (9,12) (9,29) (10,32) (10,28) (10,18) (10,20) (10,33) (10,21) (10,16) (10,13) (10,23) (10,12) (10,24) (10,29) (11,32) (11,26) (11,30) (11,19) (11,22) (11,20) (11,31) (11,25) (11,33) (11,21) (11,14) (11,24) (11,29) (12,32) (12,26) (12,30) (12,19) (12,22) (12,18) (12,33) (12,21) (12,14) (12,23) (13,32) (13,26) (13,19) (13,22) (13,28) (13,18) (13,20) (13,31) (13,33) (13,23) (13,24) (13,29) (14,32) (14,26) (14,30) (14,19) (14,22) (14,28) (14,18) (14,20) (14,31) (14,25) (14,21) (14,16) (14,23) (15,17) (16,26) (16,19) (16,22) (16,28) (16,25) (16,33) (16,21) (16,29) (18,26) (18,30) (18,19) (18,22) (18,28) (18,31) (18,25) (18,21) (18,23) (18,29) (19,32) (19,26) (19,30) (19,22) (19,28) (19,25) (19,33) (19,23) (19,24) (19,29) (20,32) (20,26) (20,30) (20,22) (20,25) (20,33) (20,29) (21,26) (21,30) (21,22) (21,28) (21,31) (21,25) (21,33) (21,23) (21,29) (22,32) (22,26) (22,28) (22,31) (23,32) (23,31) (23,25) (23,33) (23,24) (23,29) (24,32) (24,26) (24,30) (24,28) (24,25) (24,33) (25,32) (25,26) (25,30) (25,33) (25,29) (26,33) (26,29) (28,30) (28,31) (28,33) (28,29) (29,32) (29,33) (30,33) (31,32) (32,33)\nIs there a path between node 12 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph327-2_16", + "image": "data/connectivity/graph_visual/hard/graph327.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,3) (0,10) (0,27) (0,1) (0,29) (0,7) (0,14) (0,13) (0,20) (0,6) (1,3) (1,4) (1,10) (1,27) (1,7) (1,16) (1,14) (1,13) (1,20) (1,15) (1,6) (2,30) (2,12) (2,5) (2,11) (2,21) (2,28) (2,22) (2,25) (2,31) (2,19) (3,4) (3,29) (3,16) (3,14) (3,13) (3,20) (3,15) (4,10) (4,7) (4,16) (4,13) (4,15) (4,6) (5,12) (5,23) (5,24) (5,21) (5,28) (5,25) (5,31) (5,19) (6,27) (6,29) (6,7) (6,14) (6,13) (6,20) (6,15) (7,10) (7,27) (7,20) (8,18) (9,26) (9,18) (10,27) (10,29) (10,16) (10,13) (10,15) (11,30) (11,24) (11,21) (11,17) (11,28) (11,25) (12,23) (12,24) (12,21) (12,17) (12,28) (12,22) (12,25) (12,19) (13,27) (13,16) (13,20) (13,15) (14,27) (14,29) (14,16) (14,15) (15,27) (15,29) (15,16) (15,20) (16,27) (16,29) (16,20) (17,30) (17,23) (17,24) (17,21) (17,28) (17,22) (17,25) (17,31) (17,19) (18,26) (19,30) (19,23) (19,24) (19,21) (19,28) (19,25) (19,31) (20,27) (21,30) (21,24) (21,28) (21,22) (21,25) (21,31) (22,30) (22,23) (22,24) (22,28) (22,25) (22,31) (23,30) (23,24) (23,25) (23,31) (24,28) (24,25) (24,31) (25,30) (25,28) (25,31) (27,29) (28,30) (30,31)\nIs there a path between node 2 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph635-2_5", + "image": "data/connectivity/graph_visual/hard/graph635.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,25) (0,21) (0,13) (0,34) (0,12) (0,32) (0,31) (0,24) (0,15) (0,29) (1,23) (1,31) (1,14) (1,24) (1,15) (2,5) (2,25) (2,13) (2,17) (2,15) (2,29) (2,16) (3,6) (3,10) (4,20) (4,19) (5,7) (5,13) (5,17) (5,12) (5,14) (5,30) (5,26) (6,19) (6,8) (6,18) (6,27) (7,22) (7,21) (7,34) (7,32) (7,14) (7,24) (8,11) (8,19) (8,10) (9,11) (9,19) (9,10) (10,28) (11,19) (11,18) (12,21) (12,34) (12,14) (12,15) (12,30) (13,22) (13,33) (13,32) (14,34) (14,31) (14,24) (14,15) (14,29) (15,22) (15,25) (15,34) (15,31) (15,30) (16,25) (16,21) (17,23) (17,33) (17,32) (17,29) (18,20) (18,28) (20,28) (20,27) (21,25) (21,33) (21,24) (22,23) (22,33) (22,34) (23,29) (26,30) (27,28) (29,33) (30,31) (31,32) (32,33)\nIs there a path between node 2 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph289-14_1", + "image": "data/connectivity/graph_visual/hard/graph289.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,21) (0,23) (0,2) (0,8) (1,18) (1,3) (1,16) (2,4) (2,5) (3,25) (3,13) (4,6) (4,27) (4,17) (4,8) (5,26) (5,19) (5,30) (5,28) (5,23) (5,15) (5,8) (6,26) (6,19) (6,30) (6,8) (8,26) (8,21) (8,23) (8,27) (9,14) (11,20) (11,16) (12,19) (12,30) (13,18) (13,29) (15,28) (16,24) (16,20) (16,29) (17,30) (17,21) (17,27) (19,30) (19,27) (20,25) (21,26) (21,28) (23,27) (25,29) (27,30) (27,28)\nIs there a path between node 14 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph643-32_3", + "image": "data/connectivity/graph_visual/hard/graph643.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,19) (0,3) (0,23) (0,8) (0,1) (0,28) (0,27) (0,9) (0,11) (0,32) (1,3) (1,26) (1,8) (1,15) (1,28) (1,27) (1,9) (1,11) (1,32) (2,29) (2,20) (2,12) (2,5) (2,33) (2,6) (2,18) (2,21) (2,25) (2,31) (2,14) (2,24) (2,16) (3,19) (3,23) (3,26) (3,8) (3,34) (3,27) (3,11) (3,32) (3,30) (4,20) (4,12) (4,5) (4,6) (4,18) (4,21) (4,7) (4,25) (4,13) (4,14) (4,16) (4,22) (5,29) (5,20) (5,12) (5,6) (5,17) (5,7) (5,25) (5,31) (5,24) (5,22) (6,29) (6,12) (6,33) (6,17) (6,7) (6,25) (6,13) (6,31) (6,24) (6,16) (6,22) (7,29) (7,18) (7,13) (7,14) (7,24) (8,19) (8,23) (8,26) (8,28) (8,9) (8,11) (8,32) (8,30) (9,19) (9,26) (9,34) (9,15) (9,28) (9,27) (9,11) (9,32) (10,29) (10,12) (10,33) (10,21) (10,25) (10,13) (10,31) (10,14) (10,24) (10,16) (11,23) (11,26) (11,34) (11,15) (11,28) (11,27) (11,32) (12,29) (12,20) (12,33) (12,17) (12,18) (12,21) (12,25) (12,13) (12,24) (12,16) (12,22) (13,29) (13,20) (13,33) (13,17) (13,18) (13,25) (13,31) (13,24) (13,16) (14,20) (14,18) (14,21) (14,25) (14,31) (14,24) (14,16) (14,22) (15,19) (15,23) (15,34) (15,28) (15,27) (15,32) (15,30) (16,29) (16,20) (16,33) (16,17) (16,31) (16,24) (17,29) (17,33) (17,18) (17,21) (17,31) (17,24) (17,22) (18,29) (18,20) (18,25) (18,31) (18,24) (18,22) (19,26) (19,34) (19,28) (19,27) (19,32) (19,30) (20,21) (20,25) (20,31) (20,24) (20,22) (21,29) (21,33) (21,31) (21,24) (21,22) (22,29) (22,33) (22,25) (22,31) (22,24) (23,26) (23,28) (23,27) (23,30) (24,33) (24,25) (24,31) (25,29) (25,33) (25,31) (26,34) (26,28) (26,27) (26,30) (27,34) (27,30) (28,32) (28,30) (29,33) (29,31) (30,34) (30,32) (31,33) (32,34)\nIs there a path between node 32 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph405-29_14", + "image": "data/connectivity/graph_visual/hard/graph405.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,25) (0,29) (0,14) (0,17) (0,4) (0,26) (1,21) (1,32) (1,18) (1,31) (1,22) (2,11) (2,23) (2,28) (2,3) (2,12) (2,19) (2,6) (2,16) (3,11) (3,23) (3,28) (3,12) (3,19) (3,27) (4,24) (4,10) (4,25) (4,29) (4,17) (4,26) (5,21) (5,32) (5,18) (5,31) (5,22) (6,9) (6,23) (6,28) (6,12) (6,19) (6,27) (6,16) (7,15) (7,8) (8,13) (9,11) (9,28) (9,12) (9,19) (9,16) (10,24) (10,30) (10,25) (10,14) (10,26) (11,28) (11,19) (11,16) (12,19) (12,27) (12,16) (13,15) (14,17) (14,26) (16,28) (17,24) (17,20) (17,30) (17,25) (17,29) (17,26) (18,32) (18,31) (18,22) (19,28) (19,27) (20,29) (21,32) (21,31) (21,22) (22,32) (23,28) (23,27) (24,25) (24,29) (25,30) (26,30) (27,28) (29,30) (31,32)\nIs there a path between node 29 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph665-15_5", + "image": "data/connectivity/graph_visual/hard/graph665.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,3) (0,29) (0,7) (0,32) (0,4) (0,17) (0,9) (1,12) (1,14) (1,7) (1,28) (1,23) (1,9) (1,33) (1,30) (1,6) (1,8) (2,14) (2,29) (2,32) (2,15) (2,30) (2,6) (2,10) (3,12) (3,14) (3,4) (3,23) (3,9) (3,31) (3,30) (3,20) (4,27) (4,19) (4,17) (4,15) (4,31) (4,30) (5,34) (5,18) (5,13) (6,7) (6,16) (6,23) (6,22) (6,30) (7,12) (7,15) (7,11) (7,31) (7,30) (7,24) (7,10) (8,29) (8,32) (8,16) (8,27) (8,23) (8,20) (9,28) (9,15) (9,33) (9,31) (9,30) (9,24) (9,10) (10,12) (10,19) (10,17) (10,33) (10,22) (10,20) (11,32) (11,16) (11,19) (11,17) (11,22) (12,32) (12,28) (12,23) (12,33) (14,32) (14,30) (14,20) (15,17) (15,30) (16,19) (16,17) (16,23) (16,33) (16,30) (17,29) (17,27) (17,30) (17,24) (17,20) (18,25) (19,32) (19,28) (19,30) (19,20) (20,28) (20,23) (20,30) (22,28) (22,33) (23,29) (23,31) (24,31) (26,34) (28,29) (28,33) (29,31) (30,33)\nIs there a path between node 15 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph698-13_11", + "image": "data/connectivity/graph_visual/hard/graph698.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,16) (0,9) (0,7) (0,30) (0,29) (1,34) (1,19) (1,6) (1,18) (2,8) (2,15) (2,31) (2,24) (2,12) (2,20) (2,14) (2,3) (2,25) (2,32) (2,4) (2,23) (2,28) (3,8) (3,33) (3,15) (3,12) (3,5) (3,14) (3,26) (3,25) (3,17) (3,22) (3,11) (4,8) (4,24) (4,12) (4,20) (4,5) (4,14) (4,26) (4,25) (4,32) (4,17) (4,23) (4,28) (4,11) (5,8) (5,15) (5,31) (5,14) (5,26) (5,25) (5,32) (5,10) (5,28) (5,11) (6,13) (6,19) (6,18) (7,16) (7,9) (7,30) (7,21) (7,29) (8,33) (8,15) (8,31) (8,24) (8,12) (8,20) (8,14) (8,26) (8,25) (8,32) (8,17) (8,22) (8,23) (8,28) (9,16) (9,30) (10,33) (10,15) (10,31) (10,24) (10,12) (10,14) (10,26) (10,25) (10,17) (10,22) (10,23) (10,28) (11,33) (11,15) (11,24) (11,12) (11,26) (11,25) (11,32) (11,22) (11,23) (11,28) (11,27) (12,15) (12,24) (12,20) (12,14) (12,26) (12,25) (12,32) (12,17) (12,22) (13,34) (13,19) (13,18) (14,33) (14,15) (14,31) (14,24) (14,26) (14,25) (14,32) (14,17) (14,22) (14,28) (14,27) (15,31) (15,24) (15,20) (15,25) (15,32) (15,17) (15,28) (15,27) (17,31) (17,24) (17,20) (17,25) (17,32) (17,23) (17,27) (18,34) (18,19) (19,34) (20,31) (20,24) (20,26) (20,25) (20,22) (20,23) (20,28) (20,27) (21,29) (22,33) (22,31) (22,24) (22,26) (22,32) (22,23) (22,28) (22,27) (23,33) (23,31) (23,24) (23,26) (23,25) (23,32) (23,27) (24,33) (24,26) (24,25) (24,32) (24,27) (25,31) (25,32) (25,28) (25,27) (26,33) (26,31) (26,32) (26,28) (26,27) (27,31) (27,32) (27,28) (28,33) (28,31) (28,32) (29,30) (31,33) (31,32) (32,33)\nIs there a path between node 13 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph629-4_27", + "image": "data/connectivity/graph_visual/hard/graph629.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,1) (0,28) (0,7) (0,32) (0,34) (0,29) (1,16) (1,9) (1,27) (1,4) (1,22) (1,34) (2,16) (2,28) (2,9) (2,5) (2,31) (2,22) (3,13) (3,17) (3,26) (3,12) (4,24) (4,11) (4,7) (4,5) (4,27) (4,22) (5,16) (5,9) (5,31) (5,23) (6,17) (6,12) (7,24) (7,32) (7,31) (7,23) (8,21) (9,28) (9,11) (11,31) (11,19) (11,23) (12,18) (12,17) (13,20) (13,26) (14,24) (14,32) (14,27) (14,19) (14,29) (15,30) (16,24) (16,23) (19,27) (20,33) (21,25) (22,32) (22,29) (23,28) (23,24) (23,27) (24,27) (24,31) (27,32) (27,34) (31,34)\nIs there a path between node 4 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph581-12_31", + "image": "data/connectivity/graph_visual/hard/graph581.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,28) (0,6) (0,33) (0,2) (0,27) (0,5) (0,13) (0,17) (0,16) (0,21) (0,29) (0,15) (0,32) (0,8) (1,31) (1,7) (1,26) (1,30) (1,14) (1,11) (1,19) (1,22) (1,9) (1,24) (1,3) (1,4) (1,10) (2,28) (2,6) (2,33) (2,27) (2,5) (2,13) (2,20) (2,16) (2,25) (2,21) (2,29) (2,8) (3,23) (3,31) (3,7) (3,30) (3,12) (3,14) (3,11) (3,19) (3,22) (3,18) (3,9) (3,24) (3,4) (3,10) (4,23) (4,31) (4,26) (4,30) (4,12) (4,14) (4,19) (4,18) (4,9) (5,6) (5,33) (5,27) (5,13) (5,20) (5,16) (5,25) (5,21) (5,29) (5,8) (6,17) (6,16) (6,29) (6,15) (6,32) (6,8) (7,31) (7,26) (7,30) (7,19) (7,22) (7,18) (7,9) (7,24) (7,10) (8,27) (8,17) (8,20) (8,16) (8,25) (8,15) (9,31) (9,26) (9,30) (9,12) (9,14) (9,19) (9,22) (9,24) (9,10) (10,23) (10,31) (10,30) (10,14) (10,11) (10,24) (11,23) (11,26) (11,30) (11,19) (11,24) (12,23) (12,26) (12,30) (12,14) (12,19) (12,22) (12,24) (13,27) (13,17) (13,20) (13,16) (13,25) (13,21) (13,29) (13,32) (14,23) (14,26) (14,30) (14,19) (14,18) (14,24) (15,33) (15,27) (15,17) (15,25) (15,21) (15,29) (15,32) (16,28) (16,33) (16,17) (16,20) (16,25) (16,29) (16,32) (17,27) (17,20) (17,25) (17,21) (17,29) (17,32) (18,23) (18,26) (18,30) (18,22) (19,31) (19,26) (19,30) (19,24) (20,33) (20,25) (20,29) (21,28) (21,27) (21,25) (21,32) (22,31) (22,26) (22,30) (23,26) (23,30) (23,24) (24,26) (24,30) (25,28) (25,33) (25,27) (25,29) (26,30) (27,28) (27,33) (27,29) (28,29) (28,32) (29,33) (30,31)\nIs there a path between node 12 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph391-4_27", + "image": "data/connectivity/graph_visual/hard/graph391.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,9) (0,18) (0,31) (0,7) (0,30) (0,1) (0,21) (0,2) (1,13) (1,18) (1,12) (1,26) (1,24) (1,2) (2,14) (2,16) (2,22) (3,27) (4,27) (5,27) (6,7) (6,30) (6,24) (6,23) (7,13) (7,32) (7,23) (8,19) (8,12) (8,26) (8,21) (8,23) (8,16) (8,22) (9,18) (9,24) (9,23) (11,18) (11,12) (11,23) (11,16) (12,13) (12,14) (12,26) (12,24) (12,21) (12,16) (13,19) (13,18) (13,14) (13,24) (13,16) (14,19) (14,18) (14,30) (14,21) (14,16) (14,22) (16,31) (16,24) (16,23) (16,22) (18,26) (18,32) (21,26) (21,23) (21,22) (22,26) (22,24) (25,28) (31,32)\nIs there a path between node 4 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph58-0_24", + "image": "data/connectivity/graph_visual/hard/graph58.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,6) (0,4) (0,17) (0,13) (0,3) (0,25) (0,11) (0,19) (0,23) (0,9) (0,2) (0,1) (0,12) (0,5) (0,8) (1,6) (1,4) (1,14) (1,17) (1,15) (1,3) (1,25) (1,11) (1,19) (1,9) (1,2) (1,12) (1,5) (1,8) (1,10) (1,20) (2,26) (2,6) (2,4) (2,14) (2,17) (2,13) (2,15) (2,18) (2,3) (2,25) (2,11) (2,19) (2,9) (2,7) (2,12) (2,8) (2,10) (2,20) (3,26) (3,6) (3,4) (3,17) (3,13) (3,15) (3,18) (3,19) (3,23) (3,5) (3,8) (3,10) (3,20) (4,13) (4,15) (4,18) (4,25) (4,11) (4,19) (4,23) (4,9) (4,12) (4,10) (4,20) (5,26) (5,6) (5,14) (5,17) (5,15) (5,18) (5,25) (5,11) (5,19) (5,9) (5,12) (5,8) (5,20) (6,14) (6,13) (6,25) (6,11) (6,23) (6,12) (6,10) (6,20) (7,26) (7,17) (7,18) (7,25) (7,11) (7,19) (7,23) (7,8) (7,20) (8,14) (8,17) (8,13) (8,15) (8,25) (8,11) (8,19) (8,23) (8,9) (8,20) (9,26) (9,14) (9,17) (9,13) (9,15) (9,25) (9,11) (9,19) (9,23) (9,20) (10,26) (10,14) (10,17) (10,13) (10,15) (10,18) (10,25) (10,11) (10,19) (10,23) (10,12) (11,14) (11,13) (11,15) (11,18) (11,25) (11,19) (11,23) (11,20) (12,17) (12,13) (12,18) (12,25) (12,23) (12,20) (13,26) (13,14) (13,17) (13,15) (13,25) (13,19) (14,26) (14,15) (14,25) (14,19) (14,23) (14,20) (15,17) (15,18) (15,19) (15,23) (17,25) (17,19) (17,23) (18,26) (18,25) (18,19) (18,23) (18,20) (19,23) (19,20) (20,23) (23,26) (23,25) (25,26)\nIs there a path between node 0 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph307-30_15", + "image": "data/connectivity/graph_visual/hard/graph307.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,19) (0,9) (1,14) (1,21) (1,6) (1,12) (1,22) (1,3) (2,11) (2,5) (3,24) (3,30) (3,13) (3,19) (3,9) (3,22) (4,6) (5,28) (5,26) (6,14) (6,24) (6,18) (6,22) (8,24) (8,21) (8,12) (8,20) (8,19) (8,22) (9,21) (9,20) (11,25) (12,24) (12,13) (13,24) (13,21) (13,30) (14,21) (14,30) (14,19) (16,17) (16,31) (17,25) (18,30) (18,27) (19,21) (19,27) (20,27) (21,24) (21,27) (22,30) (23,25) (25,28) (26,29) (26,31) (28,29)\nIs there a path between node 30 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph0-21_5", + "image": "data/connectivity/graph_visual/hard/graph0.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,9) (1,18) (1,8) (1,4) (2,15) (2,18) (2,11) (2,23) (2,4) (3,12) (3,5) (4,23) (4,25) (5,12) (5,17) (6,22) (6,13) (7,18) (7,23) (7,8) (9,17) (10,19) (10,17) (11,15) (12,24) (14,20) (14,22) (15,18) (16,20) (16,22) (20,22) (21,22) (23,25)\nIs there a path between node 21 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph591-7_5", + "image": "data/connectivity/graph_visual/hard/graph591.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,13) (0,31) (0,32) (0,33) (0,15) (1,5) (1,19) (1,16) (1,18) (1,11) (1,10) (1,9) (1,28) (1,14) (1,3) (1,8) (2,7) (2,5) (2,19) (2,16) (2,29) (2,18) (2,11) (2,25) (2,9) (2,28) (2,14) (2,3) (2,30) (2,8) (2,27) (3,7) (3,5) (3,19) (3,29) (3,18) (3,11) (3,6) (3,10) (3,25) (3,9) (3,28) (3,14) (3,30) (3,8) (4,26) (4,32) (4,17) (4,33) (4,15) (5,7) (5,19) (5,16) (5,18) (5,11) (5,10) (5,14) (5,30) (5,8) (5,27) (6,7) (6,19) (6,16) (6,11) (6,10) (6,25) (6,9) (6,28) (6,14) (6,30) (6,27) (7,16) (7,18) (7,11) (7,10) (7,25) (7,28) (7,14) (7,8) (7,27) (8,19) (8,16) (8,11) (8,10) (8,9) (8,27) (9,19) (9,16) (9,29) (9,11) (9,10) (9,27) (10,29) (10,11) (10,14) (10,30) (10,27) (11,19) (11,18) (11,30) (11,27) (12,24) (12,20) (13,26) (13,32) (13,17) (13,33) (13,15) (14,19) (14,16) (14,29) (14,25) (14,28) (14,30) (14,27) (15,31) (15,26) (15,32) (15,17) (16,19) (16,18) (16,25) (16,27) (17,31) (17,23) (17,26) (17,32) (17,33) (18,19) (18,29) (18,28) (18,30) (18,27) (19,29) (19,25) (19,28) (19,30) (19,27) (20,22) (20,24) (20,21) (21,24) (22,24) (23,31) (23,26) (23,33) (25,29) (25,28) (25,30) (25,27) (26,31) (26,32) (26,33) (27,29) (27,30) (28,29) (28,30) (29,30) (31,32) (32,33)\nIs there a path between node 7 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph568-24_29", + "image": "data/connectivity/graph_visual/hard/graph568.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,17) (0,26) (0,2) (0,5) (0,4) (0,25) (0,18) (0,29) (1,24) (1,6) (1,21) (2,22) (2,8) (2,30) (2,17) (2,33) (2,26) (2,11) (2,7) (2,5) (2,23) (2,18) (2,29) (3,27) (4,13) (4,9) (4,33) (4,11) (4,5) (4,23) (4,25) (4,29) (5,22) (5,16) (5,30) (5,9) (5,19) (5,10) (5,15) (5,29) (6,24) (6,31) (7,17) (7,23) (7,25) (8,16) (8,32) (8,10) (8,18) (8,29) (9,22) (9,30) (9,23) (10,22) (10,16) (10,19) (11,22) (11,13) (11,30) (11,33) (11,23) (11,18) (12,28) (12,31) (13,30) (13,32) (13,23) (14,17) (14,32) (14,23) (14,25) (14,15) (14,29) (15,16) (15,33) (15,32) (15,18) (16,22) (16,17) (16,32) (16,23) (16,18) (16,29) (17,32) (17,18) (17,29) (18,19) (18,32) (18,23) (19,29) (20,24) (20,21) (21,27) (22,32) (22,25) (25,33) (25,26) (25,29) (26,33) (26,29) (27,28) (28,31) (29,30)\nIs there a path between node 24 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph563-19_14", + "image": "data/connectivity/graph_visual/hard/graph563.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,24) (0,25) (0,5) (0,19) (0,33) (0,29) (0,4) (1,24) (1,17) (1,10) (1,16) (2,8) (3,28) (3,12) (3,15) (3,23) (3,20) (3,13) (4,7) (4,29) (5,17) (5,7) (5,25) (5,33) (6,8) (6,18) (7,24) (7,17) (7,25) (7,19) (8,22) (9,12) (9,14) (9,23) (10,24) (10,16) (10,33) (11,31) (12,14) (12,23) (12,20) (13,20) (14,28) (14,32) (14,20) (15,20) (16,19) (17,33) (18,22) (19,24) (19,26) (21,23) (22,27) (23,30) (24,25) (25,26) (25,29) (26,33) (29,33)\nIs there a path between node 19 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph32-6_21", + "image": "data/connectivity/graph_visual/hard/graph32.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,13) (0,12) (0,20) (0,15) (0,4) (0,8) (0,18) (0,24) (0,10) (0,14) (0,9) (0,16) (0,2) (0,7) (0,11) (0,17) (1,20) (1,19) (1,23) (1,5) (1,15) (1,4) (1,18) (1,24) (1,10) (1,14) (1,16) (1,21) (1,7) (1,11) (1,17) (2,13) (2,12) (2,19) (2,5) (2,15) (2,18) (2,24) (2,14) (2,9) (2,21) (2,17) (3,13) (3,20) (3,23) (3,15) (3,4) (3,18) (3,24) (3,14) (3,9) (3,16) (3,21) (3,7) (3,11) (4,13) (4,12) (4,20) (4,19) (4,15) (4,24) (4,10) (4,9) (4,16) (4,7) (4,11) (4,17) (5,12) (5,20) (5,19) (5,23) (5,15) (5,18) (5,24) (5,10) (5,14) (5,9) (5,21) (5,7) (5,17) (6,22) (7,12) (7,20) (7,19) (7,23) (7,15) (7,8) (7,18) (7,24) (7,10) (7,14) (7,9) (7,21) (7,11) (8,13) (8,15) (8,18) (8,24) (8,10) (8,14) (8,16) (8,17) (9,19) (9,23) (9,15) (9,18) (9,24) (9,10) (9,21) (9,17) (10,13) (10,23) (10,15) (10,24) (10,14) (10,21) (10,11) (11,13) (11,12) (11,20) (11,19) (11,23) (11,15) (11,18) (11,14) (11,16) (11,21) (12,13) (12,20) (12,15) (12,24) (12,14) (12,16) (12,21) (12,17) (13,20) (13,19) (13,15) (13,18) (13,21) (13,17) (14,20) (14,19) (14,23) (14,15) (14,18) (14,16) (14,17) (15,20) (15,19) (15,23) (15,18) (15,24) (15,17) (16,19) (16,23) (16,18) (17,20) (17,19) (17,24) (18,20) (18,19) (18,21) (19,20) (19,23) (19,24) (19,21) (20,23) (20,24) (20,21) (21,23) (21,24) (22,25) (23,24)\nIs there a path between node 6 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph319-8_25", + "image": "data/connectivity/graph_visual/hard/graph319.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,2) (0,28) (0,1) (1,20) (1,27) (1,18) (2,16) (3,19) (3,27) (3,13) (3,18) (4,26) (4,21) (4,17) (4,12) (4,22) (4,10) (5,23) (5,15) (5,18) (6,19) (6,23) (7,9) (7,31) (7,17) (7,10) (8,20) (8,23) (8,15) (9,24) (9,10) (10,31) (10,24) (10,14) (11,17) (11,12) (12,26) (12,21) (12,17) (12,14) (13,19) (13,20) (13,23) (13,18) (13,30) (13,16) (14,31) (15,20) (15,30) (16,29) (17,21) (17,31) (18,19) (18,23) (19,27) (19,29) (20,23) (20,28) (21,31) (21,25) (22,26) (23,30) (23,29) (24,31) (24,25) (25,26) (26,31) (28,29) (29,30)\nIs there a path between node 8 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph413-15_25", + "image": "data/connectivity/graph_visual/hard/graph413.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,21) (0,3) (0,26) (0,18) (0,27) (2,20) (2,21) (2,28) (2,27) (3,30) (4,16) (4,15) (6,12) (8,21) (8,14) (8,18) (9,10) (10,12) (10,15) (10,32) (11,20) (11,21) (11,28) (11,25) (12,16) (12,32) (14,20) (14,23) (14,26) (14,27) (14,17) (15,32) (17,30) (17,21) (17,29) (17,27) (18,30) (18,27) (19,22) (20,23) (20,29) (23,25) (23,29) (25,27) (26,27) (27,30) (28,30)\nIs there a path between node 15 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph672-30_32", + "image": "data/connectivity/graph_visual/hard/graph672.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,15) (1,5) (1,31) (1,30) (1,18) (2,17) (2,25) (2,15) (2,7) (2,23) (2,24) (2,5) (2,13) (3,34) (3,8) (4,16) (4,12) (4,9) (4,33) (5,17) (5,7) (5,23) (5,20) (5,31) (5,13) (6,26) (6,11) (6,22) (6,9) (6,21) (7,14) (7,25) (7,20) (7,13) (8,26) (8,29) (8,11) (8,21) (9,26) (9,29) (9,21) (9,33) (10,26) (10,29) (10,22) (10,12) (12,22) (12,21) (13,28) (13,31) (13,19) (14,17) (14,15) (14,19) (15,17) (15,25) (15,28) (15,30) (15,19) (16,26) (17,28) (17,31) (17,19) (18,28) (18,20) (19,27) (19,20) (19,32) (20,30) (20,32) (21,34) (21,33) (24,31) (26,29) (26,34) (27,30) (28,31) (28,30) (29,34) (30,32)\nIs there a path between node 30 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph132-7_6", + "image": "data/connectivity/graph_visual/hard/graph132.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,23) (0,17) (0,27) (0,18) (0,13) (0,9) (0,19) (0,8) (0,16) (0,22) (0,25) (0,3) (1,4) (1,12) (1,7) (1,20) (1,26) (2,23) (2,27) (2,13) (2,9) (2,24) (2,14) (2,19) (2,16) (2,22) (2,3) (3,21) (3,23) (3,15) (3,27) (3,18) (3,9) (3,24) (3,14) (3,8) (3,16) (3,22) (3,25) (4,12) (4,11) (4,20) (4,26) (4,5) (5,12) (5,7) (5,11) (5,20) (5,26) (6,10) (7,12) (7,20) (8,21) (8,17) (8,15) (8,27) (8,9) (8,24) (8,14) (8,19) (8,16) (8,22) (9,17) (9,27) (9,24) (11,12) (11,20) (12,26) (13,21) (13,23) (13,17) (13,15) (13,18) (13,14) (13,19) (13,22) (13,25) (14,21) (14,23) (14,17) (14,27) (14,18) (14,24) (14,19) (14,22) (14,25) (15,21) (15,23) (15,17) (15,27) (15,18) (15,24) (15,19) (15,16) (15,22) (15,25) (16,21) (16,23) (16,27) (16,18) (16,24) (16,22) (16,25) (17,23) (17,27) (18,21) (18,27) (18,24) (18,19) (18,22) (18,25) (19,23) (19,27) (19,22) (19,25) (20,26) (21,23) (21,27) (22,27) (23,27) (24,27) (24,25) (25,27)\nIs there a path between node 7 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph173-27_28", + "image": "data/connectivity/graph_visual/hard/graph173.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,24) (0,8) (0,18) (0,26) (0,14) (0,15) (0,9) (0,25) (0,17) (0,4) (0,2) (1,27) (1,16) (1,5) (1,22) (1,19) (2,26) (2,13) (2,14) (2,3) (2,15) (2,25) (2,4) (2,21) (3,8) (3,13) (3,23) (3,15) (3,17) (3,6) (3,21) (4,24) (4,8) (4,18) (4,26) (4,13) (4,14) (4,25) (4,6) (4,21) (5,16) (5,10) (5,19) (6,24) (6,8) (6,13) (6,23) (6,14) (6,15) (6,9) (6,17) (6,21) (7,28) (7,20) (7,11) (8,24) (8,18) (8,13) (8,23) (8,14) (8,9) (8,21) (9,24) (9,26) (9,23) (9,14) (9,25) (10,27) (10,16) (10,22) (10,19) (12,27) (12,16) (12,22) (13,24) (13,26) (13,23) (13,14) (13,15) (13,25) (13,17) (13,21) (14,26) (14,15) (14,25) (15,26) (15,23) (15,25) (15,17) (15,21) (16,27) (16,22) (16,19) (17,24) (17,18) (17,23) (18,24) (18,26) (18,21) (19,27) (19,22) (20,28) (21,24) (21,23) (21,25) (23,26) (23,25) (24,26) (24,25) (25,26)\nIs there a path between node 27 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph446-15_16", + "image": "data/connectivity/graph_visual/hard/graph446.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (0,27) (0,21) (0,12) (0,24) (0,16) (0,13) (0,20) (0,23) (0,22) (0,31) (0,29) (1,32) (2,25) (3,5) (3,24) (3,19) (3,13) (3,18) (3,15) (3,10) (3,22) (3,7) (3,17) (4,5) (4,13) (4,18) (4,15) (4,31) (4,17) (4,26) (5,21) (5,14) (5,19) (5,15) (5,22) (5,26) (6,28) (7,19) (7,13) (7,18) (7,10) (7,29) (7,17) (8,12) (8,24) (8,20) (8,18) (8,15) (8,26) (9,27) (9,24) (9,16) (9,13) (9,20) (9,18) (9,10) (9,26) (10,27) (10,12) (10,19) (10,18) (10,15) (10,23) (10,22) (10,11) (10,31) (10,29) (10,30) (11,27) (11,12) (11,24) (11,16) (11,20) (11,18) (11,22) (11,30) (12,18) (12,15) (12,31) (12,29) (12,17) (13,19) (13,16) (13,20) (13,23) (14,21) (14,16) (14,15) (14,30) (15,18) (15,22) (15,30) (15,26) (16,19) (16,29) (16,30) (17,18) (18,24) (18,23) (18,22) (19,20) (19,23) (20,24) (20,22) (21,27) (21,23) (21,30) (22,23) (23,31) (23,26) (24,27) (24,26) (25,28) (29,31)\nIs there a path between node 15 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph513-18_9", + "image": "data/connectivity/graph_visual/hard/graph513.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,17) (0,8) (0,6) (0,1) (0,22) (0,25) (0,11) (0,2) (1,10) (1,8) (1,22) (1,25) (1,11) (1,32) (1,29) (1,7) (1,3) (2,10) (2,18) (2,25) (2,30) (2,11) (2,15) (2,28) (2,7) (3,33) (3,8) (3,20) (3,30) (3,15) (3,19) (4,14) (4,12) (4,13) (5,33) (5,17) (5,21) (5,18) (5,22) (5,28) (5,7) (6,20) (6,30) (6,32) (6,27) (7,33) (7,21) (7,18) (7,22) (7,30) (7,15) (7,27) (7,28) (7,29) (8,21) (8,25) (8,20) (8,11) (8,27) (10,17) (10,20) (10,32) (10,27) (11,22) (11,25) (11,15) (11,27) (12,31) (12,16) (12,23) (13,16) (13,23) (14,31) (14,26) (15,25) (15,20) (15,27) (17,22) (17,20) (17,32) (17,29) (18,32) (19,25) (19,30) (19,32) (19,27) (20,33) (20,25) (20,30) (20,32) (20,27) (21,22) (21,29) (22,28) (23,31) (23,24) (24,31) (25,29) (26,31) (28,33) (29,30) (32,33)\nIs there a path between node 18 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph389-32_20", + "image": "data/connectivity/graph_visual/hard/graph389.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,22) (0,12) (0,24) (0,18) (0,19) (0,30) (0,1) (0,21) (0,9) (0,5) (0,6) (0,7) (0,2) (1,22) (1,24) (1,18) (1,19) (1,30) (1,21) (1,9) (1,5) (1,6) (1,11) (1,7) (1,31) (1,2) (2,12) (2,24) (2,18) (2,19) (2,21) (2,5) (2,6) (2,11) (2,7) (2,31) (3,26) (3,16) (3,4) (3,28) (3,13) (3,20) (4,26) (4,16) (4,8) (4,28) (5,12) (5,24) (5,30) (5,21) (5,9) (5,11) (5,7) (5,31) (6,22) (6,12) (6,24) (6,30) (6,21) (6,9) (6,11) (6,7) (7,12) (7,18) (7,30) (7,9) (7,11) (7,31) (8,26) (8,16) (8,28) (9,22) (9,12) (9,24) (9,18) (9,19) (9,30) (9,11) (9,31) (10,25) (10,14) (10,29) (10,32) (10,15) (10,23) (11,22) (11,12) (11,24) (11,18) (11,30) (11,21) (12,24) (12,30) (12,21) (12,31) (13,26) (13,28) (14,27) (14,17) (14,29) (14,32) (14,15) (15,25) (15,27) (15,17) (15,29) (15,32) (15,23) (16,26) (17,29) (18,22) (18,24) (18,19) (18,21) (19,22) (19,30) (19,21) (20,26) (21,22) (21,24) (21,31) (22,24) (23,25) (23,27) (23,32) (24,30) (24,31) (25,27) (25,29) (25,32) (26,28) (27,29) (27,32) (30,31)\nIs there a path between node 32 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph565-26_1", + "image": "data/connectivity/graph_visual/hard/graph565.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,13) (1,11) (1,26) (1,32) (1,29) (1,15) (1,18) (1,2) (1,6) (1,22) (1,9) (1,16) (2,7) (2,30) (2,22) (4,12) (5,12) (5,17) (6,30) (6,11) (6,26) (6,25) (6,15) (6,21) (6,33) (6,9) (7,19) (7,13) (7,32) (7,15) (7,18) (7,16) (7,10) (9,30) (9,31) (9,29) (9,21) (9,28) (9,14) (9,33) (9,10) (10,27) (10,31) (10,26) (10,32) (10,21) (10,14) (11,27) (11,31) (11,26) (11,32) (11,18) (11,14) (11,16) (12,24) (13,30) (13,26) (13,29) (13,21) (13,22) (14,32) (14,29) (14,25) (15,19) (15,16) (16,19) (16,27) (16,30) (16,26) (16,32) (16,21) (17,24) (18,33) (18,22) (19,30) (19,26) (19,25) (19,21) (20,23) (21,26) (21,28) (22,25) (25,31) (26,30) (26,31) (26,29) (26,28) (26,33) (28,33) (29,30) (29,31) (29,32) (29,33) (30,31) (32,33)\nIs there a path between node 26 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph466-12_18", + "image": "data/connectivity/graph_visual/hard/graph466.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,17) (0,32) (0,5) (0,31) (0,29) (0,27) (0,1) (0,18) (0,13) (0,2) (0,23) (1,7) (1,17) (1,20) (1,14) (1,13) (1,28) (2,3) (2,26) (2,32) (2,20) (2,31) (2,27) (2,23) (3,17) (3,25) (3,5) (3,19) (3,31) (3,14) (3,29) (3,11) (3,27) (3,18) (3,13) (3,22) (3,9) (4,20) (4,31) (4,14) (4,11) (4,16) (4,27) (4,18) (4,10) (4,9) (5,7) (5,17) (5,25) (5,32) (5,20) (5,18) (6,15) (6,12) (7,20) (7,19) (7,9) (7,23) (8,17) (8,32) (8,19) (8,29) (8,11) (8,22) (8,21) (9,17) (9,25) (9,28) (10,25) (10,20) (10,31) (10,14) (11,26) (11,17) (11,13) (11,22) (11,28) (11,21) (12,30) (13,19) (13,16) (13,28) (13,23) (14,29) (14,16) (14,18) (14,22) (15,30) (15,24) (16,19) (16,27) (16,28) (17,32) (17,20) (17,31) (17,23) (18,25) (18,31) (19,20) (19,28) (19,21) (20,25) (20,32) (20,27) (20,21) (21,23) (22,26) (22,31) (22,23) (23,26) (23,32) (23,29) (24,30) (26,32) (26,29) (26,28) (27,31) (28,32) (29,32) (29,31)\nIs there a path between node 12 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph540-22_2", + "image": "data/connectivity/graph_visual/hard/graph540.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,20) (0,31) (0,16) (0,30) (1,20) (1,17) (1,31) (1,24) (3,29) (3,6) (3,33) (3,9) (3,15) (3,11) (3,21) (3,8) (3,27) (3,19) (3,25) (3,32) (3,12) (3,5) (3,10) (3,18) (3,26) (4,29) (4,6) (4,15) (4,11) (4,21) (4,8) (4,27) (4,19) (4,25) (4,12) (4,5) (4,18) (4,26) (4,14) (4,7) (5,29) (5,6) (5,33) (5,15) (5,28) (5,11) (5,21) (5,8) (5,23) (5,27) (5,19) (5,25) (5,12) (5,10) (5,18) (5,13) (5,26) (5,14) (5,7) (6,29) (6,11) (6,21) (6,8) (6,23) (6,19) (6,25) (6,12) (6,18) (6,26) (6,7) (7,33) (7,15) (7,28) (7,8) (7,27) (7,25) (7,10) (7,18) (7,13) (8,33) (8,9) (8,15) (8,28) (8,11) (8,27) (8,19) (8,32) (8,12) (8,10) (8,18) (8,13) (9,33) (9,15) (9,28) (9,11) (9,21) (9,23) (9,27) (9,32) (9,12) (9,10) (9,26) (10,33) (10,15) (10,11) (10,21) (10,23) (10,27) (10,19) (10,25) (10,32) (10,12) (10,18) (10,13) (10,26) (11,29) (11,33) (11,15) (11,28) (11,21) (11,23) (11,19) (11,25) (11,12) (11,26) (11,14) (12,29) (12,33) (12,15) (12,28) (12,27) (12,19) (12,25) (12,32) (12,18) (12,13) (12,26) (12,14) (13,29) (13,33) (13,15) (13,28) (13,21) (13,23) (13,27) (13,19) (13,25) (13,32) (13,18) (14,29) (14,15) (14,21) (14,27) (14,19) (14,32) (14,18) (14,26) (15,29) (15,33) (15,28) (15,21) (15,27) (15,19) (15,26) (16,20) (16,17) (16,22) (16,30) (16,24) (17,20) (17,31) (17,30) (18,29) (18,33) (18,21) (18,25) (18,32) (18,26) (19,29) (19,33) (19,28) (19,23) (19,25) (19,32) (19,26) (20,22) (20,31) (20,30) (21,29) (21,33) (21,28) (21,23) (21,27) (21,25) (21,26) (22,31) (22,24) (23,33) (23,28) (23,27) (23,32) (23,26) (25,29) (25,33) (25,27) (25,26) (26,29) (26,33) (26,28) (26,27) (26,32) (27,29) (27,33) (27,28) (27,32) (28,29) (28,33) (28,32) (29,33) (29,32) (30,31) (32,33)\nIs there a path between node 22 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph584-5_8", + "image": "data/connectivity/graph_visual/hard/graph584.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,20) (0,12) (0,16) (1,29) (1,2) (1,14) (1,15) (1,5) (1,6) (1,13) (2,3) (2,6) (2,13) (3,29) (3,13) (4,20) (4,21) (4,7) (4,25) (4,26) (4,31) (5,14) (5,6) (6,14) (7,20) (7,16) (7,24) (7,25) (8,23) (8,30) (8,32) (8,27) (8,22) (8,9) (8,33) (8,11) (8,28) (9,23) (9,19) (9,30) (9,17) (9,10) (9,27) (9,18) (9,22) (9,33) (9,11) (9,28) (10,19) (10,30) (10,27) (10,18) (10,22) (10,33) (10,11) (10,28) (11,23) (11,19) (11,30) (11,17) (11,32) (11,27) (11,18) (11,22) (11,33) (11,28) (12,20) (12,21) (12,16) (12,24) (12,25) (12,26) (12,31) (13,29) (14,29) (14,15) (15,29) (16,20) (16,21) (16,24) (16,26) (16,31) (17,23) (17,30) (17,18) (17,22) (17,28) (18,23) (18,19) (18,30) (18,32) (18,27) (18,22) (18,33) (18,28) (19,23) (19,30) (19,32) (19,27) (19,33) (19,28) (20,21) (20,24) (20,25) (20,31) (21,24) (21,25) (21,31) (22,23) (22,30) (22,27) (22,33) (22,28) (23,30) (23,32) (23,28) (24,26) (24,31) (25,31) (26,31) (27,32) (27,33) (27,28) (28,30) (28,33) (30,32) (30,33) (32,33)\nIs there a path between node 5 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph348-27_1", + "image": "data/connectivity/graph_visual/hard/graph348.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,31) (0,20) (0,13) (0,6) (0,9) (0,3) (0,21) (0,29) (1,16) (1,20) (1,6) (1,22) (1,30) (2,10) (2,5) (2,20) (2,19) (2,30) (3,16) (3,19) (3,23) (3,22) (3,21) (3,29) (3,28) (5,31) (5,25) (5,28) (5,30) (6,31) (6,19) (6,14) (7,27) (7,18) (8,27) (8,11) (8,18) (9,12) (9,23) (9,30) (10,16) (10,23) (10,15) (10,14) (10,30) (11,26) (11,18) (12,16) (12,13) (12,23) (12,21) (12,14) (13,16) (13,31) (13,20) (13,15) (13,21) (13,30) (14,21) (14,28) (14,30) (15,17) (15,31) (15,20) (15,19) (15,30) (16,20) (16,23) (16,22) (16,21) (17,31) (17,25) (17,30) (18,27) (19,31) (19,23) (19,25) (19,29) (19,28) (19,30) (21,23) (21,28) (22,31) (22,25) (22,29) (23,31) (23,28) (23,30) (24,27) (25,28) (26,27) (28,31) (28,29) (29,31) (30,31)\nIs there a path between node 27 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph572-24_15", + "image": "data/connectivity/graph_visual/hard/graph572.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,10) (0,4) (1,15) (1,11) (1,24) (1,5) (2,6) (2,7) (2,9) (2,30) (3,9) (3,20) (3,14) (3,23) (3,18) (4,10) (4,6) (4,29) (4,9) (4,17) (4,8) (4,23) (4,18) (4,30) (5,15) (5,22) (5,24) (6,10) (6,7) (6,14) (6,21) (6,30) (7,28) (7,29) (7,9) (7,27) (7,17) (7,21) (7,30) (8,10) (8,9) (8,27) (8,14) (8,23) (8,21) (9,10) (9,28) (9,27) (9,17) (10,28) (10,29) (10,18) (12,16) (12,31) (12,33) (13,19) (14,27) (14,17) (14,18) (15,24) (16,31) (16,33) (16,24) (17,29) (18,28) (18,30) (19,22) (20,27) (20,21) (21,28) (22,33) (22,24) (24,31) (24,33) (25,26)\nIs there a path between node 24 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph360-15_5", + "image": "data/connectivity/graph_visual/hard/graph360.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,28) (0,24) (0,31) (0,30) (0,27) (0,20) (1,21) (1,6) (1,19) (1,12) (1,22) (1,4) (1,17) (1,13) (1,30) (2,23) (2,3) (2,14) (3,25) (4,5) (4,17) (4,27) (5,17) (5,31) (5,20) (6,26) (6,16) (6,28) (6,10) (6,19) (6,12) (6,22) (6,13) (7,21) (7,28) (7,19) (7,17) (7,13) (7,18) (7,27) (8,23) (8,11) (8,25) (10,26) (10,28) (10,22) (10,31) (10,18) (11,23) (12,30) (13,21) (13,19) (13,31) (15,26) (15,16) (15,17) (15,18) (15,20) (16,21) (16,28) (16,19) (16,30) (16,27) (16,20) (17,24) (17,22) (17,18) (18,22) (19,22) (19,31) (19,20) (20,28) (21,22) (21,31) (22,30) (24,31) (27,28) (28,31)\nIs there a path between node 15 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph300-9_6", + "image": "data/connectivity/graph_visual/hard/graph300.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,22) (0,19) (0,24) (0,1) (0,2) (0,5) (0,28) (0,29) (0,31) (0,12) (0,23) (0,15) (0,11) (0,10) (1,6) (1,22) (1,19) (1,24) (1,2) (1,5) (1,28) (1,29) (1,31) (1,14) (1,23) (1,15) (1,11) (2,6) (2,22) (2,19) (2,5) (2,28) (2,18) (2,31) (2,14) (2,12) (2,15) (2,11) (2,10) (3,6) (3,19) (3,28) (3,29) (3,18) (3,23) (3,15) (3,10) (4,25) (4,20) (4,17) (4,30) (4,27) (4,9) (4,21) (4,26) (4,13) (4,7) (4,16) (5,6) (5,19) (5,24) (5,28) (5,18) (5,31) (5,14) (5,12) (5,23) (5,15) (5,11) (6,19) (6,24) (6,29) (6,18) (6,31) (6,12) (6,15) (6,10) (7,25) (7,20) (7,17) (7,30) (7,27) (7,9) (7,21) (7,26) (7,13) (7,16) (8,25) (8,9) (9,25) (9,20) (9,17) (9,30) (9,21) (9,26) (9,13) (9,16) (10,22) (10,24) (10,28) (10,29) (10,18) (10,31) (10,14) (10,15) (11,24) (11,28) (11,29) (11,18) (11,14) (11,12) (11,15) (12,29) (12,18) (12,31) (12,15) (13,20) (13,17) (13,30) (13,27) (13,21) (13,26) (13,16) (14,22) (14,19) (14,24) (14,18) (14,31) (14,23) (14,15) (15,22) (15,19) (15,24) (15,28) (15,29) (15,18) (16,20) (16,17) (16,30) (16,21) (16,26) (17,25) (17,20) (17,27) (18,22) (18,19) (18,24) (18,28) (18,29) (18,31) (19,22) (19,24) (19,28) (19,29) (19,23) (20,30) (20,27) (20,21) (20,26) (21,25) (21,30) (21,27) (21,26) (22,24) (22,28) (22,31) (22,23) (23,28) (23,29) (23,31) (24,28) (24,31) (25,30) (26,30) (26,27) (28,29) (28,31) (29,31)\nIs there a path between node 9 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph709-32_27", + "image": "data/connectivity/graph_visual/hard/graph709.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,10) (0,2) (0,34) (0,21) (1,18) (1,31) (1,3) (1,4) (1,8) (1,20) (1,23) (1,14) (1,26) (1,16) (1,5) (1,17) (1,27) (1,9) (1,19) (1,15) (1,33) (2,10) (3,31) (3,29) (3,22) (3,12) (3,7) (3,4) (3,28) (3,8) (3,6) (3,20) (3,23) (3,14) (3,16) (3,13) (3,17) (3,24) (3,27) (3,15) (4,29) (4,22) (4,12) (4,11) (4,28) (4,20) (4,23) (4,14) (4,26) (4,16) (4,5) (4,13) (4,24) (4,27) (4,19) (4,33) (5,18) (5,31) (5,29) (5,12) (5,11) (5,7) (5,28) (5,8) (5,6) (5,20) (5,32) (5,23) (5,26) (5,16) (5,13) (5,17) (5,24) (5,9) (5,15) (5,33) (6,18) (6,31) (6,22) (6,12) (6,11) (6,7) (6,20) (6,23) (6,14) (6,16) (6,17) (6,27) (6,9) (6,19) (6,15) (7,18) (7,22) (7,12) (7,11) (7,8) (7,20) (7,14) (7,26) (7,16) (7,13) (7,17) (7,24) (7,9) (7,15) (7,33) (8,18) (8,29) (8,12) (8,11) (8,28) (8,20) (8,32) (8,23) (8,26) (8,17) (8,24) (8,27) (8,9) (8,19) (8,15) (8,33) (9,31) (9,22) (9,12) (9,28) (9,20) (9,32) (9,23) (9,14) (9,16) (9,13) (9,17) (9,24) (9,15) (10,30) (10,25) (10,34) (11,18) (11,31) (11,22) (11,12) (11,28) (11,20) (11,32) (11,23) (11,26) (11,13) (11,17) (11,24) (11,27) (11,19) (11,15) (12,18) (12,31) (12,29) (12,22) (12,20) (12,23) (12,14) (12,26) (12,17) (12,27) (12,19) (12,15) (12,33) (13,18) (13,29) (13,28) (13,20) (13,32) (13,23) (13,26) (13,16) (13,24) (13,15) (14,29) (14,22) (14,20) (14,32) (14,23) (14,16) (14,17) (14,27) (14,19) (15,18) (15,31) (15,29) (15,22) (15,28) (15,32) (15,23) (15,26) (15,16) (15,17) (15,24) (15,19) (15,33) (16,18) (16,31) (16,22) (16,28) (16,26) (16,27) (16,33) (17,28) (17,32) (17,23) (17,24) (17,27) (17,19) (18,31) (18,29) (18,22) (18,32) (18,26) (18,24) (18,19) (18,33) (19,31) (19,28) (19,20) (19,23) (19,33) (20,31) (20,32) (20,26) (21,25) (21,34) (22,29) (22,28) (22,32) (22,23) (22,27) (22,33) (23,31) (23,29) (23,28) (23,32) (23,26) (23,24) (23,27) (24,28) (24,26) (24,27) (24,33) (25,30) (26,31) (26,29) (26,28) (26,33) (27,31) (27,28) (27,32) (27,33) (28,29) (28,32) (29,32) (29,33) (31,33) (32,33)\nIs there a path between node 32 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph288-3_2", + "image": "data/connectivity/graph_visual/hard/graph288.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,23) (1,9) (1,11) (1,25) (1,30) (1,15) (1,21) (1,26) (2,16) (2,5) (2,19) (2,25) (2,24) (3,8) (4,27) (4,19) (4,30) (4,15) (4,20) (4,21) (5,27) (5,16) (5,18) (5,19) (5,15) (5,14) (5,31) (6,13) (7,10) (7,23) (8,12) (8,9) (8,28) (8,20) (9,11) (9,20) (9,21) (9,14) (10,29) (11,12) (11,30) (11,20) (11,21) (11,26) (12,19) (12,20) (12,14) (12,26) (13,17) (13,29) (14,28) (14,21) (14,26) (14,24) (15,27) (15,18) (15,21) (16,22) (16,25) (16,26) (16,24) (18,25) (18,31) (19,27) (19,28) (19,21) (20,28) (20,25) (20,30) (20,24) (21,28) (21,30) (21,26) (21,31) (22,27) (22,28) (22,31) (23,29) (24,28) (24,26) (24,31) (25,31) (26,27) (26,31) (27,31) (30,31)\nIs there a path between node 3 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph245-17_28", + "image": "data/connectivity/graph_visual/hard/graph245.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,3) (0,14) (0,17) (0,2) (0,25) (0,8) (0,21) (0,10) (0,18) (0,19) (0,26) (0,4) (0,29) (0,20) (0,13) (0,12) (1,3) (1,14) (1,17) (1,25) (1,8) (1,21) (1,16) (1,15) (1,10) (1,19) (1,9) (1,4) (1,5) (1,29) (1,30) (1,27) (1,13) (1,12) (2,3) (2,17) (2,24) (2,8) (2,16) (2,15) (2,26) (2,4) (2,29) (2,30) (2,27) (2,13) (3,14) (3,17) (3,24) (3,25) (3,8) (3,21) (3,16) (3,10) (3,9) (3,26) (3,29) (3,30) (3,27) (3,20) (3,13) (3,12) (4,25) (4,8) (4,21) (4,16) (4,10) (4,18) (4,19) (4,9) (4,5) (4,30) (4,27) (4,20) (5,14) (5,17) (5,24) (5,8) (5,21) (5,16) (5,15) (5,10) (5,18) (5,19) (5,9) (5,26) (5,30) (5,27) (5,20) (6,22) (6,7) (6,23) (8,14) (8,17) (8,25) (8,16) (8,15) (8,18) (8,19) (8,9) (8,26) (8,29) (8,30) (8,27) (8,13) (9,14) (9,17) (9,24) (9,25) (9,16) (9,15) (9,10) (9,26) (9,30) (9,20) (9,13) (10,14) (10,17) (10,24) (10,25) (10,21) (10,18) (10,29) (10,30) (10,27) (10,20) (10,13) (10,12) (11,28) (12,14) (12,25) (12,21) (12,16) (12,18) (12,19) (12,29) (12,27) (13,14) (13,17) (13,24) (13,16) (13,15) (13,19) (13,29) (13,30) (13,27) (14,17) (14,25) (14,21) (14,18) (14,19) (14,26) (14,29) (14,27) (14,20) (15,17) (15,24) (15,25) (15,16) (15,18) (15,19) (15,26) (15,29) (15,30) (15,20) (16,17) (16,24) (16,19) (16,26) (16,29) (16,30) (16,27) (16,20) (17,24) (17,21) (17,19) (17,30) (17,27) (18,24) (18,25) (18,21) (18,19) (18,26) (18,29) (18,30) (18,27) (19,25) (19,26) (19,29) (19,27) (19,20) (20,24) (20,25) (20,26) (20,29) (20,30) (20,27) (21,25) (21,26) (21,29) (21,30) (21,27) (24,25) (24,26) (24,29) (24,27) (25,26) (25,30) (25,27) (26,30) (26,27) (27,29) (29,30)\nIs there a path between node 17 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph135-21_16", + "image": "data/connectivity/graph_visual/hard/graph135.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,10) (0,7) (0,5) (0,3) (0,6) (0,27) (0,16) (0,8) (0,19) (0,24) (0,22) (0,21) (0,17) (0,20) (0,1) (0,25) (1,23) (1,3) (1,6) (1,26) (1,27) (1,16) (1,8) (1,19) (1,4) (1,22) (1,21) (1,17) (1,25) (2,13) (2,11) (3,10) (3,7) (3,5) (3,26) (3,16) (3,8) (3,19) (3,24) (3,18) (3,20) (3,15) (3,25) (4,5) (4,6) (4,26) (4,16) (4,8) (4,19) (4,24) (4,22) (4,21) (4,9) (4,17) (4,15) (5,10) (5,7) (5,6) (5,26) (5,27) (5,16) (5,8) (5,19) (5,22) (5,18) (5,21) (5,17) (5,20) (5,25) (6,10) (6,7) (6,23) (6,26) (6,27) (6,16) (6,19) (6,24) (6,22) (6,18) (6,21) (6,9) (6,17) (6,15) (6,25) (7,10) (7,23) (7,26) (7,8) (7,19) (7,24) (7,21) (7,9) (7,17) (7,20) (7,25) (8,10) (8,23) (8,26) (8,27) (8,16) (8,19) (8,24) (8,22) (8,9) (8,15) (9,10) (9,23) (9,27) (9,16) (9,24) (9,22) (9,18) (9,21) (9,17) (9,20) (9,15) (10,23) (10,27) (10,16) (10,24) (10,22) (10,17) (10,25) (11,13) (11,14) (12,13) (12,14) (15,23) (15,27) (15,19) (15,24) (15,22) (15,18) (15,21) (15,20) (15,25) (16,23) (16,27) (16,24) (16,22) (16,18) (16,17) (16,25) (17,23) (17,26) (17,27) (17,19) (17,22) (17,21) (17,20) (17,25) (18,26) (18,27) (18,19) (18,24) (18,22) (19,23) (19,24) (19,21) (19,25) (20,27) (20,24) (20,22) (20,25) (21,23) (21,26) (21,27) (21,24) (21,22) (21,25) (22,23) (22,26) (22,24) (23,26) (23,27) (23,24) (23,25) (24,27) (24,25) (25,27)\nIs there a path between node 21 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph12-14_17", + "image": "data/connectivity/graph_visual/hard/graph12.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,25) (0,7) (0,15) (0,3) (0,17) (0,23) (0,2) (0,19) (0,16) (0,6) (0,4) (0,22) (0,1) (0,8) (0,13) (0,21) (1,25) (1,11) (1,7) (1,20) (1,5) (1,15) (1,3) (1,23) (1,12) (1,18) (1,2) (1,19) (1,9) (1,16) (1,4) (1,22) (1,13) (1,21) (2,11) (2,5) (2,3) (2,17) (2,23) (2,12) (2,19) (2,9) (2,16) (2,6) (2,22) (2,8) (2,13) (2,21) (3,25) (3,11) (3,5) (3,15) (3,23) (3,12) (3,18) (3,19) (3,9) (3,16) (3,4) (3,22) (3,8) (3,13) (4,11) (4,20) (4,5) (4,15) (4,17) (4,23) (4,12) (4,18) (4,19) (4,9) (4,16) (4,6) (4,22) (5,15) (5,17) (5,18) (5,19) (5,9) (5,16) (5,6) (5,22) (5,13) (5,21) (6,11) (6,7) (6,20) (6,15) (6,23) (6,12) (6,19) (6,9) (6,16) (6,22) (6,8) (6,13) (6,21) (7,11) (7,15) (7,23) (7,12) (7,19) (7,9) (7,16) (7,8) (7,13) (8,25) (8,11) (8,15) (8,17) (8,12) (8,18) (8,19) (8,9) (8,22) (8,13) (8,21) (9,25) (9,11) (9,15) (9,17) (9,23) (9,12) (9,18) (9,19) (9,16) (9,22) (10,24) (10,14) (11,25) (11,20) (11,23) (11,12) (11,18) (11,19) (11,13) (11,21) (12,25) (12,20) (12,15) (12,17) (12,23) (12,18) (12,19) (12,16) (12,21) (13,25) (13,20) (13,15) (13,23) (13,18) (13,16) (13,22) (14,24) (15,20) (15,17) (15,23) (15,18) (15,19) (15,16) (15,22) (15,21) (16,25) (16,20) (16,17) (16,23) (16,18) (16,19) (16,22) (17,25) (17,20) (17,23) (17,19) (17,22) (17,21) (18,25) (18,20) (19,25) (19,20) (19,22) (20,25) (20,21) (21,25) (21,22) (22,25) (23,25)\nIs there a path between node 14 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph348-7_27", + "image": "data/connectivity/graph_visual/hard/graph348.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,31) (0,20) (0,13) (0,6) (0,9) (0,3) (0,21) (0,29) (1,16) (1,20) (1,6) (1,22) (1,30) (2,10) (2,5) (2,20) (2,19) (2,30) (3,16) (3,19) (3,23) (3,22) (3,21) (3,29) (3,28) (5,31) (5,25) (5,28) (5,30) (6,31) (6,19) (6,14) (7,27) (7,18) (8,27) (8,11) (8,18) (9,12) (9,23) (9,30) (10,16) (10,23) (10,15) (10,14) (10,30) (11,26) (11,18) (12,16) (12,13) (12,23) (12,21) (12,14) (13,16) (13,31) (13,20) (13,15) (13,21) (13,30) (14,21) (14,28) (14,30) (15,17) (15,31) (15,20) (15,19) (15,30) (16,20) (16,23) (16,22) (16,21) (17,31) (17,25) (17,30) (18,27) (19,31) (19,23) (19,25) (19,29) (19,28) (19,30) (21,23) (21,28) (22,31) (22,25) (22,29) (23,31) (23,28) (23,30) (24,27) (25,28) (26,27) (28,31) (28,29) (29,31) (30,31)\nIs there a path between node 7 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph317-24_7", + "image": "data/connectivity/graph_visual/hard/graph317.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,31) (0,12) (0,22) (0,2) (1,18) (1,31) (1,30) (1,10) (1,2) (2,9) (2,31) (2,30) (2,12) (2,17) (2,16) (2,24) (3,20) (3,28) (3,14) (4,27) (4,29) (4,28) (4,7) (4,26) (5,29) (5,28) (6,8) (6,27) (6,15) (6,29) (7,20) (7,19) (7,29) (8,19) (8,11) (8,21) (8,29) (8,28) (9,18) (9,23) (9,16) (9,22) (10,30) (11,25) (11,19) (11,14) (11,26) (12,31) (13,25) (13,27) (13,29) (14,20) (14,28) (14,26) (15,20) (15,27) (15,26) (16,31) (16,30) (17,18) (18,31) (18,30) (18,22) (19,28) (20,21) (20,29) (20,28) (20,26) (21,25) (21,27) (22,24) (23,31) (24,31) (26,29)\nIs there a path between node 24 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph186-8_27", + "image": "data/connectivity/graph_visual/hard/graph186.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,14) (0,10) (0,2) (2,15) (2,20) (2,23) (2,14) (2,17) (2,24) (2,18) (3,21) (4,27) (5,9) (5,22) (6,29) (6,8) (7,29) (7,25) (7,20) (7,17) (7,18) (7,8) (8,23) (8,24) (10,23) (10,18) (11,27) (12,13) (13,21) (14,25) (14,23) (14,17) (14,24) (15,29) (15,25) (15,23) (15,16) (16,29) (16,17) (17,25) (17,23) (17,24) (17,18) (18,29) (20,25) (22,26) (23,25) (24,29) (26,27)\nIs there a path between node 8 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph245-12_10", + "image": "data/connectivity/graph_visual/hard/graph245.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,3) (0,14) (0,17) (0,2) (0,25) (0,8) (0,21) (0,10) (0,18) (0,19) (0,26) (0,4) (0,29) (0,20) (0,13) (0,12) (1,3) (1,14) (1,17) (1,25) (1,8) (1,21) (1,16) (1,15) (1,10) (1,19) (1,9) (1,4) (1,5) (1,29) (1,30) (1,27) (1,13) (1,12) (2,3) (2,17) (2,24) (2,8) (2,16) (2,15) (2,26) (2,4) (2,29) (2,30) (2,27) (2,13) (3,14) (3,17) (3,24) (3,25) (3,8) (3,21) (3,16) (3,10) (3,9) (3,26) (3,29) (3,30) (3,27) (3,20) (3,13) (3,12) (4,25) (4,8) (4,21) (4,16) (4,10) (4,18) (4,19) (4,9) (4,5) (4,30) (4,27) (4,20) (5,14) (5,17) (5,24) (5,8) (5,21) (5,16) (5,15) (5,10) (5,18) (5,19) (5,9) (5,26) (5,30) (5,27) (5,20) (6,22) (6,7) (6,23) (8,14) (8,17) (8,25) (8,16) (8,15) (8,18) (8,19) (8,9) (8,26) (8,29) (8,30) (8,27) (8,13) (9,14) (9,17) (9,24) (9,25) (9,16) (9,15) (9,10) (9,26) (9,30) (9,20) (9,13) (10,14) (10,17) (10,24) (10,25) (10,21) (10,18) (10,29) (10,30) (10,27) (10,20) (10,13) (10,12) (11,28) (12,14) (12,25) (12,21) (12,16) (12,18) (12,19) (12,29) (12,27) (13,14) (13,17) (13,24) (13,16) (13,15) (13,19) (13,29) (13,30) (13,27) (14,17) (14,25) (14,21) (14,18) (14,19) (14,26) (14,29) (14,27) (14,20) (15,17) (15,24) (15,25) (15,16) (15,18) (15,19) (15,26) (15,29) (15,30) (15,20) (16,17) (16,24) (16,19) (16,26) (16,29) (16,30) (16,27) (16,20) (17,24) (17,21) (17,19) (17,30) (17,27) (18,24) (18,25) (18,21) (18,19) (18,26) (18,29) (18,30) (18,27) (19,25) (19,26) (19,29) (19,27) (19,20) (20,24) (20,25) (20,26) (20,29) (20,30) (20,27) (21,25) (21,26) (21,29) (21,30) (21,27) (24,25) (24,26) (24,29) (24,27) (25,26) (25,30) (25,27) (26,30) (26,27) (27,29) (29,30)\nIs there a path between node 12 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph41-16_2", + "image": "data/connectivity/graph_visual/hard/graph41.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,17) (0,2) (0,25) (0,14) (0,9) (0,15) (0,12) (0,1) (0,7) (0,16) (0,18) (0,11) (0,10) (0,5) (1,17) (1,2) (1,21) (1,14) (1,9) (1,15) (1,12) (1,19) (1,8) (1,7) (1,18) (1,11) (1,10) (1,5) (2,17) (2,21) (2,14) (2,9) (2,13) (2,3) (2,12) (2,6) (2,19) (2,7) (2,18) (2,11) (2,5) (3,17) (3,22) (3,21) (3,9) (3,15) (3,13) (3,6) (3,19) (3,8) (3,7) (3,16) (3,18) (3,11) (4,20) (4,23) (4,24) (5,17) (5,22) (5,21) (5,9) (5,15) (5,12) (5,19) (5,8) (5,16) (5,11) (5,10) (6,22) (6,25) (6,9) (6,15) (6,13) (6,12) (6,19) (6,8) (6,7) (6,16) (7,17) (7,22) (7,25) (7,9) (7,15) (7,13) (7,12) (7,19) (7,8) (7,16) (7,11) (7,10) (8,17) (8,22) (8,14) (8,12) (8,16) (8,18) (8,11) (9,17) (9,22) (9,25) (9,15) (9,13) (9,12) (9,19) (9,16) (9,18) (9,11) (10,17) (10,22) (10,25) (10,13) (10,19) (10,11) (11,17) (11,25) (11,14) (11,15) (11,13) (11,12) (11,19) (12,22) (12,21) (12,14) (12,19) (12,16) (13,22) (13,25) (13,21) (13,14) (13,16) (14,17) (14,21) (14,15) (14,19) (14,16) (14,18) (15,17) (15,25) (15,21) (15,16) (16,22) (16,25) (16,21) (16,19) (16,18) (17,22) (17,25) (17,21) (17,19) (17,18) (18,22) (18,21) (18,19) (19,22) (19,25) (19,21) (20,23) (20,24) (21,22) (21,25) (23,24)\nIs there a path between node 16 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph707-15_16", + "image": "data/connectivity/graph_visual/hard/graph707.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,20) (0,7) (0,13) (0,27) (0,34) (0,28) (0,19) (0,3) (0,17) (0,21) (0,6) (0,32) (0,31) (0,25) (0,24) (1,14) (1,29) (1,12) (1,23) (1,33) (1,11) (2,26) (2,18) (2,20) (2,7) (2,34) (2,28) (2,3) (2,15) (2,17) (2,21) (2,6) (2,32) (2,10) (2,31) (2,25) (2,22) (3,26) (3,18) (3,20) (3,7) (3,13) (3,27) (3,6) (3,32) (3,10) (3,9) (3,31) (3,25) (3,24) (4,29) (4,8) (4,5) (4,12) (4,30) (4,16) (5,14) (5,8) (5,12) (5,23) (5,30) (5,16) (5,33) (5,11) (6,7) (6,13) (6,34) (6,28) (6,19) (6,15) (6,17) (6,32) (6,31) (6,25) (6,24) (6,22) (7,18) (7,13) (7,27) (7,32) (7,9) (7,25) (7,24) (7,22) (8,29) (8,12) (8,23) (8,16) (8,33) (9,18) (9,13) (9,27) (9,34) (9,28) (9,19) (9,15) (9,17) (9,21) (9,32) (9,31) (9,25) (9,24) (9,22) (10,26) (10,20) (10,27) (10,34) (10,28) (10,19) (10,17) (10,32) (10,25) (11,29) (11,12) (11,30) (11,16) (12,23) (13,18) (13,20) (13,27) (13,28) (13,15) (13,17) (13,21) (13,32) (13,31) (13,25) (13,22) (14,29) (14,23) (14,16) (14,33) (15,18) (15,27) (15,34) (15,28) (15,19) (15,17) (15,32) (15,31) (15,24) (16,23) (16,30) (16,33) (17,26) (17,20) (17,27) (17,28) (17,19) (17,21) (17,32) (17,31) (17,25) (17,22) (18,20) (18,27) (18,28) (18,19) (18,32) (18,31) (18,25) (19,20) (19,27) (19,34) (19,21) (19,32) (19,31) (19,25) (19,24) (19,22) (20,26) (20,34) (20,21) (20,32) (20,31) (20,24) (21,26) (21,27) (21,32) (21,31) (21,25) (21,22) (22,28) (22,32) (22,31) (22,24) (23,29) (23,30) (23,33) (24,34) (24,28) (24,32) (24,25) (25,26) (25,27) (25,28) (25,32) (25,31) (26,27) (26,34) (26,28) (26,32) (26,31) (27,34) (27,28) (27,32) (27,31) (28,34) (28,32) (28,31) (29,30) (29,33) (30,33) (31,34) (32,34)\nIs there a path between node 15 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph167-22_26", + "image": "data/connectivity/graph_visual/hard/graph167.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,15) (0,8) (0,7) (0,4) (0,28) (0,18) (1,21) (1,15) (1,19) (1,25) (1,10) (1,4) (1,27) (1,5) (2,6) (2,14) (2,12) (2,8) (2,4) (2,11) (2,17) (3,21) (3,15) (3,6) (3,20) (3,23) (3,10) (3,7) (3,16) (3,28) (3,5) (3,18) (4,15) (4,14) (4,24) (4,20) (4,10) (4,11) (5,8) (5,27) (5,16) (5,11) (6,20) (6,16) (6,26) (6,18) (7,14) (7,19) (7,25) (7,12) (7,23) (7,8) (7,17) (7,13) (8,20) (8,16) (8,13) (10,25) (10,11) (10,26) (11,20) (11,28) (11,17) (11,18) (12,20) (12,28) (13,19) (13,27) (13,18) (14,21) (14,15) (14,23) (15,21) (15,19) (15,24) (15,16) (16,21) (16,20) (16,23) (16,26) (17,24) (17,20) (17,27) (18,19) (18,28) (19,21) (19,27) (19,28) (19,26) (20,28) (23,25) (24,25) (24,28) (25,28)\nIs there a path between node 22 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph13-23_13", + "image": "data/connectivity/graph_visual/hard/graph13.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,8) (0,5) (0,19) (1,8) (1,5) (1,19) (2,12) (2,15) (2,16) (2,24) (2,17) (2,3) (2,20) (2,9) (2,21) (2,23) (2,25) (2,11) (2,14) (2,22) (3,10) (3,15) (3,16) (3,24) (3,20) (3,4) (3,21) (3,23) (3,25) (3,14) (3,6) (3,22) (4,10) (4,13) (4,15) (4,16) (4,24) (4,20) (4,21) (4,23) (4,25) (4,14) (4,6) (4,22) (5,18) (5,7) (5,19) (6,12) (6,13) (6,24) (6,17) (6,20) (6,9) (6,23) (6,14) (6,22) (7,8) (8,18) (9,10) (9,12) (9,15) (9,16) (9,24) (9,17) (9,23) (9,25) (9,11) (9,14) (9,22) (10,12) (10,13) (10,16) (10,24) (10,17) (10,21) (10,23) (10,25) (10,11) (10,14) (10,22) (11,13) (11,16) (11,20) (11,21) (11,23) (11,25) (11,22) (12,24) (12,17) (12,20) (12,23) (12,22) (13,15) (13,24) (13,17) (13,20) (13,21) (13,25) (13,22) (14,15) (14,16) (14,24) (14,17) (14,20) (14,21) (14,23) (14,25) (15,24) (15,17) (15,20) (15,23) (15,25) (16,24) (16,17) (16,20) (16,21) (16,23) (16,25) (16,22) (17,24) (17,20) (17,23) (17,22) (18,19) (20,24) (20,21) (20,22) (21,24) (21,25) (21,22) (22,23) (22,25) (23,24) (23,25) (24,25)\nIs there a path between node 23 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph254-16_26", + "image": "data/connectivity/graph_visual/hard/graph254.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,30) (0,16) (0,1) (0,22) (0,25) (1,20) (1,23) (1,2) (1,12) (2,20) (2,23) (2,22) (3,21) (3,7) (4,16) (4,8) (4,22) (4,5) (5,23) (5,12) (6,25) (7,17) (7,28) (7,13) (8,16) (9,26) (11,15) (11,28) (11,14) (12,16) (12,25) (13,21) (13,18) (15,28) (15,18) (16,30) (20,23) (21,28) (23,27) (29,30)\nIs there a path between node 16 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph620-27_12", + "image": "data/connectivity/graph_visual/hard/graph620.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,20) (0,34) (0,1) (0,10) (0,12) (1,12) (2,24) (3,31) (3,30) (3,25) (4,19) (4,6) (5,8) (7,26) (10,20) (10,28) (10,17) (10,18) (12,20) (12,32) (12,17) (13,14) (13,15) (13,21) (13,26) (13,23) (14,15) (14,21) (15,26) (15,23) (16,21) (16,30) (17,20) (17,27) (17,32) (18,27) (18,34) (19,33) (20,27) (21,31) (21,22) (22,26) (22,31) (23,31) (26,31) (28,34) (30,31)\nIs there a path between node 27 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph611-1_26", + "image": "data/connectivity/graph_visual/hard/graph611.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,4) (1,32) (1,22) (1,34) (1,7) (1,5) (1,28) (1,11) (1,13) (1,30) (1,31) (1,26) (2,12) (2,3) (2,24) (2,15) (2,18) (2,8) (2,20) (2,25) (2,19) (2,17) (2,16) (3,10) (3,24) (3,15) (3,18) (3,8) (3,20) (3,14) (3,19) (3,21) (4,23) (4,6) (5,32) (5,22) (5,7) (5,33) (5,11) (5,13) (5,27) (5,31) (5,26) (6,23) (7,22) (7,34) (7,28) (7,13) (7,27) (7,30) (7,26) (7,29) (8,10) (8,24) (8,15) (8,18) (8,20) (8,14) (8,17) (8,21) (8,16) (9,32) (9,22) (9,34) (9,28) (9,13) (9,27) (9,31) (9,26) (9,29) (10,12) (10,24) (10,15) (10,18) (10,20) (10,25) (10,17) (11,32) (11,22) (11,34) (11,28) (11,13) (11,27) (11,30) (11,31) (11,26) (12,24) (12,25) (12,14) (12,17) (12,21) (12,16) (13,34) (13,33) (13,27) (13,30) (13,31) (13,29) (14,15) (14,18) (14,20) (14,25) (14,19) (14,17) (14,21) (14,16) (15,24) (15,18) (15,20) (15,17) (15,21) (16,24) (16,20) (16,19) (16,17) (17,24) (17,20) (17,21) (18,20) (18,25) (18,19) (20,24) (20,25) (20,21) (21,25) (22,32) (22,28) (22,27) (22,30) (22,31) (22,26) (24,25) (26,34) (26,33) (26,31) (27,34) (27,33) (27,28) (27,30) (27,31) (27,29) (28,32) (28,33) (28,30) (28,31) (28,29) (29,32) (29,33) (30,32) (31,32) (31,34) (32,34) (32,33) (33,34)\nIs there a path between node 1 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph208-11_7", + "image": "data/connectivity/graph_visual/hard/graph208.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,25) (0,2) (1,25) (1,8) (1,18) (1,2) (2,25) (3,28) (3,19) (3,26) (4,23) (4,10) (5,14) (6,23) (6,10) (6,9) (7,21) (7,26) (7,15) (8,14) (9,20) (9,23) (9,29) (9,11) (10,29) (10,11) (11,23) (11,29) (11,17) (12,16) (15,27) (15,19) (15,26) (16,19) (16,21) (16,26) (17,29) (19,28) (20,29) (20,22) (21,24) (22,29) (23,29) (24,28) (27,28)\nIs there a path between node 11 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph350-11_27", + "image": "data/connectivity/graph_visual/hard/graph350.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,21) (0,2) (1,19) (1,26) (2,27) (2,9) (3,31) (3,4) (3,25) (3,11) (4,31) (4,6) (4,20) (4,5) (4,10) (4,25) (4,24) (5,31) (5,21) (6,20) (6,21) (6,10) (6,18) (6,11) (6,24) (7,15) (7,17) (8,27) (8,11) (8,9) (9,18) (10,28) (10,16) (10,24) (11,28) (13,22) (13,17) (15,17) (16,21) (16,27) (17,26) (18,21) (18,25) (18,28) (18,24) (20,31) (21,28) (24,29) (24,27) (27,31) (28,31)\nIs there a path between node 11 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph183-18_1", + "image": "data/connectivity/graph_visual/hard/graph183.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,5) (0,10) (0,4) (0,16) (0,9) (0,8) (0,12) (0,11) (0,7) (0,24) (0,1) (0,22) (1,5) (1,21) (1,10) (1,23) (1,4) (1,16) (1,9) (1,20) (1,8) (1,3) (1,6) (1,26) (1,11) (1,7) (1,14) (1,13) (1,15) (1,22) (2,25) (3,21) (3,10) (3,23) (3,4) (3,16) (3,9) (3,20) (3,17) (3,8) (3,6) (3,26) (3,11) (3,7) (3,14) (3,24) (3,15) (3,22) (3,28) (4,18) (4,5) (4,21) (4,23) (4,16) (4,17) (4,8) (4,26) (4,12) (4,14) (4,24) (4,28) (5,18) (5,21) (5,10) (5,23) (5,20) (5,17) (5,6) (5,12) (5,11) (5,14) (5,13) (5,24) (5,15) (5,22) (5,28) (6,21) (6,10) (6,23) (6,9) (6,20) (6,17) (6,8) (6,26) (6,11) (6,7) (6,13) (6,24) (6,28) (7,18) (7,21) (7,10) (7,23) (7,16) (7,9) (7,17) (7,8) (7,26) (7,12) (7,14) (7,13) (7,24) (7,15) (7,22) (8,10) (8,16) (8,9) (8,20) (8,26) (8,12) (8,11) (8,24) (8,15) (8,22) (9,18) (9,10) (9,23) (9,16) (9,20) (9,17) (9,26) (9,12) (9,11) (9,14) (9,13) (9,24) (9,15) (9,22) (9,28) (10,18) (10,21) (10,23) (10,20) (10,26) (10,12) (10,11) (10,14) (10,13) (10,24) (10,15) (10,22) (10,28) (11,18) (11,21) (11,20) (11,17) (11,12) (11,14) (11,13) (11,24) (11,15) (11,28) (12,18) (12,21) (12,23) (12,20) (12,17) (12,26) (12,13) (12,15) (12,22) (13,21) (13,16) (13,20) (13,26) (13,14) (13,15) (13,22) (14,21) (14,23) (14,16) (14,20) (14,17) (14,26) (14,24) (14,15) (14,22) (14,28) (15,21) (15,23) (15,16) (15,17) (15,26) (15,22) (16,18) (16,21) (16,23) (16,20) (16,26) (16,28) (17,18) (17,23) (17,20) (17,26) (17,28) (18,23) (18,20) (18,26) (19,25) (20,21) (20,26) (20,22) (20,28) (21,26) (21,24) (21,28) (22,23) (22,26) (22,24) (22,28) (23,26) (23,24) (24,26) (25,27)\nIs there a path between node 18 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph653-8_29", + "image": "data/connectivity/graph_visual/hard/graph653.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,20) (0,13) (0,1) (1,4) (1,12) (1,34) (1,6) (1,28) (3,32) (4,20) (4,12) (4,34) (4,6) (4,28) (4,13) (5,26) (5,23) (5,18) (5,24) (5,30) (5,8) (5,21) (5,10) (5,25) (5,29) (5,22) (5,33) (5,15) (5,11) (6,20) (6,12) (6,28) (6,13) (7,16) (8,9) (8,31) (8,26) (8,23) (8,18) (8,24) (8,19) (8,21) (8,10) (8,25) (8,22) (8,33) (8,11) (8,17) (9,31) (9,26) (9,23) (9,18) (9,24) (9,21) (9,10) (9,25) (9,29) (9,22) (9,33) (9,15) (9,17) (10,31) (10,26) (10,23) (10,18) (10,24) (10,30) (10,19) (10,21) (10,29) (10,33) (10,15) (11,31) (11,23) (11,18) (11,24) (11,30) (11,19) (11,21) (11,25) (11,29) (11,33) (11,15) (11,17) (12,20) (12,34) (12,13) (13,20) (14,16) (15,31) (15,26) (15,18) (15,24) (15,30) (15,19) (15,21) (15,25) (15,22) (15,17) (15,27) (17,31) (17,23) (17,18) (17,24) (17,22) (17,27) (18,31) (18,26) (18,23) (18,24) (18,30) (18,19) (18,21) (18,25) (18,29) (18,22) (18,27) (19,31) (19,26) (19,24) (19,21) (19,25) (19,22) (19,33) (19,27) (20,34) (20,28) (21,31) (21,26) (21,23) (21,25) (21,29) (21,22) (21,33) (21,27) (22,24) (22,25) (22,29) (22,33) (22,27) (23,26) (23,29) (23,27) (24,31) (24,26) (24,30) (24,25) (24,29) (25,26) (25,30) (25,29) (25,33) (25,27) (26,31) (26,30) (26,29) (26,33) (26,27) (27,30) (27,29) (27,33) (28,34) (29,31) (29,33) (30,31) (31,33)\nIs there a path between node 8 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph666-7_24", + "image": "data/connectivity/graph_visual/hard/graph666.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,10) (0,28) (0,12) (0,26) (0,31) (0,13) (0,15) (0,22) (0,8) (0,7) (1,23) (1,27) (1,16) (2,11) (2,17) (2,10) (2,28) (2,3) (2,13) (2,15) (2,22) (2,19) (3,17) (3,10) (3,12) (3,32) (3,24) (4,11) (4,17) (4,29) (4,32) (4,24) (4,7) (5,10) (5,31) (5,32) (5,15) (5,22) (5,33) (6,11) (6,28) (6,26) (6,15) (6,14) (7,21) (7,13) (7,33) (7,24) (8,17) (8,10) (8,32) (8,15) (8,33) (8,34) (8,19) (9,18) (9,16) (10,17) (10,28) (10,22) (10,24) (11,28) (11,31) (11,15) (12,28) (12,29) (12,33) (13,15) (13,14) (14,28) (14,32) (14,22) (15,29) (15,26) (15,32) (15,22) (15,24) (16,20) (16,30) (17,21) (17,22) (17,34) (18,30) (20,23) (20,27) (21,29) (21,33) (21,34) (22,34) (22,24) (24,29) (24,33) (25,30) (25,27) (26,31) (28,32) (28,33) (28,34)\nIs there a path between node 7 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph697-0_17", + "image": "data/connectivity/graph_visual/hard/graph697.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,18) (0,11) (0,9) (0,15) (0,17) (0,12) (1,33) (1,16) (1,24) (1,32) (1,34) (1,22) (1,26) (1,20) (1,2) (1,19) (1,23) (1,29) (1,7) (2,33) (2,16) (2,32) (2,34) (2,22) (2,20) (2,14) (2,7) (3,27) (3,6) (3,10) (4,8) (4,13) (5,18) (5,11) (5,28) (5,17) (5,12) (6,27) (7,25) (7,16) (7,32) (7,22) (7,21) (7,20) (7,14) (7,19) (7,23) (7,29) (8,30) (9,18) (9,11) (9,28) (9,15) (9,17) (9,12) (10,27) (11,28) (11,17) (12,18) (12,17) (13,30) (13,31) (14,25) (14,16) (14,32) (14,34) (14,26) (14,20) (14,23) (14,29) (15,18) (15,28) (15,17) (16,33) (16,25) (16,24) (16,32) (16,34) (16,22) (16,21) (16,26) (16,20) (16,19) (17,28) (18,28) (19,33) (19,25) (19,24) (19,32) (19,34) (19,22) (19,21) (19,26) (19,20) (19,23) (19,29) (20,25) (20,24) (20,32) (20,21) (20,26) (20,23) (20,29) (21,33) (21,25) (21,24) (21,34) (21,22) (21,26) (21,23) (22,25) (22,24) (22,32) (22,26) (22,23) (23,33) (23,24) (23,34) (23,26) (23,29) (24,25) (24,26) (24,29) (25,33) (25,34) (25,26) (25,29) (26,33) (26,29) (29,33) (30,31) (32,33) (32,34)\nIs there a path between node 0 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph208-10_22", + "image": "data/connectivity/graph_visual/hard/graph208.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,25) (0,2) (1,25) (1,8) (1,18) (1,2) (2,25) (3,28) (3,19) (3,26) (4,23) (4,10) (5,14) (6,23) (6,10) (6,9) (7,21) (7,26) (7,15) (8,14) (9,20) (9,23) (9,29) (9,11) (10,29) (10,11) (11,23) (11,29) (11,17) (12,16) (15,27) (15,19) (15,26) (16,19) (16,21) (16,26) (17,29) (19,28) (20,29) (20,22) (21,24) (22,29) (23,29) (24,28) (27,28)\nIs there a path between node 10 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph404-20_21", + "image": "data/connectivity/graph_visual/hard/graph404.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,31) (0,26) (0,2) (0,22) (0,1) (0,13) (0,16) (0,18) (0,30) (0,14) (0,21) (1,31) (1,4) (1,26) (1,2) (1,22) (1,7) (1,16) (1,18) (1,11) (1,29) (1,30) (1,23) (1,14) (1,10) (1,32) (1,27) (1,12) (1,21) (2,31) (2,4) (2,26) (2,22) (2,7) (2,13) (2,16) (2,18) (2,11) (2,29) (2,30) (2,23) (2,14) (2,32) (2,12) (4,26) (4,7) (4,16) (4,18) (4,11) (4,29) (4,23) (4,14) (4,10) (4,12) (4,21) (5,17) (5,28) (5,6) (5,15) (5,25) (5,20) (5,8) (6,24) (6,25) (6,20) (6,8) (7,26) (7,18) (7,11) (7,29) (7,23) (7,14) (7,10) (7,32) (7,27) (7,12) (7,21) (8,17) (8,19) (8,28) (8,9) (8,15) (8,24) (9,17) (9,19) (9,28) (9,15) (9,24) (9,25) (9,20) (10,26) (10,22) (10,16) (10,11) (10,29) (10,30) (10,23) (10,14) (10,32) (10,27) (10,12) (11,31) (11,26) (11,22) (11,13) (11,16) (11,18) (11,30) (11,23) (11,14) (11,32) (12,26) (12,13) (12,16) (12,18) (12,29) (12,30) (12,23) (12,14) (12,32) (12,27) (12,21) (13,31) (13,18) (13,29) (13,30) (13,32) (13,21) (14,31) (14,26) (14,22) (14,16) (14,18) (14,29) (14,30) (14,23) (14,32) (14,27) (15,19) (15,28) (15,20) (16,31) (16,22) (16,29) (16,30) (16,23) (16,32) (16,27) (17,28) (17,20) (18,31) (18,22) (18,29) (18,23) (18,32) (18,27) (18,21) (19,28) (19,24) (19,20) (20,28) (20,24) (20,25) (21,22) (21,30) (21,32) (21,27) (22,31) (22,26) (22,29) (22,30) (22,23) (22,32) (22,27) (23,31) (23,30) (23,32) (23,27) (24,28) (24,25) (26,31) (26,30) (26,32) (26,27) (27,31) (27,29) (29,30) (29,32) (30,31) (31,32)\nIs there a path between node 20 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph696-28_25", + "image": "data/connectivity/graph_visual/hard/graph696.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,18) (0,15) (0,33) (0,8) (0,1) (0,24) (0,17) (0,4) (0,31) (0,12) (0,26) (0,14) (0,30) (0,32) (0,29) (0,2) (1,25) (1,19) (1,33) (1,8) (1,21) (1,24) (1,17) (1,4) (1,31) (1,12) (1,27) (1,10) (1,26) (1,14) (1,30) (1,29) (1,5) (1,3) (1,22) (2,18) (2,15) (2,19) (2,33) (2,8) (2,24) (2,17) (2,4) (2,27) (2,7) (2,10) (2,26) (2,14) (2,34) (2,30) (2,16) (2,29) (2,3) (2,22) (3,18) (3,33) (3,8) (3,21) (3,17) (3,4) (3,31) (3,12) (3,27) (3,7) (3,10) (3,26) (3,14) (3,34) (3,30) (3,29) (4,18) (4,25) (4,19) (4,33) (4,8) (4,21) (4,17) (4,27) (4,7) (4,10) (4,14) (4,30) (4,32) (4,16) (4,29) (4,5) (4,22) (5,15) (5,25) (5,8) (5,21) (5,17) (5,31) (5,26) (5,34) (5,30) (5,32) (5,16) (5,29) (6,23) (6,28) (6,9) (6,13) (7,18) (7,15) (7,25) (7,8) (7,21) (7,24) (7,17) (7,27) (7,10) (7,34) (7,30) (7,32) (7,16) (7,29) (7,22) (8,18) (8,15) (8,19) (8,21) (8,24) (8,17) (8,31) (8,27) (8,10) (8,26) (8,34) (8,30) (8,32) (8,16) (8,29) (8,22) (9,28) (9,20) (9,13) (9,11) (10,18) (10,15) (10,19) (10,21) (10,31) (10,12) (10,27) (10,26) (10,14) (10,30) (10,16) (10,29) (11,23) (11,28) (12,18) (12,15) (12,25) (12,19) (12,33) (12,24) (12,31) (12,27) (12,14) (12,34) (12,30) (12,32) (12,29) (12,22) (13,23) (13,28) (13,20) (14,18) (14,15) (14,25) (14,19) (14,21) (14,24) (14,17) (14,31) (14,27) (14,26) (14,30) (14,32) (14,16) (14,29) (14,22) (15,18) (15,25) (15,24) (15,17) (15,31) (15,27) (15,26) (15,30) (15,32) (15,16) (15,29) (16,18) (16,25) (16,19) (16,33) (16,21) (16,17) (16,27) (16,26) (16,30) (16,32) (16,29) (16,22) (17,18) (17,25) (17,19) (17,33) (17,24) (17,31) (17,27) (17,26) (17,30) (17,32) (17,29) (18,25) (18,19) (18,33) (18,21) (18,31) (18,27) (18,26) (18,34) (18,30) (18,32) (18,29) (19,33) (19,21) (19,31) (19,27) (19,26) (19,34) (19,30) (19,32) (19,22) (20,23) (20,28) (21,25) (21,24) (21,31) (21,27) (21,26) (21,34) (21,32) (21,29) (22,33) (22,31) (22,26) (22,34) (22,32) (22,29) (24,25) (24,31) (24,26) (24,34) (24,30) (24,29) (25,33) (25,31) (25,27) (25,34) (25,30) (25,32) (25,29) (26,31) (26,34) (26,30) (27,33) (27,34) (29,33) (29,31) (29,34) (29,30) (30,33) (30,31) (30,34) (30,32) (31,34) (31,32) (32,33) (33,34)\nIs there a path between node 28 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph24-12_21", + "image": "data/connectivity/graph_visual/hard/graph24.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,17) (0,4) (0,15) (0,3) (0,18) (0,5) (0,25) (0,14) (0,6) (0,20) (1,4) (1,12) (1,23) (1,15) (1,3) (1,25) (1,16) (1,13) (2,4) (2,9) (2,15) (2,11) (2,3) (2,18) (2,5) (2,25) (2,8) (2,20) (3,12) (3,11) (3,25) (3,14) (3,13) (3,20) (4,23) (4,24) (4,10) (4,18) (4,5) (4,20) (5,12) (5,18) (5,6) (5,20) (6,17) (6,19) (6,11) (6,10) (6,18) (6,25) (6,21) (6,8) (6,14) (6,13) (6,20) (8,19) (8,12) (8,11) (8,25) (8,20) (9,17) (9,11) (9,25) (9,16) (10,17) (10,12) (10,18) (10,21) (11,19) (11,18) (11,14) (11,13) (11,20) (12,23) (12,25) (12,14) (12,20) (13,17) (13,15) (14,25) (14,21) (15,19) (16,19) (16,24) (16,21) (17,23) (17,24) (17,18) (18,25) (20,24) (24,25)\nIs there a path between node 12 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph368-18_20", + "image": "data/connectivity/graph_visual/hard/graph368.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,10) (0,4) (0,3) (0,16) (0,24) (0,17) (0,25) (0,8) (1,18) (1,10) (1,4) (1,30) (1,16) (1,24) (1,17) (2,21) (2,14) (2,29) (2,11) (2,9) (2,5) (2,13) (3,18) (3,4) (3,23) (3,7) (3,16) (3,24) (3,20) (3,17) (3,8) (4,10) (4,30) (4,24) (4,20) (4,17) (4,8) (5,14) (5,11) (5,28) (5,9) (6,22) (6,19) (6,12) (7,18) (7,10) (7,23) (7,16) (7,24) (7,20) (7,17) (7,8) (8,18) (8,10) (8,23) (8,30) (8,16) (8,20) (9,26) (9,14) (9,29) (9,11) (9,28) (9,13) (10,18) (10,23) (10,30) (10,16) (10,24) (10,20) (10,17) (11,26) (11,21) (11,14) (11,29) (11,28) (11,13) (12,22) (12,27) (12,19) (12,31) (13,26) (13,21) (13,14) (13,29) (14,26) (14,21) (14,29) (14,28) (15,27) (15,19) (15,31) (16,18) (16,23) (16,30) (16,24) (16,20) (16,17) (17,30) (17,20) (18,30) (18,24) (18,20) (18,25) (19,22) (19,27) (19,31) (20,25) (21,29) (22,27) (23,30) (23,25) (24,25) (25,30) (26,28) (27,31) (28,29)\nIs there a path between node 18 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph213-10_26", + "image": "data/connectivity/graph_visual/hard/graph213.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,26) (0,1) (0,27) (0,11) (1,27) (1,17) (1,8) (1,20) (1,28) (1,11) (1,18) (1,12) (1,22) (2,24) (2,13) (2,3) (2,7) (3,13) (3,10) (3,4) (3,14) (4,15) (4,21) (4,24) (4,13) (4,10) (5,15) (5,21) (5,24) (5,7) (6,27) (6,29) (6,8) (6,20) (6,9) (6,28) (6,18) (6,25) (7,13) (7,16) (8,27) (8,28) (8,18) (9,17) (9,28) (9,25) (10,16) (11,28) (11,18) (11,25) (12,27) (12,17) (12,28) (12,19) (13,15) (14,15) (14,24) (14,23) (15,16) (15,23) (17,19) (18,25) (18,19) (19,20) (19,28) (19,25) (20,27) (23,24) (25,29) (25,28) (26,29) (28,29)\nIs there a path between node 10 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph48-7_23", + "image": "data/connectivity/graph_visual/hard/graph48.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,1) (0,19) (1,21) (2,8) (2,10) (3,8) (3,10) (4,7) (4,21) (4,18) (4,19) (4,5) (5,16) (6,12) (6,23) (6,13) (6,11) (7,19) (8,14) (8,23) (8,25) (9,20) (9,18) (9,26) (10,23) (10,22) (10,15) (11,14) (11,23) (12,14) (12,24) (12,13) (12,25) (12,22) (13,14) (13,24) (13,15) (14,24) (14,23) (14,15) (16,18) (16,17) (16,26) (17,26) (18,20) (22,24) (23,24) (23,25)\nIs there a path between node 7 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph509-15_10", + "image": "data/connectivity/graph_visual/hard/graph509.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,14) (0,15) (0,9) (0,19) (0,5) (0,31) (0,10) (0,3) (0,1) (0,6) (0,12) (0,27) (0,8) (0,25) (0,20) (0,23) (0,13) (0,18) (0,17) (0,33) (1,15) (1,9) (1,5) (1,24) (1,31) (1,10) (1,3) (1,4) (1,12) (1,27) (1,16) (1,26) (1,8) (1,25) (1,20) (1,28) (1,23) (1,29) (1,18) (1,17) (1,33) (2,14) (2,9) (2,5) (2,24) (2,31) (2,3) (2,4) (2,12) (2,8) (2,23) (2,13) (2,29) (2,18) (2,17) (2,33) (3,14) (3,15) (3,9) (3,19) (3,5) (3,24) (3,31) (3,10) (3,4) (3,30) (3,6) (3,12) (3,27) (3,16) (3,26) (3,28) (3,29) (3,18) (3,17) (3,33) (4,14) (4,15) (4,5) (4,31) (4,10) (4,30) (4,12) (4,27) (4,8) (4,25) (4,21) (4,20) (4,23) (4,13) (4,29) (4,18) (4,33) (5,15) (5,9) (5,24) (5,10) (5,30) (5,6) (5,12) (5,27) (5,16) (5,26) (5,8) (5,21) (5,20) (5,28) (5,23) (5,13) (5,29) (5,18) (5,17) (5,33) (6,14) (6,9) (6,19) (6,30) (6,27) (6,16) (6,26) (6,8) (6,25) (6,21) (6,28) (6,23) (6,18) (6,17) (6,33) (8,14) (8,15) (8,9) (8,10) (8,30) (8,12) (8,27) (8,16) (8,25) (8,21) (8,23) (8,13) (8,29) (8,17) (8,33) (9,14) (9,15) (9,19) (9,31) (9,10) (9,12) (9,27) (9,16) (9,25) (9,21) (9,20) (9,23) (9,13) (9,29) (9,18) (10,15) (10,19) (10,31) (10,30) (10,12) (10,27) (10,16) (10,26) (10,21) (10,20) (10,28) (10,23) (10,13) (10,29) (10,18) (10,17) (10,33) (11,32) (11,22) (12,19) (12,24) (12,31) (12,27) (12,16) (12,25) (12,21) (12,28) (12,23) (12,13) (12,18) (12,17) (12,33) (13,15) (13,24) (13,31) (13,27) (13,26) (13,21) (13,28) (13,23) (13,18) (13,17) (14,15) (14,19) (14,24) (14,16) (14,25) (14,21) (14,28) (14,29) (14,33) (15,19) (15,24) (15,31) (15,30) (15,27) (15,26) (15,21) (15,20) (15,28) (15,23) (15,18) (15,17) (15,33) (16,19) (16,31) (16,30) (16,27) (16,26) (16,20) (16,28) (16,23) (16,29) (16,18) (16,33) (17,19) (17,24) (17,31) (17,26) (17,25) (17,21) (17,20) (17,29) (17,33) (18,19) (18,24) (18,27) (18,25) (18,20) (18,23) (18,29) (18,33) (19,24) (19,31) (19,27) (19,26) (19,25) (19,21) (19,20) (19,23) (19,29) (19,33) (20,24) (20,31) (20,30) (20,27) (20,26) (20,25) (20,28) (20,33) (21,24) (21,31) (21,30) (21,27) (21,26) (21,25) (21,28) (21,23) (21,29) (21,33) (22,32) (23,31) (23,30) (23,27) (23,26) (23,25) (23,28) (23,29) (23,33) (24,31) (24,27) (24,26) (24,25) (24,29) (24,33) (25,30) (25,26) (25,29) (25,33) (26,30) (26,27) (26,28) (26,29) (26,33) (27,30) (27,33) (28,29) (28,33) (29,31) (29,30) (29,33) (30,31) (30,33) (31,33)\nIs there a path between node 15 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph186-6_7", + "image": "data/connectivity/graph_visual/hard/graph186.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,14) (0,10) (0,2) (2,15) (2,20) (2,23) (2,14) (2,17) (2,24) (2,18) (3,21) (4,27) (5,9) (5,22) (6,29) (6,8) (7,29) (7,25) (7,20) (7,17) (7,18) (7,8) (8,23) (8,24) (10,23) (10,18) (11,27) (12,13) (13,21) (14,25) (14,23) (14,17) (14,24) (15,29) (15,25) (15,23) (15,16) (16,29) (16,17) (17,25) (17,23) (17,24) (17,18) (18,29) (20,25) (22,26) (23,25) (24,29) (26,27)\nIs there a path between node 6 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph496-17_29", + "image": "data/connectivity/graph_visual/hard/graph496.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,15) (0,27) (0,3) (1,6) (1,8) (1,12) (1,4) (1,10) (1,19) (2,9) (2,8) (2,26) (2,31) (2,18) (2,4) (3,15) (3,5) (4,6) (4,8) (4,28) (4,18) (4,13) (4,10) (4,23) (5,15) (5,27) (6,31) (6,10) (6,20) (7,25) (8,29) (8,28) (8,18) (9,26) (9,13) (9,10) (9,33) (10,26) (10,13) (11,26) (11,12) (11,22) (11,24) (11,13) (11,20) (12,26) (12,22) (12,24) (12,18) (12,20) (12,23) (12,33) (13,33) (14,17) (14,25) (14,32) (18,29) (18,22) (19,28) (19,24) (19,33) (20,29) (21,25) (21,32) (22,26) (22,23) (22,33) (23,28) (23,31) (23,33) (24,33) (26,28) (26,31) (26,33) (28,29) (29,31) (29,33) (30,32) (31,33)\nIs there a path between node 17 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph311-10_7", + "image": "data/connectivity/graph_visual/hard/graph311.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,21) (1,6) (1,16) (2,5) (2,29) (4,14) (4,8) (4,28) (4,19) (5,23) (5,8) (5,15) (5,11) (5,9) (6,26) (7,23) (7,8) (7,19) (7,30) (8,14) (9,10) (9,19) (9,15) (9,22) (10,23) (10,14) (10,28) (10,25) (10,30) (11,23) (11,29) (12,31) (12,13) (13,18) (14,27) (15,23) (15,25) (19,28) (20,24) (22,23) (23,30) (23,29) (24,26) (28,29) (29,30)\nIs there a path between node 10 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph197-9_24", + "image": "data/connectivity/graph_visual/hard/graph197.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,5) (0,18) (0,28) (0,10) (0,13) (0,8) (0,22) (0,20) (1,3) (1,29) (1,23) (1,26) (1,6) (1,24) (1,15) (2,4) (2,27) (3,25) (3,29) (3,23) (3,26) (3,6) (3,24) (3,14) (3,16) (3,9) (4,27) (5,11) (5,18) (5,7) (5,10) (5,8) (5,22) (5,21) (5,20) (6,25) (6,29) (6,23) (6,12) (6,26) (6,24) (6,16) (6,15) (6,9) (7,11) (7,28) (7,19) (7,10) (7,13) (7,8) (7,22) (7,21) (7,20) (8,11) (8,18) (8,19) (8,10) (8,13) (8,22) (8,21) (8,20) (9,25) (9,29) (9,12) (9,26) (9,24) (9,14) (9,16) (9,15) (10,11) (10,18) (10,28) (10,19) (10,13) (10,22) (10,21) (11,18) (11,28) (11,19) (11,13) (11,22) (11,21) (12,25) (12,29) (12,23) (12,24) (12,14) (12,15) (13,18) (13,28) (13,19) (13,21) (14,25) (14,29) (14,16) (15,29) (15,23) (15,26) (15,24) (15,16) (16,25) (16,23) (16,26) (16,24) (18,28) (18,21) (19,28) (19,22) (19,21) (19,20) (20,28) (20,21) (21,22) (22,28) (23,29) (24,25) (24,29) (24,26) (25,29)\nIs there a path between node 9 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph72-17_2", + "image": "data/connectivity/graph_visual/hard/graph72.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,13) (0,14) (0,10) (0,19) (0,8) (0,26) (0,15) (0,1) (0,4) (1,22) (1,14) (1,23) (1,5) (1,26) (1,15) (1,11) (2,20) (2,14) (2,10) (2,15) (2,6) (2,17) (2,3) (2,11) (3,13) (3,12) (3,10) (3,5) (3,7) (3,4) (4,12) (4,14) (4,10) (4,23) (4,7) (4,26) (4,15) (4,17) (4,11) (5,12) (5,19) (5,26) (5,17) (6,20) (6,13) (6,14) (6,10) (6,19) (6,8) (6,26) (6,15) (6,21) (6,17) (7,13) (7,16) (7,21) (7,17) (7,24) (8,22) (8,15) (8,21) (10,19) (10,23) (10,11) (11,16) (11,21) (12,13) (12,14) (12,23) (12,26) (12,15) (12,24) (13,23) (13,26) (13,17) (14,20) (14,23) (14,17) (14,24) (15,20) (16,20) (16,21) (17,21) (19,22) (20,23) (20,26) (22,23) (24,26)\nIs there a path between node 17 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph102-20_3", + "image": "data/connectivity/graph_visual/hard/graph102.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,14) (0,27) (0,17) (0,9) (0,10) (0,2) (0,4) (0,20) (1,22) (1,13) (1,7) (1,21) (1,12) (1,19) (1,6) (1,26) (1,5) (1,16) (1,8) (2,14) (2,24) (2,17) (2,9) (2,15) (2,10) (2,18) (3,14) (3,24) (3,15) (3,10) (3,18) (4,14) (4,27) (4,9) (4,15) (4,10) (4,18) (4,20) (5,13) (5,7) (5,23) (5,25) (5,12) (5,19) (5,6) (5,26) (5,11) (5,16) (6,22) (6,13) (6,7) (6,23) (6,21) (6,12) (6,19) (6,11) (6,16) (6,8) (7,22) (7,13) (7,23) (7,12) (7,19) (7,26) (7,11) (7,16) (7,8) (8,22) (8,13) (8,23) (8,25) (8,21) (8,19) (8,16) (9,14) (9,24) (9,17) (9,10) (9,20) (10,14) (10,24) (10,17) (10,18) (11,22) (11,13) (11,12) (11,19) (11,26) (11,16) (12,22) (12,13) (12,21) (12,19) (12,26) (12,16) (13,22) (13,23) (13,19) (14,24) (14,17) (14,15) (14,18) (14,20) (15,27) (15,17) (15,18) (16,22) (16,23) (16,25) (16,21) (16,26) (17,27) (17,18) (17,20) (18,27) (18,20) (19,22) (19,23) (19,25) (19,21) (20,24) (20,27) (21,22) (21,23) (21,25) (21,26) (22,25) (22,26) (23,26) (24,27) (25,26)\nIs there a path between node 20 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph205-24_23", + "image": "data/connectivity/graph_visual/hard/graph205.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,21) (0,12) (0,22) (0,29) (0,26) (0,4) (0,28) (1,22) (1,16) (1,19) (1,23) (1,25) (2,12) (2,22) (2,29) (2,5) (2,8) (3,15) (3,10) (3,18) (3,21) (3,12) (3,22) (3,26) (3,14) (3,27) (3,28) (3,8) (4,10) (4,20) (4,16) (4,26) (4,27) (4,28) (4,5) (5,15) (5,10) (5,12) (5,20) (5,16) (5,7) (5,14) (5,27) (5,17) (7,29) (7,16) (7,23) (7,28) (8,15) (8,23) (8,26) (8,11) (8,17) (10,18) (10,13) (10,22) (10,16) (11,21) (11,12) (11,29) (11,16) (11,14) (12,21) (12,20) (12,23) (12,17) (13,29) (13,20) (14,18) (14,21) (14,23) (14,26) (14,27) (14,17) (15,29) (15,19) (15,23) (15,26) (15,25) (16,18) (16,21) (16,29) (16,27) (16,25) (16,28) (16,17) (17,26) (18,21) (18,20) (18,19) (18,23) (19,26) (20,23) (20,25) (21,22) (22,23) (22,27) (22,28) (23,29) (23,26) (23,27) (23,28) (25,29) (25,27)\nIs there a path between node 24 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph314-17_12", + "image": "data/connectivity/graph_visual/hard/graph314.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,7) (1,5) (1,10) (1,23) (1,20) (2,30) (2,24) (2,18) (2,12) (2,16) (2,3) (2,11) (3,30) (3,4) (3,12) (3,10) (3,22) (3,19) (3,20) (4,30) (4,28) (4,18) (4,12) (4,10) (4,23) (4,22) (4,19) (5,28) (5,18) (5,12) (5,10) (5,19) (5,11) (6,8) (6,21) (6,13) (6,29) (7,8) (7,21) (7,13) (7,17) (7,29) (8,17) (8,15) (9,26) (9,23) (9,22) (9,19) (9,25) (9,20) (10,18) (10,16) (10,26) (10,22) (10,11) (11,30) (11,12) (11,22) (12,28) (12,16) (12,23) (13,17) (13,29) (14,31) (15,31) (15,29) (16,24) (16,28) (16,19) (16,20) (17,27) (17,21) (18,26) (18,19) (19,23) (20,24) (20,23) (22,28) (22,23) (22,25) (23,26) (24,28) (24,25) (25,30)\nIs there a path between node 17 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph386-6_29", + "image": "data/connectivity/graph_visual/hard/graph386.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,16) (0,20) (0,21) (0,24) (0,6) (0,31) (0,26) (0,2) (0,7) (0,14) (0,27) (0,11) (0,1) (1,16) (1,21) (1,24) (1,31) (1,18) (1,25) (1,26) (1,2) (1,7) (1,14) (1,27) (1,11) (1,10) (2,16) (2,20) (2,21) (2,24) (2,6) (2,31) (2,14) (2,27) (2,10) (3,15) (3,29) (3,4) (3,13) (3,8) (3,19) (3,5) (3,22) (4,30) (4,12) (4,17) (4,29) (4,13) (4,5) (4,22) (5,30) (5,12) (5,15) (5,28) (5,29) (5,19) (5,22) (5,23) (6,9) (6,16) (6,24) (6,31) (6,25) (6,7) (6,27) (6,11) (7,16) (7,21) (7,24) (7,18) (7,14) (7,11) (7,10) (8,12) (8,17) (8,15) (8,13) (8,19) (8,22) (8,23) (9,20) (9,21) (9,24) (9,31) (9,18) (9,26) (9,14) (10,21) (10,31) (10,18) (10,25) (10,26) (10,14) (10,27) (10,11) (11,16) (11,20) (11,21) (11,31) (11,18) (11,25) (11,26) (11,14) (12,28) (12,29) (12,13) (12,23) (13,30) (13,17) (13,15) (13,28) (13,19) (13,23) (14,20) (14,21) (14,31) (14,18) (14,25) (14,26) (14,27) (15,17) (15,28) (15,19) (15,23) (16,20) (16,21) (16,24) (16,18) (16,26) (17,30) (17,22) (17,23) (18,21) (18,31) (18,25) (18,27) (19,30) (19,28) (19,22) (19,23) (20,21) (20,31) (20,26) (20,27) (21,24) (21,31) (21,25) (21,26) (21,27) (22,30) (22,29) (23,30) (23,28) (23,29) (24,31) (24,25) (24,26) (25,31) (25,26) (25,27) (26,27) (27,31) (28,30) (28,29)\nIs there a path between node 6 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph321-19_6", + "image": "data/connectivity/graph_visual/hard/graph321.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,5) (0,21) (0,7) (0,6) (0,3) (0,17) (0,20) (0,22) (0,16) (0,23) (0,25) (0,27) (1,5) (1,21) (1,4) (1,7) (1,15) (1,18) (1,2) (1,24) (1,20) (1,11) (1,16) (1,25) (1,27) (2,14) (2,5) (2,21) (2,4) (2,15) (2,24) (2,22) (2,11) (2,23) (2,25) (2,27) (3,14) (3,13) (3,21) (3,7) (3,15) (3,6) (3,17) (3,24) (3,22) (3,11) (3,16) (3,23) (4,14) (4,13) (4,5) (4,19) (4,7) (4,18) (4,17) (4,22) (4,11) (4,23) (4,25) (4,27) (5,13) (5,19) (5,15) (5,18) (5,24) (5,20) (5,22) (5,11) (5,23) (5,27) (6,14) (6,21) (6,19) (6,7) (6,15) (6,18) (6,17) (6,24) (6,20) (6,11) (6,16) (6,25) (6,27) (7,14) (7,13) (7,21) (7,19) (7,15) (7,18) (7,17) (7,20) (7,22) (7,11) (7,23) (7,27) (8,30) (8,28) (9,31) (9,10) (9,26) (9,29) (10,31) (10,26) (10,29) (11,13) (11,21) (11,19) (11,15) (11,24) (11,22) (11,25) (11,27) (12,28) (13,14) (13,21) (13,15) (13,18) (13,17) (13,24) (13,20) (13,16) (13,23) (13,25) (13,27) (14,21) (14,19) (14,24) (14,20) (14,22) (14,16) (14,23) (14,25) (15,21) (15,18) (15,17) (15,24) (15,20) (15,22) (15,16) (15,25) (15,27) (16,21) (16,18) (16,17) (16,24) (16,20) (16,22) (16,25) (17,21) (17,19) (17,18) (17,24) (17,20) (17,22) (17,23) (17,25) (17,27) (18,21) (18,24) (18,20) (18,25) (18,27) (19,21) (19,20) (19,22) (19,27) (20,21) (20,24) (20,22) (20,23) (20,27) (21,24) (21,22) (21,25) (21,27) (22,25) (23,25) (23,27) (25,27) (26,31) (26,29) (29,31)\nIs there a path between node 19 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph354-17_16", + "image": "data/connectivity/graph_visual/hard/graph354.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,28) (1,7) (1,14) (1,13) (1,3) (1,5) (1,2) (1,21) (2,8) (2,27) (2,22) (3,8) (3,6) (3,7) (3,14) (4,30) (4,10) (5,14) (5,25) (5,23) (5,19) (6,11) (6,14) (6,22) (6,9) (6,16) (7,27) (7,9) (7,31) (7,23) (8,11) (8,20) (8,16) (8,19) (8,21) (9,25) (9,13) (9,31) (9,23) (9,19) (10,30) (10,12) (10,26) (11,31) (11,19) (11,21) (12,15) (12,30) (13,14) (13,23) (13,21) (14,20) (14,17) (14,23) (15,26) (16,22) (16,31) (17,20) (18,29) (19,23) (20,25) (21,25) (21,22) (22,31) (23,25) (23,31) (24,28) (24,30) (25,31) (26,30) (28,30) (28,29)\nIs there a path between node 17 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph229-21_9", + "image": "data/connectivity/graph_visual/hard/graph229.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,26) (0,13) (1,23) (1,10) (1,16) (1,11) (1,19) (1,8) (1,2) (1,14) (1,29) (1,25) (1,9) (1,17) (1,28) (2,24) (2,23) (2,10) (2,16) (2,11) (2,19) (2,20) (2,21) (2,14) (2,25) (2,9) (2,4) (2,17) (2,28) (3,5) (3,15) (3,6) (3,7) (4,24) (4,16) (4,11) (4,19) (4,8) (4,18) (4,14) (4,29) (4,25) (4,22) (4,17) (4,28) (5,27) (5,15) (5,6) (6,27) (7,27) (7,15) (8,24) (8,23) (8,10) (8,19) (8,20) (8,18) (8,29) (8,25) (8,17) (8,28) (9,24) (9,23) (9,10) (9,19) (9,18) (9,29) (9,25) (9,22) (9,17) (10,24) (10,23) (10,16) (10,11) (10,19) (10,20) (10,21) (10,18) (10,29) (10,25) (10,22) (10,17) (10,28) (11,24) (11,23) (11,16) (11,19) (11,21) (11,18) (11,14) (11,29) (11,22) (11,28) (12,26) (13,26) (14,24) (14,16) (14,20) (14,21) (14,18) (14,29) (14,25) (14,22) (15,27) (16,23) (16,20) (16,18) (16,29) (16,25) (17,23) (17,20) (17,29) (17,22) (17,28) (18,23) (18,19) (18,20) (18,21) (18,29) (18,25) (18,28) (19,24) (19,21) (19,29) (19,25) (19,22) (19,28) (20,24) (20,21) (20,25) (20,22) (20,28) (21,23) (21,29) (21,22) (22,23) (22,29) (23,29) (23,25) (23,28) (24,25) (25,28) (28,29)\nIs there a path between node 21 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph468-13_7", + "image": "data/connectivity/graph_visual/hard/graph468.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,6) (0,2) (0,22) (0,32) (0,27) (0,5) (0,14) (0,3) (0,21) (0,7) (0,25) (0,29) (0,9) (0,18) (0,19) (0,11) (0,31) (0,10) (0,8) (1,6) (1,2) (1,5) (1,3) (1,21) (1,7) (1,29) (1,9) (1,19) (1,10) (1,8) (2,32) (2,5) (2,14) (2,3) (2,7) (2,29) (2,9) (2,18) (2,23) (2,11) (2,10) (2,8) (3,22) (3,27) (3,5) (3,21) (3,7) (3,25) (3,29) (3,19) (3,23) (3,10) (4,20) (4,15) (4,28) (4,12) (4,30) (5,6) (5,22) (5,32) (5,27) (5,14) (5,21) (5,25) (5,29) (5,9) (5,18) (5,19) (5,11) (5,31) (5,10) (5,8) (6,24) (6,32) (6,27) (6,14) (6,21) (6,25) (6,29) (6,9) (6,18) (6,19) (6,23) (6,8) (7,22) (7,24) (7,27) (7,14) (7,21) (7,29) (7,9) (7,23) (7,11) (7,10) (7,8) (8,24) (8,32) (8,27) (8,14) (8,25) (8,29) (8,9) (8,18) (8,19) (8,23) (8,11) (8,31) (9,22) (9,24) (9,32) (9,27) (9,21) (9,29) (9,18) (9,19) (9,23) (9,11) (9,10) (10,22) (10,32) (10,27) (10,14) (10,21) (10,19) (10,23) (10,31) (11,22) (11,24) (11,32) (11,27) (11,14) (11,21) (11,25) (11,29) (11,18) (11,19) (11,31) (12,20) (12,15) (12,28) (12,30) (13,16) (13,17) (14,24) (14,32) (14,21) (14,25) (14,29) (14,19) (14,23) (14,31) (15,20) (15,28) (15,30) (16,17) (16,26) (17,26) (18,32) (18,27) (18,21) (18,25) (18,29) (18,23) (18,31) (19,22) (19,32) (19,27) (19,21) (19,25) (20,28) (20,30) (21,22) (21,24) (21,32) (21,27) (21,29) (21,23) (22,32) (22,25) (22,29) (22,23) (22,31) (23,24) (23,27) (23,31) (24,32) (24,27) (24,25) (24,31) (25,27) (25,29) (27,29) (27,31) (28,30) (29,32) (31,32)\nIs there a path between node 13 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph287-29_18", + "image": "data/connectivity/graph_visual/hard/graph287.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,16) (0,19) (1,31) (1,27) (1,7) (2,26) (2,12) (2,4) (2,7) (2,23) (3,28) (3,10) (3,14) (3,19) (3,11) (3,25) (4,27) (4,24) (4,17) (5,20) (5,13) (5,10) (5,14) (5,19) (6,31) (6,15) (6,27) (6,21) (8,13) (9,13) (9,11) (9,18) (10,28) (10,14) (10,16) (10,19) (10,11) (10,18) (11,20) (11,22) (11,14) (11,16) (11,18) (12,31) (12,30) (12,27) (12,24) (12,23) (13,22) (13,14) (13,25) (14,22) (14,25) (14,18) (15,31) (15,26) (15,24) (16,18) (17,31) (17,26) (17,23) (18,19) (19,22) (20,25) (21,31) (21,24) (21,29) (21,23) (22,28) (22,25) (23,27) (23,29) (24,30) (26,27) (29,31)\nIs there a path between node 29 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph480-17_12", + "image": "data/connectivity/graph_visual/hard/graph480.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,28) (0,10) (0,15) (0,27) (0,11) (0,31) (0,4) (0,30) (0,5) (0,26) (0,24) (0,17) (0,21) (0,25) (0,9) (0,19) (0,18) (0,7) (0,14) (0,22) (0,6) (1,32) (1,12) (1,29) (2,28) (2,10) (2,15) (2,16) (2,31) (2,4) (2,5) (2,26) (2,24) (2,17) (2,21) (2,25) (2,9) (2,19) (2,18) (2,7) (2,14) (2,23) (2,3) (2,6) (3,28) (3,27) (3,11) (3,16) (3,31) (3,30) (3,8) (3,5) (3,26) (3,24) (3,17) (3,21) (3,25) (3,19) (3,18) (3,14) (3,23) (3,20) (3,22) (3,6) (4,28) (4,10) (4,15) (4,11) (4,16) (4,31) (4,30) (4,8) (4,5) (4,26) (4,24) (4,17) (4,21) (4,9) (4,18) (4,7) (4,14) (4,23) (4,20) (4,22) (4,6) (5,28) (5,10) (5,15) (5,27) (5,11) (5,16) (5,30) (5,8) (5,26) (5,17) (5,21) (5,25) (5,19) (5,18) (5,7) (5,23) (5,20) (5,6) (6,28) (6,10) (6,27) (6,16) (6,8) (6,26) (6,24) (6,17) (6,21) (6,25) (6,18) (6,7) (6,14) (7,28) (7,15) (7,27) (7,11) (7,16) (7,31) (7,30) (7,8) (7,26) (7,24) (7,17) (7,21) (7,25) (7,19) (7,14) (7,23) (7,22) (8,28) (8,11) (8,31) (8,26) (8,24) (8,17) (8,21) (8,9) (8,19) (8,18) (8,20) (8,22) (9,28) (9,10) (9,15) (9,11) (9,16) (9,31) (9,30) (9,26) (9,24) (9,17) (9,19) (9,14) (9,20) (9,22) (10,28) (10,15) (10,11) (10,31) (10,30) (10,26) (10,24) (10,17) (10,21) (10,19) (10,18) (10,14) (10,23) (10,20) (10,22) (11,27) (11,16) (11,31) (11,30) (11,26) (11,24) (11,21) (11,25) (11,14) (11,20) (11,22) (12,13) (13,32) (13,29) (14,28) (14,27) (14,16) (14,31) (14,30) (14,26) (14,24) (14,17) (14,21) (14,19) (14,23) (14,20) (14,22) (15,27) (15,31) (15,24) (15,17) (15,21) (15,25) (15,19) (15,23) (15,20) (15,22) (16,28) (16,30) (16,26) (16,24) (16,17) (16,25) (16,23) (16,20) (16,22) (17,31) (17,30) (17,26) (17,24) (17,25) (17,18) (18,28) (18,27) (18,31) (18,30) (18,26) (18,24) (18,21) (18,25) (18,19) (18,23) (18,22) (19,27) (19,31) (19,30) (19,24) (19,21) (19,25) (19,20) (20,27) (20,31) (20,30) (20,26) (20,24) (20,25) (20,23) (20,22) (21,28) (21,27) (21,31) (21,30) (21,26) (21,25) (21,23) (21,22) (22,27) (22,31) (22,26) (22,25) (23,28) (23,27) (23,31) (23,26) (23,24) (24,31) (24,26) (24,25) (25,28) (25,27) (25,31) (25,30) (25,26) (26,28) (26,27) (26,31) (26,30) (27,28) (27,31) (27,30) (28,30) (29,32)\nIs there a path between node 17 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph28-21_1", + "image": "data/connectivity/graph_visual/hard/graph28.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,1) (0,11) (1,18) (1,17) (1,2) (4,16) (4,18) (4,22) (5,13) (5,24) (5,10) (7,12) (8,16) (8,11) (9,13) (9,14) (10,15) (10,14) (11,18) (13,14) (14,15) (15,24) (16,19) (16,22) (17,18) (18,20) (18,21) (18,25) (19,20) (19,21) (19,22) (20,21) (22,25) (23,24)\nIs there a path between node 21 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph283-16_9", + "image": "data/connectivity/graph_visual/hard/graph283.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,14) (0,27) (0,23) (0,15) (1,2) (1,20) (1,13) (1,30) (1,16) (1,7) (1,22) (1,26) (2,9) (2,20) (2,13) (2,30) (2,16) (2,7) (2,22) (2,26) (3,29) (3,14) (3,27) (3,24) (3,23) (3,15) (4,21) (4,25) (4,28) (4,5) (4,18) (4,17) (4,8) (5,21) (5,25) (5,28) (5,10) (5,18) (5,17) (5,8) (6,29) (6,14) (6,27) (6,24) (6,23) (6,15) (7,9) (7,13) (7,30) (7,16) (7,26) (8,19) (8,21) (8,25) (8,28) (8,11) (8,10) (8,17) (9,20) (9,13) (9,30) (9,22) (9,26) (10,19) (10,21) (10,25) (10,28) (10,18) (10,17) (11,19) (11,21) (11,25) (11,28) (11,18) (12,29) (12,14) (12,27) (12,24) (12,15) (13,30) (13,16) (13,22) (14,29) (14,27) (14,24) (14,15) (15,29) (15,27) (15,24) (15,23) (16,20) (16,30) (16,26) (17,21) (17,25) (17,28) (17,18) (18,19) (18,21) (18,25) (19,21) (19,25) (20,22) (20,26) (21,25) (22,30) (23,27) (24,29) (24,27)\nIs there a path between node 16 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph545-8_19", + "image": "data/connectivity/graph_visual/hard/graph545.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,23) (1,15) (1,33) (1,7) (1,12) (1,25) (1,27) (1,17) (1,2) (1,6) (1,31) (1,5) (1,9) (1,13) (2,23) (2,33) (2,7) (2,26) (2,19) (2,8) (2,29) (2,25) (2,27) (2,6) (2,9) (2,13) (3,32) (3,11) (3,24) (3,30) (3,10) (3,16) (4,20) (4,21) (4,32) (4,11) (4,18) (4,24) (4,30) (4,10) (4,16) (5,15) (5,33) (5,7) (5,12) (5,26) (5,14) (5,19) (5,29) (5,17) (5,6) (5,31) (5,9) (5,13) (6,33) (6,7) (6,12) (6,26) (6,14) (6,8) (6,29) (6,27) (6,17) (6,28) (6,31) (6,9) (6,13) (7,23) (7,15) (7,12) (7,26) (7,19) (7,8) (7,25) (7,17) (7,28) (7,31) (7,9) (8,15) (8,33) (8,12) (8,14) (8,19) (8,27) (8,17) (8,13) (9,33) (9,12) (9,19) (9,27) (9,17) (9,28) (9,31) (9,13) (10,20) (10,32) (10,11) (10,18) (10,30) (10,16) (11,20) (11,21) (11,32) (11,22) (11,18) (11,24) (11,30) (12,19) (12,29) (12,13) (13,23) (13,33) (13,14) (13,19) (13,27) (13,17) (13,28) (13,31) (14,23) (14,33) (14,26) (14,19) (14,29) (14,25) (14,17) (14,28) (14,31) (15,23) (15,33) (15,26) (15,29) (15,25) (15,17) (15,28) (15,31) (16,20) (16,22) (16,18) (16,24) (16,30) (17,23) (17,26) (17,19) (17,29) (17,27) (17,28) (17,31) (18,20) (18,21) (18,32) (18,22) (18,30) (19,26) (19,29) (19,25) (19,27) (19,28) (19,31) (20,32) (20,22) (20,24) (21,22) (21,24) (22,24) (23,33) (23,29) (23,27) (23,28) (23,31) (24,32) (24,30) (25,33) (25,26) (25,29) (25,27) (25,28) (25,31) (26,33) (26,29) (26,27) (26,28) (27,33) (27,29) (27,28) (28,33) (28,29) (28,31) (31,33)\nIs there a path between node 8 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph301-12_5", + "image": "data/connectivity/graph_visual/hard/graph301.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,25) (0,1) (0,26) (0,12) (0,4) (0,31) (0,30) (0,15) (0,3) (0,2) (1,25) (1,26) (1,31) (1,3) (1,2) (2,25) (2,26) (2,12) (2,4) (2,31) (2,15) (2,3) (3,25) (3,26) (3,12) (3,4) (3,31) (3,30) (3,15) (4,12) (4,30) (4,15) (5,27) (5,6) (5,28) (5,24) (5,10) (5,13) (5,19) (6,7) (6,27) (6,17) (6,24) (6,13) (7,27) (7,17) (7,14) (7,28) (7,24) (7,10) (7,13) (7,19) (8,18) (8,22) (8,20) (8,16) (8,23) (9,21) (9,18) (9,11) (9,20) (9,16) (10,17) (10,14) (10,28) (10,24) (10,13) (10,19) (11,21) (11,18) (11,22) (11,20) (11,16) (11,23) (12,25) (12,26) (12,31) (12,30) (12,15) (13,17) (13,14) (13,28) (13,24) (13,19) (14,27) (14,24) (14,19) (15,25) (15,26) (15,31) (15,30) (16,21) (16,18) (16,22) (16,20) (16,23) (16,29) (17,27) (17,24) (17,19) (18,21) (18,20) (18,23) (18,29) (19,27) (19,24) (20,21) (20,22) (20,23) (20,29) (21,23) (22,23) (22,29) (23,29) (25,31) (25,30) (26,31) (26,30) (30,31)\nIs there a path between node 12 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph589-30_23", + "image": "data/connectivity/graph_visual/hard/graph589.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,11) (0,16) (0,3) (0,26) (0,15) (0,30) (0,20) (0,27) (0,17) (0,18) (0,7) (0,1) (0,23) (0,24) (0,12) (1,8) (1,16) (1,25) (1,10) (1,5) (1,26) (1,15) (1,20) (1,27) (1,18) (1,13) (1,23) (1,2) (1,24) (1,31) (1,33) (1,12) (1,4) (1,6) (2,8) (2,11) (2,21) (2,25) (2,3) (2,10) (2,5) (2,26) (2,15) (2,27) (2,28) (2,14) (2,13) (2,31) (2,33) (2,4) (3,8) (3,9) (3,16) (3,25) (3,5) (3,26) (3,22) (3,30) (3,20) (3,17) (3,7) (3,28) (3,23) (3,24) (3,12) (3,4) (4,8) (4,11) (4,21) (4,25) (4,10) (4,15) (4,22) (4,20) (4,27) (4,18) (4,7) (4,28) (4,14) (4,23) (4,24) (4,31) (4,12) (5,8) (5,11) (5,9) (5,16) (5,21) (5,25) (5,10) (5,26) (5,15) (5,22) (5,30) (5,27) (5,18) (5,7) (5,28) (5,14) (5,13) (5,31) (6,8) (6,21) (6,25) (6,10) (6,26) (6,15) (6,22) (6,30) (6,20) (6,27) (6,28) (6,13) (6,31) (6,33) (7,11) (7,9) (7,16) (7,21) (7,25) (7,10) (7,26) (7,15) (7,22) (7,30) (7,20) (7,27) (7,28) (7,14) (7,13) (7,23) (7,24) (7,31) (7,12) (8,11) (8,9) (8,16) (8,21) (8,25) (8,10) (8,26) (8,30) (8,20) (8,17) (8,18) (8,28) (8,14) (8,23) (8,24) (8,31) (8,12) (9,11) (9,16) (9,21) (9,10) (9,26) (9,15) (9,22) (9,30) (9,27) (9,17) (9,18) (9,28) (9,14) (9,13) (9,24) (9,31) (10,26) (10,30) (10,27) (10,17) (10,18) (10,28) (10,14) (10,13) (10,31) (10,33) (10,12) (11,16) (11,21) (11,25) (11,26) (11,15) (11,22) (11,30) (11,20) (11,27) (11,17) (11,18) (11,28) (11,14) (11,13) (11,24) (11,31) (11,33) (11,12) (12,21) (12,25) (12,26) (12,22) (12,20) (12,17) (12,18) (12,28) (12,14) (12,13) (12,23) (12,31) (12,33) (13,25) (13,26) (13,15) (13,30) (13,20) (13,17) (13,18) (13,14) (13,23) (13,24) (13,31) (13,33) (14,16) (14,21) (14,25) (14,26) (14,22) (14,20) (14,17) (14,18) (14,28) (14,23) (14,31) (14,33) (15,16) (15,22) (15,30) (15,18) (15,28) (15,23) (15,24) (15,31) (15,33) (16,21) (16,25) (16,22) (16,20) (16,27) (16,17) (16,18) (16,28) (16,23) (16,33) (17,25) (17,22) (17,30) (17,20) (17,27) (17,18) (17,28) (17,23) (17,24) (17,33) (18,25) (18,22) (18,30) (18,20) (18,27) (18,23) (18,24) (18,33) (19,29) (19,32) (20,26) (20,22) (20,30) (20,27) (20,28) (20,23) (20,24) (20,31) (20,33) (21,25) (21,26) (21,30) (21,27) (21,28) (21,23) (21,33) (22,26) (22,30) (22,23) (22,33) (23,25) (23,26) (23,27) (23,28) (23,24) (23,31) (23,33) (24,25) (24,26) (24,28) (24,31) (25,26) (25,30) (25,27) (25,28) (25,33) (26,30) (26,27) (26,28) (26,31) (27,30) (27,28) (27,33) (28,31) (28,33) (29,32) (30,33) (31,33)\nIs there a path between node 30 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph307-0_21", + "image": "data/connectivity/graph_visual/hard/graph307.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,19) (0,9) (1,14) (1,21) (1,6) (1,12) (1,22) (1,3) (2,11) (2,5) (3,24) (3,30) (3,13) (3,19) (3,9) (3,22) (4,6) (5,28) (5,26) (6,14) (6,24) (6,18) (6,22) (8,24) (8,21) (8,12) (8,20) (8,19) (8,22) (9,21) (9,20) (11,25) (12,24) (12,13) (13,24) (13,21) (13,30) (14,21) (14,30) (14,19) (16,17) (16,31) (17,25) (18,30) (18,27) (19,21) (19,27) (20,27) (21,24) (21,27) (22,30) (23,25) (25,28) (26,29) (26,31) (28,29)\nIs there a path between node 0 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph414-18_15", + "image": "data/connectivity/graph_visual/hard/graph414.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,2) (0,26) (0,21) (0,6) (0,12) (0,28) (0,15) (0,7) (1,21) (1,14) (1,25) (1,8) (1,18) (1,15) (1,27) (1,7) (2,26) (2,21) (2,14) (2,8) (2,24) (2,16) (2,13) (2,19) (2,28) (2,15) (2,27) (2,7) (3,26) (3,13) (3,18) (3,12) (3,9) (3,15) (3,27) (3,7) (3,4) (4,17) (4,8) (4,16) (4,12) (4,20) (5,14) (5,25) (5,13) (5,18) (5,28) (5,27) (5,32) (6,17) (6,25) (6,16) (6,9) (6,32) (6,11) (7,21) (7,24) (7,18) (7,12) (7,28) (7,15) (7,31) (8,25) (8,24) (8,9) (8,15) (8,31) (8,27) (8,32) (9,17) (9,16) (9,19) (9,12) (9,28) (9,15) (9,27) (10,22) (11,13) (11,18) (11,19) (11,12) (11,31) (11,27) (12,21) (12,25) (12,24) (12,16) (12,15) (12,32) (13,17) (13,14) (13,24) (13,18) (13,15) (13,20) (13,32) (14,24) (14,19) (14,28) (14,15) (14,20) (14,32) (15,28) (16,24) (16,18) (17,25) (17,28) (17,27) (18,21) (19,25) (19,28) (20,24) (20,32) (21,26) (21,25) (22,30) (23,30) (23,29) (24,25) (25,26) (25,28) (25,32) (26,31) (27,28) (27,31) (28,31) (28,32)\nIs there a path between node 18 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph449-22_7", + "image": "data/connectivity/graph_visual/hard/graph449.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (0,8) (0,32) (0,4) (0,26) (0,9) (0,5) (1,23) (1,19) (1,26) (1,29) (2,20) (2,6) (3,19) (3,32) (3,22) (3,9) (4,8) (4,10) (4,7) (4,24) (4,9) (5,23) (5,18) (5,31) (5,9) (6,16) (7,13) (7,32) (7,29) (8,28) (8,19) (8,18) (8,32) (8,10) (8,31) (8,22) (9,19) (9,29) (10,23) (10,19) (10,18) (10,13) (10,32) (10,22) (11,25) (11,21) (12,16) (12,30) (13,28) (13,23) (13,18) (13,31) (15,20) (15,16) (15,30) (15,21) (16,17) (17,25) (18,28) (18,23) (19,32) (19,24) (20,30) (22,26) (23,26) (23,31) (24,29) (26,32) (28,32) (29,32) (29,31)\nIs there a path between node 22 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph165-15_7", + "image": "data/connectivity/graph_visual/hard/graph165.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,9) (1,22) (1,11) (1,25) (2,9) (2,8) (2,12) (2,20) (2,26) (2,13) (2,11) (2,6) (2,27) (2,25) (3,7) (5,15) (5,28) (5,22) (5,19) (5,17) (5,24) (5,13) (5,21) (5,14) (5,25) (6,18) (6,8) (6,20) (6,11) (6,14) (6,25) (8,15) (8,28) (8,9) (8,17) (8,20) (8,23) (8,26) (8,11) (9,18) (9,15) (9,28) (9,17) (9,24) (9,11) (9,14) (9,27) (10,18) (10,12) (11,18) (11,22) (11,19) (11,17) (11,23) (11,24) (11,26) (12,28) (12,24) (13,15) (13,19) (13,17) (13,23) (13,26) (13,25) (14,15) (14,28) (15,25) (17,28) (17,24) (17,25) (18,22) (18,25) (19,28) (19,22) (19,26) (19,27) (20,23) (20,25) (21,23) (21,26) (22,24) (22,25) (23,28) (25,28) (27,28)\nIs there a path between node 15 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph176-15_28", + "image": "data/connectivity/graph_visual/hard/graph176.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,19) (0,13) (0,4) (0,28) (0,3) (0,11) (0,9) (0,18) (1,22) (1,6) (1,20) (1,21) (2,8) (2,15) (2,25) (2,19) (2,23) (2,4) (2,28) (2,24) (2,16) (2,11) (2,9) (2,26) (2,18) (3,25) (3,19) (3,23) (3,24) (3,11) (3,12) (3,9) (3,26) (3,18) (4,8) (4,15) (4,25) (4,13) (4,23) (4,28) (4,16) (4,11) (4,12) (4,9) (4,26) (4,18) (5,14) (5,22) (5,10) (5,6) (5,17) (5,21) (5,27) (5,7) (6,14) (6,10) (6,17) (6,27) (7,14) (7,22) (7,10) (8,15) (8,25) (8,19) (8,23) (8,28) (8,16) (8,9) (8,18) (9,19) (9,28) (9,24) (9,11) (9,12) (10,14) (10,22) (10,17) (10,20) (10,21) (10,27) (11,15) (11,23) (11,24) (11,16) (11,26) (11,18) (12,15) (12,25) (12,19) (12,13) (12,23) (12,24) (12,26) (13,15) (13,19) (13,24) (13,16) (13,18) (14,22) (14,17) (14,20) (14,21) (15,25) (15,19) (15,23) (15,16) (15,18) (16,25) (16,19) (16,28) (16,24) (16,26) (16,18) (17,20) (17,21) (17,27) (18,25) (18,19) (18,23) (18,28) (19,25) (19,23) (19,28) (19,24) (19,26) (20,22) (20,21) (21,22) (21,27) (22,27) (23,28) (23,24) (24,25) (24,26) (25,26) (26,28)\nIs there a path between node 15 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph283-19_10", + "image": "data/connectivity/graph_visual/hard/graph283.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,14) (0,27) (0,23) (0,15) (1,2) (1,20) (1,13) (1,30) (1,16) (1,7) (1,22) (1,26) (2,9) (2,20) (2,13) (2,30) (2,16) (2,7) (2,22) (2,26) (3,29) (3,14) (3,27) (3,24) (3,23) (3,15) (4,21) (4,25) (4,28) (4,5) (4,18) (4,17) (4,8) (5,21) (5,25) (5,28) (5,10) (5,18) (5,17) (5,8) (6,29) (6,14) (6,27) (6,24) (6,23) (6,15) (7,9) (7,13) (7,30) (7,16) (7,26) (8,19) (8,21) (8,25) (8,28) (8,11) (8,10) (8,17) (9,20) (9,13) (9,30) (9,22) (9,26) (10,19) (10,21) (10,25) (10,28) (10,18) (10,17) (11,19) (11,21) (11,25) (11,28) (11,18) (12,29) (12,14) (12,27) (12,24) (12,15) (13,30) (13,16) (13,22) (14,29) (14,27) (14,24) (14,15) (15,29) (15,27) (15,24) (15,23) (16,20) (16,30) (16,26) (17,21) (17,25) (17,28) (17,18) (18,19) (18,21) (18,25) (19,21) (19,25) (20,22) (20,26) (21,25) (22,30) (23,27) (24,29) (24,27)\nIs there a path between node 19 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph472-15_22", + "image": "data/connectivity/graph_visual/hard/graph472.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,23) (0,29) (0,31) (0,6) (0,24) (0,27) (0,20) (0,16) (0,10) (0,25) (0,26) (0,8) (0,9) (0,7) (0,18) (0,1) (1,30) (1,23) (1,15) (1,29) (1,6) (1,24) (1,27) (1,20) (1,5) (1,25) (1,8) (1,12) (1,9) (1,7) (1,21) (2,23) (2,15) (2,29) (2,6) (2,24) (2,27) (2,20) (2,16) (2,5) (2,25) (2,8) (2,12) (2,9) (2,11) (2,7) (2,21) (2,18) (3,30) (3,23) (3,15) (3,29) (3,31) (3,6) (3,24) (3,27) (3,20) (3,16) (3,10) (3,25) (3,26) (3,8) (3,12) (3,11) (3,7) (3,21) (4,28) (4,22) (4,32) (4,13) (4,14) (5,30) (5,29) (5,31) (5,6) (5,20) (5,16) (5,10) (5,8) (5,12) (5,9) (5,7) (5,21) (5,18) (6,23) (6,15) (6,29) (6,31) (6,27) (6,20) (6,10) (6,25) (6,26) (6,12) (6,9) (6,7) (6,21) (6,18) (7,30) (7,23) (7,29) (7,27) (7,20) (7,16) (7,26) (7,9) (7,11) (7,21) (7,18) (8,23) (8,15) (8,29) (8,24) (8,16) (8,10) (8,25) (8,12) (8,9) (8,11) (8,21) (8,18) (9,30) (9,23) (9,15) (9,31) (9,24) (9,27) (9,20) (9,16) (9,10) (9,26) (9,12) (9,11) (9,21) (10,30) (10,15) (10,31) (10,24) (10,27) (10,16) (10,25) (10,26) (10,12) (10,11) (10,21) (10,18) (11,30) (11,15) (11,31) (11,24) (11,26) (11,12) (11,21) (12,15) (12,29) (12,31) (12,24) (12,27) (12,25) (12,21) (12,18) (13,28) (13,22) (13,32) (13,14) (14,28) (14,32) (14,19) (15,30) (15,23) (15,31) (15,24) (15,27) (15,20) (15,16) (15,25) (15,26) (15,21) (16,30) (16,29) (16,24) (16,21) (18,30) (18,23) (18,29) (18,24) (18,27) (18,20) (18,25) (19,28) (19,22) (20,23) (20,29) (20,31) (20,24) (20,25) (20,26) (20,21) (21,30) (21,23) (21,31) (21,24) (21,27) (21,25) (22,28) (22,32) (23,30) (23,29) (23,31) (23,24) (23,25) (23,26) (24,29) (24,31) (24,27) (24,25) (24,26) (25,30) (25,29) (25,31) (25,27) (26,30) (26,29) (26,31) (26,27) (27,30) (27,29) (28,32) (29,31) (30,31)\nIs there a path between node 15 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph113-14_1", + "image": "data/connectivity/graph_visual/hard/graph113.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,19) (0,14) (0,23) (0,21) (0,15) (1,26) (1,10) (1,8) (1,20) (1,6) (1,7) (2,26) (2,13) (2,12) (2,24) (2,22) (2,3) (2,20) (2,17) (2,25) (3,26) (3,8) (3,17) (3,11) (3,25) (3,9) (4,18) (4,22) (4,11) (4,9) (5,19) (5,15) (6,18) (6,24) (6,10) (6,25) (6,7) (7,13) (7,16) (8,16) (9,13) (9,12) (9,27) (10,24) (10,25) (11,12) (11,25) (12,26) (12,18) (12,17) (12,16) (13,24) (14,23) (14,15) (16,18) (16,17) (16,25) (17,22) (18,20) (18,25) (19,23) (20,27) (22,27) (25,26)\nIs there a path between node 14 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph595-0_7", + "image": "data/connectivity/graph_visual/hard/graph595.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,29) (0,1) (0,30) (0,19) (0,23) (0,3) (0,32) (0,13) (0,24) (1,29) (1,19) (1,18) (1,28) (1,23) (1,32) (1,13) (1,4) (1,33) (1,8) (1,11) (1,12) (2,22) (2,14) (2,5) (2,26) (2,15) (2,7) (2,25) (2,9) (2,21) (2,27) (2,17) (2,31) (2,16) (3,19) (3,18) (3,28) (3,23) (3,32) (3,24) (3,33) (3,8) (3,12) (4,29) (4,19) (4,18) (4,28) (4,23) (4,32) (4,13) (4,24) (4,8) (4,11) (4,12) (5,22) (5,14) (5,26) (5,15) (5,6) (5,25) (5,9) (5,21) (5,27) (5,17) (5,10) (5,20) (6,22) (6,14) (6,26) (6,15) (6,7) (6,25) (6,27) (6,17) (6,10) (6,20) (6,31) (6,16) (7,22) (7,14) (7,26) (7,27) (7,17) (7,10) (7,20) (7,31) (7,16) (8,29) (8,30) (8,19) (8,18) (8,28) (8,23) (8,32) (8,13) (8,33) (8,11) (9,22) (9,14) (9,26) (9,15) (9,25) (9,21) (9,27) (9,10) (9,20) (9,31) (9,16) (10,22) (10,26) (10,15) (10,21) (10,27) (10,17) (10,31) (11,29) (11,30) (11,18) (11,28) (11,23) (11,32) (11,13) (11,24) (12,29) (12,19) (12,18) (12,23) (12,32) (12,24) (12,33) (13,30) (13,19) (13,18) (13,23) (13,32) (13,33) (14,22) (14,26) (14,15) (14,25) (14,21) (14,27) (14,17) (14,31) (14,16) (15,22) (15,25) (15,21) (15,27) (15,17) (15,20) (16,22) (16,26) (16,25) (16,27) (16,17) (16,20) (16,31) (17,22) (17,25) (17,21) (17,27) (17,20) (18,29) (18,30) (18,19) (18,23) (18,32) (18,33) (19,28) (19,23) (19,24) (19,33) (20,22) (20,21) (20,27) (20,31) (21,26) (21,27) (21,31) (22,25) (22,27) (22,31) (23,29) (23,30) (23,32) (23,24) (23,33) (24,29) (24,32) (25,26) (25,27) (25,31) (26,31) (27,31) (28,29) (28,30) (28,33) (29,30) (29,33) (30,32) (30,33) (32,33)\nIs there a path between node 0 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph347-22_2", + "image": "data/connectivity/graph_visual/hard/graph347.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,6) (0,15) (0,10) (0,16) (0,25) (1,13) (1,6) (1,3) (1,22) (1,31) (1,9) (1,4) (1,27) (1,29) (2,21) (2,28) (3,13) (3,6) (3,10) (3,26) (3,20) (3,16) (4,19) (4,23) (4,18) (4,27) (4,25) (4,14) (5,30) (5,28) (5,11) (6,19) (6,7) (6,31) (6,9) (6,25) (7,18) (7,26) (7,25) (7,14) (8,21) (9,19) (9,12) (9,15) (9,26) (9,27) (9,29) (10,19) (10,31) (10,16) (10,25) (10,24) (11,30) (11,28) (12,19) (12,13) (12,17) (12,22) (12,31) (12,20) (12,16) (12,29) (13,18) (13,26) (13,16) (13,27) (14,22) (14,23) (15,19) (15,18) (15,29) (16,19) (16,22) (16,23) (16,18) (16,27) (16,29) (17,19) (17,20) (17,29) (18,19) (18,22) (18,23) (18,26) (18,27) (18,25) (18,29) (19,23) (19,20) (19,24) (20,27) (20,24) (20,29) (21,30) (22,26) (22,27) (23,31) (23,26) (23,27) (23,29) (24,26) (24,27) (24,25) (25,31) (25,27)\nIs there a path between node 22 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph52-22_0", + "image": "data/connectivity/graph_visual/hard/graph52.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,26) (0,19) (0,14) (0,23) (0,10) (1,21) (1,6) (1,19) (2,16) (3,13) (5,25) (5,15) (6,14) (7,13) (8,24) (8,17) (8,13) (8,15) (9,12) (9,20) (9,19) (10,26) (10,19) (12,20) (13,25) (13,15) (14,21) (14,26) (15,24) (18,22) (18,25) (19,26) (22,24)\nIs there a path between node 22 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph107-18_6", + "image": "data/connectivity/graph_visual/hard/graph107.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,27) (0,4) (0,11) (0,9) (0,25) (1,12) (1,16) (2,3) (2,27) (2,11) (2,12) (2,22) (2,25) (2,15) (3,25) (3,15) (4,18) (4,11) (4,26) (4,22) (4,9) (4,24) (4,13) (5,7) (5,14) (5,19) (5,17) (6,14) (7,17) (9,20) (9,26) (9,12) (9,25) (9,15) (10,20) (10,27) (10,11) (10,21) (10,26) (10,16) (11,27) (11,25) (12,27) (12,21) (12,26) (12,24) (13,24) (14,17) (15,20) (15,27) (15,18) (15,26) (15,22) (15,25) (16,20) (16,27) (18,26) (18,25) (20,25) (25,26)\nIs there a path between node 18 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph95-22_17", + "image": "data/connectivity/graph_visual/hard/graph95.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,21) (1,10) (1,6) (1,19) (1,13) (1,23) (1,5) (2,19) (2,13) (2,23) (2,20) (2,18) (3,12) (3,27) (3,13) (3,23) (3,11) (3,26) (3,16) (3,5) (4,27) (4,20) (4,18) (5,24) (5,13) (5,16) (6,23) (6,11) (6,18) (8,9) (8,10) (8,17) (8,27) (8,23) (9,24) (9,17) (9,14) (9,26) (9,18) (10,21) (10,12) (10,19) (10,26) (10,20) (10,18) (11,25) (11,17) (11,13) (11,23) (11,26) (11,20) (12,24) (12,20) (12,18) (14,27) (14,19) (14,23) (14,20) (14,18) (15,22) (16,27) (16,19) (16,23) (16,26) (16,20) (17,24) (17,19) (17,26) (17,20) (18,21) (18,19) (18,26) (20,25) (20,21) (20,27) (20,23) (20,26) (21,24) (23,26)\nIs there a path between node 22 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph182-16_8", + "image": "data/connectivity/graph_visual/hard/graph182.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,20) (0,27) (0,23) (0,28) (0,10) (0,16) (0,22) (0,2) (0,6) (0,14) (0,25) (0,26) (0,4) (0,21) (1,20) (1,27) (1,23) (1,28) (1,16) (1,22) (1,17) (1,2) (1,12) (1,14) (1,25) (1,26) (1,15) (1,4) (1,21) (1,9) (1,5) (2,20) (2,27) (2,23) (2,10) (2,7) (2,16) (2,22) (2,17) (2,6) (2,14) (2,26) (2,15) (2,4) (2,21) (2,9) (2,5) (3,8) (3,19) (3,24) (4,20) (4,27) (4,23) (4,10) (4,16) (4,22) (4,17) (4,12) (4,6) (4,14) (4,25) (4,26) (4,15) (4,21) (4,5) (5,20) (5,27) (5,23) (5,28) (5,10) (5,16) (5,22) (5,17) (5,12) (5,6) (5,26) (5,15) (5,21) (6,20) (6,27) (6,23) (6,28) (6,10) (6,7) (6,16) (6,22) (6,17) (6,12) (6,14) (6,25) (6,26) (6,15) (6,9) (7,20) (7,23) (7,28) (7,10) (7,16) (7,22) (7,17) (7,15) (7,21) (7,9) (8,19) (8,24) (8,11) (8,13) (8,18) (9,28) (9,10) (9,22) (9,17) (9,26) (9,15) (10,20) (10,27) (10,23) (10,28) (10,16) (10,22) (10,17) (10,12) (10,14) (10,25) (10,26) (10,15) (10,21) (11,19) (11,18) (12,20) (12,27) (12,23) (12,28) (12,17) (12,26) (12,15) (12,21) (13,19) (13,24) (13,18) (14,20) (14,23) (14,16) (14,22) (14,25) (14,26) (14,15) (14,21) (15,20) (15,27) (15,22) (15,17) (15,25) (15,26) (16,20) (16,27) (16,17) (16,25) (16,26) (17,27) (17,23) (17,28) (17,22) (17,25) (17,26) (17,21) (18,24) (19,24) (20,28) (20,22) (20,25) (20,26) (21,23) (21,25) (21,26) (22,28) (22,26) (23,26) (25,27) (25,28) (25,26) (26,27) (26,28) (27,28)\nIs there a path between node 16 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph609-25_31", + "image": "data/connectivity/graph_visual/hard/graph609.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,29) (0,26) (0,2) (0,25) (0,17) (1,26) (1,30) (2,29) (2,7) (2,25) (2,30) (2,28) (3,21) (3,34) (3,11) (3,4) (4,21) (4,19) (4,34) (4,31) (5,20) (6,7) (6,26) (6,32) (6,30) (7,23) (8,15) (9,10) (9,14) (10,13) (11,21) (11,22) (11,15) (11,27) (12,32) (12,17) (12,28) (13,14) (14,16) (14,20) (15,19) (15,27) (16,24) (17,29) (17,26) (17,32) (18,32) (18,23) (18,28) (19,21) (19,34) (19,27) (19,31) (21,34) (21,31) (22,34) (23,29) (23,26) (25,32) (26,29) (26,32) (30,32) (31,34)\nIs there a path between node 25 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph61-7_4", + "image": "data/connectivity/graph_visual/hard/graph61.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,15) (1,10) (1,16) (1,26) (1,3) (1,12) (2,7) (3,5) (3,10) (3,21) (3,9) (3,24) (3,20) (3,25) (3,12) (3,14) (4,23) (4,22) (4,18) (5,17) (5,16) (5,14) (6,8) (6,21) (6,26) (6,12) (8,11) (8,10) (8,13) (8,16) (8,20) (8,12) (9,13) (9,19) (9,25) (9,14) (10,15) (10,11) (10,16) (10,25) (11,24) (11,20) (11,25) (12,17) (12,16) (12,19) (13,17) (13,24) (13,26) (14,17) (14,21) (15,16) (15,26) (16,19) (17,21) (17,25) (18,22) (19,21) (20,24) (20,26) (21,24) (24,26) (25,26)\nIs there a path between node 7 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph99-17_3", + "image": "data/connectivity/graph_visual/hard/graph99.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,1) (0,13) (0,22) (0,23) (0,9) (0,18) (0,7) (0,2) (0,15) (0,10) (0,16) (0,21) (0,4) (0,25) (0,27) (1,8) (1,13) (1,14) (1,22) (1,6) (1,24) (1,9) (1,18) (1,7) (1,2) (1,15) (1,26) (1,10) (1,12) (1,16) (1,11) (1,4) (1,5) (2,13) (2,14) (2,23) (2,6) (2,24) (2,9) (2,12) (2,16) (2,21) (2,11) (2,4) (2,25) (3,19) (4,8) (4,13) (4,14) (4,22) (4,6) (4,24) (4,18) (4,7) (4,15) (4,20) (4,16) (4,21) (4,11) (4,17) (4,27) (5,8) (5,13) (5,14) (5,23) (5,6) (5,9) (5,18) (5,7) (5,15) (5,26) (5,20) (5,12) (5,16) (5,21) (6,8) (6,13) (6,14) (6,22) (6,24) (6,9) (6,18) (6,7) (6,15) (6,26) (6,20) (6,10) (6,25) (6,17) (6,27) (7,8) (7,13) (7,14) (7,22) (7,24) (7,9) (7,15) (7,26) (7,10) (7,11) (7,25) (7,17) (8,13) (8,14) (8,22) (8,23) (8,24) (8,9) (8,26) (8,10) (8,12) (8,11) (8,25) (8,17) (9,14) (9,22) (9,23) (9,24) (9,18) (9,15) (9,26) (9,16) (9,21) (9,11) (9,25) (10,23) (10,24) (10,18) (10,15) (10,12) (10,21) (10,25) (10,17) (10,27) (11,14) (11,22) (11,15) (11,26) (11,20) (11,12) (11,21) (11,25) (11,17) (11,27) (12,13) (12,14) (12,22) (12,23) (12,24) (12,18) (12,15) (12,26) (12,16) (12,21) (12,17) (13,14) (13,22) (13,24) (13,26) (13,20) (13,16) (13,25) (13,17) (13,27) (14,22) (14,18) (14,15) (14,26) (14,20) (14,16) (14,25) (15,23) (15,24) (15,18) (15,26) (15,20) (15,16) (15,21) (15,25) (15,17) (15,27) (16,22) (16,26) (16,20) (16,21) (16,25) (16,17) (16,27) (17,22) (17,23) (17,25) (18,22) (18,23) (18,24) (18,26) (18,21) (18,25) (20,26) (20,21) (21,23) (21,26) (21,25) (21,27) (22,23) (22,26) (22,27) (23,24) (23,27) (24,26) (24,27) (25,27) (26,27)\nIs there a path between node 17 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph99-11_3", + "image": "data/connectivity/graph_visual/hard/graph99.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,1) (0,13) (0,22) (0,23) (0,9) (0,18) (0,7) (0,2) (0,15) (0,10) (0,16) (0,21) (0,4) (0,25) (0,27) (1,8) (1,13) (1,14) (1,22) (1,6) (1,24) (1,9) (1,18) (1,7) (1,2) (1,15) (1,26) (1,10) (1,12) (1,16) (1,11) (1,4) (1,5) (2,13) (2,14) (2,23) (2,6) (2,24) (2,9) (2,12) (2,16) (2,21) (2,11) (2,4) (2,25) (3,19) (4,8) (4,13) (4,14) (4,22) (4,6) (4,24) (4,18) (4,7) (4,15) (4,20) (4,16) (4,21) (4,11) (4,17) (4,27) (5,8) (5,13) (5,14) (5,23) (5,6) (5,9) (5,18) (5,7) (5,15) (5,26) (5,20) (5,12) (5,16) (5,21) (6,8) (6,13) (6,14) (6,22) (6,24) (6,9) (6,18) (6,7) (6,15) (6,26) (6,20) (6,10) (6,25) (6,17) (6,27) (7,8) (7,13) (7,14) (7,22) (7,24) (7,9) (7,15) (7,26) (7,10) (7,11) (7,25) (7,17) (8,13) (8,14) (8,22) (8,23) (8,24) (8,9) (8,26) (8,10) (8,12) (8,11) (8,25) (8,17) (9,14) (9,22) (9,23) (9,24) (9,18) (9,15) (9,26) (9,16) (9,21) (9,11) (9,25) (10,23) (10,24) (10,18) (10,15) (10,12) (10,21) (10,25) (10,17) (10,27) (11,14) (11,22) (11,15) (11,26) (11,20) (11,12) (11,21) (11,25) (11,17) (11,27) (12,13) (12,14) (12,22) (12,23) (12,24) (12,18) (12,15) (12,26) (12,16) (12,21) (12,17) (13,14) (13,22) (13,24) (13,26) (13,20) (13,16) (13,25) (13,17) (13,27) (14,22) (14,18) (14,15) (14,26) (14,20) (14,16) (14,25) (15,23) (15,24) (15,18) (15,26) (15,20) (15,16) (15,21) (15,25) (15,17) (15,27) (16,22) (16,26) (16,20) (16,21) (16,25) (16,17) (16,27) (17,22) (17,23) (17,25) (18,22) (18,23) (18,24) (18,26) (18,21) (18,25) (20,26) (20,21) (21,23) (21,26) (21,25) (21,27) (22,23) (22,26) (22,27) (23,24) (23,27) (24,26) (24,27) (25,27) (26,27)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph1-24_11", + "image": "data/connectivity/graph_visual/hard/graph1.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,4) (0,8) (0,2) (0,20) (0,16) (0,14) (0,15) (0,7) (1,18) (1,24) (1,22) (1,5) (1,19) (1,11) (1,17) (2,6) (2,4) (2,23) (2,8) (2,20) (2,16) (2,21) (2,14) (2,15) (2,10) (3,6) (3,4) (3,23) (3,8) (3,16) (3,14) (3,25) (3,15) (3,7) (4,6) (4,23) (4,8) (4,20) (4,16) (4,21) (4,14) (4,15) (4,10) (4,7) (5,18) (5,24) (5,22) (5,13) (5,9) (5,11) (5,12) (6,23) (6,8) (6,20) (6,16) (6,14) (6,25) (6,15) (7,23) (7,20) (7,16) (7,21) (7,14) (7,25) (7,15) (7,10) (8,20) (8,16) (8,14) (8,25) (8,15) (9,18) (9,24) (9,22) (9,19) (9,11) (9,17) (9,12) (10,23) (10,20) (10,16) (10,21) (10,14) (10,25) (11,22) (11,19) (11,17) (11,12) (12,18) (12,13) (12,19) (13,18) (13,24) (13,22) (13,17) (14,23) (14,20) (14,16) (14,25) (15,20) (15,16) (15,21) (15,25) (16,23) (16,20) (16,25) (17,18) (17,22) (17,19) (18,24) (18,22) (18,19) (19,24) (19,22) (20,21) (20,25) (21,23) (21,25) (22,24) (23,25)\nIs there a path between node 24 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph489-26_24", + "image": "data/connectivity/graph_visual/hard/graph489.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (0,6) (0,16) (0,18) (0,29) (0,24) (0,21) (0,28) (0,11) (0,14) (0,9) (0,8) (0,25) (1,23) (1,26) (1,19) (1,17) (1,12) (1,22) (1,13) (1,7) (1,15) (2,23) (2,26) (2,19) (2,12) (2,7) (2,15) (2,30) (2,3) (3,23) (3,26) (3,19) (3,17) (3,12) (3,22) (3,13) (3,7) (3,15) (3,30) (4,5) (4,27) (4,6) (4,16) (4,18) (4,29) (4,24) (4,10) (4,20) (4,21) (4,28) (4,31) (4,32) (4,25) (5,27) (5,16) (5,18) (5,29) (5,10) (5,11) (5,14) (5,31) (5,9) (5,8) (5,32) (5,25) (6,27) (6,16) (6,18) (6,24) (6,10) (6,20) (6,21) (6,28) (6,11) (6,31) (6,9) (6,8) (7,23) (7,26) (7,19) (7,12) (7,15) (7,30) (8,27) (8,18) (8,29) (8,10) (8,20) (8,21) (8,28) (8,11) (8,9) (9,16) (9,18) (9,29) (9,24) (9,10) (9,21) (9,28) (9,11) (9,14) (9,32) (9,25) (10,16) (10,18) (10,29) (10,24) (10,11) (10,32) (10,25) (11,27) (11,16) (11,18) (11,29) (11,24) (11,20) (11,21) (11,14) (11,31) (11,25) (12,23) (12,26) (12,19) (12,17) (12,22) (12,13) (12,15) (12,30) (13,23) (13,26) (13,19) (13,17) (13,22) (13,15) (13,30) (14,27) (14,29) (14,24) (14,21) (14,28) (14,31) (14,25) (15,23) (15,19) (15,17) (15,22) (16,27) (16,18) (16,29) (16,24) (16,20) (16,21) (16,28) (16,31) (16,32) (16,25) (17,26) (17,19) (17,30) (18,27) (18,29) (18,28) (18,31) (18,25) (19,30) (20,27) (20,24) (20,21) (20,28) (20,31) (20,32) (20,25) (21,27) (21,29) (21,24) (21,28) (21,31) (21,32) (21,25) (22,30) (23,26) (23,30) (24,27) (24,29) (24,28) (24,31) (24,32) (24,25) (25,27) (25,32) (26,30) (27,29) (27,31) (27,32) (28,29) (28,32) (29,31) (29,32)\nIs there a path between node 26 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph480-5_25", + "image": "data/connectivity/graph_visual/hard/graph480.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,28) (0,10) (0,15) (0,27) (0,11) (0,31) (0,4) (0,30) (0,5) (0,26) (0,24) (0,17) (0,21) (0,25) (0,9) (0,19) (0,18) (0,7) (0,14) (0,22) (0,6) (1,32) (1,12) (1,29) (2,28) (2,10) (2,15) (2,16) (2,31) (2,4) (2,5) (2,26) (2,24) (2,17) (2,21) (2,25) (2,9) (2,19) (2,18) (2,7) (2,14) (2,23) (2,3) (2,6) (3,28) (3,27) (3,11) (3,16) (3,31) (3,30) (3,8) (3,5) (3,26) (3,24) (3,17) (3,21) (3,25) (3,19) (3,18) (3,14) (3,23) (3,20) (3,22) (3,6) (4,28) (4,10) (4,15) (4,11) (4,16) (4,31) (4,30) (4,8) (4,5) (4,26) (4,24) (4,17) (4,21) (4,9) (4,18) (4,7) (4,14) (4,23) (4,20) (4,22) (4,6) (5,28) (5,10) (5,15) (5,27) (5,11) (5,16) (5,30) (5,8) (5,26) (5,17) (5,21) (5,25) (5,19) (5,18) (5,7) (5,23) (5,20) (5,6) (6,28) (6,10) (6,27) (6,16) (6,8) (6,26) (6,24) (6,17) (6,21) (6,25) (6,18) (6,7) (6,14) (7,28) (7,15) (7,27) (7,11) (7,16) (7,31) (7,30) (7,8) (7,26) (7,24) (7,17) (7,21) (7,25) (7,19) (7,14) (7,23) (7,22) (8,28) (8,11) (8,31) (8,26) (8,24) (8,17) (8,21) (8,9) (8,19) (8,18) (8,20) (8,22) (9,28) (9,10) (9,15) (9,11) (9,16) (9,31) (9,30) (9,26) (9,24) (9,17) (9,19) (9,14) (9,20) (9,22) (10,28) (10,15) (10,11) (10,31) (10,30) (10,26) (10,24) (10,17) (10,21) (10,19) (10,18) (10,14) (10,23) (10,20) (10,22) (11,27) (11,16) (11,31) (11,30) (11,26) (11,24) (11,21) (11,25) (11,14) (11,20) (11,22) (12,13) (13,32) (13,29) (14,28) (14,27) (14,16) (14,31) (14,30) (14,26) (14,24) (14,17) (14,21) (14,19) (14,23) (14,20) (14,22) (15,27) (15,31) (15,24) (15,17) (15,21) (15,25) (15,19) (15,23) (15,20) (15,22) (16,28) (16,30) (16,26) (16,24) (16,17) (16,25) (16,23) (16,20) (16,22) (17,31) (17,30) (17,26) (17,24) (17,25) (17,18) (18,28) (18,27) (18,31) (18,30) (18,26) (18,24) (18,21) (18,25) (18,19) (18,23) (18,22) (19,27) (19,31) (19,30) (19,24) (19,21) (19,25) (19,20) (20,27) (20,31) (20,30) (20,26) (20,24) (20,25) (20,23) (20,22) (21,28) (21,27) (21,31) (21,30) (21,26) (21,25) (21,23) (21,22) (22,27) (22,31) (22,26) (22,25) (23,28) (23,27) (23,31) (23,26) (23,24) (24,31) (24,26) (24,25) (25,28) (25,27) (25,31) (25,30) (25,26) (26,28) (26,27) (26,31) (26,30) (27,28) (27,31) (27,30) (28,30) (29,32)\nIs there a path between node 5 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph361-19_24", + "image": "data/connectivity/graph_visual/hard/graph361.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,14) (0,30) (0,15) (0,20) (0,12) (1,28) (1,23) (1,19) (1,27) (2,31) (2,8) (2,14) (2,7) (2,6) (2,12) (3,25) (3,18) (3,13) (3,23) (4,31) (4,24) (4,22) (4,30) (4,12) (5,28) (5,23) (6,31) (6,22) (6,8) (6,10) (6,7) (6,15) (6,20) (6,21) (6,12) (7,22) (7,15) (7,20) (8,10) (8,14) (9,18) (9,13) (9,28) (11,30) (11,15) (11,16) (11,21) (12,22) (12,16) (13,18) (13,28) (14,22) (14,17) (14,30) (15,22) (16,17) (16,21) (17,30) (18,26) (18,29) (18,19) (19,28) (20,21) (21,30) (24,31) (25,26) (25,28) (28,29)\nIs there a path between node 19 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph575-3_26", + "image": "data/connectivity/graph_visual/hard/graph575.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,30) (0,10) (0,23) (0,11) (0,31) (1,28) (1,26) (1,5) (1,20) (1,18) (1,29) (1,8) (1,9) (1,13) (2,3) (2,28) (2,26) (2,15) (2,20) (2,21) (2,12) (2,18) (2,29) (2,8) (2,9) (2,13) (2,16) (3,22) (3,28) (3,15) (3,20) (3,21) (3,12) (3,18) (3,29) (3,8) (3,9) (3,13) (3,16) (4,24) (4,30) (4,10) (4,23) (4,7) (4,17) (4,6) (5,28) (5,26) (5,27) (5,21) (5,12) (5,18) (5,29) (5,8) (5,9) (5,13) (5,16) (6,30) (6,10) (6,23) (6,11) (6,31) (6,7) (6,17) (7,30) (7,10) (7,23) (7,11) (7,31) (8,28) (8,32) (8,26) (8,27) (8,15) (8,18) (8,29) (8,9) (8,16) (9,27) (9,15) (9,21) (9,29) (9,16) (10,24) (10,30) (10,23) (10,11) (10,31) (10,17) (11,30) (11,31) (12,22) (12,32) (12,27) (12,15) (12,20) (12,21) (12,13) (12,16) (13,32) (13,26) (13,15) (13,20) (13,21) (13,29) (13,16) (14,33) (14,19) (15,28) (15,26) (15,27) (15,21) (15,16) (16,22) (16,28) (16,32) (16,26) (16,27) (16,18) (16,29) (17,23) (17,31) (18,22) (18,28) (18,32) (18,26) (18,27) (18,20) (18,21) (19,33) (20,22) (20,28) (20,26) (20,21) (20,29) (21,22) (21,32) (21,26) (21,27) (22,26) (22,27) (23,30) (23,31) (26,27) (26,29) (27,28) (27,32) (27,29)\nIs there a path between node 3 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph619-21_26", + "image": "data/connectivity/graph_visual/hard/graph619.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,4) (0,1) (0,27) (0,25) (0,8) (0,34) (0,6) (0,14) (0,28) (0,5) (0,29) (0,9) (0,2) (0,17) (0,21) (0,12) (0,10) (0,7) (1,4) (1,15) (1,33) (1,27) (1,34) (1,20) (1,6) (1,14) (1,28) (1,13) (1,5) (1,29) (1,2) (1,17) (1,12) (1,10) (1,7) (2,15) (2,33) (2,27) (2,25) (2,8) (2,20) (2,32) (2,6) (2,14) (2,13) (2,19) (2,29) (2,9) (2,17) (2,12) (3,22) (3,26) (3,16) (3,31) (3,18) (3,24) (3,30) (4,15) (4,33) (4,27) (4,25) (4,8) (4,20) (4,32) (4,6) (4,14) (4,28) (4,19) (4,5) (4,17) (4,21) (5,15) (5,33) (5,25) (5,8) (5,34) (5,32) (5,6) (5,14) (5,13) (5,19) (5,29) (5,9) (5,17) (5,21) (5,12) (5,10) (6,33) (6,27) (6,25) (6,8) (6,20) (6,13) (6,19) (6,29) (6,9) (6,17) (6,12) (6,10) (6,7) (7,15) (7,33) (7,27) (7,25) (7,34) (7,20) (7,14) (7,28) (7,29) (7,9) (7,21) (7,10) (8,27) (8,25) (8,34) (8,20) (8,14) (8,28) (8,13) (8,9) (8,17) (8,12) (8,10) (9,15) (9,33) (9,27) (9,25) (9,34) (9,20) (9,32) (9,28) (9,13) (9,19) (9,29) (9,17) (9,21) (9,12) (9,10) (10,15) (10,33) (10,27) (10,34) (10,20) (10,32) (10,28) (10,13) (10,19) (10,29) (10,17) (10,21) (10,12) (11,22) (11,23) (11,31) (11,30) (12,15) (12,33) (12,27) (12,34) (12,20) (12,28) (12,13) (12,19) (12,29) (12,17) (13,15) (13,27) (13,14) (13,28) (13,19) (13,29) (13,17) (13,21) (14,34) (14,20) (14,32) (14,19) (14,29) (14,17) (14,21) (15,27) (15,25) (15,20) (15,32) (15,19) (15,29) (15,17) (15,21) (16,22) (16,26) (16,23) (16,31) (16,24) (16,30) (17,33) (17,25) (17,34) (17,32) (17,28) (17,19) (17,21) (18,22) (18,26) (18,31) (18,24) (18,30) (19,27) (19,25) (19,34) (19,32) (19,28) (20,33) (20,27) (20,34) (20,32) (20,29) (20,21) (21,33) (21,27) (21,25) (21,34) (21,32) (22,26) (22,31) (22,24) (22,30) (23,26) (23,31) (23,24) (23,30) (24,26) (24,31) (25,27) (25,34) (25,32) (25,29) (26,31) (27,34) (27,32) (27,28) (27,29) (28,33) (28,34) (29,33) (32,34)\nIs there a path between node 21 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph541-22_27", + "image": "data/connectivity/graph_visual/hard/graph541.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,13) (0,30) (0,32) (0,15) (0,8) (0,17) (0,21) (0,19) (0,14) (0,26) (0,3) (0,4) (0,18) (0,11) (0,10) (0,7) (0,28) (0,31) (1,13) (1,30) (1,32) (1,23) (1,15) (1,8) (1,17) (1,21) (1,19) (1,33) (1,26) (1,9) (1,4) (1,11) (1,7) (2,20) (2,13) (2,30) (2,32) (2,23) (2,17) (2,22) (2,19) (2,33) (2,14) (2,26) (2,3) (2,18) (2,11) (2,7) (2,28) (2,31) (3,20) (3,13) (3,30) (3,32) (3,23) (3,15) (3,8) (3,17) (3,21) (3,14) (3,26) (3,9) (3,18) (3,11) (3,28) (3,31) (4,20) (4,13) (4,30) (4,32) (4,23) (4,15) (4,33) (4,26) (4,18) (4,11) (4,10) (4,7) (4,28) (4,31) (5,12) (5,27) (6,29) (6,24) (6,12) (6,27) (7,20) (7,13) (7,30) (7,23) (7,15) (7,8) (7,17) (7,22) (7,19) (7,14) (7,26) (7,18) (7,10) (7,28) (7,31) (8,20) (8,30) (8,15) (8,17) (8,22) (8,21) (8,19) (8,33) (8,14) (8,26) (8,9) (8,18) (8,10) (9,13) (9,30) (9,32) (9,23) (9,22) (9,21) (9,33) (9,14) (9,26) (9,18) (9,11) (9,10) (9,28) (9,31) (10,13) (10,30) (10,32) (10,15) (10,22) (10,21) (10,19) (10,33) (10,26) (10,18) (10,11) (10,28) (11,20) (11,13) (11,30) (11,32) (11,23) (11,15) (11,17) (11,22) (11,21) (11,19) (11,26) (11,28) (11,31) (12,29) (12,24) (12,16) (12,27) (13,20) (13,32) (13,15) (13,17) (13,22) (13,21) (13,33) (13,14) (13,28) (13,31) (14,20) (14,32) (14,15) (14,17) (14,22) (14,18) (14,28) (14,31) (15,20) (15,30) (15,32) (15,17) (15,22) (15,21) (15,19) (15,33) (15,26) (15,18) (15,31) (16,29) (16,27) (17,20) (17,30) (17,22) (17,21) (17,19) (17,33) (17,26) (17,18) (17,28) (17,31) (18,20) (18,30) (18,23) (18,22) (18,21) (18,28) (18,31) (19,20) (19,32) (19,21) (19,26) (19,28) (20,30) (20,32) (20,23) (20,22) (20,21) (20,28) (21,30) (21,32) (21,23) (21,22) (21,33) (21,26) (21,31) (22,32) (22,28) (22,31) (23,30) (23,32) (23,33) (23,26) (23,31) (24,29) (24,27) (26,30) (26,32) (26,33) (26,28) (27,29) (28,31) (30,32) (30,33) (30,31) (31,32) (32,33)\nIs there a path between node 22 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph613-26_25", + "image": "data/connectivity/graph_visual/hard/graph613.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,13) (0,19) (0,6) (0,21) (0,10) (0,31) (0,16) (0,7) (0,20) (0,8) (0,17) (0,12) (0,3) (0,11) (0,23) (0,2) (0,22) (0,1) (0,18) (1,33) (1,32) (1,13) (1,19) (1,29) (1,26) (1,27) (1,6) (1,21) (1,10) (1,31) (1,16) (1,28) (1,7) (1,20) (1,8) (1,17) (1,12) (1,3) (1,2) (1,14) (1,22) (1,18) (1,5) (2,33) (2,13) (2,19) (2,29) (2,26) (2,27) (2,6) (2,10) (2,31) (2,16) (2,28) (2,7) (2,20) (2,24) (2,8) (2,17) (2,12) (2,22) (2,18) (3,32) (3,29) (3,27) (3,6) (3,21) (3,31) (3,16) (3,28) (3,7) (3,20) (3,8) (3,12) (3,23) (3,14) (3,22) (3,18) (3,5) (4,25) (4,34) (5,33) (5,32) (5,13) (5,19) (5,29) (5,26) (5,27) (5,6) (5,21) (5,10) (5,31) (5,16) (5,28) (5,20) (5,8) (5,12) (5,11) (5,23) (5,14) (5,22) (5,18) (6,32) (6,13) (6,19) (6,26) (6,27) (6,21) (6,10) (6,16) (6,28) (6,7) (6,20) (6,17) (6,12) (6,11) (6,23) (6,14) (6,22) (6,18) (7,32) (7,13) (7,29) (7,27) (7,21) (7,10) (7,16) (7,28) (7,20) (7,24) (7,17) (7,12) (7,11) (7,23) (7,14) (7,22) (7,18) (8,33) (8,32) (8,13) (8,19) (8,29) (8,26) (8,21) (8,10) (8,31) (8,16) (8,28) (8,20) (8,24) (8,17) (8,12) (8,11) (8,23) (8,14) (8,22) (8,18) (9,25) (9,34) (9,15) (9,30) (10,33) (10,32) (10,13) (10,19) (10,29) (10,26) (10,27) (10,16) (10,28) (10,12) (10,11) (10,14) (10,22) (11,33) (11,32) (11,13) (11,19) (11,29) (11,21) (11,28) (11,20) (11,24) (11,17) (11,12) (11,23) (11,14) (11,22) (11,18) (12,33) (12,32) (12,13) (12,19) (12,29) (12,26) (12,31) (12,16) (12,28) (12,20) (12,23) (12,18) (13,33) (13,32) (13,19) (13,29) (13,26) (13,27) (13,21) (13,31) (13,16) (13,28) (13,20) (13,17) (13,23) (13,14) (13,18) (14,33) (14,32) (14,19) (14,29) (14,26) (14,27) (14,21) (14,31) (14,16) (14,28) (14,20) (14,17) (14,22) (15,25) (15,30) (16,33) (16,32) (16,19) (16,29) (16,26) (16,27) (16,21) (16,31) (16,28) (16,20) (16,24) (16,17) (16,23) (16,22) (17,33) (17,32) (17,19) (17,29) (17,21) (17,28) (17,20) (17,24) (17,23) (17,22) (17,18) (18,32) (18,19) (18,29) (18,26) (18,27) (18,21) (18,31) (18,28) (18,24) (18,23) (18,22) (19,29) (19,27) (19,21) (19,31) (19,28) (19,20) (19,23) (20,33) (20,29) (20,26) (20,31) (20,28) (20,22) (21,33) (21,32) (21,29) (21,31) (21,24) (21,23) (22,29) (22,31) (22,24) (23,29) (23,26) (23,27) (23,31) (23,28) (23,24) (24,32) (24,26) (24,27) (24,31) (25,34) (26,32) (26,29) (26,27) (26,31) (26,28) (27,33) (27,29) (27,31) (28,33) (28,31) (29,33) (29,32) (30,34) (31,33) (31,32) (32,33)\nIs there a path between node 26 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph216-4_7", + "image": "data/connectivity/graph_visual/hard/graph216.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,8) (1,27) (1,21) (1,29) (1,26) (1,19) (1,10) (1,5) (2,4) (2,28) (2,13) (2,25) (2,17) (2,5) (3,6) (3,28) (3,15) (3,13) (3,18) (3,22) (3,7) (3,19) (3,17) (3,5) (3,16) (4,12) (4,6) (4,15) (4,21) (4,10) (4,5) (4,14) (4,16) (5,28) (5,27) (5,23) (5,22) (5,25) (5,10) (6,9) (6,15) (6,20) (6,18) (6,25) (6,17) (6,14) (7,15) (7,13) (7,18) (7,23) (7,25) (7,26) (7,19) (9,15) (9,27) (9,18) (9,23) (9,22) (9,26) (9,10) (10,15) (10,20) (10,27) (10,21) (10,22) (10,25) (10,19) (10,17) (10,14) (12,28) (12,18) (12,22) (12,14) (13,20) (13,27) (13,18) (13,23) (13,19) (13,17) (13,16) (14,18) (14,21) (14,19) (15,27) (15,19) (15,17) (16,27) (16,23) (16,25) (17,28) (17,18) (17,23) (17,21) (17,22) (17,29) (18,27) (18,26) (19,28) (20,28) (20,22) (20,29) (21,29) (21,25) (23,28) (23,27) (23,26) (25,28) (25,29) (26,27) (27,29) (28,29)\nIs there a path between node 4 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph228-23_18", + "image": "data/connectivity/graph_visual/hard/graph228.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,18) (0,15) (0,8) (0,20) (1,22) (1,4) (1,25) (1,11) (1,7) (1,24) (1,28) (1,21) (2,23) (2,27) (2,18) (2,16) (2,3) (2,8) (2,5) (2,20) (3,27) (3,16) (3,12) (3,15) (3,8) (3,5) (4,29) (4,22) (4,6) (4,10) (4,17) (4,14) (4,25) (4,11) (4,7) (4,24) (4,28) (4,21) (4,26) (5,23) (5,27) (5,18) (5,16) (5,12) (5,15) (5,8) (5,20) (6,29) (6,22) (6,19) (6,10) (6,25) (6,9) (6,7) (6,13) (6,24) (6,28) (6,26) (7,10) (7,17) (7,14) (7,25) (7,9) (7,13) (7,24) (7,28) (7,21) (7,26) (8,23) (8,18) (8,12) (8,20) (9,29) (9,22) (9,19) (9,10) (9,25) (9,11) (9,13) (9,24) (9,28) (9,26) (10,29) (10,22) (10,19) (10,14) (10,25) (10,11) (10,13) (10,24) (10,26) (11,22) (11,19) (11,17) (11,25) (11,13) (11,24) (11,21) (11,26) (12,23) (12,27) (12,18) (12,16) (12,15) (13,29) (13,19) (13,17) (13,14) (13,25) (13,28) (13,21) (13,26) (14,19) (14,17) (14,25) (14,28) (14,21) (14,26) (15,23) (15,27) (15,18) (15,16) (15,20) (16,23) (16,18) (16,20) (17,22) (17,19) (17,25) (17,28) (17,26) (18,23) (18,27) (19,22) (19,25) (19,28) (19,26) (21,29) (21,25) (21,24) (21,28) (21,26) (22,29) (22,25) (22,28) (22,26) (23,27) (24,29) (24,25) (24,28) (24,26) (25,29) (25,28) (25,26) (26,29) (26,28)\nIs there a path between node 23 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph386-17_26", + "image": "data/connectivity/graph_visual/hard/graph386.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,16) (0,20) (0,21) (0,24) (0,6) (0,31) (0,26) (0,2) (0,7) (0,14) (0,27) (0,11) (0,1) (1,16) (1,21) (1,24) (1,31) (1,18) (1,25) (1,26) (1,2) (1,7) (1,14) (1,27) (1,11) (1,10) (2,16) (2,20) (2,21) (2,24) (2,6) (2,31) (2,14) (2,27) (2,10) (3,15) (3,29) (3,4) (3,13) (3,8) (3,19) (3,5) (3,22) (4,30) (4,12) (4,17) (4,29) (4,13) (4,5) (4,22) (5,30) (5,12) (5,15) (5,28) (5,29) (5,19) (5,22) (5,23) (6,9) (6,16) (6,24) (6,31) (6,25) (6,7) (6,27) (6,11) (7,16) (7,21) (7,24) (7,18) (7,14) (7,11) (7,10) (8,12) (8,17) (8,15) (8,13) (8,19) (8,22) (8,23) (9,20) (9,21) (9,24) (9,31) (9,18) (9,26) (9,14) (10,21) (10,31) (10,18) (10,25) (10,26) (10,14) (10,27) (10,11) (11,16) (11,20) (11,21) (11,31) (11,18) (11,25) (11,26) (11,14) (12,28) (12,29) (12,13) (12,23) (13,30) (13,17) (13,15) (13,28) (13,19) (13,23) (14,20) (14,21) (14,31) (14,18) (14,25) (14,26) (14,27) (15,17) (15,28) (15,19) (15,23) (16,20) (16,21) (16,24) (16,18) (16,26) (17,30) (17,22) (17,23) (18,21) (18,31) (18,25) (18,27) (19,30) (19,28) (19,22) (19,23) (20,21) (20,31) (20,26) (20,27) (21,24) (21,31) (21,25) (21,26) (21,27) (22,30) (22,29) (23,30) (23,28) (23,29) (24,31) (24,25) (24,26) (25,31) (25,26) (25,27) (26,27) (27,31) (28,30) (28,29)\nIs there a path between node 17 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph193-13_27", + "image": "data/connectivity/graph_visual/hard/graph193.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,27) (0,4) (0,20) (0,21) (0,19) (1,29) (1,24) (1,14) (1,28) (1,23) (2,29) (2,12) (2,24) (2,3) (2,28) (2,8) (2,25) (3,29) (3,12) (3,24) (3,17) (3,8) (4,9) (4,21) (4,6) (5,13) (5,26) (5,29) (5,14) (5,7) (5,28) (6,18) (6,19) (7,26) (7,12) (7,14) (7,25) (8,26) (8,24) (8,11) (8,23) (9,27) (9,20) (9,19) (10,18) (10,19) (11,13) (11,26) (11,29) (11,12) (11,24) (11,28) (12,24) (12,14) (13,26) (13,25) (15,22) (15,21) (15,16) (16,21) (16,18) (17,26) (17,29) (17,23) (17,25) (18,20) (18,19) (19,22) (20,21) (21,27) (21,22) (22,27) (23,26) (23,28) (23,25) (26,28)\nIs there a path between node 13 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph172-8_5", + "image": "data/connectivity/graph_visual/hard/graph172.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,17) (0,11) (0,6) (0,9) (1,23) (1,21) (1,3) (1,19) (1,15) (1,22) (1,24) (1,5) (1,14) (1,25) (1,27) (1,18) (2,28) (2,13) (2,6) (3,23) (3,21) (3,12) (3,19) (3,15) (3,22) (3,24) (3,10) (3,14) (3,26) (3,25) (3,27) (4,21) (4,12) (4,15) (4,22) (4,24) (4,5) (4,14) (4,26) (4,25) (4,16) (4,27) (5,23) (5,21) (5,19) (5,15) (5,24) (5,10) (5,26) (5,8) (5,27) (6,28) (6,13) (6,17) (6,11) (7,28) (7,13) (7,11) (7,20) (8,21) (8,12) (8,19) (8,15) (8,22) (8,14) (8,26) (8,25) (8,16) (8,27) (9,17) (9,11) (9,20) (10,23) (10,12) (10,15) (10,22) (10,24) (10,14) (10,26) (10,25) (10,16) (10,18) (11,28) (11,13) (11,17) (11,20) (12,23) (12,21) (12,15) (12,22) (12,24) (12,16) (12,18) (13,28) (13,17) (13,20) (14,23) (14,21) (14,19) (14,15) (14,24) (14,25) (14,16) (14,27) (15,23) (15,19) (15,26) (15,25) (15,16) (15,27) (15,18) (16,23) (16,21) (16,19) (16,24) (16,26) (16,27) (16,18) (17,28) (18,23) (18,21) (18,19) (18,22) (18,24) (18,26) (18,25) (19,23) (19,22) (19,24) (19,26) (19,25) (19,27) (20,28) (21,23) (21,22) (21,24) (21,26) (21,25) (21,27) (22,24) (22,25) (23,24) (24,26) (24,25) (24,27)\nIs there a path between node 8 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph230-2_7", + "image": "data/connectivity/graph_visual/hard/graph230.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,16) (0,8) (0,24) (0,3) (0,6) (0,21) (0,15) (0,29) (0,14) (0,1) (0,17) (0,12) (0,26) (1,16) (1,24) (1,3) (1,6) (1,21) (1,15) (1,20) (1,25) (1,29) (1,17) (1,12) (1,26) (2,22) (2,28) (2,4) (2,5) (2,19) (2,18) (2,9) (3,16) (3,24) (3,6) (3,21) (3,29) (3,11) (3,17) (3,12) (3,26) (4,22) (4,5) (4,19) (4,18) (4,23) (4,10) (4,13) (4,27) (5,22) (5,28) (5,18) (5,23) (5,9) (5,13) (5,27) (6,16) (6,8) (6,24) (6,21) (6,20) (6,11) (6,14) (6,17) (6,12) (6,26) (7,22) (7,28) (7,19) (7,18) (7,23) (7,9) (7,13) (7,27) (8,16) (8,24) (8,21) (8,20) (8,29) (8,11) (8,14) (8,12) (8,26) (9,23) (9,10) (9,13) (9,27) (10,22) (10,18) (10,23) (10,27) (11,16) (11,24) (11,21) (11,15) (11,20) (11,25) (11,14) (11,17) (11,12) (11,26) (12,16) (12,21) (12,15) (12,20) (12,25) (12,14) (12,17) (12,26) (13,19) (13,18) (14,16) (14,24) (14,21) (14,20) (14,25) (14,29) (14,17) (15,16) (15,24) (15,21) (15,20) (15,17) (15,26) (16,24) (16,20) (16,29) (16,17) (17,24) (17,21) (17,25) (17,29) (18,22) (18,28) (18,19) (18,23) (18,27) (19,22) (19,28) (19,23) (19,27) (20,21) (20,25) (20,29) (21,24) (21,25) (21,29) (21,26) (22,28) (22,23) (23,28) (23,27) (24,25) (24,29) (24,26) (25,29) (27,28)\nIs there a path between node 2 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph202-7_20", + "image": "data/connectivity/graph_visual/hard/graph202.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,29) (1,27) (1,24) (1,21) (1,3) (2,10) (2,22) (2,6) (2,18) (2,25) (2,12) (3,19) (3,27) (3,24) (4,10) (4,6) (4,18) (4,25) (5,28) (5,16) (6,10) (6,13) (6,25) (6,12) (6,9) (7,28) (8,10) (8,14) (8,18) (8,29) (8,25) (8,23) (9,13) (9,14) (10,29) (10,25) (12,22) (12,18) (12,17) (13,29) (13,26) (14,20) (14,17) (15,19) (17,25) (18,20) (18,25) (20,29) (20,26) (20,23) (21,27) (21,24) (23,26) (23,25) (24,27) (26,29)\nIs there a path between node 7 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph81-22_0", + "image": "data/connectivity/graph_visual/hard/graph81.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,7) (0,10) (0,11) (0,20) (0,14) (0,24) (0,16) (0,25) (0,3) (0,12) (0,8) (0,19) (0,6) (1,23) (1,7) (1,10) (1,11) (1,20) (1,14) (1,24) (1,3) (1,6) (2,7) (2,10) (2,11) (2,20) (2,14) (2,24) (2,16) (2,25) (2,3) (2,12) (2,13) (2,6) (3,23) (3,7) (3,10) (3,11) (3,20) (3,14) (3,24) (3,16) (3,25) (3,12) (3,8) (3,13) (4,26) (4,5) (4,9) (4,17) (5,26) (5,15) (5,9) (5,18) (5,17) (5,22) (6,10) (6,11) (6,14) (6,24) (6,25) (6,12) (6,8) (6,19) (6,13) (7,23) (7,10) (7,20) (7,14) (7,16) (7,25) (7,19) (8,23) (8,10) (8,11) (8,14) (8,24) (8,16) (8,25) (8,12) (8,13) (9,26) (9,15) (9,21) (9,18) (9,17) (9,22) (10,23) (10,20) (10,16) (10,25) (10,12) (10,13) (11,20) (11,14) (11,25) (11,12) (11,19) (11,13) (12,20) (12,24) (12,16) (12,19) (13,14) (13,24) (13,16) (13,25) (13,19) (14,23) (15,26) (15,18) (16,23) (16,20) (16,24) (16,25) (17,21) (17,18) (17,22) (18,26) (18,21) (18,22) (19,23) (19,25) (20,23) (20,24) (21,26) (21,22) (22,26) (23,24) (23,25) (24,25)\nIs there a path between node 22 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph571-25_24", + "image": "data/connectivity/graph_visual/hard/graph571.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,7) (0,31) (0,5) (0,13) (0,33) (0,4) (0,8) (0,16) (1,18) (1,29) (1,2) (2,29) (2,28) (3,20) (3,26) (3,25) (4,7) (4,11) (4,10) (4,31) (4,22) (4,24) (4,16) (5,11) (5,13) (5,17) (6,26) (6,29) (7,10) (7,32) (7,33) (7,8) (7,24) (8,14) (8,10) (8,13) (8,33) (9,12) (9,21) (10,11) (10,24) (10,17) (11,31) (11,13) (11,16) (11,17) (12,30) (13,14) (13,32) (14,31) (14,15) (15,32) (15,24) (18,26) (18,29) (18,28) (20,27) (20,28) (21,23) (22,31) (22,33) (25,29) (26,27) (27,29) (27,28) (28,29) (31,32) (31,33) (32,33)\nIs there a path between node 25 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph266-28_0", + "image": "data/connectivity/graph_visual/hard/graph266.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,20) (0,12) (0,25) (0,2) (0,23) (0,17) (0,28) (0,5) (0,10) (0,19) (1,30) (1,9) (1,15) (1,6) (1,10) (1,18) (2,20) (2,12) (2,8) (2,21) (2,28) (2,22) (2,10) (2,3) (2,4) (2,18) (3,25) (3,13) (3,21) (3,28) (3,29) (3,4) (3,18) (4,25) (4,30) (4,13) (4,23) (4,17) (4,28) (4,5) (4,15) (4,14) (4,7) (4,18) (5,20) (5,12) (5,30) (5,13) (5,9) (5,28) (5,16) (5,14) (5,11) (6,12) (6,25) (6,13) (6,21) (6,29) (6,19) (7,13) (7,8) (7,23) (7,28) (7,29) (8,27) (8,21) (8,23) (8,28) (8,22) (8,18) (9,20) (9,12) (9,18) (10,13) (10,22) (10,14) (10,29) (11,20) (11,13) (11,17) (11,15) (12,25) (12,23) (12,28) (12,18) (13,30) (13,27) (13,21) (13,16) (13,14) (14,30) (14,21) (14,16) (14,29) (14,19) (15,20) (15,30) (15,23) (16,20) (16,25) (16,21) (16,28) (17,20) (17,30) (17,28) (18,30) (18,27) (18,23) (18,22) (18,29) (19,23) (19,29) (20,30) (20,23) (20,29) (21,28) (22,29) (23,25) (23,30) (23,28) (25,29) (27,28) (28,30) (29,30)\nIs there a path between node 28 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph450-7_13", + "image": "data/connectivity/graph_visual/hard/graph450.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (0,25) (0,30) (0,26) (1,24) (2,13) (2,29) (3,15) (3,25) (3,30) (3,28) (3,31) (3,27) (4,19) (4,18) (4,30) (4,32) (4,28) (4,31) (4,27) (5,22) (5,6) (6,14) (7,15) (7,25) (7,10) (7,30) (7,32) (7,21) (8,17) (8,29) (9,25) (9,30) (9,31) (9,26) (9,27) (10,25) (10,11) (10,32) (11,25) (11,19) (11,28) (12,13) (13,29) (15,18) (15,30) (15,21) (15,31) (15,26) (18,28) (19,30) (19,27) (20,23) (20,25) (20,30) (20,32) (20,27) (21,25) (21,32) (21,31) (23,25) (23,30) (23,28) (23,26) (25,32) (25,31) (26,30) (26,28) (27,32)\nIs there a path between node 7 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph13-12_9", + "image": "data/connectivity/graph_visual/hard/graph13.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,8) (0,5) (0,19) (1,8) (1,5) (1,19) (2,12) (2,15) (2,16) (2,24) (2,17) (2,3) (2,20) (2,9) (2,21) (2,23) (2,25) (2,11) (2,14) (2,22) (3,10) (3,15) (3,16) (3,24) (3,20) (3,4) (3,21) (3,23) (3,25) (3,14) (3,6) (3,22) (4,10) (4,13) (4,15) (4,16) (4,24) (4,20) (4,21) (4,23) (4,25) (4,14) (4,6) (4,22) (5,18) (5,7) (5,19) (6,12) (6,13) (6,24) (6,17) (6,20) (6,9) (6,23) (6,14) (6,22) (7,8) (8,18) (9,10) (9,12) (9,15) (9,16) (9,24) (9,17) (9,23) (9,25) (9,11) (9,14) (9,22) (10,12) (10,13) (10,16) (10,24) (10,17) (10,21) (10,23) (10,25) (10,11) (10,14) (10,22) (11,13) (11,16) (11,20) (11,21) (11,23) (11,25) (11,22) (12,24) (12,17) (12,20) (12,23) (12,22) (13,15) (13,24) (13,17) (13,20) (13,21) (13,25) (13,22) (14,15) (14,16) (14,24) (14,17) (14,20) (14,21) (14,23) (14,25) (15,24) (15,17) (15,20) (15,23) (15,25) (16,24) (16,17) (16,20) (16,21) (16,23) (16,25) (16,22) (17,24) (17,20) (17,23) (17,22) (18,19) (20,24) (20,21) (20,22) (21,24) (21,25) (21,22) (22,23) (22,25) (23,24) (23,25) (24,25)\nIs there a path between node 12 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph136-5_15", + "image": "data/connectivity/graph_visual/hard/graph136.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,4) (0,18) (0,17) (0,10) (1,7) (1,24) (1,27) (2,4) (2,8) (2,13) (2,19) (2,27) (3,16) (3,28) (3,9) (4,18) (4,6) (4,10) (4,11) (4,27) (6,20) (6,8) (6,7) (6,27) (7,8) (7,18) (7,17) (7,23) (7,24) (7,10) (7,13) (7,19) (7,11) (7,14) (8,17) (8,22) (8,24) (8,10) (8,11) (10,18) (10,17) (10,12) (10,11) (10,27) (11,17) (11,12) (12,20) (12,18) (12,17) (12,14) (13,20) (13,18) (13,24) (13,27) (13,26) (14,18) (15,28) (15,25) (16,25) (17,20) (17,18) (17,26) (18,22) (18,23) (18,19) (18,27) (19,23) (19,27) (19,26) (20,24) (22,23) (22,24) (22,26) (26,27)\nIs there a path between node 5 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph418-6_8", + "image": "data/connectivity/graph_visual/hard/graph418.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,23) (1,29) (1,2) (2,10) (2,7) (2,14) (2,30) (3,31) (3,13) (3,17) (3,12) (5,15) (5,22) (6,13) (6,26) (6,8) (6,25) (8,17) (9,27) (10,11) (10,14) (10,16) (11,18) (12,31) (12,24) (13,31) (13,28) (13,25) (14,30) (15,19) (17,26) (17,24) (18,29) (20,27) (25,28) (25,32) (26,28) (26,32) (28,32) (31,32)\nIs there a path between node 6 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph546-25_29", + "image": "data/connectivity/graph_visual/hard/graph546.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,8) (2,3) (2,28) (2,27) (2,22) (2,11) (2,21) (2,9) (2,26) (2,6) (2,14) (2,7) (2,5) (2,13) (2,10) (3,30) (3,28) (3,27) (3,22) (3,11) (3,4) (3,9) (3,7) (3,12) (3,16) (3,13) (3,10) (4,30) (4,28) (4,27) (4,22) (4,11) (4,21) (4,9) (4,26) (4,6) (4,14) (4,12) (4,5) (4,13) (5,30) (5,27) (5,21) (5,9) (5,26) (5,6) (5,14) (5,16) (5,13) (5,10) (6,30) (6,28) (6,27) (6,22) (6,21) (6,9) (6,12) (6,16) (6,13) (6,10) (7,27) (7,11) (7,9) (7,26) (7,14) (7,16) (7,10) (9,30) (9,28) (9,27) (9,22) (9,21) (9,26) (9,14) (9,13) (10,30) (10,28) (10,27) (10,22) (10,11) (10,21) (10,26) (10,12) (10,16) (10,13) (11,30) (11,28) (11,22) (11,21) (11,14) (11,16) (11,13) (12,30) (12,28) (12,27) (12,21) (12,26) (12,16) (12,13) (13,28) (13,27) (13,22) (13,26) (14,30) (14,28) (14,21) (14,16) (15,18) (15,20) (15,25) (15,31) (15,32) (15,19) (15,33) (16,30) (16,28) (16,27) (16,21) (17,18) (17,24) (17,20) (17,25) (17,31) (17,32) (17,23) (17,19) (17,33) (18,24) (18,20) (18,31) (18,32) (18,23) (18,19) (19,29) (19,20) (19,25) (19,31) (19,32) (19,33) (20,29) (20,24) (20,25) (20,31) (20,32) (20,33) (21,22) (21,26) (22,30) (22,27) (22,26) (23,24) (23,25) (23,31) (23,33) (24,29) (24,25) (24,33) (25,29) (25,32) (26,30) (26,28) (26,27) (27,30) (27,28) (28,30) (29,31) (29,32) (29,33) (31,32) (31,33)\nIs there a path between node 25 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph473-26_21", + "image": "data/connectivity/graph_visual/hard/graph473.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,17) (1,2) (1,14) (1,9) (1,18) (1,5) (1,25) (1,28) (1,13) (1,10) (2,31) (2,14) (2,4) (2,18) (2,5) (2,28) (2,13) (2,19) (2,22) (2,10) (2,15) (3,27) (4,21) (4,9) (4,18) (4,25) (4,28) (4,13) (4,22) (4,7) (4,16) (5,21) (5,31) (5,9) (5,18) (5,25) (5,28) (5,13) (5,19) (5,22) (5,16) (5,10) (5,15) (6,17) (6,32) (7,31) (7,14) (7,9) (7,18) (7,25) (7,28) (7,13) (7,19) (7,16) (7,10) (8,11) (8,23) (8,30) (8,12) (8,29) (9,21) (9,31) (9,18) (9,25) (9,13) (9,10) (10,31) (10,18) (10,28) (10,19) (10,22) (10,16) (10,15) (11,24) (11,30) (11,26) (12,24) (12,23) (12,20) (12,26) (12,29) (13,14) (13,18) (13,28) (13,19) (13,22) (13,16) (14,31) (14,18) (14,16) (14,15) (15,31) (15,18) (15,19) (15,22) (15,16) (16,21) (16,31) (16,18) (16,28) (16,19) (18,21) (18,31) (18,25) (18,28) (18,22) (19,31) (19,25) (19,28) (19,22) (20,24) (20,23) (20,30) (20,29) (21,31) (21,28) (21,22) (22,25) (22,28) (23,30) (23,26) (23,29) (24,30) (25,31) (25,28) (26,30) (28,31) (29,30)\nIs there a path between node 26 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph637-0_25", + "image": "data/connectivity/graph_visual/hard/graph637.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,24) (0,28) (0,32) (0,1) (0,27) (0,13) (0,9) (1,31) (1,8) (1,15) (1,14) (1,21) (1,28) (1,4) (1,6) (2,3) (2,11) (2,24) (2,31) (2,14) (2,32) (2,4) (2,27) (2,9) (3,22) (3,14) (3,32) (3,20) (3,9) (4,11) (4,24) (4,34) (4,7) (4,19) (4,18) (4,29) (4,28) (4,32) (4,27) (4,13) (5,22) (5,7) (5,18) (5,6) (5,27) (5,13) (6,15) (6,29) (6,27) (6,13) (7,22) (7,33) (7,24) (7,8) (7,19) (7,25) (7,18) (7,30) (7,21) (7,28) (8,11) (8,33) (8,14) (8,25) (8,30) (8,32) (9,27) (9,20) (10,23) (11,22) (11,31) (11,15) (11,19) (11,30) (11,29) (12,17) (13,22) (13,33) (13,19) (13,16) (13,30) (13,21) (13,20) (14,34) (14,30) (15,22) (15,33) (15,24) (15,31) (15,18) (15,30) (15,21) (15,27) (16,24) (16,30) (18,22) (18,33) (18,31) (18,32) (19,22) (19,26) (19,25) (19,28) (19,32) (20,33) (20,24) (20,28) (21,25) (21,30) (21,29) (22,31) (22,28) (22,27) (24,34) (24,31) (24,26) (25,26) (25,29) (25,28) (26,34) (26,30) (26,28) (27,34) (27,28) (28,31) (30,31) (31,34) (32,33) (33,34)\nIs there a path between node 0 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph231-21_9", + "image": "data/connectivity/graph_visual/hard/graph231.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,21) (0,13) (0,14) (0,8) (0,6) (0,3) (0,15) (1,25) (1,27) (1,18) (1,23) (1,19) (1,10) (1,16) (2,20) (2,11) (2,29) (2,4) (2,7) (3,12) (3,17) (3,21) (3,5) (3,13) (3,14) (3,8) (3,24) (3,15) (4,20) (4,28) (4,22) (4,9) (5,26) (5,17) (5,21) (5,13) (5,14) (5,8) (5,6) (5,15) (6,12) (6,26) (6,21) (6,13) (6,14) (6,8) (6,24) (6,15) (7,20) (7,28) (7,11) (7,29) (7,9) (8,12) (8,26) (8,21) (8,14) (8,24) (9,20) (9,28) (9,11) (9,29) (9,22) (10,25) (10,27) (10,18) (10,23) (10,19) (11,20) (11,29) (12,26) (12,17) (12,21) (12,13) (12,24) (12,15) (13,26) (13,17) (13,21) (13,24) (13,15) (14,17) (14,21) (14,24) (14,15) (15,26) (15,21) (15,24) (16,27) (16,18) (16,23) (16,19) (17,26) (17,21) (18,25) (18,27) (18,19) (19,25) (19,27) (19,23) (20,28) (20,29) (20,22) (21,26) (21,24) (22,28) (22,29) (23,25) (23,27) (24,26) (28,29)\nIs there a path between node 21 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph544-16_29", + "image": "data/connectivity/graph_visual/hard/graph544.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,11) (0,20) (0,7) (0,4) (0,24) (0,13) (0,18) (0,31) (0,32) (0,1) (0,28) (0,3) (0,29) (0,25) (0,16) (0,19) (1,11) (1,17) (1,20) (1,5) (1,4) (1,13) (1,18) (1,31) (1,32) (1,27) (1,3) (1,16) (1,19) (2,33) (2,12) (3,8) (3,11) (3,17) (3,20) (3,4) (3,24) (3,13) (3,18) (3,31) (3,32) (3,14) (3,28) (3,29) (3,16) (3,19) (4,8) (4,11) (4,15) (4,5) (4,7) (4,24) (4,13) (4,18) (4,31) (4,32) (4,14) (4,28) (4,30) (4,29) (4,25) (4,26) (5,17) (5,20) (5,13) (5,31) (5,14) (5,30) (5,29) (5,25) (5,16) (5,26) (5,19) (6,21) (6,9) (7,8) (7,17) (7,20) (7,15) (7,24) (7,32) (7,14) (7,30) (7,29) (7,26) (8,11) (8,17) (8,20) (8,15) (8,24) (8,18) (8,27) (8,14) (8,28) (8,29) (8,26) (9,23) (9,21) (9,10) (10,23) (10,21) (11,17) (11,20) (11,24) (11,13) (11,31) (11,32) (11,14) (11,28) (11,29) (11,16) (11,26) (13,24) (13,27) (13,14) (13,29) (13,16) (13,26) (13,19) (14,17) (14,20) (14,15) (14,24) (14,18) (14,31) (14,32) (14,27) (14,28) (14,30) (14,29) (14,25) (14,19) (15,17) (15,20) (15,24) (15,18) (15,31) (15,32) (15,27) (15,28) (15,29) (15,25) (15,16) (15,26) (15,19) (16,17) (16,20) (16,24) (16,32) (16,27) (16,28) (16,30) (16,29) (16,25) (16,26) (17,24) (17,18) (17,31) (17,32) (17,28) (17,29) (17,25) (17,26) (17,19) (18,20) (18,31) (18,32) (18,27) (18,28) (18,29) (18,25) (18,26) (18,19) (19,20) (19,24) (19,32) (19,28) (19,29) (19,25) (20,24) (20,31) (20,32) (20,27) (20,28) (20,30) (20,29) (20,26) (21,23) (24,31) (24,32) (24,27) (24,28) (24,30) (24,29) (24,25) (25,31) (25,32) (25,27) (25,29) (25,26) (26,31) (26,32) (26,28) (27,32) (27,28) (28,32) (28,30) (29,32) (29,30) (30,31) (30,32) (31,32)\nIs there a path between node 16 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph187-23_21", + "image": "data/connectivity/graph_visual/hard/graph187.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,20) (1,9) (1,25) (1,14) (1,8) (1,7) (1,27) (1,3) (1,13) (2,4) (2,10) (3,14) (3,7) (3,21) (3,13) (4,5) (5,18) (6,9) (6,16) (6,28) (6,8) (6,17) (6,7) (6,15) (6,24) (6,22) (6,13) (7,29) (7,17) (8,28) (8,23) (8,29) (8,17) (8,27) (9,14) (9,15) (10,20) (10,18) (11,15) (11,24) (11,22) (13,25) (13,23) (13,21) (14,28) (14,23) (14,29) (14,24) (15,16) (15,28) (15,29) (15,27) (15,22) (16,29) (16,27) (17,25) (17,29) (17,27) (21,25) (21,28) (22,25) (23,28) (23,29) (27,29)\nIs there a path between node 23 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph469-15_13", + "image": "data/connectivity/graph_visual/hard/graph469.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,29) (0,16) (0,3) (0,25) (0,26) (0,13) (0,14) (0,5) (0,4) (0,22) (0,20) (0,21) (0,24) (0,17) (0,32) (0,2) (0,10) (0,7) (0,12) (1,28) (1,16) (1,6) (1,25) (1,13) (1,14) (1,18) (1,5) (1,23) (1,4) (1,22) (1,20) (1,21) (1,24) (1,15) (1,2) (1,10) (1,7) (1,12) (2,28) (2,29) (2,16) (2,6) (2,3) (2,25) (2,26) (2,13) (2,14) (2,18) (2,5) (2,23) (2,8) (2,4) (2,19) (2,20) (2,21) (2,24) (2,17) (2,15) (2,12) (3,29) (3,6) (3,25) (3,13) (3,14) (3,5) (3,23) (3,8) (3,4) (3,19) (3,20) (3,21) (3,24) (3,17) (3,32) (3,15) (3,10) (3,7) (3,12) (4,28) (4,29) (4,16) (4,6) (4,25) (4,26) (4,14) (4,5) (4,8) (4,27) (4,22) (4,19) (4,21) (4,15) (4,10) (4,7) (5,28) (5,25) (5,13) (5,18) (5,23) (5,8) (5,27) (5,19) (5,20) (5,21) (5,24) (5,32) (5,15) (5,10) (5,7) (5,12) (6,28) (6,29) (6,16) (6,14) (6,18) (6,8) (6,22) (6,19) (6,20) (6,21) (6,17) (6,12) (7,28) (7,23) (7,8) (7,22) (7,19) (7,21) (7,32) (7,15) (7,10) (7,12) (8,29) (8,16) (8,26) (8,13) (8,22) (8,19) (8,20) (8,24) (8,17) (8,32) (8,15) (8,10) (8,12) (9,31) (10,28) (10,16) (10,25) (10,26) (10,13) (10,18) (10,23) (10,22) (10,19) (10,21) (10,17) (10,32) (10,15) (10,12) (11,31) (11,30) (12,28) (12,29) (12,16) (12,14) (12,22) (12,20) (12,24) (12,17) (12,32) (12,15) (13,29) (13,16) (13,26) (13,14) (13,23) (13,27) (13,22) (13,19) (13,20) (13,21) (13,32) (14,28) (14,29) (14,26) (14,18) (14,27) (14,19) (14,20) (14,21) (14,17) (14,15) (15,28) (15,29) (15,16) (15,25) (15,26) (15,18) (15,27) (15,22) (15,21) (15,24) (15,32) (16,25) (16,26) (16,18) (16,27) (16,22) (16,19) (16,20) (16,21) (16,24) (16,17) (16,32) (17,28) (17,25) (17,27) (17,22) (17,19) (17,21) (17,32) (18,28) (18,29) (18,26) (18,27) (18,19) (18,20) (18,21) (18,24) (18,32) (19,29) (19,25) (19,26) (19,23) (19,27) (19,20) (19,21) (19,24) (19,32) (20,28) (20,29) (20,27) (20,22) (20,24) (20,32) (21,26) (21,24) (22,28) (22,29) (22,25) (22,26) (22,23) (22,27) (22,24) (23,28) (23,29) (23,25) (23,26) (23,24) (24,28) (24,25) (25,28) (25,26) (25,27) (25,32) (26,29) (26,32) (27,28) (27,29) (27,32) (28,29) (28,32) (29,32) (30,31)\nIs there a path between node 15 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph587-17_25", + "image": "data/connectivity/graph_visual/hard/graph587.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,21) (0,30) (0,33) (0,6) (0,24) (0,25) (0,1) (0,17) (0,11) (0,16) (1,10) (1,30) (1,4) (1,33) (1,6) (1,25) (1,31) (1,5) (1,17) (1,11) (1,16) (2,27) (3,15) (3,28) (3,12) (3,32) (3,14) (3,20) (3,13) (4,21) (4,33) (4,6) (4,24) (4,25) (4,31) (4,5) (4,17) (4,11) (5,10) (5,21) (5,30) (5,33) (5,6) (5,24) (5,25) (5,31) (5,17) (5,11) (6,30) (6,33) (6,24) (6,25) (6,31) (6,17) (6,11) (6,16) (7,19) (7,29) (7,22) (7,18) (7,9) (8,23) (8,15) (8,28) (8,32) (8,14) (8,20) (9,19) (9,29) (9,22) (9,18) (10,30) (10,33) (10,24) (10,25) (10,31) (10,17) (10,11) (11,21) (11,30) (11,33) (11,24) (11,25) (11,17) (11,16) (12,23) (12,15) (12,32) (12,14) (12,13) (13,15) (13,28) (13,32) (13,14) (14,15) (14,28) (14,32) (15,23) (15,28) (15,32) (15,20) (16,30) (16,25) (16,17) (17,33) (17,31) (18,19) (18,29) (18,22) (19,29) (20,28) (20,32) (21,33) (21,24) (21,25) (21,31) (23,32) (24,30) (24,33) (24,25) (24,31) (25,33) (25,31) (26,27) (30,31)\nIs there a path between node 17 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph90-26_3", + "image": "data/connectivity/graph_visual/hard/graph90.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,7) (0,13) (0,8) (0,18) (0,25) (0,14) (0,17) (0,21) (1,13) (1,26) (1,14) (1,20) (1,17) (1,24) (1,6) (2,8) (2,18) (2,9) (2,26) (2,14) (2,10) (2,15) (3,16) (3,12) (4,13) (4,8) (4,18) (4,25) (4,6) (5,19) (5,13) (5,10) (5,20) (5,22) (5,17) (5,6) (6,8) (6,18) (6,9) (6,26) (6,14) (6,17) (6,21) (6,15) (6,23) (7,25) (7,14) (7,22) (7,24) (7,15) (7,23) (8,13) (8,25) (8,24) (8,23) (9,25) (9,27) (9,26) (9,14) (9,17) (9,24) (9,23) (10,19) (10,13) (10,25) (10,22) (11,12) (12,16) (13,19) (13,18) (13,21) (14,19) (14,18) (14,22) (15,19) (15,25) (15,23) (17,25) (17,22) (17,21) (17,24) (18,21) (18,24) (19,26) (19,22) (19,24) (19,23) (20,25) (20,26) (20,24) (20,23) (21,27) (21,23) (22,25) (22,26) (22,23) (25,27) (25,26)\nIs there a path between node 26 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph233-14_5", + "image": "data/connectivity/graph_visual/hard/graph233.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,8) (0,16) (0,2) (0,21) (0,12) (0,22) (0,14) (0,1) (0,5) (0,27) (0,10) (0,23) (0,20) (1,8) (1,18) (1,26) (1,21) (1,22) (1,14) (1,6) (1,27) (1,3) (1,15) (1,10) (1,7) (1,23) (1,20) (2,18) (2,26) (2,21) (2,22) (2,14) (2,6) (2,3) (2,15) (2,10) (2,13) (2,7) (2,23) (2,20) (3,21) (3,14) (3,6) (3,15) (3,13) (3,7) (3,23) (4,11) (4,17) (4,9) (4,19) (5,8) (5,16) (5,21) (5,12) (5,14) (5,6) (5,15) (5,10) (5,13) (5,7) (6,16) (6,26) (6,21) (6,12) (6,27) (6,13) (6,7) (6,23) (7,8) (7,16) (7,18) (7,12) (7,22) (7,14) (7,27) (7,15) (7,10) (7,13) (7,23) (7,20) (8,16) (8,18) (8,26) (8,21) (8,22) (8,14) (8,27) (8,15) (8,13) (8,23) (8,20) (9,17) (10,16) (10,18) (10,26) (10,21) (10,12) (10,22) (10,14) (10,23) (10,20) (11,17) (11,28) (11,25) (11,19) (11,29) (12,16) (12,21) (12,22) (12,14) (12,27) (12,15) (12,13) (12,20) (13,16) (13,26) (13,21) (13,22) (13,14) (13,15) (13,23) (13,20) (14,16) (14,26) (14,21) (14,27) (14,15) (15,16) (15,18) (15,26) (15,21) (15,27) (15,23) (16,18) (16,26) (16,21) (16,22) (16,27) (16,20) (17,28) (17,25) (17,19) (17,29) (18,23) (19,28) (19,25) (20,26) (20,21) (20,27) (20,23) (21,26) (21,23) (22,26) (22,27) (23,26) (25,28) (25,29) (26,27) (28,29)\nIs there a path between node 14 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph478-10_21", + "image": "data/connectivity/graph_visual/hard/graph478.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (0,6) (0,31) (0,20) (0,8) (0,4) (0,2) (0,28) (0,32) (0,3) (0,10) (0,5) (0,27) (0,16) (0,15) (0,14) (0,9) (0,26) (0,19) (1,17) (1,31) (1,20) (1,4) (1,29) (1,28) (1,32) (1,3) (1,10) (1,5) (1,16) (1,15) (1,9) (1,26) (1,19) (1,24) (2,17) (2,31) (2,20) (2,8) (2,4) (2,29) (2,3) (2,5) (2,27) (2,15) (2,14) (2,9) (3,6) (3,17) (3,31) (3,20) (3,8) (3,4) (3,28) (3,32) (3,10) (3,27) (3,15) (3,14) (3,9) (3,19) (4,6) (4,17) (4,31) (4,20) (4,8) (4,29) (4,28) (4,32) (4,10) (4,5) (4,27) (4,14) (4,26) (4,19) (4,24) (5,6) (5,17) (5,20) (5,8) (5,29) (5,32) (5,10) (5,27) (5,15) (5,14) (5,9) (5,26) (5,19) (5,24) (6,17) (6,8) (6,29) (6,32) (6,10) (6,16) (6,14) (6,9) (6,19) (6,24) (7,23) (7,25) (7,13) (7,21) (7,22) (7,30) (7,12) (8,17) (8,31) (8,20) (8,29) (8,28) (8,32) (8,10) (8,27) (8,16) (8,15) (8,14) (8,19) (8,24) (9,31) (9,28) (9,32) (9,10) (9,27) (9,16) (9,15) (9,14) (9,26) (9,19) (9,24) (10,17) (10,28) (10,32) (10,27) (10,16) (10,15) (10,26) (10,19) (10,24) (11,23) (11,18) (11,25) (11,13) (11,21) (11,22) (11,12) (12,18) (12,25) (12,13) (12,22) (12,30) (13,23) (13,18) (13,25) (13,21) (13,22) (14,17) (14,28) (14,27) (14,16) (14,15) (14,26) (14,19) (15,31) (15,20) (15,28) (15,32) (15,27) (15,26) (15,19) (15,24) (16,17) (16,31) (16,20) (16,29) (16,28) (16,26) (16,19) (16,24) (17,29) (17,28) (17,26) (17,19) (18,23) (18,25) (19,31) (19,20) (19,29) (19,32) (19,27) (20,31) (20,29) (20,28) (20,26) (21,25) (21,22) (21,30) (22,23) (22,25) (22,30) (23,30) (24,31) (24,29) (24,32) (24,26) (25,30) (26,31) (26,29) (26,28) (26,32) (27,31) (27,29) (27,28) (27,32) (28,31) (28,29) (28,32) (29,31) (29,32) (31,32)\nIs there a path between node 10 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph328-14_22", + "image": "data/connectivity/graph_visual/hard/graph328.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,21) (0,17) (0,19) (0,2) (0,25) (0,23) (0,14) (0,8) (0,7) (0,28) (0,29) (0,16) (0,5) (0,12) (0,11) (0,18) (0,6) (0,24) (1,4) (1,17) (1,19) (1,14) (1,8) (1,31) (1,27) (1,7) (1,29) (1,16) (1,5) (1,12) (1,11) (1,20) (1,3) (1,18) (1,6) (1,13) (2,21) (2,17) (2,19) (2,25) (2,31) (2,15) (2,27) (2,7) (2,29) (2,16) (2,5) (2,26) (2,12) (2,11) (2,3) (2,18) (2,10) (2,13) (3,4) (3,21) (3,17) (3,19) (3,23) (3,14) (3,31) (3,15) (3,27) (3,7) (3,28) (3,16) (3,26) (3,11) (3,20) (3,18) (3,24) (3,10) (3,13) (4,21) (4,19) (4,25) (4,23) (4,8) (4,31) (4,15) (4,27) (4,7) (4,29) (4,16) (4,5) (4,26) (4,20) (4,18) (4,10) (4,13) (5,21) (5,17) (5,19) (5,23) (5,14) (5,8) (5,31) (5,15) (5,7) (5,28) (5,26) (5,12) (5,11) (5,20) (5,24) (5,10) (5,13) (6,21) (6,17) (6,23) (6,14) (6,8) (6,31) (6,15) (6,27) (6,7) (6,12) (6,11) (6,18) (6,24) (6,10) (6,13) (7,17) (7,19) (7,25) (7,14) (7,31) (7,15) (7,27) (7,28) (7,29) (7,16) (7,26) (7,12) (7,11) (7,20) (7,10) (7,13) (8,21) (8,17) (8,19) (8,25) (8,14) (8,31) (8,28) (8,29) (8,16) (8,20) (8,18) (8,24) (8,10) (8,13) (9,30) (10,21) (10,17) (10,25) (10,23) (10,14) (10,31) (10,15) (10,28) (10,29) (10,16) (10,12) (10,20) (10,18) (10,24) (11,21) (11,17) (11,19) (11,25) (11,23) (11,15) (11,28) (11,16) (11,12) (11,20) (11,18) (11,24) (11,13) (12,19) (12,25) (12,23) (12,14) (12,31) (12,15) (12,27) (12,28) (12,29) (12,16) (12,26) (12,20) (12,18) (12,24) (13,21) (13,19) (13,25) (13,23) (13,14) (13,31) (13,15) (13,29) (13,16) (13,26) (13,20) (13,24) (14,17) (14,23) (14,31) (14,15) (14,28) (14,29) (14,16) (14,26) (14,20) (14,24) (15,17) (15,25) (15,23) (15,31) (15,27) (15,28) (15,29) (15,16) (15,26) (15,20) (16,21) (16,19) (16,25) (16,23) (16,31) (16,27) (16,28) (16,29) (16,26) (16,18) (16,24) (17,21) (17,19) (17,25) (17,23) (17,31) (17,29) (17,18) (17,24) (18,21) (18,19) (18,25) (18,28) (18,29) (18,26) (18,20) (19,21) (19,25) (19,23) (19,27) (19,28) (19,29) (19,20) (20,21) (20,25) (20,23) (20,27) (20,28) (20,26) (20,24) (21,25) (21,23) (21,31) (21,27) (21,28) (21,24) (22,30) (23,31) (23,27) (24,25) (24,31) (24,27) (24,28) (24,29) (24,26) (26,31) (26,27) (26,29) (28,29) (29,31)\nIs there a path between node 14 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph396-15_8", + "image": "data/connectivity/graph_visual/hard/graph396.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,21) (1,22) (1,4) (1,27) (1,2) (1,32) (1,9) (2,20) (2,4) (2,14) (2,13) (3,28) (3,14) (3,13) (3,9) (4,24) (4,30) (4,32) (5,8) (5,11) (5,16) (5,29) (6,21) (6,26) (6,10) (6,25) (7,15) (8,29) (8,31) (9,20) (9,23) (9,28) (9,14) (9,13) (11,18) (11,31) (13,24) (13,23) (13,14) (14,22) (14,23) (14,30) (14,32) (15,18) (15,16) (15,31) (16,19) (17,26) (18,19) (20,28) (20,30) (23,24) (23,30) (23,32) (24,28) (24,32) (25,26) (27,32) (28,30)\nIs there a path between node 15 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph541-32_23", + "image": "data/connectivity/graph_visual/hard/graph541.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,13) (0,30) (0,32) (0,15) (0,8) (0,17) (0,21) (0,19) (0,14) (0,26) (0,3) (0,4) (0,18) (0,11) (0,10) (0,7) (0,28) (0,31) (1,13) (1,30) (1,32) (1,23) (1,15) (1,8) (1,17) (1,21) (1,19) (1,33) (1,26) (1,9) (1,4) (1,11) (1,7) (2,20) (2,13) (2,30) (2,32) (2,23) (2,17) (2,22) (2,19) (2,33) (2,14) (2,26) (2,3) (2,18) (2,11) (2,7) (2,28) (2,31) (3,20) (3,13) (3,30) (3,32) (3,23) (3,15) (3,8) (3,17) (3,21) (3,14) (3,26) (3,9) (3,18) (3,11) (3,28) (3,31) (4,20) (4,13) (4,30) (4,32) (4,23) (4,15) (4,33) (4,26) (4,18) (4,11) (4,10) (4,7) (4,28) (4,31) (5,12) (5,27) (6,29) (6,24) (6,12) (6,27) (7,20) (7,13) (7,30) (7,23) (7,15) (7,8) (7,17) (7,22) (7,19) (7,14) (7,26) (7,18) (7,10) (7,28) (7,31) (8,20) (8,30) (8,15) (8,17) (8,22) (8,21) (8,19) (8,33) (8,14) (8,26) (8,9) (8,18) (8,10) (9,13) (9,30) (9,32) (9,23) (9,22) (9,21) (9,33) (9,14) (9,26) (9,18) (9,11) (9,10) (9,28) (9,31) (10,13) (10,30) (10,32) (10,15) (10,22) (10,21) (10,19) (10,33) (10,26) (10,18) (10,11) (10,28) (11,20) (11,13) (11,30) (11,32) (11,23) (11,15) (11,17) (11,22) (11,21) (11,19) (11,26) (11,28) (11,31) (12,29) (12,24) (12,16) (12,27) (13,20) (13,32) (13,15) (13,17) (13,22) (13,21) (13,33) (13,14) (13,28) (13,31) (14,20) (14,32) (14,15) (14,17) (14,22) (14,18) (14,28) (14,31) (15,20) (15,30) (15,32) (15,17) (15,22) (15,21) (15,19) (15,33) (15,26) (15,18) (15,31) (16,29) (16,27) (17,20) (17,30) (17,22) (17,21) (17,19) (17,33) (17,26) (17,18) (17,28) (17,31) (18,20) (18,30) (18,23) (18,22) (18,21) (18,28) (18,31) (19,20) (19,32) (19,21) (19,26) (19,28) (20,30) (20,32) (20,23) (20,22) (20,21) (20,28) (21,30) (21,32) (21,23) (21,22) (21,33) (21,26) (21,31) (22,32) (22,28) (22,31) (23,30) (23,32) (23,33) (23,26) (23,31) (24,29) (24,27) (26,30) (26,32) (26,33) (26,28) (27,29) (28,31) (30,32) (30,33) (30,31) (31,32) (32,33)\nIs there a path between node 32 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph313-19_1", + "image": "data/connectivity/graph_visual/hard/graph313.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,29) (0,15) (0,4) (1,14) (1,12) (1,13) (2,22) (3,27) (4,5) (4,29) (4,15) (5,9) (5,29) (5,18) (5,7) (5,30) (6,12) (6,10) (7,20) (7,25) (7,9) (7,15) (7,21) (9,20) (9,19) (9,29) (9,21) (11,16) (13,27) (14,28) (15,18) (15,21) (18,30) (19,29) (20,30) (22,26) (22,31) (25,29) (25,30)\nIs there a path between node 19 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph264-3_0", + "image": "data/connectivity/graph_visual/hard/graph264.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,14) (0,8) (0,20) (0,23) (0,29) (0,15) (0,25) (0,24) (0,18) (1,2) (2,21) (3,8) (3,17) (3,20) (3,12) (3,10) (3,5) (4,26) (4,14) (4,22) (4,8) (4,12) (4,7) (4,10) (4,5) (5,22) (5,13) (5,8) (5,19) (5,17) (5,12) (5,6) (5,7) (5,24) (6,26) (6,22) (6,29) (6,24) (7,26) (7,11) (7,17) (7,20) (7,23) (7,15) (7,10) (7,24) (8,11) (8,13) (8,19) (8,17) (8,29) (8,15) (8,10) (8,25) (9,21) (10,26) (10,28) (10,17) (10,15) (10,25) (10,18) (11,22) (11,28) (11,20) (11,12) (11,29) (11,18) (12,14) (12,13) (12,28) (12,15) (12,25) (13,19) (13,25) (13,18) (14,20) (14,15) (14,25) (15,25) (16,30) (16,21) (17,19) (17,23) (17,29) (17,24) (17,18) (18,22) (18,23) (18,29) (18,25) (18,24) (19,24) (20,22) (20,23) (20,25) (22,26) (22,28) (23,24) (24,26) (25,29) (26,29)\nIs there a path between node 3 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph570-27_23", + "image": "data/connectivity/graph_visual/hard/graph570.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,2) (0,29) (0,30) (0,20) (0,10) (0,1) (0,22) (0,9) (1,29) (1,8) (1,20) (1,10) (1,23) (1,27) (1,14) (2,3) (2,29) (2,20) (2,17) (2,18) (2,5) (2,22) (2,19) (2,9) (2,24) (3,29) (3,30) (3,17) (3,21) (3,32) (3,22) (3,9) (4,12) (5,29) (5,6) (5,21) (5,22) (5,9) (6,30) (6,17) (6,10) (6,21) (6,32) (6,27) (6,14) (6,9) (6,24) (7,33) (7,13) (8,29) (8,18) (8,23) (8,14) (9,10) (9,27) (10,18) (10,21) (10,23) (13,33) (14,16) (14,32) (14,23) (14,19) (14,27) (14,24) (16,17) (16,18) (16,32) (16,23) (16,22) (16,19) (16,27) (17,29) (17,30) (17,23) (17,22) (17,19) (17,24) (18,22) (18,19) (18,27) (18,24) (19,29) (19,21) (19,32) (19,23) (19,24) (20,32) (20,23) (21,23) (21,22) (22,32) (22,27) (23,30) (23,27) (25,33) (25,26) (27,29) (27,30) (29,32) (30,32)\nIs there a path between node 27 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph381-8_16", + "image": "data/connectivity/graph_visual/hard/graph381.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,17) (0,4) (0,14) (0,22) (0,9) (0,5) (0,16) (0,25) (0,31) (0,23) (0,28) (0,15) (0,2) (0,8) (0,19) (0,6) (1,12) (1,3) (1,21) (2,13) (2,17) (2,4) (2,24) (2,14) (2,30) (2,22) (2,9) (2,16) (2,25) (2,29) (2,31) (2,20) (2,28) (2,15) (2,8) (2,19) (2,6) (3,18) (3,12) (3,21) (4,13) (4,7) (4,14) (4,30) (4,22) (4,9) (4,5) (4,26) (4,23) (4,20) (4,28) (4,15) (4,8) (4,19) (4,6) (5,24) (5,7) (5,14) (5,30) (5,22) (5,9) (5,29) (5,26) (5,23) (5,28) (5,15) (5,8) (5,19) (5,6) (6,13) (6,17) (6,11) (6,24) (6,14) (6,22) (6,16) (6,29) (6,31) (6,23) (6,20) (6,28) (7,13) (7,17) (7,11) (7,24) (7,30) (7,9) (7,16) (7,25) (7,29) (7,26) (7,31) (7,23) (7,20) (7,28) (7,8) (7,19) (8,17) (8,24) (8,14) (8,30) (8,22) (8,9) (8,16) (8,20) (8,28) (8,15) (8,19) (9,13) (9,17) (9,11) (9,24) (9,14) (9,30) (9,22) (9,16) (9,25) (9,29) (9,26) (9,23) (9,20) (9,15) (9,19) (11,13) (11,14) (11,30) (11,22) (11,16) (11,29) (11,26) (11,23) (11,20) (11,15) (11,19) (12,18) (12,21) (13,14) (13,25) (13,26) (13,31) (13,20) (13,15) (13,19) (14,17) (14,24) (14,22) (14,16) (14,25) (14,26) (14,31) (14,20) (14,28) (15,17) (15,24) (15,30) (15,22) (15,16) (15,25) (15,29) (15,19) (16,17) (16,24) (16,30) (16,29) (16,26) (16,31) (16,23) (16,20) (16,28) (16,19) (17,24) (17,30) (17,22) (17,31) (17,23) (17,20) (17,28) (17,19) (19,24) (19,25) (19,26) (19,31) (19,23) (19,20) (20,30) (20,22) (20,26) (20,23) (22,30) (22,25) (22,29) (22,23) (22,28) (23,24) (23,30) (23,25) (23,29) (23,26) (24,30) (24,25) (24,29) (24,28) (25,30) (25,26) (25,31) (25,28) (26,30) (26,29) (26,31) (28,30) (28,29) (30,31)\nIs there a path between node 8 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph701-16_22", + "image": "data/connectivity/graph_visual/hard/graph701.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,12) (0,6) (0,25) (0,9) (0,33) (0,3) (0,2) (0,24) (0,10) (0,28) (0,4) (0,29) (0,31) (0,21) (0,26) (0,13) (0,8) (0,5) (1,20) (1,34) (1,32) (1,19) (1,16) (2,15) (2,12) (2,25) (2,9) (2,33) (2,3) (2,28) (2,4) (2,29) (2,31) (2,26) (2,8) (2,5) (3,15) (3,12) (3,33) (3,28) (3,4) (3,29) (3,31) (3,21) (3,26) (3,8) (4,25) (4,9) (4,28) (4,31) (4,13) (4,8) (5,15) (5,12) (5,25) (5,33) (5,24) (5,10) (5,26) (5,13) (5,8) (6,12) (6,25) (6,9) (6,33) (6,24) (6,10) (6,28) (6,29) (6,31) (6,21) (6,13) (6,8) (7,20) (7,34) (7,32) (7,19) (7,16) (8,12) (8,25) (8,33) (8,10) (8,28) (8,29) (8,21) (8,26) (9,12) (9,33) (9,24) (9,10) (9,28) (9,26) (10,15) (10,12) (10,33) (10,24) (10,29) (10,31) (10,21) (10,26) (10,13) (11,22) (11,23) (11,14) (11,17) (12,28) (12,29) (12,21) (12,26) (12,13) (13,25) (13,33) (13,24) (13,28) (13,29) (13,31) (13,21) (13,26) (14,18) (14,22) (14,23) (14,27) (14,17) (14,30) (15,33) (15,24) (15,28) (15,29) (15,31) (15,21) (15,26) (16,20) (16,34) (16,32) (17,22) (17,23) (17,30) (18,27) (18,30) (19,20) (19,32) (20,34) (20,32) (21,25) (21,24) (21,28) (21,29) (21,26) (22,23) (22,27) (22,30) (23,30) (24,25) (24,28) (24,29) (24,26) (25,33) (25,28) (25,29) (25,31) (26,33) (26,29) (27,30) (28,33) (28,29) (29,33) (29,31) (31,33) (32,34)\nIs there a path between node 16 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph93-18_4", + "image": "data/connectivity/graph_visual/hard/graph93.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,19) (0,18) (0,16) (0,13) (0,4) (0,8) (0,10) (0,22) (1,2) (2,7) (3,19) (3,18) (3,12) (3,20) (3,10) (4,11) (4,14) (4,5) (4,20) (4,8) (5,11) (5,14) (5,18) (5,16) (5,13) (5,12) (6,19) (6,11) (6,12) (6,20) (6,8) (7,26) (8,24) (8,14) (8,18) (8,25) (9,17) (10,15) (10,27) (10,21) (10,18) (10,13) (10,12) (10,20) (11,27) (11,21) (11,13) (11,12) (11,25) (12,24) (12,16) (12,25) (13,24) (13,27) (13,25) (13,20) (13,22) (14,16) (14,22) (15,20) (16,25) (17,26) (17,23) (18,27) (19,25) (19,20) (20,24) (20,25) (20,22) (21,27) (22,25) (23,26) (25,27)\nIs there a path between node 18 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph155-24_19", + "image": "data/connectivity/graph_visual/hard/graph155.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,9) (0,15) (1,5) (1,22) (1,4) (1,20) (1,12) (1,25) (2,5) (2,22) (2,13) (2,12) (2,10) (3,23) (4,19) (4,14) (4,18) (4,28) (4,11) (5,12) (5,24) (5,28) (6,16) (6,17) (7,15) (8,15) (10,19) (10,14) (10,24) (10,28) (11,22) (11,19) (12,13) (12,27) (12,20) (13,19) (13,20) (13,25) (14,26) (14,18) (14,24) (14,25) (17,21) (18,26) (18,27) (18,20) (18,28) (18,25) (19,26) (19,27) (19,24) (19,28) (20,27) (20,24) (24,28) (26,28)\nIs there a path between node 24 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph372-25_11", + "image": "data/connectivity/graph_visual/hard/graph372.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,15) (0,8) (0,20) (0,14) (0,1) (0,9) (0,29) (0,22) (0,28) (0,17) (0,5) (0,16) (0,2) (0,11) (0,6) (0,10) (0,31) (0,19) (1,13) (1,15) (1,8) (1,20) (1,9) (1,29) (1,7) (1,22) (1,28) (1,25) (1,12) (1,17) (1,21) (1,5) (1,16) (1,2) (1,18) (1,30) (1,11) (1,10) (1,31) (1,19) (2,13) (2,14) (2,9) (2,29) (2,22) (2,28) (2,25) (2,12) (2,27) (2,21) (2,5) (2,16) (2,18) (2,30) (2,11) (2,6) (2,10) (2,26) (2,31) (3,24) (4,13) (4,15) (4,8) (4,20) (4,14) (4,9) (4,29) (4,7) (4,22) (4,25) (4,27) (4,17) (4,16) (4,30) (4,11) (4,6) (4,10) (4,26) (5,13) (5,15) (5,20) (5,14) (5,9) (5,29) (5,7) (5,22) (5,28) (5,25) (5,12) (5,27) (5,17) (5,16) (5,18) (5,30) (5,6) (5,10) (5,26) (5,31) (5,19) (6,13) (6,15) (6,8) (6,20) (6,14) (6,9) (6,29) (6,7) (6,22) (6,28) (6,25) (6,12) (6,27) (6,17) (6,21) (6,10) (6,26) (6,19) (7,13) (7,15) (7,8) (7,28) (7,25) (7,12) (7,17) (7,18) (7,11) (7,10) (7,26) (7,31) (7,19) (8,9) (8,29) (8,22) (8,28) (8,25) (8,17) (8,21) (8,16) (8,18) (8,30) (8,11) (8,19) (9,13) (9,20) (9,14) (9,29) (9,22) (9,28) (9,25) (9,12) (9,17) (9,16) (9,30) (9,11) (9,10) (9,26) (10,13) (10,20) (10,14) (10,22) (10,28) (10,25) (10,12) (10,27) (10,17) (10,21) (10,16) (10,18) (10,11) (10,26) (10,31) (11,15) (11,14) (11,29) (11,22) (11,28) (11,25) (11,12) (11,27) (11,21) (11,16) (11,18) (11,26) (11,31) (11,19) (12,13) (12,15) (12,14) (12,29) (12,22) (12,28) (12,17) (12,16) (12,30) (12,26) (12,31) (12,19) (13,15) (13,20) (13,14) (13,29) (13,28) (13,25) (13,27) (13,16) (13,18) (13,30) (13,19) (14,29) (14,28) (14,25) (14,17) (14,21) (14,16) (14,18) (14,30) (14,26) (14,31) (14,19) (15,20) (15,29) (15,22) (15,28) (15,25) (15,27) (15,17) (15,16) (15,18) (15,31) (15,19) (16,29) (16,22) (16,28) (16,25) (16,27) (16,17) (16,21) (16,18) (16,30) (16,26) (16,31) (16,19) (17,20) (17,22) (17,28) (17,25) (17,27) (17,21) (17,18) (17,31) (18,20) (18,29) (18,22) (18,28) (18,25) (18,27) (18,21) (18,26) (18,31) (19,20) (19,29) (19,22) (19,28) (19,25) (19,27) (19,30) (19,26) (20,22) (20,28) (20,25) (20,27) (20,21) (20,30) (20,26) (20,31) (21,22) (21,28) (21,27) (21,30) (21,31) (22,29) (22,25) (22,30) (22,26) (23,24) (25,27) (25,26) (26,29) (26,30) (26,31) (27,29) (27,28) (27,30) (27,31) (28,30) (28,31) (29,30) (30,31)\nIs there a path between node 25 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph375-11_3", + "image": "data/connectivity/graph_visual/hard/graph375.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,20) (0,4) (0,29) (0,11) (0,3) (0,1) (0,22) (0,10) (0,13) (0,16) (0,19) (0,7) (0,15) (0,25) (0,2) (0,23) (0,5) (1,18) (1,12) (1,9) (1,27) (1,20) (1,14) (1,11) (1,3) (1,24) (1,28) (1,6) (1,22) (1,10) (1,13) (1,15) (1,25) (1,2) (1,23) (1,5) (1,17) (2,18) (2,12) (2,9) (2,27) (2,29) (2,14) (2,11) (2,28) (2,6) (2,22) (2,10) (2,16) (2,7) (2,15) (2,25) (2,23) (2,17) (3,9) (3,27) (3,4) (3,29) (3,11) (3,24) (3,6) (3,21) (3,22) (3,10) (3,13) (3,16) (3,19) (3,7) (3,15) (3,25) (3,23) (4,18) (4,9) (4,27) (4,29) (4,14) (4,21) (4,22) (4,16) (4,19) (4,25) (4,23) (5,9) (5,27) (5,20) (5,29) (5,14) (5,28) (5,6) (5,22) (5,13) (5,16) (5,15) (5,25) (5,23) (6,12) (6,9) (6,27) (6,20) (6,14) (6,11) (6,24) (6,21) (6,22) (6,10) (6,13) (6,16) (6,19) (6,15) (6,25) (6,23) (7,18) (7,12) (7,9) (7,27) (7,11) (7,24) (7,28) (7,21) (7,13) (7,19) (7,25) (9,18) (9,12) (9,27) (9,20) (9,14) (9,28) (9,21) (9,22) (9,10) (9,19) (9,25) (9,23) (9,17) (10,18) (10,12) (10,20) (10,29) (10,14) (10,11) (10,21) (10,22) (10,13) (10,16) (10,19) (10,15) (10,17) (11,18) (11,27) (11,20) (11,14) (11,28) (11,13) (11,19) (11,15) (11,25) (11,23) (12,27) (12,22) (12,13) (12,16) (12,19) (12,25) (12,23) (13,20) (13,14) (13,24) (13,28) (13,21) (13,22) (13,16) (13,15) (13,25) (13,23) (13,17) (14,18) (14,27) (14,20) (14,29) (14,24) (14,28) (14,21) (14,22) (14,16) (14,19) (14,25) (14,17) (15,27) (15,20) (15,29) (15,24) (15,28) (15,21) (15,22) (15,19) (15,25) (15,17) (16,18) (16,20) (16,29) (16,24) (16,22) (16,19) (16,25) (16,17) (17,18) (17,27) (17,29) (17,24) (17,28) (17,21) (17,22) (17,19) (17,25) (17,23) (18,20) (18,29) (18,24) (18,28) (18,21) (18,19) (18,23) (19,27) (19,20) (19,29) (19,24) (19,28) (19,23) (20,22) (20,25) (21,27) (21,29) (21,24) (21,28) (21,25) (21,23) (22,27) (22,24) (22,28) (22,23) (23,27) (23,29) (23,24) (23,28) (23,25) (24,27) (24,28) (25,29) (25,28) (26,31) (27,29) (27,28) (28,29) (30,31)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph306-31_26", + "image": "data/connectivity/graph_visual/hard/graph306.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,8) (0,24) (0,6) (0,14) (0,26) (0,29) (0,10) (0,27) (0,5) (1,15) (2,18) (2,3) (2,6) (2,7) (2,13) (2,17) (2,20) (3,24) (3,22) (3,21) (3,12) (3,7) (3,19) (3,13) (3,25) (5,31) (5,16) (5,22) (5,7) (5,9) (5,14) (5,26) (5,25) (5,29) (5,30) (6,12) (6,14) (6,17) (6,20) (6,29) (6,27) (7,8) (7,18) (7,22) (7,28) (7,14) (7,26) (7,25) (7,30) (8,16) (8,9) (8,14) (8,19) (8,10) (9,31) (9,16) (9,21) (9,12) (9,13) (9,27) (10,31) (10,26) (10,17) (10,25) (10,29) (12,18) (12,26) (12,20) (13,28) (13,26) (13,29) (14,24) (14,21) (14,26) (14,17) (14,29) (15,23) (16,24) (16,31) (16,21) (16,26) (16,20) (16,29) (16,30) (17,31) (17,22) (17,19) (17,20) (17,29) (18,22) (18,21) (18,25) (18,29) (19,31) (19,22) (19,26) (19,20) (19,30) (20,25) (21,25) (22,26) (24,28) (25,28) (25,29) (25,27) (25,30) (27,31) (28,31)\nIs there a path between node 31 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph45-10_6", + "image": "data/connectivity/graph_visual/hard/graph45.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,18) (0,10) (0,23) (0,3) (0,9) (0,26) (1,8) (1,20) (1,6) (1,4) (1,19) (1,16) (1,13) (1,24) (2,8) (2,20) (2,4) (2,19) (2,16) (2,13) (2,24) (2,12) (3,10) (3,9) (3,21) (3,22) (4,6) (4,19) (4,13) (4,24) (4,12) (5,15) (5,25) (5,11) (5,7) (6,8) (6,20) (6,19) (6,16) (6,13) (6,24) (7,15) (7,25) (7,14) (8,19) (8,13) (8,24) (8,12) (9,18) (9,23) (10,18) (10,23) (10,21) (10,26) (11,15) (11,17) (11,25) (12,20) (12,19) (12,16) (12,24) (13,20) (13,19) (13,16) (13,24) (14,17) (14,25) (15,17) (15,25) (16,20) (16,24) (17,25) (18,21) (18,22) (19,20) (19,24) (20,24) (21,23) (22,23) (22,26) (23,26)\nIs there a path between node 10 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph680-8_4", + "image": "data/connectivity/graph_visual/hard/graph680.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,21) (0,4) (0,30) (0,19) (0,26) (1,27) (1,21) (1,32) (1,8) (1,34) (1,3) (2,27) (2,11) (2,7) (2,30) (2,9) (2,13) (2,26) (3,32) (3,4) (3,18) (3,8) (3,30) (3,31) (3,33) (3,26) (4,11) (4,21) (4,32) (4,8) (4,30) (4,9) (4,13) (5,29) (5,23) (5,17) (6,25) (6,29) (6,23) (6,22) (7,28) (7,8) (7,31) (7,26) (8,15) (8,28) (8,18) (8,33) (8,26) (9,27) (9,21) (9,24) (9,19) (9,33) (10,14) (11,31) (11,13) (11,20) (12,14) (12,23) (13,16) (13,34) (13,31) (14,25) (14,29) (14,23) (15,28) (15,30) (16,21) (16,32) (16,18) (16,34) (16,33) (17,25) (18,21) (18,32) (18,30) (18,19) (19,28) (19,31) (20,27) (20,30) (20,34) (20,31) (20,33) (21,27) (21,30) (21,31) (21,33) (24,28) (26,32) (26,34) (26,31) (27,28) (27,30) (27,33) (28,30) (28,34) (28,33) (31,33) (32,34) (32,33) (33,34)\nIs there a path between node 8 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph59-15_17", + "image": "data/connectivity/graph_visual/hard/graph59.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,4) (0,22) (0,15) (0,18) (0,14) (0,5) (0,2) (0,13) (1,16) (1,20) (1,6) (1,24) (1,8) (1,21) (1,23) (2,4) (2,22) (2,15) (2,25) (2,14) (2,19) (2,5) (2,3) (3,4) (3,22) (3,15) (3,18) (3,25) (3,19) (3,5) (3,13) (4,22) (4,15) (4,26) (4,25) (4,14) (4,13) (5,22) (5,15) (5,26) (5,18) (5,25) (5,14) (5,19) (5,13) (6,16) (6,17) (6,20) (6,9) (6,7) (6,24) (6,12) (6,11) (7,16) (7,17) (7,20) (7,9) (7,24) (7,8) (7,10) (7,23) (8,16) (8,17) (8,20) (8,9) (8,24) (8,12) (8,21) (8,10) (9,16) (9,17) (9,20) (9,24) (9,11) (9,21) (9,23) (10,16) (10,17) (10,20) (10,24) (10,12) (10,21) (11,16) (11,12) (11,21) (11,23) (12,16) (12,17) (12,20) (12,21) (13,22) (13,15) (13,26) (13,25) (13,14) (13,19) (14,22) (14,15) (14,26) (14,18) (14,25) (14,19) (15,26) (15,19) (16,17) (16,20) (16,21) (16,23) (17,20) (17,21) (18,22) (18,26) (18,25) (18,19) (19,22) (19,26) (19,25) (20,24) (21,24) (21,23) (22,26) (22,25) (23,24) (25,26)\nIs there a path between node 15 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph120-19_17", + "image": "data/connectivity/graph_visual/hard/graph120.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,22) (0,13) (0,25) (2,21) (2,6) (2,3) (3,27) (3,24) (4,14) (4,21) (4,27) (5,17) (6,27) (7,18) (7,22) (8,18) (8,26) (8,20) (9,15) (10,22) (10,12) (10,16) (10,25) (12,18) (12,15) (12,26) (13,22) (13,26) (13,20) (14,21) (14,19) (15,22) (17,19) (17,23) (18,22) (19,21) (20,26) (21,27) (21,23)\nIs there a path between node 19 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph413-31_8", + "image": "data/connectivity/graph_visual/hard/graph413.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,21) (0,3) (0,26) (0,18) (0,27) (2,20) (2,21) (2,28) (2,27) (3,30) (4,16) (4,15) (6,12) (8,21) (8,14) (8,18) (9,10) (10,12) (10,15) (10,32) (11,20) (11,21) (11,28) (11,25) (12,16) (12,32) (14,20) (14,23) (14,26) (14,27) (14,17) (15,32) (17,30) (17,21) (17,29) (17,27) (18,30) (18,27) (19,22) (20,23) (20,29) (23,25) (23,29) (25,27) (26,27) (27,30) (28,30)\nIs there a path between node 31 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph572-1_24", + "image": "data/connectivity/graph_visual/hard/graph572.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,10) (0,4) (1,15) (1,11) (1,24) (1,5) (2,6) (2,7) (2,9) (2,30) (3,9) (3,20) (3,14) (3,23) (3,18) (4,10) (4,6) (4,29) (4,9) (4,17) (4,8) (4,23) (4,18) (4,30) (5,15) (5,22) (5,24) (6,10) (6,7) (6,14) (6,21) (6,30) (7,28) (7,29) (7,9) (7,27) (7,17) (7,21) (7,30) (8,10) (8,9) (8,27) (8,14) (8,23) (8,21) (9,10) (9,28) (9,27) (9,17) (10,28) (10,29) (10,18) (12,16) (12,31) (12,33) (13,19) (14,27) (14,17) (14,18) (15,24) (16,31) (16,33) (16,24) (17,29) (18,28) (18,30) (19,22) (20,27) (20,21) (21,28) (22,33) (22,24) (24,31) (24,33) (25,26)\nIs there a path between node 1 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph682-3_28", + "image": "data/connectivity/graph_visual/hard/graph682.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,8) (0,28) (0,29) (0,16) (0,5) (0,6) (0,12) (0,15) (1,28) (1,18) (1,4) (1,3) (1,21) (1,14) (1,12) (2,22) (3,8) (3,29) (3,33) (3,5) (3,21) (3,30) (3,26) (3,14) (3,7) (3,31) (3,24) (3,12) (3,32) (4,17) (4,5) (4,34) (4,12) (4,32) (4,19) (5,18) (5,16) (5,33) (5,21) (5,6) (5,30) (5,20) (5,11) (6,27) (6,17) (6,26) (6,7) (6,24) (6,15) (7,28) (7,18) (7,29) (7,17) (7,21) (7,26) (7,14) (7,11) (7,32) (8,28) (8,18) (8,29) (8,34) (8,10) (8,30) (8,26) (8,23) (8,14) (8,20) (10,21) (10,30) (10,14) (10,24) (10,20) (10,12) (10,11) (11,16) (11,34) (11,30) (11,14) (11,24) (11,20) (12,27) (12,28) (12,29) (12,17) (12,16) (12,20) (12,32) (12,19) (13,27) (13,17) (13,16) (13,33) (13,23) (13,14) (13,24) (14,33) (14,34) (14,21) (14,30) (14,20) (14,32) (14,19) (14,15) (15,18) (15,29) (15,21) (15,30) (15,23) (16,27) (16,18) (16,17) (16,24) (17,28) (17,33) (17,34) (17,31) (17,32) (18,33) (18,34) (18,21) (18,30) (18,23) (18,24) (18,32) (19,29) (19,33) (19,21) (19,26) (19,32) (20,28) (20,29) (20,33) (20,30) (21,29) (21,33) (21,26) (23,33) (24,27) (24,29) (24,33) (24,30) (24,26) (26,28) (26,29) (27,29) (28,31) (28,32) (29,32)\nIs there a path between node 3 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph68-15_6", + "image": "data/connectivity/graph_visual/hard/graph68.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,24) (0,11) (0,6) (1,22) (1,26) (1,12) (2,14) (2,11) (2,4) (3,21) (3,11) (3,18) (3,9) (4,17) (4,21) (4,14) (5,7) (5,25) (5,10) (5,20) (6,16) (7,15) (7,26) (8,20) (9,17) (9,23) (9,24) (9,13) (9,11) (9,18) (10,25) (11,14) (12,20) (13,17) (13,21) (13,24) (13,19) (14,18) (15,25) (16,23) (16,21) (18,23) (19,23) (19,24) (20,26) (21,24) (22,25)\nIs there a path between node 15 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph613-12_9", + "image": "data/connectivity/graph_visual/hard/graph613.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,13) (0,19) (0,6) (0,21) (0,10) (0,31) (0,16) (0,7) (0,20) (0,8) (0,17) (0,12) (0,3) (0,11) (0,23) (0,2) (0,22) (0,1) (0,18) (1,33) (1,32) (1,13) (1,19) (1,29) (1,26) (1,27) (1,6) (1,21) (1,10) (1,31) (1,16) (1,28) (1,7) (1,20) (1,8) (1,17) (1,12) (1,3) (1,2) (1,14) (1,22) (1,18) (1,5) (2,33) (2,13) (2,19) (2,29) (2,26) (2,27) (2,6) (2,10) (2,31) (2,16) (2,28) (2,7) (2,20) (2,24) (2,8) (2,17) (2,12) (2,22) (2,18) (3,32) (3,29) (3,27) (3,6) (3,21) (3,31) (3,16) (3,28) (3,7) (3,20) (3,8) (3,12) (3,23) (3,14) (3,22) (3,18) (3,5) (4,25) (4,34) (5,33) (5,32) (5,13) (5,19) (5,29) (5,26) (5,27) (5,6) (5,21) (5,10) (5,31) (5,16) (5,28) (5,20) (5,8) (5,12) (5,11) (5,23) (5,14) (5,22) (5,18) (6,32) (6,13) (6,19) (6,26) (6,27) (6,21) (6,10) (6,16) (6,28) (6,7) (6,20) (6,17) (6,12) (6,11) (6,23) (6,14) (6,22) (6,18) (7,32) (7,13) (7,29) (7,27) (7,21) (7,10) (7,16) (7,28) (7,20) (7,24) (7,17) (7,12) (7,11) (7,23) (7,14) (7,22) (7,18) (8,33) (8,32) (8,13) (8,19) (8,29) (8,26) (8,21) (8,10) (8,31) (8,16) (8,28) (8,20) (8,24) (8,17) (8,12) (8,11) (8,23) (8,14) (8,22) (8,18) (9,25) (9,34) (9,15) (9,30) (10,33) (10,32) (10,13) (10,19) (10,29) (10,26) (10,27) (10,16) (10,28) (10,12) (10,11) (10,14) (10,22) (11,33) (11,32) (11,13) (11,19) (11,29) (11,21) (11,28) (11,20) (11,24) (11,17) (11,12) (11,23) (11,14) (11,22) (11,18) (12,33) (12,32) (12,13) (12,19) (12,29) (12,26) (12,31) (12,16) (12,28) (12,20) (12,23) (12,18) (13,33) (13,32) (13,19) (13,29) (13,26) (13,27) (13,21) (13,31) (13,16) (13,28) (13,20) (13,17) (13,23) (13,14) (13,18) (14,33) (14,32) (14,19) (14,29) (14,26) (14,27) (14,21) (14,31) (14,16) (14,28) (14,20) (14,17) (14,22) (15,25) (15,30) (16,33) (16,32) (16,19) (16,29) (16,26) (16,27) (16,21) (16,31) (16,28) (16,20) (16,24) (16,17) (16,23) (16,22) (17,33) (17,32) (17,19) (17,29) (17,21) (17,28) (17,20) (17,24) (17,23) (17,22) (17,18) (18,32) (18,19) (18,29) (18,26) (18,27) (18,21) (18,31) (18,28) (18,24) (18,23) (18,22) (19,29) (19,27) (19,21) (19,31) (19,28) (19,20) (19,23) (20,33) (20,29) (20,26) (20,31) (20,28) (20,22) (21,33) (21,32) (21,29) (21,31) (21,24) (21,23) (22,29) (22,31) (22,24) (23,29) (23,26) (23,27) (23,31) (23,28) (23,24) (24,32) (24,26) (24,27) (24,31) (25,34) (26,32) (26,29) (26,27) (26,31) (26,28) (27,33) (27,29) (27,31) (28,33) (28,31) (29,33) (29,32) (30,34) (31,33) (31,32) (32,33)\nIs there a path between node 12 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph282-17_1", + "image": "data/connectivity/graph_visual/hard/graph282.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,13) (0,28) (0,2) (0,25) (0,9) (0,3) (0,1) (0,19) (0,23) (0,29) (0,16) (0,8) (0,27) (0,14) (0,22) (1,28) (1,2) (1,25) (1,9) (1,11) (1,3) (1,10) (1,20) (1,19) (1,29) (1,16) (1,8) (1,14) (1,26) (1,22) (1,4) (2,28) (2,25) (2,11) (2,10) (2,20) (2,19) (2,23) (2,29) (2,8) (2,21) (2,22) (3,13) (3,25) (3,9) (3,11) (3,20) (3,23) (3,29) (3,27) (3,26) (3,21) (3,22) (3,4) (4,25) (4,9) (4,11) (4,10) (4,20) (4,23) (4,29) (4,16) (4,14) (4,21) (4,22) (5,24) (6,12) (6,15) (6,18) (7,12) (7,18) (8,13) (8,28) (8,25) (8,9) (8,11) (8,10) (8,20) (8,23) (8,29) (8,16) (8,27) (8,26) (9,13) (9,28) (9,25) (9,10) (9,20) (9,19) (9,23) (9,29) (9,16) (9,27) (9,14) (9,26) (9,21) (9,22) (10,13) (10,28) (10,25) (10,11) (10,20) (10,19) (10,23) (10,29) (10,16) (10,27) (10,14) (10,21) (10,22) (11,13) (11,25) (11,20) (11,19) (11,23) (11,29) (11,16) (11,27) (11,14) (11,26) (11,21) (11,22) (12,15) (12,18) (13,28) (13,25) (13,20) (13,19) (13,29) (13,14) (13,26) (13,22) (14,20) (14,19) (14,23) (14,29) (14,27) (14,26) (14,22) (15,18) (16,28) (16,25) (16,20) (16,23) (16,27) (16,26) (16,22) (17,30) (17,24) (19,28) (19,25) (19,23) (19,27) (19,26) (19,21) (19,22) (20,28) (20,25) (20,29) (20,26) (20,21) (20,22) (21,25) (21,23) (21,27) (21,22) (22,28) (22,29) (22,27) (22,26) (23,28) (23,25) (23,29) (23,27) (24,30) (25,28) (25,29) (25,27) (25,26) (26,28) (26,29) (27,28) (27,29) (28,29)\nIs there a path between node 17 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph544-23_14", + "image": "data/connectivity/graph_visual/hard/graph544.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,11) (0,20) (0,7) (0,4) (0,24) (0,13) (0,18) (0,31) (0,32) (0,1) (0,28) (0,3) (0,29) (0,25) (0,16) (0,19) (1,11) (1,17) (1,20) (1,5) (1,4) (1,13) (1,18) (1,31) (1,32) (1,27) (1,3) (1,16) (1,19) (2,33) (2,12) (3,8) (3,11) (3,17) (3,20) (3,4) (3,24) (3,13) (3,18) (3,31) (3,32) (3,14) (3,28) (3,29) (3,16) (3,19) (4,8) (4,11) (4,15) (4,5) (4,7) (4,24) (4,13) (4,18) (4,31) (4,32) (4,14) (4,28) (4,30) (4,29) (4,25) (4,26) (5,17) (5,20) (5,13) (5,31) (5,14) (5,30) (5,29) (5,25) (5,16) (5,26) (5,19) (6,21) (6,9) (7,8) (7,17) (7,20) (7,15) (7,24) (7,32) (7,14) (7,30) (7,29) (7,26) (8,11) (8,17) (8,20) (8,15) (8,24) (8,18) (8,27) (8,14) (8,28) (8,29) (8,26) (9,23) (9,21) (9,10) (10,23) (10,21) (11,17) (11,20) (11,24) (11,13) (11,31) (11,32) (11,14) (11,28) (11,29) (11,16) (11,26) (13,24) (13,27) (13,14) (13,29) (13,16) (13,26) (13,19) (14,17) (14,20) (14,15) (14,24) (14,18) (14,31) (14,32) (14,27) (14,28) (14,30) (14,29) (14,25) (14,19) (15,17) (15,20) (15,24) (15,18) (15,31) (15,32) (15,27) (15,28) (15,29) (15,25) (15,16) (15,26) (15,19) (16,17) (16,20) (16,24) (16,32) (16,27) (16,28) (16,30) (16,29) (16,25) (16,26) (17,24) (17,18) (17,31) (17,32) (17,28) (17,29) (17,25) (17,26) (17,19) (18,20) (18,31) (18,32) (18,27) (18,28) (18,29) (18,25) (18,26) (18,19) (19,20) (19,24) (19,32) (19,28) (19,29) (19,25) (20,24) (20,31) (20,32) (20,27) (20,28) (20,30) (20,29) (20,26) (21,23) (24,31) (24,32) (24,27) (24,28) (24,30) (24,29) (24,25) (25,31) (25,32) (25,27) (25,29) (25,26) (26,31) (26,32) (26,28) (27,32) (27,28) (28,32) (28,30) (29,32) (29,30) (30,31) (30,32) (31,32)\nIs there a path between node 23 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph36-24_15", + "image": "data/connectivity/graph_visual/hard/graph36.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,19) (0,18) (0,23) (0,22) (0,1) (0,21) (0,24) (0,7) (0,4) (0,3) (0,15) (0,12) (0,5) (1,22) (1,7) (1,4) (1,15) (1,12) (2,17) (2,9) (2,11) (2,25) (2,14) (3,19) (3,22) (3,21) (3,7) (3,4) (3,15) (3,12) (3,5) (4,19) (4,23) (4,7) (4,15) (4,12) (4,5) (5,19) (5,23) (5,22) (5,21) (5,7) (5,12) (6,20) (7,19) (7,23) (7,24) (7,15) (7,12) (8,10) (8,13) (9,17) (9,11) (9,25) (9,16) (10,13) (10,20) (11,17) (11,16) (11,14) (12,18) (12,22) (12,21) (12,15) (13,20) (14,25) (14,16) (15,19) (15,18) (15,23) (15,22) (15,21) (15,24) (16,17) (16,25) (17,25) (18,19) (18,23) (18,22) (18,21) (18,24) (19,23) (19,21) (19,24) (21,23) (21,22) (21,24) (22,24) (23,24)\nIs there a path between node 24 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph388-22_14", + "image": "data/connectivity/graph_visual/hard/graph388.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,17) (0,10) (0,28) (0,30) (0,29) (0,3) (1,14) (1,2) (2,25) (2,20) (2,7) (2,32) (2,22) (3,24) (3,19) (3,23) (3,4) (3,12) (3,29) (4,26) (4,24) (4,23) (4,8) (4,13) (5,26) (5,19) (5,23) (5,8) (5,15) (5,21) (6,14) (7,32) (8,16) (8,12) (8,29) (9,26) (9,13) (9,18) (9,29) (9,31) (10,17) (10,11) (10,30) (10,23) (10,13) (11,16) (11,17) (11,19) (11,28) (11,23) (12,26) (12,24) (12,21) (13,26) (13,17) (13,19) (13,30) (13,31) (14,25) (14,22) (15,16) (15,17) (15,23) (15,18) (15,29) (16,26) (16,24) (16,18) (16,21) (17,24) (17,19) (17,28) (17,30) (17,23) (18,24) (18,21) (19,26) (19,24) (19,28) (19,23) (20,32) (22,32) (22,27) (24,26) (24,30) (26,29) (28,29)\nIs there a path between node 22 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph306-14_23", + "image": "data/connectivity/graph_visual/hard/graph306.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,8) (0,24) (0,6) (0,14) (0,26) (0,29) (0,10) (0,27) (0,5) (1,15) (2,18) (2,3) (2,6) (2,7) (2,13) (2,17) (2,20) (3,24) (3,22) (3,21) (3,12) (3,7) (3,19) (3,13) (3,25) (5,31) (5,16) (5,22) (5,7) (5,9) (5,14) (5,26) (5,25) (5,29) (5,30) (6,12) (6,14) (6,17) (6,20) (6,29) (6,27) (7,8) (7,18) (7,22) (7,28) (7,14) (7,26) (7,25) (7,30) (8,16) (8,9) (8,14) (8,19) (8,10) (9,31) (9,16) (9,21) (9,12) (9,13) (9,27) (10,31) (10,26) (10,17) (10,25) (10,29) (12,18) (12,26) (12,20) (13,28) (13,26) (13,29) (14,24) (14,21) (14,26) (14,17) (14,29) (15,23) (16,24) (16,31) (16,21) (16,26) (16,20) (16,29) (16,30) (17,31) (17,22) (17,19) (17,20) (17,29) (18,22) (18,21) (18,25) (18,29) (19,31) (19,22) (19,26) (19,20) (19,30) (20,25) (21,25) (22,26) (24,28) (25,28) (25,29) (25,27) (25,30) (27,31) (28,31)\nIs there a path between node 14 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph398-16_11", + "image": "data/connectivity/graph_visual/hard/graph398.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,27) (0,2) (0,28) (0,32) (0,14) (0,1) (0,10) (1,30) (1,20) (1,2) (1,28) (1,32) (1,12) (1,16) (2,30) (2,8) (2,26) (2,16) (2,17) (2,3) (3,20) (3,4) (3,5) (3,28) (3,16) (3,10) (4,8) (4,27) (4,20) (4,28) (4,26) (4,25) (4,17) (5,30) (5,21) (5,31) (5,26) (5,25) (5,18) (6,29) (6,13) (7,22) (8,24) (8,32) (8,12) (8,26) (8,23) (8,18) (9,13) (10,30) (10,24) (10,27) (10,15) (10,12) (10,19) (11,22) (12,15) (12,26) (12,17) (14,30) (14,26) (14,16) (14,19) (15,30) (15,31) (15,32) (15,23) (15,19) (16,27) (16,28) (16,31) (16,32) (16,25) (16,23) (17,24) (17,27) (18,24) (18,28) (18,32) (18,23) (18,19) (19,20) (19,28) (20,24) (20,21) (20,26) (20,25) (21,28) (21,32) (21,26) (21,23) (22,29) (23,24) (23,28) (23,31) (24,30) (24,28) (24,26) (26,32) (30,31)\nIs there a path between node 16 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph145-2_9", + "image": "data/connectivity/graph_visual/hard/graph145.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,3) (0,24) (0,15) (0,16) (0,19) (0,7) (0,25) (0,26) (1,28) (1,23) (3,6) (3,18) (3,11) (3,24) (3,22) (3,4) (3,7) (3,25) (4,27) (4,24) (4,22) (4,12) (4,21) (4,16) (4,19) (5,6) (5,13) (5,22) (5,12) (5,16) (6,11) (6,21) (6,15) (6,25) (6,26) (7,14) (7,25) (8,23) (9,11) (9,13) (10,11) (10,15) (10,19) (11,27) (11,18) (11,22) (11,12) (11,21) (11,19) (11,25) (12,27) (12,14) (13,27) (13,18) (13,14) (13,21) (14,18) (14,24) (14,15) (15,22) (15,16) (15,26) (16,18) (16,22) (17,28) (17,23) (17,20) (18,27) (19,27) (19,24) (21,26) (22,25) (22,26) (23,28) (24,25) (24,26)\nIs there a path between node 2 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph315-23_16", + "image": "data/connectivity/graph_visual/hard/graph315.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,14) (0,31) (0,28) (0,20) (0,26) (0,13) (0,2) (1,7) (1,10) (2,14) (2,17) (2,31) (2,9) (2,15) (2,13) (2,16) (3,21) (3,29) (3,12) (3,15) (3,24) (3,16) (3,27) (4,14) (4,22) (4,15) (4,19) (4,26) (4,24) (4,16) (5,7) (5,18) (5,10) (6,25) (6,10) (7,25) (7,18) (8,11) (9,14) (9,17) (9,31) (9,28) (9,12) (9,20) (9,24) (11,30) (11,25) (11,18) (12,14) (12,21) (13,14) (13,17) (13,29) (13,23) (13,15) (13,20) (13,16) (14,21) (14,29) (14,24) (15,29) (15,28) (15,19) (15,26) (15,27) (16,29) (16,23) (16,19) (16,24) (17,29) (17,22) (17,24) (18,25) (19,24) (20,23) (20,26) (20,27) (21,28) (21,24) (23,31) (23,26) (23,27) (24,28) (24,26)\nIs there a path between node 23 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph8-21_20", + "image": "data/connectivity/graph_visual/hard/graph8.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,15) (0,14) (1,20) (2,24) (2,3) (2,13) (4,8) (4,6) (4,11) (4,5) (5,19) (5,21) (5,23) (6,19) (6,20) (7,14) (7,10) (8,21) (9,19) (9,11) (10,15) (10,22) (11,23) (12,18) (13,24) (13,25) (14,22) (15,22) (18,25) (19,20) (21,23)\nIs there a path between node 21 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph266-22_26", + "image": "data/connectivity/graph_visual/hard/graph266.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,20) (0,12) (0,25) (0,2) (0,23) (0,17) (0,28) (0,5) (0,10) (0,19) (1,30) (1,9) (1,15) (1,6) (1,10) (1,18) (2,20) (2,12) (2,8) (2,21) (2,28) (2,22) (2,10) (2,3) (2,4) (2,18) (3,25) (3,13) (3,21) (3,28) (3,29) (3,4) (3,18) (4,25) (4,30) (4,13) (4,23) (4,17) (4,28) (4,5) (4,15) (4,14) (4,7) (4,18) (5,20) (5,12) (5,30) (5,13) (5,9) (5,28) (5,16) (5,14) (5,11) (6,12) (6,25) (6,13) (6,21) (6,29) (6,19) (7,13) (7,8) (7,23) (7,28) (7,29) (8,27) (8,21) (8,23) (8,28) (8,22) (8,18) (9,20) (9,12) (9,18) (10,13) (10,22) (10,14) (10,29) (11,20) (11,13) (11,17) (11,15) (12,25) (12,23) (12,28) (12,18) (13,30) (13,27) (13,21) (13,16) (13,14) (14,30) (14,21) (14,16) (14,29) (14,19) (15,20) (15,30) (15,23) (16,20) (16,25) (16,21) (16,28) (17,20) (17,30) (17,28) (18,30) (18,27) (18,23) (18,22) (18,29) (19,23) (19,29) (20,30) (20,23) (20,29) (21,28) (22,29) (23,25) (23,30) (23,28) (25,29) (27,28) (28,30) (29,30)\nIs there a path between node 22 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph27-7_15", + "image": "data/connectivity/graph_visual/hard/graph27.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,17) (0,6) (0,9) (0,20) (0,21) (2,5) (2,9) (2,20) (2,7) (2,21) (3,5) (3,24) (3,6) (3,4) (3,25) (3,19) (3,8) (4,12) (4,6) (5,17) (5,11) (5,9) (5,19) (6,14) (6,20) (6,7) (6,13) (7,11) (7,25) (7,20) (8,12) (8,19) (8,13) (9,12) (9,14) (9,17) (9,25) (9,19) (9,21) (10,23) (12,14) (12,24) (12,17) (12,13) (13,14) (13,24) (13,20) (14,21) (15,16) (17,24) (17,25) (17,19) (18,23) (19,20) (21,25)\nIs there a path between node 7 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph352-31_25", + "image": "data/connectivity/graph_visual/hard/graph352.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,20) (0,30) (0,29) (0,2) (0,15) (0,19) (0,6) (0,23) (2,20) (2,13) (2,16) (2,6) (2,23) (3,14) (3,9) (3,28) (3,10) (3,12) (4,25) (4,28) (4,10) (5,25) (5,31) (5,10) (6,20) (6,7) (6,30) (6,27) (6,23) (7,26) (7,27) (8,26) (8,16) (8,11) (9,18) (9,25) (9,21) (10,14) (10,24) (10,21) (11,30) (11,23) (12,14) (12,24) (12,28) (12,21) (13,30) (13,16) (13,22) (13,19) (14,21) (15,26) (15,29) (15,16) (15,22) (15,27) (15,17) (16,26) (16,22) (16,27) (16,17) (17,29) (17,27) (17,23) (18,24) (19,26) (19,22) (22,26) (22,29) (23,30) (23,29) (25,28) (26,27) (28,31)\nIs there a path between node 31 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph10-3_0", + "image": "data/connectivity/graph_visual/hard/graph10.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,4) (0,16) (0,25) (0,14) (0,21) (0,11) (0,9) (0,5) (0,23) (0,6) (1,4) (1,16) (1,14) (1,13) (1,21) (1,11) (1,9) (1,10) (1,5) (1,23) (1,15) (1,20) (1,6) (2,18) (2,4) (2,16) (2,25) (2,14) (2,21) (2,9) (2,10) (2,5) (2,15) (2,20) (2,6) (3,12) (3,19) (3,24) (3,17) (3,7) (3,22) (3,8) (4,16) (4,25) (4,14) (4,21) (4,11) (4,9) (4,10) (4,5) (4,23) (4,15) (4,20) (4,6) (5,18) (5,16) (5,25) (5,13) (5,21) (5,11) (5,10) (5,15) (5,6) (6,18) (6,16) (6,25) (6,14) (6,13) (6,21) (6,11) (6,9) (6,10) (6,23) (6,20) (7,12) (7,24) (7,17) (7,22) (8,12) (8,19) (9,18) (9,25) (9,14) (9,13) (9,21) (9,11) (9,10) (9,23) (9,20) (10,18) (10,16) (10,25) (10,14) (10,21) (10,11) (10,15) (11,18) (11,16) (11,25) (11,14) (11,21) (11,23) (12,19) (12,24) (12,17) (12,22) (13,16) (13,14) (13,21) (13,23) (13,20) (14,18) (14,25) (14,20) (15,18) (15,16) (15,25) (15,21) (15,23) (15,20) (16,18) (16,25) (16,23) (17,19) (17,24) (17,22) (18,25) (18,21) (18,23) (19,22) (20,25) (20,21) (21,25) (21,23) (22,24) (23,25)\nIs there a path between node 3 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph696-24_6", + "image": "data/connectivity/graph_visual/hard/graph696.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,18) (0,15) (0,33) (0,8) (0,1) (0,24) (0,17) (0,4) (0,31) (0,12) (0,26) (0,14) (0,30) (0,32) (0,29) (0,2) (1,25) (1,19) (1,33) (1,8) (1,21) (1,24) (1,17) (1,4) (1,31) (1,12) (1,27) (1,10) (1,26) (1,14) (1,30) (1,29) (1,5) (1,3) (1,22) (2,18) (2,15) (2,19) (2,33) (2,8) (2,24) (2,17) (2,4) (2,27) (2,7) (2,10) (2,26) (2,14) (2,34) (2,30) (2,16) (2,29) (2,3) (2,22) (3,18) (3,33) (3,8) (3,21) (3,17) (3,4) (3,31) (3,12) (3,27) (3,7) (3,10) (3,26) (3,14) (3,34) (3,30) (3,29) (4,18) (4,25) (4,19) (4,33) (4,8) (4,21) (4,17) (4,27) (4,7) (4,10) (4,14) (4,30) (4,32) (4,16) (4,29) (4,5) (4,22) (5,15) (5,25) (5,8) (5,21) (5,17) (5,31) (5,26) (5,34) (5,30) (5,32) (5,16) (5,29) (6,23) (6,28) (6,9) (6,13) (7,18) (7,15) (7,25) (7,8) (7,21) (7,24) (7,17) (7,27) (7,10) (7,34) (7,30) (7,32) (7,16) (7,29) (7,22) (8,18) (8,15) (8,19) (8,21) (8,24) (8,17) (8,31) (8,27) (8,10) (8,26) (8,34) (8,30) (8,32) (8,16) (8,29) (8,22) (9,28) (9,20) (9,13) (9,11) (10,18) (10,15) (10,19) (10,21) (10,31) (10,12) (10,27) (10,26) (10,14) (10,30) (10,16) (10,29) (11,23) (11,28) (12,18) (12,15) (12,25) (12,19) (12,33) (12,24) (12,31) (12,27) (12,14) (12,34) (12,30) (12,32) (12,29) (12,22) (13,23) (13,28) (13,20) (14,18) (14,15) (14,25) (14,19) (14,21) (14,24) (14,17) (14,31) (14,27) (14,26) (14,30) (14,32) (14,16) (14,29) (14,22) (15,18) (15,25) (15,24) (15,17) (15,31) (15,27) (15,26) (15,30) (15,32) (15,16) (15,29) (16,18) (16,25) (16,19) (16,33) (16,21) (16,17) (16,27) (16,26) (16,30) (16,32) (16,29) (16,22) (17,18) (17,25) (17,19) (17,33) (17,24) (17,31) (17,27) (17,26) (17,30) (17,32) (17,29) (18,25) (18,19) (18,33) (18,21) (18,31) (18,27) (18,26) (18,34) (18,30) (18,32) (18,29) (19,33) (19,21) (19,31) (19,27) (19,26) (19,34) (19,30) (19,32) (19,22) (20,23) (20,28) (21,25) (21,24) (21,31) (21,27) (21,26) (21,34) (21,32) (21,29) (22,33) (22,31) (22,26) (22,34) (22,32) (22,29) (24,25) (24,31) (24,26) (24,34) (24,30) (24,29) (25,33) (25,31) (25,27) (25,34) (25,30) (25,32) (25,29) (26,31) (26,34) (26,30) (27,33) (27,34) (29,33) (29,31) (29,34) (29,30) (30,33) (30,31) (30,34) (30,32) (31,34) (31,32) (32,33) (33,34)\nIs there a path between node 24 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph652-26_34", + "image": "data/connectivity/graph_visual/hard/graph652.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,33) (0,8) (0,17) (0,12) (0,13) (0,3) (0,6) (0,27) (0,15) (0,11) (0,29) (0,7) (0,19) (0,1) (0,25) (1,33) (1,8) (1,4) (1,13) (1,3) (1,6) (1,27) (1,15) (1,11) (1,10) (1,25) (1,31) (2,24) (2,21) (2,23) (3,8) (3,17) (3,12) (3,4) (3,13) (3,6) (3,27) (3,11) (3,29) (3,7) (3,19) (3,10) (3,31) (4,13) (4,6) (4,27) (4,7) (4,19) (4,10) (4,25) (5,30) (5,22) (5,18) (5,14) (6,33) (6,17) (6,12) (6,13) (6,27) (6,15) (6,11) (6,29) (6,7) (6,10) (6,25) (6,31) (7,8) (7,17) (7,15) (7,11) (7,29) (7,19) (7,31) (8,33) (8,12) (8,13) (8,15) (8,19) (8,25) (8,31) (9,16) (9,26) (9,32) (9,28) (9,20) (10,33) (10,17) (10,12) (10,13) (10,27) (10,15) (10,29) (10,19) (10,25) (11,33) (11,17) (11,13) (11,15) (11,29) (11,19) (11,25) (11,31) (12,33) (12,17) (12,13) (12,27) (12,15) (12,29) (12,19) (12,25) (12,31) (13,33) (13,27) (13,15) (13,19) (13,31) (14,30) (14,22) (14,18) (15,33) (15,27) (15,29) (15,19) (15,25) (15,31) (16,26) (16,32) (17,29) (18,22) (19,33) (19,27) (19,31) (20,26) (20,32) (20,28) (20,34) (21,24) (21,23) (22,30) (23,24) (25,27) (25,31) (26,32) (26,34) (27,33) (27,29) (27,31) (28,34) (29,33) (31,33) (32,34)\nIs there a path between node 26 and node 34 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph593-32_26", + "image": "data/connectivity/graph_visual/hard/graph593.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,3) (0,18) (0,13) (0,17) (0,4) (0,15) (0,28) (0,19) (0,14) (0,31) (0,25) (0,29) (0,30) (0,26) (0,2) (0,23) (0,5) (0,8) (1,3) (1,18) (1,13) (1,17) (1,15) (1,28) (1,19) (1,14) (1,25) (1,2) (1,23) (1,5) (1,8) (2,18) (2,13) (2,17) (2,28) (2,14) (2,29) (2,30) (2,23) (2,5) (2,32) (2,8) (3,13) (3,4) (3,15) (3,28) (3,19) (3,14) (3,31) (3,29) (3,10) (3,30) (3,5) (3,32) (4,18) (4,13) (4,17) (4,15) (4,28) (4,31) (4,25) (4,29) (4,10) (4,30) (4,26) (4,5) (4,22) (4,32) (4,8) (5,13) (5,28) (5,19) (5,14) (5,25) (5,29) (5,10) (5,30) (5,26) (5,23) (5,22) (5,8) (6,16) (6,27) (6,9) (6,21) (6,12) (6,11) (6,20) (7,16) (7,27) (7,33) (7,9) (7,21) (7,12) (7,11) (8,13) (8,17) (8,15) (8,14) (8,25) (8,29) (8,10) (8,30) (8,23) (9,16) (9,27) (9,33) (9,21) (9,12) (9,20) (10,13) (10,17) (10,15) (10,28) (10,14) (10,25) (10,23) (10,22) (10,32) (11,16) (11,27) (11,33) (11,20) (12,16) (12,33) (12,24) (13,18) (13,28) (13,31) (13,25) (13,29) (13,30) (13,26) (13,23) (13,22) (14,18) (14,15) (14,19) (14,31) (14,25) (14,29) (14,23) (14,22) (14,32) (15,18) (15,17) (15,28) (15,31) (15,29) (15,30) (15,26) (15,23) (15,22) (15,32) (16,27) (16,33) (17,18) (17,28) (17,19) (17,31) (17,25) (17,29) (17,26) (17,23) (17,22) (17,32) (18,19) (18,29) (18,22) (19,28) (19,31) (19,25) (19,29) (19,30) (19,26) (19,23) (19,22) (19,32) (20,27) (20,21) (20,24) (21,27) (21,24) (22,28) (22,25) (22,29) (22,30) (22,26) (22,23) (22,32) (23,28) (23,29) (23,30) (23,26) (25,31) (25,26) (26,28) (26,29) (26,30) (27,33) (28,30) (28,32) (29,30) (29,32) (30,31) (30,32) (31,32)\nIs there a path between node 32 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph706-6_1", + "image": "data/connectivity/graph_visual/hard/graph706.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,21) (0,17) (0,24) (0,27) (0,4) (0,10) (0,7) (1,29) (1,14) (1,5) (1,26) (1,18) (1,23) (1,28) (1,34) (1,8) (1,6) (2,29) (2,16) (2,30) (2,5) (2,26) (2,19) (2,25) (2,11) (2,18) (2,23) (2,28) (2,20) (2,9) (2,8) (2,6) (3,33) (3,32) (4,13) (4,17) (4,22) (4,24) (4,15) (4,27) (4,12) (4,10) (4,7) (5,29) (5,14) (5,26) (5,19) (5,25) (5,11) (5,31) (5,28) (5,34) (5,6) (6,29) (6,14) (6,30) (6,26) (6,19) (6,25) (6,11) (6,18) (6,28) (6,20) (6,9) (6,8) (7,13) (7,21) (7,17) (7,22) (7,24) (7,27) (7,10) (8,16) (8,14) (8,30) (8,26) (8,25) (8,11) (8,31) (8,18) (8,23) (8,20) (8,9) (8,34) (9,29) (9,16) (9,30) (9,26) (9,19) (9,25) (9,11) (9,31) (9,23) (10,13) (10,21) (10,17) (10,24) (10,15) (10,27) (11,29) (11,16) (11,14) (11,30) (11,26) (11,19) (11,25) (11,23) (12,13) (12,17) (12,22) (12,27) (13,21) (13,17) (13,22) (13,24) (13,15) (13,27) (14,29) (14,16) (14,30) (14,26) (14,25) (14,31) (14,18) (14,28) (14,34) (15,22) (15,24) (15,27) (16,29) (16,30) (16,26) (16,25) (16,31) (16,23) (17,21) (17,24) (17,27) (18,29) (18,30) (18,26) (18,19) (18,25) (18,31) (18,23) (18,34) (19,29) (19,30) (19,26) (19,31) (19,23) (19,20) (19,34) (20,29) (20,30) (20,31) (20,23) (20,28) (20,34) (21,22) (21,24) (22,24) (22,27) (23,29) (23,26) (23,34) (24,27) (25,29) (25,30) (25,31) (25,28) (25,34) (26,29) (26,30) (26,31) (26,28) (26,34) (28,29) (28,31) (29,30) (29,31) (29,34) (30,31) (30,34) (31,34)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph380-17_16", + "image": "data/connectivity/graph_visual/hard/graph380.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,23) (0,8) (0,15) (0,6) (0,5) (0,13) (0,21) (0,18) (1,4) (1,7) (1,23) (1,15) (1,6) (1,21) (2,10) (2,16) (2,26) (2,12) (2,22) (2,27) (2,30) (2,17) (2,31) (3,9) (3,25) (3,20) (3,28) (3,11) (3,19) (4,8) (4,15) (4,5) (4,13) (4,21) (4,18) (5,7) (5,8) (5,15) (5,6) (5,13) (5,21) (5,18) (6,23) (6,8) (6,15) (6,21) (6,18) (7,23) (7,8) (7,21) (7,18) (8,23) (8,15) (8,13) (8,18) (9,25) (9,28) (9,11) (9,19) (10,26) (10,12) (10,24) (10,14) (10,30) (10,17) (10,31) (12,26) (12,27) (12,14) (12,30) (12,31) (13,23) (13,21) (14,16) (14,26) (14,22) (14,24) (14,30) (14,31) (15,23) (15,21) (15,18) (16,24) (16,27) (16,30) (16,17) (16,31) (17,26) (17,22) (17,27) (18,23) (19,25) (19,20) (19,28) (20,25) (20,28) (21,23) (22,26) (22,27) (22,30) (24,26) (24,27) (24,30) (24,31) (26,27) (26,30) (26,31) (27,30) (27,31) (30,31)\nIs there a path between node 17 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph9-11_19", + "image": "data/connectivity/graph_visual/hard/graph9.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,2) (0,10) (0,13) (0,12) (0,9) (0,18) (0,24) (0,5) (0,20) (0,21) (0,7) (0,3) (0,23) (1,2) (1,13) (1,16) (1,12) (1,18) (1,24) (1,20) (1,4) (1,7) (1,3) (1,19) (1,23) (2,13) (2,16) (2,12) (2,9) (2,11) (2,18) (2,24) (2,5) (2,20) (2,4) (2,21) (2,7) (2,3) (2,23) (3,13) (3,16) (3,12) (3,9) (3,11) (3,24) (3,5) (3,20) (3,21) (3,7) (3,19) (3,23) (4,10) (4,16) (4,12) (4,11) (4,18) (4,24) (4,5) (4,20) (4,21) (4,7) (4,19) (4,23) (5,13) (5,12) (5,11) (5,18) (5,24) (5,20) (5,21) (5,7) (5,23) (6,15) (6,25) (6,22) (6,8) (7,13) (7,12) (7,9) (7,11) (7,18) (7,20) (7,21) (7,19) (8,17) (8,15) (8,22) (8,14) (9,10) (9,13) (9,16) (9,11) (9,18) (9,21) (9,19) (9,23) (10,13) (10,12) (10,11) (10,24) (10,20) (10,21) (10,19) (10,23) (11,13) (11,16) (11,24) (11,20) (11,21) (11,19) (11,23) (12,13) (12,16) (12,18) (12,24) (12,20) (12,21) (12,19) (12,23) (13,16) (13,24) (13,21) (13,23) (14,17) (14,15) (14,22) (15,17) (15,25) (15,22) (16,18) (16,24) (16,21) (16,23) (17,25) (17,22) (18,20) (18,21) (18,19) (18,23) (19,20) (19,23) (20,24) (20,21) (21,23) (22,25) (23,24)\nIs there a path between node 11 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph693-29_6", + "image": "data/connectivity/graph_visual/hard/graph693.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,14) (0,13) (0,12) (0,26) (0,34) (0,28) (0,32) (0,5) (0,19) (0,3) (0,2) (0,6) (0,1) (0,23) (0,15) (0,9) (0,22) (0,7) (0,16) (0,31) (1,13) (1,12) (1,26) (1,34) (1,28) (1,32) (1,10) (1,5) (1,27) (1,19) (1,3) (1,18) (1,21) (1,2) (1,6) (1,23) (1,15) (1,9) (1,17) (1,22) (1,7) (1,16) (1,31) (2,14) (2,13) (2,12) (2,34) (2,28) (2,4) (2,5) (2,27) (2,25) (2,19) (2,3) (2,18) (2,21) (2,23) (2,15) (2,9) (2,30) (2,22) (2,7) (2,16) (2,31) (3,14) (3,12) (3,26) (3,4) (3,10) (3,5) (3,27) (3,25) (3,18) (3,21) (3,6) (3,15) (3,9) (3,17) (3,30) (3,7) (3,16) (3,31) (4,14) (4,13) (4,12) (4,26) (4,28) (4,32) (4,10) (4,5) (4,27) (4,25) (4,19) (4,23) (4,9) (4,30) (4,22) (4,7) (4,16) (4,31) (5,13) (5,12) (5,26) (5,34) (5,28) (5,32) (5,10) (5,25) (5,19) (5,18) (5,6) (5,23) (5,9) (5,30) (5,16) (5,31) (6,14) (6,12) (6,26) (6,34) (6,28) (6,32) (6,27) (6,19) (6,21) (6,15) (6,17) (6,22) (6,7) (6,31) (7,14) (7,13) (7,12) (7,26) (7,34) (7,28) (7,32) (7,10) (7,27) (7,19) (7,18) (7,21) (7,23) (7,15) (7,9) (7,17) (7,30) (7,22) (7,16) (8,20) (8,33) (8,11) (8,24) (9,14) (9,13) (9,12) (9,26) (9,34) (9,28) (9,10) (9,27) (9,19) (9,18) (9,23) (9,15) (9,17) (9,30) (9,22) (9,16) (10,14) (10,13) (10,12) (10,26) (10,25) (10,18) (10,21) (10,23) (10,15) (10,17) (10,30) (10,31) (11,20) (11,33) (11,24) (11,29) (12,26) (12,28) (12,32) (12,25) (12,18) (12,21) (12,23) (12,17) (12,30) (13,14) (13,26) (13,34) (13,28) (13,32) (13,27) (13,25) (13,19) (13,21) (13,23) (13,15) (13,17) (13,16) (13,31) (14,34) (14,28) (14,32) (14,27) (14,25) (14,18) (14,21) (14,23) (14,15) (14,17) (14,30) (14,22) (14,31) (15,34) (15,28) (15,32) (15,27) (15,25) (15,19) (15,21) (15,23) (15,22) (15,16) (15,31) (16,26) (16,28) (16,32) (16,25) (16,18) (16,21) (16,23) (16,17) (16,30) (17,26) (17,34) (17,28) (17,32) (17,27) (17,19) (17,18) (17,23) (17,30) (17,22) (17,31) (18,26) (18,32) (18,27) (18,25) (18,19) (18,23) (18,30) (18,31) (19,26) (19,34) (19,32) (19,21) (19,23) (19,30) (19,22) (19,31) (20,33) (20,29) (21,26) (21,34) (21,28) (21,25) (21,30) (21,22) (21,31) (22,28) (22,27) (22,25) (22,30) (22,31) (23,26) (23,34) (23,32) (23,27) (23,25) (23,30) (23,31) (24,33) (25,26) (25,32) (25,27) (25,30) (25,31) (26,28) (26,27) (26,31) (27,28) (27,32) (27,30) (27,31) (28,34) (29,33) (30,34) (30,32) (30,31) (31,34) (31,32)\nIs there a path between node 29 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph672-0_26", + "image": "data/connectivity/graph_visual/hard/graph672.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,15) (1,5) (1,31) (1,30) (1,18) (2,17) (2,25) (2,15) (2,7) (2,23) (2,24) (2,5) (2,13) (3,34) (3,8) (4,16) (4,12) (4,9) (4,33) (5,17) (5,7) (5,23) (5,20) (5,31) (5,13) (6,26) (6,11) (6,22) (6,9) (6,21) (7,14) (7,25) (7,20) (7,13) (8,26) (8,29) (8,11) (8,21) (9,26) (9,29) (9,21) (9,33) (10,26) (10,29) (10,22) (10,12) (12,22) (12,21) (13,28) (13,31) (13,19) (14,17) (14,15) (14,19) (15,17) (15,25) (15,28) (15,30) (15,19) (16,26) (17,28) (17,31) (17,19) (18,28) (18,20) (19,27) (19,20) (19,32) (20,30) (20,32) (21,34) (21,33) (24,31) (26,29) (26,34) (27,30) (28,31) (28,30) (29,34) (30,32)\nIs there a path between node 0 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph285-19_9", + "image": "data/connectivity/graph_visual/hard/graph285.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,3) (0,11) (0,15) (0,25) (0,31) (0,23) (0,14) (1,28) (1,20) (1,12) (1,21) (1,19) (1,24) (1,27) (1,13) (1,6) (2,20) (2,22) (2,21) (2,19) (2,13) (2,6) (3,15) (3,4) (3,25) (3,23) (4,9) (4,15) (4,14) (5,8) (5,17) (5,10) (5,26) (5,7) (5,16) (6,20) (6,21) (6,19) (6,27) (6,13) (7,17) (7,16) (7,29) (8,17) (9,11) (9,15) (9,31) (9,23) (9,14) (10,17) (11,15) (11,30) (11,23) (11,14) (12,20) (12,22) (12,19) (12,27) (12,13) (12,18) (13,28) (13,22) (13,21) (13,24) (13,27) (13,18) (14,15) (14,25) (14,31) (14,23) (15,25) (15,30) (15,23) (16,26) (17,26) (17,29) (18,28) (18,20) (18,22) (18,21) (18,19) (18,24) (18,27) (19,22) (19,21) (19,24) (19,27) (20,28) (20,22) (20,21) (20,24) (20,27) (21,28) (21,22) (21,24) (22,24) (22,27) (23,30) (23,31) (24,28) (25,31) (27,28) (30,31)\nIs there a path between node 19 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph451-24_1", + "image": "data/connectivity/graph_visual/hard/graph451.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (2,30) (2,8) (2,22) (2,17) (2,12) (2,18) (3,27) (3,6) (3,20) (3,12) (4,16) (6,30) (6,8) (6,22) (6,26) (6,17) (6,12) (6,28) (7,13) (7,21) (8,9) (8,24) (8,18) (9,27) (9,20) (9,32) (9,24) (10,30) (10,17) (10,20) (10,12) (10,28) (11,23) (12,27) (12,30) (12,20) (12,24) (13,14) (13,29) (13,25) (14,31) (15,23) (17,32) (17,24) (17,18) (18,27) (18,26) (19,21) (20,30) (20,22) (20,26) (21,31) (21,29) (21,25) (22,24) (24,30) (24,32) (24,28) (25,31) (26,30) (27,28) (28,30) (30,32)\nIs there a path between node 24 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph551-13_6", + "image": "data/connectivity/graph_visual/hard/graph551.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,21) (0,30) (0,19) (0,25) (1,24) (1,18) (1,19) (1,31) (1,25) (1,26) (2,22) (2,23) (3,8) (3,13) (3,10) (5,14) (6,24) (6,8) (6,9) (6,13) (6,10) (6,28) (6,15) (7,11) (8,30) (8,9) (8,13) (8,26) (9,24) (9,16) (9,30) (9,10) (9,27) (10,18) (10,28) (10,15) (11,22) (11,29) (13,18) (13,21) (14,17) (15,18) (15,30) (15,19) (15,33) (15,31) (15,27) (15,26) (16,30) (16,19) (16,27) (18,30) (18,19) (18,28) (18,27) (19,24) (19,33) (19,28) (20,22) (20,29) (21,33) (21,25) (21,27) (23,32) (24,30) (24,28) (24,31) (25,31) (26,30) (26,28) (28,30) (31,33)\nIs there a path between node 13 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph20-7_24", + "image": "data/connectivity/graph_visual/hard/graph20.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,5) (0,14) (0,23) (1,10) (1,6) (1,3) (1,22) (2,16) (2,12) (3,8) (3,14) (3,22) (4,21) (4,25) (6,7) (6,18) (6,14) (6,15) (6,22) (7,18) (7,22) (8,10) (8,23) (11,16) (11,21) (12,17) (12,21) (12,25) (13,20) (14,20) (14,22) (15,18) (16,21) (16,25) (17,21) (19,21) (20,23) (21,25)\nIs there a path between node 7 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph215-0_9", + "image": "data/connectivity/graph_visual/hard/graph215.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,11) (0,27) (0,29) (1,16) (1,11) (1,20) (1,14) (2,8) (2,18) (2,15) (2,11) (2,27) (2,19) (2,25) (2,29) (3,5) (4,8) (4,24) (4,23) (4,26) (4,13) (4,7) (4,28) (4,6) (4,20) (4,19) (6,15) (6,27) (6,25) (7,22) (7,24) (7,23) (7,26) (7,13) (7,28) (7,29) (8,18) (8,26) (8,12) (9,17) (11,22) (11,24) (11,28) (11,20) (12,22) (12,15) (12,28) (12,27) (12,20) (12,29) (13,16) (13,23) (13,28) (13,27) (13,20) (13,19) (14,19) (15,28) (15,25) (16,26) (16,25) (18,20) (18,29) (19,23) (19,20) (20,24) (20,26) (20,28) (20,27) (20,25) (22,23) (22,28) (22,29) (23,24) (23,26) (23,29) (24,27) (25,27) (26,29) (27,28)\nIs there a path between node 0 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph463-32_13", + "image": "data/connectivity/graph_visual/hard/graph463.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,17) (0,9) (1,12) (2,29) (2,26) (2,13) (2,23) (2,15) (2,18) (2,11) (3,9) (4,31) (4,7) (4,16) (4,29) (4,10) (4,23) (4,18) (5,12) (5,17) (5,22) (6,30) (6,31) (6,27) (6,16) (6,10) (6,21) (6,11) (7,16) (7,26) (7,10) (7,21) (7,20) (7,28) (8,30) (8,10) (8,23) (8,15) (8,25) (8,18) (9,19) (9,24) (10,32) (11,13) (12,19) (13,27) (13,21) (13,15) (13,25) (14,19) (15,27) (15,16) (15,25) (15,28) (16,30) (16,31) (16,23) (16,18) (16,28) (17,19) (17,24) (18,32) (18,20) (18,28) (20,31) (20,23) (20,21) (20,25) (21,30) (21,25) (22,24) (23,30) (23,29) (23,28) (25,30) (25,28) (26,31) (27,32) (28,31) (29,30) (29,31)\nIs there a path between node 32 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph605-22_1", + "image": "data/connectivity/graph_visual/hard/graph605.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,3) (0,18) (0,9) (1,3) (1,31) (1,23) (2,22) (2,5) (3,27) (3,20) (4,12) (4,22) (4,33) (4,10) (4,26) (5,22) (5,17) (5,33) (5,14) (6,32) (6,29) (7,26) (8,28) (8,25) (8,17) (9,34) (9,13) (10,28) (10,17) (10,16) (11,18) (11,13) (11,19) (12,24) (12,22) (12,17) (12,16) (13,31) (13,20) (14,28) (14,30) (14,17) (15,25) (15,30) (15,17) (16,30) (16,26) (18,27) (18,20) (20,23) (22,25) (22,30) (22,33) (22,26) (23,27) (25,28) (26,28) (28,33)\nIs there a path between node 22 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph534-12_24", + "image": "data/connectivity/graph_visual/hard/graph534.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,1) (0,3) (0,22) (0,28) (0,2) (0,26) (0,14) (0,10) (0,32) (0,30) (0,16) (0,31) (0,9) (0,23) (0,20) (0,4) (0,19) (0,17) (0,18) (1,21) (1,22) (1,28) (1,15) (1,16) (1,31) (1,20) (1,13) (1,8) (1,19) (1,18) (2,3) (2,28) (2,29) (2,14) (2,10) (2,32) (2,30) (2,16) (2,9) (2,23) (2,20) (2,13) (2,5) (2,4) (2,8) (2,19) (2,17) (2,18) (3,21) (3,22) (3,28) (3,26) (3,10) (3,32) (3,15) (3,31) (3,9) (3,23) (3,20) (3,5) (3,7) (3,4) (3,19) (3,18) (4,22) (4,28) (4,29) (4,14) (4,10) (4,32) (4,15) (4,30) (4,31) (4,23) (4,20) (4,13) (4,7) (4,17) (4,18) (5,22) (5,28) (5,10) (5,9) (5,20) (5,13) (5,7) (5,19) (5,17) (5,18) (6,25) (6,33) (6,24) (6,11) (6,27) (7,21) (7,22) (7,28) (7,26) (7,14) (7,10) (7,32) (7,15) (7,30) (7,9) (7,20) (7,19) (7,18) (8,22) (8,28) (8,29) (8,26) (8,14) (8,10) (8,32) (8,15) (8,30) (8,31) (8,23) (8,20) (8,19) (8,17) (9,21) (9,29) (9,26) (9,10) (9,32) (9,30) (9,16) (9,23) (9,20) (9,13) (9,19) (9,17) (10,21) (10,22) (10,28) (10,29) (10,26) (10,14) (10,32) (10,15) (10,30) (10,16) (10,31) (10,23) (10,20) (10,17) (11,12) (11,27) (12,24) (13,21) (13,22) (13,32) (13,15) (13,30) (13,23) (13,20) (13,19) (13,17) (13,18) (14,21) (14,22) (14,28) (14,26) (14,15) (14,30) (14,16) (14,23) (14,19) (14,17) (14,18) (15,21) (15,22) (15,26) (15,32) (15,30) (15,16) (15,31) (15,23) (15,20) (15,17) (15,18) (16,21) (16,28) (16,29) (16,32) (16,19) (16,17) (16,18) (17,21) (17,22) (17,28) (17,29) (17,26) (17,32) (17,30) (17,23) (17,20) (17,19) (18,21) (18,22) (18,28) (18,29) (18,26) (18,32) (18,30) (18,31) (18,23) (18,20) (18,19) (19,21) (19,22) (19,28) (19,29) (19,26) (19,30) (19,31) (19,23) (19,20) (20,28) (20,29) (20,23) (21,22) (21,28) (21,26) (21,32) (21,30) (21,31) (21,23) (22,28) (22,29) (22,26) (22,32) (23,28) (23,26) (23,31) (24,25) (24,33) (24,27) (25,33) (25,27) (26,29) (26,32) (26,30) (26,31) (27,33) (28,29) (28,32) (28,30) (28,31) (29,32) (29,30) (29,31) (30,31) (31,32)\nIs there a path between node 12 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph591-2_23", + "image": "data/connectivity/graph_visual/hard/graph591.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,13) (0,31) (0,32) (0,33) (0,15) (1,5) (1,19) (1,16) (1,18) (1,11) (1,10) (1,9) (1,28) (1,14) (1,3) (1,8) (2,7) (2,5) (2,19) (2,16) (2,29) (2,18) (2,11) (2,25) (2,9) (2,28) (2,14) (2,3) (2,30) (2,8) (2,27) (3,7) (3,5) (3,19) (3,29) (3,18) (3,11) (3,6) (3,10) (3,25) (3,9) (3,28) (3,14) (3,30) (3,8) (4,26) (4,32) (4,17) (4,33) (4,15) (5,7) (5,19) (5,16) (5,18) (5,11) (5,10) (5,14) (5,30) (5,8) (5,27) (6,7) (6,19) (6,16) (6,11) (6,10) (6,25) (6,9) (6,28) (6,14) (6,30) (6,27) (7,16) (7,18) (7,11) (7,10) (7,25) (7,28) (7,14) (7,8) (7,27) (8,19) (8,16) (8,11) (8,10) (8,9) (8,27) (9,19) (9,16) (9,29) (9,11) (9,10) (9,27) (10,29) (10,11) (10,14) (10,30) (10,27) (11,19) (11,18) (11,30) (11,27) (12,24) (12,20) (13,26) (13,32) (13,17) (13,33) (13,15) (14,19) (14,16) (14,29) (14,25) (14,28) (14,30) (14,27) (15,31) (15,26) (15,32) (15,17) (16,19) (16,18) (16,25) (16,27) (17,31) (17,23) (17,26) (17,32) (17,33) (18,19) (18,29) (18,28) (18,30) (18,27) (19,29) (19,25) (19,28) (19,30) (19,27) (20,22) (20,24) (20,21) (21,24) (22,24) (23,31) (23,26) (23,33) (25,29) (25,28) (25,30) (25,27) (26,31) (26,32) (26,33) (27,29) (27,30) (28,29) (28,30) (29,30) (31,32) (32,33)\nIs there a path between node 2 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph331-11_13", + "image": "data/connectivity/graph_visual/hard/graph331.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,16) (0,12) (0,23) (0,10) (0,31) (0,3) (0,26) (0,22) (0,6) (0,25) (0,14) (0,24) (0,5) (1,29) (1,7) (1,16) (1,27) (1,12) (1,23) (1,31) (1,3) (1,19) (1,15) (1,9) (1,26) (1,6) (1,28) (1,13) (1,14) (1,24) (1,5) (2,20) (2,4) (2,17) (2,21) (2,30) (3,29) (3,7) (3,16) (3,27) (3,23) (3,31) (3,19) (3,15) (3,26) (3,6) (3,25) (3,28) (3,8) (3,13) (3,14) (3,24) (3,5) (4,20) (4,18) (4,30) (5,29) (5,7) (5,27) (5,12) (5,10) (5,9) (5,11) (5,26) (5,6) (5,28) (5,14) (5,24) (6,7) (6,16) (6,27) (6,23) (6,10) (6,15) (6,11) (6,26) (6,22) (6,25) (6,28) (6,13) (6,14) (7,29) (7,12) (7,23) (7,19) (7,15) (7,26) (7,22) (7,13) (7,14) (7,24) (8,29) (8,27) (8,23) (8,10) (8,19) (8,9) (8,11) (8,26) (8,22) (8,25) (8,14) (9,29) (9,12) (9,23) (9,10) (9,31) (9,19) (9,15) (9,22) (9,13) (9,24) (10,27) (10,12) (10,15) (10,11) (10,26) (10,25) (10,28) (10,13) (10,14) (11,29) (11,16) (11,27) (11,12) (11,23) (11,19) (11,15) (11,26) (11,28) (11,14) (11,24) (12,29) (12,23) (12,31) (12,19) (12,26) (12,22) (12,25) (12,28) (12,13) (12,24) (13,29) (13,16) (13,27) (13,31) (13,19) (13,22) (13,28) (13,14) (13,24) (14,29) (14,16) (14,27) (14,23) (14,31) (14,19) (14,26) (14,22) (14,25) (14,28) (14,24) (15,29) (15,16) (15,31) (15,19) (15,26) (15,22) (15,25) (15,28) (15,24) (16,29) (16,31) (16,26) (16,22) (16,25) (16,28) (16,24) (17,20) (17,18) (17,21) (17,30) (18,21) (18,30) (19,29) (19,27) (19,23) (19,22) (19,25) (20,21) (21,30) (22,29) (22,27) (22,23) (22,31) (22,25) (22,28) (22,24) (23,29) (23,27) (23,31) (23,24) (24,29) (24,27) (24,31) (24,26) (24,25) (24,28) (25,29) (25,27) (25,31) (25,28) (26,29) (26,27) (26,31) (27,29) (27,28) (28,29) (29,31)\nIs there a path between node 11 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph469-9_13", + "image": "data/connectivity/graph_visual/hard/graph469.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,29) (0,16) (0,3) (0,25) (0,26) (0,13) (0,14) (0,5) (0,4) (0,22) (0,20) (0,21) (0,24) (0,17) (0,32) (0,2) (0,10) (0,7) (0,12) (1,28) (1,16) (1,6) (1,25) (1,13) (1,14) (1,18) (1,5) (1,23) (1,4) (1,22) (1,20) (1,21) (1,24) (1,15) (1,2) (1,10) (1,7) (1,12) (2,28) (2,29) (2,16) (2,6) (2,3) (2,25) (2,26) (2,13) (2,14) (2,18) (2,5) (2,23) (2,8) (2,4) (2,19) (2,20) (2,21) (2,24) (2,17) (2,15) (2,12) (3,29) (3,6) (3,25) (3,13) (3,14) (3,5) (3,23) (3,8) (3,4) (3,19) (3,20) (3,21) (3,24) (3,17) (3,32) (3,15) (3,10) (3,7) (3,12) (4,28) (4,29) (4,16) (4,6) (4,25) (4,26) (4,14) (4,5) (4,8) (4,27) (4,22) (4,19) (4,21) (4,15) (4,10) (4,7) (5,28) (5,25) (5,13) (5,18) (5,23) (5,8) (5,27) (5,19) (5,20) (5,21) (5,24) (5,32) (5,15) (5,10) (5,7) (5,12) (6,28) (6,29) (6,16) (6,14) (6,18) (6,8) (6,22) (6,19) (6,20) (6,21) (6,17) (6,12) (7,28) (7,23) (7,8) (7,22) (7,19) (7,21) (7,32) (7,15) (7,10) (7,12) (8,29) (8,16) (8,26) (8,13) (8,22) (8,19) (8,20) (8,24) (8,17) (8,32) (8,15) (8,10) (8,12) (9,31) (10,28) (10,16) (10,25) (10,26) (10,13) (10,18) (10,23) (10,22) (10,19) (10,21) (10,17) (10,32) (10,15) (10,12) (11,31) (11,30) (12,28) (12,29) (12,16) (12,14) (12,22) (12,20) (12,24) (12,17) (12,32) (12,15) (13,29) (13,16) (13,26) (13,14) (13,23) (13,27) (13,22) (13,19) (13,20) (13,21) (13,32) (14,28) (14,29) (14,26) (14,18) (14,27) (14,19) (14,20) (14,21) (14,17) (14,15) (15,28) (15,29) (15,16) (15,25) (15,26) (15,18) (15,27) (15,22) (15,21) (15,24) (15,32) (16,25) (16,26) (16,18) (16,27) (16,22) (16,19) (16,20) (16,21) (16,24) (16,17) (16,32) (17,28) (17,25) (17,27) (17,22) (17,19) (17,21) (17,32) (18,28) (18,29) (18,26) (18,27) (18,19) (18,20) (18,21) (18,24) (18,32) (19,29) (19,25) (19,26) (19,23) (19,27) (19,20) (19,21) (19,24) (19,32) (20,28) (20,29) (20,27) (20,22) (20,24) (20,32) (21,26) (21,24) (22,28) (22,29) (22,25) (22,26) (22,23) (22,27) (22,24) (23,28) (23,29) (23,25) (23,26) (23,24) (24,28) (24,25) (25,28) (25,26) (25,27) (25,32) (26,29) (26,32) (27,28) (27,29) (27,32) (28,29) (28,32) (29,32) (30,31)\nIs there a path between node 9 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph645-7_1", + "image": "data/connectivity/graph_visual/hard/graph645.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,16) (0,18) (0,5) (0,29) (0,21) (0,22) (0,7) (0,2) (0,13) (0,27) (0,26) (0,14) (0,33) (0,8) (0,10) (1,32) (1,16) (1,18) (1,29) (1,17) (1,2) (1,13) (1,26) (1,14) (1,31) (1,33) (1,10) (2,23) (2,32) (2,16) (2,18) (2,5) (2,29) (2,17) (2,21) (2,7) (2,13) (2,27) (2,9) (2,31) (2,33) (2,8) (3,12) (3,15) (3,19) (3,20) (3,34) (3,4) (3,11) (4,12) (4,28) (4,6) (4,15) (4,19) (4,34) (4,30) (4,11) (5,16) (5,18) (5,17) (5,21) (5,22) (5,13) (5,24) (5,9) (5,26) (5,31) (5,33) (5,10) (6,12) (6,28) (6,15) (6,19) (6,20) (6,30) (6,11) (6,25) (7,32) (7,16) (7,18) (7,22) (7,13) (7,24) (7,27) (7,9) (7,26) (7,14) (7,31) (7,33) (7,8) (7,10) (8,23) (8,16) (8,18) (8,29) (8,17) (8,21) (8,22) (8,13) (8,24) (8,26) (8,14) (8,31) (8,33) (8,10) (9,23) (9,32) (9,16) (9,18) (9,17) (9,21) (9,22) (9,13) (9,24) (9,27) (9,26) (9,14) (9,31) (9,33) (9,10) (10,23) (10,32) (10,16) (10,18) (10,17) (10,21) (10,13) (10,24) (10,27) (10,26) (10,14) (11,28) (11,15) (11,34) (11,30) (11,25) (12,28) (12,15) (12,20) (12,30) (12,25) (13,23) (13,32) (13,16) (13,18) (13,29) (13,17) (13,22) (13,24) (13,27) (13,26) (13,14) (13,33) (14,23) (14,29) (14,17) (14,21) (14,22) (14,27) (14,26) (15,20) (15,30) (16,23) (16,29) (16,17) (16,21) (16,22) (16,24) (16,27) (16,26) (16,31) (17,23) (17,32) (17,18) (17,21) (17,24) (17,27) (17,31) (18,23) (18,29) (18,21) (18,27) (18,26) (18,31) (18,33) (19,20) (19,34) (19,30) (19,25) (20,28) (20,34) (20,30) (20,25) (21,32) (21,22) (21,24) (21,27) (21,26) (21,31) (22,23) (22,32) (22,29) (22,24) (22,26) (22,31) (22,33) (23,32) (23,29) (23,24) (23,26) (23,31) (24,29) (24,27) (24,26) (24,33) (25,28) (25,34) (25,30) (26,32) (26,29) (27,29) (27,33) (28,30) (29,32) (30,34) (31,32) (32,33)\nIs there a path between node 7 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph675-26_4", + "image": "data/connectivity/graph_visual/hard/graph675.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (1,28) (1,5) (1,3) (2,15) (2,12) (2,11) (2,18) (2,29) (2,10) (3,24) (3,21) (5,23) (6,16) (6,18) (6,29) (6,9) (6,27) (6,10) (7,25) (7,16) (7,11) (7,18) (7,20) (7,26) (9,15) (9,25) (9,12) (9,20) (9,29) (10,17) (10,30) (10,25) (10,14) (10,16) (10,29) (10,22) (11,16) (11,19) (11,29) (11,27) (12,30) (12,19) (13,32) (13,19) (13,29) (13,27) (13,26) (14,15) (14,19) (14,26) (15,17) (15,25) (15,16) (15,18) (16,19) (16,18) (16,29) (17,30) (17,18) (17,29) (17,26) (18,22) (18,31) (18,26) (19,32) (19,22) (19,31) (20,34) (20,29) (20,27) (22,30) (22,31) (25,27) (27,34) (27,30) (27,32) (27,29) (27,31) (29,32) (29,31) (30,32) (31,34) (32,34)\nIs there a path between node 26 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph453-29_6", + "image": "data/connectivity/graph_visual/hard/graph453.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,18) (0,26) (0,7) (0,3) (0,13) (0,11) (0,19) (1,8) (1,12) (1,23) (1,24) (1,15) (1,6) (2,4) (2,15) (2,6) (3,28) (3,11) (3,19) (4,8) (4,5) (4,15) (4,6) (5,32) (5,8) (5,30) (5,27) (5,12) (5,23) (6,32) (6,23) (7,31) (7,19) (8,23) (8,15) (9,22) (10,25) (10,13) (10,11) (11,14) (11,26) (12,29) (13,28) (13,31) (13,19) (14,18) (15,29) (15,27) (15,24) (16,18) (18,28) (19,26) (23,30) (24,27) (25,28) (26,28)\nIs there a path between node 29 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph86-20_22", + "image": "data/connectivity/graph_visual/hard/graph86.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,25) (0,5) (0,14) (0,24) (1,7) (1,23) (1,18) (1,15) (1,26) (1,9) (1,22) (1,2) (1,3) (2,12) (2,16) (2,7) (2,15) (2,26) (2,9) (2,22) (2,3) (3,12) (3,16) (3,23) (3,8) (3,18) (3,26) (3,9) (3,22) (3,19) (4,10) (4,25) (4,20) (4,11) (4,14) (4,24) (4,13) (5,25) (5,14) (6,10) (6,21) (6,20) (6,13) (7,16) (7,23) (7,15) (7,26) (7,9) (7,22) (7,17) (7,19) (8,12) (8,16) (8,23) (8,18) (8,15) (8,26) (8,9) (8,22) (8,17) (8,19) (9,16) (9,18) (9,15) (9,26) (10,21) (10,20) (10,11) (10,14) (10,13) (11,21) (11,25) (11,20) (11,13) (12,16) (12,23) (12,15) (12,26) (12,22) (12,19) (13,21) (13,25) (13,20) (13,14) (13,24) (14,25) (15,16) (15,23) (15,18) (15,22) (15,17) (16,23) (16,26) (16,17) (16,19) (17,23) (17,18) (17,26) (17,22) (17,19) (18,23) (18,26) (18,22) (19,23) (19,26) (19,22) (20,21) (20,25) (20,24) (21,25) (21,24) (22,23) (22,26) (23,26) (24,25)\nIs there a path between node 20 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph647-13_7", + "image": "data/connectivity/graph_visual/hard/graph647.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,12) (0,21) (0,10) (0,22) (0,23) (0,29) (0,17) (0,28) (0,9) (0,14) (1,4) (1,26) (1,5) (1,8) (1,15) (1,30) (2,19) (2,18) (2,16) (2,11) (2,7) (2,6) (2,34) (3,12) (3,21) (3,10) (3,24) (3,22) (3,23) (3,29) (3,17) (3,32) (3,28) (3,9) (3,27) (4,26) (4,15) (4,30) (5,26) (5,15) (6,13) (6,31) (6,18) (6,16) (6,34) (7,13) (7,31) (7,19) (7,18) (7,11) (7,34) (8,15) (8,30) (9,12) (9,10) (9,22) (9,23) (9,29) (9,32) (9,33) (9,28) (9,27) (9,14) (10,12) (10,21) (10,22) (10,23) (10,29) (10,17) (10,32) (10,33) (10,28) (10,20) (10,27) (10,14) (11,13) (11,31) (11,19) (11,25) (11,18) (11,16) (12,21) (12,24) (12,29) (12,17) (12,32) (12,33) (12,28) (12,20) (12,27) (12,14) (13,31) (13,19) (13,18) (13,16) (13,34) (14,21) (14,22) (14,23) (14,17) (14,32) (14,28) (14,20) (14,27) (15,26) (15,30) (16,31) (16,19) (16,25) (16,34) (17,24) (17,22) (17,23) (17,29) (17,32) (17,20) (18,31) (18,25) (18,34) (19,31) (19,25) (19,34) (20,24) (20,33) (20,28) (20,27) (21,23) (21,32) (21,33) (22,24) (22,23) (22,29) (22,33) (22,27) (23,33) (23,28) (23,27) (24,29) (24,32) (24,33) (24,27) (25,31) (25,34) (26,30) (27,32) (27,28) (28,29) (28,32) (28,33) (29,32)\nIs there a path between node 13 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph646-10_3", + "image": "data/connectivity/graph_visual/hard/graph646.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,13) (0,16) (0,5) (0,12) (0,29) (0,33) (0,18) (0,8) (0,15) (0,10) (0,34) (0,14) (0,21) (0,25) (1,11) (1,9) (1,19) (1,20) (1,7) (1,3) (1,28) (1,4) (1,24) (1,32) (1,26) (1,22) (2,6) (2,13) (2,17) (2,5) (2,31) (2,23) (2,27) (2,12) (2,29) (2,33) (2,18) (2,8) (2,15) (2,10) (2,30) (2,21) (2,25) (3,11) (3,9) (3,19) (3,28) (3,4) (3,24) (3,32) (3,26) (4,11) (4,9) (4,19) (4,20) (4,7) (4,28) (4,32) (4,26) (4,22) (5,17) (5,16) (5,23) (5,27) (5,12) (5,29) (5,33) (5,18) (5,8) (5,10) (5,25) (6,13) (6,17) (6,16) (6,31) (6,27) (6,12) (6,29) (6,8) (6,15) (6,10) (6,30) (6,14) (6,25) (7,11) (7,28) (7,24) (7,32) (7,22) (8,13) (8,16) (8,31) (8,27) (8,12) (8,29) (8,33) (8,18) (8,15) (8,10) (8,34) (8,14) (8,25) (9,11) (9,19) (9,20) (9,24) (9,22) (10,13) (10,17) (10,27) (10,12) (10,33) (10,18) (10,30) (10,14) (10,25) (11,19) (11,20) (11,28) (11,32) (11,26) (11,22) (12,13) (12,17) (12,31) (12,23) (12,29) (12,15) (12,30) (12,34) (12,21) (12,25) (13,16) (13,31) (13,29) (13,33) (13,30) (13,34) (13,14) (13,25) (14,17) (14,16) (14,31) (14,27) (14,29) (14,33) (14,18) (14,15) (14,34) (14,25) (15,17) (15,23) (15,27) (15,33) (15,30) (15,34) (15,21) (16,23) (16,27) (16,33) (16,18) (16,34) (17,23) (17,27) (17,33) (17,30) (17,34) (17,21) (17,25) (18,31) (18,27) (18,29) (18,34) (19,20) (19,28) (19,24) (19,32) (19,26) (19,22) (20,28) (20,24) (20,22) (21,31) (21,27) (21,33) (21,30) (21,25) (22,24) (22,32) (23,31) (23,27) (23,29) (23,33) (23,34) (23,25) (24,28) (24,32) (24,26) (25,27) (25,30) (25,34) (27,29) (27,33) (27,30) (28,32) (29,31) (29,33) (29,30) (29,34) (30,31) (30,33) (30,34) (33,34)\nIs there a path between node 10 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph547-22_17", + "image": "data/connectivity/graph_visual/hard/graph547.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,31) (0,26) (0,8) (0,6) (0,29) (0,20) (0,22) (0,28) (0,17) (0,32) (0,13) (0,19) (0,1) (1,26) (1,6) (1,29) (1,22) (1,28) (1,17) (1,32) (1,19) (1,10) (2,7) (2,5) (2,24) (2,4) (2,18) (2,16) (2,3) (2,30) (2,11) (2,33) (2,15) (2,21) (2,12) (3,7) (3,5) (3,18) (3,30) (3,14) (3,33) (3,23) (3,9) (3,21) (4,5) (4,27) (4,18) (4,25) (4,30) (4,14) (4,11) (4,33) (4,15) (4,23) (4,9) (4,21) (4,12) (5,7) (5,24) (5,27) (5,18) (5,16) (5,25) (5,30) (5,14) (5,11) (5,33) (5,15) (5,23) (5,9) (5,21) (5,12) (6,26) (6,8) (6,29) (6,20) (6,28) (6,17) (6,32) (6,19) (6,10) (7,27) (7,18) (7,16) (7,30) (7,14) (7,33) (7,15) (7,23) (7,12) (8,31) (8,22) (8,28) (8,17) (8,32) (8,13) (8,19) (9,24) (9,27) (9,16) (9,25) (9,30) (9,14) (9,11) (9,33) (9,15) (9,12) (10,31) (10,29) (10,20) (10,32) (10,13) (10,19) (11,27) (11,18) (11,16) (11,25) (11,30) (11,33) (11,21) (11,12) (12,24) (12,18) (12,16) (12,25) (12,30) (12,14) (12,23) (12,21) (13,31) (13,26) (13,29) (13,20) (13,22) (13,28) (13,17) (13,32) (14,27) (14,18) (14,16) (14,25) (14,30) (14,33) (14,15) (14,21) (15,24) (15,18) (15,16) (15,25) (15,33) (15,21) (16,18) (16,30) (16,33) (16,23) (16,21) (17,29) (17,28) (17,32) (17,19) (18,27) (18,25) (18,30) (18,33) (18,21) (19,31) (19,26) (19,20) (19,22) (19,32) (20,31) (20,26) (20,22) (20,32) (21,24) (21,27) (21,30) (22,26) (22,29) (22,28) (22,32) (23,24) (23,27) (23,25) (23,30) (23,33) (24,27) (24,25) (24,30) (24,33) (25,30) (26,29) (26,28) (26,32) (27,30) (27,33) (28,31) (28,29) (28,32) (29,32) (30,33) (31,32)\nIs there a path between node 22 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph639-18_14", + "image": "data/connectivity/graph_visual/hard/graph639.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,25) (0,17) (0,1) (0,33) (0,7) (0,3) (0,18) (0,13) (0,22) (0,19) (0,24) (0,21) (0,11) (1,4) (1,10) (1,25) (1,17) (1,32) (1,33) (1,7) (1,3) (1,13) (1,22) (1,31) (1,6) (1,24) (1,21) (1,5) (1,27) (3,4) (3,10) (3,7) (3,18) (3,13) (3,22) (3,19) (3,31) (3,6) (3,24) (3,21) (3,5) (3,11) (3,27) (4,15) (4,17) (4,33) (4,7) (4,13) (4,19) (4,31) (4,6) (4,24) (4,21) (4,5) (4,27) (5,10) (5,25) (5,17) (5,33) (5,7) (5,18) (5,13) (5,22) (5,31) (5,21) (5,11) (6,15) (6,25) (6,17) (6,32) (6,33) (6,22) (6,19) (6,31) (6,21) (6,11) (6,27) (7,15) (7,17) (7,18) (7,31) (7,24) (7,21) (7,27) (8,9) (8,12) (8,16) (8,30) (8,28) (8,20) (8,14) (8,34) (8,29) (8,23) (8,26) (9,12) (9,16) (9,30) (9,28) (9,20) (9,14) (9,34) (9,29) (9,23) (10,15) (10,25) (10,17) (10,32) (10,33) (10,18) (10,13) (10,22) (10,19) (10,24) (10,11) (11,15) (11,17) (11,32) (11,33) (11,13) (11,22) (11,31) (11,21) (11,27) (12,16) (12,30) (12,28) (12,20) (12,14) (12,34) (12,29) (12,23) (13,15) (13,25) (13,32) (13,18) (13,22) (13,31) (13,24) (13,21) (13,27) (14,16) (14,28) (14,20) (14,34) (14,29) (14,23) (14,26) (15,25) (15,32) (15,33) (15,18) (15,22) (15,19) (15,24) (15,27) (16,28) (16,20) (16,29) (16,23) (17,25) (17,33) (17,18) (17,22) (17,31) (17,24) (17,21) (17,27) (18,33) (18,31) (18,24) (18,21) (18,27) (19,25) (19,32) (19,22) (19,31) (19,21) (19,27) (20,30) (20,29) (20,23) (20,26) (21,25) (21,33) (21,22) (21,31) (21,24) (21,27) (22,25) (22,32) (22,33) (22,31) (22,24) (23,30) (23,28) (23,34) (24,31) (24,27) (25,32) (25,33) (25,31) (26,28) (26,29) (27,32) (27,31) (28,30) (29,34) (30,34) (31,33)\nIs there a path between node 18 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph556-21_5", + "image": "data/connectivity/graph_visual/hard/graph556.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,2) (0,20) (0,30) (0,26) (0,15) (0,32) (0,13) (1,25) (2,31) (2,3) (2,30) (2,12) (2,11) (2,23) (2,27) (2,15) (2,6) (2,21) (3,31) (3,14) (3,33) (3,18) (3,11) (3,26) (3,23) (3,27) (3,16) (3,32) (3,29) (4,7) (4,25) (5,33) (5,12) (5,29) (5,6) (5,8) (6,33) (6,22) (6,18) (6,19) (6,16) (7,10) (8,22) (8,19) (8,11) (8,15) (8,32) (9,33) (9,19) (9,15) (9,29) (9,13) (11,27) (11,15) (11,32) (11,29) (13,33) (13,22) (13,23) (13,28) (13,21) (14,31) (14,33) (14,22) (14,18) (14,26) (14,15) (14,16) (14,21) (15,33) (15,19) (15,21) (16,20) (16,33) (16,27) (18,22) (18,30) (18,19) (18,32) (18,29) (19,26) (19,23) (19,21) (20,31) (20,30) (20,23) (20,28) (21,31) (21,26) (21,32) (22,26) (22,32) (22,29) (22,28) (23,33) (23,30) (23,27) (26,32) (28,31) (28,30) (28,29) (29,31) (29,32) (30,32) (31,33)\nIs there a path between node 21 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph385-25_16", + "image": "data/connectivity/graph_visual/hard/graph385.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,25) (0,9) (0,21) (0,29) (0,20) (0,22) (0,10) (0,15) (0,17) (0,23) (0,5) (0,31) (1,4) (1,26) (1,18) (1,6) (1,19) (1,24) (1,27) (1,30) (1,28) (1,13) (1,11) (2,12) (2,4) (2,18) (2,6) (2,24) (2,27) (2,28) (2,13) (2,11) (3,25) (3,21) (3,29) (3,20) (3,22) (3,10) (3,14) (3,8) (3,17) (3,23) (3,7) (4,12) (4,26) (4,18) (4,6) (4,19) (4,30) (4,28) (4,13) (4,11) (5,25) (5,9) (5,21) (5,29) (5,16) (5,20) (5,22) (5,8) (5,15) (5,17) (5,7) (5,31) (6,26) (6,18) (6,19) (6,24) (6,27) (6,28) (6,13) (6,11) (7,25) (7,9) (7,21) (7,29) (7,16) (7,20) (7,22) (7,14) (7,8) (7,15) (7,23) (8,9) (8,21) (8,29) (8,16) (8,22) (8,10) (8,15) (8,17) (8,23) (8,31) (9,25) (9,21) (9,16) (9,20) (9,10) (9,14) (9,17) (9,23) (9,31) (10,21) (10,29) (10,16) (10,20) (10,22) (10,15) (10,23) (11,26) (11,24) (11,27) (11,30) (11,28) (11,13) (12,26) (12,18) (12,24) (12,28) (13,26) (13,18) (13,19) (13,24) (13,27) (13,28) (14,21) (14,29) (14,20) (14,15) (14,23) (14,31) (15,25) (15,21) (15,16) (15,20) (15,22) (15,23) (15,31) (16,21) (16,29) (16,22) (16,17) (16,23) (16,31) (17,21) (17,29) (17,20) (17,22) (17,23) (18,26) (18,19) (18,24) (18,30) (19,26) (19,24) (19,27) (20,21) (20,29) (21,25) (21,22) (21,23) (22,29) (22,23) (22,31) (23,25) (23,31) (24,26) (24,30) (24,28) (25,31) (26,27) (26,30) (26,28) (27,30) (28,30) (29,31)\nIs there a path between node 25 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph149-25_14", + "image": "data/connectivity/graph_visual/hard/graph149.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,27) (0,6) (0,23) (0,8) (1,24) (1,12) (1,5) (1,22) (1,26) (1,18) (1,9) (1,7) (1,15) (1,19) (1,11) (1,16) (1,2) (1,3) (1,10) (2,24) (2,13) (2,5) (2,22) (2,21) (2,26) (2,18) (2,9) (2,14) (2,19) (2,20) (2,28) (2,10) (3,13) (3,12) (3,5) (3,22) (3,21) (3,26) (3,18) (3,7) (3,14) (3,15) (3,19) (3,11) (3,16) (3,17) (3,28) (3,10) (4,25) (4,27) (4,6) (4,23) (5,13) (5,22) (5,21) (5,26) (5,18) (5,7) (5,15) (5,19) (5,11) (5,20) (5,16) (5,10) (6,25) (6,27) (6,23) (7,13) (7,12) (7,21) (7,26) (7,18) (7,14) (7,15) (7,11) (7,17) (7,10) (8,25) (8,27) (8,23) (9,24) (9,12) (9,21) (9,14) (9,15) (9,19) (9,16) (10,24) (10,22) (10,26) (10,15) (10,20) (10,28) (11,24) (11,13) (11,12) (11,22) (11,21) (11,26) (11,15) (11,20) (11,17) (12,13) (12,22) (12,21) (12,18) (12,14) (12,15) (12,19) (12,20) (12,28) (13,24) (13,22) (13,21) (13,26) (13,18) (13,14) (13,15) (13,19) (13,16) (13,17) (13,28) (14,24) (14,21) (14,26) (14,18) (14,15) (14,19) (14,16) (14,28) (15,22) (15,21) (15,18) (15,20) (15,16) (15,17) (15,28) (16,22) (16,21) (16,26) (16,19) (16,28) (17,22) (17,21) (17,26) (17,19) (17,20) (18,22) (18,26) (18,20) (19,22) (19,21) (19,20) (19,28) (20,24) (20,22) (20,21) (20,28) (21,24) (21,22) (21,26) (21,28) (22,24) (22,26) (22,28) (23,25) (23,27) (24,26) (24,28) (25,27)\nIs there a path between node 25 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph159-19_23", + "image": "data/connectivity/graph_visual/hard/graph159.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,2) (0,26) (0,21) (0,9) (0,24) (0,17) (0,22) (1,16) (2,20) (2,11) (2,26) (2,27) (2,21) (2,12) (2,9) (2,23) (2,4) (2,19) (3,25) (4,8) (4,23) (4,17) (4,7) (4,13) (6,16) (7,10) (7,20) (7,12) (7,9) (7,23) (7,17) (7,22) (7,13) (7,19) (8,18) (8,11) (8,9) (8,17) (9,10) (9,11) (9,24) (9,23) (10,20) (10,11) (10,24) (10,13) (11,18) (11,12) (12,20) (12,24) (13,18) (13,20) (13,22) (13,14) (14,20) (14,24) (14,23) (14,19) (15,27) (15,23) (15,19) (17,28) (17,23) (18,21) (18,24) (18,19) (19,22) (20,28) (20,24) (21,28) (21,27) (22,28) (22,27) (23,26) (23,27) (23,24) (24,26) (26,28) (26,27) (27,28)\nIs there a path between node 19 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph510-3_8", + "image": "data/connectivity/graph_visual/hard/graph510.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,31) (0,1) (0,27) (0,13) (0,10) (0,25) (0,7) (0,21) (0,19) (0,15) (0,16) (0,17) (0,9) (0,20) (0,26) (0,30) (0,28) (0,2) (0,5) (0,24) (0,3) (1,10) (1,33) (1,23) (1,25) (1,8) (1,7) (1,21) (1,19) (1,16) (1,17) (1,26) (1,30) (1,22) (1,28) (1,5) (1,24) (1,3) (2,31) (2,13) (2,10) (2,33) (2,14) (2,23) (2,25) (2,8) (2,7) (2,21) (2,19) (2,15) (2,20) (2,26) (2,30) (2,22) (2,24) (2,3) (3,31) (3,27) (3,13) (3,33) (3,14) (3,23) (3,25) (3,21) (3,15) (3,16) (3,9) (3,30) (3,5) (3,24) (4,18) (4,11) (4,12) (4,29) (5,31) (5,27) (5,13) (5,10) (5,33) (5,25) (5,8) (5,7) (5,21) (5,19) (5,16) (5,20) (5,26) (5,30) (5,22) (6,12) (6,29) (6,32) (7,31) (7,13) (7,33) (7,25) (7,8) (7,19) (7,16) (7,17) (7,9) (7,20) (7,26) (7,30) (7,22) (7,28) (7,24) (8,31) (8,27) (8,10) (8,14) (8,21) (8,19) (8,15) (8,17) (8,9) (8,22) (8,28) (8,24) (9,31) (9,27) (9,13) (9,33) (9,23) (9,25) (9,16) (9,17) (9,26) (9,30) (9,28) (9,24) (10,31) (10,27) (10,13) (10,14) (10,23) (10,25) (10,21) (10,19) (10,15) (10,20) (10,26) (10,30) (10,22) (11,12) (11,29) (11,32) (12,18) (12,32) (13,31) (13,27) (13,33) (13,23) (13,25) (13,19) (13,15) (13,17) (13,20) (13,26) (13,22) (13,28) (13,24) (14,31) (14,27) (14,33) (14,23) (14,25) (14,21) (14,16) (14,17) (14,20) (14,26) (14,30) (14,22) (14,24) (15,31) (15,27) (15,33) (15,23) (15,25) (15,19) (15,17) (15,20) (15,30) (15,22) (15,24) (16,31) (16,17) (16,20) (16,30) (16,28) (16,24) (17,31) (17,27) (17,33) (17,25) (17,20) (17,30) (17,22) (19,31) (19,25) (19,21) (19,20) (19,26) (19,22) (19,28) (19,24) (20,27) (20,33) (20,23) (20,21) (20,26) (20,22) (20,28) (20,24) (21,31) (21,33) (21,23) (21,30) (21,28) (21,24) (22,31) (22,27) (22,23) (22,25) (22,30) (22,28) (22,24) (23,31) (23,27) (23,33) (24,31) (24,27) (24,33) (24,26) (24,30) (24,28) (25,30) (25,28) (26,31) (26,33) (26,30) (27,31) (27,30) (27,28) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nIs there a path between node 3 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph510-17_30", + "image": "data/connectivity/graph_visual/hard/graph510.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,31) (0,1) (0,27) (0,13) (0,10) (0,25) (0,7) (0,21) (0,19) (0,15) (0,16) (0,17) (0,9) (0,20) (0,26) (0,30) (0,28) (0,2) (0,5) (0,24) (0,3) (1,10) (1,33) (1,23) (1,25) (1,8) (1,7) (1,21) (1,19) (1,16) (1,17) (1,26) (1,30) (1,22) (1,28) (1,5) (1,24) (1,3) (2,31) (2,13) (2,10) (2,33) (2,14) (2,23) (2,25) (2,8) (2,7) (2,21) (2,19) (2,15) (2,20) (2,26) (2,30) (2,22) (2,24) (2,3) (3,31) (3,27) (3,13) (3,33) (3,14) (3,23) (3,25) (3,21) (3,15) (3,16) (3,9) (3,30) (3,5) (3,24) (4,18) (4,11) (4,12) (4,29) (5,31) (5,27) (5,13) (5,10) (5,33) (5,25) (5,8) (5,7) (5,21) (5,19) (5,16) (5,20) (5,26) (5,30) (5,22) (6,12) (6,29) (6,32) (7,31) (7,13) (7,33) (7,25) (7,8) (7,19) (7,16) (7,17) (7,9) (7,20) (7,26) (7,30) (7,22) (7,28) (7,24) (8,31) (8,27) (8,10) (8,14) (8,21) (8,19) (8,15) (8,17) (8,9) (8,22) (8,28) (8,24) (9,31) (9,27) (9,13) (9,33) (9,23) (9,25) (9,16) (9,17) (9,26) (9,30) (9,28) (9,24) (10,31) (10,27) (10,13) (10,14) (10,23) (10,25) (10,21) (10,19) (10,15) (10,20) (10,26) (10,30) (10,22) (11,12) (11,29) (11,32) (12,18) (12,32) (13,31) (13,27) (13,33) (13,23) (13,25) (13,19) (13,15) (13,17) (13,20) (13,26) (13,22) (13,28) (13,24) (14,31) (14,27) (14,33) (14,23) (14,25) (14,21) (14,16) (14,17) (14,20) (14,26) (14,30) (14,22) (14,24) (15,31) (15,27) (15,33) (15,23) (15,25) (15,19) (15,17) (15,20) (15,30) (15,22) (15,24) (16,31) (16,17) (16,20) (16,30) (16,28) (16,24) (17,31) (17,27) (17,33) (17,25) (17,20) (17,30) (17,22) (19,31) (19,25) (19,21) (19,20) (19,26) (19,22) (19,28) (19,24) (20,27) (20,33) (20,23) (20,21) (20,26) (20,22) (20,28) (20,24) (21,31) (21,33) (21,23) (21,30) (21,28) (21,24) (22,31) (22,27) (22,23) (22,25) (22,30) (22,28) (22,24) (23,31) (23,27) (23,33) (24,31) (24,27) (24,33) (24,26) (24,30) (24,28) (25,30) (25,28) (26,31) (26,33) (26,30) (27,31) (27,30) (27,28) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nIs there a path between node 17 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph669-29_0", + "image": "data/connectivity/graph_visual/hard/graph669.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,17) (0,33) (0,14) (1,18) (1,14) (2,28) (2,24) (2,25) (2,20) (2,31) (2,22) (2,8) (3,30) (3,23) (3,17) (3,29) (3,21) (4,7) (4,11) (4,31) (4,22) (4,8) (5,28) (5,9) (5,34) (5,22) (6,20) (6,9) (6,15) (6,8) (7,11) (7,16) (8,25) (8,20) (8,9) (8,31) (8,15) (8,22) (8,19) (9,28) (9,32) (9,11) (9,31) (10,32) (10,20) (10,15) (10,22) (10,19) (11,28) (11,31) (11,15) (11,34) (12,18) (12,23) (12,13) (13,23) (13,29) (13,33) (14,26) (14,17) (14,29) (14,33) (16,24) (16,32) (16,22) (17,30) (17,23) (18,26) (18,23) (18,29) (18,21) (21,26) (21,23) (22,34) (23,26) (24,28) (24,32) (25,28) (25,34) (28,32) (29,30)\nIs there a path between node 29 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph209-7_18", + "image": "data/connectivity/graph_visual/hard/graph209.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,22) (1,18) (1,25) (1,8) (1,16) (1,11) (1,6) (1,24) (2,22) (2,18) (2,17) (2,20) (2,11) (2,6) (3,13) (4,22) (4,25) (4,21) (4,17) (4,11) (4,6) (5,27) (5,13) (6,29) (6,24) (7,22) (7,21) (7,17) (7,16) (7,11) (7,24) (7,15) (7,19) (8,18) (8,12) (8,11) (8,24) (9,28) (10,26) (10,23) (11,17) (12,17) (12,20) (12,16) (13,27) (16,22) (16,25) (16,21) (16,29) (16,19) (17,29) (17,20) (19,21) (19,29) (19,20) (20,22) (21,22) (21,25) (21,29) (27,28)\nIs there a path between node 7 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph693-4_11", + "image": "data/connectivity/graph_visual/hard/graph693.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,14) (0,13) (0,12) (0,26) (0,34) (0,28) (0,32) (0,5) (0,19) (0,3) (0,2) (0,6) (0,1) (0,23) (0,15) (0,9) (0,22) (0,7) (0,16) (0,31) (1,13) (1,12) (1,26) (1,34) (1,28) (1,32) (1,10) (1,5) (1,27) (1,19) (1,3) (1,18) (1,21) (1,2) (1,6) (1,23) (1,15) (1,9) (1,17) (1,22) (1,7) (1,16) (1,31) (2,14) (2,13) (2,12) (2,34) (2,28) (2,4) (2,5) (2,27) (2,25) (2,19) (2,3) (2,18) (2,21) (2,23) (2,15) (2,9) (2,30) (2,22) (2,7) (2,16) (2,31) (3,14) (3,12) (3,26) (3,4) (3,10) (3,5) (3,27) (3,25) (3,18) (3,21) (3,6) (3,15) (3,9) (3,17) (3,30) (3,7) (3,16) (3,31) (4,14) (4,13) (4,12) (4,26) (4,28) (4,32) (4,10) (4,5) (4,27) (4,25) (4,19) (4,23) (4,9) (4,30) (4,22) (4,7) (4,16) (4,31) (5,13) (5,12) (5,26) (5,34) (5,28) (5,32) (5,10) (5,25) (5,19) (5,18) (5,6) (5,23) (5,9) (5,30) (5,16) (5,31) (6,14) (6,12) (6,26) (6,34) (6,28) (6,32) (6,27) (6,19) (6,21) (6,15) (6,17) (6,22) (6,7) (6,31) (7,14) (7,13) (7,12) (7,26) (7,34) (7,28) (7,32) (7,10) (7,27) (7,19) (7,18) (7,21) (7,23) (7,15) (7,9) (7,17) (7,30) (7,22) (7,16) (8,20) (8,33) (8,11) (8,24) (9,14) (9,13) (9,12) (9,26) (9,34) (9,28) (9,10) (9,27) (9,19) (9,18) (9,23) (9,15) (9,17) (9,30) (9,22) (9,16) (10,14) (10,13) (10,12) (10,26) (10,25) (10,18) (10,21) (10,23) (10,15) (10,17) (10,30) (10,31) (11,20) (11,33) (11,24) (11,29) (12,26) (12,28) (12,32) (12,25) (12,18) (12,21) (12,23) (12,17) (12,30) (13,14) (13,26) (13,34) (13,28) (13,32) (13,27) (13,25) (13,19) (13,21) (13,23) (13,15) (13,17) (13,16) (13,31) (14,34) (14,28) (14,32) (14,27) (14,25) (14,18) (14,21) (14,23) (14,15) (14,17) (14,30) (14,22) (14,31) (15,34) (15,28) (15,32) (15,27) (15,25) (15,19) (15,21) (15,23) (15,22) (15,16) (15,31) (16,26) (16,28) (16,32) (16,25) (16,18) (16,21) (16,23) (16,17) (16,30) (17,26) (17,34) (17,28) (17,32) (17,27) (17,19) (17,18) (17,23) (17,30) (17,22) (17,31) (18,26) (18,32) (18,27) (18,25) (18,19) (18,23) (18,30) (18,31) (19,26) (19,34) (19,32) (19,21) (19,23) (19,30) (19,22) (19,31) (20,33) (20,29) (21,26) (21,34) (21,28) (21,25) (21,30) (21,22) (21,31) (22,28) (22,27) (22,25) (22,30) (22,31) (23,26) (23,34) (23,32) (23,27) (23,25) (23,30) (23,31) (24,33) (25,26) (25,32) (25,27) (25,30) (25,31) (26,28) (26,27) (26,31) (27,28) (27,32) (27,30) (27,31) (28,34) (29,33) (30,34) (30,32) (30,31) (31,34) (31,32)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph138-5_0", + "image": "data/connectivity/graph_visual/hard/graph138.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,12) (0,10) (0,25) (0,16) (0,24) (0,4) (0,8) (0,27) (0,19) (1,5) (1,28) (2,15) (3,12) (3,13) (3,21) (3,24) (3,4) (3,8) (4,26) (4,20) (4,21) (4,11) (4,9) (6,13) (6,14) (6,22) (6,21) (6,7) (6,23) (6,11) (7,12) (7,26) (7,20) (7,17) (7,14) (7,10) (7,25) (7,24) (7,8) (7,11) (7,19) (7,9) (8,25) (8,27) (8,11) (9,17) (9,14) (9,21) (9,23) (9,27) (9,11) (10,26) (10,20) (10,14) (10,25) (10,23) (10,24) (11,13) (11,17) (11,21) (11,25) (11,23) (11,19) (12,20) (12,17) (12,24) (13,26) (13,20) (13,17) (13,22) (13,25) (13,24) (13,19) (14,20) (14,16) (15,28) (15,18) (16,26) (16,21) (16,23) (17,26) (17,22) (17,23) (17,27) (18,28) (19,22) (20,23) (20,24) (20,27) (21,26) (21,27) (23,25) (24,25) (24,27) (25,27)\nIs there a path between node 5 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph561-7_26", + "image": "data/connectivity/graph_visual/hard/graph561.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,23) (0,31) (0,10) (0,14) (0,28) (0,18) (0,8) (0,21) (0,33) (0,22) (0,2) (0,1) (1,12) (1,31) (1,14) (1,28) (1,18) (1,8) (1,21) (1,19) (1,7) (1,5) (2,3) (2,31) (2,16) (2,19) (2,9) (2,22) (2,7) (3,10) (3,29) (3,11) (3,9) (4,23) (4,10) (4,14) (4,16) (4,29) (4,17) (4,8) (4,25) (4,30) (4,15) (5,27) (5,12) (5,23) (5,10) (5,16) (5,18) (5,13) (5,19) (5,9) (6,20) (7,12) (7,14) (7,26) (7,8) (7,30) (8,31) (8,28) (8,29) (8,33) (8,15) (9,12) (9,16) (9,13) (9,19) (9,15) (9,22) (10,27) (10,12) (10,16) (10,28) (11,27) (11,23) (11,31) (11,18) (12,27) (12,13) (12,21) (12,25) (12,19) (13,23) (13,14) (13,28) (13,18) (13,17) (13,33) (13,15) (14,28) (15,27) (15,18) (15,29) (15,25) (15,30) (16,27) (16,28) (16,19) (17,31) (17,28) (17,25) (18,28) (18,25) (19,29) (19,25) (19,22) (21,27) (22,25) (23,29) (23,33) (26,29) (27,28) (27,29) (27,30) (28,31) (29,31) (29,33)\nIs there a path between node 7 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph601-33_12", + "image": "data/connectivity/graph_visual/hard/graph601.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,25) (0,3) (1,25) (1,29) (2,14) (2,13) (2,20) (2,18) (2,31) (2,9) (2,27) (2,21) (2,12) (2,7) (2,33) (2,11) (2,24) (2,26) (2,30) (3,25) (4,23) (4,22) (4,34) (4,5) (5,23) (5,22) (5,34) (6,14) (6,13) (6,20) (6,18) (6,27) (6,21) (6,12) (6,7) (6,28) (6,24) (6,26) (6,30) (7,14) (7,13) (7,20) (7,31) (7,17) (7,9) (7,27) (7,21) (7,12) (7,10) (7,33) (7,28) (7,30) (8,14) (8,13) (8,31) (8,17) (8,9) (8,27) (8,12) (8,33) (8,11) (8,28) (8,26) (8,30) (9,14) (9,13) (9,20) (9,18) (9,27) (9,21) (9,12) (9,10) (9,33) (9,24) (9,26) (9,19) (9,30) (10,13) (10,20) (10,18) (10,31) (10,17) (10,27) (10,12) (10,33) (10,11) (10,28) (10,24) (11,14) (11,13) (11,20) (11,18) (11,31) (11,12) (11,33) (11,28) (11,24) (11,26) (11,30) (12,14) (12,13) (12,20) (12,18) (12,17) (12,27) (12,21) (12,33) (12,19) (13,14) (13,20) (13,18) (13,31) (13,17) (13,21) (13,28) (13,24) (13,26) (14,18) (14,31) (14,17) (14,27) (14,21) (14,33) (14,26) (15,32) (17,18) (17,31) (17,27) (17,33) (17,28) (17,24) (17,26) (17,19) (17,30) (18,20) (18,31) (18,33) (18,24) (18,26) (18,19) (18,30) (19,31) (19,27) (19,21) (19,33) (19,28) (19,26) (20,31) (20,27) (20,21) (20,33) (20,24) (20,26) (20,30) (21,27) (21,33) (21,28) (21,24) (21,30) (22,23) (22,34) (23,34) (24,33) (24,26) (25,29) (26,31) (26,33) (26,30) (27,31) (27,33) (27,28) (27,30) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nIs there a path between node 33 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph241-7_30", + "image": "data/connectivity/graph_visual/hard/graph241.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,22) (0,15) (0,7) (0,13) (0,8) (1,2) (1,11) (1,29) (1,15) (1,20) (1,17) (1,23) (1,6) (2,12) (2,11) (2,5) (2,29) (2,10) (2,16) (2,28) (2,13) (2,8) (4,22) (4,9) (4,15) (4,16) (4,19) (4,20) (5,11) (5,22) (5,16) (5,19) (5,18) (5,23) (5,13) (6,22) (6,27) (6,10) (6,18) (6,17) (6,7) (7,27) (7,10) (7,9) (7,15) (7,14) (7,23) (7,8) (8,26) (8,27) (8,29) (8,14) (8,16) (8,28) (8,17) (9,12) (9,11) (9,26) (9,29) (9,16) (9,18) (9,24) (9,23) (9,13) (10,12) (10,11) (10,27) (10,15) (10,28) (10,18) (10,24) (11,27) (11,20) (11,25) (12,29) (12,19) (12,18) (12,25) (12,17) (12,24) (13,15) (13,16) (13,25) (13,24) (14,18) (14,25) (14,23) (15,29) (15,16) (15,28) (15,19) (15,24) (15,23) (16,24) (16,23) (17,29) (17,19) (18,27) (18,19) (19,20) (19,25) (20,27) (20,24) (22,29) (23,26) (23,24) (24,26) (24,27) (26,27) (26,29) (27,28) (28,29)\nIs there a path between node 7 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph688-8_2", + "image": "data/connectivity/graph_visual/hard/graph688.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,29) (0,30) (1,19) (1,22) (1,13) (1,28) (1,26) (1,24) (1,3) (1,12) (1,7) (1,16) (1,25) (1,27) (1,11) (2,31) (2,10) (2,18) (2,9) (2,14) (2,23) (2,33) (2,32) (3,19) (3,21) (3,22) (3,28) (3,26) (3,24) (3,12) (3,7) (3,16) (3,25) (3,27) (3,11) (4,17) (5,8) (5,9) (5,23) (5,32) (6,29) (6,15) (7,19) (7,22) (7,28) (7,26) (7,24) (7,12) (7,16) (7,25) (7,27) (8,31) (8,10) (8,18) (8,14) (8,23) (8,33) (8,32) (9,31) (9,10) (9,18) (9,14) (9,23) (9,32) (10,31) (10,18) (10,14) (10,23) (10,33) (10,32) (11,19) (11,21) (11,22) (11,13) (11,28) (11,26) (11,12) (11,16) (11,27) (12,22) (12,13) (12,24) (12,16) (12,25) (12,27) (13,19) (13,22) (13,28) (13,26) (13,24) (13,16) (13,25) (14,31) (14,18) (14,23) (14,33) (14,32) (15,34) (15,30) (16,21) (16,22) (16,25) (16,27) (17,20) (18,31) (18,23) (18,32) (19,21) (19,22) (19,28) (19,26) (19,24) (19,25) (21,22) (21,28) (21,26) (21,24) (21,25) (21,27) (22,28) (22,27) (23,31) (23,33) (23,32) (24,28) (24,26) (24,27) (25,28) (25,26) (25,27) (26,28) (26,27) (30,34) (31,33)\nIs there a path between node 8 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph507-28_4", + "image": "data/connectivity/graph_visual/hard/graph507.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,29) (0,21) (0,6) (0,28) (0,24) (0,9) (0,2) (0,13) (0,15) (0,10) (1,30) (1,25) (1,33) (1,5) (1,27) (1,11) (1,22) (2,29) (2,6) (2,14) (2,8) (2,9) (2,13) (2,15) (2,26) (2,17) (2,32) (3,19) (3,20) (5,30) (5,27) (5,11) (5,31) (5,22) (6,29) (6,28) (6,14) (6,8) (6,9) (6,12) (6,18) (6,15) (6,26) (6,17) (6,32) (6,7) (6,10) (7,21) (7,28) (7,14) (7,8) (7,9) (7,16) (7,18) (7,15) (7,17) (7,32) (8,21) (8,28) (8,24) (8,9) (8,16) (8,12) (8,13) (8,23) (8,18) (8,15) (8,26) (8,17) (8,32) (8,10) (9,28) (9,14) (9,24) (9,12) (9,13) (9,23) (9,18) (9,15) (9,26) (9,17) (9,10) (10,29) (10,21) (10,28) (10,14) (10,24) (10,12) (10,13) (10,23) (10,18) (10,17) (11,30) (11,25) (11,33) (11,27) (11,31) (11,22) (12,29) (12,21) (12,28) (12,24) (12,16) (12,13) (12,23) (12,18) (12,15) (12,26) (12,32) (13,21) (13,28) (13,14) (13,24) (13,16) (13,23) (13,18) (13,26) (13,17) (14,29) (14,21) (14,28) (14,24) (14,16) (14,18) (14,32) (15,29) (15,21) (15,28) (15,24) (15,23) (15,32) (16,29) (16,21) (16,28) (16,24) (16,23) (16,18) (16,26) (16,32) (17,21) (17,23) (17,18) (17,26) (18,29) (18,21) (18,28) (18,24) (18,23) (18,26) (18,32) (19,20) (21,28) (21,23) (21,26) (21,32) (22,30) (22,25) (22,33) (22,27) (22,31) (23,29) (23,28) (23,24) (23,26) (23,32) (24,26) (24,32) (25,33) (25,31) (26,29) (26,28) (26,32) (27,30) (27,33) (28,29) (29,32) (30,33) (31,33)\nIs there a path between node 28 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph577-31_32", + "image": "data/connectivity/graph_visual/hard/graph577.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,10) (0,13) (0,4) (0,23) (0,22) (0,25) (0,18) (0,17) (0,21) (0,32) (0,1) (0,2) (0,27) (0,3) (1,6) (1,7) (1,23) (1,22) (1,25) (1,18) (1,14) (1,17) (1,21) (1,32) (1,2) (1,27) (1,3) (1,24) (2,6) (2,13) (2,4) (2,16) (2,22) (2,14) (2,32) (2,29) (2,27) (2,3) (2,24) (3,10) (3,23) (3,16) (3,14) (3,17) (3,32) (3,27) (3,24) (4,10) (4,13) (4,7) (4,23) (4,22) (4,18) (4,17) (4,21) (4,32) (4,29) (4,27) (4,24) (5,9) (5,8) (5,28) (5,11) (5,19) (5,33) (5,15) (5,20) (5,12) (5,31) (6,10) (6,13) (6,7) (6,16) (6,22) (6,25) (6,14) (6,21) (6,32) (6,29) (6,27) (7,10) (7,23) (7,16) (7,22) (7,18) (7,21) (7,32) (7,29) (7,24) (8,28) (8,11) (8,19) (8,12) (8,31) (9,26) (9,28) (9,30) (9,19) (9,15) (9,20) (9,12) (9,31) (10,16) (10,25) (10,18) (10,14) (10,17) (10,29) (10,27) (10,24) (11,26) (11,30) (11,19) (11,33) (11,15) (11,20) (11,12) (11,31) (12,28) (12,30) (12,19) (12,33) (12,15) (12,20) (13,16) (13,25) (13,18) (13,17) (13,32) (13,29) (13,27) (13,24) (14,23) (14,16) (14,29) (14,27) (15,26) (15,28) (15,30) (15,33) (15,20) (15,31) (16,22) (16,21) (16,29) (16,27) (16,24) (17,23) (17,18) (17,29) (17,24) (18,23) (18,22) (18,25) (18,21) (18,32) (18,27) (19,26) (19,28) (19,30) (19,20) (19,31) (20,28) (20,30) (20,33) (20,31) (21,25) (21,32) (21,29) (21,27) (21,24) (22,32) (22,24) (23,25) (23,32) (23,29) (23,27) (24,25) (24,32) (24,29) (24,27) (25,32) (25,29) (25,27) (26,30) (26,33) (27,32) (27,29) (28,30) (28,31) (29,32)\nIs there a path between node 31 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph473-26_10", + "image": "data/connectivity/graph_visual/hard/graph473.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,17) (1,2) (1,14) (1,9) (1,18) (1,5) (1,25) (1,28) (1,13) (1,10) (2,31) (2,14) (2,4) (2,18) (2,5) (2,28) (2,13) (2,19) (2,22) (2,10) (2,15) (3,27) (4,21) (4,9) (4,18) (4,25) (4,28) (4,13) (4,22) (4,7) (4,16) (5,21) (5,31) (5,9) (5,18) (5,25) (5,28) (5,13) (5,19) (5,22) (5,16) (5,10) (5,15) (6,17) (6,32) (7,31) (7,14) (7,9) (7,18) (7,25) (7,28) (7,13) (7,19) (7,16) (7,10) (8,11) (8,23) (8,30) (8,12) (8,29) (9,21) (9,31) (9,18) (9,25) (9,13) (9,10) (10,31) (10,18) (10,28) (10,19) (10,22) (10,16) (10,15) (11,24) (11,30) (11,26) (12,24) (12,23) (12,20) (12,26) (12,29) (13,14) (13,18) (13,28) (13,19) (13,22) (13,16) (14,31) (14,18) (14,16) (14,15) (15,31) (15,18) (15,19) (15,22) (15,16) (16,21) (16,31) (16,18) (16,28) (16,19) (18,21) (18,31) (18,25) (18,28) (18,22) (19,31) (19,25) (19,28) (19,22) (20,24) (20,23) (20,30) (20,29) (21,31) (21,28) (21,22) (22,25) (22,28) (23,30) (23,26) (23,29) (24,30) (25,31) (25,28) (26,30) (28,31) (29,30)\nIs there a path between node 26 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph128-4_1", + "image": "data/connectivity/graph_visual/hard/graph128.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,12) (0,14) (0,10) (0,17) (0,18) (0,1) (0,13) (0,11) (0,23) (0,4) (1,19) (1,12) (1,14) (1,6) (1,17) (1,18) (1,13) (1,7) (1,27) (1,23) (2,5) (2,8) (3,21) (3,20) (3,15) (3,25) (4,19) (4,22) (4,10) (4,6) (4,17) (4,18) (4,13) (4,7) (4,27) (5,8) (6,22) (6,12) (6,14) (6,10) (6,17) (6,18) (6,13) (6,11) (6,23) (7,22) (7,26) (7,14) (7,10) (7,17) (7,18) (7,9) (9,26) (9,14) (9,10) (9,17) (9,13) (9,11) (9,27) (9,23) (10,19) (10,26) (10,14) (10,17) (10,18) (10,13) (10,27) (10,23) (11,19) (11,22) (11,26) (11,12) (11,14) (11,17) (11,13) (11,27) (12,19) (12,22) (12,14) (12,17) (12,18) (12,27) (13,19) (13,26) (13,14) (13,17) (13,18) (14,19) (14,18) (14,23) (15,21) (15,16) (15,20) (15,25) (16,21) (17,23) (18,19) (18,22) (18,26) (19,27) (20,21) (20,24) (21,25) (22,26) (22,27) (22,23) (23,26) (23,27) (24,25) (26,27)\nIs there a path between node 4 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph291-6_21", + "image": "data/connectivity/graph_visual/hard/graph291.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (1,20) (1,19) (1,8) (1,21) (1,15) (2,27) (2,21) (2,17) (3,20) (3,14) (3,25) (3,21) (4,6) (4,31) (4,5) (4,10) (5,13) (5,6) (5,18) (5,16) (5,22) (5,10) (6,13) (6,7) (6,26) (7,13) (7,31) (7,29) (7,12) (7,22) (7,9) (8,20) (8,25) (8,27) (8,21) (8,15) (9,31) (9,26) (9,11) (10,26) (10,16) (11,31) (12,28) (12,31) (12,16) (13,22) (14,21) (14,15) (14,17) (15,20) (15,17) (16,29) (16,18) (17,27) (17,21) (18,29) (19,30) (19,25) (19,21) (19,23) (20,21) (21,25) (21,27) (22,31) (22,29) (23,30) (24,27) (25,30) (26,29) (28,31)\nIs there a path between node 6 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph444-3_11", + "image": "data/connectivity/graph_visual/hard/graph444.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,32) (0,17) (0,24) (0,25) (0,20) (0,9) (1,31) (1,3) (1,5) (2,7) (2,16) (2,10) (2,32) (2,19) (2,9) (3,31) (3,12) (3,13) (3,27) (3,29) (4,18) (4,14) (4,29) (4,21) (5,12) (5,18) (6,28) (6,30) (6,19) (6,20) (6,9) (6,11) (7,23) (7,10) (7,19) (7,15) (7,26) (7,24) (7,25) (7,11) (8,26) (8,9) (9,23) (9,10) (9,17) (9,26) (9,24) (9,20) (10,22) (10,30) (10,19) (10,17) (10,25) (10,20) (11,23) (11,25) (12,13) (12,14) (13,31) (14,27) (14,21) (15,22) (15,30) (15,16) (15,24) (15,25) (15,20) (16,22) (16,23) (16,19) (17,30) (17,32) (17,19) (19,23) (19,24) (20,30) (20,25) (21,27) (22,28) (22,32) (22,26) (22,24) (23,28) (23,24) (24,25) (25,28) (25,32) (26,30) (26,32) (27,29) (30,32)\nIs there a path between node 3 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph636-19_27", + "image": "data/connectivity/graph_visual/hard/graph636.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,32) (0,18) (0,25) (1,13) (1,17) (1,28) (1,2) (1,33) (2,17) (2,28) (2,15) (2,26) (2,16) (3,30) (3,26) (5,17) (5,28) (5,27) (6,22) (6,21) (7,34) (7,22) (7,24) (8,19) (10,29) (10,22) (10,31) (10,24) (10,21) (10,11) (11,34) (13,30) (13,15) (13,27) (13,33) (13,26) (13,16) (14,32) (15,28) (15,26) (16,28) (16,26) (17,30) (18,25) (20,28) (20,26) (21,31) (21,24) (22,34) (22,31) (22,24) (23,32) (24,29) (26,33) (28,33) (31,34)\nIs there a path between node 19 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph629-27_16", + "image": "data/connectivity/graph_visual/hard/graph629.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,1) (0,28) (0,7) (0,32) (0,34) (0,29) (1,16) (1,9) (1,27) (1,4) (1,22) (1,34) (2,16) (2,28) (2,9) (2,5) (2,31) (2,22) (3,13) (3,17) (3,26) (3,12) (4,24) (4,11) (4,7) (4,5) (4,27) (4,22) (5,16) (5,9) (5,31) (5,23) (6,17) (6,12) (7,24) (7,32) (7,31) (7,23) (8,21) (9,28) (9,11) (11,31) (11,19) (11,23) (12,18) (12,17) (13,20) (13,26) (14,24) (14,32) (14,27) (14,19) (14,29) (15,30) (16,24) (16,23) (19,27) (20,33) (21,25) (22,32) (22,29) (23,28) (23,24) (23,27) (24,27) (24,31) (27,32) (27,34) (31,34)\nIs there a path between node 27 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph495-20_18", + "image": "data/connectivity/graph_visual/hard/graph495.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,31) (0,22) (0,13) (0,7) (0,1) (0,30) (0,6) (0,15) (0,14) (0,12) (1,13) (1,4) (1,33) (1,24) (1,30) (1,27) (1,28) (1,25) (1,15) (1,21) (1,18) (1,5) (1,12) (3,31) (3,23) (3,27) (3,28) (3,25) (3,15) (4,33) (4,24) (4,25) (4,8) (5,33) (5,30) (5,27) (5,6) (5,15) (6,22) (6,11) (6,19) (6,33) (6,8) (7,31) (7,22) (7,19) (7,33) (7,24) (7,30) (7,18) (8,24) (8,18) (9,29) (11,15) (11,14) (11,18) (12,31) (12,13) (12,24) (12,27) (12,25) (13,24) (13,15) (14,22) (14,30) (14,21) (14,18) (15,31) (15,25) (16,20) (18,33) (19,23) (19,28) (19,21) (19,32) (20,26) (21,27) (21,32) (22,28) (22,25) (22,32) (23,30) (23,25) (23,32) (24,30) (24,28) (24,32) (25,31) (25,33) (27,33) (27,30) (27,28) (28,32) (30,31) (31,32)\nIs there a path between node 20 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph2-9_3", + "image": "data/connectivity/graph_visual/hard/graph2.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,24) (0,1) (0,6) (0,14) (1,10) (2,25) (2,5) (2,20) (2,18) (3,22) (3,6) (3,19) (3,23) (4,9) (4,18) (5,15) (5,25) (5,17) (5,20) (6,11) (6,24) (6,14) (6,7) (6,21) (7,24) (8,25) (8,17) (8,20) (8,18) (9,25) (10,24) (10,22) (10,21) (11,22) (11,19) (11,23) (12,15) (12,16) (12,17) (13,19) (13,14) (14,22) (14,19) (15,16) (15,18) (16,17) (17,20) (18,25) (19,24) (19,22) (20,25) (21,23) (22,24) (22,23)\nIs there a path between node 9 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph222-6_13", + "image": "data/connectivity/graph_visual/hard/graph222.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,2) (0,11) (1,20) (1,26) (1,8) (1,14) (1,16) (1,5) (1,18) (1,15) (1,17) (1,10) (1,22) (1,27) (1,24) (1,28) (1,29) (2,11) (3,9) (3,21) (3,12) (3,13) (4,25) (4,26) (4,8) (4,14) (4,6) (4,23) (4,16) (4,5) (4,18) (4,15) (4,17) (4,19) (4,10) (4,27) (4,24) (4,7) (5,20) (5,26) (5,14) (5,6) (5,23) (5,16) (5,15) (5,17) (5,19) (5,22) (5,24) (5,28) (5,29) (6,26) (6,8) (6,14) (6,23) (6,18) (6,15) (6,19) (6,10) (6,22) (6,27) (6,28) (6,29) (6,7) (7,25) (7,26) (7,14) (7,16) (7,18) (7,22) (7,27) (7,28) (8,25) (8,20) (8,26) (8,14) (8,23) (8,16) (8,18) (8,17) (8,10) (8,27) (8,24) (8,28) (8,29) (9,21) (9,12) (9,13) (10,25) (10,20) (10,26) (10,14) (10,23) (10,18) (10,15) (10,17) (10,19) (10,22) (10,24) (10,28) (10,29) (12,21) (12,13) (13,21) (14,25) (14,23) (14,16) (14,18) (14,15) (14,17) (14,22) (14,27) (14,24) (14,28) (15,25) (15,20) (15,26) (15,16) (15,18) (15,22) (15,27) (15,28) (15,29) (16,25) (16,20) (16,26) (16,23) (16,18) (16,19) (16,22) (16,27) (16,24) (17,25) (17,26) (17,18) (17,24) (18,25) (18,20) (18,26) (18,23) (18,22) (18,27) (18,28) (18,29) (19,25) (19,20) (19,23) (19,22) (19,27) (19,24) (19,28) (19,29) (20,25) (20,22) (20,27) (20,28) (22,25) (22,26) (22,23) (22,27) (22,28) (22,29) (23,27) (23,28) (23,29) (24,26) (24,29) (25,26) (25,27) (25,28) (26,27) (26,28) (26,29) (27,28) (27,29) (28,29)\nIs there a path between node 6 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph162-10_11", + "image": "data/connectivity/graph_visual/hard/graph162.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,6) (0,22) (0,7) (0,3) (1,15) (1,16) (1,10) (2,15) (2,24) (2,16) (3,6) (3,7) (3,27) (3,5) (3,20) (4,11) (4,7) (4,27) (4,21) (5,26) (5,22) (5,19) (5,21) (5,20) (5,9) (6,7) (6,27) (6,21) (6,20) (7,21) (7,20) (8,13) (8,12) (8,16) (8,14) (9,11) (9,26) (9,19) (12,15) (12,16) (13,18) (16,18) (16,25) (17,24) (18,25) (19,22) (21,26)\nIs there a path between node 10 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph83-19_14", + "image": "data/connectivity/graph_visual/hard/graph83.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,18) (0,14) (0,16) (0,12) (0,2) (0,22) (0,1) (0,21) (1,18) (1,14) (1,16) (1,21) (2,18) (2,14) (2,5) (2,12) (2,22) (2,21) (3,7) (3,9) (3,15) (3,25) (3,23) (3,26) (3,19) (4,7) (4,10) (4,20) (4,13) (4,15) (4,17) (4,25) (4,23) (4,26) (4,6) (4,11) (4,24) (5,18) (5,14) (5,16) (5,22) (5,21) (6,13) (6,8) (6,15) (6,17) (6,25) (6,26) (6,19) (6,24) (7,9) (7,10) (7,20) (7,13) (7,17) (7,25) (7,23) (7,26) (7,19) (7,11) (8,9) (8,10) (8,17) (8,23) (8,26) (8,11) (8,24) (9,10) (9,20) (9,15) (9,17) (9,23) (9,24) (10,15) (10,25) (10,26) (11,20) (11,15) (11,17) (11,25) (11,23) (12,18) (12,16) (12,22) (13,15) (13,17) (13,25) (13,26) (13,19) (13,24) (14,16) (15,20) (15,17) (15,25) (15,23) (15,26) (15,19) (16,18) (16,21) (17,20) (17,23) (17,26) (17,24) (18,22) (18,21) (19,25) (19,23) (19,26) (19,24) (20,25) (20,26) (20,24) (21,22) (23,24) (24,25) (25,26)\nIs there a path between node 19 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph368-23_16", + "image": "data/connectivity/graph_visual/hard/graph368.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,10) (0,4) (0,3) (0,16) (0,24) (0,17) (0,25) (0,8) (1,18) (1,10) (1,4) (1,30) (1,16) (1,24) (1,17) (2,21) (2,14) (2,29) (2,11) (2,9) (2,5) (2,13) (3,18) (3,4) (3,23) (3,7) (3,16) (3,24) (3,20) (3,17) (3,8) (4,10) (4,30) (4,24) (4,20) (4,17) (4,8) (5,14) (5,11) (5,28) (5,9) (6,22) (6,19) (6,12) (7,18) (7,10) (7,23) (7,16) (7,24) (7,20) (7,17) (7,8) (8,18) (8,10) (8,23) (8,30) (8,16) (8,20) (9,26) (9,14) (9,29) (9,11) (9,28) (9,13) (10,18) (10,23) (10,30) (10,16) (10,24) (10,20) (10,17) (11,26) (11,21) (11,14) (11,29) (11,28) (11,13) (12,22) (12,27) (12,19) (12,31) (13,26) (13,21) (13,14) (13,29) (14,26) (14,21) (14,29) (14,28) (15,27) (15,19) (15,31) (16,18) (16,23) (16,30) (16,24) (16,20) (16,17) (17,30) (17,20) (18,30) (18,24) (18,20) (18,25) (19,22) (19,27) (19,31) (20,25) (21,29) (22,27) (23,30) (23,25) (24,25) (25,30) (26,28) (27,31) (28,29)\nIs there a path between node 23 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph649-31_17", + "image": "data/connectivity/graph_visual/hard/graph649.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,2) (0,15) (0,11) (0,22) (0,25) (0,10) (0,3) (0,6) (0,34) (0,12) (0,33) (0,27) (0,26) (0,31) (0,7) (0,19) (0,23) (0,5) (0,9) (0,28) (0,24) (1,17) (1,13) (1,4) (2,8) (2,15) (2,11) (2,22) (2,25) (2,3) (2,34) (2,33) (2,27) (2,26) (2,31) (2,7) (2,19) (2,23) (2,5) (2,32) (2,20) (2,28) (2,24) (3,8) (3,22) (3,25) (3,10) (3,6) (3,34) (3,33) (3,14) (3,26) (3,31) (3,7) (3,19) (3,23) (3,32) (3,16) (3,9) (3,30) (3,29) (3,24) (4,17) (4,13) (5,8) (5,15) (5,11) (5,22) (5,25) (5,6) (5,34) (5,33) (5,14) (5,18) (5,19) (5,23) (5,21) (5,32) (5,16) (5,20) (5,9) (5,30) (5,29) (6,8) (6,11) (6,22) (6,10) (6,34) (6,33) (6,27) (6,14) (6,31) (6,7) (6,21) (6,32) (6,16) (6,20) (6,29) (6,28) (6,24) (7,8) (7,11) (7,22) (7,10) (7,33) (7,27) (7,14) (7,18) (7,31) (7,19) (7,23) (7,21) (7,16) (7,9) (7,30) (7,29) (7,28) (7,24) (8,11) (8,22) (8,25) (8,10) (8,34) (8,33) (8,27) (8,14) (8,26) (8,31) (8,19) (8,32) (8,16) (8,20) (8,30) (8,29) (9,15) (9,22) (9,25) (9,34) (9,33) (9,27) (9,14) (9,18) (9,26) (9,31) (9,19) (9,23) (9,32) (9,16) (9,30) (9,29) (9,28) (9,24) (10,15) (10,11) (10,22) (10,34) (10,27) (10,14) (10,18) (10,19) (10,21) (10,32) (10,16) (10,20) (10,30) (10,29) (10,28) (11,15) (11,22) (11,12) (11,33) (11,27) (11,14) (11,18) (11,26) (11,19) (11,32) (11,16) (11,20) (11,29) (11,24) (12,25) (12,33) (12,27) (12,14) (12,18) (12,23) (12,21) (12,32) (12,16) (12,20) (12,29) (12,28) (12,24) (14,22) (14,34) (14,33) (14,27) (14,18) (14,26) (14,31) (14,19) (14,21) (14,32) (14,16) (14,28) (14,24) (15,22) (15,34) (15,33) (15,27) (15,26) (15,19) (15,23) (15,21) (15,32) (15,20) (15,30) (15,24) (16,22) (16,34) (16,33) (16,27) (16,31) (16,19) (16,23) (16,32) (16,30) (16,28) (16,24) (18,22) (18,25) (18,27) (18,26) (18,19) (18,23) (18,21) (18,32) (18,29) (18,28) (18,24) (19,25) (19,34) (19,33) (19,27) (19,26) (19,21) (19,32) (19,20) (19,30) (19,29) (19,28) (19,24) (20,25) (20,34) (20,33) (20,27) (20,31) (20,32) (20,30) (20,29) (20,28) (21,22) (21,25) (21,33) (21,27) (21,31) (21,23) (21,32) (21,30) (21,28) (22,25) (22,34) (22,33) (22,27) (22,23) (22,32) (22,29) (22,24) (23,25) (23,33) (23,26) (23,31) (23,30) (23,28) (24,25) (24,34) (24,33) (24,26) (24,32) (24,30) (24,29) (24,28) (25,34) (25,27) (25,26) (25,32) (25,29) (26,34) (26,33) (26,27) (26,31) (26,32) (26,30) (26,29) (27,34) (27,33) (27,31) (27,32) (27,29) (28,34) (28,32) (28,29) (29,33) (29,31) (29,32) (30,34) (30,32) (31,34) (31,32) (32,33) (33,34)\nIs there a path between node 31 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph31-10_19", + "image": "data/connectivity/graph_visual/hard/graph31.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,25) (0,18) (0,8) (0,24) (0,6) (0,12) (0,5) (0,7) (0,16) (0,1) (0,22) (1,25) (1,18) (1,8) (1,4) (1,9) (1,6) (1,12) (1,11) (1,7) (1,13) (1,16) (1,20) (2,8) (2,9) (2,24) (2,6) (2,12) (2,11) (2,15) (2,5) (2,7) (2,16) (2,20) (2,22) (3,19) (3,23) (3,21) (3,14) (4,25) (4,18) (4,8) (4,9) (4,11) (4,15) (4,13) (4,22) (5,25) (5,8) (5,9) (5,24) (5,6) (5,15) (5,7) (5,13) (5,16) (5,20) (5,22) (6,25) (6,8) (6,9) (6,24) (6,12) (6,15) (6,7) (6,16) (7,25) (7,18) (7,24) (7,12) (7,16) (7,22) (8,18) (8,24) (8,12) (8,15) (9,25) (9,18) (9,24) (9,12) (9,11) (9,15) (9,16) (9,20) (9,22) (10,17) (11,24) (11,12) (11,16) (11,20) (12,25) (12,18) (12,24) (12,15) (12,13) (12,16) (12,22) (13,18) (13,20) (13,22) (14,19) (14,23) (14,21) (15,25) (15,18) (15,24) (15,20) (16,25) (16,18) (16,24) (16,20) (16,22) (18,25) (18,20) (18,22) (19,23) (19,21) (20,25) (20,24) (21,23) (22,24)\nIs there a path between node 10 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph235-19_26", + "image": "data/connectivity/graph_visual/hard/graph235.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,29) (0,27) (0,23) (0,4) (0,20) (0,17) (0,6) (1,5) (1,22) (1,11) (1,19) (1,24) (1,2) (1,15) (1,8) (1,30) (1,9) (1,28) (1,18) (2,5) (2,22) (2,24) (2,15) (2,8) (2,30) (2,9) (2,28) (2,18) (3,26) (3,13) (4,21) (4,29) (4,23) (4,20) (4,17) (4,6) (5,22) (5,19) (5,24) (5,14) (5,30) (5,28) (5,18) (6,21) (6,29) (6,27) (6,23) (6,20) (6,17) (7,26) (7,10) (7,13) (7,16) (7,12) (8,11) (8,24) (8,14) (8,30) (8,9) (8,28) (8,18) (9,22) (9,11) (9,19) (9,15) (9,28) (10,16) (10,12) (11,15) (11,30) (11,28) (11,18) (12,13) (12,16) (13,26) (13,16) (13,25) (14,22) (14,19) (14,15) (14,30) (15,19) (15,30) (15,28) (15,18) (16,26) (16,25) (17,29) (17,23) (18,19) (18,24) (18,28) (19,30) (19,28) (20,21) (20,27) (21,29) (21,27) (21,23) (22,24) (22,28) (23,27) (24,30) (24,28) (25,26) (28,30)\nIs there a path between node 19 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph140-13_26", + "image": "data/connectivity/graph_visual/hard/graph140.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,21) (0,25) (0,12) (0,26) (1,15) (1,23) (1,17) (1,13) (2,27) (2,10) (2,24) (4,9) (4,20) (4,13) (5,28) (5,11) (6,16) (6,23) (6,7) (6,13) (7,15) (7,16) (7,23) (7,17) (7,28) (8,12) (11,17) (11,20) (12,18) (12,14) (12,25) (12,19) (12,26) (13,23) (15,16) (16,23) (17,28) (18,26) (25,26)\nIs there a path between node 13 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph44-7_23", + "image": "data/connectivity/graph_visual/hard/graph44.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,26) (0,15) (0,25) (0,14) (0,7) (0,2) (0,9) (0,5) (1,26) (1,15) (1,25) (1,7) (1,6) (1,2) (1,20) (1,22) (2,25) (2,19) (2,14) (2,4) (3,12) (3,16) (4,15) (4,7) (4,6) (4,8) (5,26) (5,20) (5,8) (5,9) (5,22) (5,13) (6,19) (6,17) (6,7) (6,20) (6,22) (7,19) (7,17) (7,9) (8,19) (9,26) (9,14) (9,24) (11,12) (12,21) (12,18) (12,16) (13,17) (13,22) (14,26) (14,22) (15,19) (15,20) (16,21) (18,23) (19,20) (19,22) (25,26)\nIs there a path between node 7 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph428-7_23", + "image": "data/connectivity/graph_visual/hard/graph428.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,30) (0,7) (0,26) (0,13) (0,21) (0,22) (0,1) (1,24) (1,7) (1,26) (1,11) (2,32) (2,18) (2,9) (2,8) (2,12) (2,29) (2,14) (2,16) (2,10) (2,3) (2,5) (2,17) (2,28) (3,27) (3,32) (3,18) (3,9) (3,8) (3,12) (3,29) (3,16) (3,4) (3,23) (3,5) (3,31) (3,17) (3,15) (3,28) (4,18) (4,9) (4,29) (4,16) (4,10) (4,23) (4,5) (4,17) (4,15) (5,27) (5,32) (5,18) (5,20) (5,9) (5,16) (5,10) (5,17) (5,15) (5,28) (6,25) (6,19) (7,24) (7,30) (7,13) (7,21) (7,22) (8,27) (8,32) (8,18) (8,20) (8,9) (8,29) (8,14) (8,16) (8,10) (8,23) (8,31) (8,17) (8,15) (8,28) (9,27) (9,32) (9,20) (9,12) (9,14) (9,10) (9,23) (9,17) (9,15) (9,28) (10,32) (10,18) (10,20) (10,12) (10,29) (10,16) (10,31) (10,15) (10,28) (11,24) (11,30) (11,26) (11,22) (12,32) (12,18) (12,14) (12,16) (12,23) (12,31) (12,15) (12,28) (13,24) (13,30) (13,26) (14,27) (14,32) (14,18) (14,20) (14,29) (14,17) (14,28) (15,27) (15,32) (15,20) (15,23) (15,31) (15,17) (15,28) (16,27) (16,32) (16,18) (16,20) (16,23) (16,31) (16,28) (17,32) (17,20) (17,29) (17,23) (17,28) (18,27) (18,32) (18,20) (18,29) (18,31) (20,27) (20,32) (20,29) (20,23) (20,31) (20,28) (21,24) (21,30) (21,26) (21,22) (22,30) (22,26) (23,29) (23,31) (24,26) (26,30) (27,32) (28,29) (28,31) (31,32)\nIs there a path between node 7 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph127-3_2", + "image": "data/connectivity/graph_visual/hard/graph127.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,14) (0,20) (0,10) (0,6) (0,18) (1,24) (1,16) (1,27) (1,19) (1,12) (1,11) (1,17) (1,23) (1,26) (1,15) (1,4) (2,14) (2,25) (2,20) (2,6) (3,7) (4,24) (4,16) (4,12) (4,11) (4,8) (4,23) (4,26) (4,5) (5,27) (5,19) (5,17) (5,23) (5,13) (5,26) (5,15) (5,22) (6,14) (6,20) (6,10) (6,21) (6,18) (8,24) (8,16) (8,27) (8,12) (8,11) (8,17) (8,23) (8,26) (8,22) (10,14) (10,20) (10,21) (10,18) (11,24) (11,16) (11,19) (11,17) (11,23) (11,26) (11,15) (11,22) (12,27) (12,19) (12,17) (12,13) (12,26) (12,15) (12,22) (13,24) (13,19) (13,17) (13,23) (13,15) (13,22) (14,25) (14,20) (15,24) (15,16) (15,17) (15,23) (15,26) (15,22) (16,24) (16,17) (16,23) (16,22) (17,24) (17,19) (17,23) (17,22) (18,25) (18,20) (18,21) (19,23) (19,26) (20,25) (22,24) (22,23) (22,26) (24,27) (24,26)\nIs there a path between node 3 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph248-27_12", + "image": "data/connectivity/graph_visual/hard/graph248.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,9) (0,1) (0,25) (0,19) (0,16) (0,23) (0,6) (0,17) (0,13) (0,22) (0,21) (0,24) (0,8) (0,4) (1,29) (1,11) (1,25) (1,19) (1,16) (1,18) (1,23) (1,6) (1,17) (1,13) (1,5) (1,12) (1,22) (1,7) (1,24) (1,10) (1,28) (1,8) (1,4) (2,14) (2,26) (3,14) (3,26) (3,20) (4,29) (4,9) (4,11) (4,25) (4,19) (4,16) (4,15) (4,23) (4,6) (4,17) (4,13) (4,5) (4,12) (4,22) (4,21) (4,7) (4,24) (4,28) (4,8) (5,29) (5,27) (5,11) (5,25) (5,19) (5,16) (5,18) (5,23) (5,6) (5,17) (5,13) (5,12) (5,21) (5,7) (5,24) (5,28) (5,8) (6,29) (6,9) (6,11) (6,25) (6,15) (6,23) (6,17) (6,12) (6,21) (6,7) (6,24) (6,10) (6,28) (6,8) (7,9) (7,27) (7,11) (7,16) (7,18) (7,15) (7,17) (7,13) (7,22) (7,21) (7,24) (7,10) (7,28) (8,29) (8,27) (8,11) (8,25) (8,19) (8,16) (8,15) (8,13) (8,22) (8,21) (8,24) (8,10) (9,27) (9,11) (9,25) (9,19) (9,16) (9,18) (9,23) (9,17) (9,13) (9,12) (9,24) (9,10) (9,28) (10,29) (10,27) (10,11) (10,25) (10,19) (10,15) (10,23) (10,17) (10,13) (10,21) (10,24) (10,28) (11,27) (11,25) (11,19) (11,16) (11,18) (11,15) (11,23) (11,17) (11,13) (11,22) (11,21) (11,24) (11,28) (12,29) (12,27) (12,19) (12,16) (12,18) (12,23) (12,17) (12,13) (12,21) (12,24) (12,28) (13,29) (13,25) (13,16) (13,18) (13,23) (13,22) (13,24) (13,28) (14,26) (14,20) (15,29) (15,16) (15,23) (15,17) (15,22) (15,21) (15,28) (16,19) (16,18) (16,23) (16,22) (16,21) (16,24) (16,28) (17,29) (17,25) (17,19) (17,18) (17,23) (17,21) (17,28) (18,25) (18,19) (18,23) (18,22) (18,21) (19,27) (19,25) (19,23) (19,22) (19,21) (19,24) (19,28) (20,26) (21,29) (21,27) (21,22) (21,28) (22,29) (22,23) (22,24) (22,28) (23,25) (23,24) (24,29) (24,27) (24,25) (24,28) (25,28) (27,28) (28,29)\nIs there a path between node 27 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph344-28_13", + "image": "data/connectivity/graph_visual/hard/graph344.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,19) (0,22) (0,8) (0,14) (1,9) (1,11) (1,21) (1,16) (1,28) (1,25) (1,6) (1,10) (2,12) (2,18) (2,25) (2,20) (2,10) (3,18) (3,23) (3,5) (4,24) (5,26) (5,21) (5,29) (5,25) (5,20) (5,31) (6,12) (6,18) (6,17) (7,15) (7,14) (8,30) (8,19) (8,13) (9,21) (9,28) (9,25) (9,17) (10,26) (10,11) (10,25) (10,17) (11,18) (11,23) (11,25) (11,20) (12,21) (12,18) (12,23) (13,24) (13,19) (13,15) (13,14) (14,27) (14,22) (15,24) (15,22) (16,23) (16,17) (18,26) (18,28) (18,23) (18,20) (19,24) (19,30) (20,21) (20,28) (21,26) (21,25) (23,26) (24,30) (25,31) (26,28) (26,31) (28,31)\nIs there a path between node 28 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph480-17_16", + "image": "data/connectivity/graph_visual/hard/graph480.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,28) (0,10) (0,15) (0,27) (0,11) (0,31) (0,4) (0,30) (0,5) (0,26) (0,24) (0,17) (0,21) (0,25) (0,9) (0,19) (0,18) (0,7) (0,14) (0,22) (0,6) (1,32) (1,12) (1,29) (2,28) (2,10) (2,15) (2,16) (2,31) (2,4) (2,5) (2,26) (2,24) (2,17) (2,21) (2,25) (2,9) (2,19) (2,18) (2,7) (2,14) (2,23) (2,3) (2,6) (3,28) (3,27) (3,11) (3,16) (3,31) (3,30) (3,8) (3,5) (3,26) (3,24) (3,17) (3,21) (3,25) (3,19) (3,18) (3,14) (3,23) (3,20) (3,22) (3,6) (4,28) (4,10) (4,15) (4,11) (4,16) (4,31) (4,30) (4,8) (4,5) (4,26) (4,24) (4,17) (4,21) (4,9) (4,18) (4,7) (4,14) (4,23) (4,20) (4,22) (4,6) (5,28) (5,10) (5,15) (5,27) (5,11) (5,16) (5,30) (5,8) (5,26) (5,17) (5,21) (5,25) (5,19) (5,18) (5,7) (5,23) (5,20) (5,6) (6,28) (6,10) (6,27) (6,16) (6,8) (6,26) (6,24) (6,17) (6,21) (6,25) (6,18) (6,7) (6,14) (7,28) (7,15) (7,27) (7,11) (7,16) (7,31) (7,30) (7,8) (7,26) (7,24) (7,17) (7,21) (7,25) (7,19) (7,14) (7,23) (7,22) (8,28) (8,11) (8,31) (8,26) (8,24) (8,17) (8,21) (8,9) (8,19) (8,18) (8,20) (8,22) (9,28) (9,10) (9,15) (9,11) (9,16) (9,31) (9,30) (9,26) (9,24) (9,17) (9,19) (9,14) (9,20) (9,22) (10,28) (10,15) (10,11) (10,31) (10,30) (10,26) (10,24) (10,17) (10,21) (10,19) (10,18) (10,14) (10,23) (10,20) (10,22) (11,27) (11,16) (11,31) (11,30) (11,26) (11,24) (11,21) (11,25) (11,14) (11,20) (11,22) (12,13) (13,32) (13,29) (14,28) (14,27) (14,16) (14,31) (14,30) (14,26) (14,24) (14,17) (14,21) (14,19) (14,23) (14,20) (14,22) (15,27) (15,31) (15,24) (15,17) (15,21) (15,25) (15,19) (15,23) (15,20) (15,22) (16,28) (16,30) (16,26) (16,24) (16,17) (16,25) (16,23) (16,20) (16,22) (17,31) (17,30) (17,26) (17,24) (17,25) (17,18) (18,28) (18,27) (18,31) (18,30) (18,26) (18,24) (18,21) (18,25) (18,19) (18,23) (18,22) (19,27) (19,31) (19,30) (19,24) (19,21) (19,25) (19,20) (20,27) (20,31) (20,30) (20,26) (20,24) (20,25) (20,23) (20,22) (21,28) (21,27) (21,31) (21,30) (21,26) (21,25) (21,23) (21,22) (22,27) (22,31) (22,26) (22,25) (23,28) (23,27) (23,31) (23,26) (23,24) (24,31) (24,26) (24,25) (25,28) (25,27) (25,31) (25,30) (25,26) (26,28) (26,27) (26,31) (26,30) (27,28) (27,31) (27,30) (28,30) (29,32)\nIs there a path between node 17 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph541-32_9", + "image": "data/connectivity/graph_visual/hard/graph541.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,13) (0,30) (0,32) (0,15) (0,8) (0,17) (0,21) (0,19) (0,14) (0,26) (0,3) (0,4) (0,18) (0,11) (0,10) (0,7) (0,28) (0,31) (1,13) (1,30) (1,32) (1,23) (1,15) (1,8) (1,17) (1,21) (1,19) (1,33) (1,26) (1,9) (1,4) (1,11) (1,7) (2,20) (2,13) (2,30) (2,32) (2,23) (2,17) (2,22) (2,19) (2,33) (2,14) (2,26) (2,3) (2,18) (2,11) (2,7) (2,28) (2,31) (3,20) (3,13) (3,30) (3,32) (3,23) (3,15) (3,8) (3,17) (3,21) (3,14) (3,26) (3,9) (3,18) (3,11) (3,28) (3,31) (4,20) (4,13) (4,30) (4,32) (4,23) (4,15) (4,33) (4,26) (4,18) (4,11) (4,10) (4,7) (4,28) (4,31) (5,12) (5,27) (6,29) (6,24) (6,12) (6,27) (7,20) (7,13) (7,30) (7,23) (7,15) (7,8) (7,17) (7,22) (7,19) (7,14) (7,26) (7,18) (7,10) (7,28) (7,31) (8,20) (8,30) (8,15) (8,17) (8,22) (8,21) (8,19) (8,33) (8,14) (8,26) (8,9) (8,18) (8,10) (9,13) (9,30) (9,32) (9,23) (9,22) (9,21) (9,33) (9,14) (9,26) (9,18) (9,11) (9,10) (9,28) (9,31) (10,13) (10,30) (10,32) (10,15) (10,22) (10,21) (10,19) (10,33) (10,26) (10,18) (10,11) (10,28) (11,20) (11,13) (11,30) (11,32) (11,23) (11,15) (11,17) (11,22) (11,21) (11,19) (11,26) (11,28) (11,31) (12,29) (12,24) (12,16) (12,27) (13,20) (13,32) (13,15) (13,17) (13,22) (13,21) (13,33) (13,14) (13,28) (13,31) (14,20) (14,32) (14,15) (14,17) (14,22) (14,18) (14,28) (14,31) (15,20) (15,30) (15,32) (15,17) (15,22) (15,21) (15,19) (15,33) (15,26) (15,18) (15,31) (16,29) (16,27) (17,20) (17,30) (17,22) (17,21) (17,19) (17,33) (17,26) (17,18) (17,28) (17,31) (18,20) (18,30) (18,23) (18,22) (18,21) (18,28) (18,31) (19,20) (19,32) (19,21) (19,26) (19,28) (20,30) (20,32) (20,23) (20,22) (20,21) (20,28) (21,30) (21,32) (21,23) (21,22) (21,33) (21,26) (21,31) (22,32) (22,28) (22,31) (23,30) (23,32) (23,33) (23,26) (23,31) (24,29) (24,27) (26,30) (26,32) (26,33) (26,28) (27,29) (28,31) (30,32) (30,33) (30,31) (31,32) (32,33)\nIs there a path between node 32 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph146-25_26", + "image": "data/connectivity/graph_visual/hard/graph146.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,14) (0,13) (0,11) (0,21) (0,8) (0,18) (0,3) (0,7) (0,15) (0,20) (0,17) (0,10) (0,22) (0,1) (0,9) (0,6) (0,19) (1,23) (1,14) (1,5) (1,13) (1,11) (1,12) (1,21) (1,8) (1,18) (1,3) (1,25) (1,7) (1,28) (1,15) (1,20) (1,17) (1,10) (1,22) (1,9) (1,6) (1,16) (1,19) (3,27) (3,14) (3,5) (3,13) (3,4) (3,21) (3,18) (3,25) (3,28) (3,15) (3,20) (3,17) (3,22) (3,6) (3,16) (3,19) (4,27) (4,23) (4,5) (4,13) (4,11) (4,12) (4,8) (4,28) (4,15) (4,20) (4,17) (4,10) (4,24) (4,6) (5,27) (5,23) (5,14) (5,13) (5,11) (5,12) (5,21) (5,8) (5,18) (5,25) (5,7) (5,15) (5,10) (5,22) (5,24) (5,9) (5,6) (5,16) (5,19) (6,27) (6,14) (6,11) (6,12) (6,18) (6,25) (6,7) (6,20) (6,17) (6,10) (6,22) (6,24) (6,9) (6,16) (6,19) (7,23) (7,14) (7,13) (7,12) (7,21) (7,8) (7,25) (7,28) (7,20) (7,10) (7,22) (7,16) (7,19) (8,27) (8,13) (8,18) (8,25) (8,15) (8,17) (8,10) (8,22) (8,24) (8,9) (8,16) (8,19) (9,27) (9,23) (9,11) (9,21) (9,25) (9,28) (9,15) (9,20) (9,17) (9,10) (9,22) (9,24) (9,16) (9,19) (10,27) (10,14) (10,11) (10,12) (10,25) (10,28) (10,15) (10,20) (10,17) (10,24) (10,16) (10,19) (11,23) (11,21) (11,18) (11,25) (11,28) (11,15) (11,17) (11,22) (11,24) (11,19) (12,27) (12,23) (12,13) (12,21) (12,18) (12,25) (12,28) (12,15) (12,17) (12,22) (12,24) (12,16) (13,27) (13,14) (13,21) (13,18) (13,28) (13,15) (13,17) (13,24) (13,16) (13,19) (14,27) (14,25) (14,28) (14,15) (14,17) (14,22) (14,24) (14,16) (15,23) (15,21) (15,18) (15,25) (15,20) (15,24) (16,27) (16,23) (16,17) (16,24) (16,19) (17,27) (17,23) (17,18) (17,25) (17,28) (17,20) (17,22) (17,24) (17,19) (18,23) (18,21) (18,25) (18,28) (18,20) (18,22) (18,24) (18,19) (19,27) (19,23) (19,21) (19,25) (19,24) (20,27) (20,23) (20,21) (20,25) (20,24) (21,23) (21,22) (23,27) (23,24) (25,27) (25,28) (27,28)\nIs there a path between node 25 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph365-28_19", + "image": "data/connectivity/graph_visual/hard/graph365.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,29) (0,27) (0,31) (0,21) (0,10) (0,5) (0,11) (0,19) (0,18) (0,6) (0,20) (0,26) (1,14) (1,22) (1,23) (1,9) (1,28) (1,25) (1,12) (1,13) (1,2) (1,30) (2,23) (2,9) (2,28) (2,25) (2,12) (2,13) (3,15) (3,7) (3,17) (3,16) (4,29) (4,27) (4,31) (4,10) (4,5) (4,11) (4,20) (4,26) (5,29) (5,27) (5,24) (5,31) (5,19) (5,18) (5,26) (6,29) (6,27) (6,24) (6,31) (6,21) (6,11) (6,19) (6,18) (6,20) (7,15) (7,16) (8,15) (8,17) (8,16) (9,22) (9,23) (9,28) (9,25) (9,12) (9,13) (9,30) (10,29) (10,24) (10,31) (10,11) (10,19) (10,20) (11,29) (11,27) (11,24) (11,31) (11,18) (11,20) (12,14) (12,22) (12,13) (12,30) (13,22) (13,23) (13,28) (13,25) (13,30) (14,22) (14,28) (14,25) (14,30) (16,17) (18,29) (18,27) (18,24) (18,31) (18,19) (19,29) (19,24) (19,31) (19,21) (19,20) (19,26) (20,27) (20,24) (20,31) (20,21) (21,29) (21,27) (21,24) (21,26) (23,25) (24,27) (24,26) (25,30) (26,29) (26,27) (26,31) (27,29) (27,31) (28,30) (29,31)\nIs there a path between node 28 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph505-32_11", + "image": "data/connectivity/graph_visual/hard/graph505.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,33) (0,8) (0,16) (0,5) (0,17) (0,23) (1,6) (1,7) (1,27) (1,14) (1,4) (1,13) (1,24) (1,21) (2,32) (2,19) (2,29) (2,12) (2,28) (2,15) (3,32) (3,19) (3,26) (3,12) (3,20) (3,30) (3,28) (3,15) (4,6) (4,9) (4,7) (4,14) (4,10) (4,24) (5,33) (5,8) (5,16) (5,31) (5,17) (5,23) (6,7) (6,27) (6,10) (6,25) (6,13) (7,27) (7,14) (7,10) (7,25) (7,24) (7,21) (8,16) (8,17) (9,27) (9,14) (9,10) (9,24) (9,21) (10,25) (10,21) (11,32) (11,19) (11,26) (11,12) (11,20) (11,30) (11,28) (11,22) (12,19) (12,29) (12,26) (12,20) (12,15) (12,22) (13,27) (13,14) (13,25) (13,24) (13,21) (14,25) (14,24) (14,21) (15,32) (15,19) (15,26) (15,20) (15,30) (15,28) (16,33) (16,18) (16,31) (16,23) (17,33) (17,18) (17,23) (18,33) (18,31) (19,32) (19,29) (19,26) (19,30) (19,28) (19,22) (20,32) (20,30) (20,28) (21,25) (22,32) (22,29) (22,26) (22,30) (22,28) (23,33) (24,27) (24,25) (25,27) (26,29) (26,30) (26,28) (28,30) (29,32) (29,30) (30,32) (31,33)\nIs there a path between node 32 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph357-2_27", + "image": "data/connectivity/graph_visual/hard/graph357.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,22) (0,27) (1,18) (1,21) (1,15) (1,6) (1,29) (1,9) (1,4) (1,8) (1,28) (1,17) (2,13) (2,24) (2,14) (2,30) (2,12) (2,17) (2,5) (3,20) (3,14) (3,23) (3,15) (3,26) (3,9) (3,25) (3,8) (3,28) (3,17) (4,20) (4,18) (4,23) (4,15) (4,10) (4,30) (4,6) (4,26) (4,12) (4,16) (5,24) (5,14) (5,15) (5,6) (5,29) (5,12) (5,9) (5,8) (6,18) (6,10) (6,29) (6,28) (6,17) (7,27) (8,18) (8,21) (8,13) (8,23) (8,12) (8,25) (8,19) (8,17) (9,15) (9,30) (9,29) (9,25) (9,19) (9,17) (10,29) (10,26) (10,28) (10,17) (11,18) (11,15) (11,30) (11,26) (11,28) (11,17) (12,20) (12,14) (12,23) (13,18) (13,30) (13,29) (13,26) (13,25) (13,19) (13,28) (13,17) (14,20) (14,19) (15,18) (16,20) (16,26) (16,25) (16,19) (17,30) (17,26) (17,19) (18,21) (18,24) (18,30) (18,25) (18,28) (19,21) (19,23) (20,24) (20,26) (20,28) (21,24) (21,30) (24,30) (24,26) (25,30) (26,29) (26,28)\nIs there a path between node 2 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph575-29_17", + "image": "data/connectivity/graph_visual/hard/graph575.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,30) (0,10) (0,23) (0,11) (0,31) (1,28) (1,26) (1,5) (1,20) (1,18) (1,29) (1,8) (1,9) (1,13) (2,3) (2,28) (2,26) (2,15) (2,20) (2,21) (2,12) (2,18) (2,29) (2,8) (2,9) (2,13) (2,16) (3,22) (3,28) (3,15) (3,20) (3,21) (3,12) (3,18) (3,29) (3,8) (3,9) (3,13) (3,16) (4,24) (4,30) (4,10) (4,23) (4,7) (4,17) (4,6) (5,28) (5,26) (5,27) (5,21) (5,12) (5,18) (5,29) (5,8) (5,9) (5,13) (5,16) (6,30) (6,10) (6,23) (6,11) (6,31) (6,7) (6,17) (7,30) (7,10) (7,23) (7,11) (7,31) (8,28) (8,32) (8,26) (8,27) (8,15) (8,18) (8,29) (8,9) (8,16) (9,27) (9,15) (9,21) (9,29) (9,16) (10,24) (10,30) (10,23) (10,11) (10,31) (10,17) (11,30) (11,31) (12,22) (12,32) (12,27) (12,15) (12,20) (12,21) (12,13) (12,16) (13,32) (13,26) (13,15) (13,20) (13,21) (13,29) (13,16) (14,33) (14,19) (15,28) (15,26) (15,27) (15,21) (15,16) (16,22) (16,28) (16,32) (16,26) (16,27) (16,18) (16,29) (17,23) (17,31) (18,22) (18,28) (18,32) (18,26) (18,27) (18,20) (18,21) (19,33) (20,22) (20,28) (20,26) (20,21) (20,29) (21,22) (21,32) (21,26) (21,27) (22,26) (22,27) (23,30) (23,31) (26,27) (26,29) (27,28) (27,32) (27,29)\nIs there a path between node 29 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph271-3_14", + "image": "data/connectivity/graph_visual/hard/graph271.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,20) (1,3) (1,27) (1,23) (1,9) (1,26) (1,29) (1,15) (1,11) (1,24) (1,22) (1,10) (1,21) (1,18) (1,17) (1,2) (1,5) (1,4) (1,28) (1,7) (1,25) (2,20) (2,19) (2,3) (2,27) (2,23) (2,26) (2,29) (2,11) (2,24) (2,22) (2,21) (2,30) (2,18) (2,5) (2,4) (2,28) (2,7) (2,13) (2,25) (3,20) (3,19) (3,9) (3,26) (3,29) (3,15) (3,11) (3,24) (3,22) (3,10) (3,21) (3,30) (3,8) (3,28) (3,12) (3,7) (3,13) (3,25) (4,20) (4,19) (4,27) (4,26) (4,29) (4,15) (4,11) (4,24) (4,10) (4,30) (4,18) (4,17) (4,12) (4,7) (4,13) (4,25) (5,20) (5,19) (5,27) (5,26) (5,29) (5,24) (5,22) (5,30) (5,18) (5,8) (5,17) (5,6) (5,12) (5,13) (5,25) (6,19) (6,27) (6,23) (6,9) (6,26) (6,29) (6,15) (6,11) (6,22) (6,21) (6,30) (6,17) (6,28) (6,12) (6,7) (6,13) (6,25) (7,19) (7,27) (7,9) (7,26) (7,29) (7,15) (7,11) (7,22) (7,21) (7,30) (7,18) (7,8) (7,17) (7,28) (7,12) (7,13) (7,25) (8,20) (8,19) (8,27) (8,23) (8,9) (8,29) (8,15) (8,24) (8,22) (8,10) (8,30) (8,18) (8,17) (8,28) (8,13) (8,25) (9,20) (9,19) (9,27) (9,23) (9,11) (9,24) (9,22) (9,10) (9,30) (9,17) (9,12) (9,13) (9,25) (10,27) (10,23) (10,29) (10,15) (10,11) (10,24) (10,21) (10,30) (10,17) (10,28) (10,13) (10,25) (11,20) (11,27) (11,23) (11,29) (11,15) (11,24) (11,22) (11,21) (11,30) (11,12) (11,13) (11,25) (12,19) (12,27) (12,23) (12,26) (12,29) (12,15) (12,24) (12,22) (12,30) (12,18) (12,13) (12,25) (13,20) (13,19) (13,27) (13,26) (13,29) (13,24) (13,21) (13,18) (13,28) (14,16) (15,20) (15,19) (15,23) (15,26) (15,29) (15,24) (15,22) (15,21) (15,18) (15,28) (15,25) (17,20) (17,23) (17,24) (17,22) (17,21) (17,30) (17,28) (17,25) (18,20) (18,19) (18,23) (18,26) (18,24) (18,22) (18,30) (18,28) (18,25) (19,27) (19,29) (19,22) (19,21) (19,30) (19,25) (20,27) (20,26) (20,29) (20,24) (20,22) (20,21) (21,27) (21,23) (21,22) (21,30) (21,28) (21,25) (22,27) (22,23) (22,29) (22,24) (22,30) (22,28) (22,25) (23,27) (23,26) (23,29) (23,30) (23,28) (23,25) (24,27) (24,25) (25,26) (25,29) (25,30) (25,28) (26,30) (27,30) (27,28) (29,30)\nIs there a path between node 3 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph701-8_27", + "image": "data/connectivity/graph_visual/hard/graph701.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,12) (0,6) (0,25) (0,9) (0,33) (0,3) (0,2) (0,24) (0,10) (0,28) (0,4) (0,29) (0,31) (0,21) (0,26) (0,13) (0,8) (0,5) (1,20) (1,34) (1,32) (1,19) (1,16) (2,15) (2,12) (2,25) (2,9) (2,33) (2,3) (2,28) (2,4) (2,29) (2,31) (2,26) (2,8) (2,5) (3,15) (3,12) (3,33) (3,28) (3,4) (3,29) (3,31) (3,21) (3,26) (3,8) (4,25) (4,9) (4,28) (4,31) (4,13) (4,8) (5,15) (5,12) (5,25) (5,33) (5,24) (5,10) (5,26) (5,13) (5,8) (6,12) (6,25) (6,9) (6,33) (6,24) (6,10) (6,28) (6,29) (6,31) (6,21) (6,13) (6,8) (7,20) (7,34) (7,32) (7,19) (7,16) (8,12) (8,25) (8,33) (8,10) (8,28) (8,29) (8,21) (8,26) (9,12) (9,33) (9,24) (9,10) (9,28) (9,26) (10,15) (10,12) (10,33) (10,24) (10,29) (10,31) (10,21) (10,26) (10,13) (11,22) (11,23) (11,14) (11,17) (12,28) (12,29) (12,21) (12,26) (12,13) (13,25) (13,33) (13,24) (13,28) (13,29) (13,31) (13,21) (13,26) (14,18) (14,22) (14,23) (14,27) (14,17) (14,30) (15,33) (15,24) (15,28) (15,29) (15,31) (15,21) (15,26) (16,20) (16,34) (16,32) (17,22) (17,23) (17,30) (18,27) (18,30) (19,20) (19,32) (20,34) (20,32) (21,25) (21,24) (21,28) (21,29) (21,26) (22,23) (22,27) (22,30) (23,30) (24,25) (24,28) (24,29) (24,26) (25,33) (25,28) (25,29) (25,31) (26,33) (26,29) (27,30) (28,33) (28,29) (29,33) (29,31) (31,33) (32,34)\nIs there a path between node 8 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph480-5_18", + "image": "data/connectivity/graph_visual/hard/graph480.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,28) (0,10) (0,15) (0,27) (0,11) (0,31) (0,4) (0,30) (0,5) (0,26) (0,24) (0,17) (0,21) (0,25) (0,9) (0,19) (0,18) (0,7) (0,14) (0,22) (0,6) (1,32) (1,12) (1,29) (2,28) (2,10) (2,15) (2,16) (2,31) (2,4) (2,5) (2,26) (2,24) (2,17) (2,21) (2,25) (2,9) (2,19) (2,18) (2,7) (2,14) (2,23) (2,3) (2,6) (3,28) (3,27) (3,11) (3,16) (3,31) (3,30) (3,8) (3,5) (3,26) (3,24) (3,17) (3,21) (3,25) (3,19) (3,18) (3,14) (3,23) (3,20) (3,22) (3,6) (4,28) (4,10) (4,15) (4,11) (4,16) (4,31) (4,30) (4,8) (4,5) (4,26) (4,24) (4,17) (4,21) (4,9) (4,18) (4,7) (4,14) (4,23) (4,20) (4,22) (4,6) (5,28) (5,10) (5,15) (5,27) (5,11) (5,16) (5,30) (5,8) (5,26) (5,17) (5,21) (5,25) (5,19) (5,18) (5,7) (5,23) (5,20) (5,6) (6,28) (6,10) (6,27) (6,16) (6,8) (6,26) (6,24) (6,17) (6,21) (6,25) (6,18) (6,7) (6,14) (7,28) (7,15) (7,27) (7,11) (7,16) (7,31) (7,30) (7,8) (7,26) (7,24) (7,17) (7,21) (7,25) (7,19) (7,14) (7,23) (7,22) (8,28) (8,11) (8,31) (8,26) (8,24) (8,17) (8,21) (8,9) (8,19) (8,18) (8,20) (8,22) (9,28) (9,10) (9,15) (9,11) (9,16) (9,31) (9,30) (9,26) (9,24) (9,17) (9,19) (9,14) (9,20) (9,22) (10,28) (10,15) (10,11) (10,31) (10,30) (10,26) (10,24) (10,17) (10,21) (10,19) (10,18) (10,14) (10,23) (10,20) (10,22) (11,27) (11,16) (11,31) (11,30) (11,26) (11,24) (11,21) (11,25) (11,14) (11,20) (11,22) (12,13) (13,32) (13,29) (14,28) (14,27) (14,16) (14,31) (14,30) (14,26) (14,24) (14,17) (14,21) (14,19) (14,23) (14,20) (14,22) (15,27) (15,31) (15,24) (15,17) (15,21) (15,25) (15,19) (15,23) (15,20) (15,22) (16,28) (16,30) (16,26) (16,24) (16,17) (16,25) (16,23) (16,20) (16,22) (17,31) (17,30) (17,26) (17,24) (17,25) (17,18) (18,28) (18,27) (18,31) (18,30) (18,26) (18,24) (18,21) (18,25) (18,19) (18,23) (18,22) (19,27) (19,31) (19,30) (19,24) (19,21) (19,25) (19,20) (20,27) (20,31) (20,30) (20,26) (20,24) (20,25) (20,23) (20,22) (21,28) (21,27) (21,31) (21,30) (21,26) (21,25) (21,23) (21,22) (22,27) (22,31) (22,26) (22,25) (23,28) (23,27) (23,31) (23,26) (23,24) (24,31) (24,26) (24,25) (25,28) (25,27) (25,31) (25,30) (25,26) (26,28) (26,27) (26,31) (26,30) (27,28) (27,31) (27,30) (28,30) (29,32)\nIs there a path between node 5 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph70-9_22", + "image": "data/connectivity/graph_visual/hard/graph70.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,12) (0,19) (0,15) (1,5) (1,20) (1,14) (1,25) (1,10) (2,23) (3,5) (3,11) (3,7) (3,19) (3,18) (4,5) (4,20) (4,25) (4,19) (5,20) (5,25) (5,11) (5,17) (5,19) (5,15) (6,22) (6,25) (6,11) (6,15) (7,20) (7,19) (8,16) (8,26) (9,23) (10,20) (10,17) (10,13) (11,20) (11,17) (11,13) (11,19) (12,14) (12,25) (12,19) (13,14) (14,17) (15,25) (16,21) (16,23) (17,22) (17,20) (17,25) (22,25)\nIs there a path between node 9 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph318-28_20", + "image": "data/connectivity/graph_visual/hard/graph318.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,22) (0,20) (0,21) (0,12) (0,4) (1,27) (1,9) (1,14) (1,25) (2,17) (2,14) (2,31) (3,13) (3,6) (3,20) (3,21) (3,19) (4,13) (5,11) (5,8) (5,7) (7,29) (7,16) (7,30) (8,29) (8,11) (8,10) (9,17) (9,27) (9,25) (10,16) (12,21) (12,19) (13,28) (13,20) (13,21) (14,27) (14,23) (14,31) (15,27) (15,23) (15,26) (17,23) (17,26) (18,21) (21,28) (23,31) (25,31) (25,26) (27,31) (29,30)\nIs there a path between node 28 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph251-29_16", + "image": "data/connectivity/graph_visual/hard/graph251.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,17) (1,8) (1,29) (1,10) (1,7) (1,11) (1,25) (1,18) (1,14) (1,30) (1,16) (1,5) (1,26) (1,4) (1,23) (1,27) (2,21) (3,21) (4,17) (4,29) (4,9) (4,10) (4,6) (4,7) (4,11) (4,14) (4,22) (4,26) (4,13) (4,24) (4,23) (4,19) (5,17) (5,29) (5,9) (5,10) (5,6) (5,7) (5,11) (5,18) (5,14) (5,30) (5,16) (5,26) (5,15) (5,13) (5,24) (5,19) (5,27) (6,17) (6,9) (6,10) (6,11) (6,18) (6,14) (6,30) (6,16) (6,22) (6,15) (6,24) (6,19) (6,27) (7,17) (7,8) (7,29) (7,9) (7,10) (7,25) (7,18) (7,30) (7,16) (7,22) (7,24) (7,23) (7,19) (7,27) (8,17) (8,11) (8,25) (8,18) (8,14) (8,30) (8,16) (8,15) (8,13) (8,24) (8,19) (8,27) (9,17) (9,29) (9,10) (9,11) (9,25) (9,14) (9,30) (9,16) (9,22) (9,15) (9,13) (9,24) (9,19) (9,27) (10,17) (10,11) (10,25) (10,18) (10,14) (10,30) (10,16) (10,22) (10,15) (10,13) (10,24) (10,23) (10,27) (11,29) (11,25) (11,14) (11,30) (11,16) (11,26) (11,15) (11,13) (11,24) (11,23) (11,19) (11,27) (12,28) (13,29) (13,18) (13,14) (13,30) (13,16) (13,22) (13,26) (13,15) (13,24) (13,19) (13,27) (14,17) (14,25) (14,18) (14,30) (14,16) (14,22) (14,26) (14,15) (14,19) (14,27) (15,17) (15,25) (15,18) (15,30) (15,16) (15,22) (15,26) (15,24) (15,23) (15,19) (15,27) (16,29) (16,25) (16,30) (16,23) (16,27) (17,29) (17,25) (17,18) (17,30) (17,26) (17,19) (17,27) (18,22) (18,26) (18,24) (18,23) (18,19) (19,29) (19,25) (19,22) (19,26) (19,24) (19,23) (19,27) (22,29) (22,25) (22,26) (22,24) (22,23) (22,27) (23,25) (23,30) (23,24) (24,29) (24,25) (24,26) (24,27) (25,29) (25,30) (25,26) (25,27) (26,29) (26,30) (29,30)\nIs there a path between node 29 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph442-3_24", + "image": "data/connectivity/graph_visual/hard/graph442.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,11) (0,32) (0,29) (0,7) (0,15) (1,30) (1,10) (1,8) (2,27) (2,18) (2,20) (2,7) (2,26) (3,14) (3,9) (4,18) (4,11) (4,13) (4,15) (5,30) (5,21) (6,14) (6,21) (6,17) (7,18) (7,22) (7,31) (7,29) (7,26) (8,14) (8,10) (9,21) (10,12) (10,21) (10,17) (11,19) (11,22) (11,28) (11,32) (11,29) (11,15) (11,26) (12,30) (12,21) (13,27) (13,20) (13,28) (13,31) (14,17) (15,20) (15,31) (15,26) (16,27) (16,32) (17,30) (18,27) (18,28) (18,32) (18,26) (18,24) (18,23) (19,27) (19,20) (19,31) (19,29) (19,26) (19,24) (20,25) (20,28) (20,32) (20,26) (22,31) (22,23) (23,27) (23,28) (23,26) (25,26) (26,27) (26,28) (26,29) (28,32) (28,31) (29,31)\nIs there a path between node 3 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph313-24_1", + "image": "data/connectivity/graph_visual/hard/graph313.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,29) (0,15) (0,4) (1,14) (1,12) (1,13) (2,22) (3,27) (4,5) (4,29) (4,15) (5,9) (5,29) (5,18) (5,7) (5,30) (6,12) (6,10) (7,20) (7,25) (7,9) (7,15) (7,21) (9,20) (9,19) (9,29) (9,21) (11,16) (13,27) (14,28) (15,18) (15,21) (18,30) (19,29) (20,30) (22,26) (22,31) (25,29) (25,30)\nIs there a path between node 24 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph181-1_23", + "image": "data/connectivity/graph_visual/hard/graph181.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,18) (1,25) (1,22) (1,15) (1,20) (1,19) (1,11) (1,2) (1,23) (1,24) (2,25) (2,22) (2,15) (2,3) (2,11) (2,7) (2,6) (2,14) (2,24) (3,22) (3,16) (3,15) (3,19) (3,7) (3,23) (3,6) (3,14) (4,21) (4,9) (4,28) (4,8) (4,26) (4,17) (5,9) (5,12) (5,27) (5,26) (5,17) (6,25) (6,16) (6,15) (6,20) (6,19) (6,7) (6,14) (6,24) (7,25) (7,22) (7,16) (7,20) (7,19) (7,11) (7,23) (7,24) (8,21) (8,9) (8,12) (8,26) (8,17) (9,21) (9,10) (9,28) (9,12) (9,27) (9,26) (9,17) (10,21) (10,28) (10,12) (10,26) (10,17) (11,22) (11,16) (11,15) (11,20) (11,19) (11,23) (11,14) (11,24) (12,27) (12,26) (12,17) (13,18) (14,16) (14,15) (14,20) (14,24) (15,22) (15,16) (15,20) (15,23) (15,24) (16,25) (16,22) (16,20) (16,19) (16,23) (16,24) (17,21) (17,27) (17,26) (19,25) (19,22) (19,23) (19,24) (20,22) (20,23) (20,24) (21,28) (21,27) (21,26) (22,25) (23,25) (23,24) (24,25) (26,27)\nIs there a path between node 1 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph97-12_21", + "image": "data/connectivity/graph_visual/hard/graph97.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,2) (0,8) (0,4) (0,9) (0,16) (0,21) (0,12) (0,23) (0,7) (0,11) (1,25) (1,22) (2,8) (2,26) (2,16) (2,20) (3,10) (3,16) (3,13) (3,14) (3,11) (4,26) (4,21) (4,12) (4,14) (5,10) (5,21) (5,13) (5,23) (5,7) (5,14) (5,15) (6,10) (6,9) (6,13) (6,12) (6,23) (6,14) (6,20) (6,15) (7,9) (7,16) (7,18) (7,23) (7,14) (7,15) (7,17) (8,10) (8,9) (8,16) (8,15) (8,11) (9,10) (9,26) (9,14) (9,17) (10,16) (12,18) (12,13) (13,18) (13,15) (14,21) (14,15) (15,26) (15,20) (16,18) (16,20) (17,20) (19,24) (19,22) (20,26) (20,21) (22,27)\nIs there a path between node 12 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph620-18_28", + "image": "data/connectivity/graph_visual/hard/graph620.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,20) (0,34) (0,1) (0,10) (0,12) (1,12) (2,24) (3,31) (3,30) (3,25) (4,19) (4,6) (5,8) (7,26) (10,20) (10,28) (10,17) (10,18) (12,20) (12,32) (12,17) (13,14) (13,15) (13,21) (13,26) (13,23) (14,15) (14,21) (15,26) (15,23) (16,21) (16,30) (17,20) (17,27) (17,32) (18,27) (18,34) (19,33) (20,27) (21,31) (21,22) (22,26) (22,31) (23,31) (26,31) (28,34) (30,31)\nIs there a path between node 18 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph395-11_0", + "image": "data/connectivity/graph_visual/hard/graph395.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,24) (0,18) (0,29) (0,9) (0,4) (0,14) (0,3) (0,13) (1,21) (1,24) (1,20) (1,9) (1,3) (2,10) (2,26) (2,28) (3,20) (3,6) (3,8) (3,5) (3,27) (4,21) (4,24) (4,29) (4,6) (4,9) (4,8) (4,17) (4,15) (4,27) (4,32) (4,13) (5,21) (5,16) (5,24) (5,9) (5,27) (6,24) (6,9) (6,17) (6,15) (6,32) (7,31) (8,16) (8,24) (8,11) (8,9) (8,27) (9,21) (9,16) (9,24) (9,11) (9,15) (9,14) (9,13) (11,16) (12,25) (13,16) (13,20) (13,30) (13,27) (14,16) (14,24) (14,18) (14,27) (15,24) (15,18) (15,20) (15,17) (16,21) (16,30) (16,27) (17,21) (17,20) (17,29) (18,20) (18,29) (18,30) (18,27) (19,25) (19,26) (19,22) (20,24) (21,24) (21,29) (22,26) (22,28) (23,25) (24,30) (26,28) (27,32) (29,32)\nIs there a path between node 11 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph54-14_4", + "image": "data/connectivity/graph_visual/hard/graph54.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,14) (0,25) (0,10) (0,26) (0,16) (0,1) (0,5) (0,22) (0,21) (0,15) (0,2) (0,24) (0,13) (0,7) (1,14) (1,25) (1,10) (1,16) (1,5) (1,22) (1,17) (1,2) (1,24) (1,19) (1,12) (2,25) (2,16) (2,23) (2,22) (2,17) (2,21) (2,8) (2,24) (2,13) (2,7) (2,12) (3,18) (3,9) (4,25) (4,10) (4,26) (4,16) (4,5) (4,22) (4,21) (4,15) (4,8) (4,24) (4,12) (5,14) (5,25) (5,26) (5,16) (5,23) (5,22) (5,17) (5,21) (5,15) (5,13) (5,19) (5,7) (5,12) (7,14) (7,25) (7,10) (7,16) (7,22) (7,21) (7,8) (7,13) (7,19) (7,12) (8,14) (8,25) (8,26) (8,16) (8,23) (8,22) (8,17) (8,15) (8,19) (8,12) (9,11) (9,18) (9,20) (10,25) (10,26) (10,16) (10,23) (10,22) (10,17) (10,21) (10,24) (10,13) (10,19) (10,12) (11,18) (11,20) (12,14) (12,25) (12,26) (12,16) (12,23) (12,22) (12,24) (12,13) (13,14) (13,26) (13,23) (13,17) (13,21) (13,15) (14,26) (14,16) (14,23) (14,22) (14,17) (14,21) (14,15) (14,24) (14,19) (15,25) (15,26) (15,23) (15,17) (15,21) (15,24) (15,19) (16,25) (16,26) (16,23) (16,21) (16,19) (17,25) (17,23) (17,22) (17,21) (17,24) (17,19) (19,25) (19,26) (19,23) (19,22) (19,21) (19,24) (21,25) (21,26) (22,25) (22,26) (22,23) (22,24) (23,25) (23,26) (23,24) (24,25) (25,26)\nIs there a path between node 14 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph59-1_13", + "image": "data/connectivity/graph_visual/hard/graph59.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,4) (0,22) (0,15) (0,18) (0,14) (0,5) (0,2) (0,13) (1,16) (1,20) (1,6) (1,24) (1,8) (1,21) (1,23) (2,4) (2,22) (2,15) (2,25) (2,14) (2,19) (2,5) (2,3) (3,4) (3,22) (3,15) (3,18) (3,25) (3,19) (3,5) (3,13) (4,22) (4,15) (4,26) (4,25) (4,14) (4,13) (5,22) (5,15) (5,26) (5,18) (5,25) (5,14) (5,19) (5,13) (6,16) (6,17) (6,20) (6,9) (6,7) (6,24) (6,12) (6,11) (7,16) (7,17) (7,20) (7,9) (7,24) (7,8) (7,10) (7,23) (8,16) (8,17) (8,20) (8,9) (8,24) (8,12) (8,21) (8,10) (9,16) (9,17) (9,20) (9,24) (9,11) (9,21) (9,23) (10,16) (10,17) (10,20) (10,24) (10,12) (10,21) (11,16) (11,12) (11,21) (11,23) (12,16) (12,17) (12,20) (12,21) (13,22) (13,15) (13,26) (13,25) (13,14) (13,19) (14,22) (14,15) (14,26) (14,18) (14,25) (14,19) (15,26) (15,19) (16,17) (16,20) (16,21) (16,23) (17,20) (17,21) (18,22) (18,26) (18,25) (18,19) (19,22) (19,26) (19,25) (20,24) (21,24) (21,23) (22,26) (22,25) (23,24) (25,26)\nIs there a path between node 1 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph389-10_1", + "image": "data/connectivity/graph_visual/hard/graph389.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,22) (0,12) (0,24) (0,18) (0,19) (0,30) (0,1) (0,21) (0,9) (0,5) (0,6) (0,7) (0,2) (1,22) (1,24) (1,18) (1,19) (1,30) (1,21) (1,9) (1,5) (1,6) (1,11) (1,7) (1,31) (1,2) (2,12) (2,24) (2,18) (2,19) (2,21) (2,5) (2,6) (2,11) (2,7) (2,31) (3,26) (3,16) (3,4) (3,28) (3,13) (3,20) (4,26) (4,16) (4,8) (4,28) (5,12) (5,24) (5,30) (5,21) (5,9) (5,11) (5,7) (5,31) (6,22) (6,12) (6,24) (6,30) (6,21) (6,9) (6,11) (6,7) (7,12) (7,18) (7,30) (7,9) (7,11) (7,31) (8,26) (8,16) (8,28) (9,22) (9,12) (9,24) (9,18) (9,19) (9,30) (9,11) (9,31) (10,25) (10,14) (10,29) (10,32) (10,15) (10,23) (11,22) (11,12) (11,24) (11,18) (11,30) (11,21) (12,24) (12,30) (12,21) (12,31) (13,26) (13,28) (14,27) (14,17) (14,29) (14,32) (14,15) (15,25) (15,27) (15,17) (15,29) (15,32) (15,23) (16,26) (17,29) (18,22) (18,24) (18,19) (18,21) (19,22) (19,30) (19,21) (20,26) (21,22) (21,24) (21,31) (22,24) (23,25) (23,27) (23,32) (24,30) (24,31) (25,27) (25,29) (25,32) (26,28) (27,29) (27,32) (30,31)\nIs there a path between node 10 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph237-1_24", + "image": "data/connectivity/graph_visual/hard/graph237.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,29) (0,12) (0,18) (0,24) (0,22) (0,2) (0,3) (1,14) (1,20) (1,26) (1,29) (1,12) (1,30) (1,15) (1,19) (1,3) (1,7) (2,17) (2,6) (2,23) (3,28) (3,30) (3,18) (3,19) (3,7) (4,26) (4,29) (4,12) (4,30) (4,18) (4,19) (4,7) (6,8) (6,24) (6,10) (6,19) (7,17) (7,26) (7,30) (7,18) (7,8) (7,13) (7,15) (7,23) (8,16) (8,14) (8,20) (8,26) (8,30) (10,14) (10,20) (10,29) (10,18) (10,13) (10,22) (10,19) (10,11) (11,21) (11,16) (11,14) (11,26) (11,18) (12,16) (12,26) (12,18) (13,17) (13,26) (13,15) (14,28) (14,26) (14,24) (14,23) (15,28) (15,16) (15,29) (15,30) (16,21) (16,20) (16,29) (16,24) (17,28) (17,20) (17,29) (17,30) (17,19) (18,21) (18,28) (18,23) (19,28) (19,20) (19,26) (19,22) (19,23) (20,29) (20,24) (20,22) (21,29) (22,28) (23,28) (23,29) (24,26) (24,29) (25,27) (26,29)\nIs there a path between node 1 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph105-17_16", + "image": "data/connectivity/graph_visual/hard/graph105.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,7) (0,2) (0,24) (0,25) (0,12) (0,3) (0,1) (0,14) (0,26) (0,11) (0,10) (0,6) (0,16) (0,22) (0,9) (1,18) (1,7) (1,2) (1,21) (1,15) (1,24) (1,4) (1,12) (1,26) (1,11) (1,10) (1,16) (1,9) (2,7) (2,21) (2,23) (2,25) (2,12) (2,3) (2,26) (2,11) (2,6) (3,18) (3,7) (3,21) (3,19) (3,24) (3,4) (3,14) (3,26) (3,11) (3,20) (3,6) (3,16) (3,22) (3,9) (4,7) (4,17) (4,19) (4,15) (4,25) (4,14) (4,26) (4,20) (4,10) (4,6) (4,16) (4,9) (5,8) (6,7) (6,21) (6,19) (6,15) (6,23) (6,25) (6,12) (6,14) (6,26) (6,11) (6,20) (6,10) (6,16) (6,22) (6,9) (7,17) (7,21) (7,19) (7,15) (7,24) (7,25) (7,12) (7,14) (7,26) (7,10) (7,22) (8,13) (9,18) (9,17) (9,19) (9,23) (9,24) (9,25) (9,12) (9,14) (9,26) (9,11) (9,20) (9,22) (10,18) (10,17) (10,21) (10,19) (10,24) (10,25) (10,11) (10,22) (11,17) (11,21) (11,15) (11,23) (11,24) (11,25) (11,14) (11,20) (11,16) (11,22) (12,18) (12,17) (12,21) (12,15) (12,23) (12,14) (12,26) (12,20) (12,16) (12,22) (14,18) (14,17) (14,21) (14,19) (14,24) (14,25) (14,26) (14,20) (15,18) (15,17) (15,21) (15,23) (15,24) (15,25) (15,20) (15,16) (15,22) (16,17) (16,21) (16,23) (16,24) (16,25) (16,26) (16,20) (16,22) (17,18) (17,21) (17,19) (17,23) (17,24) (17,25) (17,26) (17,20) (18,19) (18,23) (18,24) (18,25) (18,26) (18,20) (18,22) (19,23) (19,25) (19,26) (20,23) (20,24) (20,26) (20,22) (21,25) (21,26) (21,22) (22,23) (22,24) (22,26) (23,24) (23,26) (24,25) (24,26)\nIs there a path between node 17 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph626-29_5", + "image": "data/connectivity/graph_visual/hard/graph626.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,16) (0,33) (0,10) (1,27) (2,15) (2,34) (2,3) (2,23) (3,14) (3,8) (3,34) (3,23) (4,13) (4,9) (4,20) (4,30) (4,29) (4,5) (5,27) (5,30) (5,24) (5,29) (5,7) (6,13) (6,28) (6,24) (6,29) (6,18) (7,28) (7,24) (8,32) (8,31) (9,28) (9,27) (9,24) (9,29) (10,26) (12,15) (12,21) (12,32) (12,23) (13,20) (13,30) (13,29) (13,18) (14,15) (14,23) (14,17) (15,31) (17,32) (18,29) (20,24) (21,32) (21,25) (24,28) (27,28) (28,29)\nIs there a path between node 29 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph274-12_30", + "image": "data/connectivity/graph_visual/hard/graph274.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,27) (0,3) (0,14) (0,23) (0,10) (0,25) (1,22) (1,28) (1,8) (1,30) (1,2) (1,4) (1,21) (1,29) (1,9) (2,22) (2,28) (2,8) (2,30) (2,4) (2,9) (3,27) (3,6) (3,14) (3,15) (3,7) (3,5) (3,20) (3,10) (3,25) (4,28) (4,30) (4,21) (4,29) (4,9) (4,13) (5,27) (5,6) (5,15) (5,7) (5,23) (5,20) (5,10) (6,27) (6,14) (6,15) (6,23) (6,20) (6,10) (7,27) (7,14) (7,15) (7,10) (7,25) (8,22) (8,30) (8,21) (8,9) (9,22) (9,28) (9,30) (9,29) (9,13) (10,27) (10,23) (10,20) (10,25) (11,24) (11,19) (11,26) (11,18) (11,12) (11,17) (11,16) (12,19) (12,26) (12,18) (12,17) (12,16) (13,22) (13,28) (13,30) (13,21) (13,29) (14,27) (14,15) (14,23) (14,25) (15,27) (15,23) (15,20) (16,24) (16,26) (16,17) (17,24) (17,19) (17,26) (17,18) (18,26) (19,24) (20,27) (20,23) (20,25) (21,22) (21,28) (22,28) (22,30) (22,29) (23,27) (24,26) (25,27) (28,30) (28,29)\nIs there a path between node 12 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph338-7_23", + "image": "data/connectivity/graph_visual/hard/graph338.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (1,11) (1,9) (1,19) (1,31) (1,20) (2,15) (2,11) (2,27) (2,29) (2,16) (2,31) (3,8) (3,4) (3,12) (3,18) (3,17) (3,10) (3,25) (3,31) (3,20) (4,30) (4,24) (4,19) (5,26) (5,23) (6,13) (7,15) (7,9) (7,30) (7,12) (7,16) (7,19) (7,10) (7,25) (8,15) (8,11) (8,30) (8,24) (8,10) (8,31) (9,11) (9,30) (9,27) (9,29) (9,10) (10,15) (10,30) (10,12) (10,18) (10,19) (10,17) (10,14) (11,30) (11,29) (11,19) (12,15) (12,19) (12,14) (12,20) (13,28) (14,27) (14,24) (14,20) (15,27) (15,18) (15,25) (15,20) (16,29) (16,24) (16,19) (17,29) (17,19) (17,31) (18,30) (18,24) (18,19) (18,31) (19,30) (19,25) (21,28) (21,23) (22,23) (25,27) (25,31) (26,28) (29,31)\nIs there a path between node 7 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph398-20_5", + "image": "data/connectivity/graph_visual/hard/graph398.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,27) (0,2) (0,28) (0,32) (0,14) (0,1) (0,10) (1,30) (1,20) (1,2) (1,28) (1,32) (1,12) (1,16) (2,30) (2,8) (2,26) (2,16) (2,17) (2,3) (3,20) (3,4) (3,5) (3,28) (3,16) (3,10) (4,8) (4,27) (4,20) (4,28) (4,26) (4,25) (4,17) (5,30) (5,21) (5,31) (5,26) (5,25) (5,18) (6,29) (6,13) (7,22) (8,24) (8,32) (8,12) (8,26) (8,23) (8,18) (9,13) (10,30) (10,24) (10,27) (10,15) (10,12) (10,19) (11,22) (12,15) (12,26) (12,17) (14,30) (14,26) (14,16) (14,19) (15,30) (15,31) (15,32) (15,23) (15,19) (16,27) (16,28) (16,31) (16,32) (16,25) (16,23) (17,24) (17,27) (18,24) (18,28) (18,32) (18,23) (18,19) (19,20) (19,28) (20,24) (20,21) (20,26) (20,25) (21,28) (21,32) (21,26) (21,23) (22,29) (23,24) (23,28) (23,31) (24,30) (24,28) (24,26) (26,32) (30,31)\nIs there a path between node 20 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph129-25_12", + "image": "data/connectivity/graph_visual/hard/graph129.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,6) (0,7) (0,19) (0,18) (0,12) (0,17) (0,13) (0,24) (0,3) (0,1) (0,15) (0,11) (0,27) (0,16) (1,6) (1,8) (1,26) (1,7) (1,10) (1,19) (1,18) (1,24) (1,3) (1,9) (1,15) (1,11) (1,27) (2,20) (2,25) (2,14) (2,21) (3,6) (3,8) (3,26) (3,7) (3,10) (3,19) (3,18) (3,12) (3,17) (3,24) (3,9) (3,15) (3,11) (4,22) (5,23) (5,20) (5,25) (6,8) (6,26) (6,19) (6,18) (6,12) (6,17) (6,13) (6,24) (6,15) (6,11) (6,27) (6,16) (7,10) (7,19) (7,18) (7,17) (7,13) (7,24) (7,9) (7,16) (8,26) (8,19) (8,18) (8,12) (8,17) (8,13) (8,24) (8,9) (8,15) (8,27) (8,16) (9,26) (9,10) (9,18) (9,12) (9,17) (9,13) (9,15) (9,27) (9,16) (10,26) (10,19) (10,17) (10,13) (10,15) (10,16) (11,26) (11,19) (11,18) (11,12) (11,17) (11,15) (12,26) (12,19) (12,18) (12,13) (12,24) (13,18) (13,24) (13,27) (13,16) (14,23) (14,20) (14,21) (15,26) (15,19) (15,18) (15,17) (15,16) (16,26) (16,19) (16,24) (16,27) (17,26) (17,24) (17,27) (18,26) (18,19) (18,27) (19,26) (19,27) (20,25) (21,23) (21,25)\nIs there a path between node 25 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph571-2_20", + "image": "data/connectivity/graph_visual/hard/graph571.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,7) (0,31) (0,5) (0,13) (0,33) (0,4) (0,8) (0,16) (1,18) (1,29) (1,2) (2,29) (2,28) (3,20) (3,26) (3,25) (4,7) (4,11) (4,10) (4,31) (4,22) (4,24) (4,16) (5,11) (5,13) (5,17) (6,26) (6,29) (7,10) (7,32) (7,33) (7,8) (7,24) (8,14) (8,10) (8,13) (8,33) (9,12) (9,21) (10,11) (10,24) (10,17) (11,31) (11,13) (11,16) (11,17) (12,30) (13,14) (13,32) (14,31) (14,15) (15,32) (15,24) (18,26) (18,29) (18,28) (20,27) (20,28) (21,23) (22,31) (22,33) (25,29) (26,27) (27,29) (27,28) (28,29) (31,32) (31,33) (32,33)\nIs there a path between node 2 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph51-10_7", + "image": "data/connectivity/graph_visual/hard/graph51.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,4) (0,11) (0,16) (2,19) (2,4) (2,11) (3,4) (3,11) (5,8) (5,20) (5,25) (6,8) (6,22) (6,7) (6,18) (6,25) (7,22) (8,18) (8,24) (8,20) (8,21) (10,20) (10,26) (10,13) (11,19) (11,23) (13,22) (13,25) (15,24) (15,20) (15,25) (15,21) (16,23) (18,26) (19,23) (21,24) (21,25) (22,25) (22,26) (24,26)\nIs there a path between node 10 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph206-5_18", + "image": "data/connectivity/graph_visual/hard/graph206.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,23) (0,26) (0,24) (0,27) (1,4) (1,16) (1,15) (1,10) (1,29) (1,17) (1,11) (2,9) (2,7) (2,6) (2,27) (3,13) (3,28) (3,16) (3,18) (3,29) (3,21) (4,20) (4,16) (4,5) (4,15) (4,18) (4,14) (4,25) (5,28) (5,16) (5,15) (5,18) (5,14) (5,29) (5,19) (5,17) (5,11) (7,23) (7,26) (7,27) (8,26) (10,29) (10,19) (11,13) (11,28) (11,15) (11,17) (13,20) (13,28) (13,19) (14,16) (14,15) (14,29) (14,19) (14,21) (15,20) (15,28) (15,29) (15,19) (16,28) (16,25) (16,17) (17,19) (18,20) (18,21) (20,21) (21,29) (21,25) (22,28) (23,24) (26,27) (28,29)\nIs there a path between node 5 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph395-28_6", + "image": "data/connectivity/graph_visual/hard/graph395.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,24) (0,18) (0,29) (0,9) (0,4) (0,14) (0,3) (0,13) (1,21) (1,24) (1,20) (1,9) (1,3) (2,10) (2,26) (2,28) (3,20) (3,6) (3,8) (3,5) (3,27) (4,21) (4,24) (4,29) (4,6) (4,9) (4,8) (4,17) (4,15) (4,27) (4,32) (4,13) (5,21) (5,16) (5,24) (5,9) (5,27) (6,24) (6,9) (6,17) (6,15) (6,32) (7,31) (8,16) (8,24) (8,11) (8,9) (8,27) (9,21) (9,16) (9,24) (9,11) (9,15) (9,14) (9,13) (11,16) (12,25) (13,16) (13,20) (13,30) (13,27) (14,16) (14,24) (14,18) (14,27) (15,24) (15,18) (15,20) (15,17) (16,21) (16,30) (16,27) (17,21) (17,20) (17,29) (18,20) (18,29) (18,30) (18,27) (19,25) (19,26) (19,22) (20,24) (21,24) (21,29) (22,26) (22,28) (23,25) (24,30) (26,28) (27,32) (29,32)\nIs there a path between node 28 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph420-29_7", + "image": "data/connectivity/graph_visual/hard/graph420.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,12) (0,5) (0,20) (0,28) (1,14) (1,27) (2,21) (2,16) (3,29) (3,31) (3,22) (3,17) (4,13) (4,9) (5,12) (5,32) (5,11) (6,14) (6,12) (6,32) (6,28) (7,10) (7,20) (7,27) (8,21) (8,15) (9,26) (9,31) (9,30) (9,17) (10,20) (10,28) (11,14) (11,12) (12,20) (12,32) (12,28) (13,29) (13,31) (13,22) (14,28) (15,16) (15,24) (16,19) (17,26) (17,18) (20,23) (21,24) (22,26) (22,31) (26,30)\nIs there a path between node 29 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph285-19_20", + "image": "data/connectivity/graph_visual/hard/graph285.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,3) (0,11) (0,15) (0,25) (0,31) (0,23) (0,14) (1,28) (1,20) (1,12) (1,21) (1,19) (1,24) (1,27) (1,13) (1,6) (2,20) (2,22) (2,21) (2,19) (2,13) (2,6) (3,15) (3,4) (3,25) (3,23) (4,9) (4,15) (4,14) (5,8) (5,17) (5,10) (5,26) (5,7) (5,16) (6,20) (6,21) (6,19) (6,27) (6,13) (7,17) (7,16) (7,29) (8,17) (9,11) (9,15) (9,31) (9,23) (9,14) (10,17) (11,15) (11,30) (11,23) (11,14) (12,20) (12,22) (12,19) (12,27) (12,13) (12,18) (13,28) (13,22) (13,21) (13,24) (13,27) (13,18) (14,15) (14,25) (14,31) (14,23) (15,25) (15,30) (15,23) (16,26) (17,26) (17,29) (18,28) (18,20) (18,22) (18,21) (18,19) (18,24) (18,27) (19,22) (19,21) (19,24) (19,27) (20,28) (20,22) (20,21) (20,24) (20,27) (21,28) (21,22) (21,24) (22,24) (22,27) (23,30) (23,31) (24,28) (25,31) (27,28) (30,31)\nIs there a path between node 19 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph636-28_30", + "image": "data/connectivity/graph_visual/hard/graph636.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,32) (0,18) (0,25) (1,13) (1,17) (1,28) (1,2) (1,33) (2,17) (2,28) (2,15) (2,26) (2,16) (3,30) (3,26) (5,17) (5,28) (5,27) (6,22) (6,21) (7,34) (7,22) (7,24) (8,19) (10,29) (10,22) (10,31) (10,24) (10,21) (10,11) (11,34) (13,30) (13,15) (13,27) (13,33) (13,26) (13,16) (14,32) (15,28) (15,26) (16,28) (16,26) (17,30) (18,25) (20,28) (20,26) (21,31) (21,24) (22,34) (22,31) (22,24) (23,32) (24,29) (26,33) (28,33) (31,34)\nIs there a path between node 28 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph83-19_23", + "image": "data/connectivity/graph_visual/hard/graph83.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,18) (0,14) (0,16) (0,12) (0,2) (0,22) (0,1) (0,21) (1,18) (1,14) (1,16) (1,21) (2,18) (2,14) (2,5) (2,12) (2,22) (2,21) (3,7) (3,9) (3,15) (3,25) (3,23) (3,26) (3,19) (4,7) (4,10) (4,20) (4,13) (4,15) (4,17) (4,25) (4,23) (4,26) (4,6) (4,11) (4,24) (5,18) (5,14) (5,16) (5,22) (5,21) (6,13) (6,8) (6,15) (6,17) (6,25) (6,26) (6,19) (6,24) (7,9) (7,10) (7,20) (7,13) (7,17) (7,25) (7,23) (7,26) (7,19) (7,11) (8,9) (8,10) (8,17) (8,23) (8,26) (8,11) (8,24) (9,10) (9,20) (9,15) (9,17) (9,23) (9,24) (10,15) (10,25) (10,26) (11,20) (11,15) (11,17) (11,25) (11,23) (12,18) (12,16) (12,22) (13,15) (13,17) (13,25) (13,26) (13,19) (13,24) (14,16) (15,20) (15,17) (15,25) (15,23) (15,26) (15,19) (16,18) (16,21) (17,20) (17,23) (17,26) (17,24) (18,22) (18,21) (19,25) (19,23) (19,26) (19,24) (20,25) (20,26) (20,24) (21,22) (23,24) (24,25) (25,26)\nIs there a path between node 19 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph493-12_25", + "image": "data/connectivity/graph_visual/hard/graph493.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,4) (0,1) (0,5) (0,24) (0,3) (0,21) (0,19) (0,9) (0,15) (0,20) (0,27) (0,13) (1,24) (1,21) (1,31) (1,10) (1,7) (1,20) (1,27) (1,13) (2,6) (2,5) (2,24) (2,3) (2,21) (2,19) (2,9) (2,31) (2,15) (2,7) (2,27) (2,13) (3,6) (3,4) (3,5) (3,22) (3,24) (3,21) (3,19) (3,9) (3,31) (3,18) (3,7) (3,20) (4,5) (4,21) (4,19) (4,9) (4,31) (4,7) (4,20) (4,27) (4,13) (5,6) (5,22) (5,24) (5,21) (5,9) (5,31) (5,10) (5,15) (5,18) (5,20) (5,27) (5,13) (6,22) (6,21) (6,19) (6,9) (6,31) (6,10) (6,15) (6,18) (6,7) (6,27) (6,13) (7,22) (7,9) (7,10) (7,15) (7,18) (7,20) (7,27) (7,13) (8,16) (8,11) (8,28) (8,12) (8,25) (8,30) (8,14) (8,32) (8,29) (9,22) (9,24) (9,21) (9,19) (9,31) (9,10) (9,15) (9,18) (9,20) (10,22) (10,19) (10,31) (10,15) (10,20) (10,27) (10,13) (11,16) (11,28) (11,26) (11,23) (11,30) (11,14) (11,32) (11,17) (12,16) (12,28) (12,23) (12,30) (12,14) (12,33) (12,32) (12,17) (12,29) (13,22) (13,24) (13,21) (13,19) (13,15) (13,18) (13,20) (14,28) (14,26) (14,23) (14,25) (14,33) (14,32) (14,29) (15,22) (15,24) (15,21) (15,19) (15,20) (15,27) (16,26) (16,25) (16,30) (16,33) (16,32) (16,17) (16,29) (17,28) (17,26) (17,25) (17,30) (17,33) (17,32) (17,29) (18,24) (18,19) (18,31) (19,22) (19,24) (19,31) (19,20) (19,27) (20,21) (20,31) (20,27) (21,31) (23,28) (23,26) (23,25) (23,30) (24,31) (24,27) (25,26) (25,30) (25,33) (25,32) (25,29) (26,28) (26,33) (26,32) (28,30) (28,29) (29,30) (29,33) (29,32) (30,32)\nIs there a path between node 12 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph702-9_29", + "image": "data/connectivity/graph_visual/hard/graph702.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,12) (0,4) (0,34) (0,32) (0,13) (0,20) (0,11) (0,14) (0,6) (0,3) (1,12) (1,17) (1,33) (1,20) (1,23) (1,11) (1,6) (1,3) (2,31) (2,30) (2,21) (2,27) (2,7) (2,29) (2,15) (2,19) (2,5) (2,9) (2,16) (2,18) (2,24) (2,26) (3,12) (3,33) (3,4) (3,34) (3,32) (3,20) (3,11) (3,6) (4,33) (4,13) (4,14) (5,25) (5,10) (5,21) (5,27) (5,7) (5,29) (5,8) (5,16) (5,18) (5,22) (5,24) (6,34) (6,13) (6,23) (6,11) (6,14) (7,31) (7,25) (7,30) (7,27) (7,29) (7,9) (7,8) (7,18) (7,22) (7,24) (7,26) (8,25) (8,30) (8,21) (8,27) (8,19) (8,9) (8,16) (8,22) (8,28) (8,24) (9,31) (9,25) (9,30) (9,21) (9,27) (9,29) (9,16) (9,22) (9,28) (9,24) (10,31) (10,25) (10,30) (10,21) (10,29) (10,15) (10,19) (10,16) (10,18) (10,22) (10,26) (11,33) (11,34) (11,32) (11,23) (11,14) (12,17) (12,32) (12,23) (12,14) (13,17) (13,33) (13,34) (13,32) (13,20) (13,23) (13,14) (14,17) (14,34) (14,32) (14,20) (15,25) (15,21) (15,29) (15,19) (15,16) (15,18) (15,28) (15,24) (16,31) (16,25) (16,21) (16,27) (16,29) (16,19) (16,22) (16,28) (16,24) (16,26) (17,33) (17,34) (17,32) (17,20) (18,31) (18,25) (18,30) (18,21) (18,27) (18,29) (18,19) (18,22) (18,28) (18,24) (18,26) (19,31) (19,25) (19,21) (19,28) (19,26) (20,33) (20,34) (20,32) (20,23) (21,31) (21,25) (21,30) (21,27) (21,24) (22,31) (22,25) (22,30) (22,27) (22,29) (22,28) (22,24) (22,26) (23,34) (23,32) (24,31) (24,25) (24,30) (24,29) (24,28) (25,31) (25,30) (25,29) (25,28) (25,26) (26,27) (26,29) (26,28) (27,31) (27,29) (27,28) (28,30) (29,31) (29,30) (30,31) (33,34)\nIs there a path between node 9 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph209-26_6", + "image": "data/connectivity/graph_visual/hard/graph209.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,22) (1,18) (1,25) (1,8) (1,16) (1,11) (1,6) (1,24) (2,22) (2,18) (2,17) (2,20) (2,11) (2,6) (3,13) (4,22) (4,25) (4,21) (4,17) (4,11) (4,6) (5,27) (5,13) (6,29) (6,24) (7,22) (7,21) (7,17) (7,16) (7,11) (7,24) (7,15) (7,19) (8,18) (8,12) (8,11) (8,24) (9,28) (10,26) (10,23) (11,17) (12,17) (12,20) (12,16) (13,27) (16,22) (16,25) (16,21) (16,29) (16,19) (17,29) (17,20) (19,21) (19,29) (19,20) (20,22) (21,22) (21,25) (21,29) (27,28)\nIs there a path between node 26 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph381-13_1", + "image": "data/connectivity/graph_visual/hard/graph381.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,17) (0,4) (0,14) (0,22) (0,9) (0,5) (0,16) (0,25) (0,31) (0,23) (0,28) (0,15) (0,2) (0,8) (0,19) (0,6) (1,12) (1,3) (1,21) (2,13) (2,17) (2,4) (2,24) (2,14) (2,30) (2,22) (2,9) (2,16) (2,25) (2,29) (2,31) (2,20) (2,28) (2,15) (2,8) (2,19) (2,6) (3,18) (3,12) (3,21) (4,13) (4,7) (4,14) (4,30) (4,22) (4,9) (4,5) (4,26) (4,23) (4,20) (4,28) (4,15) (4,8) (4,19) (4,6) (5,24) (5,7) (5,14) (5,30) (5,22) (5,9) (5,29) (5,26) (5,23) (5,28) (5,15) (5,8) (5,19) (5,6) (6,13) (6,17) (6,11) (6,24) (6,14) (6,22) (6,16) (6,29) (6,31) (6,23) (6,20) (6,28) (7,13) (7,17) (7,11) (7,24) (7,30) (7,9) (7,16) (7,25) (7,29) (7,26) (7,31) (7,23) (7,20) (7,28) (7,8) (7,19) (8,17) (8,24) (8,14) (8,30) (8,22) (8,9) (8,16) (8,20) (8,28) (8,15) (8,19) (9,13) (9,17) (9,11) (9,24) (9,14) (9,30) (9,22) (9,16) (9,25) (9,29) (9,26) (9,23) (9,20) (9,15) (9,19) (11,13) (11,14) (11,30) (11,22) (11,16) (11,29) (11,26) (11,23) (11,20) (11,15) (11,19) (12,18) (12,21) (13,14) (13,25) (13,26) (13,31) (13,20) (13,15) (13,19) (14,17) (14,24) (14,22) (14,16) (14,25) (14,26) (14,31) (14,20) (14,28) (15,17) (15,24) (15,30) (15,22) (15,16) (15,25) (15,29) (15,19) (16,17) (16,24) (16,30) (16,29) (16,26) (16,31) (16,23) (16,20) (16,28) (16,19) (17,24) (17,30) (17,22) (17,31) (17,23) (17,20) (17,28) (17,19) (19,24) (19,25) (19,26) (19,31) (19,23) (19,20) (20,30) (20,22) (20,26) (20,23) (22,30) (22,25) (22,29) (22,23) (22,28) (23,24) (23,30) (23,25) (23,29) (23,26) (24,30) (24,25) (24,29) (24,28) (25,30) (25,26) (25,31) (25,28) (26,30) (26,29) (26,31) (28,30) (28,29) (30,31)\nIs there a path between node 13 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph259-26_24", + "image": "data/connectivity/graph_visual/hard/graph259.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,21) (1,27) (1,29) (1,22) (1,26) (1,7) (1,28) (1,16) (1,12) (1,3) (2,17) (2,22) (2,15) (2,10) (2,8) (3,22) (3,24) (3,15) (3,10) (3,12) (5,17) (5,29) (5,20) (5,26) (5,7) (5,10) (5,28) (6,9) (6,18) (6,25) (6,21) (6,23) (7,11) (7,12) (7,8) (8,16) (9,18) (9,25) (9,30) (9,21) (10,17) (10,20) (10,15) (10,11) (10,12) (11,27) (11,20) (11,22) (11,24) (12,22) (12,24) (14,19) (14,30) (14,21) (14,23) (15,20) (16,17) (16,28) (17,22) (19,21) (19,23) (21,25) (22,26) (22,28) (23,25) (24,27) (24,28) (26,27) (26,28) (28,29)\nIs there a path between node 26 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph531-9_30", + "image": "data/connectivity/graph_visual/hard/graph531.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,7) (0,14) (0,15) (0,29) (0,19) (0,11) (0,32) (0,13) (0,3) (0,6) (0,8) (0,23) (0,10) (0,17) (1,7) (1,14) (1,27) (1,24) (1,29) (1,33) (1,19) (1,11) (1,26) (1,13) (1,3) (1,6) (1,10) (1,17) (2,22) (2,25) (2,31) (2,12) (2,16) (3,7) (3,14) (3,27) (3,33) (3,9) (3,30) (3,13) (3,6) (3,8) (3,17) (4,22) (4,28) (4,12) (4,16) (4,21) (4,18) (5,7) (5,14) (5,15) (5,24) (5,29) (5,19) (5,9) (5,30) (5,32) (5,26) (5,8) (5,10) (5,17) (6,11) (6,9) (6,26) (6,13) (6,8) (6,23) (6,17) (7,14) (7,27) (7,29) (7,33) (7,9) (7,30) (7,13) (7,8) (7,10) (8,14) (8,27) (8,15) (8,24) (8,29) (8,11) (8,9) (8,30) (8,32) (8,13) (8,23) (8,10) (8,17) (9,27) (9,15) (9,24) (9,29) (9,33) (9,19) (9,11) (9,30) (9,32) (9,13) (9,23) (9,10) (10,14) (10,27) (10,24) (10,29) (10,33) (10,19) (10,11) (10,30) (10,32) (10,26) (10,23) (10,17) (11,27) (11,15) (11,29) (11,33) (11,19) (11,30) (11,32) (11,26) (11,23) (11,17) (12,22) (12,25) (12,31) (12,28) (12,16) (12,21) (12,20) (12,18) (13,14) (13,27) (13,15) (13,24) (13,29) (13,33) (13,19) (13,32) (13,26) (13,23) (13,17) (14,15) (14,24) (14,29) (14,19) (14,30) (14,32) (14,17) (15,33) (15,30) (15,32) (15,23) (15,17) (16,22) (16,25) (16,31) (16,28) (16,21) (16,18) (17,27) (17,29) (17,26) (18,22) (18,25) (18,31) (18,28) (18,21) (18,20) (19,27) (19,24) (19,29) (19,33) (19,30) (19,32) (19,23) (20,25) (20,31) (21,22) (21,31) (22,31) (22,28) (23,24) (23,29) (23,32) (23,26) (24,29) (24,33) (24,30) (24,32) (25,31) (25,28) (26,27) (26,29) (26,33) (26,30) (26,32) (27,29) (27,30) (27,32) (28,31) (29,33) (29,30) (32,33)\nIs there a path between node 9 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph645-14_11", + "image": "data/connectivity/graph_visual/hard/graph645.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,16) (0,18) (0,5) (0,29) (0,21) (0,22) (0,7) (0,2) (0,13) (0,27) (0,26) (0,14) (0,33) (0,8) (0,10) (1,32) (1,16) (1,18) (1,29) (1,17) (1,2) (1,13) (1,26) (1,14) (1,31) (1,33) (1,10) (2,23) (2,32) (2,16) (2,18) (2,5) (2,29) (2,17) (2,21) (2,7) (2,13) (2,27) (2,9) (2,31) (2,33) (2,8) (3,12) (3,15) (3,19) (3,20) (3,34) (3,4) (3,11) (4,12) (4,28) (4,6) (4,15) (4,19) (4,34) (4,30) (4,11) (5,16) (5,18) (5,17) (5,21) (5,22) (5,13) (5,24) (5,9) (5,26) (5,31) (5,33) (5,10) (6,12) (6,28) (6,15) (6,19) (6,20) (6,30) (6,11) (6,25) (7,32) (7,16) (7,18) (7,22) (7,13) (7,24) (7,27) (7,9) (7,26) (7,14) (7,31) (7,33) (7,8) (7,10) (8,23) (8,16) (8,18) (8,29) (8,17) (8,21) (8,22) (8,13) (8,24) (8,26) (8,14) (8,31) (8,33) (8,10) (9,23) (9,32) (9,16) (9,18) (9,17) (9,21) (9,22) (9,13) (9,24) (9,27) (9,26) (9,14) (9,31) (9,33) (9,10) (10,23) (10,32) (10,16) (10,18) (10,17) (10,21) (10,13) (10,24) (10,27) (10,26) (10,14) (11,28) (11,15) (11,34) (11,30) (11,25) (12,28) (12,15) (12,20) (12,30) (12,25) (13,23) (13,32) (13,16) (13,18) (13,29) (13,17) (13,22) (13,24) (13,27) (13,26) (13,14) (13,33) (14,23) (14,29) (14,17) (14,21) (14,22) (14,27) (14,26) (15,20) (15,30) (16,23) (16,29) (16,17) (16,21) (16,22) (16,24) (16,27) (16,26) (16,31) (17,23) (17,32) (17,18) (17,21) (17,24) (17,27) (17,31) (18,23) (18,29) (18,21) (18,27) (18,26) (18,31) (18,33) (19,20) (19,34) (19,30) (19,25) (20,28) (20,34) (20,30) (20,25) (21,32) (21,22) (21,24) (21,27) (21,26) (21,31) (22,23) (22,32) (22,29) (22,24) (22,26) (22,31) (22,33) (23,32) (23,29) (23,24) (23,26) (23,31) (24,29) (24,27) (24,26) (24,33) (25,28) (25,34) (25,30) (26,32) (26,29) (27,29) (27,33) (28,30) (29,32) (30,34) (31,32) (32,33)\nIs there a path between node 14 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph580-14_17", + "image": "data/connectivity/graph_visual/hard/graph580.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,5) (0,29) (0,21) (0,24) (0,15) (0,16) (0,27) (0,33) (0,11) (0,8) (0,19) (0,32) (1,22) (1,18) (2,9) (2,29) (2,4) (2,21) (2,20) (2,15) (2,16) (2,27) (2,33) (2,8) (2,19) (2,30) (2,32) (3,14) (3,23) (3,17) (3,12) (3,7) (3,13) (3,28) (3,31) (3,10) (4,9) (4,21) (4,20) (4,15) (4,16) (4,27) (4,11) (4,8) (4,19) (5,9) (5,29) (5,21) (5,24) (5,15) (5,33) (5,11) (5,8) (5,19) (5,32) (6,14) (6,26) (6,25) (6,12) (6,13) (6,28) (7,23) (7,17) (7,26) (7,25) (7,31) (7,10) (8,9) (8,29) (8,24) (8,15) (8,16) (8,27) (8,33) (8,11) (8,30) (8,32) (9,29) (9,21) (9,24) (9,20) (9,15) (9,16) (9,33) (9,11) (9,19) (9,30) (9,32) (10,14) (10,17) (10,26) (10,25) (10,12) (10,13) (10,28) (10,31) (11,29) (11,21) (11,24) (11,20) (11,15) (11,16) (11,27) (11,19) (11,30) (12,14) (12,17) (12,25) (12,13) (12,28) (12,31) (13,14) (13,17) (13,26) (13,31) (14,26) (14,31) (15,29) (15,20) (15,16) (15,27) (15,33) (15,19) (15,30) (15,32) (16,29) (16,21) (16,20) (16,27) (16,33) (16,19) (16,30) (16,32) (17,23) (17,25) (17,28) (18,22) (19,29) (19,21) (19,24) (19,20) (19,27) (19,33) (19,32) (20,21) (20,27) (20,33) (20,30) (21,29) (21,33) (21,30) (23,26) (23,31) (24,29) (24,27) (25,26) (26,28) (27,29) (27,33) (27,30) (27,32) (28,31) (29,33) (29,30) (30,33) (30,32) (32,33)\nIs there a path between node 14 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph190-10_17", + "image": "data/connectivity/graph_visual/hard/graph190.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,3) (0,16) (0,26) (0,9) (0,8) (1,28) (1,22) (1,20) (1,26) (1,9) (2,17) (2,28) (2,3) (2,14) (3,15) (3,6) (3,22) (3,26) (3,8) (3,29) (4,12) (4,20) (4,26) (5,7) (5,25) (5,19) (6,22) (6,14) (7,24) (7,23) (7,19) (7,13) (7,10) (8,17) (8,28) (8,18) (8,29) (9,17) (9,15) (9,20) (9,11) (10,24) (11,17) (11,16) (11,26) (12,28) (12,20) (12,26) (12,14) (13,19) (14,17) (15,17) (16,22) (17,20) (17,26) (17,29) (19,25) (20,22) (20,26) (21,27) (22,28) (22,26) (24,25) (25,27) (26,29) (28,29)\nIs there a path between node 10 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph319-22_15", + "image": "data/connectivity/graph_visual/hard/graph319.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,2) (0,28) (0,1) (1,20) (1,27) (1,18) (2,16) (3,19) (3,27) (3,13) (3,18) (4,26) (4,21) (4,17) (4,12) (4,22) (4,10) (5,23) (5,15) (5,18) (6,19) (6,23) (7,9) (7,31) (7,17) (7,10) (8,20) (8,23) (8,15) (9,24) (9,10) (10,31) (10,24) (10,14) (11,17) (11,12) (12,26) (12,21) (12,17) (12,14) (13,19) (13,20) (13,23) (13,18) (13,30) (13,16) (14,31) (15,20) (15,30) (16,29) (17,21) (17,31) (18,19) (18,23) (19,27) (19,29) (20,23) (20,28) (21,31) (21,25) (22,26) (23,30) (23,29) (24,31) (24,25) (25,26) (26,31) (28,29) (29,30)\nIs there a path between node 22 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph522-15_7", + "image": "data/connectivity/graph_visual/hard/graph522.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,11) (0,33) (0,7) (0,13) (1,25) (1,30) (1,27) (2,6) (2,5) (2,13) (3,30) (3,17) (3,15) (3,32) (3,14) (3,21) (3,8) (3,12) (3,4) (3,24) (4,25) (4,17) (4,32) (4,12) (5,9) (7,16) (7,33) (8,28) (8,25) (8,32) (8,26) (8,21) (8,27) (8,20) (9,11) (9,16) (9,13) (10,28) (10,15) (10,26) (10,27) (10,24) (10,18) (11,16) (11,33) (12,28) (12,25) (12,24) (13,33) (14,27) (15,27) (15,29) (15,24) (17,25) (17,21) (18,25) (18,31) (18,21) (18,27) (20,25) (20,32) (20,22) (20,21) (20,27) (20,29) (20,24) (21,28) (21,29) (21,24) (22,24) (24,30) (24,31) (24,26) (25,31) (25,32) (25,26) (25,27) (26,30) (27,31) (28,29) (30,32)\nIs there a path between node 15 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph71-18_21", + "image": "data/connectivity/graph_visual/hard/graph71.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,7) (0,14) (0,16) (0,2) (0,26) (0,17) (0,9) (1,7) (1,14) (1,21) (1,16) (1,20) (1,2) (1,6) (1,8) (1,19) (1,11) (1,17) (2,13) (2,21) (2,22) (2,16) (2,3) (2,24) (2,6) (2,11) (3,13) (3,7) (3,25) (3,20) (3,24) (3,6) (3,23) (4,5) (4,16) (4,24) (4,6) (4,8) (4,19) (5,25) (5,15) (5,19) (6,13) (6,14) (6,21) (6,25) (6,22) (6,16) (6,24) (6,19) (6,23) (6,17) (7,22) (7,16) (7,8) (7,17) (7,9) (8,13) (8,15) (8,11) (8,23) (8,17) (8,9) (9,14) (9,25) (9,22) (9,16) (9,20) (9,15) (9,19) (9,11) (9,26) (10,18) (11,21) (11,16) (11,20) (11,24) (11,23) (11,17) (12,18) (13,22) (13,20) (13,24) (13,23) (14,21) (14,25) (14,22) (14,16) (14,20) (14,15) (14,19) (15,25) (15,19) (15,26) (15,17) (16,25) (16,19) (16,23) (16,26) (16,17) (17,20) (17,23) (17,26) (19,25) (19,20) (19,24) (20,22) (21,22) (22,23) (23,25)\nIs there a path between node 18 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph76-10_23", + "image": "data/connectivity/graph_visual/hard/graph76.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,25) (0,17) (0,1) (0,22) (0,5) (0,26) (0,12) (0,6) (0,11) (0,2) (0,10) (0,9) (0,3) (0,14) (0,4) (0,23) (0,21) (1,17) (1,22) (1,5) (1,26) (1,24) (1,8) (1,16) (1,10) (1,9) (1,3) (1,14) (1,4) (1,23) (2,17) (2,18) (2,24) (2,12) (2,6) (2,11) (2,16) (2,10) (2,15) (2,9) (2,3) (2,14) (2,23) (3,25) (3,22) (3,5) (3,26) (3,24) (3,12) (3,6) (3,8) (3,11) (3,16) (3,10) (3,15) (3,14) (3,4) (3,23) (3,21) (4,25) (4,22) (4,18) (4,26) (4,8) (4,11) (4,16) (4,10) (4,15) (4,14) (4,21) (5,25) (5,22) (5,18) (5,24) (5,12) (5,6) (5,8) (5,11) (5,16) (5,10) (5,15) (5,9) (5,14) (5,23) (5,21) (6,25) (6,17) (6,18) (6,24) (6,8) (6,11) (6,16) (6,15) (6,9) (6,14) (7,13) (7,19) (7,20) (8,22) (8,26) (8,24) (8,12) (8,11) (8,15) (8,9) (9,25) (9,17) (9,22) (9,18) (9,26) (9,24) (9,10) (9,15) (9,14) (9,23) (9,21) (10,25) (10,18) (10,26) (10,11) (10,14) (10,23) (10,21) (11,25) (11,17) (11,22) (11,24) (11,16) (11,15) (11,14) (11,21) (12,18) (12,24) (12,23) (13,20) (14,25) (14,18) (14,26) (14,24) (14,15) (14,23) (14,21) (15,25) (15,17) (15,22) (15,18) (15,24) (15,16) (15,23) (16,17) (16,22) (16,18) (16,26) (17,22) (17,18) (17,24) (17,23) (18,25) (18,22) (18,24) (18,21) (19,20) (21,25) (21,26) (21,24) (21,23) (22,25) (22,23) (23,24) (24,25) (24,26)\nIs there a path between node 10 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph419-18_1", + "image": "data/connectivity/graph_visual/hard/graph419.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,27) (0,28) (0,23) (0,2) (1,24) (1,13) (2,5) (2,28) (2,31) (3,7) (3,25) (4,5) (4,18) (5,23) (5,18) (6,15) (6,21) (6,20) (8,32) (8,19) (8,26) (9,11) (9,15) (9,29) (9,20) (10,24) (10,13) (10,19) (10,26) (11,29) (12,16) (13,32) (13,26) (14,32) (14,30) (15,21) (15,29) (17,20) (18,27) (18,28) (18,31) (19,24) (19,32) (19,26) (20,29) (21,29) (22,24) (22,32) (22,30) (23,31) (24,30) (26,30)\nIs there a path between node 18 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph265-4_25", + "image": "data/connectivity/graph_visual/hard/graph265.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,25) (0,9) (0,15) (0,27) (0,29) (1,25) (1,28) (1,23) (1,15) (1,18) (1,8) (1,13) (1,4) (1,29) (1,26) (2,20) (3,6) (3,28) (3,23) (3,14) (3,8) (3,12) (3,17) (4,5) (4,9) (4,12) (4,26) (5,16) (5,14) (5,12) (6,23) (6,21) (7,23) (7,16) (7,8) (7,12) (8,23) (8,14) (8,27) (8,19) (8,12) (8,17) (9,25) (9,28) (9,22) (9,15) (9,16) (9,14) (9,19) (9,12) (9,26) (11,24) (12,22) (12,15) (12,18) (12,14) (12,19) (12,13) (12,21) (12,26) (13,22) (13,27) (14,16) (15,22) (15,27) (15,17) (15,21) (15,26) (16,25) (16,28) (16,27) (16,19) (17,25) (17,27) (17,26) (18,25) (18,28) (18,21) (18,26) (19,22) (19,29) (20,24) (20,30) (21,26) (23,27) (25,27) (25,29)\nIs there a path between node 4 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph326-11_26", + "image": "data/connectivity/graph_visual/hard/graph326.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,21) (0,6) (0,10) (0,29) (0,17) (0,1) (0,7) (0,13) (0,19) (0,20) (1,18) (1,21) (1,5) (1,6) (1,29) (1,3) (1,25) (1,17) (1,7) (1,13) (1,2) (1,30) (1,19) (2,18) (2,21) (2,5) (2,6) (2,10) (2,29) (2,3) (2,25) (2,7) (2,13) (2,19) (3,18) (3,21) (3,6) (3,10) (3,25) (3,31) (3,17) (3,16) (3,7) (3,30) (3,19) (4,12) (4,27) (4,9) (4,14) (4,23) (4,8) (4,26) (4,11) (5,21) (5,6) (5,10) (5,29) (5,25) (5,31) (5,17) (5,16) (5,7) (5,20) (6,21) (6,10) (6,25) (6,31) (6,16) (6,30) (7,18) (7,21) (7,29) (7,25) (7,31) (7,17) (7,13) (7,30) (7,20) (8,12) (8,22) (8,27) (8,28) (8,9) (8,15) (8,14) (8,23) (8,26) (8,11) (9,12) (9,22) (9,27) (9,28) (9,15) (9,14) (9,23) (9,11) (10,18) (10,21) (10,25) (10,31) (10,17) (10,16) (10,13) (10,30) (10,19) (10,20) (11,22) (11,28) (11,15) (11,23) (11,26) (12,27) (12,15) (12,14) (12,23) (12,26) (13,29) (13,16) (13,30) (13,19) (13,20) (14,22) (14,27) (14,28) (14,15) (14,23) (14,24) (15,22) (15,27) (15,23) (15,24) (16,18) (16,25) (16,17) (16,30) (16,20) (17,18) (17,21) (17,29) (17,25) (17,31) (17,30) (17,19) (17,20) (18,29) (18,25) (18,31) (18,30) (18,19) (18,20) (19,21) (19,29) (19,25) (19,30) (20,21) (20,29) (20,25) (20,31) (20,30) (21,25) (21,31) (21,30) (22,27) (22,28) (22,26) (22,24) (23,27) (23,28) (23,24) (24,27) (24,28) (25,31) (26,28) (27,28) (29,31) (29,30)\nIs there a path between node 11 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph608-27_14", + "image": "data/connectivity/graph_visual/hard/graph608.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,16) (0,32) (0,6) (0,11) (0,34) (1,26) (1,18) (2,13) (2,8) (2,34) (2,20) (3,30) (3,8) (3,11) (4,10) (5,7) (5,29) (6,32) (6,13) (6,28) (6,20) (7,22) (7,12) (7,23) (7,33) (8,16) (8,32) (8,13) (8,28) (8,20) (9,31) (10,19) (11,34) (13,34) (13,28) (13,20) (14,21) (16,32) (16,30) (16,28) (17,34) (17,28) (19,21) (20,32) (21,25) (22,26) (25,27) (28,30) (30,32)\nIs there a path between node 27 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph585-4_22", + "image": "data/connectivity/graph_visual/hard/graph585.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,9) (0,27) (0,18) (0,16) (0,5) (0,21) (0,29) (0,24) (1,10) (1,7) (1,15) (2,31) (2,14) (2,25) (2,23) (2,11) (2,20) (3,33) (3,4) (4,33) (4,13) (4,32) (5,9) (5,27) (5,12) (5,26) (5,21) (5,29) (5,24) (6,31) (6,14) (6,19) (6,20) (7,10) (7,8) (8,28) (8,10) (8,15) (9,27) (9,18) (9,12) (9,16) (9,29) (9,24) (10,28) (10,15) (11,25) (11,19) (11,20) (12,16) (12,26) (12,21) (12,24) (13,22) (13,33) (14,31) (14,25) (14,20) (16,26) (16,21) (16,29) (16,24) (17,22) (17,33) (17,32) (18,27) (18,26) (18,21) (18,29) (18,24) (19,31) (19,23) (19,20) (20,31) (20,25) (20,23) (21,26) (21,29) (21,24) (22,30) (22,32) (25,31) (26,27) (26,29) (27,29) (30,33) (30,32) (32,33)\nIs there a path between node 4 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph41-25_4", + "image": "data/connectivity/graph_visual/hard/graph41.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,17) (0,2) (0,25) (0,14) (0,9) (0,15) (0,12) (0,1) (0,7) (0,16) (0,18) (0,11) (0,10) (0,5) (1,17) (1,2) (1,21) (1,14) (1,9) (1,15) (1,12) (1,19) (1,8) (1,7) (1,18) (1,11) (1,10) (1,5) (2,17) (2,21) (2,14) (2,9) (2,13) (2,3) (2,12) (2,6) (2,19) (2,7) (2,18) (2,11) (2,5) (3,17) (3,22) (3,21) (3,9) (3,15) (3,13) (3,6) (3,19) (3,8) (3,7) (3,16) (3,18) (3,11) (4,20) (4,23) (4,24) (5,17) (5,22) (5,21) (5,9) (5,15) (5,12) (5,19) (5,8) (5,16) (5,11) (5,10) (6,22) (6,25) (6,9) (6,15) (6,13) (6,12) (6,19) (6,8) (6,7) (6,16) (7,17) (7,22) (7,25) (7,9) (7,15) (7,13) (7,12) (7,19) (7,8) (7,16) (7,11) (7,10) (8,17) (8,22) (8,14) (8,12) (8,16) (8,18) (8,11) (9,17) (9,22) (9,25) (9,15) (9,13) (9,12) (9,19) (9,16) (9,18) (9,11) (10,17) (10,22) (10,25) (10,13) (10,19) (10,11) (11,17) (11,25) (11,14) (11,15) (11,13) (11,12) (11,19) (12,22) (12,21) (12,14) (12,19) (12,16) (13,22) (13,25) (13,21) (13,14) (13,16) (14,17) (14,21) (14,15) (14,19) (14,16) (14,18) (15,17) (15,25) (15,21) (15,16) (16,22) (16,25) (16,21) (16,19) (16,18) (17,22) (17,25) (17,21) (17,19) (17,18) (18,22) (18,21) (18,19) (19,22) (19,25) (19,21) (20,23) (20,24) (21,22) (21,25) (23,24)\nIs there a path between node 25 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph240-0_9", + "image": "data/connectivity/graph_visual/hard/graph240.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,13) (0,2) (0,9) (1,5) (1,13) (1,19) (1,16) (1,18) (1,9) (1,7) (1,3) (1,6) (2,30) (2,16) (2,18) (2,4) (2,9) (2,7) (2,14) (3,19) (3,24) (3,17) (3,7) (3,6) (3,23) (4,30) (4,16) (4,6) (5,26) (5,17) (5,14) (6,19) (6,29) (6,16) (6,7) (7,16) (7,24) (8,28) (9,26) (9,13) (9,19) (9,29) (9,25) (9,14) (10,22) (10,11) (10,20) (10,27) (11,27) (11,28) (12,20) (12,21) (13,26) (13,30) (13,29) (13,18) (13,14) (14,29) (14,16) (16,26) (16,17) (16,23) (17,18) (17,23) (18,30) (18,25) (19,29) (19,25) (20,27) (21,22) (21,28) (23,26) (23,30) (24,29) (24,25) (25,30) (26,29) (27,28)\nIs there a path between node 0 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph221-7_6", + "image": "data/connectivity/graph_visual/hard/graph221.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,19) (0,14) (0,22) (0,24) (0,26) (0,8) (0,18) (0,10) (1,15) (1,9) (1,3) (1,20) (1,11) (1,5) (1,4) (1,7) (1,21) (1,12) (1,6) (1,27) (1,29) (1,25) (1,17) (2,19) (2,14) (2,16) (2,22) (2,24) (2,26) (2,8) (2,18) (2,28) (3,15) (3,20) (3,23) (3,11) (3,5) (3,7) (3,21) (3,6) (3,27) (3,29) (3,25) (3,17) (4,15) (4,23) (4,5) (4,7) (4,13) (4,21) (4,12) (4,29) (5,15) (5,23) (5,11) (5,21) (5,6) (5,27) (5,29) (5,25) (5,17) (6,15) (6,20) (6,23) (6,11) (6,13) (6,21) (6,12) (6,29) (6,25) (6,17) (7,15) (7,9) (7,20) (7,23) (7,11) (7,13) (7,21) (7,12) (7,27) (7,25) (7,17) (8,19) (8,14) (8,22) (8,26) (8,18) (8,28) (8,10) (9,20) (9,23) (9,11) (9,13) (9,21) (9,12) (9,27) (9,29) (9,25) (9,17) (10,16) (10,22) (10,24) (10,26) (10,18) (10,28) (11,15) (11,20) (11,23) (11,21) (11,27) (11,29) (12,15) (12,20) (12,13) (12,21) (12,27) (12,29) (12,25) (12,17) (13,15) (13,23) (13,21) (13,29) (13,25) (14,19) (14,16) (14,22) (14,24) (14,26) (14,18) (15,20) (15,23) (15,21) (15,29) (15,17) (16,19) (16,22) (17,20) (17,23) (17,21) (17,29) (17,25) (18,22) (18,24) (18,26) (18,28) (19,22) (19,24) (19,26) (19,28) (20,23) (20,27) (20,29) (21,23) (21,29) (21,25) (22,26) (22,28) (23,29) (24,26) (26,28) (27,29)\nIs there a path between node 7 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph393-6_29", + "image": "data/connectivity/graph_visual/hard/graph393.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,6) (0,1) (0,4) (0,30) (0,11) (0,19) (0,17) (0,2) (1,6) (1,4) (1,30) (1,3) (1,22) (2,31) (2,23) (2,22) (2,11) (2,19) (2,17) (3,28) (3,5) (3,18) (3,23) (3,21) (3,11) (3,20) (3,10) (3,32) (4,6) (4,5) (4,31) (4,9) (4,25) (4,20) (4,10) (5,28) (5,23) (5,16) (5,26) (5,9) (5,25) (5,11) (5,17) (5,29) (5,12) (5,32) (6,14) (6,18) (6,21) (6,22) (6,25) (6,17) (6,20) (7,24) (8,13) (8,27) (9,23) (9,26) (10,14) (10,31) (10,23) (10,26) (10,30) (10,25) (10,19) (11,14) (11,31) (11,18) (11,23) (11,30) (11,19) (12,14) (12,30) (13,15) (14,31) (14,18) (14,30) (14,17) (16,28) (16,31) (16,18) (16,21) (16,30) (16,22) (16,25) (16,17) (16,29) (16,32) (17,31) (17,18) (18,23) (18,26) (18,19) (18,20) (19,23) (19,21) (20,28) (20,31) (20,30) (20,25) (20,29) (21,23) (21,22) (22,26) (23,26) (23,30) (24,27) (25,29) (28,31) (28,32)\nIs there a path between node 6 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph553-13_8", + "image": "data/connectivity/graph_visual/hard/graph553.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,24) (0,26) (0,31) (0,22) (1,25) (1,28) (1,20) (1,30) (1,14) (1,2) (1,17) (1,5) (2,9) (2,6) (2,33) (2,30) (2,17) (3,24) (3,12) (3,16) (3,29) (4,15) (4,25) (4,28) (4,20) (4,21) (5,15) (5,10) (5,28) (5,6) (5,33) (5,20) (5,13) (5,17) (6,15) (6,9) (6,21) (6,17) (7,15) (7,10) (7,20) (7,14) (7,21) (8,24) (8,26) (8,16) (9,25) (9,13) (9,21) (10,15) (10,32) (10,20) (10,18) (11,27) (12,26) (13,17) (14,30) (14,21) (15,18) (15,17) (16,31) (16,23) (16,29) (17,25) (17,33) (17,32) (17,18) (18,30) (19,27) (22,26) (23,24) (25,33) (25,32) (26,31) (28,32)\nIs there a path between node 13 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph575-1_20", + "image": "data/connectivity/graph_visual/hard/graph575.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,30) (0,10) (0,23) (0,11) (0,31) (1,28) (1,26) (1,5) (1,20) (1,18) (1,29) (1,8) (1,9) (1,13) (2,3) (2,28) (2,26) (2,15) (2,20) (2,21) (2,12) (2,18) (2,29) (2,8) (2,9) (2,13) (2,16) (3,22) (3,28) (3,15) (3,20) (3,21) (3,12) (3,18) (3,29) (3,8) (3,9) (3,13) (3,16) (4,24) (4,30) (4,10) (4,23) (4,7) (4,17) (4,6) (5,28) (5,26) (5,27) (5,21) (5,12) (5,18) (5,29) (5,8) (5,9) (5,13) (5,16) (6,30) (6,10) (6,23) (6,11) (6,31) (6,7) (6,17) (7,30) (7,10) (7,23) (7,11) (7,31) (8,28) (8,32) (8,26) (8,27) (8,15) (8,18) (8,29) (8,9) (8,16) (9,27) (9,15) (9,21) (9,29) (9,16) (10,24) (10,30) (10,23) (10,11) (10,31) (10,17) (11,30) (11,31) (12,22) (12,32) (12,27) (12,15) (12,20) (12,21) (12,13) (12,16) (13,32) (13,26) (13,15) (13,20) (13,21) (13,29) (13,16) (14,33) (14,19) (15,28) (15,26) (15,27) (15,21) (15,16) (16,22) (16,28) (16,32) (16,26) (16,27) (16,18) (16,29) (17,23) (17,31) (18,22) (18,28) (18,32) (18,26) (18,27) (18,20) (18,21) (19,33) (20,22) (20,28) (20,26) (20,21) (20,29) (21,22) (21,32) (21,26) (21,27) (22,26) (22,27) (23,30) (23,31) (26,27) (26,29) (27,28) (27,32) (27,29)\nIs there a path between node 1 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph634-4_24", + "image": "data/connectivity/graph_visual/hard/graph634.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,6) (0,1) (0,8) (0,13) (0,32) (0,2) (1,33) (1,34) (1,30) (1,8) (1,10) (1,19) (1,31) (1,2) (2,15) (2,34) (2,18) (2,8) (2,3) (2,16) (2,32) (2,4) (3,5) (3,26) (3,15) (3,11) (3,16) (3,4) (3,14) (4,5) (4,26) (4,12) (4,33) (4,34) (4,30) (4,13) (4,19) (5,34) (5,21) (5,6) (5,8) (5,19) (5,32) (5,31) (6,33) (6,15) (6,34) (6,13) (6,31) (7,23) (7,20) (8,33) (8,15) (8,34) (8,21) (8,11) (9,24) (10,33) (10,21) (10,27) (10,13) (10,11) (10,19) (11,26) (11,33) (11,13) (11,32) (12,30) (12,16) (13,33) (13,34) (13,19) (13,14) (15,33) (15,34) (15,27) (16,34) (16,30) (16,27) (16,32) (17,29) (18,27) (18,32) (19,30) (19,21) (19,32) (20,28) (21,27) (21,32) (26,33) (26,30) (26,31) (27,34)\nIs there a path between node 4 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph504-5_28", + "image": "data/connectivity/graph_visual/hard/graph504.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,23) (0,22) (0,17) (0,15) (0,9) (0,8) (0,6) (0,13) (0,7) (0,18) (0,12) (0,20) (0,24) (0,33) (0,27) (0,11) (0,30) (1,2) (1,16) (2,16) (2,5) (3,23) (3,19) (3,25) (3,22) (3,32) (3,15) (3,21) (3,8) (3,10) (3,14) (3,6) (3,13) (3,7) (3,18) (3,24) (3,31) (3,33) (3,27) (3,11) (3,30) (4,16) (4,5) (6,23) (6,28) (6,19) (6,25) (6,26) (6,29) (6,22) (6,17) (6,8) (6,10) (6,14) (6,13) (6,18) (6,12) (6,20) (6,24) (6,31) (6,33) (6,27) (6,30) (7,23) (7,28) (7,19) (7,26) (7,29) (7,22) (7,17) (7,21) (7,9) (7,10) (7,14) (7,13) (7,18) (7,12) (7,31) (7,33) (7,27) (7,11) (8,23) (8,25) (8,26) (8,29) (8,32) (8,17) (8,21) (8,9) (8,10) (8,14) (8,13) (8,18) (8,12) (8,20) (8,24) (8,31) (8,33) (8,27) (8,11) (9,25) (9,26) (9,29) (9,22) (9,32) (9,17) (9,21) (9,14) (9,13) (9,18) (9,12) (9,20) (9,24) (9,33) (9,11) (10,28) (10,19) (10,26) (10,22) (10,32) (10,17) (10,15) (10,13) (10,18) (10,12) (10,24) (10,33) (10,27) (10,30) (11,23) (11,28) (11,25) (11,26) (11,29) (11,32) (11,17) (11,13) (11,12) (11,20) (11,24) (11,27) (11,30) (12,28) (12,25) (12,26) (12,29) (12,32) (12,13) (12,18) (12,20) (12,31) (12,27) (12,30) (13,23) (13,19) (13,25) (13,26) (13,29) (13,22) (13,32) (13,17) (13,14) (13,24) (13,31) (13,33) (13,27) (14,23) (14,28) (14,19) (14,25) (14,22) (14,15) (14,21) (14,18) (14,20) (14,24) (14,27) (14,30) (15,28) (15,26) (15,29) (15,22) (15,20) (15,31) (15,33) (15,27) (15,30) (17,23) (17,28) (17,19) (17,25) (17,26) (17,22) (17,32) (17,21) (17,18) (17,20) (17,24) (17,27) (17,30) (18,23) (18,28) (18,19) (18,25) (18,26) (18,32) (18,21) (18,20) (18,24) (18,31) (18,33) (18,27) (18,30) (19,23) (19,28) (19,25) (19,26) (19,29) (19,22) (19,32) (19,21) (19,30) (20,22) (20,32) (20,21) (20,31) (20,33) (20,27) (21,23) (21,25) (21,26) (21,22) (21,32) (21,24) (21,31) (21,33) (21,27) (21,30) (22,23) (22,26) (22,29) (22,32) (22,31) (22,33) (22,30) (23,26) (23,29) (23,32) (23,24) (23,31) (23,33) (24,25) (24,26) (24,29) (24,32) (24,31) (24,33) (24,27) (24,30) (25,26) (25,32) (25,31) (25,33) (25,30) (26,28) (26,29) (26,32) (26,31) (26,27) (27,28) (27,29) (27,31) (27,33) (27,30) (28,29) (28,31) (28,33) (29,32) (29,33) (29,30) (30,32) (30,31) (30,33) (31,32) (31,33) (32,33)\nIs there a path between node 5 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph93-17_19", + "image": "data/connectivity/graph_visual/hard/graph93.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,19) (0,18) (0,16) (0,13) (0,4) (0,8) (0,10) (0,22) (1,2) (2,7) (3,19) (3,18) (3,12) (3,20) (3,10) (4,11) (4,14) (4,5) (4,20) (4,8) (5,11) (5,14) (5,18) (5,16) (5,13) (5,12) (6,19) (6,11) (6,12) (6,20) (6,8) (7,26) (8,24) (8,14) (8,18) (8,25) (9,17) (10,15) (10,27) (10,21) (10,18) (10,13) (10,12) (10,20) (11,27) (11,21) (11,13) (11,12) (11,25) (12,24) (12,16) (12,25) (13,24) (13,27) (13,25) (13,20) (13,22) (14,16) (14,22) (15,20) (16,25) (17,26) (17,23) (18,27) (19,25) (19,20) (20,24) (20,25) (20,22) (21,27) (22,25) (23,26) (25,27)\nIs there a path between node 17 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph626-8_20", + "image": "data/connectivity/graph_visual/hard/graph626.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,16) (0,33) (0,10) (1,27) (2,15) (2,34) (2,3) (2,23) (3,14) (3,8) (3,34) (3,23) (4,13) (4,9) (4,20) (4,30) (4,29) (4,5) (5,27) (5,30) (5,24) (5,29) (5,7) (6,13) (6,28) (6,24) (6,29) (6,18) (7,28) (7,24) (8,32) (8,31) (9,28) (9,27) (9,24) (9,29) (10,26) (12,15) (12,21) (12,32) (12,23) (13,20) (13,30) (13,29) (13,18) (14,15) (14,23) (14,17) (15,31) (17,32) (18,29) (20,24) (21,32) (21,25) (24,28) (27,28) (28,29)\nIs there a path between node 8 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph453-30_19", + "image": "data/connectivity/graph_visual/hard/graph453.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,18) (0,26) (0,7) (0,3) (0,13) (0,11) (0,19) (1,8) (1,12) (1,23) (1,24) (1,15) (1,6) (2,4) (2,15) (2,6) (3,28) (3,11) (3,19) (4,8) (4,5) (4,15) (4,6) (5,32) (5,8) (5,30) (5,27) (5,12) (5,23) (6,32) (6,23) (7,31) (7,19) (8,23) (8,15) (9,22) (10,25) (10,13) (10,11) (11,14) (11,26) (12,29) (13,28) (13,31) (13,19) (14,18) (15,29) (15,27) (15,24) (16,18) (18,28) (19,26) (23,30) (24,27) (25,28) (26,28)\nIs there a path between node 30 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph218-4_15", + "image": "data/connectivity/graph_visual/hard/graph218.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,7) (0,15) (0,18) (0,27) (0,9) (0,13) (0,25) (0,3) (1,8) (1,5) (1,26) (1,12) (1,2) (1,16) (1,14) (2,8) (2,26) (2,12) (2,16) (2,14) (3,7) (3,4) (3,15) (3,18) (3,27) (3,13) (4,7) (4,15) (4,18) (4,27) (4,13) (5,8) (5,12) (5,11) (5,16) (5,14) (5,20) (6,17) (6,21) (6,29) (6,28) (7,15) (7,18) (7,27) (7,9) (7,13) (8,26) (8,23) (8,16) (8,14) (9,15) (10,29) (10,24) (11,12) (11,16) (11,14) (11,20) (12,22) (12,23) (12,14) (12,20) (13,18) (13,27) (14,26) (14,22) (14,23) (14,20) (15,18) (15,27) (15,25) (16,26) (16,22) (16,23) (16,20) (17,21) (17,19) (17,24) (17,28) (19,21) (19,29) (19,24) (19,28) (20,26) (20,22) (20,23) (21,29) (21,24) (22,26) (22,23) (24,29) (24,28) (25,27)\nIs there a path between node 4 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph391-11_3", + "image": "data/connectivity/graph_visual/hard/graph391.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,9) (0,18) (0,31) (0,7) (0,30) (0,1) (0,21) (0,2) (1,13) (1,18) (1,12) (1,26) (1,24) (1,2) (2,14) (2,16) (2,22) (3,27) (4,27) (5,27) (6,7) (6,30) (6,24) (6,23) (7,13) (7,32) (7,23) (8,19) (8,12) (8,26) (8,21) (8,23) (8,16) (8,22) (9,18) (9,24) (9,23) (11,18) (11,12) (11,23) (11,16) (12,13) (12,14) (12,26) (12,24) (12,21) (12,16) (13,19) (13,18) (13,14) (13,24) (13,16) (14,19) (14,18) (14,30) (14,21) (14,16) (14,22) (16,31) (16,24) (16,23) (16,22) (18,26) (18,32) (21,26) (21,23) (21,22) (22,26) (22,24) (25,28) (31,32)\nIs there a path between node 11 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph525-7_28", + "image": "data/connectivity/graph_visual/hard/graph525.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,12) (0,30) (0,8) (0,15) (1,20) (1,21) (1,29) (1,19) (1,5) (1,16) (2,32) (2,4) (2,27) (2,24) (2,19) (2,18) (2,16) (3,20) (3,18) (3,16) (4,20) (4,21) (4,14) (4,5) (4,16) (5,20) (5,17) (5,31) (6,28) (6,30) (7,29) (7,31) (8,30) (8,15) (9,21) (9,27) (9,14) (9,29) (10,25) (13,22) (13,28) (14,21) (14,27) (14,17) (16,32) (16,20) (16,24) (16,29) (17,21) (17,27) (17,31) (18,20) (18,21) (18,24) (19,24) (20,21) (20,24) (20,31) (21,24) (21,29) (21,31) (27,29)\nIs there a path between node 7 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph557-9_8", + "image": "data/connectivity/graph_visual/hard/graph557.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,10) (0,11) (1,18) (4,10) (4,11) (4,24) (4,12) (5,30) (5,9) (5,32) (5,26) (5,8) (6,30) (6,19) (7,28) (8,19) (8,15) (8,13) (9,19) (9,13) (10,11) (10,31) (10,17) (10,12) (11,14) (11,22) (12,23) (12,16) (13,15) (14,24) (14,16) (15,26) (15,29) (16,22) (16,17) (17,22) (17,23) (19,26) (20,28) (21,23) (22,23) (22,31) (23,31) (29,32)\nIs there a path between node 9 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph135-9_10", + "image": "data/connectivity/graph_visual/hard/graph135.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,10) (0,7) (0,5) (0,3) (0,6) (0,27) (0,16) (0,8) (0,19) (0,24) (0,22) (0,21) (0,17) (0,20) (0,1) (0,25) (1,23) (1,3) (1,6) (1,26) (1,27) (1,16) (1,8) (1,19) (1,4) (1,22) (1,21) (1,17) (1,25) (2,13) (2,11) (3,10) (3,7) (3,5) (3,26) (3,16) (3,8) (3,19) (3,24) (3,18) (3,20) (3,15) (3,25) (4,5) (4,6) (4,26) (4,16) (4,8) (4,19) (4,24) (4,22) (4,21) (4,9) (4,17) (4,15) (5,10) (5,7) (5,6) (5,26) (5,27) (5,16) (5,8) (5,19) (5,22) (5,18) (5,21) (5,17) (5,20) (5,25) (6,10) (6,7) (6,23) (6,26) (6,27) (6,16) (6,19) (6,24) (6,22) (6,18) (6,21) (6,9) (6,17) (6,15) (6,25) (7,10) (7,23) (7,26) (7,8) (7,19) (7,24) (7,21) (7,9) (7,17) (7,20) (7,25) (8,10) (8,23) (8,26) (8,27) (8,16) (8,19) (8,24) (8,22) (8,9) (8,15) (9,10) (9,23) (9,27) (9,16) (9,24) (9,22) (9,18) (9,21) (9,17) (9,20) (9,15) (10,23) (10,27) (10,16) (10,24) (10,22) (10,17) (10,25) (11,13) (11,14) (12,13) (12,14) (15,23) (15,27) (15,19) (15,24) (15,22) (15,18) (15,21) (15,20) (15,25) (16,23) (16,27) (16,24) (16,22) (16,18) (16,17) (16,25) (17,23) (17,26) (17,27) (17,19) (17,22) (17,21) (17,20) (17,25) (18,26) (18,27) (18,19) (18,24) (18,22) (19,23) (19,24) (19,21) (19,25) (20,27) (20,24) (20,22) (20,25) (21,23) (21,26) (21,27) (21,24) (21,22) (21,25) (22,23) (22,26) (22,24) (23,26) (23,27) (23,24) (23,25) (24,27) (24,25) (25,27)\nIs there a path between node 9 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph501-17_25", + "image": "data/connectivity/graph_visual/hard/graph501.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,22) (0,2) (0,17) (0,14) (0,6) (0,28) (0,23) (0,21) (1,22) (1,8) (1,17) (1,14) (1,19) (1,6) (1,10) (1,23) (1,16) (2,22) (2,4) (2,8) (2,18) (2,32) (2,27) (2,16) (3,4) (3,17) (3,14) (3,33) (3,18) (4,7) (4,19) (4,9) (4,18) (4,28) (4,21) (5,25) (5,13) (6,22) (6,14) (6,9) (6,18) (6,10) (6,12) (6,32) (7,17) (7,33) (7,9) (7,32) (8,22) (8,26) (8,9) (8,28) (8,10) (8,31) (8,16) (9,14) (9,18) (9,28) (9,10) (9,12) (9,31) (9,11) (9,27) (9,16) (10,22) (10,26) (10,29) (10,19) (10,23) (10,21) (11,26) (11,18) (11,12) (11,23) (11,32) (11,27) (11,16) (12,22) (12,14) (12,18) (12,31) (12,23) (12,27) (13,24) (14,22) (14,26) (14,29) (14,19) (14,28) (14,32) (14,16) (15,20) (15,24) (16,22) (16,19) (16,32) (17,33) (17,18) (17,28) (17,23) (18,22) (18,27) (19,32) (20,24) (20,30) (22,26) (22,31) (23,32) (24,30) (25,30) (26,29) (26,33) (27,33) (27,28) (27,31) (29,33) (29,32)\nIs there a path between node 17 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph279-11_24", + "image": "data/connectivity/graph_visual/hard/graph279.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,7) (0,22) (0,14) (0,1) (0,12) (0,23) (1,8) (1,14) (1,12) (1,2) (1,23) (2,7) (2,22) (2,19) (2,12) (2,23) (3,13) (3,26) (3,21) (3,20) (3,6) (3,10) (3,11) (3,4) (3,17) (3,27) (3,24) (3,28) (3,30) (4,29) (4,21) (4,18) (4,20) (4,6) (4,16) (4,17) (4,27) (4,28) (4,9) (4,30) (5,25) (5,13) (5,26) (5,21) (5,20) (5,6) (5,10) (5,11) (5,15) (5,16) (5,17) (5,27) (5,24) (5,28) (6,25) (6,13) (6,29) (6,26) (6,21) (6,18) (6,11) (6,15) (6,16) (6,17) (6,27) (6,24) (6,28) (7,8) (7,22) (7,19) (7,14) (7,12) (7,23) (8,19) (8,12) (8,23) (9,25) (9,13) (9,26) (9,21) (9,18) (9,11) (9,16) (9,27) (10,25) (10,26) (10,18) (10,15) (10,17) (10,24) (10,30) (11,29) (11,21) (11,18) (11,20) (11,15) (11,17) (11,27) (11,24) (11,28) (12,22) (12,14) (12,23) (13,25) (13,26) (13,18) (13,20) (13,15) (13,16) (13,24) (13,28) (13,30) (14,22) (14,23) (15,25) (15,29) (15,26) (15,21) (15,18) (15,16) (15,27) (15,28) (15,30) (16,25) (16,29) (16,26) (16,20) (16,17) (16,30) (17,29) (17,21) (17,18) (17,20) (17,27) (18,25) (18,29) (18,26) (18,21) (18,20) (18,28) (18,30) (19,22) (20,25) (20,29) (20,26) (20,21) (20,24) (20,28) (21,25) (21,26) (21,27) (21,24) (21,28) (21,30) (24,29) (24,26) (24,27) (24,28) (24,30) (25,29) (25,26) (25,28) (25,30) (26,29) (26,27) (26,30) (27,29) (27,28) (29,30)\nIs there a path between node 11 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph525-19_31", + "image": "data/connectivity/graph_visual/hard/graph525.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,12) (0,30) (0,8) (0,15) (1,20) (1,21) (1,29) (1,19) (1,5) (1,16) (2,32) (2,4) (2,27) (2,24) (2,19) (2,18) (2,16) (3,20) (3,18) (3,16) (4,20) (4,21) (4,14) (4,5) (4,16) (5,20) (5,17) (5,31) (6,28) (6,30) (7,29) (7,31) (8,30) (8,15) (9,21) (9,27) (9,14) (9,29) (10,25) (13,22) (13,28) (14,21) (14,27) (14,17) (16,32) (16,20) (16,24) (16,29) (17,21) (17,27) (17,31) (18,20) (18,21) (18,24) (19,24) (20,21) (20,24) (20,31) (21,24) (21,29) (21,31) (27,29)\nIs there a path between node 19 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph690-32_17", + "image": "data/connectivity/graph_visual/hard/graph690.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,10) (0,7) (0,14) (0,32) (0,24) (0,29) (1,27) (1,31) (1,25) (1,3) (1,18) (1,9) (1,16) (1,33) (1,15) (1,13) (1,19) (1,22) (1,21) (1,30) (2,11) (3,31) (3,25) (3,18) (3,34) (3,20) (3,9) (3,16) (3,33) (3,13) (3,22) (3,21) (3,30) (4,27) (4,31) (4,34) (4,20) (4,9) (4,16) (4,15) (4,13) (4,19) (4,30) (5,17) (5,8) (6,12) (6,10) (6,28) (6,7) (6,14) (6,32) (6,29) (7,26) (7,12) (7,14) (7,32) (7,23) (7,24) (7,29) (8,17) (9,31) (9,18) (9,34) (9,20) (9,16) (9,22) (10,26) (10,12) (10,28) (10,32) (10,24) (12,26) (12,14) (12,24) (12,29) (13,27) (13,31) (13,25) (13,18) (13,34) (13,16) (13,33) (13,19) (13,22) (13,21) (13,30) (14,26) (14,28) (14,32) (15,25) (15,18) (15,34) (15,20) (15,33) (15,19) (15,22) (15,30) (16,27) (16,18) (16,34) (16,20) (16,33) (16,19) (16,22) (16,21) (18,25) (18,34) (18,22) (18,21) (18,30) (19,27) (19,31) (19,25) (19,20) (19,33) (19,22) (19,21) (19,30) (20,27) (20,31) (20,34) (20,33) (20,22) (20,21) (21,31) (21,22) (21,30) (22,27) (22,31) (22,25) (22,34) (22,30) (23,26) (23,28) (23,32) (23,29) (24,28) (24,32) (24,29) (25,27) (25,31) (25,33) (25,30) (26,28) (27,31) (27,34) (27,30) (28,29) (29,32) (30,34) (30,33) (31,34) (31,33)\nIs there a path between node 32 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph21-14_19", + "image": "data/connectivity/graph_visual/hard/graph21.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,19) (1,15) (1,18) (1,9) (1,21) (2,5) (2,10) (2,23) (3,6) (3,18) (4,22) (4,13) (4,9) (4,11) (6,17) (6,22) (6,18) (6,9) (6,7) (6,12) (6,21) (7,15) (7,17) (8,15) (8,18) (8,9) (8,11) (8,21) (9,15) (9,22) (10,25) (11,15) (11,17) (11,22) (11,13) (11,12) (11,21) (12,13) (13,15) (13,17) (14,15) (14,18) (14,21) (15,17) (15,21) (16,25) (17,22) (17,18) (18,22)\nIs there a path between node 14 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph552-30_31", + "image": "data/connectivity/graph_visual/hard/graph552.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,27) (0,26) (0,3) (0,13) (0,22) (0,12) (0,31) (0,17) (1,2) (1,20) (1,23) (1,13) (1,4) (1,29) (2,20) (2,5) (2,6) (2,22) (2,16) (2,31) (2,17) (2,29) (3,27) (3,5) (3,23) (3,24) (3,15) (3,13) (3,4) (3,17) (4,7) (4,5) (4,15) (4,13) (4,10) (4,22) (4,16) (4,18) (4,12) (4,21) (5,27) (5,20) (5,14) (5,23) (5,6) (5,15) (5,13) (5,28) (5,12) (5,21) (5,8) (5,25) (6,26) (6,20) (6,23) (6,24) (6,15) (6,9) (6,28) (6,22) (6,16) (6,8) (7,9) (7,19) (7,12) (7,21) (7,25) (8,24) (8,15) (8,32) (8,31) (8,25) (9,23) (9,22) (9,19) (9,12) (9,17) (10,26) (10,14) (10,23) (10,28) (10,29) (11,33) (12,15) (12,28) (12,16) (12,29) (13,14) (13,24) (13,32) (13,18) (13,17) (14,27) (14,26) (14,15) (14,31) (14,17) (14,25) (15,27) (15,26) (15,28) (15,19) (15,25) (16,20) (16,19) (16,18) (16,25) (17,20) (17,24) (17,32) (17,18) (17,25) (18,27) (18,24) (18,22) (18,31) (18,29) (19,26) (19,29) (19,25) (20,27) (20,23) (20,24) (20,22) (20,31) (21,22) (22,32) (22,28) (22,29) (22,25) (23,32) (23,25) (24,31) (26,27) (26,32) (27,29) (28,32) (28,31) (29,31)\nIs there a path between node 30 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph489-1_13", + "image": "data/connectivity/graph_visual/hard/graph489.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (0,6) (0,16) (0,18) (0,29) (0,24) (0,21) (0,28) (0,11) (0,14) (0,9) (0,8) (0,25) (1,23) (1,26) (1,19) (1,17) (1,12) (1,22) (1,13) (1,7) (1,15) (2,23) (2,26) (2,19) (2,12) (2,7) (2,15) (2,30) (2,3) (3,23) (3,26) (3,19) (3,17) (3,12) (3,22) (3,13) (3,7) (3,15) (3,30) (4,5) (4,27) (4,6) (4,16) (4,18) (4,29) (4,24) (4,10) (4,20) (4,21) (4,28) (4,31) (4,32) (4,25) (5,27) (5,16) (5,18) (5,29) (5,10) (5,11) (5,14) (5,31) (5,9) (5,8) (5,32) (5,25) (6,27) (6,16) (6,18) (6,24) (6,10) (6,20) (6,21) (6,28) (6,11) (6,31) (6,9) (6,8) (7,23) (7,26) (7,19) (7,12) (7,15) (7,30) (8,27) (8,18) (8,29) (8,10) (8,20) (8,21) (8,28) (8,11) (8,9) (9,16) (9,18) (9,29) (9,24) (9,10) (9,21) (9,28) (9,11) (9,14) (9,32) (9,25) (10,16) (10,18) (10,29) (10,24) (10,11) (10,32) (10,25) (11,27) (11,16) (11,18) (11,29) (11,24) (11,20) (11,21) (11,14) (11,31) (11,25) (12,23) (12,26) (12,19) (12,17) (12,22) (12,13) (12,15) (12,30) (13,23) (13,26) (13,19) (13,17) (13,22) (13,15) (13,30) (14,27) (14,29) (14,24) (14,21) (14,28) (14,31) (14,25) (15,23) (15,19) (15,17) (15,22) (16,27) (16,18) (16,29) (16,24) (16,20) (16,21) (16,28) (16,31) (16,32) (16,25) (17,26) (17,19) (17,30) (18,27) (18,29) (18,28) (18,31) (18,25) (19,30) (20,27) (20,24) (20,21) (20,28) (20,31) (20,32) (20,25) (21,27) (21,29) (21,24) (21,28) (21,31) (21,32) (21,25) (22,30) (23,26) (23,30) (24,27) (24,29) (24,28) (24,31) (24,32) (24,25) (25,27) (25,32) (26,30) (27,29) (27,31) (27,32) (28,29) (28,32) (29,31) (29,32)\nIs there a path between node 1 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph391-25_14", + "image": "data/connectivity/graph_visual/hard/graph391.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,9) (0,18) (0,31) (0,7) (0,30) (0,1) (0,21) (0,2) (1,13) (1,18) (1,12) (1,26) (1,24) (1,2) (2,14) (2,16) (2,22) (3,27) (4,27) (5,27) (6,7) (6,30) (6,24) (6,23) (7,13) (7,32) (7,23) (8,19) (8,12) (8,26) (8,21) (8,23) (8,16) (8,22) (9,18) (9,24) (9,23) (11,18) (11,12) (11,23) (11,16) (12,13) (12,14) (12,26) (12,24) (12,21) (12,16) (13,19) (13,18) (13,14) (13,24) (13,16) (14,19) (14,18) (14,30) (14,21) (14,16) (14,22) (16,31) (16,24) (16,23) (16,22) (18,26) (18,32) (21,26) (21,23) (21,22) (22,26) (22,24) (25,28) (31,32)\nIs there a path between node 25 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph146-14_2", + "image": "data/connectivity/graph_visual/hard/graph146.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,14) (0,13) (0,11) (0,21) (0,8) (0,18) (0,3) (0,7) (0,15) (0,20) (0,17) (0,10) (0,22) (0,1) (0,9) (0,6) (0,19) (1,23) (1,14) (1,5) (1,13) (1,11) (1,12) (1,21) (1,8) (1,18) (1,3) (1,25) (1,7) (1,28) (1,15) (1,20) (1,17) (1,10) (1,22) (1,9) (1,6) (1,16) (1,19) (3,27) (3,14) (3,5) (3,13) (3,4) (3,21) (3,18) (3,25) (3,28) (3,15) (3,20) (3,17) (3,22) (3,6) (3,16) (3,19) (4,27) (4,23) (4,5) (4,13) (4,11) (4,12) (4,8) (4,28) (4,15) (4,20) (4,17) (4,10) (4,24) (4,6) (5,27) (5,23) (5,14) (5,13) (5,11) (5,12) (5,21) (5,8) (5,18) (5,25) (5,7) (5,15) (5,10) (5,22) (5,24) (5,9) (5,6) (5,16) (5,19) (6,27) (6,14) (6,11) (6,12) (6,18) (6,25) (6,7) (6,20) (6,17) (6,10) (6,22) (6,24) (6,9) (6,16) (6,19) (7,23) (7,14) (7,13) (7,12) (7,21) (7,8) (7,25) (7,28) (7,20) (7,10) (7,22) (7,16) (7,19) (8,27) (8,13) (8,18) (8,25) (8,15) (8,17) (8,10) (8,22) (8,24) (8,9) (8,16) (8,19) (9,27) (9,23) (9,11) (9,21) (9,25) (9,28) (9,15) (9,20) (9,17) (9,10) (9,22) (9,24) (9,16) (9,19) (10,27) (10,14) (10,11) (10,12) (10,25) (10,28) (10,15) (10,20) (10,17) (10,24) (10,16) (10,19) (11,23) (11,21) (11,18) (11,25) (11,28) (11,15) (11,17) (11,22) (11,24) (11,19) (12,27) (12,23) (12,13) (12,21) (12,18) (12,25) (12,28) (12,15) (12,17) (12,22) (12,24) (12,16) (13,27) (13,14) (13,21) (13,18) (13,28) (13,15) (13,17) (13,24) (13,16) (13,19) (14,27) (14,25) (14,28) (14,15) (14,17) (14,22) (14,24) (14,16) (15,23) (15,21) (15,18) (15,25) (15,20) (15,24) (16,27) (16,23) (16,17) (16,24) (16,19) (17,27) (17,23) (17,18) (17,25) (17,28) (17,20) (17,22) (17,24) (17,19) (18,23) (18,21) (18,25) (18,28) (18,20) (18,22) (18,24) (18,19) (19,27) (19,23) (19,21) (19,25) (19,24) (20,27) (20,23) (20,21) (20,25) (20,24) (21,23) (21,22) (23,27) (23,24) (25,27) (25,28) (27,28)\nIs there a path between node 14 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph623-33_3", + "image": "data/connectivity/graph_visual/hard/graph623.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,29) (0,9) (0,17) (0,30) (0,16) (1,31) (1,25) (1,5) (1,16) (2,13) (2,15) (2,23) (2,30) (2,25) (2,5) (3,14) (5,13) (5,9) (5,17) (5,15) (5,23) (5,19) (5,30) (5,16) (5,22) (7,20) (7,34) (7,8) (7,17) (7,31) (7,18) (7,16) (7,32) (8,12) (8,34) (8,11) (8,18) (9,12) (9,34) (9,31) (9,18) (9,30) (9,16) (10,26) (10,28) (11,12) (11,20) (11,23) (11,19) (11,18) (11,30) (12,34) (12,13) (12,17) (12,23) (12,19) (12,18) (13,34) (13,15) (13,31) (13,21) (13,24) (13,32) (15,17) (15,23) (15,19) (15,30) (15,25) (15,21) (16,20) (16,17) (16,18) (16,25) (16,24) (16,27) (16,22) (17,20) (17,34) (17,29) (17,30) (17,21) (18,20) (18,27) (19,30) (20,34) (20,23) (20,25) (20,24) (20,27) (21,25) (22,23) (22,25) (23,29) (23,30) (23,27) (24,29) (24,31) (24,32) (25,29) (26,33) (28,33) (29,31) (29,32) (30,31) (31,34)\nIs there a path between node 33 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph138-3_22", + "image": "data/connectivity/graph_visual/hard/graph138.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,12) (0,10) (0,25) (0,16) (0,24) (0,4) (0,8) (0,27) (0,19) (1,5) (1,28) (2,15) (3,12) (3,13) (3,21) (3,24) (3,4) (3,8) (4,26) (4,20) (4,21) (4,11) (4,9) (6,13) (6,14) (6,22) (6,21) (6,7) (6,23) (6,11) (7,12) (7,26) (7,20) (7,17) (7,14) (7,10) (7,25) (7,24) (7,8) (7,11) (7,19) (7,9) (8,25) (8,27) (8,11) (9,17) (9,14) (9,21) (9,23) (9,27) (9,11) (10,26) (10,20) (10,14) (10,25) (10,23) (10,24) (11,13) (11,17) (11,21) (11,25) (11,23) (11,19) (12,20) (12,17) (12,24) (13,26) (13,20) (13,17) (13,22) (13,25) (13,24) (13,19) (14,20) (14,16) (15,28) (15,18) (16,26) (16,21) (16,23) (17,26) (17,22) (17,23) (17,27) (18,28) (19,22) (20,23) (20,24) (20,27) (21,26) (21,27) (23,25) (24,25) (24,27) (25,27)\nIs there a path between node 3 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph485-8_28", + "image": "data/connectivity/graph_visual/hard/graph485.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,7) (0,31) (0,25) (0,22) (0,24) (0,23) (0,5) (0,9) (0,21) (0,30) (1,26) (1,14) (1,7) (1,6) (1,31) (1,24) (1,23) (1,9) (1,21) (1,30) (2,27) (2,20) (2,12) (2,19) (2,32) (2,28) (2,13) (2,17) (3,26) (3,11) (3,18) (3,7) (3,31) (3,25) (3,22) (3,23) (3,5) (3,9) (3,21) (3,30) (4,27) (4,20) (4,12) (4,19) (4,28) (4,17) (4,29) (5,26) (5,11) (5,14) (5,18) (5,7) (5,6) (5,31) (5,22) (5,24) (5,23) (5,21) (5,30) (6,26) (6,11) (6,18) (6,7) (6,31) (6,25) (6,22) (6,23) (7,11) (7,18) (7,31) (7,25) (7,22) (7,23) (7,9) (8,16) (8,10) (8,15) (9,26) (9,11) (9,18) (9,25) (9,24) (9,23) (9,21) (9,30) (10,16) (11,26) (11,14) (11,31) (11,25) (11,23) (11,21) (11,30) (12,19) (12,28) (12,13) (12,17) (12,29) (13,27) (13,19) (13,32) (13,28) (13,17) (13,29) (14,18) (14,25) (14,22) (14,24) (14,23) (14,21) (14,30) (17,27) (17,19) (17,32) (17,28) (17,29) (18,31) (18,25) (18,22) (18,23) (18,21) (19,27) (19,32) (19,28) (19,29) (20,27) (20,32) (20,28) (20,29) (21,22) (21,24) (21,23) (22,26) (22,31) (22,24) (22,23) (22,30) (23,26) (23,31) (23,25) (24,31) (24,25) (25,26) (26,31) (27,32) (27,29) (29,32)\nIs there a path between node 8 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph392-11_24", + "image": "data/connectivity/graph_visual/hard/graph392.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,27) (0,32) (0,31) (0,24) (0,20) (0,23) (1,21) (1,15) (1,19) (1,30) (1,31) (1,26) (2,29) (2,3) (4,21) (4,15) (4,19) (4,30) (4,24) (4,23) (5,26) (5,20) (6,18) (7,32) (7,23) (7,9) (7,11) (8,17) (8,13) (9,30) (9,16) (10,30) (11,15) (11,19) (11,30) (11,31) (11,20) (11,23) (13,17) (14,18) (15,28) (15,25) (16,21) (16,19) (16,27) (16,26) (16,20) (16,23) (18,22) (19,21) (19,32) (19,23) (20,25) (21,27) (21,28) (21,30) (21,26) (21,24) (23,30) (24,28) (24,32) (24,26) (24,25) (25,27) (25,26) (26,30) (27,32) (27,30) (27,31) (28,30) (28,31) (31,32)\nIs there a path between node 11 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph77-23_25", + "image": "data/connectivity/graph_visual/hard/graph77.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,14) (0,7) (0,20) (0,17) (0,19) (0,8) (0,11) (0,18) (0,10) (0,23) (0,15) (0,25) (0,24) (1,14) (1,7) (1,9) (1,17) (1,19) (1,5) (1,8) (1,11) (1,18) (1,10) (1,3) (1,23) (1,25) (1,24) (2,4) (2,26) (2,13) (2,12) (2,21) (2,22) (3,14) (3,7) (3,9) (3,17) (3,19) (3,5) (3,8) (3,6) (3,10) (3,23) (3,25) (3,24) (4,21) (4,16) (5,14) (5,20) (5,9) (5,17) (5,8) (5,6) (5,18) (5,10) (5,15) (5,25) (5,24) (6,7) (6,20) (6,8) (6,18) (6,10) (6,23) (6,15) (6,25) (6,24) (7,14) (7,20) (7,9) (7,19) (7,11) (7,10) (7,15) (8,20) (8,17) (8,19) (8,11) (8,18) (8,10) (8,23) (8,24) (9,20) (9,19) (9,11) (9,18) (9,10) (9,23) (9,25) (10,14) (10,17) (10,19) (10,11) (10,18) (10,23) (10,15) (10,24) (11,14) (11,20) (11,18) (11,23) (11,15) (11,25) (12,26) (12,16) (12,22) (13,26) (13,16) (13,22) (14,20) (14,17) (14,19) (14,18) (14,23) (14,25) (15,20) (15,19) (15,18) (15,25) (16,21) (16,22) (17,20) (17,19) (17,23) (18,20) (18,19) (18,23) (18,24) (19,20) (19,23) (19,25) (20,23) (20,25) (20,24) (21,22) (22,26)\nIs there a path between node 23 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph637-25_3", + "image": "data/connectivity/graph_visual/hard/graph637.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,24) (0,28) (0,32) (0,1) (0,27) (0,13) (0,9) (1,31) (1,8) (1,15) (1,14) (1,21) (1,28) (1,4) (1,6) (2,3) (2,11) (2,24) (2,31) (2,14) (2,32) (2,4) (2,27) (2,9) (3,22) (3,14) (3,32) (3,20) (3,9) (4,11) (4,24) (4,34) (4,7) (4,19) (4,18) (4,29) (4,28) (4,32) (4,27) (4,13) (5,22) (5,7) (5,18) (5,6) (5,27) (5,13) (6,15) (6,29) (6,27) (6,13) (7,22) (7,33) (7,24) (7,8) (7,19) (7,25) (7,18) (7,30) (7,21) (7,28) (8,11) (8,33) (8,14) (8,25) (8,30) (8,32) (9,27) (9,20) (10,23) (11,22) (11,31) (11,15) (11,19) (11,30) (11,29) (12,17) (13,22) (13,33) (13,19) (13,16) (13,30) (13,21) (13,20) (14,34) (14,30) (15,22) (15,33) (15,24) (15,31) (15,18) (15,30) (15,21) (15,27) (16,24) (16,30) (18,22) (18,33) (18,31) (18,32) (19,22) (19,26) (19,25) (19,28) (19,32) (20,33) (20,24) (20,28) (21,25) (21,30) (21,29) (22,31) (22,28) (22,27) (24,34) (24,31) (24,26) (25,26) (25,29) (25,28) (26,34) (26,30) (26,28) (27,34) (27,28) (28,31) (30,31) (31,34) (32,33) (33,34)\nIs there a path between node 25 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph563-0_27", + "image": "data/connectivity/graph_visual/hard/graph563.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,24) (0,25) (0,5) (0,19) (0,33) (0,29) (0,4) (1,24) (1,17) (1,10) (1,16) (2,8) (3,28) (3,12) (3,15) (3,23) (3,20) (3,13) (4,7) (4,29) (5,17) (5,7) (5,25) (5,33) (6,8) (6,18) (7,24) (7,17) (7,25) (7,19) (8,22) (9,12) (9,14) (9,23) (10,24) (10,16) (10,33) (11,31) (12,14) (12,23) (12,20) (13,20) (14,28) (14,32) (14,20) (15,20) (16,19) (17,33) (18,22) (19,24) (19,26) (21,23) (22,27) (23,30) (24,25) (25,26) (25,29) (26,33) (29,33)\nIs there a path between node 0 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph286-14_22", + "image": "data/connectivity/graph_visual/hard/graph286.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,1) (0,20) (0,8) (0,31) (0,22) (1,4) (1,24) (1,19) (1,16) (1,5) (1,2) (1,8) (1,18) (1,27) (2,4) (2,19) (2,12) (2,17) (2,21) (2,31) (2,22) (3,25) (3,20) (3,14) (3,31) (3,22) (3,27) (4,7) (4,21) (4,26) (4,27) (5,11) (5,24) (5,20) (5,19) (5,12) (5,16) (5,17) (5,21) (5,9) (5,22) (6,15) (7,24) (7,20) (7,19) (7,16) (7,29) (7,17) (7,21) (7,14) (7,9) (7,8) (7,18) (7,22) (7,30) (8,20) (8,12) (8,14) (9,20) (9,16) (9,14) (9,18) (9,26) (9,23) (10,15) (11,25) (11,28) (11,20) (11,21) (11,26) (12,28) (12,24) (12,20) (12,29) (12,14) (12,18) (12,26) (12,22) (12,27) (12,23) (14,24) (14,16) (14,18) (14,31) (16,25) (16,26) (16,31) (16,23) (17,31) (17,27) (18,25) (18,28) (18,24) (18,21) (18,26) (18,27) (19,29) (19,21) (19,22) (20,25) (20,21) (20,26) (21,24) (21,29) (21,31) (21,23) (22,29) (22,26) (22,23) (23,25) (23,26) (24,25) (24,26) (24,30) (25,29) (25,31) (26,29) (26,31) (27,28) (27,31) (28,29) (29,31) (29,30) (30,31)\nIs there a path between node 14 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph101-27_22", + "image": "data/connectivity/graph_visual/hard/graph101.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,14) (0,21) (0,23) (0,9) (0,6) (0,17) (0,2) (0,10) (0,25) (0,7) (0,27) (0,26) (0,8) (0,5) (1,22) (1,24) (1,20) (1,4) (1,15) (1,12) (2,21) (2,9) (2,6) (2,17) (2,18) (2,3) (2,27) (2,26) (2,5) (3,23) (3,9) (3,6) (3,17) (3,19) (3,16) (3,18) (3,11) (3,10) (3,7) (3,26) (3,8) (3,5) (4,22) (4,20) (4,13) (4,15) (5,14) (5,23) (5,9) (5,6) (5,17) (5,16) (5,18) (5,11) (5,10) (5,25) (5,7) (5,27) (5,26) (5,8) (6,14) (6,21) (6,23) (6,9) (6,17) (6,19) (6,16) (6,18) (6,10) (6,7) (6,27) (6,8) (7,14) (7,21) (7,23) (7,9) (7,17) (7,19) (7,18) (7,11) (7,10) (7,25) (7,26) (7,8) (8,14) (8,21) (8,23) (8,9) (8,17) (8,19) (8,18) (8,11) (8,10) (8,25) (8,27) (8,26) (9,21) (9,19) (9,10) (9,25) (9,27) (9,26) (10,21) (10,19) (10,11) (10,25) (10,27) (10,26) (11,14) (11,21) (11,23) (11,17) (11,19) (11,16) (11,18) (11,25) (12,22) (12,24) (12,13) (13,22) (13,24) (13,20) (14,21) (14,23) (14,17) (14,19) (14,16) (14,18) (14,25) (14,26) (15,22) (15,20) (16,21) (16,23) (16,17) (16,19) (16,18) (16,26) (17,21) (17,23) (17,25) (17,27) (17,26) (18,21) (18,23) (19,21) (19,23) (19,25) (19,27) (19,26) (20,22) (20,24) (21,23) (21,25) (22,24) (23,25) (25,27) (25,26) (26,27)\nIs there a path between node 27 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph541-12_19", + "image": "data/connectivity/graph_visual/hard/graph541.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,13) (0,30) (0,32) (0,15) (0,8) (0,17) (0,21) (0,19) (0,14) (0,26) (0,3) (0,4) (0,18) (0,11) (0,10) (0,7) (0,28) (0,31) (1,13) (1,30) (1,32) (1,23) (1,15) (1,8) (1,17) (1,21) (1,19) (1,33) (1,26) (1,9) (1,4) (1,11) (1,7) (2,20) (2,13) (2,30) (2,32) (2,23) (2,17) (2,22) (2,19) (2,33) (2,14) (2,26) (2,3) (2,18) (2,11) (2,7) (2,28) (2,31) (3,20) (3,13) (3,30) (3,32) (3,23) (3,15) (3,8) (3,17) (3,21) (3,14) (3,26) (3,9) (3,18) (3,11) (3,28) (3,31) (4,20) (4,13) (4,30) (4,32) (4,23) (4,15) (4,33) (4,26) (4,18) (4,11) (4,10) (4,7) (4,28) (4,31) (5,12) (5,27) (6,29) (6,24) (6,12) (6,27) (7,20) (7,13) (7,30) (7,23) (7,15) (7,8) (7,17) (7,22) (7,19) (7,14) (7,26) (7,18) (7,10) (7,28) (7,31) (8,20) (8,30) (8,15) (8,17) (8,22) (8,21) (8,19) (8,33) (8,14) (8,26) (8,9) (8,18) (8,10) (9,13) (9,30) (9,32) (9,23) (9,22) (9,21) (9,33) (9,14) (9,26) (9,18) (9,11) (9,10) (9,28) (9,31) (10,13) (10,30) (10,32) (10,15) (10,22) (10,21) (10,19) (10,33) (10,26) (10,18) (10,11) (10,28) (11,20) (11,13) (11,30) (11,32) (11,23) (11,15) (11,17) (11,22) (11,21) (11,19) (11,26) (11,28) (11,31) (12,29) (12,24) (12,16) (12,27) (13,20) (13,32) (13,15) (13,17) (13,22) (13,21) (13,33) (13,14) (13,28) (13,31) (14,20) (14,32) (14,15) (14,17) (14,22) (14,18) (14,28) (14,31) (15,20) (15,30) (15,32) (15,17) (15,22) (15,21) (15,19) (15,33) (15,26) (15,18) (15,31) (16,29) (16,27) (17,20) (17,30) (17,22) (17,21) (17,19) (17,33) (17,26) (17,18) (17,28) (17,31) (18,20) (18,30) (18,23) (18,22) (18,21) (18,28) (18,31) (19,20) (19,32) (19,21) (19,26) (19,28) (20,30) (20,32) (20,23) (20,22) (20,21) (20,28) (21,30) (21,32) (21,23) (21,22) (21,33) (21,26) (21,31) (22,32) (22,28) (22,31) (23,30) (23,32) (23,33) (23,26) (23,31) (24,29) (24,27) (26,30) (26,32) (26,33) (26,28) (27,29) (28,31) (30,32) (30,33) (30,31) (31,32) (32,33)\nIs there a path between node 12 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph669-32_25", + "image": "data/connectivity/graph_visual/hard/graph669.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,17) (0,33) (0,14) (1,18) (1,14) (2,28) (2,24) (2,25) (2,20) (2,31) (2,22) (2,8) (3,30) (3,23) (3,17) (3,29) (3,21) (4,7) (4,11) (4,31) (4,22) (4,8) (5,28) (5,9) (5,34) (5,22) (6,20) (6,9) (6,15) (6,8) (7,11) (7,16) (8,25) (8,20) (8,9) (8,31) (8,15) (8,22) (8,19) (9,28) (9,32) (9,11) (9,31) (10,32) (10,20) (10,15) (10,22) (10,19) (11,28) (11,31) (11,15) (11,34) (12,18) (12,23) (12,13) (13,23) (13,29) (13,33) (14,26) (14,17) (14,29) (14,33) (16,24) (16,32) (16,22) (17,30) (17,23) (18,26) (18,23) (18,29) (18,21) (21,26) (21,23) (22,34) (23,26) (24,28) (24,32) (25,28) (25,34) (28,32) (29,30)\nIs there a path between node 32 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph26-12_19", + "image": "data/connectivity/graph_visual/hard/graph26.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,22) (0,2) (0,24) (0,25) (1,22) (1,15) (1,25) (2,22) (2,10) (2,15) (2,12) (2,11) (2,25) (2,20) (2,13) (3,8) (3,4) (4,17) (4,8) (4,5) (5,23) (5,8) (6,10) (6,15) (6,11) (6,9) (7,19) (8,17) (9,15) (9,25) (9,21) (9,13) (10,18) (10,15) (10,11) (10,21) (10,13) (11,22) (11,24) (12,22) (12,14) (12,13) (13,22) (13,14) (13,21) (14,21) (15,22) (15,18) (16,22) (16,24) (17,19) (18,22) (20,22) (20,21) (22,24) (24,25)\nIs there a path between node 12 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph455-20_0", + "image": "data/connectivity/graph_visual/hard/graph455.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,27) (0,29) (0,23) (0,28) (1,8) (1,9) (1,2) (1,20) (1,26) (1,23) (2,24) (2,8) (2,27) (2,20) (2,23) (3,11) (3,15) (3,16) (3,6) (3,12) (4,10) (4,9) (4,27) (4,20) (4,17) (4,32) (5,11) (5,22) (5,19) (5,6) (5,25) (5,18) (5,12) (6,22) (6,16) (6,25) (6,18) (7,24) (7,20) (7,29) (8,24) (8,17) (8,26) (8,32) (9,26) (9,21) (10,24) (10,30) (10,29) (11,25) (11,13) (13,15) (13,16) (13,14) (14,22) (14,19) (15,22) (15,25) (16,31) (16,19) (16,25) (17,24) (17,23) (17,28) (17,21) (18,22) (19,31) (20,26) (20,32) (21,30) (21,23) (22,25) (23,30) (24,30) (24,29) (26,27) (26,32) (28,32) (30,32)\nIs there a path between node 20 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph3-1_18", + "image": "data/connectivity/graph_visual/hard/graph3.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,2) (0,10) (0,6) (0,8) (0,17) (0,25) (2,23) (2,21) (2,24) (2,15) (2,5) (2,22) (2,12) (2,19) (3,23) (3,8) (3,16) (4,14) (4,23) (4,10) (4,6) (4,8) (4,17) (4,16) (5,14) (5,18) (5,15) (5,10) (5,17) (6,22) (8,14) (8,23) (8,21) (8,24) (8,10) (9,18) (9,15) (9,22) (9,17) (10,20) (10,14) (10,23) (11,20) (11,14) (11,23) (11,22) (11,12) (11,17) (12,22) (12,17) (14,24) (15,23) (15,24) (15,25) (16,21) (16,24) (16,18) (17,20) (17,23) (17,21) (17,24) (18,20) (18,19) (19,20) (19,24) (19,22) (19,25) (20,23) (20,21) (22,25) (23,25)\nIs there a path between node 1 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph320-21_6", + "image": "data/connectivity/graph_visual/hard/graph320.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,6) (0,28) (1,30) (1,7) (1,26) (1,29) (1,8) (2,19) (2,22) (2,9) (2,20) (3,13) (3,23) (3,26) (3,17) (3,8) (3,4) (4,5) (4,28) (4,17) (5,10) (5,27) (5,26) (5,6) (6,15) (6,7) (6,27) (6,21) (6,23) (6,29) (6,28) (7,30) (7,10) (7,23) (7,26) (7,29) (8,15) (8,30) (8,29) (8,28) (9,18) (10,15) (10,27) (10,23) (10,26) (10,28) (11,14) (11,16) (11,18) (12,19) (12,20) (13,17) (14,19) (14,24) (14,25) (14,31) (15,21) (15,28) (16,22) (16,24) (17,30) (17,23) (17,29) (18,19) (18,22) (18,31) (19,31) (20,24) (21,30) (21,28) (26,30) (26,29) (28,30)\nIs there a path between node 21 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph445-24_4", + "image": "data/connectivity/graph_visual/hard/graph445.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,25) (0,13) (0,7) (0,20) (0,19) (0,10) (1,20) (1,19) (1,31) (1,24) (1,9) (1,3) (2,25) (2,13) (2,22) (2,31) (2,14) (2,24) (2,4) (2,30) (2,3) (2,5) (2,10) (3,6) (3,14) (3,18) (3,30) (4,13) (4,24) (4,21) (4,30) (4,5) (5,12) (5,31) (5,14) (6,20) (6,12) (6,9) (6,27) (7,13) (7,18) (7,10) (8,28) (8,32) (8,23) (8,17) (8,16) (8,26) (9,25) (9,20) (9,12) (9,19) (9,14) (10,13) (10,19) (10,24) (10,21) (10,30) (10,27) (11,15) (11,29) (11,32) (11,23) (11,26) (12,25) (12,22) (12,31) (12,30) (13,20) (13,14) (13,24) (13,30) (14,25) (14,24) (15,29) (15,32) (15,26) (17,23) (17,26) (18,24) (18,30) (19,25) (19,21) (19,30) (19,27) (20,31) (21,25) (21,30) (22,24) (23,28) (23,32) (25,30) (26,28) (26,32) (27,31)\nIs there a path between node 24 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph256-28_15", + "image": "data/connectivity/graph_visual/hard/graph256.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,16) (0,13) (0,1) (0,18) (0,12) (0,23) (1,20) (1,30) (1,16) (1,27) (1,15) (1,7) (1,18) (1,11) (1,23) (2,3) (3,28) (4,27) (4,15) (4,8) (4,11) (4,25) (5,26) (5,6) (5,21) (5,25) (6,9) (6,26) (6,30) (6,24) (6,13) (6,15) (6,7) (7,18) (7,23) (8,26) (8,15) (8,14) (8,22) (8,12) (9,26) (9,30) (9,16) (9,17) (9,15) (9,14) (9,12) (9,23) (11,30) (11,16) (11,17) (11,27) (11,15) (11,14) (11,22) (11,12) (12,16) (12,15) (12,18) (12,22) (12,19) (12,25) (12,23) (13,16) (13,27) (13,14) (13,18) (13,23) (14,30) (14,16) (14,27) (14,22) (15,30) (15,17) (15,18) (15,19) (15,23) (16,21) (17,24) (17,25) (18,22) (19,30) (19,27) (19,23) (20,26) (21,24) (21,27) (21,25) (21,23) (22,27) (23,25) (24,26) (24,25) (25,30) (28,29)\nIs there a path between node 28 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph626-15_21", + "image": "data/connectivity/graph_visual/hard/graph626.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,16) (0,33) (0,10) (1,27) (2,15) (2,34) (2,3) (2,23) (3,14) (3,8) (3,34) (3,23) (4,13) (4,9) (4,20) (4,30) (4,29) (4,5) (5,27) (5,30) (5,24) (5,29) (5,7) (6,13) (6,28) (6,24) (6,29) (6,18) (7,28) (7,24) (8,32) (8,31) (9,28) (9,27) (9,24) (9,29) (10,26) (12,15) (12,21) (12,32) (12,23) (13,20) (13,30) (13,29) (13,18) (14,15) (14,23) (14,17) (15,31) (17,32) (18,29) (20,24) (21,32) (21,25) (24,28) (27,28) (28,29)\nIs there a path between node 15 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph432-29_15", + "image": "data/connectivity/graph_visual/hard/graph432.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (0,28) (0,2) (0,26) (0,6) (0,8) (0,10) (0,16) (0,5) (0,21) (0,7) (0,24) (0,27) (1,9) (1,15) (1,17) (1,30) (1,3) (1,31) (1,25) (2,23) (2,28) (2,26) (2,6) (2,8) (2,18) (2,10) (2,16) (2,21) (2,7) (2,24) (3,13) (3,9) (3,15) (3,17) (3,12) (3,30) (3,31) (3,25) (4,20) (4,32) (4,29) (4,22) (4,14) (4,11) (5,28) (5,6) (5,18) (5,24) (5,27) (6,23) (6,28) (6,8) (6,18) (6,16) (6,7) (6,24) (6,27) (7,23) (7,28) (7,26) (7,8) (7,10) (7,21) (7,24) (7,27) (8,26) (8,18) (8,16) (8,21) (8,24) (8,27) (9,17) (9,12) (9,30) (9,31) (10,23) (10,26) (10,18) (10,16) (10,21) (11,29) (11,22) (11,14) (12,13) (12,17) (12,30) (12,31) (13,15) (13,17) (13,25) (14,20) (14,32) (14,29) (14,19) (14,22) (15,17) (15,31) (15,25) (16,23) (16,21) (16,24) (17,30) (17,31) (17,25) (18,23) (18,28) (18,26) (18,21) (18,24) (18,27) (19,20) (19,32) (19,29) (19,22) (20,29) (20,22) (21,26) (22,32) (22,29) (23,28) (23,26) (23,27) (24,28) (24,26) (24,27) (25,30) (25,31) (26,27) (27,28) (29,32)\nIs there a path between node 29 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph156-26_25", + "image": "data/connectivity/graph_visual/hard/graph156.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,19) (0,17) (1,24) (1,25) (2,10) (2,3) (2,16) (3,20) (3,15) (4,5) (5,9) (5,23) (5,13) (6,21) (6,26) (7,25) (7,21) (8,24) (8,22) (9,23) (9,25) (10,20) (10,11) (10,27) (10,17) (11,15) (11,14) (12,27) (13,23) (13,22) (14,20) (14,15) (14,28) (14,16) (14,17) (15,28) (15,27) (20,28) (21,23) (21,22) (21,26) (22,25) (23,25) (24,26) (25,26)\nIs there a path between node 26 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph407-25_20", + "image": "data/connectivity/graph_visual/hard/graph407.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,12) (0,24) (0,31) (0,6) (0,1) (0,2) (0,19) (0,30) (1,26) (1,24) (1,31) (1,6) (1,2) (1,15) (1,5) (1,19) (1,30) (1,13) (2,22) (2,26) (2,24) (2,15) (2,5) (2,19) (2,30) (3,29) (3,16) (3,4) (3,28) (3,7) (3,8) (3,11) (3,20) (3,21) (3,25) (3,32) (3,23) (3,18) (4,29) (4,16) (4,28) (4,7) (4,8) (4,11) (4,21) (4,27) (4,17) (4,32) (4,23) (4,18) (5,22) (5,12) (5,24) (5,31) (5,6) (5,15) (5,19) (5,30) (6,26) (6,12) (6,24) (6,15) (6,19) (6,30) (6,13) (7,29) (7,16) (7,28) (7,8) (7,25) (7,27) (7,17) (7,32) (7,23) (7,18) (7,9) (8,28) (8,11) (8,25) (8,27) (8,17) (8,18) (8,9) (9,29) (9,28) (9,20) (9,21) (9,25) (9,27) (9,17) (9,32) (9,23) (9,18) (10,14) (11,29) (11,28) (11,20) (11,21) (11,25) (11,27) (11,17) (11,32) (11,23) (11,18) (12,24) (12,15) (12,19) (13,22) (13,26) (13,24) (13,31) (13,15) (13,19) (13,30) (15,26) (15,30) (16,29) (16,20) (16,21) (16,27) (16,17) (16,18) (17,29) (17,28) (17,20) (17,25) (17,27) (17,23) (17,18) (18,29) (18,28) (18,20) (18,21) (18,32) (19,26) (19,24) (19,31) (20,28) (20,27) (20,32) (20,23) (21,29) (21,28) (21,25) (21,32) (21,23) (22,24) (23,29) (23,25) (23,27) (23,32) (24,30) (25,29) (25,28) (25,27) (25,32) (26,30) (27,29) (27,28) (27,32) (28,32) (29,32) (30,31)\nIs there a path between node 25 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph611-25_14", + "image": "data/connectivity/graph_visual/hard/graph611.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,4) (1,32) (1,22) (1,34) (1,7) (1,5) (1,28) (1,11) (1,13) (1,30) (1,31) (1,26) (2,12) (2,3) (2,24) (2,15) (2,18) (2,8) (2,20) (2,25) (2,19) (2,17) (2,16) (3,10) (3,24) (3,15) (3,18) (3,8) (3,20) (3,14) (3,19) (3,21) (4,23) (4,6) (5,32) (5,22) (5,7) (5,33) (5,11) (5,13) (5,27) (5,31) (5,26) (6,23) (7,22) (7,34) (7,28) (7,13) (7,27) (7,30) (7,26) (7,29) (8,10) (8,24) (8,15) (8,18) (8,20) (8,14) (8,17) (8,21) (8,16) (9,32) (9,22) (9,34) (9,28) (9,13) (9,27) (9,31) (9,26) (9,29) (10,12) (10,24) (10,15) (10,18) (10,20) (10,25) (10,17) (11,32) (11,22) (11,34) (11,28) (11,13) (11,27) (11,30) (11,31) (11,26) (12,24) (12,25) (12,14) (12,17) (12,21) (12,16) (13,34) (13,33) (13,27) (13,30) (13,31) (13,29) (14,15) (14,18) (14,20) (14,25) (14,19) (14,17) (14,21) (14,16) (15,24) (15,18) (15,20) (15,17) (15,21) (16,24) (16,20) (16,19) (16,17) (17,24) (17,20) (17,21) (18,20) (18,25) (18,19) (20,24) (20,25) (20,21) (21,25) (22,32) (22,28) (22,27) (22,30) (22,31) (22,26) (24,25) (26,34) (26,33) (26,31) (27,34) (27,33) (27,28) (27,30) (27,31) (27,29) (28,32) (28,33) (28,30) (28,31) (28,29) (29,32) (29,33) (30,32) (31,32) (31,34) (32,34) (32,33) (33,34)\nIs there a path between node 25 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph181-7_23", + "image": "data/connectivity/graph_visual/hard/graph181.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,18) (1,25) (1,22) (1,15) (1,20) (1,19) (1,11) (1,2) (1,23) (1,24) (2,25) (2,22) (2,15) (2,3) (2,11) (2,7) (2,6) (2,14) (2,24) (3,22) (3,16) (3,15) (3,19) (3,7) (3,23) (3,6) (3,14) (4,21) (4,9) (4,28) (4,8) (4,26) (4,17) (5,9) (5,12) (5,27) (5,26) (5,17) (6,25) (6,16) (6,15) (6,20) (6,19) (6,7) (6,14) (6,24) (7,25) (7,22) (7,16) (7,20) (7,19) (7,11) (7,23) (7,24) (8,21) (8,9) (8,12) (8,26) (8,17) (9,21) (9,10) (9,28) (9,12) (9,27) (9,26) (9,17) (10,21) (10,28) (10,12) (10,26) (10,17) (11,22) (11,16) (11,15) (11,20) (11,19) (11,23) (11,14) (11,24) (12,27) (12,26) (12,17) (13,18) (14,16) (14,15) (14,20) (14,24) (15,22) (15,16) (15,20) (15,23) (15,24) (16,25) (16,22) (16,20) (16,19) (16,23) (16,24) (17,21) (17,27) (17,26) (19,25) (19,22) (19,23) (19,24) (20,22) (20,23) (20,24) (21,28) (21,27) (21,26) (22,25) (23,25) (23,24) (24,25) (26,27)\nIs there a path between node 7 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph481-7_18", + "image": "data/connectivity/graph_visual/hard/graph481.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,17) (0,21) (0,16) (0,23) (0,24) (0,8) (0,28) (0,31) (0,10) (0,32) (0,3) (0,5) (1,23) (1,15) (1,29) (1,28) (1,31) (1,26) (1,30) (1,10) (1,32) (1,3) (1,2) (1,5) (2,17) (2,27) (2,16) (2,23) (2,15) (2,24) (2,8) (2,31) (2,32) (2,3) (2,5) (3,27) (3,16) (3,23) (3,15) (3,8) (3,29) (3,28) (3,26) (3,10) (4,6) (5,17) (5,27) (5,21) (5,16) (5,23) (5,15) (5,8) (5,29) (5,28) (5,26) (5,7) (5,30) (5,10) (6,19) (7,17) (7,21) (7,16) (7,23) (7,24) (7,8) (7,29) (7,28) (7,31) (7,30) (7,32) (8,17) (8,27) (8,23) (8,15) (8,24) (8,28) (8,31) (8,26) (8,30) (8,10) (8,32) (9,13) (9,18) (9,12) (9,20) (9,11) (10,27) (10,16) (10,23) (10,15) (10,24) (10,29) (10,28) (10,26) (10,30) (11,13) (11,18) (11,12) (11,25) (11,14) (11,22) (12,13) (12,18) (12,25) (12,14) (12,20) (13,18) (13,14) (13,20) (13,22) (14,18) (14,22) (15,17) (15,24) (15,28) (15,31) (15,26) (15,30) (15,32) (16,27) (16,21) (16,23) (16,29) (16,28) (16,31) (16,30) (17,23) (17,24) (17,29) (17,28) (17,30) (17,32) (18,20) (20,22) (21,23) (21,24) (21,29) (21,31) (21,26) (21,30) (21,32) (22,25) (23,29) (23,31) (23,32) (24,27) (24,29) (26,27) (26,29) (26,31) (26,30) (26,32) (27,28) (27,31) (27,32) (28,29) (28,30) (28,32) (29,31) (29,32) (30,31) (31,32)\nIs there a path between node 7 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph355-4_24", + "image": "data/connectivity/graph_visual/hard/graph355.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,2) (1,16) (1,8) (1,6) (1,13) (1,18) (1,22) (1,10) (1,17) (1,12) (3,5) (3,30) (3,17) (3,12) (4,28) (5,29) (5,6) (5,25) (5,22) (5,10) (5,17) (5,12) (6,15) (6,13) (6,7) (6,30) (6,11) (6,12) (6,26) (7,29) (7,21) (7,25) (7,14) (7,19) (7,17) (7,12) (8,20) (8,21) (8,13) (8,11) (8,25) (8,14) (8,17) (10,15) (10,27) (10,18) (10,26) (11,20) (11,31) (11,13) (11,27) (11,24) (11,17) (12,21) (12,16) (12,31) (12,25) (13,21) (13,31) (13,27) (13,22) (13,19) (14,29) (14,16) (14,24) (14,25) (14,17) (14,26) (15,18) (16,20) (16,30) (16,24) (16,17) (16,26) (17,25) (18,20) (18,21) (18,31) (18,24) (19,27) (19,25) (19,22) (20,29) (20,27) (20,22) (21,30) (21,24) (21,26) (22,30) (24,27) (24,26) (25,26) (26,29) (26,27) (27,29) (27,30)\nIs there a path between node 4 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph250-6_12", + "image": "data/connectivity/graph_visual/hard/graph250.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,21) (0,16) (0,11) (0,5) (0,14) (0,8) (0,23) (0,15) (0,10) (0,7) (0,27) (0,6) (0,29) (0,19) (0,18) (0,22) (0,28) (0,2) (0,1) (0,9) (0,4) (1,26) (1,16) (1,11) (1,5) (1,14) (1,8) (1,10) (1,7) (1,6) (1,3) (1,29) (1,19) (1,17) (1,18) (1,28) (1,20) (1,9) (1,4) (2,26) (2,11) (2,5) (2,8) (2,15) (2,10) (2,7) (2,29) (2,19) (2,17) (2,18) (2,22) (2,28) (2,20) (2,4) (3,26) (3,21) (3,16) (3,11) (3,8) (3,15) (3,10) (3,27) (3,6) (3,29) (3,19) (3,17) (3,18) (3,22) (3,28) (3,30) (3,9) (3,4) (4,26) (4,16) (4,11) (4,5) (4,23) (4,15) (4,7) (4,27) (4,29) (4,20) (5,26) (5,16) (5,11) (5,8) (5,23) (5,10) (5,6) (5,29) (5,19) (5,17) (5,18) (5,22) (5,28) (5,30) (5,9) (6,16) (6,11) (6,8) (6,23) (6,15) (6,10) (6,27) (6,29) (6,19) (6,17) (6,18) (6,28) (6,20) (6,30) (6,9) (7,26) (7,21) (7,11) (7,8) (7,23) (7,15) (7,10) (7,27) (7,29) (7,19) (7,18) (7,22) (7,20) (7,30) (8,16) (8,23) (8,17) (8,18) (8,28) (8,20) (8,30) (8,9) (9,21) (9,16) (9,15) (9,10) (9,27) (9,29) (9,19) (9,17) (9,18) (9,22) (9,28) (9,20) (9,30) (10,26) (10,21) (10,16) (10,11) (10,15) (10,29) (10,19) (10,17) (10,18) (10,22) (10,28) (10,20) (10,30) (11,26) (11,21) (11,16) (11,14) (11,23) (11,29) (11,17) (11,18) (11,28) (11,20) (12,24) (13,24) (13,25) (14,26) (14,16) (14,23) (14,27) (14,19) (14,22) (14,28) (15,23) (15,29) (15,19) (15,17) (15,18) (15,22) (15,28) (15,20) (16,26) (16,21) (16,27) (16,19) (16,17) (16,18) (16,20) (17,26) (17,23) (17,19) (17,22) (17,28) (17,20) (18,26) (18,21) (18,23) (18,27) (18,19) (18,28) (18,30) (19,21) (19,23) (19,27) (19,29) (19,22) (19,20) (19,30) (20,26) (20,21) (20,23) (20,27) (20,22) (20,30) (21,26) (21,23) (21,27) (21,29) (21,28) (21,30) (22,26) (22,23) (22,29) (22,28) (22,30) (23,26) (23,27) (23,29) (23,30) (26,27) (26,30) (27,29) (27,28) (27,30) (28,29) (28,30) (29,30)\nIs there a path between node 6 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph230-7_12", + "image": "data/connectivity/graph_visual/hard/graph230.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,16) (0,8) (0,24) (0,3) (0,6) (0,21) (0,15) (0,29) (0,14) (0,1) (0,17) (0,12) (0,26) (1,16) (1,24) (1,3) (1,6) (1,21) (1,15) (1,20) (1,25) (1,29) (1,17) (1,12) (1,26) (2,22) (2,28) (2,4) (2,5) (2,19) (2,18) (2,9) (3,16) (3,24) (3,6) (3,21) (3,29) (3,11) (3,17) (3,12) (3,26) (4,22) (4,5) (4,19) (4,18) (4,23) (4,10) (4,13) (4,27) (5,22) (5,28) (5,18) (5,23) (5,9) (5,13) (5,27) (6,16) (6,8) (6,24) (6,21) (6,20) (6,11) (6,14) (6,17) (6,12) (6,26) (7,22) (7,28) (7,19) (7,18) (7,23) (7,9) (7,13) (7,27) (8,16) (8,24) (8,21) (8,20) (8,29) (8,11) (8,14) (8,12) (8,26) (9,23) (9,10) (9,13) (9,27) (10,22) (10,18) (10,23) (10,27) (11,16) (11,24) (11,21) (11,15) (11,20) (11,25) (11,14) (11,17) (11,12) (11,26) (12,16) (12,21) (12,15) (12,20) (12,25) (12,14) (12,17) (12,26) (13,19) (13,18) (14,16) (14,24) (14,21) (14,20) (14,25) (14,29) (14,17) (15,16) (15,24) (15,21) (15,20) (15,17) (15,26) (16,24) (16,20) (16,29) (16,17) (17,24) (17,21) (17,25) (17,29) (18,22) (18,28) (18,19) (18,23) (18,27) (19,22) (19,28) (19,23) (19,27) (20,21) (20,25) (20,29) (21,24) (21,25) (21,29) (21,26) (22,28) (22,23) (23,28) (23,27) (24,25) (24,29) (24,26) (25,29) (27,28)\nIs there a path between node 7 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph570-30_9", + "image": "data/connectivity/graph_visual/hard/graph570.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,2) (0,29) (0,30) (0,20) (0,10) (0,1) (0,22) (0,9) (1,29) (1,8) (1,20) (1,10) (1,23) (1,27) (1,14) (2,3) (2,29) (2,20) (2,17) (2,18) (2,5) (2,22) (2,19) (2,9) (2,24) (3,29) (3,30) (3,17) (3,21) (3,32) (3,22) (3,9) (4,12) (5,29) (5,6) (5,21) (5,22) (5,9) (6,30) (6,17) (6,10) (6,21) (6,32) (6,27) (6,14) (6,9) (6,24) (7,33) (7,13) (8,29) (8,18) (8,23) (8,14) (9,10) (9,27) (10,18) (10,21) (10,23) (13,33) (14,16) (14,32) (14,23) (14,19) (14,27) (14,24) (16,17) (16,18) (16,32) (16,23) (16,22) (16,19) (16,27) (17,29) (17,30) (17,23) (17,22) (17,19) (17,24) (18,22) (18,19) (18,27) (18,24) (19,29) (19,21) (19,32) (19,23) (19,24) (20,32) (20,23) (21,23) (21,22) (22,32) (22,27) (23,30) (23,27) (25,33) (25,26) (27,29) (27,30) (29,32) (30,32)\nIs there a path between node 30 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph214-27_17", + "image": "data/connectivity/graph_visual/hard/graph214.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,5) (0,4) (0,22) (0,15) (2,28) (4,9) (4,15) (5,20) (5,22) (5,18) (6,25) (6,12) (7,10) (7,11) (8,21) (8,20) (8,15) (9,22) (9,18) (10,11) (11,24) (11,17) (11,27) (12,19) (12,13) (12,25) (13,25) (14,17) (15,20) (16,28) (18,21) (19,26) (21,22) (24,27) (25,29) (26,29)\nIs there a path between node 27 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph385-6_26", + "image": "data/connectivity/graph_visual/hard/graph385.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,25) (0,9) (0,21) (0,29) (0,20) (0,22) (0,10) (0,15) (0,17) (0,23) (0,5) (0,31) (1,4) (1,26) (1,18) (1,6) (1,19) (1,24) (1,27) (1,30) (1,28) (1,13) (1,11) (2,12) (2,4) (2,18) (2,6) (2,24) (2,27) (2,28) (2,13) (2,11) (3,25) (3,21) (3,29) (3,20) (3,22) (3,10) (3,14) (3,8) (3,17) (3,23) (3,7) (4,12) (4,26) (4,18) (4,6) (4,19) (4,30) (4,28) (4,13) (4,11) (5,25) (5,9) (5,21) (5,29) (5,16) (5,20) (5,22) (5,8) (5,15) (5,17) (5,7) (5,31) (6,26) (6,18) (6,19) (6,24) (6,27) (6,28) (6,13) (6,11) (7,25) (7,9) (7,21) (7,29) (7,16) (7,20) (7,22) (7,14) (7,8) (7,15) (7,23) (8,9) (8,21) (8,29) (8,16) (8,22) (8,10) (8,15) (8,17) (8,23) (8,31) (9,25) (9,21) (9,16) (9,20) (9,10) (9,14) (9,17) (9,23) (9,31) (10,21) (10,29) (10,16) (10,20) (10,22) (10,15) (10,23) (11,26) (11,24) (11,27) (11,30) (11,28) (11,13) (12,26) (12,18) (12,24) (12,28) (13,26) (13,18) (13,19) (13,24) (13,27) (13,28) (14,21) (14,29) (14,20) (14,15) (14,23) (14,31) (15,25) (15,21) (15,16) (15,20) (15,22) (15,23) (15,31) (16,21) (16,29) (16,22) (16,17) (16,23) (16,31) (17,21) (17,29) (17,20) (17,22) (17,23) (18,26) (18,19) (18,24) (18,30) (19,26) (19,24) (19,27) (20,21) (20,29) (21,25) (21,22) (21,23) (22,29) (22,23) (22,31) (23,25) (23,31) (24,26) (24,30) (24,28) (25,31) (26,27) (26,30) (26,28) (27,30) (28,30) (29,31)\nIs there a path between node 6 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph674-12_10", + "image": "data/connectivity/graph_visual/hard/graph674.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,6) (0,23) (0,25) (0,8) (0,29) (1,19) (1,30) (2,7) (2,4) (2,3) (2,31) (2,8) (2,34) (3,23) (4,9) (4,17) (4,8) (4,13) (4,34) (5,15) (5,24) (6,9) (6,7) (6,12) (6,23) (6,31) (7,10) (7,23) (7,22) (7,29) (9,10) (9,22) (9,29) (10,12) (10,22) (11,23) (11,22) (12,22) (12,17) (12,13) (12,34) (13,31) (13,17) (14,16) (15,21) (15,19) (15,27) (17,26) (17,25) (17,31) (18,20) (18,33) (19,21) (19,30) (19,32) (19,27) (20,28) (20,33) (21,24) (21,30) (21,27) (22,34) (25,26) (25,34) (26,31) (27,32) (30,32)\nIs there a path between node 12 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph247-21_8", + "image": "data/connectivity/graph_visual/hard/graph247.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,12) (0,22) (0,14) (0,30) (0,18) (0,17) (0,16) (0,10) (0,1) (0,11) (0,9) (0,7) (0,21) (0,2) (1,14) (1,30) (1,17) (1,6) (1,29) (1,16) (1,11) (1,9) (1,7) (1,8) (1,2) (2,12) (2,22) (2,14) (2,30) (2,18) (2,17) (2,6) (2,16) (2,10) (2,11) (2,7) (2,21) (3,24) (3,25) (3,5) (3,19) (4,24) (4,28) (4,25) (4,5) (4,19) (4,13) (4,20) (4,26) (5,28) (5,25) (5,19) (5,23) (5,20) (5,26) (6,22) (6,14) (6,17) (6,29) (6,10) (6,11) (6,9) (6,7) (6,8) (7,22) (7,14) (7,30) (7,17) (7,29) (7,9) (7,21) (8,12) (8,22) (8,14) (8,30) (8,18) (8,17) (8,29) (8,10) (9,22) (9,14) (9,18) (9,17) (9,29) (9,10) (9,21) (10,12) (10,22) (10,14) (10,18) (10,29) (10,16) (10,11) (10,21) (11,12) (11,22) (11,14) (11,30) (11,18) (11,16) (11,21) (12,22) (12,14) (12,30) (12,17) (12,29) (12,16) (12,21) (13,24) (13,28) (13,25) (13,19) (13,23) (13,20) (14,22) (14,17) (14,29) (15,27) (15,28) (15,19) (15,20) (15,26) (16,22) (16,30) (16,18) (16,17) (17,22) (17,21) (18,22) (18,30) (18,29) (18,21) (19,24) (19,28) (19,25) (19,23) (19,26) (20,24) (20,27) (20,28) (20,23) (20,26) (21,22) (21,30) (21,29) (22,30) (22,29) (23,24) (23,28) (23,25) (24,28) (24,25) (25,28) (26,27) (26,28)\nIs there a path between node 21 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph140-19_21", + "image": "data/connectivity/graph_visual/hard/graph140.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,21) (0,25) (0,12) (0,26) (1,15) (1,23) (1,17) (1,13) (2,27) (2,10) (2,24) (4,9) (4,20) (4,13) (5,28) (5,11) (6,16) (6,23) (6,7) (6,13) (7,15) (7,16) (7,23) (7,17) (7,28) (8,12) (11,17) (11,20) (12,18) (12,14) (12,25) (12,19) (12,26) (13,23) (15,16) (16,23) (17,28) (18,26) (25,26)\nIs there a path between node 19 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph209-21_27", + "image": "data/connectivity/graph_visual/hard/graph209.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,22) (1,18) (1,25) (1,8) (1,16) (1,11) (1,6) (1,24) (2,22) (2,18) (2,17) (2,20) (2,11) (2,6) (3,13) (4,22) (4,25) (4,21) (4,17) (4,11) (4,6) (5,27) (5,13) (6,29) (6,24) (7,22) (7,21) (7,17) (7,16) (7,11) (7,24) (7,15) (7,19) (8,18) (8,12) (8,11) (8,24) (9,28) (10,26) (10,23) (11,17) (12,17) (12,20) (12,16) (13,27) (16,22) (16,25) (16,21) (16,29) (16,19) (17,29) (17,20) (19,21) (19,29) (19,20) (20,22) (21,22) (21,25) (21,29) (27,28)\nIs there a path between node 21 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph279-30_8", + "image": "data/connectivity/graph_visual/hard/graph279.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,7) (0,22) (0,14) (0,1) (0,12) (0,23) (1,8) (1,14) (1,12) (1,2) (1,23) (2,7) (2,22) (2,19) (2,12) (2,23) (3,13) (3,26) (3,21) (3,20) (3,6) (3,10) (3,11) (3,4) (3,17) (3,27) (3,24) (3,28) (3,30) (4,29) (4,21) (4,18) (4,20) (4,6) (4,16) (4,17) (4,27) (4,28) (4,9) (4,30) (5,25) (5,13) (5,26) (5,21) (5,20) (5,6) (5,10) (5,11) (5,15) (5,16) (5,17) (5,27) (5,24) (5,28) (6,25) (6,13) (6,29) (6,26) (6,21) (6,18) (6,11) (6,15) (6,16) (6,17) (6,27) (6,24) (6,28) (7,8) (7,22) (7,19) (7,14) (7,12) (7,23) (8,19) (8,12) (8,23) (9,25) (9,13) (9,26) (9,21) (9,18) (9,11) (9,16) (9,27) (10,25) (10,26) (10,18) (10,15) (10,17) (10,24) (10,30) (11,29) (11,21) (11,18) (11,20) (11,15) (11,17) (11,27) (11,24) (11,28) (12,22) (12,14) (12,23) (13,25) (13,26) (13,18) (13,20) (13,15) (13,16) (13,24) (13,28) (13,30) (14,22) (14,23) (15,25) (15,29) (15,26) (15,21) (15,18) (15,16) (15,27) (15,28) (15,30) (16,25) (16,29) (16,26) (16,20) (16,17) (16,30) (17,29) (17,21) (17,18) (17,20) (17,27) (18,25) (18,29) (18,26) (18,21) (18,20) (18,28) (18,30) (19,22) (20,25) (20,29) (20,26) (20,21) (20,24) (20,28) (21,25) (21,26) (21,27) (21,24) (21,28) (21,30) (24,29) (24,26) (24,27) (24,28) (24,30) (25,29) (25,26) (25,28) (25,30) (26,29) (26,27) (26,30) (27,29) (27,28) (29,30)\nIs there a path between node 30 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph32-16_1", + "image": "data/connectivity/graph_visual/hard/graph32.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,13) (0,12) (0,20) (0,15) (0,4) (0,8) (0,18) (0,24) (0,10) (0,14) (0,9) (0,16) (0,2) (0,7) (0,11) (0,17) (1,20) (1,19) (1,23) (1,5) (1,15) (1,4) (1,18) (1,24) (1,10) (1,14) (1,16) (1,21) (1,7) (1,11) (1,17) (2,13) (2,12) (2,19) (2,5) (2,15) (2,18) (2,24) (2,14) (2,9) (2,21) (2,17) (3,13) (3,20) (3,23) (3,15) (3,4) (3,18) (3,24) (3,14) (3,9) (3,16) (3,21) (3,7) (3,11) (4,13) (4,12) (4,20) (4,19) (4,15) (4,24) (4,10) (4,9) (4,16) (4,7) (4,11) (4,17) (5,12) (5,20) (5,19) (5,23) (5,15) (5,18) (5,24) (5,10) (5,14) (5,9) (5,21) (5,7) (5,17) (6,22) (7,12) (7,20) (7,19) (7,23) (7,15) (7,8) (7,18) (7,24) (7,10) (7,14) (7,9) (7,21) (7,11) (8,13) (8,15) (8,18) (8,24) (8,10) (8,14) (8,16) (8,17) (9,19) (9,23) (9,15) (9,18) (9,24) (9,10) (9,21) (9,17) (10,13) (10,23) (10,15) (10,24) (10,14) (10,21) (10,11) (11,13) (11,12) (11,20) (11,19) (11,23) (11,15) (11,18) (11,14) (11,16) (11,21) (12,13) (12,20) (12,15) (12,24) (12,14) (12,16) (12,21) (12,17) (13,20) (13,19) (13,15) (13,18) (13,21) (13,17) (14,20) (14,19) (14,23) (14,15) (14,18) (14,16) (14,17) (15,20) (15,19) (15,23) (15,18) (15,24) (15,17) (16,19) (16,23) (16,18) (17,20) (17,19) (17,24) (18,20) (18,19) (18,21) (19,20) (19,23) (19,24) (19,21) (20,23) (20,24) (20,21) (21,23) (21,24) (22,25) (23,24)\nIs there a path between node 16 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph147-25_0", + "image": "data/connectivity/graph_visual/hard/graph147.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,8) (0,19) (0,26) (0,7) (0,14) (0,5) (0,21) (0,13) (0,24) (0,17) (0,1) (0,9) (0,3) (0,16) (0,25) (1,8) (1,19) (1,26) (1,2) (1,7) (1,14) (1,5) (1,27) (1,4) (1,28) (1,15) (1,24) (1,17) (1,9) (1,23) (1,11) (1,3) (1,16) (2,12) (2,8) (2,22) (2,19) (2,26) (2,7) (2,18) (2,21) (2,27) (2,13) (2,15) (2,17) (2,9) (2,10) (2,23) (2,3) (2,16) (2,25) (3,12) (3,22) (3,19) (3,26) (3,7) (3,14) (3,18) (3,5) (3,21) (3,27) (3,4) (3,28) (3,13) (3,15) (3,24) (3,17) (3,9) (3,23) (3,11) (3,16) (4,12) (4,8) (4,26) (4,14) (4,18) (4,21) (4,13) (4,15) (4,24) (4,17) (4,23) (4,16) (5,12) (5,8) (5,22) (5,26) (5,14) (5,18) (5,21) (5,27) (5,28) (5,13) (5,15) (5,17) (5,10) (5,11) (5,25) (7,12) (7,8) (7,26) (7,14) (7,18) (7,21) (7,27) (7,13) (7,15) (7,17) (7,9) (7,10) (7,11) (7,16) (7,25) (8,12) (8,19) (8,14) (8,18) (8,21) (8,27) (8,13) (8,24) (8,17) (8,9) (8,10) (8,23) (8,16) (8,25) (9,12) (9,19) (9,14) (9,18) (9,27) (9,28) (9,13) (9,15) (9,17) (9,10) (9,23) (9,11) (9,16) (9,25) (10,12) (10,22) (10,19) (10,14) (10,18) (10,21) (10,27) (10,28) (10,13) (10,24) (10,23) (10,11) (10,25) (11,22) (11,19) (11,27) (11,13) (11,15) (11,23) (11,25) (12,19) (12,14) (12,18) (12,21) (12,27) (12,15) (12,24) (12,17) (12,25) (13,22) (13,19) (13,26) (13,14) (13,18) (13,21) (13,28) (13,15) (13,17) (13,23) (13,16) (13,25) (14,18) (14,21) (14,27) (14,28) (14,17) (14,23) (14,16) (14,25) (15,22) (15,19) (15,18) (15,24) (15,17) (15,23) (15,25) (16,22) (16,19) (16,26) (16,18) (16,21) (16,27) (16,28) (16,24) (16,17) (16,23) (16,25) (17,22) (17,19) (17,18) (17,21) (17,27) (17,24) (17,23) (17,25) (18,22) (18,19) (18,26) (18,21) (18,27) (18,28) (18,24) (18,23) (19,22) (19,26) (19,28) (19,24) (19,23) (19,25) (21,22) (21,26) (21,27) (21,28) (21,25) (22,26) (22,27) (22,24) (22,23) (22,25) (23,26) (23,27) (23,28) (23,24) (23,25) (24,26) (24,28) (24,25) (25,26) (25,27) (25,28) (27,28)\nIs there a path between node 25 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph329-22_30", + "image": "data/connectivity/graph_visual/hard/graph329.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,28) (0,2) (0,25) (0,6) (0,27) (0,4) (0,31) (0,9) (0,1) (0,29) (0,10) (0,11) (0,16) (0,21) (1,28) (1,2) (1,25) (1,27) (1,4) (1,31) (1,9) (1,14) (1,11) (1,16) (1,22) (1,20) (2,28) (2,25) (2,6) (2,27) (2,4) (2,9) (2,14) (2,10) (2,19) (2,11) (2,16) (2,20) (2,26) (2,21) (3,24) (3,18) (3,8) (4,28) (4,25) (4,27) (4,31) (4,14) (4,10) (4,19) (4,22) (4,20) (4,26) (4,21) (5,17) (5,12) (5,15) (5,30) (5,13) (6,28) (6,25) (6,27) (6,9) (6,14) (6,29) (6,19) (6,11) (6,16) (6,20) (6,21) (7,24) (7,18) (7,8) (8,24) (9,28) (9,25) (9,31) (9,29) (9,10) (9,19) (9,11) (9,22) (9,20) (9,26) (9,21) (10,25) (10,31) (10,14) (10,11) (10,16) (10,20) (10,26) (10,21) (11,25) (11,27) (11,31) (11,29) (11,19) (11,16) (11,22) (11,26) (12,15) (12,30) (12,13) (13,17) (13,15) (13,30) (14,28) (14,25) (14,27) (14,29) (14,19) (14,16) (14,22) (14,20) (14,26) (14,21) (15,17) (16,28) (16,25) (16,27) (16,31) (16,22) (16,20) (16,21) (19,28) (19,25) (19,27) (19,31) (19,22) (19,20) (19,26) (19,21) (20,28) (20,25) (20,27) (20,31) (20,29) (20,22) (20,26) (20,21) (21,27) (21,29) (21,22) (21,26) (22,28) (22,25) (22,31) (22,29) (22,26) (25,27) (25,31) (25,26) (26,28) (26,27) (27,29) (28,31) (29,31)\nIs there a path between node 22 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph424-13_2", + "image": "data/connectivity/graph_visual/hard/graph424.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,16) (0,10) (0,29) (0,2) (0,12) (0,18) (0,26) (0,8) (1,19) (1,16) (1,24) (1,18) (2,19) (2,17) (2,7) (2,32) (2,24) (2,18) (3,15) (3,14) (4,9) (4,25) (5,30) (5,25) (5,6) (6,9) (6,30) (6,25) (7,19) (7,16) (7,26) (8,27) (8,16) (8,12) (8,32) (8,18) (10,27) (10,19) (10,16) (10,12) (10,32) (11,18) (11,26) (12,27) (12,19) (12,17) (12,28) (12,24) (12,18) (12,26) (13,23) (16,31) (16,29) (17,24) (18,31) (19,28) (19,24) (20,28) (20,24) (21,28) (21,26) (26,28) (27,31) (28,31) (28,29) (31,32)\nIs there a path between node 13 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph296-27_24", + "image": "data/connectivity/graph_visual/hard/graph296.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,1) (0,24) (0,3) (0,16) (0,17) (0,30) (0,27) (0,19) (0,11) (0,23) (0,31) (1,10) (1,24) (1,2) (1,17) (1,30) (1,29) (1,4) (1,27) (1,21) (1,11) (2,10) (2,18) (2,3) (2,15) (2,17) (2,29) (2,27) (2,19) (2,21) (2,26) (2,31) (3,10) (3,18) (3,24) (3,16) (3,17) (3,29) (3,4) (3,19) (3,21) (3,26) (3,31) (4,18) (4,15) (4,16) (4,17) (4,30) (4,27) (4,19) (4,21) (4,31) (6,22) (7,12) (7,8) (7,28) (7,20) (7,9) (8,13) (8,12) (8,20) (8,9) (9,13) (9,12) (9,25) (9,28) (10,18) (10,24) (10,15) (10,17) (10,30) (10,27) (10,19) (10,21) (10,11) (10,23) (10,31) (11,18) (11,24) (11,15) (11,16) (11,30) (11,27) (11,19) (11,21) (11,23) (11,26) (11,31) (12,13) (12,25) (12,28) (13,25) (13,28) (13,20) (15,17) (15,29) (15,27) (15,19) (15,23) (15,31) (16,24) (16,17) (16,29) (16,19) (16,21) (16,23) (16,26) (17,18) (17,24) (17,30) (17,29) (17,27) (17,19) (17,23) (17,26) (17,31) (18,24) (18,30) (18,27) (18,19) (18,23) (19,30) (19,29) (19,27) (19,21) (19,23) (19,26) (20,28) (21,29) (21,27) (21,26) (21,31) (23,24) (23,26) (23,31) (24,30) (24,27) (24,26) (25,28) (26,30) (26,29) (26,27) (26,31) (27,30) (27,31) (29,30) (29,31) (30,31)\nIs there a path between node 27 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph310-17_3", + "image": "data/connectivity/graph_visual/hard/graph310.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,16) (0,29) (0,2) (0,24) (1,7) (2,23) (2,12) (2,4) (2,8) (2,10) (3,17) (3,26) (3,27) (4,11) (4,12) (4,5) (5,31) (5,16) (5,28) (6,16) (6,11) (6,14) (6,28) (8,31) (8,11) (8,12) (10,11) (10,14) (11,31) (12,16) (12,23) (13,19) (13,20) (13,26) (14,16) (14,29) (15,19) (16,29) (16,23) (18,27) (19,20) (19,27) (19,22) (21,23) (23,28) (25,29)\nIs there a path between node 17 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph568-8_16", + "image": "data/connectivity/graph_visual/hard/graph568.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,17) (0,26) (0,2) (0,5) (0,4) (0,25) (0,18) (0,29) (1,24) (1,6) (1,21) (2,22) (2,8) (2,30) (2,17) (2,33) (2,26) (2,11) (2,7) (2,5) (2,23) (2,18) (2,29) (3,27) (4,13) (4,9) (4,33) (4,11) (4,5) (4,23) (4,25) (4,29) (5,22) (5,16) (5,30) (5,9) (5,19) (5,10) (5,15) (5,29) (6,24) (6,31) (7,17) (7,23) (7,25) (8,16) (8,32) (8,10) (8,18) (8,29) (9,22) (9,30) (9,23) (10,22) (10,16) (10,19) (11,22) (11,13) (11,30) (11,33) (11,23) (11,18) (12,28) (12,31) (13,30) (13,32) (13,23) (14,17) (14,32) (14,23) (14,25) (14,15) (14,29) (15,16) (15,33) (15,32) (15,18) (16,22) (16,17) (16,32) (16,23) (16,18) (16,29) (17,32) (17,18) (17,29) (18,19) (18,32) (18,23) (19,29) (20,24) (20,21) (21,27) (22,32) (22,25) (25,33) (25,26) (25,29) (26,33) (26,29) (27,28) (28,31) (29,30)\nIs there a path between node 8 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph523-33_32", + "image": "data/connectivity/graph_visual/hard/graph523.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,30) (0,1) (0,22) (0,18) (0,3) (1,7) (1,22) (1,14) (1,20) (1,32) (1,17) (1,23) (1,12) (2,7) (2,11) (2,16) (2,31) (2,14) (2,20) (2,17) (3,7) (3,11) (3,33) (3,30) (3,22) (3,9) (3,14) (3,5) (3,6) (3,24) (3,12) (4,30) (4,31) (4,29) (4,5) (4,25) (4,24) (4,28) (4,23) (5,27) (5,7) (5,22) (5,16) (5,20) (5,26) (5,13) (5,23) (6,11) (6,30) (6,16) (6,14) (6,20) (6,25) (7,11) (7,30) (7,29) (7,20) (7,32) (7,28) (8,19) (9,27) (9,29) (9,14) (9,32) (9,28) (9,23) (9,12) (10,19) (11,33) (11,21) (11,16) (11,31) (11,18) (11,26) (11,25) (12,22) (12,18) (12,14) (12,17) (12,25) (12,24) (13,21) (13,22) (13,16) (13,32) (13,17) (13,25) (13,24) (14,33) (14,15) (14,16) (14,28) (15,22) (15,18) (15,26) (15,17) (15,25) (16,21) (16,29) (16,20) (16,32) (16,17) (17,31) (17,25) (17,28) (18,21) (18,25) (18,23) (20,33) (20,22) (20,32) (21,27) (21,30) (22,23) (23,33) (23,29) (23,26) (24,33) (24,30) (24,31) (24,32) (24,28) (25,31) (25,29) (25,26) (26,29) (26,28) (27,29) (27,28) (29,32) (31,32) (32,33)\nIs there a path between node 33 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph206-15_22", + "image": "data/connectivity/graph_visual/hard/graph206.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,23) (0,26) (0,24) (0,27) (1,4) (1,16) (1,15) (1,10) (1,29) (1,17) (1,11) (2,9) (2,7) (2,6) (2,27) (3,13) (3,28) (3,16) (3,18) (3,29) (3,21) (4,20) (4,16) (4,5) (4,15) (4,18) (4,14) (4,25) (5,28) (5,16) (5,15) (5,18) (5,14) (5,29) (5,19) (5,17) (5,11) (7,23) (7,26) (7,27) (8,26) (10,29) (10,19) (11,13) (11,28) (11,15) (11,17) (13,20) (13,28) (13,19) (14,16) (14,15) (14,29) (14,19) (14,21) (15,20) (15,28) (15,29) (15,19) (16,28) (16,25) (16,17) (17,19) (18,20) (18,21) (20,21) (21,29) (21,25) (22,28) (23,24) (26,27) (28,29)\nIs there a path between node 15 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph353-0_23", + "image": "data/connectivity/graph_visual/hard/graph353.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,1) (0,17) (0,20) (0,10) (0,24) (1,11) (1,4) (1,30) (1,20) (2,18) (2,29) (2,17) (2,14) (2,31) (2,25) (2,13) (3,21) (3,16) (3,6) (4,11) (4,26) (4,29) (4,30) (4,20) (4,10) (5,6) (5,7) (5,23) (6,16) (6,23) (6,22) (7,21) (7,16) (7,23) (8,29) (8,13) (8,10) (9,29) (9,28) (9,31) (9,10) (9,27) (10,11) (10,18) (10,28) (10,31) (10,15) (11,26) (11,18) (11,25) (11,13) (11,27) (11,15) (12,21) (12,19) (13,18) (13,29) (13,17) (13,28) (13,31) (13,20) (13,24) (14,25) (14,20) (15,18) (15,29) (15,28) (17,28) (18,20) (20,26) (20,29) (20,31) (21,22) (24,26) (24,30) (24,28) (25,28) (26,31) (27,28) (27,31) (28,29) (29,30) (29,31) (30,31)\nIs there a path between node 0 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph516-21_17", + "image": "data/connectivity/graph_visual/hard/graph516.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,4) (1,33) (1,21) (1,17) (2,10) (2,30) (2,23) (3,10) (3,16) (3,30) (3,23) (5,26) (6,22) (6,25) (6,10) (6,13) (6,30) (6,11) (6,15) (6,29) (6,20) (7,8) (7,13) (7,33) (7,27) (7,14) (7,29) (8,10) (8,33) (8,15) (9,10) (9,12) (9,11) (9,15) (9,17) (10,22) (10,31) (10,16) (10,33) (10,27) (10,20) (11,25) (11,31) (11,12) (11,27) (11,14) (12,22) (12,31) (12,30) (12,33) (12,21) (12,27) (12,17) (12,14) (13,25) (13,31) (13,29) (14,33) (14,23) (14,20) (15,33) (15,20) (16,25) (16,33) (16,21) (16,17) (16,20) (17,29) (19,24) (20,25) (20,31) (20,30) (21,29) (22,25) (23,25) (23,33) (25,27) (27,29) (29,31) (31,33)\nIs there a path between node 21 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph617-0_8", + "image": "data/connectivity/graph_visual/hard/graph617.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,19) (0,23) (0,18) (0,2) (0,24) (0,14) (0,6) (0,7) (0,33) (0,30) (0,21) (0,11) (0,29) (0,10) (1,25) (1,31) (1,16) (1,34) (1,28) (2,22) (2,23) (2,18) (2,24) (2,32) (2,14) (2,6) (2,33) (2,8) (2,27) (2,21) (2,4) (2,29) (3,9) (3,13) (3,15) (3,5) (3,26) (4,19) (4,23) (4,18) (4,24) (4,12) (4,32) (4,6) (4,7) (4,33) (4,8) (4,27) (4,30) (4,17) (4,10) (5,9) (5,13) (5,15) (5,26) (6,19) (6,12) (6,32) (6,14) (6,33) (6,27) (6,10) (7,22) (7,19) (7,18) (7,24) (7,32) (7,14) (7,27) (7,30) (7,11) (7,10) (8,22) (8,19) (8,23) (8,12) (8,33) (8,30) (8,17) (8,11) (8,29) (8,10) (9,13) (9,15) (9,26) (10,19) (10,18) (10,12) (10,32) (10,33) (10,27) (10,17) (10,11) (10,29) (11,19) (11,23) (11,18) (11,24) (11,32) (11,33) (11,27) (11,21) (11,29) (12,19) (12,23) (12,18) (12,32) (12,14) (12,33) (12,27) (12,30) (12,21) (12,17) (13,26) (14,22) (14,19) (14,23) (14,18) (14,32) (14,30) (14,21) (14,29) (15,26) (16,25) (16,31) (16,34) (16,28) (17,19) (17,23) (17,18) (17,24) (17,33) (17,27) (17,29) (18,22) (18,19) (18,23) (18,33) (18,27) (18,21) (18,29) (19,22) (19,23) (19,33) (19,27) (19,29) (20,25) (20,31) (20,34) (21,22) (21,23) (21,32) (21,33) (21,27) (21,30) (21,29) (22,33) (22,27) (22,30) (23,24) (23,32) (23,33) (23,27) (23,29) (24,32) (24,33) (24,27) (24,30) (24,29) (25,31) (25,34) (27,32) (27,33) (27,29) (29,33) (30,32) (30,33) (31,34) (32,33)\nIs there a path between node 0 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph384-26_21", + "image": "data/connectivity/graph_visual/hard/graph384.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,5) (0,30) (0,29) (0,17) (0,3) (0,22) (0,12) (0,15) (0,27) (1,2) (1,9) (1,31) (1,13) (1,16) (1,20) (1,18) (1,25) (2,9) (2,31) (2,13) (2,21) (2,16) (2,10) (2,20) (3,23) (3,4) (3,5) (3,24) (3,17) (3,7) (3,22) (3,19) (3,15) (3,27) (3,14) (4,23) (4,24) (4,30) (4,29) (4,7) (4,22) (4,26) (4,19) (4,28) (4,15) (4,27) (4,14) (5,23) (5,24) (5,29) (5,7) (5,26) (5,19) (5,12) (5,28) (5,15) (5,27) (6,9) (6,31) (6,13) (6,21) (6,16) (6,10) (6,18) (6,25) (7,23) (7,24) (7,30) (7,29) (7,17) (7,22) (7,28) (7,15) (7,27) (8,11) (9,13) (9,21) (9,16) (9,10) (9,18) (9,25) (10,31) (10,13) (10,21) (10,16) (12,23) (12,30) (12,17) (12,22) (12,26) (12,19) (12,28) (12,27) (13,31) (13,21) (13,25) (14,24) (14,30) (14,29) (14,17) (14,22) (14,19) (14,28) (14,15) (14,27) (15,23) (15,24) (15,17) (15,22) (15,26) (15,28) (15,27) (16,31) (16,18) (16,25) (17,23) (17,24) (17,30) (17,22) (17,28) (18,31) (18,20) (18,25) (19,23) (19,24) (19,29) (19,22) (19,27) (20,31) (21,25) (22,23) (22,30) (22,29) (22,26) (22,28) (22,27) (23,30) (23,29) (23,26) (23,28) (24,30) (24,29) (24,28) (24,27) (25,31) (26,30) (26,29) (26,28) (26,27) (27,28) (28,30) (28,29)\nIs there a path between node 26 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph436-24_13", + "image": "data/connectivity/graph_visual/hard/graph436.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,21) (0,28) (0,12) (0,18) (0,1) (0,7) (0,3) (0,2) (0,17) (0,27) (0,30) (0,6) (0,8) (0,9) (0,15) (1,21) (1,28) (1,23) (1,11) (1,20) (1,7) (1,2) (1,17) (1,27) (1,30) (1,6) (1,8) (1,15) (2,21) (2,28) (2,12) (2,23) (2,18) (2,11) (2,20) (2,7) (2,17) (2,27) (2,30) (2,8) (2,9) (2,15) (3,16) (3,21) (3,28) (3,12) (3,23) (3,18) (3,17) (3,27) (3,8) (3,15) (4,5) (4,10) (4,25) (4,26) (4,29) (4,13) (4,24) (4,22) (4,14) (5,10) (5,25) (5,13) (5,31) (5,24) (5,22) (6,16) (6,21) (6,28) (6,12) (6,18) (6,11) (6,20) (6,17) (6,27) (6,8) (6,15) (7,16) (7,28) (7,12) (7,23) (7,18) (7,20) (7,30) (7,8) (7,9) (7,15) (8,16) (8,18) (8,11) (8,30) (8,9) (8,15) (9,21) (9,12) (9,23) (9,18) (9,20) (9,27) (9,15) (10,19) (10,25) (10,26) (10,32) (10,29) (10,13) (10,31) (10,24) (10,22) (10,14) (11,16) (11,28) (11,23) (11,18) (11,17) (11,27) (11,30) (11,15) (12,16) (12,21) (12,28) (12,18) (12,20) (12,27) (12,15) (13,19) (13,25) (13,26) (13,31) (13,22) (13,14) (14,25) (14,26) (14,32) (14,29) (14,31) (14,24) (14,22) (15,16) (15,21) (15,23) (15,20) (15,17) (15,27) (15,30) (16,18) (16,20) (16,17) (16,27) (16,30) (17,21) (17,28) (17,23) (17,18) (17,20) (17,27) (17,30) (18,28) (18,23) (18,20) (18,30) (19,25) (19,26) (19,29) (19,31) (19,22) (20,28) (20,23) (20,27) (21,28) (21,27) (21,30) (22,26) (22,32) (22,29) (22,31) (22,24) (23,28) (23,27) (24,25) (24,26) (24,29) (24,31) (25,26) (25,32) (25,31) (26,32) (26,31) (27,28) (27,30) (28,30) (29,31)\nIs there a path between node 24 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph621-28_13", + "image": "data/connectivity/graph_visual/hard/graph621.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,9) (0,26) (0,24) (0,27) (0,11) (1,3) (1,2) (1,20) (1,6) (1,31) (2,3) (2,33) (2,30) (2,32) (2,19) (2,7) (3,31) (3,5) (4,33) (4,9) (4,30) (4,16) (4,25) (4,24) (5,30) (5,26) (5,27) (5,15) (6,33) (6,20) (6,24) (6,27) (6,11) (6,7) (7,33) (7,23) (7,30) (9,26) (9,29) (9,24) (9,31) (9,15) (10,28) (10,13) (10,22) (10,21) (11,16) (11,24) (12,15) (13,14) (13,17) (15,23) (15,20) (15,31) (16,20) (16,24) (16,19) (17,21) (19,33) (19,23) (19,25) (19,32) (20,33) (20,23) (20,32) (20,24) (20,27) (21,28) (23,33) (23,32) (24,30) (24,32) (24,29) (25,30) (25,32) (25,29) (25,27) (26,30) (26,32) (26,29) (27,33) (27,30) (29,30) (29,31) (30,32) (31,32)\nIs there a path between node 28 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph94-12_20", + "image": "data/connectivity/graph_visual/hard/graph94.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,20) (0,24) (0,3) (0,19) (0,9) (0,21) (1,2) (2,13) (2,6) (3,24) (3,8) (3,12) (4,20) (4,8) (4,19) (4,17) (4,23) (4,21) (5,7) (5,25) (5,18) (6,13) (7,25) (8,20) (8,24) (8,14) (8,11) (8,23) (9,26) (9,15) (9,24) (9,14) (9,11) (9,23) (10,26) (10,15) (10,12) (10,23) (11,26) (11,15) (11,27) (11,12) (11,17) (11,23) (12,20) (12,24) (12,14) (13,22) (14,19) (14,17) (14,21) (15,19) (15,23) (15,21) (16,24) (16,19) (16,21) (17,24) (18,25) (19,26) (19,24) (20,27) (21,24) (21,27) (23,26) (23,24) (24,26)\nIs there a path between node 12 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph117-4_7", + "image": "data/connectivity/graph_visual/hard/graph117.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,19) (0,15) (0,14) (0,24) (0,5) (0,25) (0,2) (1,7) (1,11) (1,8) (1,17) (1,25) (1,16) (1,21) (1,2) (2,15) (2,12) (2,3) (2,16) (3,15) (3,11) (3,10) (3,20) (3,16) (3,21) (5,7) (5,14) (5,12) (5,11) (5,24) (5,10) (5,26) (5,6) (6,19) (6,9) (6,14) (6,11) (6,24) (6,10) (6,25) (6,21) (7,19) (7,15) (7,18) (7,11) (7,24) (8,19) (8,24) (8,10) (9,15) (9,18) (9,11) (9,27) (9,26) (9,20) (9,25) (9,21) (9,23) (10,17) (10,25) (11,27) (11,26) (11,17) (11,20) (11,16) (12,19) (12,14) (12,24) (12,17) (14,26) (15,18) (15,17) (16,24) (16,26) (16,17) (17,27) (17,25) (18,24) (18,25) (19,27) (19,23) (20,24) (20,27) (20,23) (21,24) (21,27)\nIs there a path between node 4 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph296-13_25", + "image": "data/connectivity/graph_visual/hard/graph296.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,1) (0,24) (0,3) (0,16) (0,17) (0,30) (0,27) (0,19) (0,11) (0,23) (0,31) (1,10) (1,24) (1,2) (1,17) (1,30) (1,29) (1,4) (1,27) (1,21) (1,11) (2,10) (2,18) (2,3) (2,15) (2,17) (2,29) (2,27) (2,19) (2,21) (2,26) (2,31) (3,10) (3,18) (3,24) (3,16) (3,17) (3,29) (3,4) (3,19) (3,21) (3,26) (3,31) (4,18) (4,15) (4,16) (4,17) (4,30) (4,27) (4,19) (4,21) (4,31) (6,22) (7,12) (7,8) (7,28) (7,20) (7,9) (8,13) (8,12) (8,20) (8,9) (9,13) (9,12) (9,25) (9,28) (10,18) (10,24) (10,15) (10,17) (10,30) (10,27) (10,19) (10,21) (10,11) (10,23) (10,31) (11,18) (11,24) (11,15) (11,16) (11,30) (11,27) (11,19) (11,21) (11,23) (11,26) (11,31) (12,13) (12,25) (12,28) (13,25) (13,28) (13,20) (15,17) (15,29) (15,27) (15,19) (15,23) (15,31) (16,24) (16,17) (16,29) (16,19) (16,21) (16,23) (16,26) (17,18) (17,24) (17,30) (17,29) (17,27) (17,19) (17,23) (17,26) (17,31) (18,24) (18,30) (18,27) (18,19) (18,23) (19,30) (19,29) (19,27) (19,21) (19,23) (19,26) (20,28) (21,29) (21,27) (21,26) (21,31) (23,24) (23,26) (23,31) (24,30) (24,27) (24,26) (25,28) (26,30) (26,29) (26,27) (26,31) (27,30) (27,31) (29,30) (29,31) (30,31)\nIs there a path between node 13 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph698-12_9", + "image": "data/connectivity/graph_visual/hard/graph698.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,16) (0,9) (0,7) (0,30) (0,29) (1,34) (1,19) (1,6) (1,18) (2,8) (2,15) (2,31) (2,24) (2,12) (2,20) (2,14) (2,3) (2,25) (2,32) (2,4) (2,23) (2,28) (3,8) (3,33) (3,15) (3,12) (3,5) (3,14) (3,26) (3,25) (3,17) (3,22) (3,11) (4,8) (4,24) (4,12) (4,20) (4,5) (4,14) (4,26) (4,25) (4,32) (4,17) (4,23) (4,28) (4,11) (5,8) (5,15) (5,31) (5,14) (5,26) (5,25) (5,32) (5,10) (5,28) (5,11) (6,13) (6,19) (6,18) (7,16) (7,9) (7,30) (7,21) (7,29) (8,33) (8,15) (8,31) (8,24) (8,12) (8,20) (8,14) (8,26) (8,25) (8,32) (8,17) (8,22) (8,23) (8,28) (9,16) (9,30) (10,33) (10,15) (10,31) (10,24) (10,12) (10,14) (10,26) (10,25) (10,17) (10,22) (10,23) (10,28) (11,33) (11,15) (11,24) (11,12) (11,26) (11,25) (11,32) (11,22) (11,23) (11,28) (11,27) (12,15) (12,24) (12,20) (12,14) (12,26) (12,25) (12,32) (12,17) (12,22) (13,34) (13,19) (13,18) (14,33) (14,15) (14,31) (14,24) (14,26) (14,25) (14,32) (14,17) (14,22) (14,28) (14,27) (15,31) (15,24) (15,20) (15,25) (15,32) (15,17) (15,28) (15,27) (17,31) (17,24) (17,20) (17,25) (17,32) (17,23) (17,27) (18,34) (18,19) (19,34) (20,31) (20,24) (20,26) (20,25) (20,22) (20,23) (20,28) (20,27) (21,29) (22,33) (22,31) (22,24) (22,26) (22,32) (22,23) (22,28) (22,27) (23,33) (23,31) (23,24) (23,26) (23,25) (23,32) (23,27) (24,33) (24,26) (24,25) (24,32) (24,27) (25,31) (25,32) (25,28) (25,27) (26,33) (26,31) (26,32) (26,28) (26,27) (27,31) (27,32) (27,28) (28,33) (28,31) (28,32) (29,30) (31,33) (31,32) (32,33)\nIs there a path between node 12 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph216-9_11", + "image": "data/connectivity/graph_visual/hard/graph216.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,8) (1,27) (1,21) (1,29) (1,26) (1,19) (1,10) (1,5) (2,4) (2,28) (2,13) (2,25) (2,17) (2,5) (3,6) (3,28) (3,15) (3,13) (3,18) (3,22) (3,7) (3,19) (3,17) (3,5) (3,16) (4,12) (4,6) (4,15) (4,21) (4,10) (4,5) (4,14) (4,16) (5,28) (5,27) (5,23) (5,22) (5,25) (5,10) (6,9) (6,15) (6,20) (6,18) (6,25) (6,17) (6,14) (7,15) (7,13) (7,18) (7,23) (7,25) (7,26) (7,19) (9,15) (9,27) (9,18) (9,23) (9,22) (9,26) (9,10) (10,15) (10,20) (10,27) (10,21) (10,22) (10,25) (10,19) (10,17) (10,14) (12,28) (12,18) (12,22) (12,14) (13,20) (13,27) (13,18) (13,23) (13,19) (13,17) (13,16) (14,18) (14,21) (14,19) (15,27) (15,19) (15,17) (16,27) (16,23) (16,25) (17,28) (17,18) (17,23) (17,21) (17,22) (17,29) (18,27) (18,26) (19,28) (20,28) (20,22) (20,29) (21,29) (21,25) (23,28) (23,27) (23,26) (25,28) (25,29) (26,27) (27,29) (28,29)\nIs there a path between node 9 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph215-21_1", + "image": "data/connectivity/graph_visual/hard/graph215.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,11) (0,27) (0,29) (1,16) (1,11) (1,20) (1,14) (2,8) (2,18) (2,15) (2,11) (2,27) (2,19) (2,25) (2,29) (3,5) (4,8) (4,24) (4,23) (4,26) (4,13) (4,7) (4,28) (4,6) (4,20) (4,19) (6,15) (6,27) (6,25) (7,22) (7,24) (7,23) (7,26) (7,13) (7,28) (7,29) (8,18) (8,26) (8,12) (9,17) (11,22) (11,24) (11,28) (11,20) (12,22) (12,15) (12,28) (12,27) (12,20) (12,29) (13,16) (13,23) (13,28) (13,27) (13,20) (13,19) (14,19) (15,28) (15,25) (16,26) (16,25) (18,20) (18,29) (19,23) (19,20) (20,24) (20,26) (20,28) (20,27) (20,25) (22,23) (22,28) (22,29) (23,24) (23,26) (23,29) (24,27) (25,27) (26,29) (27,28)\nIs there a path between node 21 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph319-22_26", + "image": "data/connectivity/graph_visual/hard/graph319.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,2) (0,28) (0,1) (1,20) (1,27) (1,18) (2,16) (3,19) (3,27) (3,13) (3,18) (4,26) (4,21) (4,17) (4,12) (4,22) (4,10) (5,23) (5,15) (5,18) (6,19) (6,23) (7,9) (7,31) (7,17) (7,10) (8,20) (8,23) (8,15) (9,24) (9,10) (10,31) (10,24) (10,14) (11,17) (11,12) (12,26) (12,21) (12,17) (12,14) (13,19) (13,20) (13,23) (13,18) (13,30) (13,16) (14,31) (15,20) (15,30) (16,29) (17,21) (17,31) (18,19) (18,23) (19,27) (19,29) (20,23) (20,28) (21,31) (21,25) (22,26) (23,30) (23,29) (24,31) (24,25) (25,26) (26,31) (28,29) (29,30)\nIs there a path between node 22 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph4-9_21", + "image": "data/connectivity/graph_visual/hard/graph4.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,7) (0,23) (0,6) (1,15) (1,3) (2,14) (2,22) (3,14) (3,20) (3,22) (3,15) (4,25) (4,13) (5,20) (6,7) (6,25) (6,13) (7,23) (7,17) (8,25) (8,17) (9,12) (9,20) (9,24) (9,11) (10,16) (10,13) (11,15) (11,19) (12,21) (12,15) (12,24) (12,19) (14,21) (14,22) (14,15) (14,24) (15,21) (16,23) (18,24) (18,19) (19,24) (20,21) (21,22) (21,24)\nIs there a path between node 9 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph334-4_21", + "image": "data/connectivity/graph_visual/hard/graph334.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,28) (0,16) (0,30) (0,27) (0,22) (0,18) (1,4) (1,29) (1,2) (1,8) (1,21) (1,6) (1,23) (1,17) (1,11) (1,15) (1,10) (1,12) (1,3) (1,31) (1,25) (1,14) (2,29) (2,8) (2,21) (2,11) (2,15) (2,10) (2,12) (2,3) (2,31) (2,9) (2,19) (3,4) (3,29) (3,8) (3,21) (3,6) (3,17) (3,20) (3,11) (3,12) (3,31) (3,19) (3,14) (4,29) (4,21) (4,23) (4,17) (4,20) (4,11) (4,15) (4,10) (4,12) (4,31) (4,9) (4,19) (4,14) (5,29) (5,8) (5,21) (5,6) (5,23) (5,17) (5,20) (5,11) (5,15) (5,10) (5,12) (5,31) (5,25) (5,19) (5,14) (6,8) (6,21) (6,23) (6,20) (6,11) (6,10) (6,12) (6,31) (6,25) (7,16) (7,30) (7,24) (7,22) (7,18) (8,29) (8,23) (8,17) (8,11) (8,15) (8,10) (8,12) (8,31) (8,25) (8,9) (8,14) (9,29) (9,20) (9,11) (9,15) (9,10) (9,31) (9,19) (9,14) (10,29) (10,23) (10,20) (10,11) (10,15) (10,19) (11,29) (11,23) (11,17) (11,20) (11,12) (11,25) (11,19) (11,14) (12,21) (12,23) (12,17) (12,20) (12,31) (12,19) (12,14) (13,26) (13,28) (13,16) (13,30) (13,18) (14,29) (14,21) (14,23) (14,17) (14,20) (14,15) (14,31) (15,21) (15,20) (15,31) (15,19) (16,30) (16,24) (16,27) (16,22) (16,18) (17,29) (17,21) (17,23) (17,20) (17,31) (17,25) (18,28) (18,24) (18,27) (18,22) (19,29) (19,21) (19,23) (19,20) (19,31) (19,25) (20,23) (20,31) (20,25) (21,29) (22,26) (22,28) (22,30) (22,24) (23,29) (23,31) (24,26) (24,28) (24,27) (25,31) (26,28) (27,30) (28,30) (29,31)\nIs there a path between node 4 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph328-29_27", + "image": "data/connectivity/graph_visual/hard/graph328.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,21) (0,17) (0,19) (0,2) (0,25) (0,23) (0,14) (0,8) (0,7) (0,28) (0,29) (0,16) (0,5) (0,12) (0,11) (0,18) (0,6) (0,24) (1,4) (1,17) (1,19) (1,14) (1,8) (1,31) (1,27) (1,7) (1,29) (1,16) (1,5) (1,12) (1,11) (1,20) (1,3) (1,18) (1,6) (1,13) (2,21) (2,17) (2,19) (2,25) (2,31) (2,15) (2,27) (2,7) (2,29) (2,16) (2,5) (2,26) (2,12) (2,11) (2,3) (2,18) (2,10) (2,13) (3,4) (3,21) (3,17) (3,19) (3,23) (3,14) (3,31) (3,15) (3,27) (3,7) (3,28) (3,16) (3,26) (3,11) (3,20) (3,18) (3,24) (3,10) (3,13) (4,21) (4,19) (4,25) (4,23) (4,8) (4,31) (4,15) (4,27) (4,7) (4,29) (4,16) (4,5) (4,26) (4,20) (4,18) (4,10) (4,13) (5,21) (5,17) (5,19) (5,23) (5,14) (5,8) (5,31) (5,15) (5,7) (5,28) (5,26) (5,12) (5,11) (5,20) (5,24) (5,10) (5,13) (6,21) (6,17) (6,23) (6,14) (6,8) (6,31) (6,15) (6,27) (6,7) (6,12) (6,11) (6,18) (6,24) (6,10) (6,13) (7,17) (7,19) (7,25) (7,14) (7,31) (7,15) (7,27) (7,28) (7,29) (7,16) (7,26) (7,12) (7,11) (7,20) (7,10) (7,13) (8,21) (8,17) (8,19) (8,25) (8,14) (8,31) (8,28) (8,29) (8,16) (8,20) (8,18) (8,24) (8,10) (8,13) (9,30) (10,21) (10,17) (10,25) (10,23) (10,14) (10,31) (10,15) (10,28) (10,29) (10,16) (10,12) (10,20) (10,18) (10,24) (11,21) (11,17) (11,19) (11,25) (11,23) (11,15) (11,28) (11,16) (11,12) (11,20) (11,18) (11,24) (11,13) (12,19) (12,25) (12,23) (12,14) (12,31) (12,15) (12,27) (12,28) (12,29) (12,16) (12,26) (12,20) (12,18) (12,24) (13,21) (13,19) (13,25) (13,23) (13,14) (13,31) (13,15) (13,29) (13,16) (13,26) (13,20) (13,24) (14,17) (14,23) (14,31) (14,15) (14,28) (14,29) (14,16) (14,26) (14,20) (14,24) (15,17) (15,25) (15,23) (15,31) (15,27) (15,28) (15,29) (15,16) (15,26) (15,20) (16,21) (16,19) (16,25) (16,23) (16,31) (16,27) (16,28) (16,29) (16,26) (16,18) (16,24) (17,21) (17,19) (17,25) (17,23) (17,31) (17,29) (17,18) (17,24) (18,21) (18,19) (18,25) (18,28) (18,29) (18,26) (18,20) (19,21) (19,25) (19,23) (19,27) (19,28) (19,29) (19,20) (20,21) (20,25) (20,23) (20,27) (20,28) (20,26) (20,24) (21,25) (21,23) (21,31) (21,27) (21,28) (21,24) (22,30) (23,31) (23,27) (24,25) (24,31) (24,27) (24,28) (24,29) (24,26) (26,31) (26,27) (26,29) (28,29) (29,31)\nIs there a path between node 29 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph425-7_18", + "image": "data/connectivity/graph_visual/hard/graph425.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,7) (0,12) (0,32) (0,22) (0,9) (0,20) (0,2) (0,5) (0,14) (0,4) (0,26) (0,21) (1,11) (1,8) (1,24) (1,3) (1,31) (1,28) (1,6) (2,16) (2,7) (2,32) (2,22) (2,9) (2,20) (2,14) (2,4) (2,21) (3,11) (3,8) (3,24) (3,31) (3,28) (4,16) (4,32) (4,22) (4,9) (4,20) (4,5) (4,14) (4,26) (5,16) (5,7) (5,12) (5,32) (5,22) (5,9) (5,20) (5,14) (5,26) (5,21) (6,8) (6,24) (6,31) (6,28) (7,12) (7,32) (7,22) (7,9) (7,14) (7,26) (7,21) (8,24) (8,31) (8,28) (9,16) (9,12) (9,32) (9,20) (9,26) (9,21) (10,23) (10,13) (10,29) (10,19) (10,25) (10,18) (12,32) (12,22) (12,20) (12,26) (12,21) (13,30) (13,27) (13,29) (13,19) (13,25) (13,18) (14,16) (14,32) (14,22) (14,20) (14,26) (15,30) (15,29) (15,25) (15,18) (16,32) (16,22) (16,20) (16,26) (16,21) (17,30) (17,27) (18,30) (18,29) (19,30) (19,23) (19,27) (19,25) (20,32) (20,22) (20,26) (21,32) (21,26) (22,32) (22,26) (23,30) (23,29) (23,25) (24,28) (26,32) (27,30) (27,29) (28,31) (29,30)\nIs there a path between node 7 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph253-15_6", + "image": "data/connectivity/graph_visual/hard/graph253.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,29) (1,11) (1,5) (1,4) (1,12) (1,10) (2,17) (2,14) (2,20) (2,16) (2,8) (2,13) (3,18) (3,17) (3,14) (3,6) (3,13) (4,11) (4,27) (4,5) (4,29) (4,10) (5,9) (5,30) (5,11) (5,27) (5,21) (5,12) (6,19) (6,16) (7,11) (7,24) (7,29) (7,26) (8,19) (8,13) (9,30) (9,21) (9,29) (9,10) (10,23) (10,22) (10,15) (10,28) (11,27) (11,24) (11,29) (11,28) (12,30) (12,22) (12,21) (13,20) (14,25) (14,16) (15,23) (15,27) (15,24) (15,22) (15,26) (16,19) (16,20) (17,18) (18,19) (19,25) (21,30) (21,23) (21,29) (21,28) (22,24) (22,29) (22,26) (22,28) (23,29) (23,26) (24,30) (27,28)\nIs there a path between node 15 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph4-25_24", + "image": "data/connectivity/graph_visual/hard/graph4.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,7) (0,23) (0,6) (1,15) (1,3) (2,14) (2,22) (3,14) (3,20) (3,22) (3,15) (4,25) (4,13) (5,20) (6,7) (6,25) (6,13) (7,23) (7,17) (8,25) (8,17) (9,12) (9,20) (9,24) (9,11) (10,16) (10,13) (11,15) (11,19) (12,21) (12,15) (12,24) (12,19) (14,21) (14,22) (14,15) (14,24) (15,21) (16,23) (18,24) (18,19) (19,24) (20,21) (21,22) (21,24)\nIs there a path between node 25 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph490-6_24", + "image": "data/connectivity/graph_visual/hard/graph490.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (0,8) (0,9) (0,17) (0,14) (0,7) (0,3) (1,8) (1,15) (1,9) (1,16) (1,17) (1,14) (1,19) (1,2) (1,7) (1,3) (2,8) (2,15) (2,25) (2,9) (2,16) (2,17) (2,14) (2,19) (2,3) (3,23) (3,8) (3,15) (3,25) (3,9) (3,7) (4,30) (4,10) (4,32) (4,22) (4,6) (4,18) (4,31) (4,21) (4,24) (4,27) (4,20) (4,28) (4,26) (4,5) (5,30) (5,11) (5,10) (5,6) (5,18) (5,31) (5,21) (5,24) (5,20) (5,28) (5,29) (6,11) (6,32) (6,22) (6,18) (6,31) (6,21) (6,27) (6,13) (6,20) (6,28) (6,26) (6,29) (7,23) (7,8) (7,15) (7,25) (7,16) (7,14) (7,19) (8,23) (8,15) (8,25) (8,16) (8,17) (8,14) (8,19) (9,23) (9,16) (9,17) (9,14) (9,19) (10,30) (10,32) (10,22) (10,18) (10,31) (10,21) (10,24) (10,27) (10,13) (10,20) (10,28) (10,26) (10,29) (11,30) (11,32) (11,22) (11,18) (11,31) (11,21) (11,12) (11,24) (11,20) (11,28) (11,26) (11,29) (12,30) (12,22) (12,31) (12,21) (12,24) (12,13) (12,28) (12,26) (13,30) (13,32) (13,18) (13,21) (13,24) (13,27) (13,20) (13,28) (13,26) (13,29) (14,23) (14,15) (14,25) (14,16) (14,17) (14,19) (15,23) (15,25) (15,16) (15,17) (15,19) (16,23) (16,25) (16,19) (17,23) (17,25) (18,30) (18,32) (18,22) (18,31) (18,21) (18,27) (18,20) (18,28) (18,26) (19,23) (20,32) (20,22) (20,31) (20,21) (20,28) (20,26) (20,29) (21,30) (21,32) (21,24) (21,27) (21,28) (21,29) (22,32) (22,31) (22,24) (22,27) (22,28) (22,26) (24,32) (24,31) (24,28) (24,26) (26,30) (26,32) (26,27) (26,29) (27,30) (27,32) (27,31) (27,28) (27,29) (28,32) (28,31) (28,29) (29,32) (29,31) (30,32) (30,31) (31,32)\nIs there a path between node 6 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph587-10_12", + "image": "data/connectivity/graph_visual/hard/graph587.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,21) (0,30) (0,33) (0,6) (0,24) (0,25) (0,1) (0,17) (0,11) (0,16) (1,10) (1,30) (1,4) (1,33) (1,6) (1,25) (1,31) (1,5) (1,17) (1,11) (1,16) (2,27) (3,15) (3,28) (3,12) (3,32) (3,14) (3,20) (3,13) (4,21) (4,33) (4,6) (4,24) (4,25) (4,31) (4,5) (4,17) (4,11) (5,10) (5,21) (5,30) (5,33) (5,6) (5,24) (5,25) (5,31) (5,17) (5,11) (6,30) (6,33) (6,24) (6,25) (6,31) (6,17) (6,11) (6,16) (7,19) (7,29) (7,22) (7,18) (7,9) (8,23) (8,15) (8,28) (8,32) (8,14) (8,20) (9,19) (9,29) (9,22) (9,18) (10,30) (10,33) (10,24) (10,25) (10,31) (10,17) (10,11) (11,21) (11,30) (11,33) (11,24) (11,25) (11,17) (11,16) (12,23) (12,15) (12,32) (12,14) (12,13) (13,15) (13,28) (13,32) (13,14) (14,15) (14,28) (14,32) (15,23) (15,28) (15,32) (15,20) (16,30) (16,25) (16,17) (17,33) (17,31) (18,19) (18,29) (18,22) (19,29) (20,28) (20,32) (21,33) (21,24) (21,25) (21,31) (23,32) (24,30) (24,33) (24,25) (24,31) (25,33) (25,31) (26,27) (30,31)\nIs there a path between node 10 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph44-7_12", + "image": "data/connectivity/graph_visual/hard/graph44.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,26) (0,15) (0,25) (0,14) (0,7) (0,2) (0,9) (0,5) (1,26) (1,15) (1,25) (1,7) (1,6) (1,2) (1,20) (1,22) (2,25) (2,19) (2,14) (2,4) (3,12) (3,16) (4,15) (4,7) (4,6) (4,8) (5,26) (5,20) (5,8) (5,9) (5,22) (5,13) (6,19) (6,17) (6,7) (6,20) (6,22) (7,19) (7,17) (7,9) (8,19) (9,26) (9,14) (9,24) (11,12) (12,21) (12,18) (12,16) (13,17) (13,22) (14,26) (14,22) (15,19) (15,20) (16,21) (18,23) (19,20) (19,22) (25,26)\nIs there a path between node 7 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph88-11_14", + "image": "data/connectivity/graph_visual/hard/graph88.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,5) (0,23) (1,6) (1,19) (1,7) (2,17) (2,24) (2,10) (2,20) (3,22) (3,27) (4,17) (4,15) (5,19) (5,12) (5,25) (6,19) (6,7) (7,18) (7,23) (8,16) (8,13) (9,27) (9,13) (10,21) (10,15) (10,11) (11,17) (11,26) (11,24) (11,14) (12,25) (12,23) (14,17) (14,26) (15,21) (17,26) (17,21) (17,24) (20,21) (20,24) (21,26) (21,24) (23,25)\nIs there a path between node 11 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph263-7_25", + "image": "data/connectivity/graph_visual/hard/graph263.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,5) (0,9) (0,3) (0,18) (0,26) (0,17) (0,4) (0,1) (0,10) (0,7) (0,22) (0,28) (0,15) (0,27) (1,11) (1,3) (1,29) (1,4) (1,7) (1,15) (1,27) (3,18) (3,6) (3,10) (3,25) (4,5) (4,11) (5,11) (5,20) (5,26) (5,10) (5,16) (5,15) (5,25) (6,19) (6,26) (6,14) (6,29) (6,30) (6,7) (6,22) (6,16) (6,15) (7,11) (7,20) (7,9) (7,18) (7,17) (7,29) (7,24) (7,30) (7,22) (7,27) (9,11) (9,26) (9,29) (9,16) (10,19) (10,26) (10,17) (10,27) (11,18) (11,26) (11,14) (11,27) (13,29) (13,25) (14,22) (14,25) (15,18) (15,22) (15,16) (15,25) (16,19) (16,17) (16,29) (16,30) (16,22) (16,28) (17,20) (17,18) (17,26) (17,24) (17,28) (17,25) (18,30) (18,22) (18,28) (18,25) (19,20) (19,24) (19,30) (20,22) (20,28) (22,30) (22,28) (24,30) (24,27) (25,28) (26,30) (27,29)\nIs there a path between node 7 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph566-31_28", + "image": "data/connectivity/graph_visual/hard/graph566.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,33) (0,17) (1,5) (1,18) (1,25) (1,23) (2,13) (2,28) (2,9) (2,21) (2,22) (2,20) (3,16) (3,20) (4,6) (4,19) (4,15) (4,18) (4,30) (4,17) (5,6) (5,32) (5,10) (5,18) (5,33) (6,32) (6,19) (6,15) (6,27) (6,26) (6,18) (6,17) (6,24) (6,25) (8,12) (9,21) (9,22) (10,32) (10,18) (10,30) (10,17) (10,25) (10,23) (11,28) (11,31) (11,16) (11,20) (13,22) (15,19) (15,27) (15,18) (15,33) (15,30) (15,24) (15,25) (15,23) (16,20) (17,27) (17,18) (17,33) (17,24) (17,29) (18,26) (18,33) (18,25) (19,27) (20,21) (21,31) (23,30) (23,25) (24,32) (24,29) (24,25) (25,33) (26,33) (26,29) (27,30) (27,29) (29,30) (30,32) (30,33) (32,33)\nIs there a path between node 31 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph443-25_32", + "image": "data/connectivity/graph_visual/hard/graph443.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (1,28) (1,23) (1,20) (1,4) (1,21) (1,13) (2,28) (2,18) (2,27) (2,31) (2,21) (2,32) (3,28) (3,8) (3,20) (3,7) (3,27) (3,29) (3,10) (3,16) (3,4) (3,6) (3,17) (3,32) (4,18) (4,23) (4,8) (4,29) (4,6) (5,28) (5,24) (5,26) (5,23) (5,8) (5,7) (5,10) (5,6) (5,9) (5,11) (6,23) (6,20) (6,10) (6,16) (6,13) (6,11) (6,32) (7,25) (7,27) (7,31) (7,10) (7,17) (7,30) (7,32) (8,26) (8,9) (9,24) (9,19) (9,27) (9,30) (9,32) (10,26) (10,23) (10,29) (10,31) (10,16) (10,21) (11,28) (11,25) (11,24) (11,19) (11,23) (11,20) (11,31) (11,13) (11,17) (12,22) (13,28) (13,25) (13,24) (13,19) (13,26) (13,23) (13,29) (13,31) (13,21) (13,15) (15,25) (15,18) (15,24) (15,21) (15,30) (16,28) (16,19) (16,26) (16,23) (16,29) (16,31) (16,30) (17,23) (17,29) (18,25) (18,19) (18,23) (18,27) (18,21) (19,29) (19,31) (20,28) (20,31) (20,32) (21,26) (21,23) (21,27) (21,29) (21,31) (23,28) (23,27) (23,29) (23,30) (24,29) (24,30) (25,31) (25,30) (26,29) (26,30) (26,32) (27,28) (27,29) (27,31) (28,29) (29,31)\nIs there a path between node 25 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph688-12_8", + "image": "data/connectivity/graph_visual/hard/graph688.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,29) (0,30) (1,19) (1,22) (1,13) (1,28) (1,26) (1,24) (1,3) (1,12) (1,7) (1,16) (1,25) (1,27) (1,11) (2,31) (2,10) (2,18) (2,9) (2,14) (2,23) (2,33) (2,32) (3,19) (3,21) (3,22) (3,28) (3,26) (3,24) (3,12) (3,7) (3,16) (3,25) (3,27) (3,11) (4,17) (5,8) (5,9) (5,23) (5,32) (6,29) (6,15) (7,19) (7,22) (7,28) (7,26) (7,24) (7,12) (7,16) (7,25) (7,27) (8,31) (8,10) (8,18) (8,14) (8,23) (8,33) (8,32) (9,31) (9,10) (9,18) (9,14) (9,23) (9,32) (10,31) (10,18) (10,14) (10,23) (10,33) (10,32) (11,19) (11,21) (11,22) (11,13) (11,28) (11,26) (11,12) (11,16) (11,27) (12,22) (12,13) (12,24) (12,16) (12,25) (12,27) (13,19) (13,22) (13,28) (13,26) (13,24) (13,16) (13,25) (14,31) (14,18) (14,23) (14,33) (14,32) (15,34) (15,30) (16,21) (16,22) (16,25) (16,27) (17,20) (18,31) (18,23) (18,32) (19,21) (19,22) (19,28) (19,26) (19,24) (19,25) (21,22) (21,28) (21,26) (21,24) (21,25) (21,27) (22,28) (22,27) (23,31) (23,33) (23,32) (24,28) (24,26) (24,27) (25,28) (25,26) (25,27) (26,28) (26,27) (30,34) (31,33)\nIs there a path between node 12 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph161-17_5", + "image": "data/connectivity/graph_visual/hard/graph161.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,13) (0,10) (0,15) (0,22) (1,5) (1,18) (1,10) (1,12) (1,22) (2,5) (2,24) (2,7) (3,14) (4,20) (5,13) (5,7) (5,12) (7,27) (7,20) (7,26) (7,24) (7,22) (9,19) (9,23) (10,18) (10,27) (10,26) (10,16) (11,21) (11,14) (12,20) (12,26) (12,24) (12,17) (13,20) (13,16) (15,16) (16,18) (17,20) (17,26) (18,26) (18,22) (19,28) (20,22) (22,27) (24,26)\nIs there a path between node 17 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph98-2_16", + "image": "data/connectivity/graph_visual/hard/graph98.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,11) (0,25) (0,13) (0,3) (0,1) (1,11) (1,25) (1,13) (1,2) (1,3) (1,8) (2,21) (2,22) (2,25) (2,13) (2,3) (3,18) (3,22) (3,11) (3,13) (4,23) (4,14) (4,6) (4,12) (4,27) (4,15) (4,5) (4,16) (4,26) (4,20) (4,7) (4,19) (5,14) (5,6) (5,12) (5,27) (5,15) (5,16) (5,9) (5,20) (5,7) (6,23) (6,14) (6,12) (6,24) (6,15) (6,16) (6,9) (6,17) (6,26) (6,20) (6,7) (6,19) (7,23) (7,14) (7,12) (7,24) (7,10) (7,16) (7,9) (7,17) (7,26) (7,20) (7,19) (8,21) (8,18) (8,22) (8,11) (8,25) (8,13) (9,23) (9,12) (9,10) (9,16) (9,17) (9,26) (9,20) (10,23) (10,14) (10,12) (10,24) (10,27) (10,16) (10,17) (10,26) (10,19) (11,21) (11,22) (11,25) (11,13) (12,23) (12,14) (12,24) (12,27) (12,16) (12,26) (12,20) (12,19) (13,22) (13,25) (14,23) (14,24) (14,16) (14,26) (14,19) (15,24) (15,27) (15,16) (15,26) (16,23) (16,27) (16,17) (16,26) (16,20) (17,27) (17,26) (17,20) (17,19) (18,22) (19,23) (19,24) (19,27) (19,26) (19,20) (20,23) (20,26) (21,22) (21,25) (22,25) (23,24) (23,27) (24,27) (24,26) (26,27)\nIs there a path between node 2 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph295-30_8", + "image": "data/connectivity/graph_visual/hard/graph295.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,3) (0,10) (0,26) (0,13) (0,23) (0,14) (0,27) (0,30) (0,31) (0,28) (0,2) (0,8) (0,12) (0,9) (0,24) (0,5) (1,19) (1,15) (1,6) (1,11) (1,29) (1,17) (1,21) (1,4) (1,25) (1,7) (2,3) (2,14) (2,31) (2,28) (2,18) (2,8) (2,12) (2,9) (2,24) (2,5) (3,10) (3,13) (3,23) (3,27) (3,30) (3,31) (3,28) (3,18) (3,8) (3,12) (3,9) (3,24) (3,5) (4,20) (4,19) (4,15) (4,11) (4,29) (4,16) (4,22) (4,7) (5,10) (5,13) (5,23) (5,14) (5,27) (5,31) (5,18) (5,8) (5,12) (5,9) (6,20) (6,15) (6,11) (6,29) (6,17) (6,21) (6,16) (6,25) (6,7) (7,20) (7,15) (7,11) (7,29) (7,17) (7,21) (7,25) (8,10) (8,26) (8,13) (8,23) (8,14) (8,27) (8,30) (8,12) (8,24) (9,10) (9,26) (9,13) (9,14) (9,27) (9,30) (9,31) (9,18) (9,24) (10,26) (10,13) (10,23) (10,14) (10,27) (10,30) (10,31) (10,18) (11,20) (11,19) (11,15) (11,29) (11,17) (11,21) (11,16) (11,25) (11,22) (12,13) (12,23) (12,14) (12,27) (12,28) (13,26) (13,23) (13,14) (13,27) (13,31) (13,28) (14,23) (14,30) (14,28) (14,18) (14,24) (15,19) (15,29) (15,21) (15,16) (15,22) (16,20) (16,19) (16,29) (16,17) (16,21) (16,25) (17,20) (17,19) (17,29) (17,21) (17,25) (17,22) (18,26) (18,27) (18,30) (18,31) (18,28) (19,29) (19,21) (19,25) (19,22) (20,29) (20,22) (21,29) (21,25) (21,22) (22,25) (23,26) (23,27) (23,30) (23,31) (23,24) (24,27) (24,30) (24,31) (25,29) (26,27) (26,30) (26,28) (27,30) (27,31) (28,30) (28,31) (30,31)\nIs there a path between node 30 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph340-2_27", + "image": "data/connectivity/graph_visual/hard/graph340.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,14) (0,13) (0,27) (1,21) (1,24) (1,13) (1,5) (2,19) (3,30) (3,26) (3,10) (3,25) (5,15) (5,9) (5,27) (5,19) (6,22) (6,29) (6,16) (7,15) (7,24) (7,9) (7,19) (9,21) (9,15) (9,24) (10,31) (10,11) (10,23) (11,23) (11,26) (11,17) (12,22) (12,29) (12,16) (13,14) (13,24) (14,21) (14,24) (14,27) (15,21) (16,29) (17,23) (17,25) (18,20) (18,29) (20,22) (21,27) (24,27) (25,28)\nIs there a path between node 2 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph594-13_2", + "image": "data/connectivity/graph_visual/hard/graph594.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,3) (0,26) (0,7) (0,22) (0,17) (0,18) (0,8) (1,20) (1,33) (1,14) (1,30) (1,25) (1,12) (1,24) (1,19) (1,28) (1,9) (1,32) (1,21) (1,13) (1,2) (1,16) (2,33) (2,14) (2,23) (2,25) (2,27) (2,4) (2,19) (2,28) (2,9) (2,32) (2,21) (2,16) (3,6) (3,5) (3,26) (3,7) (3,11) (3,22) (3,17) (3,31) (3,15) (3,18) (3,29) (3,8) (3,10) (4,33) (4,14) (4,23) (4,30) (4,27) (4,24) (4,28) (4,9) (4,32) (4,21) (4,13) (4,16) (5,6) (5,11) (5,22) (5,17) (5,31) (5,15) (5,18) (5,29) (5,10) (6,26) (6,11) (6,22) (6,17) (6,31) (6,15) (6,8) (6,10) (7,26) (7,11) (7,22) (7,31) (7,15) (7,18) (7,29) (7,8) (8,26) (8,11) (8,22) (8,31) (8,15) (8,10) (9,20) (9,33) (9,14) (9,23) (9,12) (9,27) (9,24) (9,19) (9,21) (9,13) (9,16) (10,11) (10,17) (10,31) (10,15) (10,18) (11,17) (11,31) (11,18) (11,29) (12,20) (12,23) (12,25) (12,27) (12,19) (12,28) (12,32) (12,21) (12,13) (13,33) (13,14) (13,23) (13,30) (13,27) (13,24) (13,19) (13,32) (13,21) (13,16) (14,23) (14,30) (14,27) (14,19) (14,32) (14,16) (15,22) (15,31) (15,18) (15,29) (16,20) (16,23) (16,25) (16,19) (16,28) (16,32) (16,21) (17,26) (17,22) (17,31) (17,18) (17,29) (18,31) (18,29) (19,33) (19,25) (19,27) (19,28) (19,21) (20,33) (20,30) (20,25) (20,28) (20,32) (21,23) (21,30) (21,25) (21,27) (21,24) (22,31) (22,29) (23,30) (23,25) (23,27) (23,24) (23,28) (24,33) (24,27) (24,28) (24,32) (25,30) (25,27) (25,28) (25,32) (26,31) (26,29) (27,32) (28,33) (29,31) (30,32) (32,33)\nIs there a path between node 13 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph224-5_3", + "image": "data/connectivity/graph_visual/hard/graph224.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,4) (0,19) (0,29) (0,8) (0,20) (0,3) (0,17) (0,26) (0,18) (0,23) (0,28) (0,24) (0,14) (1,15) (1,11) (1,9) (1,16) (1,5) (1,2) (1,6) (1,12) (2,15) (2,21) (2,25) (2,16) (2,5) (2,7) (2,12) (3,10) (3,4) (3,27) (3,29) (3,8) (3,13) (3,20) (3,26) (3,18) (3,23) (3,24) (3,22) (3,14) (4,10) (4,27) (4,29) (4,8) (4,20) (4,17) (4,26) (4,18) (4,23) (4,28) (4,22) (4,14) (5,21) (5,11) (5,9) (5,16) (5,6) (5,7) (6,15) (6,11) (6,25) (6,9) (6,16) (6,7) (6,12) (7,21) (7,11) (7,25) (7,9) (7,12) (8,10) (8,27) (8,19) (8,13) (8,20) (8,17) (8,18) (8,23) (8,28) (8,24) (8,22) (9,15) (9,11) (9,16) (10,27) (10,19) (10,29) (10,13) (10,17) (10,26) (10,23) (10,28) (10,24) (10,22) (10,14) (11,15) (11,25) (11,16) (11,12) (12,15) (12,25) (12,16) (13,19) (13,29) (13,20) (13,17) (13,18) (13,28) (13,24) (13,22) (13,14) (14,27) (14,19) (14,29) (14,17) (14,26) (14,18) (14,23) (14,22) (15,21) (15,25) (15,16) (16,21) (16,25) (17,27) (17,19) (17,26) (17,18) (17,23) (17,28) (18,29) (18,26) (18,28) (18,24) (18,22) (19,27) (19,26) (19,23) (19,22) (20,27) (20,29) (20,26) (20,23) (20,28) (20,24) (21,25) (22,27) (22,29) (22,26) (22,23) (22,28) (22,24) (23,27) (23,26) (23,28) (24,27) (24,29) (24,26) (26,28) (27,29) (27,28) (28,29)\nIs there a path between node 5 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph161-13_19", + "image": "data/connectivity/graph_visual/hard/graph161.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,13) (0,10) (0,15) (0,22) (1,5) (1,18) (1,10) (1,12) (1,22) (2,5) (2,24) (2,7) (3,14) (4,20) (5,13) (5,7) (5,12) (7,27) (7,20) (7,26) (7,24) (7,22) (9,19) (9,23) (10,18) (10,27) (10,26) (10,16) (11,21) (11,14) (12,20) (12,26) (12,24) (12,17) (13,20) (13,16) (15,16) (16,18) (17,20) (17,26) (18,26) (18,22) (19,28) (20,22) (22,27) (24,26)\nIs there a path between node 13 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph621-17_22", + "image": "data/connectivity/graph_visual/hard/graph621.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,9) (0,26) (0,24) (0,27) (0,11) (1,3) (1,2) (1,20) (1,6) (1,31) (2,3) (2,33) (2,30) (2,32) (2,19) (2,7) (3,31) (3,5) (4,33) (4,9) (4,30) (4,16) (4,25) (4,24) (5,30) (5,26) (5,27) (5,15) (6,33) (6,20) (6,24) (6,27) (6,11) (6,7) (7,33) (7,23) (7,30) (9,26) (9,29) (9,24) (9,31) (9,15) (10,28) (10,13) (10,22) (10,21) (11,16) (11,24) (12,15) (13,14) (13,17) (15,23) (15,20) (15,31) (16,20) (16,24) (16,19) (17,21) (19,33) (19,23) (19,25) (19,32) (20,33) (20,23) (20,32) (20,24) (20,27) (21,28) (23,33) (23,32) (24,30) (24,32) (24,29) (25,30) (25,32) (25,29) (25,27) (26,30) (26,32) (26,29) (27,33) (27,30) (29,30) (29,31) (30,32) (31,32)\nIs there a path between node 17 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph502-0_5", + "image": "data/connectivity/graph_visual/hard/graph502.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,3) (0,19) (0,28) (0,27) (1,22) (1,11) (2,33) (2,17) (3,33) (3,16) (3,7) (3,9) (5,21) (5,18) (7,25) (7,12) (7,17) (7,29) (7,9) (8,15) (8,24) (8,14) (9,25) (9,29) (10,26) (10,13) (11,23) (12,25) (12,16) (12,28) (13,30) (14,15) (14,26) (15,26) (16,27) (17,33) (17,25) (17,29) (19,25) (19,27) (20,33) (20,25) (20,29) (22,31) (24,26) (26,30) (27,33) (27,29)\nIs there a path between node 0 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph195-23_6", + "image": "data/connectivity/graph_visual/hard/graph195.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,28) (0,13) (0,26) (0,17) (0,6) (0,29) (0,18) (0,27) (1,12) (1,9) (1,20) (1,4) (1,7) (1,22) (1,11) (1,15) (2,12) (2,9) (2,23) (2,20) (2,24) (2,22) (2,11) (2,15) (3,8) (3,28) (3,26) (3,17) (3,6) (3,29) (3,25) (3,18) (3,27) (4,12) (4,9) (4,20) (4,24) (4,22) (4,11) (5,10) (5,21) (6,8) (6,28) (6,13) (6,26) (6,17) (6,25) (6,18) (7,24) (7,22) (7,11) (7,15) (8,13) (8,19) (8,29) (8,25) (8,27) (9,23) (9,20) (9,24) (9,22) (10,16) (10,14) (10,21) (11,12) (11,23) (11,20) (11,24) (12,23) (12,20) (12,24) (13,28) (13,26) (13,17) (13,19) (13,29) (13,25) (13,18) (13,27) (14,16) (15,23) (15,20) (15,24) (15,22) (17,28) (17,26) (17,19) (17,29) (17,25) (17,18) (17,27) (18,28) (18,26) (18,19) (18,25) (18,27) (19,28) (19,26) (19,29) (19,25) (20,23) (20,22) (22,23) (22,24) (23,24) (25,26) (25,29) (25,27) (26,28) (26,29) (27,28)\nIs there a path between node 23 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph271-22_10", + "image": "data/connectivity/graph_visual/hard/graph271.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,20) (1,3) (1,27) (1,23) (1,9) (1,26) (1,29) (1,15) (1,11) (1,24) (1,22) (1,10) (1,21) (1,18) (1,17) (1,2) (1,5) (1,4) (1,28) (1,7) (1,25) (2,20) (2,19) (2,3) (2,27) (2,23) (2,26) (2,29) (2,11) (2,24) (2,22) (2,21) (2,30) (2,18) (2,5) (2,4) (2,28) (2,7) (2,13) (2,25) (3,20) (3,19) (3,9) (3,26) (3,29) (3,15) (3,11) (3,24) (3,22) (3,10) (3,21) (3,30) (3,8) (3,28) (3,12) (3,7) (3,13) (3,25) (4,20) (4,19) (4,27) (4,26) (4,29) (4,15) (4,11) (4,24) (4,10) (4,30) (4,18) (4,17) (4,12) (4,7) (4,13) (4,25) (5,20) (5,19) (5,27) (5,26) (5,29) (5,24) (5,22) (5,30) (5,18) (5,8) (5,17) (5,6) (5,12) (5,13) (5,25) (6,19) (6,27) (6,23) (6,9) (6,26) (6,29) (6,15) (6,11) (6,22) (6,21) (6,30) (6,17) (6,28) (6,12) (6,7) (6,13) (6,25) (7,19) (7,27) (7,9) (7,26) (7,29) (7,15) (7,11) (7,22) (7,21) (7,30) (7,18) (7,8) (7,17) (7,28) (7,12) (7,13) (7,25) (8,20) (8,19) (8,27) (8,23) (8,9) (8,29) (8,15) (8,24) (8,22) (8,10) (8,30) (8,18) (8,17) (8,28) (8,13) (8,25) (9,20) (9,19) (9,27) (9,23) (9,11) (9,24) (9,22) (9,10) (9,30) (9,17) (9,12) (9,13) (9,25) (10,27) (10,23) (10,29) (10,15) (10,11) (10,24) (10,21) (10,30) (10,17) (10,28) (10,13) (10,25) (11,20) (11,27) (11,23) (11,29) (11,15) (11,24) (11,22) (11,21) (11,30) (11,12) (11,13) (11,25) (12,19) (12,27) (12,23) (12,26) (12,29) (12,15) (12,24) (12,22) (12,30) (12,18) (12,13) (12,25) (13,20) (13,19) (13,27) (13,26) (13,29) (13,24) (13,21) (13,18) (13,28) (14,16) (15,20) (15,19) (15,23) (15,26) (15,29) (15,24) (15,22) (15,21) (15,18) (15,28) (15,25) (17,20) (17,23) (17,24) (17,22) (17,21) (17,30) (17,28) (17,25) (18,20) (18,19) (18,23) (18,26) (18,24) (18,22) (18,30) (18,28) (18,25) (19,27) (19,29) (19,22) (19,21) (19,30) (19,25) (20,27) (20,26) (20,29) (20,24) (20,22) (20,21) (21,27) (21,23) (21,22) (21,30) (21,28) (21,25) (22,27) (22,23) (22,29) (22,24) (22,30) (22,28) (22,25) (23,27) (23,26) (23,29) (23,30) (23,28) (23,25) (24,27) (24,25) (25,26) (25,29) (25,30) (25,28) (26,30) (27,30) (27,28) (29,30)\nIs there a path between node 22 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph635-5_16", + "image": "data/connectivity/graph_visual/hard/graph635.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,25) (0,21) (0,13) (0,34) (0,12) (0,32) (0,31) (0,24) (0,15) (0,29) (1,23) (1,31) (1,14) (1,24) (1,15) (2,5) (2,25) (2,13) (2,17) (2,15) (2,29) (2,16) (3,6) (3,10) (4,20) (4,19) (5,7) (5,13) (5,17) (5,12) (5,14) (5,30) (5,26) (6,19) (6,8) (6,18) (6,27) (7,22) (7,21) (7,34) (7,32) (7,14) (7,24) (8,11) (8,19) (8,10) (9,11) (9,19) (9,10) (10,28) (11,19) (11,18) (12,21) (12,34) (12,14) (12,15) (12,30) (13,22) (13,33) (13,32) (14,34) (14,31) (14,24) (14,15) (14,29) (15,22) (15,25) (15,34) (15,31) (15,30) (16,25) (16,21) (17,23) (17,33) (17,32) (17,29) (18,20) (18,28) (20,28) (20,27) (21,25) (21,33) (21,24) (22,23) (22,33) (22,34) (23,29) (26,30) (27,28) (29,33) (30,31) (31,32) (32,33)\nIs there a path between node 5 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph280-14_30", + "image": "data/connectivity/graph_visual/hard/graph280.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,12) (0,14) (0,16) (0,20) (0,8) (0,13) (0,18) (0,10) (0,29) (0,3) (0,7) (0,9) (1,26) (1,5) (1,11) (1,19) (1,28) (1,24) (1,6) (2,12) (2,14) (2,16) (2,20) (2,8) (2,13) (2,23) (2,18) (2,25) (2,3) (2,7) (2,9) (3,16) (3,8) (3,13) (3,18) (3,25) (3,10) (3,29) (3,7) (4,15) (4,27) (5,28) (5,24) (5,22) (6,26) (6,11) (6,19) (6,28) (6,24) (6,22) (7,14) (7,16) (7,20) (7,13) (7,23) (7,25) (7,10) (7,21) (7,9) (8,14) (8,20) (8,13) (8,23) (8,10) (9,14) (9,16) (9,20) (9,13) (9,18) (9,25) (9,21) (9,29) (10,14) (10,16) (10,20) (10,13) (10,23) (10,25) (10,21) (11,26) (11,17) (11,24) (11,22) (12,14) (12,16) (12,13) (12,23) (12,18) (12,25) (12,21) (12,29) (13,14) (13,16) (13,18) (13,21) (13,29) (14,16) (14,20) (14,23) (14,18) (14,21) (14,29) (15,30) (15,27) (16,20) (16,23) (16,25) (16,21) (16,29) (17,26) (17,19) (17,28) (17,22) (18,23) (18,25) (18,21) (18,29) (19,26) (20,23) (20,25) (20,29) (21,23) (21,25) (21,29) (22,26) (22,28) (22,24) (23,25) (23,29) (24,26) (24,28) (25,29) (26,28)\nIs there a path between node 14 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph668-15_0", + "image": "data/connectivity/graph_visual/hard/graph668.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,19) (0,18) (0,12) (0,21) (0,23) (0,5) (0,26) (0,11) (0,30) (1,16) (1,19) (1,21) (1,17) (1,5) (1,26) (2,22) (2,18) (2,27) (2,23) (2,28) (2,24) (3,20) (3,14) (3,5) (3,33) (3,26) (3,25) (3,30) (4,16) (4,18) (4,21) (4,23) (4,28) (4,11) (4,25) (4,6) (5,22) (5,7) (5,18) (5,9) (5,17) (5,29) (5,28) (5,24) (5,11) (6,16) (6,20) (6,7) (6,19) (6,18) (6,14) (6,12) (6,9) (6,21) (6,23) (7,31) (7,18) (7,12) (7,9) (7,32) (7,17) (7,29) (7,26) (8,31) (8,10) (8,14) (8,9) (8,21) (8,32) (8,29) (8,33) (8,26) (9,13) (9,27) (9,12) (9,17) (9,29) (9,33) (9,28) (9,11) (9,25) (10,22) (10,31) (10,20) (10,18) (10,12) (10,23) (10,29) (10,28) (11,16) (11,13) (11,14) (11,17) (11,26) (11,30) (12,16) (12,22) (12,20) (12,13) (12,27) (12,21) (12,32) (12,17) (12,25) (13,18) (14,20) (14,32) (14,28) (14,26) (16,19) (16,17) (16,28) (16,24) (16,25) (16,30) (17,19) (17,18) (17,27) (17,25) (18,20) (18,28) (18,26) (19,22) (19,31) (19,27) (19,23) (19,29) (19,33) (20,22) (20,31) (20,23) (20,32) (20,33) (20,26) (20,30) (21,22) (21,29) (21,24) (21,25) (22,31) (22,23) (22,33) (22,26) (23,32) (23,33) (23,24) (23,30) (24,27) (24,25) (25,27) (25,32) (25,28) (25,26) (26,33) (26,30) (27,33) (27,30) (28,31) (28,29) (29,31) (29,32) (30,31) (30,33) (31,33)\nIs there a path between node 15 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph433-18_7", + "image": "data/connectivity/graph_visual/hard/graph433.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,3) (0,18) (0,20) (0,22) (0,10) (0,26) (0,2) (0,13) (0,29) (0,30) (0,12) (0,23) (1,3) (1,18) (1,24) (1,5) (1,7) (1,22) (1,6) (1,10) (1,26) (1,2) (1,29) (1,30) (1,12) (2,18) (2,24) (2,5) (2,7) (2,22) (2,6) (2,10) (2,26) (2,13) (2,29) (2,30) (2,12) (2,23) (3,18) (3,20) (3,22) (3,6) (3,10) (3,26) (3,29) (3,30) (3,12) (3,23) (4,28) (4,21) (4,32) (4,27) (4,8) (4,25) (4,17) (4,19) (4,9) (4,11) (5,18) (5,20) (5,22) (5,6) (5,26) (5,13) (5,29) (5,12) (5,23) (6,7) (6,20) (6,10) (6,26) (6,29) (6,30) (6,23) (7,24) (7,22) (7,10) (7,26) (7,29) (7,30) (7,12) (7,23) (8,28) (8,21) (8,15) (8,32) (8,27) (8,17) (8,16) (8,19) (8,9) (8,11) (9,28) (9,21) (9,31) (9,15) (9,32) (9,16) (9,14) (10,24) (10,20) (10,22) (10,26) (10,29) (10,12) (10,23) (11,28) (11,21) (11,31) (11,15) (11,32) (11,27) (11,25) (11,16) (11,19) (12,18) (12,24) (12,20) (12,22) (12,26) (12,29) (12,23) (13,18) (13,24) (13,20) (13,22) (13,29) (13,30) (14,28) (14,21) (14,15) (14,32) (14,19) (15,28) (15,21) (15,31) (15,27) (15,25) (15,17) (15,16) (16,28) (16,21) (16,32) (16,27) (17,28) (17,21) (17,32) (17,27) (17,25) (17,19) (18,24) (18,22) (18,26) (18,29) (18,23) (19,28) (19,31) (19,25) (20,24) (20,22) (20,29) (20,30) (20,23) (21,28) (21,31) (21,27) (21,25) (22,29) (22,30) (22,23) (23,24) (24,26) (24,29) (25,28) (25,31) (26,29) (26,30) (27,31) (27,32) (28,31) (28,32) (31,32)\nIs there a path between node 18 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph76-13_7", + "image": "data/connectivity/graph_visual/hard/graph76.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,25) (0,17) (0,1) (0,22) (0,5) (0,26) (0,12) (0,6) (0,11) (0,2) (0,10) (0,9) (0,3) (0,14) (0,4) (0,23) (0,21) (1,17) (1,22) (1,5) (1,26) (1,24) (1,8) (1,16) (1,10) (1,9) (1,3) (1,14) (1,4) (1,23) (2,17) (2,18) (2,24) (2,12) (2,6) (2,11) (2,16) (2,10) (2,15) (2,9) (2,3) (2,14) (2,23) (3,25) (3,22) (3,5) (3,26) (3,24) (3,12) (3,6) (3,8) (3,11) (3,16) (3,10) (3,15) (3,14) (3,4) (3,23) (3,21) (4,25) (4,22) (4,18) (4,26) (4,8) (4,11) (4,16) (4,10) (4,15) (4,14) (4,21) (5,25) (5,22) (5,18) (5,24) (5,12) (5,6) (5,8) (5,11) (5,16) (5,10) (5,15) (5,9) (5,14) (5,23) (5,21) (6,25) (6,17) (6,18) (6,24) (6,8) (6,11) (6,16) (6,15) (6,9) (6,14) (7,13) (7,19) (7,20) (8,22) (8,26) (8,24) (8,12) (8,11) (8,15) (8,9) (9,25) (9,17) (9,22) (9,18) (9,26) (9,24) (9,10) (9,15) (9,14) (9,23) (9,21) (10,25) (10,18) (10,26) (10,11) (10,14) (10,23) (10,21) (11,25) (11,17) (11,22) (11,24) (11,16) (11,15) (11,14) (11,21) (12,18) (12,24) (12,23) (13,20) (14,25) (14,18) (14,26) (14,24) (14,15) (14,23) (14,21) (15,25) (15,17) (15,22) (15,18) (15,24) (15,16) (15,23) (16,17) (16,22) (16,18) (16,26) (17,22) (17,18) (17,24) (17,23) (18,25) (18,22) (18,24) (18,21) (19,20) (21,25) (21,26) (21,24) (21,23) (22,25) (22,23) (23,24) (24,25) (24,26)\nIs there a path between node 13 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph33-25_20", + "image": "data/connectivity/graph_visual/hard/graph33.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,22) (0,7) (0,18) (0,14) (0,20) (0,13) (0,24) (0,17) (1,25) (1,9) (1,21) (1,15) (1,23) (1,19) (1,16) (1,8) (2,9) (2,21) (2,23) (2,19) (2,6) (2,3) (2,8) (2,5) (3,25) (3,21) (3,15) (3,23) (3,4) (3,19) (4,25) (4,10) (4,9) (4,21) (4,23) (4,19) (4,6) (4,5) (5,25) (5,10) (5,9) (5,23) (5,16) (5,8) (6,9) (6,21) (6,15) (6,19) (6,16) (7,22) (7,14) (7,13) (7,24) (7,17) (8,25) (8,10) (8,9) (8,21) (8,15) (8,23) (8,19) (8,16) (9,10) (9,15) (9,19) (9,16) (10,23) (10,16) (11,22) (11,18) (11,14) (11,20) (11,12) (11,13) (11,24) (11,17) (12,22) (12,18) (12,20) (12,24) (12,17) (13,18) (13,14) (13,20) (13,24) (13,17) (14,22) (14,18) (14,20) (14,24) (14,17) (15,25) (15,21) (15,19) (15,16) (16,25) (16,21) (16,23) (17,18) (17,20) (17,24) (18,22) (18,20) (18,24) (19,25) (19,21) (20,22) (20,24) (21,25) (21,23) (23,25)\nIs there a path between node 25 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph477-25_24", + "image": "data/connectivity/graph_visual/hard/graph477.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,4) (0,16) (0,9) (1,2) (1,10) (1,26) (1,18) (1,3) (1,31) (1,28) (1,12) (1,23) (1,27) (1,7) (1,32) (1,8) (1,21) (1,6) (2,25) (2,11) (2,10) (2,26) (2,18) (2,3) (2,31) (2,28) (2,23) (2,19) (2,27) (2,32) (2,8) (2,6) (3,10) (3,26) (3,18) (3,12) (3,23) (3,19) (3,27) (3,7) (3,32) (3,29) (3,8) (3,21) (3,6) (4,20) (4,24) (4,30) (4,9) (5,15) (6,25) (6,11) (6,10) (6,26) (6,31) (6,28) (6,23) (6,19) (6,32) (6,29) (6,8) (6,21) (7,11) (7,10) (7,26) (7,31) (7,28) (7,12) (7,19) (7,27) (7,29) (8,25) (8,11) (8,10) (8,26) (8,28) (8,12) (8,23) (8,19) (8,27) (8,29) (8,21) (9,20) (9,24) (9,14) (9,17) (9,16) (9,30) (10,25) (10,11) (10,26) (10,18) (10,31) (10,28) (10,23) (10,19) (10,27) (10,29) (10,21) (11,25) (11,31) (11,28) (11,12) (11,19) (11,27) (11,32) (12,25) (12,26) (12,18) (12,31) (12,23) (12,19) (12,27) (12,32) (13,20) (13,22) (13,14) (13,17) (13,16) (13,30) (14,20) (14,22) (14,17) (14,30) (16,20) (16,22) (17,20) (17,22) (18,25) (18,31) (18,28) (18,23) (18,27) (18,32) (19,26) (19,31) (19,23) (19,27) (19,32) (19,29) (19,21) (20,22) (20,24) (20,30) (21,25) (21,23) (21,32) (21,29) (23,25) (23,26) (23,31) (23,27) (24,30) (25,26) (25,28) (25,27) (25,29) (26,31) (26,32) (26,29) (27,31) (27,28) (27,29) (28,32) (28,29) (29,32) (31,32)\nIs there a path between node 25 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph10-8_16", + "image": "data/connectivity/graph_visual/hard/graph10.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,4) (0,16) (0,25) (0,14) (0,21) (0,11) (0,9) (0,5) (0,23) (0,6) (1,4) (1,16) (1,14) (1,13) (1,21) (1,11) (1,9) (1,10) (1,5) (1,23) (1,15) (1,20) (1,6) (2,18) (2,4) (2,16) (2,25) (2,14) (2,21) (2,9) (2,10) (2,5) (2,15) (2,20) (2,6) (3,12) (3,19) (3,24) (3,17) (3,7) (3,22) (3,8) (4,16) (4,25) (4,14) (4,21) (4,11) (4,9) (4,10) (4,5) (4,23) (4,15) (4,20) (4,6) (5,18) (5,16) (5,25) (5,13) (5,21) (5,11) (5,10) (5,15) (5,6) (6,18) (6,16) (6,25) (6,14) (6,13) (6,21) (6,11) (6,9) (6,10) (6,23) (6,20) (7,12) (7,24) (7,17) (7,22) (8,12) (8,19) (9,18) (9,25) (9,14) (9,13) (9,21) (9,11) (9,10) (9,23) (9,20) (10,18) (10,16) (10,25) (10,14) (10,21) (10,11) (10,15) (11,18) (11,16) (11,25) (11,14) (11,21) (11,23) (12,19) (12,24) (12,17) (12,22) (13,16) (13,14) (13,21) (13,23) (13,20) (14,18) (14,25) (14,20) (15,18) (15,16) (15,25) (15,21) (15,23) (15,20) (16,18) (16,25) (16,23) (17,19) (17,24) (17,22) (18,25) (18,21) (18,23) (19,22) (20,25) (20,21) (21,25) (21,23) (22,24) (23,25)\nIs there a path between node 8 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph567-27_30", + "image": "data/connectivity/graph_visual/hard/graph567.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,5) (0,1) (0,21) (0,24) (0,33) (0,22) (1,10) (1,20) (1,18) (1,14) (1,13) (1,22) (2,7) (2,12) (2,6) (2,28) (2,31) (3,17) (3,16) (3,30) (3,28) (3,25) (5,8) (5,29) (5,19) (5,18) (5,24) (5,22) (6,26) (6,16) (6,30) (6,25) (7,12) (7,17) (7,26) (8,19) (8,24) (8,23) (9,18) (9,32) (9,22) (10,13) (10,22) (11,29) (11,20) (11,14) (11,23) (11,13) (11,32) (11,22) (12,30) (13,24) (13,23) (13,15) (14,29) (14,18) (14,24) (15,20) (15,23) (15,32) (15,22) (16,30) (16,25) (16,31) (17,25) (18,20) (18,21) (18,24) (18,27) (19,33) (19,27) (19,32) (19,22) (20,29) (20,21) (20,24) (20,23) (21,29) (22,33) (22,23) (23,29) (24,27) (25,30) (25,31) (26,28) (27,32)\nIs there a path between node 27 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph573-22_32", + "image": "data/connectivity/graph_visual/hard/graph573.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,33) (1,32) (1,10) (1,25) (1,17) (1,13) (2,22) (2,5) (2,26) (3,9) (3,15) (3,21) (5,27) (6,22) (6,12) (6,31) (6,8) (6,29) (7,31) (7,26) (8,27) (8,12) (8,26) (9,21) (10,32) (10,11) (11,32) (11,20) (11,19) (12,24) (12,29) (13,14) (13,32) (13,30) (13,19) (13,17) (15,18) (17,32) (17,23) (17,25) (19,23) (19,20) (20,25) (22,31) (22,26) (23,32) (26,27) (30,32)\nIs there a path between node 22 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph461-18_9", + "image": "data/connectivity/graph_visual/hard/graph461.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,10) (0,23) (0,27) (0,9) (1,16) (1,3) (1,4) (1,21) (1,26) (1,2) (2,31) (2,16) (2,15) (2,6) (2,17) (3,24) (3,8) (3,19) (3,16) (3,30) (3,5) (3,4) (3,15) (3,7) (3,11) (4,24) (4,8) (4,30) (4,21) (4,12) (4,26) (4,7) (4,11) (5,21) (5,6) (5,26) (6,30) (6,21) (6,11) (7,24) (8,31) (8,24) (8,19) (8,12) (9,27) (10,18) (10,23) (10,14) (11,31) (11,24) (11,21) (12,24) (12,19) (12,30) (12,15) (12,21) (13,32) (13,18) (13,29) (14,32) (14,23) (15,19) (15,16) (16,24) (16,19) (17,19) (18,32) (18,23) (18,28) (19,24) (19,30) (19,26) (21,31) (21,30) (21,26) (26,30) (27,32) (28,32) (30,31)\nIs there a path between node 18 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph114-18_1", + "image": "data/connectivity/graph_visual/hard/graph114.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,11) (0,16) (1,13) (2,27) (2,10) (2,5) (2,25) (2,16) (2,4) (3,10) (3,21) (3,7) (4,5) (4,22) (4,25) (4,21) (4,16) (4,6) (4,14) (5,10) (5,22) (5,25) (5,21) (5,11) (5,16) (5,19) (6,21) (6,19) (7,10) (7,21) (7,14) (7,19) (8,15) (9,13) (9,20) (9,23) (10,22) (10,11) (10,16) (10,19) (11,25) (12,15) (13,20) (14,16) (14,19) (15,24) (15,20) (16,27) (16,22) (16,25) (17,27) (17,22) (17,25) (19,27) (19,26) (20,23) (21,25) (21,26) (25,27) (26,27)\nIs there a path between node 18 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph266-24_17", + "image": "data/connectivity/graph_visual/hard/graph266.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,20) (0,12) (0,25) (0,2) (0,23) (0,17) (0,28) (0,5) (0,10) (0,19) (1,30) (1,9) (1,15) (1,6) (1,10) (1,18) (2,20) (2,12) (2,8) (2,21) (2,28) (2,22) (2,10) (2,3) (2,4) (2,18) (3,25) (3,13) (3,21) (3,28) (3,29) (3,4) (3,18) (4,25) (4,30) (4,13) (4,23) (4,17) (4,28) (4,5) (4,15) (4,14) (4,7) (4,18) (5,20) (5,12) (5,30) (5,13) (5,9) (5,28) (5,16) (5,14) (5,11) (6,12) (6,25) (6,13) (6,21) (6,29) (6,19) (7,13) (7,8) (7,23) (7,28) (7,29) (8,27) (8,21) (8,23) (8,28) (8,22) (8,18) (9,20) (9,12) (9,18) (10,13) (10,22) (10,14) (10,29) (11,20) (11,13) (11,17) (11,15) (12,25) (12,23) (12,28) (12,18) (13,30) (13,27) (13,21) (13,16) (13,14) (14,30) (14,21) (14,16) (14,29) (14,19) (15,20) (15,30) (15,23) (16,20) (16,25) (16,21) (16,28) (17,20) (17,30) (17,28) (18,30) (18,27) (18,23) (18,22) (18,29) (19,23) (19,29) (20,30) (20,23) (20,29) (21,28) (22,29) (23,25) (23,30) (23,28) (25,29) (27,28) (28,30) (29,30)\nIs there a path between node 24 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph285-30_17", + "image": "data/connectivity/graph_visual/hard/graph285.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,3) (0,11) (0,15) (0,25) (0,31) (0,23) (0,14) (1,28) (1,20) (1,12) (1,21) (1,19) (1,24) (1,27) (1,13) (1,6) (2,20) (2,22) (2,21) (2,19) (2,13) (2,6) (3,15) (3,4) (3,25) (3,23) (4,9) (4,15) (4,14) (5,8) (5,17) (5,10) (5,26) (5,7) (5,16) (6,20) (6,21) (6,19) (6,27) (6,13) (7,17) (7,16) (7,29) (8,17) (9,11) (9,15) (9,31) (9,23) (9,14) (10,17) (11,15) (11,30) (11,23) (11,14) (12,20) (12,22) (12,19) (12,27) (12,13) (12,18) (13,28) (13,22) (13,21) (13,24) (13,27) (13,18) (14,15) (14,25) (14,31) (14,23) (15,25) (15,30) (15,23) (16,26) (17,26) (17,29) (18,28) (18,20) (18,22) (18,21) (18,19) (18,24) (18,27) (19,22) (19,21) (19,24) (19,27) (20,28) (20,22) (20,21) (20,24) (20,27) (21,28) (21,22) (21,24) (22,24) (22,27) (23,30) (23,31) (24,28) (25,31) (27,28) (30,31)\nIs there a path between node 30 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph448-3_4", + "image": "data/connectivity/graph_visual/hard/graph448.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,10) (0,30) (0,14) (0,26) (0,7) (0,8) (0,17) (1,24) (1,21) (1,29) (1,19) (2,11) (2,10) (2,30) (2,23) (2,32) (2,7) (3,29) (3,19) (4,18) (5,11) (5,14) (5,6) (5,22) (5,7) (6,10) (6,14) (6,32) (6,17) (7,30) (8,11) (8,10) (8,27) (8,14) (8,22) (8,32) (9,28) (9,16) (10,11) (10,30) (10,27) (10,14) (10,26) (10,22) (10,17) (11,14) (12,16) (13,28) (13,31) (14,27) (14,20) (14,23) (14,32) (16,31) (17,30) (17,26) (17,23) (18,24) (18,25) (19,29) (19,25) (20,23) (21,24) (21,29) (22,30) (22,26) (23,30) (23,26) (24,29) (25,29) (26,30) (26,27) (27,30) (30,32)\nIs there a path between node 3 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph481-17_1", + "image": "data/connectivity/graph_visual/hard/graph481.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,17) (0,21) (0,16) (0,23) (0,24) (0,8) (0,28) (0,31) (0,10) (0,32) (0,3) (0,5) (1,23) (1,15) (1,29) (1,28) (1,31) (1,26) (1,30) (1,10) (1,32) (1,3) (1,2) (1,5) (2,17) (2,27) (2,16) (2,23) (2,15) (2,24) (2,8) (2,31) (2,32) (2,3) (2,5) (3,27) (3,16) (3,23) (3,15) (3,8) (3,29) (3,28) (3,26) (3,10) (4,6) (5,17) (5,27) (5,21) (5,16) (5,23) (5,15) (5,8) (5,29) (5,28) (5,26) (5,7) (5,30) (5,10) (6,19) (7,17) (7,21) (7,16) (7,23) (7,24) (7,8) (7,29) (7,28) (7,31) (7,30) (7,32) (8,17) (8,27) (8,23) (8,15) (8,24) (8,28) (8,31) (8,26) (8,30) (8,10) (8,32) (9,13) (9,18) (9,12) (9,20) (9,11) (10,27) (10,16) (10,23) (10,15) (10,24) (10,29) (10,28) (10,26) (10,30) (11,13) (11,18) (11,12) (11,25) (11,14) (11,22) (12,13) (12,18) (12,25) (12,14) (12,20) (13,18) (13,14) (13,20) (13,22) (14,18) (14,22) (15,17) (15,24) (15,28) (15,31) (15,26) (15,30) (15,32) (16,27) (16,21) (16,23) (16,29) (16,28) (16,31) (16,30) (17,23) (17,24) (17,29) (17,28) (17,30) (17,32) (18,20) (20,22) (21,23) (21,24) (21,29) (21,31) (21,26) (21,30) (21,32) (22,25) (23,29) (23,31) (23,32) (24,27) (24,29) (26,27) (26,29) (26,31) (26,30) (26,32) (27,28) (27,31) (27,32) (28,29) (28,30) (28,32) (29,31) (29,32) (30,31) (31,32)\nIs there a path between node 17 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph97-20_4", + "image": "data/connectivity/graph_visual/hard/graph97.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,2) (0,8) (0,4) (0,9) (0,16) (0,21) (0,12) (0,23) (0,7) (0,11) (1,25) (1,22) (2,8) (2,26) (2,16) (2,20) (3,10) (3,16) (3,13) (3,14) (3,11) (4,26) (4,21) (4,12) (4,14) (5,10) (5,21) (5,13) (5,23) (5,7) (5,14) (5,15) (6,10) (6,9) (6,13) (6,12) (6,23) (6,14) (6,20) (6,15) (7,9) (7,16) (7,18) (7,23) (7,14) (7,15) (7,17) (8,10) (8,9) (8,16) (8,15) (8,11) (9,10) (9,26) (9,14) (9,17) (10,16) (12,18) (12,13) (13,18) (13,15) (14,21) (14,15) (15,26) (15,20) (16,18) (16,20) (17,20) (19,24) (19,22) (20,26) (20,21) (22,27)\nIs there a path between node 20 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph49-13_11", + "image": "data/connectivity/graph_visual/hard/graph49.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,25) (0,23) (0,10) (1,22) (1,7) (1,8) (1,10) (1,20) (2,14) (2,18) (2,12) (2,26) (3,19) (3,8) (4,7) (4,25) (4,20) (5,12) (5,11) (5,26) (5,9) (6,19) (6,23) (6,16) (7,13) (7,23) (7,24) (7,16) (8,20) (9,14) (10,13) (10,22) (10,23) (10,24) (11,14) (11,21) (11,26) (12,21) (13,24) (13,16) (15,22) (15,17) (16,22) (16,20) (17,25) (17,24) (18,26) (19,22) (19,23) (19,20) (20,23) (20,24) (21,26) (23,24) (24,25)\nIs there a path between node 13 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph439-6_19", + "image": "data/connectivity/graph_visual/hard/graph439.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,12) (0,15) (0,27) (0,11) (0,32) (0,23) (0,17) (0,21) (0,19) (0,14) (0,22) (0,29) (0,16) (0,5) (0,4) (0,2) (0,1) (1,15) (1,27) (1,32) (1,23) (1,21) (1,3) (1,14) (1,20) (1,7) (1,29) (1,16) (1,5) (1,4) (1,2) (1,13) (2,12) (2,15) (2,11) (2,18) (2,32) (2,23) (2,3) (2,19) (2,14) (2,28) (2,22) (2,7) (2,29) (2,16) (2,4) (2,13) (3,27) (3,11) (3,32) (3,23) (3,21) (3,10) (3,19) (3,14) (3,28) (3,7) (3,29) (3,16) (3,4) (4,15) (4,27) (4,11) (4,18) (4,32) (4,23) (4,17) (4,21) (4,10) (4,19) (4,14) (4,20) (4,29) (4,5) (4,8) (4,13) (5,12) (5,15) (5,27) (5,11) (5,18) (5,32) (5,23) (5,17) (5,21) (5,10) (5,28) (5,29) (5,16) (5,8) (6,25) (7,12) (7,15) (7,27) (7,11) (7,18) (7,32) (7,23) (7,17) (7,21) (7,10) (7,19) (7,20) (7,29) (7,16) (7,13) (8,15) (8,11) (8,18) (8,32) (8,23) (8,17) (8,28) (8,22) (8,20) (8,13) (9,31) (9,26) (9,30) (10,27) (10,32) (10,23) (10,17) (10,21) (10,19) (10,14) (10,28) (10,22) (10,20) (10,29) (10,16) (11,12) (11,15) (11,27) (11,18) (11,32) (11,23) (11,21) (11,14) (11,28) (11,22) (11,29) (11,16) (11,13) (12,18) (12,32) (12,23) (12,17) (12,21) (12,19) (12,22) (12,29) (12,13) (13,15) (13,27) (13,18) (13,32) (13,23) (13,14) (13,28) (13,22) (13,20) (13,29) (13,16) (14,15) (14,18) (14,32) (14,17) (14,21) (14,19) (14,22) (14,29) (15,27) (15,18) (15,32) (15,21) (15,28) (15,16) (16,27) (16,18) (16,32) (16,23) (16,17) (16,21) (16,28) (16,29) (17,23) (17,21) (17,19) (17,22) (17,20) (17,29) (18,27) (18,32) (18,23) (18,21) (18,19) (18,28) (18,22) (19,32) (19,23) (19,21) (19,28) (19,20) (19,29) (20,27) (20,21) (20,22) (20,29) (21,27) (21,32) (21,23) (21,28) (21,22) (21,29) (22,27) (22,23) (22,28) (22,29) (23,27) (23,32) (23,28) (24,26) (26,31) (26,30) (27,32) (27,28) (27,29) (28,29) (29,32) (30,31)\nIs there a path between node 6 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph433-12_6", + "image": "data/connectivity/graph_visual/hard/graph433.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,3) (0,18) (0,20) (0,22) (0,10) (0,26) (0,2) (0,13) (0,29) (0,30) (0,12) (0,23) (1,3) (1,18) (1,24) (1,5) (1,7) (1,22) (1,6) (1,10) (1,26) (1,2) (1,29) (1,30) (1,12) (2,18) (2,24) (2,5) (2,7) (2,22) (2,6) (2,10) (2,26) (2,13) (2,29) (2,30) (2,12) (2,23) (3,18) (3,20) (3,22) (3,6) (3,10) (3,26) (3,29) (3,30) (3,12) (3,23) (4,28) (4,21) (4,32) (4,27) (4,8) (4,25) (4,17) (4,19) (4,9) (4,11) (5,18) (5,20) (5,22) (5,6) (5,26) (5,13) (5,29) (5,12) (5,23) (6,7) (6,20) (6,10) (6,26) (6,29) (6,30) (6,23) (7,24) (7,22) (7,10) (7,26) (7,29) (7,30) (7,12) (7,23) (8,28) (8,21) (8,15) (8,32) (8,27) (8,17) (8,16) (8,19) (8,9) (8,11) (9,28) (9,21) (9,31) (9,15) (9,32) (9,16) (9,14) (10,24) (10,20) (10,22) (10,26) (10,29) (10,12) (10,23) (11,28) (11,21) (11,31) (11,15) (11,32) (11,27) (11,25) (11,16) (11,19) (12,18) (12,24) (12,20) (12,22) (12,26) (12,29) (12,23) (13,18) (13,24) (13,20) (13,22) (13,29) (13,30) (14,28) (14,21) (14,15) (14,32) (14,19) (15,28) (15,21) (15,31) (15,27) (15,25) (15,17) (15,16) (16,28) (16,21) (16,32) (16,27) (17,28) (17,21) (17,32) (17,27) (17,25) (17,19) (18,24) (18,22) (18,26) (18,29) (18,23) (19,28) (19,31) (19,25) (20,24) (20,22) (20,29) (20,30) (20,23) (21,28) (21,31) (21,27) (21,25) (22,29) (22,30) (22,23) (23,24) (24,26) (24,29) (25,28) (25,31) (26,29) (26,30) (27,31) (27,32) (28,31) (28,32) (31,32)\nIs there a path between node 12 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph128-14_0", + "image": "data/connectivity/graph_visual/hard/graph128.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,12) (0,14) (0,10) (0,17) (0,18) (0,1) (0,13) (0,11) (0,23) (0,4) (1,19) (1,12) (1,14) (1,6) (1,17) (1,18) (1,13) (1,7) (1,27) (1,23) (2,5) (2,8) (3,21) (3,20) (3,15) (3,25) (4,19) (4,22) (4,10) (4,6) (4,17) (4,18) (4,13) (4,7) (4,27) (5,8) (6,22) (6,12) (6,14) (6,10) (6,17) (6,18) (6,13) (6,11) (6,23) (7,22) (7,26) (7,14) (7,10) (7,17) (7,18) (7,9) (9,26) (9,14) (9,10) (9,17) (9,13) (9,11) (9,27) (9,23) (10,19) (10,26) (10,14) (10,17) (10,18) (10,13) (10,27) (10,23) (11,19) (11,22) (11,26) (11,12) (11,14) (11,17) (11,13) (11,27) (12,19) (12,22) (12,14) (12,17) (12,18) (12,27) (13,19) (13,26) (13,14) (13,17) (13,18) (14,19) (14,18) (14,23) (15,21) (15,16) (15,20) (15,25) (16,21) (17,23) (18,19) (18,22) (18,26) (19,27) (20,21) (20,24) (21,25) (22,26) (22,27) (22,23) (23,26) (23,27) (24,25) (26,27)\nIs there a path between node 14 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph535-23_24", + "image": "data/connectivity/graph_visual/hard/graph535.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,15) (0,8) (0,32) (0,26) (0,11) (1,29) (1,6) (1,23) (1,31) (1,18) (1,30) (1,4) (1,24) (1,22) (1,16) (1,33) (1,5) (1,25) (2,10) (2,14) (2,28) (2,12) (2,20) (2,27) (3,29) (3,6) (3,23) (3,31) (3,9) (3,4) (3,22) (3,16) (3,33) (3,5) (3,25) (4,29) (4,6) (4,23) (4,31) (4,30) (4,9) (4,24) (4,22) (4,33) (4,25) (5,6) (5,23) (5,31) (5,18) (5,30) (5,9) (5,24) (5,7) (5,16) (5,33) (5,25) (6,29) (6,31) (6,18) (6,30) (6,9) (6,7) (6,22) (6,16) (6,33) (6,25) (7,23) (7,31) (7,18) (7,30) (7,9) (7,24) (7,22) (7,16) (7,25) (8,15) (8,19) (8,26) (9,29) (9,23) (9,18) (9,30) (9,16) (9,25) (10,21) (10,17) (10,28) (10,20) (10,27) (10,13) (11,15) (11,32) (11,19) (11,26) (12,21) (12,17) (12,28) (12,20) (12,27) (12,13) (13,21) (13,17) (13,20) (13,27) (14,21) (14,17) (14,28) (14,27) (15,26) (16,29) (16,23) (16,18) (16,30) (16,24) (16,33) (16,25) (17,21) (17,28) (17,20) (18,31) (18,30) (18,22) (18,33) (18,25) (19,32) (19,26) (20,21) (20,28) (20,27) (21,28) (22,29) (22,30) (22,33) (22,25) (23,31) (23,30) (23,33) (24,29) (24,31) (24,30) (24,33) (24,25) (25,29) (25,31) (26,32) (27,28) (29,31) (29,33) (30,33) (31,33)\nIs there a path between node 23 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph9-5_15", + "image": "data/connectivity/graph_visual/hard/graph9.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,2) (0,10) (0,13) (0,12) (0,9) (0,18) (0,24) (0,5) (0,20) (0,21) (0,7) (0,3) (0,23) (1,2) (1,13) (1,16) (1,12) (1,18) (1,24) (1,20) (1,4) (1,7) (1,3) (1,19) (1,23) (2,13) (2,16) (2,12) (2,9) (2,11) (2,18) (2,24) (2,5) (2,20) (2,4) (2,21) (2,7) (2,3) (2,23) (3,13) (3,16) (3,12) (3,9) (3,11) (3,24) (3,5) (3,20) (3,21) (3,7) (3,19) (3,23) (4,10) (4,16) (4,12) (4,11) (4,18) (4,24) (4,5) (4,20) (4,21) (4,7) (4,19) (4,23) (5,13) (5,12) (5,11) (5,18) (5,24) (5,20) (5,21) (5,7) (5,23) (6,15) (6,25) (6,22) (6,8) (7,13) (7,12) (7,9) (7,11) (7,18) (7,20) (7,21) (7,19) (8,17) (8,15) (8,22) (8,14) (9,10) (9,13) (9,16) (9,11) (9,18) (9,21) (9,19) (9,23) (10,13) (10,12) (10,11) (10,24) (10,20) (10,21) (10,19) (10,23) (11,13) (11,16) (11,24) (11,20) (11,21) (11,19) (11,23) (12,13) (12,16) (12,18) (12,24) (12,20) (12,21) (12,19) (12,23) (13,16) (13,24) (13,21) (13,23) (14,17) (14,15) (14,22) (15,17) (15,25) (15,22) (16,18) (16,24) (16,21) (16,23) (17,25) (17,22) (18,20) (18,21) (18,19) (18,23) (19,20) (19,23) (20,24) (20,21) (21,23) (22,25) (23,24)\nIs there a path between node 5 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph245-14_3", + "image": "data/connectivity/graph_visual/hard/graph245.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,3) (0,14) (0,17) (0,2) (0,25) (0,8) (0,21) (0,10) (0,18) (0,19) (0,26) (0,4) (0,29) (0,20) (0,13) (0,12) (1,3) (1,14) (1,17) (1,25) (1,8) (1,21) (1,16) (1,15) (1,10) (1,19) (1,9) (1,4) (1,5) (1,29) (1,30) (1,27) (1,13) (1,12) (2,3) (2,17) (2,24) (2,8) (2,16) (2,15) (2,26) (2,4) (2,29) (2,30) (2,27) (2,13) (3,14) (3,17) (3,24) (3,25) (3,8) (3,21) (3,16) (3,10) (3,9) (3,26) (3,29) (3,30) (3,27) (3,20) (3,13) (3,12) (4,25) (4,8) (4,21) (4,16) (4,10) (4,18) (4,19) (4,9) (4,5) (4,30) (4,27) (4,20) (5,14) (5,17) (5,24) (5,8) (5,21) (5,16) (5,15) (5,10) (5,18) (5,19) (5,9) (5,26) (5,30) (5,27) (5,20) (6,22) (6,7) (6,23) (8,14) (8,17) (8,25) (8,16) (8,15) (8,18) (8,19) (8,9) (8,26) (8,29) (8,30) (8,27) (8,13) (9,14) (9,17) (9,24) (9,25) (9,16) (9,15) (9,10) (9,26) (9,30) (9,20) (9,13) (10,14) (10,17) (10,24) (10,25) (10,21) (10,18) (10,29) (10,30) (10,27) (10,20) (10,13) (10,12) (11,28) (12,14) (12,25) (12,21) (12,16) (12,18) (12,19) (12,29) (12,27) (13,14) (13,17) (13,24) (13,16) (13,15) (13,19) (13,29) (13,30) (13,27) (14,17) (14,25) (14,21) (14,18) (14,19) (14,26) (14,29) (14,27) (14,20) (15,17) (15,24) (15,25) (15,16) (15,18) (15,19) (15,26) (15,29) (15,30) (15,20) (16,17) (16,24) (16,19) (16,26) (16,29) (16,30) (16,27) (16,20) (17,24) (17,21) (17,19) (17,30) (17,27) (18,24) (18,25) (18,21) (18,19) (18,26) (18,29) (18,30) (18,27) (19,25) (19,26) (19,29) (19,27) (19,20) (20,24) (20,25) (20,26) (20,29) (20,30) (20,27) (21,25) (21,26) (21,29) (21,30) (21,27) (24,25) (24,26) (24,29) (24,27) (25,26) (25,30) (25,27) (26,30) (26,27) (27,29) (29,30)\nIs there a path between node 14 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph548-3_27", + "image": "data/connectivity/graph_visual/hard/graph548.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,2) (0,31) (1,4) (1,27) (1,25) (2,31) (2,24) (2,13) (2,10) (3,30) (3,32) (3,27) (3,15) (4,30) (4,6) (4,28) (4,8) (5,22) (6,27) (7,20) (7,11) (7,12) (8,15) (9,14) (10,17) (10,23) (10,13) (11,14) (12,18) (13,23) (14,22) (15,30) (15,27) (15,25) (15,16) (15,28) (17,23) (17,21) (18,22) (18,33) (20,22) (21,31) (23,24) (25,30) (25,27) (25,28) (26,31) (27,30) (27,32) (28,32)\nIs there a path between node 3 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph246-14_16", + "image": "data/connectivity/graph_visual/hard/graph246.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,3) (0,15) (0,14) (0,1) (0,10) (0,29) (0,20) (0,26) (0,22) (0,18) (0,7) (0,4) (0,2) (1,27) (1,14) (1,10) (1,12) (1,20) (1,26) (1,22) (1,18) (1,11) (1,7) (1,4) (1,2) (2,3) (2,27) (2,15) (2,10) (2,12) (2,20) (2,26) (2,22) (2,18) (2,11) (2,7) (2,4) (2,25) (2,21) (2,19) (3,27) (3,15) (3,14) (3,10) (3,29) (3,20) (3,22) (3,18) (3,11) (3,4) (3,25) (3,21) (3,19) (4,15) (4,14) (4,10) (4,29) (4,12) (4,20) (4,26) (4,18) (4,25) (4,21) (4,19) (5,17) (5,6) (5,30) (5,16) (5,13) (5,24) (5,9) (6,23) (6,30) (6,16) (6,13) (6,8) (6,24) (6,9) (7,27) (7,15) (7,10) (7,29) (7,12) (7,20) (7,26) (7,22) (7,11) (7,25) (7,19) (8,17) (8,28) (8,23) (8,30) (8,16) (8,13) (8,24) (8,9) (9,28) (9,23) (9,30) (9,16) (10,15) (10,14) (10,12) (10,20) (10,26) (10,22) (10,18) (10,11) (10,25) (10,19) (11,27) (11,15) (11,14) (11,12) (11,20) (11,26) (11,22) (11,18) (11,25) (11,21) (12,27) (12,15) (12,14) (12,20) (12,26) (12,22) (12,21) (13,17) (13,28) (13,23) (13,30) (13,16) (14,27) (14,15) (14,20) (14,26) (14,22) (14,18) (14,25) (14,21) (14,19) (15,20) (15,26) (15,22) (15,18) (15,21) (16,17) (16,28) (16,23) (16,24) (17,28) (17,23) (17,30) (18,27) (18,29) (18,20) (18,21) (18,19) (19,29) (19,20) (19,25) (19,21) (20,27) (20,26) (20,22) (20,25) (20,21) (21,29) (21,26) (21,22) (21,25) (22,29) (22,25) (23,28) (23,30) (24,28) (26,27) (26,29) (27,29)\nIs there a path between node 14 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph447-30_22", + "image": "data/connectivity/graph_visual/hard/graph447.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (1,11) (1,25) (1,27) (1,20) (1,24) (2,14) (3,19) (3,17) (5,18) (5,27) (5,28) (6,7) (6,13) (6,29) (7,8) (7,10) (7,17) (8,31) (8,13) (9,10) (9,13) (10,19) (10,12) (11,25) (11,28) (12,13) (12,29) (13,29) (15,22) (15,25) (15,23) (15,27) (18,22) (18,23) (18,24) (19,31) (19,29) (20,23) (20,28) (20,24) (21,26) (22,25) (22,23) (22,27) (25,28) (27,28)\nIs there a path between node 30 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph110-21_18", + "image": "data/connectivity/graph_visual/hard/graph110.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,1) (0,14) (0,9) (0,27) (1,26) (1,14) (1,4) (1,15) (1,7) (3,22) (4,21) (4,10) (4,11) (4,5) (4,20) (4,24) (4,15) (4,8) (5,18) (5,14) (5,13) (5,12) (5,24) (6,17) (6,27) (6,24) (6,15) (7,21) (7,18) (7,13) (7,23) (7,12) (8,18) (8,13) (8,23) (8,15) (8,25) (9,21) (9,14) (9,20) (10,18) (10,17) (10,20) (11,26) (11,23) (11,19) (11,27) (11,24) (12,18) (12,13) (12,23) (12,19) (12,17) (12,20) (12,25) (13,18) (13,23) (13,27) (14,21) (14,23) (14,19) (14,25) (15,21) (15,23) (15,20) (16,22) (17,21) (18,19) (18,20) (18,27) (18,24) (19,21) (19,20) (19,27) (20,26) (20,21) (20,24) (21,25) (23,25) (24,25) (25,26) (25,27)\nIs there a path between node 21 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph595-0_1", + "image": "data/connectivity/graph_visual/hard/graph595.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,29) (0,1) (0,30) (0,19) (0,23) (0,3) (0,32) (0,13) (0,24) (1,29) (1,19) (1,18) (1,28) (1,23) (1,32) (1,13) (1,4) (1,33) (1,8) (1,11) (1,12) (2,22) (2,14) (2,5) (2,26) (2,15) (2,7) (2,25) (2,9) (2,21) (2,27) (2,17) (2,31) (2,16) (3,19) (3,18) (3,28) (3,23) (3,32) (3,24) (3,33) (3,8) (3,12) (4,29) (4,19) (4,18) (4,28) (4,23) (4,32) (4,13) (4,24) (4,8) (4,11) (4,12) (5,22) (5,14) (5,26) (5,15) (5,6) (5,25) (5,9) (5,21) (5,27) (5,17) (5,10) (5,20) (6,22) (6,14) (6,26) (6,15) (6,7) (6,25) (6,27) (6,17) (6,10) (6,20) (6,31) (6,16) (7,22) (7,14) (7,26) (7,27) (7,17) (7,10) (7,20) (7,31) (7,16) (8,29) (8,30) (8,19) (8,18) (8,28) (8,23) (8,32) (8,13) (8,33) (8,11) (9,22) (9,14) (9,26) (9,15) (9,25) (9,21) (9,27) (9,10) (9,20) (9,31) (9,16) (10,22) (10,26) (10,15) (10,21) (10,27) (10,17) (10,31) (11,29) (11,30) (11,18) (11,28) (11,23) (11,32) (11,13) (11,24) (12,29) (12,19) (12,18) (12,23) (12,32) (12,24) (12,33) (13,30) (13,19) (13,18) (13,23) (13,32) (13,33) (14,22) (14,26) (14,15) (14,25) (14,21) (14,27) (14,17) (14,31) (14,16) (15,22) (15,25) (15,21) (15,27) (15,17) (15,20) (16,22) (16,26) (16,25) (16,27) (16,17) (16,20) (16,31) (17,22) (17,25) (17,21) (17,27) (17,20) (18,29) (18,30) (18,19) (18,23) (18,32) (18,33) (19,28) (19,23) (19,24) (19,33) (20,22) (20,21) (20,27) (20,31) (21,26) (21,27) (21,31) (22,25) (22,27) (22,31) (23,29) (23,30) (23,32) (23,24) (23,33) (24,29) (24,32) (25,26) (25,27) (25,31) (26,31) (27,31) (28,29) (28,30) (28,33) (29,30) (29,33) (30,32) (30,33) (32,33)\nIs there a path between node 0 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph641-34_12", + "image": "data/connectivity/graph_visual/hard/graph641.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,28) (0,15) (0,19) (0,6) (0,2) (0,33) (0,18) (0,5) (0,7) (0,9) (0,34) (1,26) (1,23) (1,3) (1,4) (1,20) (1,25) (1,13) (1,11) (2,28) (2,14) (2,15) (2,19) (2,6) (2,27) (2,8) (2,24) (2,5) (2,7) (2,9) (3,26) (3,31) (3,23) (3,4) (3,17) (3,29) (3,20) (3,25) (3,13) (3,11) (3,30) (4,26) (4,31) (4,23) (4,29) (4,20) (4,25) (4,13) (4,11) (5,28) (5,14) (5,10) (5,19) (5,6) (5,27) (5,33) (5,8) (5,18) (5,24) (5,7) (6,28) (6,15) (6,10) (6,19) (6,27) (6,8) (6,18) (6,7) (6,9) (6,34) (7,28) (7,14) (7,10) (7,19) (7,27) (7,8) (7,18) (7,9) (7,34) (8,28) (8,14) (8,10) (8,27) (8,33) (8,24) (8,34) (9,28) (9,15) (9,10) (9,33) (9,18) (9,24) (9,34) (10,28) (10,15) (10,19) (10,27) (11,23) (11,17) (11,29) (11,20) (11,13) (12,21) (12,22) (12,16) (13,23) (13,17) (13,29) (13,25) (13,30) (14,28) (14,15) (14,27) (14,33) (14,24) (14,34) (15,28) (15,19) (15,27) (15,18) (16,21) (16,32) (17,26) (17,23) (17,29) (17,30) (18,28) (18,19) (18,27) (18,24) (19,27) (19,24) (19,34) (20,26) (20,31) (20,29) (20,30) (21,22) (21,32) (23,26) (23,29) (23,25) (24,28) (24,27) (25,26) (25,31) (25,29) (25,30) (26,31) (26,29) (26,30) (27,34) (28,33) (28,34) (29,31) (29,30) (30,31) (33,34)\nIs there a path between node 34 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph592-16_31", + "image": "data/connectivity/graph_visual/hard/graph592.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,10) (0,19) (0,2) (0,33) (0,21) (0,3) (0,18) (0,9) (0,14) (0,6) (0,17) (0,26) (0,25) (0,5) (0,28) (0,20) (0,29) (0,12) (1,19) (1,2) (1,33) (1,23) (1,32) (1,21) (1,24) (1,3) (1,18) (1,9) (1,14) (1,17) (1,15) (1,26) (1,16) (1,22) (1,8) (1,4) (1,20) (1,29) (1,12) (2,19) (2,13) (2,23) (2,3) (2,18) (2,9) (2,14) (2,6) (2,17) (2,16) (2,22) (2,25) (2,5) (2,20) (2,29) (3,10) (3,19) (3,13) (3,23) (3,32) (3,24) (3,9) (3,14) (3,6) (3,17) (3,15) (3,26) (3,16) (3,22) (3,8) (3,25) (3,5) (3,28) (3,4) (3,20) (3,12) (4,10) (4,19) (4,13) (4,23) (4,32) (4,21) (4,18) (4,9) (4,14) (4,6) (4,16) (4,22) (4,5) (4,29) (4,12) (5,10) (5,19) (5,33) (5,13) (5,21) (5,24) (5,18) (5,14) (5,6) (5,15) (5,16) (5,8) (5,25) (5,28) (5,29) (5,12) (6,10) (6,19) (6,33) (6,13) (6,21) (6,18) (6,14) (6,17) (6,16) (6,22) (6,8) (6,20) (6,29) (7,11) (7,27) (7,30) (7,31) (8,10) (8,19) (8,33) (8,13) (8,23) (8,32) (8,21) (8,18) (8,9) (8,14) (8,17) (8,15) (8,26) (8,22) (8,25) (8,28) (8,29) (8,12) (9,10) (9,33) (9,13) (9,23) (9,32) (9,21) (9,24) (9,18) (9,14) (9,26) (9,22) (9,25) (9,29) (9,12) (10,19) (10,13) (10,23) (10,32) (10,21) (10,24) (10,14) (10,17) (10,15) (10,26) (10,16) (10,22) (10,28) (10,29) (10,12) (11,30) (12,33) (12,13) (12,32) (12,21) (12,24) (12,14) (12,17) (12,15) (12,26) (12,16) (12,22) (12,20) (13,19) (13,33) (13,18) (13,14) (13,15) (13,26) (13,16) (13,22) (13,25) (13,20) (13,29) (14,19) (14,33) (14,32) (14,18) (14,17) (14,15) (14,26) (14,16) (14,22) (14,28) (14,20) (14,29) (15,19) (15,23) (15,21) (15,24) (15,18) (15,17) (15,26) (15,16) (15,20) (15,29) (16,19) (16,23) (16,24) (16,18) (16,26) (16,22) (16,28) (16,20) (16,29) (17,33) (17,23) (17,32) (17,21) (17,24) (17,18) (17,26) (17,22) (17,28) (17,29) (18,33) (18,23) (18,32) (18,21) (18,24) (18,25) (18,28) (18,20) (19,33) (19,32) (19,21) (19,24) (19,26) (19,28) (19,20) (20,33) (20,23) (20,32) (20,21) (20,24) (20,26) (20,22) (20,25) (20,28) (21,33) (21,23) (21,32) (21,26) (21,22) (21,25) (22,33) (22,32) (22,24) (22,26) (22,25) (22,29) (23,33) (23,24) (23,26) (23,25) (24,33) (24,32) (24,26) (24,25) (24,28) (24,29) (25,33) (25,26) (25,28) (25,29) (26,28) (26,29) (27,30) (27,31) (28,33) (28,32) (28,29) (29,33) (29,32) (32,33)\nIs there a path between node 16 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph315-11_4", + "image": "data/connectivity/graph_visual/hard/graph315.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,14) (0,31) (0,28) (0,20) (0,26) (0,13) (0,2) (1,7) (1,10) (2,14) (2,17) (2,31) (2,9) (2,15) (2,13) (2,16) (3,21) (3,29) (3,12) (3,15) (3,24) (3,16) (3,27) (4,14) (4,22) (4,15) (4,19) (4,26) (4,24) (4,16) (5,7) (5,18) (5,10) (6,25) (6,10) (7,25) (7,18) (8,11) (9,14) (9,17) (9,31) (9,28) (9,12) (9,20) (9,24) (11,30) (11,25) (11,18) (12,14) (12,21) (13,14) (13,17) (13,29) (13,23) (13,15) (13,20) (13,16) (14,21) (14,29) (14,24) (15,29) (15,28) (15,19) (15,26) (15,27) (16,29) (16,23) (16,19) (16,24) (17,29) (17,22) (17,24) (18,25) (19,24) (20,23) (20,26) (20,27) (21,28) (21,24) (23,31) (23,26) (23,27) (24,28) (24,26)\nIs there a path between node 11 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph311-1_22", + "image": "data/connectivity/graph_visual/hard/graph311.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,21) (1,6) (1,16) (2,5) (2,29) (4,14) (4,8) (4,28) (4,19) (5,23) (5,8) (5,15) (5,11) (5,9) (6,26) (7,23) (7,8) (7,19) (7,30) (8,14) (9,10) (9,19) (9,15) (9,22) (10,23) (10,14) (10,28) (10,25) (10,30) (11,23) (11,29) (12,31) (12,13) (13,18) (14,27) (15,23) (15,25) (19,28) (20,24) (22,23) (23,30) (23,29) (24,26) (28,29) (29,30)\nIs there a path between node 1 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph335-26_4", + "image": "data/connectivity/graph_visual/hard/graph335.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,12) (0,9) (0,4) (0,16) (0,26) (1,19) (1,31) (1,9) (1,4) (1,21) (1,26) (2,13) (2,19) (2,12) (2,31) (2,4) (2,21) (2,26) (3,22) (3,11) (3,6) (3,7) (3,5) (3,8) (3,17) (3,29) (3,28) (3,23) (3,10) (3,25) (3,24) (4,13) (4,16) (4,21) (5,22) (5,7) (5,15) (5,30) (5,8) (5,17) (5,29) (5,27) (5,28) (5,23) (5,10) (6,7) (6,8) (6,17) (6,27) (6,18) (6,28) (6,10) (6,25) (6,24) (6,20) (7,22) (7,11) (7,15) (7,30) (7,29) (7,18) (7,28) (7,23) (7,10) (7,25) (7,20) (8,11) (8,30) (8,17) (8,29) (8,27) (8,23) (8,10) (8,25) (8,20) (9,13) (9,12) (9,31) (9,14) (9,16) (9,26) (10,22) (10,15) (10,30) (10,17) (10,29) (10,27) (10,18) (10,28) (10,23) (10,24) (11,15) (11,17) (11,29) (11,18) (11,28) (11,23) (11,25) (11,24) (12,13) (12,19) (12,31) (12,14) (12,16) (13,31) (13,14) (13,21) (13,26) (14,19) (14,31) (14,16) (14,21) (14,26) (15,22) (15,30) (15,27) (15,28) (15,23) (15,25) (15,20) (16,19) (16,21) (17,22) (17,30) (17,29) (17,27) (17,18) (17,28) (17,23) (17,25) (17,20) (18,22) (18,29) (18,28) (18,25) (18,24) (19,31) (19,21) (19,26) (20,27) (20,28) (20,23) (20,25) (20,24) (21,31) (21,26) (22,27) (22,28) (22,23) (22,25) (22,24) (23,30) (23,29) (23,27) (23,28) (23,25) (23,24) (24,30) (24,29) (24,27) (24,25) (25,29) (25,28) (26,31) (27,30) (27,29) (27,28) (28,30) (28,29) (29,30)\nIs there a path between node 26 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph373-16_29", + "image": "data/connectivity/graph_visual/hard/graph373.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,12) (0,14) (0,23) (0,18) (0,24) (0,29) (0,15) (0,9) (0,22) (0,17) (0,4) (0,10) (0,3) (0,16) (0,19) (0,1) (1,18) (1,24) (1,29) (1,22) (1,31) (1,4) (1,10) (1,30) (1,3) (1,5) (1,6) (1,7) (1,19) (1,25) (2,13) (2,20) (2,28) (2,8) (2,27) (2,21) (3,24) (3,29) (3,15) (3,17) (3,4) (3,11) (3,30) (3,6) (3,7) (3,16) (3,19) (4,12) (4,23) (4,24) (4,29) (4,15) (4,22) (4,17) (4,31) (4,11) (4,5) (4,16) (4,25) (5,23) (5,18) (5,15) (5,9) (5,22) (5,17) (5,31) (5,10) (5,11) (5,6) (5,16) (5,19) (5,25) (5,26) (6,23) (6,18) (6,24) (6,29) (6,15) (6,22) (6,17) (6,31) (6,11) (6,30) (6,7) (6,19) (7,14) (7,18) (7,24) (7,29) (7,15) (7,9) (7,10) (7,11) (7,30) (7,16) (7,26) (8,13) (8,20) (8,28) (8,21) (9,12) (9,23) (9,18) (9,24) (9,29) (9,17) (9,31) (9,10) (9,11) (9,30) (9,16) (9,19) (10,12) (10,14) (10,23) (10,18) (10,24) (10,29) (10,15) (10,22) (10,17) (10,31) (10,30) (10,16) (10,19) (10,25) (10,26) (11,14) (11,18) (11,24) (11,15) (11,31) (11,30) (11,19) (11,25) (11,26) (12,14) (12,18) (12,24) (12,29) (12,15) (12,17) (12,31) (12,30) (12,16) (12,19) (12,25) (13,28) (13,27) (13,21) (14,23) (14,24) (14,29) (14,15) (14,22) (14,31) (14,30) (14,16) (14,26) (15,23) (15,18) (15,29) (15,22) (15,17) (15,31) (15,16) (15,26) (16,23) (16,18) (16,24) (16,29) (16,22) (16,17) (16,30) (17,18) (17,24) (17,22) (17,31) (17,30) (17,19) (17,25) (17,26) (18,23) (18,24) (18,22) (19,23) (19,29) (19,22) (19,31) (19,30) (19,25) (20,28) (20,21) (22,23) (22,29) (22,31) (22,30) (22,25) (22,26) (23,24) (23,31) (23,25) (24,31) (24,30) (24,25) (24,26) (25,29) (25,30) (25,26) (26,29) (26,30) (29,30) (30,31)\nIs there a path between node 16 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph555-17_19", + "image": "data/connectivity/graph_visual/hard/graph555.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,5) (0,7) (0,22) (0,1) (1,5) (1,7) (1,22) (2,31) (2,28) (2,18) (3,19) (3,23) (3,33) (4,26) (4,19) (4,31) (4,27) (5,21) (5,7) (6,24) (6,29) (7,21) (8,32) (8,26) (8,28) (8,23) (9,32) (9,26) (9,17) (9,16) (9,12) (9,19) (9,27) (11,21) (12,25) (12,27) (13,22) (14,29) (15,26) (15,17) (15,25) (15,20) (15,19) (15,18) (16,20) (16,19) (16,31) (16,18) (17,32) (17,28) (18,27) (19,31) (19,27) (19,33) (20,32) (20,27) (23,30) (23,27) (26,32) (27,28) (28,31) (28,33) (30,32) (30,33) (32,33)\nIs there a path between node 17 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph188-5_7", + "image": "data/connectivity/graph_visual/hard/graph188.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,21) (0,7) (0,2) (0,6) (0,14) (0,24) (0,23) (0,20) (1,10) (1,28) (1,3) (1,16) (1,24) (1,5) (2,3) (2,7) (2,24) (2,20) (3,25) (3,28) (3,22) (3,21) (3,16) (3,14) (4,28) (4,22) (4,16) (4,18) (4,14) (5,10) (5,7) (5,16) (6,10) (6,22) (6,7) (6,24) (6,23) (7,25) (7,22) (7,21) (7,14) (7,24) (7,20) (8,13) (10,20) (10,11) (11,18) (11,14) (11,23) (12,13) (12,17) (13,17) (13,19) (14,28) (14,23) (16,21) (16,18) (16,26) (18,22) (18,24) (18,20) (21,28) (21,23) (22,24) (23,24) (25,26)\nIs there a path between node 5 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph227-18_12", + "image": "data/connectivity/graph_visual/hard/graph227.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,27) (0,4) (0,11) (0,1) (0,17) (0,15) (0,3) (0,25) (0,18) (1,4) (1,11) (1,22) (1,17) (1,20) (1,15) (1,7) (1,25) (1,18) (1,26) (2,9) (2,23) (2,29) (2,21) (2,28) (2,6) (2,8) (3,4) (3,11) (3,13) (3,22) (3,17) (3,19) (3,15) (3,7) (3,25) (3,18) (3,16) (3,26) (4,27) (4,11) (4,13) (4,22) (4,17) (4,7) (4,25) (4,18) (4,26) (6,24) (6,10) (6,23) (6,21) (6,28) (6,8) (7,11) (7,13) (7,17) (7,25) (7,18) (7,26) (8,9) (8,24) (8,10) (8,23) (8,21) (8,28) (9,24) (9,10) (9,23) (9,29) (9,21) (9,28) (10,24) (10,23) (10,29) (10,21) (10,28) (11,27) (11,13) (11,22) (11,17) (11,20) (11,19) (11,25) (11,18) (11,16) (11,26) (12,14) (13,27) (13,22) (13,17) (13,19) (13,15) (13,25) (13,18) (13,16) (13,26) (15,27) (15,22) (15,17) (15,20) (15,25) (15,16) (15,26) (16,20) (16,25) (16,18) (16,26) (17,22) (17,20) (17,19) (17,25) (17,18) (17,26) (18,27) (18,22) (18,19) (18,25) (18,26) (19,27) (19,22) (19,20) (19,25) (19,26) (20,27) (20,25) (20,26) (21,24) (21,29) (22,27) (22,25) (22,26) (24,28) (25,27) (25,26) (26,27) (28,29)\nIs there a path between node 18 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph487-9_3", + "image": "data/connectivity/graph_visual/hard/graph487.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,8) (0,30) (0,9) (0,18) (0,2) (0,4) (0,20) (0,28) (0,1) (0,7) (0,16) (0,5) (0,17) (0,32) (0,26) (0,29) (0,21) (0,25) (0,11) (0,13) (0,31) (0,27) (1,8) (1,9) (1,18) (1,15) (1,4) (1,20) (1,28) (1,7) (1,16) (1,5) (1,32) (1,21) (1,25) (1,22) (1,11) (1,13) (1,31) (1,3) (1,27) (2,18) (2,15) (2,4) (2,20) (2,28) (2,7) (2,16) (2,23) (2,32) (2,26) (2,21) (2,25) (2,22) (2,12) (2,13) (2,31) (2,27) (3,8) (3,9) (3,18) (3,15) (3,4) (3,20) (3,7) (3,16) (3,23) (3,29) (3,21) (3,25) (3,22) (3,11) (3,27) (4,8) (4,30) (4,9) (4,18) (4,15) (4,7) (4,16) (4,5) (4,17) (4,26) (4,21) (4,25) (4,22) (4,12) (4,13) (4,31) (4,27) (5,30) (5,18) (5,15) (5,28) (5,7) (5,32) (5,26) (5,29) (5,21) (5,25) (5,22) (5,12) (5,11) (5,13) (5,31) (5,27) (6,24) (6,10) (6,19) (6,14) (7,9) (7,18) (7,15) (7,28) (7,16) (7,17) (7,23) (7,32) (7,21) (7,25) (7,22) (7,12) (7,31) (8,30) (8,9) (8,15) (8,28) (8,16) (8,17) (8,23) (8,26) (8,29) (8,21) (8,22) (8,11) (8,13) (8,27) (9,28) (9,17) (9,32) (9,26) (9,21) (9,25) (9,11) (9,31) (9,27) (10,24) (10,19) (10,14) (11,18) (11,15) (11,28) (11,16) (11,32) (11,21) (11,22) (11,13) (11,31) (11,27) (12,30) (12,18) (12,15) (12,32) (12,26) (12,21) (12,22) (12,13) (12,31) (13,18) (13,28) (13,17) (13,32) (13,26) (13,29) (13,21) (13,25) (13,22) (13,31) (13,27) (14,24) (14,19) (15,18) (15,20) (15,28) (15,17) (15,23) (15,32) (15,29) (15,25) (15,22) (15,31) (16,30) (16,18) (16,20) (16,28) (16,17) (16,26) (16,21) (16,31) (16,27) (17,30) (17,18) (17,20) (17,23) (17,32) (17,26) (17,29) (17,25) (17,31) (17,27) (18,30) (18,20) (18,28) (18,23) (18,32) (18,26) (18,29) (18,21) (18,25) (18,31) (18,27) (19,24) (20,30) (20,28) (20,32) (20,26) (20,29) (20,31) (20,27) (21,30) (21,23) (21,32) (21,29) (21,25) (21,27) (22,28) (22,26) (22,29) (22,25) (22,31) (22,27) (23,30) (23,32) (23,29) (23,25) (23,31) (23,27) (25,30) (25,28) (25,26) (25,31) (26,30) (26,28) (26,27) (27,30) (27,28) (27,32) (28,29) (28,31) (29,30) (29,32) (29,31) (30,32) (31,32)\nIs there a path between node 9 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph665-2_18", + "image": "data/connectivity/graph_visual/hard/graph665.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,3) (0,29) (0,7) (0,32) (0,4) (0,17) (0,9) (1,12) (1,14) (1,7) (1,28) (1,23) (1,9) (1,33) (1,30) (1,6) (1,8) (2,14) (2,29) (2,32) (2,15) (2,30) (2,6) (2,10) (3,12) (3,14) (3,4) (3,23) (3,9) (3,31) (3,30) (3,20) (4,27) (4,19) (4,17) (4,15) (4,31) (4,30) (5,34) (5,18) (5,13) (6,7) (6,16) (6,23) (6,22) (6,30) (7,12) (7,15) (7,11) (7,31) (7,30) (7,24) (7,10) (8,29) (8,32) (8,16) (8,27) (8,23) (8,20) (9,28) (9,15) (9,33) (9,31) (9,30) (9,24) (9,10) (10,12) (10,19) (10,17) (10,33) (10,22) (10,20) (11,32) (11,16) (11,19) (11,17) (11,22) (12,32) (12,28) (12,23) (12,33) (14,32) (14,30) (14,20) (15,17) (15,30) (16,19) (16,17) (16,23) (16,33) (16,30) (17,29) (17,27) (17,30) (17,24) (17,20) (18,25) (19,32) (19,28) (19,30) (19,20) (20,28) (20,23) (20,30) (22,28) (22,33) (23,29) (23,31) (24,31) (26,34) (28,29) (28,33) (29,31) (30,33)\nIs there a path between node 2 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph464-5_30", + "image": "data/connectivity/graph_visual/hard/graph464.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,17) (0,8) (0,21) (0,6) (1,14) (1,13) (1,30) (1,12) (1,24) (2,15) (3,8) (3,5) (4,9) (5,7) (6,32) (6,19) (7,17) (7,25) (8,32) (9,26) (9,15) (10,14) (10,13) (10,24) (11,14) (11,13) (12,13) (12,30) (12,24) (13,29) (13,24) (13,27) (14,27) (15,16) (15,18) (16,31) (17,32) (17,25) (18,26) (19,23) (20,26) (21,32) (23,25)\nIs there a path between node 5 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph380-7_1", + "image": "data/connectivity/graph_visual/hard/graph380.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,23) (0,8) (0,15) (0,6) (0,5) (0,13) (0,21) (0,18) (1,4) (1,7) (1,23) (1,15) (1,6) (1,21) (2,10) (2,16) (2,26) (2,12) (2,22) (2,27) (2,30) (2,17) (2,31) (3,9) (3,25) (3,20) (3,28) (3,11) (3,19) (4,8) (4,15) (4,5) (4,13) (4,21) (4,18) (5,7) (5,8) (5,15) (5,6) (5,13) (5,21) (5,18) (6,23) (6,8) (6,15) (6,21) (6,18) (7,23) (7,8) (7,21) (7,18) (8,23) (8,15) (8,13) (8,18) (9,25) (9,28) (9,11) (9,19) (10,26) (10,12) (10,24) (10,14) (10,30) (10,17) (10,31) (12,26) (12,27) (12,14) (12,30) (12,31) (13,23) (13,21) (14,16) (14,26) (14,22) (14,24) (14,30) (14,31) (15,23) (15,21) (15,18) (16,24) (16,27) (16,30) (16,17) (16,31) (17,26) (17,22) (17,27) (18,23) (19,25) (19,20) (19,28) (20,25) (20,28) (21,23) (22,26) (22,27) (22,30) (24,26) (24,27) (24,30) (24,31) (26,27) (26,30) (26,31) (27,30) (27,31) (30,31)\nIs there a path between node 7 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph428-12_20", + "image": "data/connectivity/graph_visual/hard/graph428.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,30) (0,7) (0,26) (0,13) (0,21) (0,22) (0,1) (1,24) (1,7) (1,26) (1,11) (2,32) (2,18) (2,9) (2,8) (2,12) (2,29) (2,14) (2,16) (2,10) (2,3) (2,5) (2,17) (2,28) (3,27) (3,32) (3,18) (3,9) (3,8) (3,12) (3,29) (3,16) (3,4) (3,23) (3,5) (3,31) (3,17) (3,15) (3,28) (4,18) (4,9) (4,29) (4,16) (4,10) (4,23) (4,5) (4,17) (4,15) (5,27) (5,32) (5,18) (5,20) (5,9) (5,16) (5,10) (5,17) (5,15) (5,28) (6,25) (6,19) (7,24) (7,30) (7,13) (7,21) (7,22) (8,27) (8,32) (8,18) (8,20) (8,9) (8,29) (8,14) (8,16) (8,10) (8,23) (8,31) (8,17) (8,15) (8,28) (9,27) (9,32) (9,20) (9,12) (9,14) (9,10) (9,23) (9,17) (9,15) (9,28) (10,32) (10,18) (10,20) (10,12) (10,29) (10,16) (10,31) (10,15) (10,28) (11,24) (11,30) (11,26) (11,22) (12,32) (12,18) (12,14) (12,16) (12,23) (12,31) (12,15) (12,28) (13,24) (13,30) (13,26) (14,27) (14,32) (14,18) (14,20) (14,29) (14,17) (14,28) (15,27) (15,32) (15,20) (15,23) (15,31) (15,17) (15,28) (16,27) (16,32) (16,18) (16,20) (16,23) (16,31) (16,28) (17,32) (17,20) (17,29) (17,23) (17,28) (18,27) (18,32) (18,20) (18,29) (18,31) (20,27) (20,32) (20,29) (20,23) (20,31) (20,28) (21,24) (21,30) (21,26) (21,22) (22,30) (22,26) (23,29) (23,31) (24,26) (26,30) (27,32) (28,29) (28,31) (31,32)\nIs there a path between node 12 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph264-30_26", + "image": "data/connectivity/graph_visual/hard/graph264.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,14) (0,8) (0,20) (0,23) (0,29) (0,15) (0,25) (0,24) (0,18) (1,2) (2,21) (3,8) (3,17) (3,20) (3,12) (3,10) (3,5) (4,26) (4,14) (4,22) (4,8) (4,12) (4,7) (4,10) (4,5) (5,22) (5,13) (5,8) (5,19) (5,17) (5,12) (5,6) (5,7) (5,24) (6,26) (6,22) (6,29) (6,24) (7,26) (7,11) (7,17) (7,20) (7,23) (7,15) (7,10) (7,24) (8,11) (8,13) (8,19) (8,17) (8,29) (8,15) (8,10) (8,25) (9,21) (10,26) (10,28) (10,17) (10,15) (10,25) (10,18) (11,22) (11,28) (11,20) (11,12) (11,29) (11,18) (12,14) (12,13) (12,28) (12,15) (12,25) (13,19) (13,25) (13,18) (14,20) (14,15) (14,25) (15,25) (16,30) (16,21) (17,19) (17,23) (17,29) (17,24) (17,18) (18,22) (18,23) (18,29) (18,25) (18,24) (19,24) (20,22) (20,23) (20,25) (22,26) (22,28) (23,24) (24,26) (25,29) (26,29)\nIs there a path between node 30 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph704-15_3", + "image": "data/connectivity/graph_visual/hard/graph704.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,8) (0,6) (0,7) (0,28) (0,4) (0,33) (0,32) (0,3) (0,24) (0,16) (0,9) (0,29) (0,14) (0,11) (0,17) (0,22) (0,5) (1,23) (1,8) (1,6) (1,7) (1,28) (1,12) (1,4) (1,33) (1,16) (1,9) (1,10) (1,14) (1,17) (2,26) (2,15) (2,19) (2,21) (3,20) (3,13) (3,25) (3,23) (3,8) (3,6) (3,7) (3,28) (3,12) (3,31) (3,4) (3,30) (3,33) (3,32) (3,27) (3,24) (3,10) (3,22) (3,5) (4,20) (4,23) (4,8) (4,6) (4,7) (4,28) (4,12) (4,30) (4,33) (4,32) (4,27) (4,24) (4,16) (4,9) (4,14) (4,17) (4,22) (4,5) (5,20) (5,6) (5,28) (5,12) (5,31) (5,30) (5,32) (5,24) (5,9) (5,29) (5,14) (5,11) (5,17) (5,22) (6,20) (6,13) (6,25) (6,23) (6,8) (6,7) (6,28) (6,12) (6,30) (6,32) (6,27) (6,24) (6,9) (6,10) (6,29) (6,14) (6,11) (6,22) (7,20) (7,25) (7,23) (7,8) (7,12) (7,31) (7,33) (7,27) (7,24) (7,16) (7,10) (7,14) (7,17) (7,22) (8,20) (8,13) (8,23) (8,12) (8,33) (8,32) (8,27) (8,24) (8,16) (8,9) (8,10) (8,29) (8,14) (8,11) (8,17) (8,22) (9,13) (9,25) (9,12) (9,31) (9,30) (9,33) (9,32) (9,27) (9,24) (9,16) (9,10) (9,29) (9,14) (9,17) (10,13) (10,25) (10,23) (10,28) (10,12) (10,32) (10,24) (10,16) (10,14) (10,11) (10,22) (11,13) (11,23) (11,28) (11,12) (11,31) (11,30) (11,32) (11,27) (11,24) (11,16) (11,29) (11,14) (11,17) (11,22) (12,20) (12,25) (12,23) (12,28) (12,31) (12,30) (12,27) (12,24) (12,16) (12,29) (12,14) (12,22) (13,20) (13,25) (13,28) (13,31) (13,30) (13,33) (13,32) (13,24) (13,16) (13,29) (13,14) (13,17) (13,22) (14,25) (14,28) (14,31) (14,30) (14,33) (14,32) (14,24) (14,16) (14,29) (14,17) (15,26) (15,19) (15,21) (16,20) (16,23) (16,28) (16,31) (16,33) (16,29) (16,17) (16,22) (17,25) (17,23) (17,28) (17,31) (17,32) (17,24) (17,29) (17,22) (19,26) (19,34) (20,25) (20,23) (20,30) (20,32) (20,27) (20,29) (20,22) (21,34) (22,23) (22,28) (22,31) (22,30) (22,33) (22,27) (22,29) (23,25) (23,30) (23,33) (23,32) (23,27) (23,24) (23,29) (24,25) (24,28) (24,31) (24,30) (24,32) (24,27) (25,28) (25,31) (25,30) (25,32) (25,29) (26,34) (27,28) (27,30) (27,33) (27,32) (27,29) (28,31) (28,32) (29,30) (29,32) (30,31) (30,33) (31,32)\nIs there a path between node 15 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph476-28_0", + "image": "data/connectivity/graph_visual/hard/graph476.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,23) (0,32) (0,27) (0,3) (0,9) (0,13) (0,4) (0,11) (0,10) (1,22) (1,28) (1,26) (1,7) (1,31) (1,20) (1,12) (1,8) (1,19) (1,5) (1,29) (1,18) (1,17) (1,25) (3,24) (3,23) (3,32) (3,21) (3,9) (3,13) (3,16) (3,4) (3,6) (4,24) (4,32) (4,21) (4,27) (4,16) (4,11) (4,6) (5,22) (5,28) (5,26) (5,30) (5,31) (5,12) (5,8) (5,29) (5,18) (5,17) (6,32) (6,21) (6,27) (6,9) (6,13) (6,16) (6,11) (7,22) (7,28) (7,26) (7,30) (7,20) (7,12) (7,8) (7,19) (7,18) (7,25) (8,22) (8,28) (8,26) (8,30) (8,31) (8,20) (8,12) (8,29) (8,17) (9,32) (9,21) (9,13) (9,16) (9,11) (9,10) (10,24) (10,23) (10,32) (10,21) (10,27) (10,11) (11,24) (11,32) (11,21) (11,27) (12,28) (12,26) (12,30) (12,31) (12,20) (12,19) (12,29) (12,18) (12,17) (12,25) (13,23) (13,32) (13,27) (16,24) (16,32) (16,27) (17,28) (17,31) (17,20) (17,19) (17,18) (17,25) (18,28) (18,26) (18,30) (18,31) (18,20) (18,19) (18,25) (19,22) (19,28) (19,26) (19,30) (19,20) (19,29) (19,25) (20,22) (20,28) (20,26) (20,30) (20,31) (20,29) (20,25) (21,24) (21,32) (21,27) (22,28) (22,31) (22,29) (22,25) (23,32) (23,27) (24,32) (25,28) (25,26) (25,30) (25,31) (25,29) (26,28) (26,30) (27,32) (28,30) (28,29) (29,31)\nIs there a path between node 28 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph258-11_6", + "image": "data/connectivity/graph_visual/hard/graph258.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,17) (0,11) (0,7) (0,15) (0,30) (0,25) (1,14) (1,6) (1,8) (2,26) (2,28) (3,11) (3,5) (3,15) (3,23) (3,16) (3,19) (3,10) (4,17) (4,22) (4,15) (4,16) (4,19) (4,30) (4,10) (5,9) (5,13) (5,22) (5,24) (5,19) (5,27) (5,21) (6,29) (7,17) (7,20) (7,16) (8,14) (9,17) (9,20) (9,15) (9,24) (9,30) (9,21) (10,16) (10,24) (10,30) (10,21) (10,25) (11,17) (11,12) (11,27) (11,21) (12,17) (12,20) (12,21) (13,17) (13,20) (15,24) (15,27) (15,30) (16,22) (16,21) (17,19) (17,30) (17,21) (17,25) (18,26) (19,20) (20,24) (20,27) (20,21) (21,24) (21,27) (21,30) (21,25) (22,23) (22,30) (25,27) (25,30) (26,28) (27,30)\nIs there a path between node 11 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph506-2_31", + "image": "data/connectivity/graph_visual/hard/graph506.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,32) (0,10) (0,4) (0,11) (0,24) (0,14) (0,21) (0,8) (0,18) (0,27) (0,13) (0,1) (0,29) (0,16) (0,28) (0,12) (0,20) (1,32) (1,4) (1,26) (1,11) (1,24) (1,8) (1,18) (1,13) (1,31) (1,29) (1,25) (1,15) (1,28) (1,12) (1,20) (2,6) (2,33) (4,10) (4,18) (4,27) (4,31) (4,22) (4,29) (4,25) (4,16) (4,15) (4,28) (4,12) (5,17) (5,23) (5,30) (5,9) (6,19) (7,19) (8,32) (8,10) (8,26) (8,11) (8,24) (8,14) (8,21) (8,18) (8,22) (8,29) (8,15) (8,20) (9,30) (10,11) (10,24) (10,14) (10,18) (10,27) (10,13) (10,31) (10,22) (10,29) (10,25) (10,28) (10,12) (10,20) (11,32) (11,26) (11,24) (11,14) (11,21) (11,27) (11,13) (11,31) (11,29) (11,16) (11,28) (11,12) (12,32) (12,24) (12,14) (12,18) (12,27) (12,31) (12,16) (12,15) (12,20) (13,32) (13,26) (13,14) (13,18) (13,22) (13,29) (13,25) (13,16) (13,15) (13,28) (13,20) (14,26) (14,24) (14,18) (14,31) (14,22) (14,29) (14,25) (14,16) (14,28) (14,20) (15,26) (15,24) (15,21) (15,18) (15,27) (15,31) (15,22) (15,25) (15,28) (15,20) (16,26) (16,24) (16,21) (16,31) (16,22) (16,25) (16,28) (16,20) (18,24) (18,21) (18,22) (18,28) (19,33) (20,32) (20,26) (20,24) (20,21) (20,31) (20,22) (20,29) (20,25) (20,28) (21,32) (21,24) (21,27) (21,31) (21,22) (21,29) (22,32) (22,26) (22,24) (22,27) (22,31) (22,29) (22,25) (22,28) (23,30) (24,32) (24,27) (24,31) (24,25) (24,28) (25,32) (25,31) (25,28) (26,32) (26,27) (26,31) (26,29) (26,28) (27,32) (27,31) (27,29) (27,28) (31,32)\nIs there a path between node 2 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph613-24_16", + "image": "data/connectivity/graph_visual/hard/graph613.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,13) (0,19) (0,6) (0,21) (0,10) (0,31) (0,16) (0,7) (0,20) (0,8) (0,17) (0,12) (0,3) (0,11) (0,23) (0,2) (0,22) (0,1) (0,18) (1,33) (1,32) (1,13) (1,19) (1,29) (1,26) (1,27) (1,6) (1,21) (1,10) (1,31) (1,16) (1,28) (1,7) (1,20) (1,8) (1,17) (1,12) (1,3) (1,2) (1,14) (1,22) (1,18) (1,5) (2,33) (2,13) (2,19) (2,29) (2,26) (2,27) (2,6) (2,10) (2,31) (2,16) (2,28) (2,7) (2,20) (2,24) (2,8) (2,17) (2,12) (2,22) (2,18) (3,32) (3,29) (3,27) (3,6) (3,21) (3,31) (3,16) (3,28) (3,7) (3,20) (3,8) (3,12) (3,23) (3,14) (3,22) (3,18) (3,5) (4,25) (4,34) (5,33) (5,32) (5,13) (5,19) (5,29) (5,26) (5,27) (5,6) (5,21) (5,10) (5,31) (5,16) (5,28) (5,20) (5,8) (5,12) (5,11) (5,23) (5,14) (5,22) (5,18) (6,32) (6,13) (6,19) (6,26) (6,27) (6,21) (6,10) (6,16) (6,28) (6,7) (6,20) (6,17) (6,12) (6,11) (6,23) (6,14) (6,22) (6,18) (7,32) (7,13) (7,29) (7,27) (7,21) (7,10) (7,16) (7,28) (7,20) (7,24) (7,17) (7,12) (7,11) (7,23) (7,14) (7,22) (7,18) (8,33) (8,32) (8,13) (8,19) (8,29) (8,26) (8,21) (8,10) (8,31) (8,16) (8,28) (8,20) (8,24) (8,17) (8,12) (8,11) (8,23) (8,14) (8,22) (8,18) (9,25) (9,34) (9,15) (9,30) (10,33) (10,32) (10,13) (10,19) (10,29) (10,26) (10,27) (10,16) (10,28) (10,12) (10,11) (10,14) (10,22) (11,33) (11,32) (11,13) (11,19) (11,29) (11,21) (11,28) (11,20) (11,24) (11,17) (11,12) (11,23) (11,14) (11,22) (11,18) (12,33) (12,32) (12,13) (12,19) (12,29) (12,26) (12,31) (12,16) (12,28) (12,20) (12,23) (12,18) (13,33) (13,32) (13,19) (13,29) (13,26) (13,27) (13,21) (13,31) (13,16) (13,28) (13,20) (13,17) (13,23) (13,14) (13,18) (14,33) (14,32) (14,19) (14,29) (14,26) (14,27) (14,21) (14,31) (14,16) (14,28) (14,20) (14,17) (14,22) (15,25) (15,30) (16,33) (16,32) (16,19) (16,29) (16,26) (16,27) (16,21) (16,31) (16,28) (16,20) (16,24) (16,17) (16,23) (16,22) (17,33) (17,32) (17,19) (17,29) (17,21) (17,28) (17,20) (17,24) (17,23) (17,22) (17,18) (18,32) (18,19) (18,29) (18,26) (18,27) (18,21) (18,31) (18,28) (18,24) (18,23) (18,22) (19,29) (19,27) (19,21) (19,31) (19,28) (19,20) (19,23) (20,33) (20,29) (20,26) (20,31) (20,28) (20,22) (21,33) (21,32) (21,29) (21,31) (21,24) (21,23) (22,29) (22,31) (22,24) (23,29) (23,26) (23,27) (23,31) (23,28) (23,24) (24,32) (24,26) (24,27) (24,31) (25,34) (26,32) (26,29) (26,27) (26,31) (26,28) (27,33) (27,29) (27,31) (28,33) (28,31) (29,33) (29,32) (30,34) (31,33) (31,32) (32,33)\nIs there a path between node 24 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph625-7_27", + "image": "data/connectivity/graph_visual/hard/graph625.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,30) (0,9) (0,23) (0,3) (2,19) (2,6) (2,31) (2,21) (2,18) (2,11) (3,7) (3,10) (3,34) (3,27) (3,23) (4,16) (4,14) (4,21) (4,18) (4,11) (4,33) (5,17) (6,21) (7,15) (7,13) (7,9) (8,16) (8,31) (8,11) (9,10) (9,15) (9,26) (9,27) (9,23) (10,34) (10,13) (10,28) (11,16) (11,19) (11,31) (12,34) (12,13) (12,30) (12,27) (12,23) (13,26) (13,27) (13,28) (14,31) (14,21) (14,32) (15,27) (15,22) (16,19) (16,25) (17,20) (18,21) (18,33) (18,32) (19,29) (19,21) (19,32) (21,29) (21,25) (21,32) (22,24) (22,28) (23,30) (23,28) (24,34) (24,30) (24,28) (25,31) (26,30) (29,31) (29,33) (29,32) (30,34) (31,33)\nIs there a path between node 7 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph313-27_9", + "image": "data/connectivity/graph_visual/hard/graph313.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,29) (0,15) (0,4) (1,14) (1,12) (1,13) (2,22) (3,27) (4,5) (4,29) (4,15) (5,9) (5,29) (5,18) (5,7) (5,30) (6,12) (6,10) (7,20) (7,25) (7,9) (7,15) (7,21) (9,20) (9,19) (9,29) (9,21) (11,16) (13,27) (14,28) (15,18) (15,21) (18,30) (19,29) (20,30) (22,26) (22,31) (25,29) (25,30)\nIs there a path between node 27 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph592-26_7", + "image": "data/connectivity/graph_visual/hard/graph592.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,10) (0,19) (0,2) (0,33) (0,21) (0,3) (0,18) (0,9) (0,14) (0,6) (0,17) (0,26) (0,25) (0,5) (0,28) (0,20) (0,29) (0,12) (1,19) (1,2) (1,33) (1,23) (1,32) (1,21) (1,24) (1,3) (1,18) (1,9) (1,14) (1,17) (1,15) (1,26) (1,16) (1,22) (1,8) (1,4) (1,20) (1,29) (1,12) (2,19) (2,13) (2,23) (2,3) (2,18) (2,9) (2,14) (2,6) (2,17) (2,16) (2,22) (2,25) (2,5) (2,20) (2,29) (3,10) (3,19) (3,13) (3,23) (3,32) (3,24) (3,9) (3,14) (3,6) (3,17) (3,15) (3,26) (3,16) (3,22) (3,8) (3,25) (3,5) (3,28) (3,4) (3,20) (3,12) (4,10) (4,19) (4,13) (4,23) (4,32) (4,21) (4,18) (4,9) (4,14) (4,6) (4,16) (4,22) (4,5) (4,29) (4,12) (5,10) (5,19) (5,33) (5,13) (5,21) (5,24) (5,18) (5,14) (5,6) (5,15) (5,16) (5,8) (5,25) (5,28) (5,29) (5,12) (6,10) (6,19) (6,33) (6,13) (6,21) (6,18) (6,14) (6,17) (6,16) (6,22) (6,8) (6,20) (6,29) (7,11) (7,27) (7,30) (7,31) (8,10) (8,19) (8,33) (8,13) (8,23) (8,32) (8,21) (8,18) (8,9) (8,14) (8,17) (8,15) (8,26) (8,22) (8,25) (8,28) (8,29) (8,12) (9,10) (9,33) (9,13) (9,23) (9,32) (9,21) (9,24) (9,18) (9,14) (9,26) (9,22) (9,25) (9,29) (9,12) (10,19) (10,13) (10,23) (10,32) (10,21) (10,24) (10,14) (10,17) (10,15) (10,26) (10,16) (10,22) (10,28) (10,29) (10,12) (11,30) (12,33) (12,13) (12,32) (12,21) (12,24) (12,14) (12,17) (12,15) (12,26) (12,16) (12,22) (12,20) (13,19) (13,33) (13,18) (13,14) (13,15) (13,26) (13,16) (13,22) (13,25) (13,20) (13,29) (14,19) (14,33) (14,32) (14,18) (14,17) (14,15) (14,26) (14,16) (14,22) (14,28) (14,20) (14,29) (15,19) (15,23) (15,21) (15,24) (15,18) (15,17) (15,26) (15,16) (15,20) (15,29) (16,19) (16,23) (16,24) (16,18) (16,26) (16,22) (16,28) (16,20) (16,29) (17,33) (17,23) (17,32) (17,21) (17,24) (17,18) (17,26) (17,22) (17,28) (17,29) (18,33) (18,23) (18,32) (18,21) (18,24) (18,25) (18,28) (18,20) (19,33) (19,32) (19,21) (19,24) (19,26) (19,28) (19,20) (20,33) (20,23) (20,32) (20,21) (20,24) (20,26) (20,22) (20,25) (20,28) (21,33) (21,23) (21,32) (21,26) (21,22) (21,25) (22,33) (22,32) (22,24) (22,26) (22,25) (22,29) (23,33) (23,24) (23,26) (23,25) (24,33) (24,32) (24,26) (24,25) (24,28) (24,29) (25,33) (25,26) (25,28) (25,29) (26,28) (26,29) (27,30) (27,31) (28,33) (28,32) (28,29) (29,33) (29,32) (32,33)\nIs there a path between node 26 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph268-23_0", + "image": "data/connectivity/graph_visual/hard/graph268.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,5) (0,11) (0,22) (0,30) (0,25) (0,19) (0,12) (0,13) (0,10) (0,29) (1,17) (1,4) (1,18) (1,7) (1,27) (1,2) (1,3) (1,9) (1,23) (1,28) (2,4) (2,21) (2,26) (2,7) (2,27) (2,9) (2,23) (2,28) (3,17) (3,4) (3,21) (3,26) (3,18) (3,7) (3,27) (3,14) (3,9) (3,23) (3,28) (3,24) (4,17) (4,21) (4,26) (4,18) (4,14) (4,9) (4,28) (4,24) (5,11) (5,22) (5,20) (5,25) (5,29) (6,8) (7,21) (7,26) (7,18) (7,27) (7,23) (7,28) (7,24) (9,21) (9,26) (9,18) (9,27) (9,14) (9,23) (9,28) (9,24) (10,11) (10,22) (10,20) (10,30) (10,25) (10,16) (10,19) (10,15) (10,13) (10,29) (11,22) (11,20) (11,30) (11,25) (11,16) (11,19) (11,12) (11,15) (11,13) (11,29) (12,22) (12,20) (12,30) (12,16) (12,15) (12,13) (13,22) (13,20) (13,30) (13,25) (13,16) (13,19) (13,15) (13,29) (14,26) (14,18) (14,23) (14,28) (14,24) (15,22) (15,30) (15,16) (15,19) (15,29) (16,22) (16,30) (16,25) (16,19) (16,29) (17,26) (17,18) (17,27) (17,23) (17,28) (18,21) (18,26) (18,27) (18,24) (19,20) (19,30) (19,25) (19,29) (20,22) (20,25) (20,29) (21,26) (21,27) (21,28) (21,24) (22,30) (22,29) (23,26) (23,27) (23,28) (23,24) (24,27) (24,28) (25,29) (26,27) (27,28) (29,30)\nIs there a path between node 23 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph415-24_6", + "image": "data/connectivity/graph_visual/hard/graph415.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,10) (0,2) (0,31) (0,17) (1,10) (1,26) (1,25) (1,31) (1,17) (2,25) (2,31) (3,18) (3,23) (3,15) (3,11) (3,22) (4,5) (4,13) (4,6) (4,11) (4,16) (4,24) (5,28) (5,23) (5,19) (5,7) (5,22) (6,18) (6,28) (6,11) (7,28) (7,23) (7,13) (7,21) (9,18) (9,15) (9,12) (9,11) (10,29) (11,30) (11,18) (11,14) (11,28) (11,15) (11,19) (12,30) (12,13) (12,19) (13,16) (13,19) (13,22) (14,28) (14,16) (15,30) (15,22) (16,30) (18,30) (18,21) (18,19) (18,24) (19,23) (19,24) (20,29) (23,24) (24,30) (25,27) (25,29) (26,27) (27,31) (29,32)\nIs there a path between node 24 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph528-24_22", + "image": "data/connectivity/graph_visual/hard/graph528.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,32) (0,22) (0,33) (0,19) (0,4) (0,13) (0,31) (0,15) (0,24) (1,23) (1,27) (2,4) (2,31) (2,29) (3,16) (3,23) (3,8) (4,33) (4,12) (4,28) (4,6) (5,26) (5,17) (5,21) (5,8) (6,32) (6,33) (6,31) (6,29) (7,32) (7,22) (7,31) (7,15) (7,29) (8,9) (9,16) (9,21) (9,27) (10,32) (10,25) (10,28) (10,24) (10,29) (11,33) (11,15) (12,22) (12,31) (12,28) (13,22) (13,29) (14,17) (14,18) (14,23) (15,32) (15,19) (15,31) (15,30) (15,24) (15,29) (16,18) (16,20) (16,27) (17,18) (17,23) (18,26) (19,33) (19,25) (19,24) (20,21) (20,23) (21,26) (22,24) (23,26) (23,27) (24,28) (24,30) (25,29) (28,32) (28,30) (30,33)\nIs there a path between node 24 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph287-14_23", + "image": "data/connectivity/graph_visual/hard/graph287.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,16) (0,19) (1,31) (1,27) (1,7) (2,26) (2,12) (2,4) (2,7) (2,23) (3,28) (3,10) (3,14) (3,19) (3,11) (3,25) (4,27) (4,24) (4,17) (5,20) (5,13) (5,10) (5,14) (5,19) (6,31) (6,15) (6,27) (6,21) (8,13) (9,13) (9,11) (9,18) (10,28) (10,14) (10,16) (10,19) (10,11) (10,18) (11,20) (11,22) (11,14) (11,16) (11,18) (12,31) (12,30) (12,27) (12,24) (12,23) (13,22) (13,14) (13,25) (14,22) (14,25) (14,18) (15,31) (15,26) (15,24) (16,18) (17,31) (17,26) (17,23) (18,19) (19,22) (20,25) (21,31) (21,24) (21,29) (21,23) (22,28) (22,25) (23,27) (23,29) (24,30) (26,27) (29,31)\nIs there a path between node 14 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph687-13_11", + "image": "data/connectivity/graph_visual/hard/graph687.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,4) (0,9) (0,10) (0,14) (0,1) (0,34) (0,6) (0,20) (0,16) (0,32) (0,12) (0,19) (0,13) (1,11) (1,24) (1,26) (1,9) (1,10) (1,14) (1,34) (1,6) (1,5) (1,20) (1,27) (1,12) (1,19) (1,7) (1,28) (1,13) (1,15) (1,17) (2,11) (2,4) (2,24) (2,33) (2,26) (2,23) (2,9) (2,10) (2,34) (2,6) (2,5) (2,20) (2,16) (2,27) (2,32) (2,19) (2,7) (2,13) (2,15) (2,17) (3,30) (3,8) (4,11) (4,24) (4,33) (4,23) (4,31) (4,34) (4,6) (4,27) (4,32) (4,29) (4,12) (4,19) (4,13) (4,17) (5,11) (5,26) (5,23) (5,9) (5,31) (5,14) (5,34) (5,6) (5,16) (5,32) (5,19) (5,28) (5,13) (5,15) (5,17) (6,11) (6,23) (6,9) (6,10) (6,31) (6,14) (6,34) (6,20) (6,16) (6,27) (6,12) (6,19) (6,7) (6,28) (6,13) (6,15) (7,33) (7,26) (7,23) (7,10) (7,31) (7,14) (7,16) (7,27) (7,32) (7,12) (7,28) (7,13) (7,15) (8,22) (8,25) (8,18) (8,21) (9,11) (9,24) (9,26) (9,23) (9,10) (9,31) (9,34) (9,20) (9,16) (9,27) (9,32) (9,19) (9,28) (9,13) (9,15) (9,17) (10,24) (10,33) (10,26) (10,23) (10,31) (10,14) (10,34) (10,16) (10,27) (10,32) (10,29) (10,12) (10,28) (10,15) (11,33) (11,26) (11,23) (11,14) (11,34) (11,20) (11,16) (11,12) (11,19) (11,28) (11,15) (11,17) (12,24) (12,33) (12,23) (12,31) (12,14) (12,20) (12,27) (12,32) (12,19) (12,17) (13,24) (13,23) (13,31) (13,14) (13,34) (13,20) (13,16) (13,27) (13,32) (13,29) (13,19) (13,28) (14,24) (14,33) (14,26) (14,23) (14,31) (14,20) (14,16) (14,27) (14,32) (14,29) (14,28) (14,15) (14,17) (15,24) (15,33) (15,26) (15,23) (15,31) (15,34) (15,20) (15,16) (15,32) (16,24) (16,33) (16,26) (16,23) (16,34) (16,20) (16,27) (16,32) (16,29) (16,19) (16,28) (17,24) (17,33) (17,26) (17,23) (17,31) (17,34) (17,20) (17,27) (17,29) (17,19) (17,28) (18,22) (18,25) (18,21) (19,24) (19,33) (19,26) (19,31) (19,34) (19,20) (19,27) (19,32) (19,29) (19,28) (20,33) (20,26) (20,23) (20,31) (20,34) (20,27) (20,32) (20,29) (20,28) (21,22) (21,25) (21,30) (22,25) (23,26) (23,34) (23,27) (23,32) (23,29) (24,33) (24,31) (24,34) (24,27) (24,29) (24,28) (25,30) (26,33) (26,27) (26,32) (26,29) (26,28) (27,31) (27,34) (27,32) (27,29) (27,28) (28,33) (28,34) (28,32) (28,29) (29,33) (29,32) (31,33) (31,34) (31,32) (32,33) (32,34) (33,34)\nIs there a path between node 13 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph136-2_6", + "image": "data/connectivity/graph_visual/hard/graph136.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,4) (0,18) (0,17) (0,10) (1,7) (1,24) (1,27) (2,4) (2,8) (2,13) (2,19) (2,27) (3,16) (3,28) (3,9) (4,18) (4,6) (4,10) (4,11) (4,27) (6,20) (6,8) (6,7) (6,27) (7,8) (7,18) (7,17) (7,23) (7,24) (7,10) (7,13) (7,19) (7,11) (7,14) (8,17) (8,22) (8,24) (8,10) (8,11) (10,18) (10,17) (10,12) (10,11) (10,27) (11,17) (11,12) (12,20) (12,18) (12,17) (12,14) (13,20) (13,18) (13,24) (13,27) (13,26) (14,18) (15,28) (15,25) (16,25) (17,20) (17,18) (17,26) (18,22) (18,23) (18,19) (18,27) (19,23) (19,27) (19,26) (20,24) (22,23) (22,24) (22,26) (26,27)\nIs there a path between node 2 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph508-27_11", + "image": "data/connectivity/graph_visual/hard/graph508.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,17) (0,33) (0,22) (0,11) (0,23) (0,28) (0,10) (0,16) (0,19) (0,13) (0,9) (0,1) (0,8) (0,18) (0,6) (0,26) (1,17) (1,33) (1,12) (1,15) (1,11) (1,24) (1,30) (1,28) (1,10) (1,16) (1,19) (1,13) (1,31) (1,29) (1,8) (1,18) (1,6) (1,26) (2,5) (3,7) (3,32) (3,20) (3,27) (3,25) (4,7) (4,32) (4,20) (4,27) (4,25) (4,14) (6,17) (6,12) (6,22) (6,15) (6,11) (6,24) (6,30) (6,28) (6,16) (6,13) (6,31) (6,9) (6,29) (6,21) (6,8) (6,18) (6,26) (7,32) (7,20) (7,27) (7,25) (8,17) (8,33) (8,12) (8,22) (8,15) (8,11) (8,23) (8,24) (8,10) (8,19) (8,31) (8,9) (8,21) (8,18) (9,17) (9,33) (9,12) (9,22) (9,15) (9,23) (9,24) (9,10) (9,16) (9,19) (9,13) (9,31) (9,29) (9,21) (9,18) (9,26) (10,17) (10,33) (10,15) (10,11) (10,23) (10,24) (10,30) (10,28) (10,13) (10,31) (10,29) (10,21) (10,18) (10,26) (11,17) (11,33) (11,22) (11,23) (11,24) (11,30) (11,28) (11,16) (11,19) (11,13) (11,31) (11,21) (11,18) (11,26) (12,17) (12,22) (12,15) (12,23) (12,30) (12,16) (12,31) (12,21) (12,18) (12,26) (13,17) (13,33) (13,22) (13,15) (13,23) (13,30) (13,28) (13,16) (13,19) (13,21) (13,18) (13,26) (14,32) (14,25) (15,17) (15,33) (15,22) (15,23) (15,24) (15,30) (15,28) (15,16) (15,29) (15,21) (15,18) (15,26) (16,17) (16,33) (16,23) (16,30) (16,28) (16,19) (16,31) (16,29) (16,21) (16,26) (17,23) (17,24) (17,19) (17,31) (17,29) (17,21) (17,26) (18,23) (18,24) (18,30) (18,28) (18,19) (18,31) (18,29) (18,21) (18,26) (19,22) (19,24) (19,30) (19,28) (19,31) (19,29) (19,21) (20,32) (20,27) (21,22) (21,24) (21,30) (21,31) (21,26) (22,33) (22,23) (22,24) (22,30) (22,31) (22,26) (23,33) (23,24) (23,28) (23,29) (24,33) (24,30) (24,28) (24,29) (24,26) (25,32) (25,27) (26,33) (26,28) (26,31) (26,29) (28,33) (28,30) (28,29) (29,33) (29,30) (29,31) (30,33) (30,31)\nIs there a path between node 27 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph442-1_22", + "image": "data/connectivity/graph_visual/hard/graph442.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,11) (0,32) (0,29) (0,7) (0,15) (1,30) (1,10) (1,8) (2,27) (2,18) (2,20) (2,7) (2,26) (3,14) (3,9) (4,18) (4,11) (4,13) (4,15) (5,30) (5,21) (6,14) (6,21) (6,17) (7,18) (7,22) (7,31) (7,29) (7,26) (8,14) (8,10) (9,21) (10,12) (10,21) (10,17) (11,19) (11,22) (11,28) (11,32) (11,29) (11,15) (11,26) (12,30) (12,21) (13,27) (13,20) (13,28) (13,31) (14,17) (15,20) (15,31) (15,26) (16,27) (16,32) (17,30) (18,27) (18,28) (18,32) (18,26) (18,24) (18,23) (19,27) (19,20) (19,31) (19,29) (19,26) (19,24) (20,25) (20,28) (20,32) (20,26) (22,31) (22,23) (23,27) (23,28) (23,26) (25,26) (26,27) (26,28) (26,29) (28,32) (28,31) (29,31)\nIs there a path between node 1 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph641-13_10", + "image": "data/connectivity/graph_visual/hard/graph641.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,28) (0,15) (0,19) (0,6) (0,2) (0,33) (0,18) (0,5) (0,7) (0,9) (0,34) (1,26) (1,23) (1,3) (1,4) (1,20) (1,25) (1,13) (1,11) (2,28) (2,14) (2,15) (2,19) (2,6) (2,27) (2,8) (2,24) (2,5) (2,7) (2,9) (3,26) (3,31) (3,23) (3,4) (3,17) (3,29) (3,20) (3,25) (3,13) (3,11) (3,30) (4,26) (4,31) (4,23) (4,29) (4,20) (4,25) (4,13) (4,11) (5,28) (5,14) (5,10) (5,19) (5,6) (5,27) (5,33) (5,8) (5,18) (5,24) (5,7) (6,28) (6,15) (6,10) (6,19) (6,27) (6,8) (6,18) (6,7) (6,9) (6,34) (7,28) (7,14) (7,10) (7,19) (7,27) (7,8) (7,18) (7,9) (7,34) (8,28) (8,14) (8,10) (8,27) (8,33) (8,24) (8,34) (9,28) (9,15) (9,10) (9,33) (9,18) (9,24) (9,34) (10,28) (10,15) (10,19) (10,27) (11,23) (11,17) (11,29) (11,20) (11,13) (12,21) (12,22) (12,16) (13,23) (13,17) (13,29) (13,25) (13,30) (14,28) (14,15) (14,27) (14,33) (14,24) (14,34) (15,28) (15,19) (15,27) (15,18) (16,21) (16,32) (17,26) (17,23) (17,29) (17,30) (18,28) (18,19) (18,27) (18,24) (19,27) (19,24) (19,34) (20,26) (20,31) (20,29) (20,30) (21,22) (21,32) (23,26) (23,29) (23,25) (24,28) (24,27) (25,26) (25,31) (25,29) (25,30) (26,31) (26,29) (26,30) (27,34) (28,33) (28,34) (29,31) (29,30) (30,31) (33,34)\nIs there a path between node 13 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph690-24_15", + "image": "data/connectivity/graph_visual/hard/graph690.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,10) (0,7) (0,14) (0,32) (0,24) (0,29) (1,27) (1,31) (1,25) (1,3) (1,18) (1,9) (1,16) (1,33) (1,15) (1,13) (1,19) (1,22) (1,21) (1,30) (2,11) (3,31) (3,25) (3,18) (3,34) (3,20) (3,9) (3,16) (3,33) (3,13) (3,22) (3,21) (3,30) (4,27) (4,31) (4,34) (4,20) (4,9) (4,16) (4,15) (4,13) (4,19) (4,30) (5,17) (5,8) (6,12) (6,10) (6,28) (6,7) (6,14) (6,32) (6,29) (7,26) (7,12) (7,14) (7,32) (7,23) (7,24) (7,29) (8,17) (9,31) (9,18) (9,34) (9,20) (9,16) (9,22) (10,26) (10,12) (10,28) (10,32) (10,24) (12,26) (12,14) (12,24) (12,29) (13,27) (13,31) (13,25) (13,18) (13,34) (13,16) (13,33) (13,19) (13,22) (13,21) (13,30) (14,26) (14,28) (14,32) (15,25) (15,18) (15,34) (15,20) (15,33) (15,19) (15,22) (15,30) (16,27) (16,18) (16,34) (16,20) (16,33) (16,19) (16,22) (16,21) (18,25) (18,34) (18,22) (18,21) (18,30) (19,27) (19,31) (19,25) (19,20) (19,33) (19,22) (19,21) (19,30) (20,27) (20,31) (20,34) (20,33) (20,22) (20,21) (21,31) (21,22) (21,30) (22,27) (22,31) (22,25) (22,34) (22,30) (23,26) (23,28) (23,32) (23,29) (24,28) (24,32) (24,29) (25,27) (25,31) (25,33) (25,30) (26,28) (27,31) (27,34) (27,30) (28,29) (29,32) (30,34) (30,33) (31,34) (31,33)\nIs there a path between node 24 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph154-9_24", + "image": "data/connectivity/graph_visual/hard/graph154.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,2) (0,23) (0,8) (1,6) (1,26) (1,11) (2,6) (2,11) (3,12) (3,19) (3,20) (4,13) (4,21) (4,17) (4,10) (4,6) (4,23) (4,8) (5,13) (5,7) (5,21) (5,17) (5,28) (5,6) (5,23) (5,8) (5,26) (5,24) (5,11) (6,13) (6,17) (6,10) (6,23) (6,24) (7,17) (7,28) (7,23) (8,21) (8,10) (9,15) (10,13) (10,21) (10,23) (10,11) (11,13) (11,17) (12,19) (12,14) (12,27) (12,15) (12,22) (13,17) (13,16) (14,22) (15,19) (16,17) (16,28) (16,24) (17,24) (18,19) (18,27) (19,27) (21,26) (21,24) (22,25) (23,28) (24,28) (25,27)\nIs there a path between node 9 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph166-16_28", + "image": "data/connectivity/graph_visual/hard/graph166.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,5) (0,17) (0,26) (0,24) (0,25) (1,6) (1,19) (1,16) (1,2) (1,22) (1,11) (1,13) (2,6) (2,19) (2,15) (3,21) (3,19) (3,27) (3,23) (3,8) (4,5) (5,7) (6,27) (6,22) (6,20) (7,12) (7,25) (8,27) (8,22) (8,23) (8,20) (8,13) (9,28) (10,11) (10,14) (11,19) (11,16) (11,27) (11,23) (11,20) (12,26) (12,28) (12,24) (13,27) (13,22) (13,14) (14,27) (14,23) (15,23) (16,27) (16,22) (16,23) (17,24) (17,25) (18,25) (19,27) (19,22) (19,23) (20,21) (20,22) (20,23) (24,28) (25,26)\nIs there a path between node 16 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph192-1_18", + "image": "data/connectivity/graph_visual/hard/graph192.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,20) (0,5) (0,18) (0,6) (1,29) (1,21) (1,14) (1,23) (1,4) (1,27) (1,3) (2,28) (2,13) (2,16) (2,12) (2,14) (2,23) (2,4) (2,17) (2,11) (2,22) (2,15) (3,26) (4,29) (4,28) (4,12) (4,7) (4,22) (5,24) (5,20) (6,24) (7,11) (7,10) (8,24) (9,28) (9,14) (9,22) (9,10) (10,27) (10,22) (11,28) (11,12) (11,27) (11,26) (11,15) (12,29) (12,19) (12,28) (12,14) (12,23) (12,26) (13,29) (13,28) (13,14) (13,17) (13,26) (14,29) (14,19) (14,28) (14,26) (15,29) (15,19) (15,21) (15,17) (16,29) (16,21) (16,23) (16,22) (17,29) (17,19) (17,25) (17,27) (18,24) (19,21) (19,27) (19,22) (21,27) (22,28) (22,27) (23,29) (23,28) (23,25) (25,27) (25,26) (26,29) (27,28)\nIs there a path between node 1 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph121-8_20", + "image": "data/connectivity/graph_visual/hard/graph121.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,12) (0,8) (0,5) (0,4) (0,25) (0,22) (0,16) (0,24) (0,21) (2,15) (2,23) (2,26) (2,10) (2,3) (2,11) (2,6) (2,27) (3,15) (3,23) (3,14) (3,26) (3,10) (3,11) (3,27) (4,8) (4,13) (4,5) (4,20) (4,18) (4,7) (4,22) (4,16) (4,24) (5,8) (5,13) (5,20) (5,7) (5,22) (5,24) (5,21) (6,15) (6,23) (6,14) (6,26) (6,10) (6,11) (6,27) (7,12) (7,20) (7,25) (7,16) (7,21) (8,12) (8,20) (8,25) (8,16) (8,24) (10,15) (10,23) (10,14) (10,26) (10,19) (10,11) (10,27) (11,15) (11,23) (11,26) (11,27) (12,16) (12,24) (12,21) (13,20) (13,18) (13,25) (13,22) (13,16) (13,24) (13,21) (14,15) (14,26) (15,26) (15,27) (16,22) (16,24) (16,21) (18,25) (18,22) (18,21) (19,23) (19,26) (19,27) (20,25) (20,24) (21,25) (21,24) (22,25) (22,24) (23,26) (23,27) (24,25) (26,27)\nIs there a path between node 8 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph278-10_8", + "image": "data/connectivity/graph_visual/hard/graph278.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,10) (0,1) (0,15) (0,17) (0,12) (0,8) (1,16) (1,10) (1,18) (1,15) (1,2) (1,17) (1,28) (2,12) (2,8) (3,29) (3,24) (3,25) (3,6) (3,27) (3,19) (3,11) (3,4) (3,5) (4,9) (4,30) (4,22) (4,11) (5,29) (5,24) (5,23) (5,9) (5,25) (5,30) (5,6) (5,22) (5,19) (5,11) (6,29) (6,24) (6,23) (6,25) (6,30) (6,27) (6,22) (6,11) (7,20) (7,21) (7,13) (7,26) (7,14) (8,16) (8,10) (8,18) (8,15) (8,17) (8,12) (8,28) (9,29) (9,23) (9,30) (9,27) (9,22) (9,19) (10,16) (10,18) (10,15) (10,17) (10,12) (10,28) (11,29) (11,25) (11,22) (12,16) (12,15) (12,17) (13,26) (13,14) (14,20) (14,21) (15,16) (15,18) (15,28) (16,18) (16,17) (16,28) (17,18) (17,28) (18,28) (19,29) (19,23) (19,25) (19,30) (19,22) (20,21) (22,29) (22,24) (22,25) (22,30) (23,24) (23,25) (23,27) (24,25) (25,29) (25,30) (25,27) (27,29) (29,30)\nIs there a path between node 10 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph682-19_14", + "image": "data/connectivity/graph_visual/hard/graph682.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,8) (0,28) (0,29) (0,16) (0,5) (0,6) (0,12) (0,15) (1,28) (1,18) (1,4) (1,3) (1,21) (1,14) (1,12) (2,22) (3,8) (3,29) (3,33) (3,5) (3,21) (3,30) (3,26) (3,14) (3,7) (3,31) (3,24) (3,12) (3,32) (4,17) (4,5) (4,34) (4,12) (4,32) (4,19) (5,18) (5,16) (5,33) (5,21) (5,6) (5,30) (5,20) (5,11) (6,27) (6,17) (6,26) (6,7) (6,24) (6,15) (7,28) (7,18) (7,29) (7,17) (7,21) (7,26) (7,14) (7,11) (7,32) (8,28) (8,18) (8,29) (8,34) (8,10) (8,30) (8,26) (8,23) (8,14) (8,20) (10,21) (10,30) (10,14) (10,24) (10,20) (10,12) (10,11) (11,16) (11,34) (11,30) (11,14) (11,24) (11,20) (12,27) (12,28) (12,29) (12,17) (12,16) (12,20) (12,32) (12,19) (13,27) (13,17) (13,16) (13,33) (13,23) (13,14) (13,24) (14,33) (14,34) (14,21) (14,30) (14,20) (14,32) (14,19) (14,15) (15,18) (15,29) (15,21) (15,30) (15,23) (16,27) (16,18) (16,17) (16,24) (17,28) (17,33) (17,34) (17,31) (17,32) (18,33) (18,34) (18,21) (18,30) (18,23) (18,24) (18,32) (19,29) (19,33) (19,21) (19,26) (19,32) (20,28) (20,29) (20,33) (20,30) (21,29) (21,33) (21,26) (23,33) (24,27) (24,29) (24,33) (24,30) (24,26) (26,28) (26,29) (27,29) (28,31) (28,32) (29,32)\nIs there a path between node 19 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph223-1_10", + "image": "data/connectivity/graph_visual/hard/graph223.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,3) (0,29) (0,1) (0,20) (0,7) (0,5) (0,9) (0,8) (0,26) (0,25) (1,21) (1,12) (1,3) (1,4) (1,29) (1,19) (1,11) (1,20) (1,7) (1,5) (1,9) (1,23) (1,8) (1,26) (1,25) (2,21) (2,3) (2,4) (2,29) (2,19) (2,7) (2,5) (2,9) (2,17) (2,25) (3,29) (3,10) (3,19) (3,11) (3,20) (3,7) (3,5) (3,9) (3,8) (3,17) (4,21) (4,29) (4,20) (4,7) (4,9) (4,23) (4,8) (4,17) (4,26) (4,25) (5,12) (5,10) (5,8) (5,17) (5,26) (5,25) (6,16) (6,18) (7,21) (7,29) (7,10) (7,19) (7,20) (7,9) (7,8) (7,17) (7,26) (7,25) (8,21) (8,29) (8,10) (8,19) (8,9) (8,23) (8,17) (8,26) (8,25) (9,21) (9,12) (9,10) (9,11) (9,20) (9,23) (9,17) (9,26) (10,29) (10,19) (10,11) (10,20) (10,25) (11,12) (11,29) (11,19) (11,20) (11,23) (11,17) (11,26) (11,25) (12,21) (12,29) (12,19) (12,23) (12,17) (12,26) (12,25) (13,22) (13,15) (14,18) (15,28) (15,27) (15,22) (15,24) (16,18) (17,21) (17,20) (17,23) (17,25) (19,29) (19,20) (19,26) (19,25) (20,21) (20,23) (20,26) (20,25) (21,25) (22,28) (22,24) (23,29) (23,26) (23,25) (24,27) (25,29) (25,26) (27,28)\nIs there a path between node 1 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph232-10_17", + "image": "data/connectivity/graph_visual/hard/graph232.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,20) (0,9) (0,21) (0,1) (0,19) (0,7) (0,3) (0,27) (0,12) (0,23) (0,17) (1,9) (1,21) (1,10) (1,4) (1,19) (1,3) (1,12) (1,23) (1,17) (2,8) (2,28) (2,16) (2,24) (2,5) (2,11) (2,15) (3,20) (3,9) (3,21) (3,19) (3,27) (3,12) (3,23) (4,20) (4,9) (4,21) (4,19) (4,12) (4,23) (4,17) (5,18) (5,28) (5,16) (5,6) (5,14) (6,18) (6,28) (6,24) (7,20) (7,9) (7,12) (7,17) (8,16) (8,24) (8,15) (9,21) (9,10) (9,27) (9,12) (9,23) (9,17) (10,19) (10,27) (10,12) (10,23) (11,28) (11,16) (11,14) (11,24) (11,15) (12,20) (12,19) (12,27) (12,23) (12,17) (13,25) (13,26) (13,29) (14,28) (14,24) (14,15) (15,18) (15,28) (15,24) (16,18) (16,28) (17,20) (17,21) (17,23) (18,28) (18,24) (19,20) (19,21) (19,23) (20,27) (21,27) (22,25) (22,26) (22,29) (25,29) (26,29)\nIs there a path between node 10 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph643-26_30", + "image": "data/connectivity/graph_visual/hard/graph643.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,19) (0,3) (0,23) (0,8) (0,1) (0,28) (0,27) (0,9) (0,11) (0,32) (1,3) (1,26) (1,8) (1,15) (1,28) (1,27) (1,9) (1,11) (1,32) (2,29) (2,20) (2,12) (2,5) (2,33) (2,6) (2,18) (2,21) (2,25) (2,31) (2,14) (2,24) (2,16) (3,19) (3,23) (3,26) (3,8) (3,34) (3,27) (3,11) (3,32) (3,30) (4,20) (4,12) (4,5) (4,6) (4,18) (4,21) (4,7) (4,25) (4,13) (4,14) (4,16) (4,22) (5,29) (5,20) (5,12) (5,6) (5,17) (5,7) (5,25) (5,31) (5,24) (5,22) (6,29) (6,12) (6,33) (6,17) (6,7) (6,25) (6,13) (6,31) (6,24) (6,16) (6,22) (7,29) (7,18) (7,13) (7,14) (7,24) (8,19) (8,23) (8,26) (8,28) (8,9) (8,11) (8,32) (8,30) (9,19) (9,26) (9,34) (9,15) (9,28) (9,27) (9,11) (9,32) (10,29) (10,12) (10,33) (10,21) (10,25) (10,13) (10,31) (10,14) (10,24) (10,16) (11,23) (11,26) (11,34) (11,15) (11,28) (11,27) (11,32) (12,29) (12,20) (12,33) (12,17) (12,18) (12,21) (12,25) (12,13) (12,24) (12,16) (12,22) (13,29) (13,20) (13,33) (13,17) (13,18) (13,25) (13,31) (13,24) (13,16) (14,20) (14,18) (14,21) (14,25) (14,31) (14,24) (14,16) (14,22) (15,19) (15,23) (15,34) (15,28) (15,27) (15,32) (15,30) (16,29) (16,20) (16,33) (16,17) (16,31) (16,24) (17,29) (17,33) (17,18) (17,21) (17,31) (17,24) (17,22) (18,29) (18,20) (18,25) (18,31) (18,24) (18,22) (19,26) (19,34) (19,28) (19,27) (19,32) (19,30) (20,21) (20,25) (20,31) (20,24) (20,22) (21,29) (21,33) (21,31) (21,24) (21,22) (22,29) (22,33) (22,25) (22,31) (22,24) (23,26) (23,28) (23,27) (23,30) (24,33) (24,25) (24,31) (25,29) (25,33) (25,31) (26,34) (26,28) (26,27) (26,30) (27,34) (27,30) (28,32) (28,30) (29,33) (29,31) (30,34) (30,32) (31,33) (32,34)\nIs there a path between node 26 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph688-31_20", + "image": "data/connectivity/graph_visual/hard/graph688.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,29) (0,30) (1,19) (1,22) (1,13) (1,28) (1,26) (1,24) (1,3) (1,12) (1,7) (1,16) (1,25) (1,27) (1,11) (2,31) (2,10) (2,18) (2,9) (2,14) (2,23) (2,33) (2,32) (3,19) (3,21) (3,22) (3,28) (3,26) (3,24) (3,12) (3,7) (3,16) (3,25) (3,27) (3,11) (4,17) (5,8) (5,9) (5,23) (5,32) (6,29) (6,15) (7,19) (7,22) (7,28) (7,26) (7,24) (7,12) (7,16) (7,25) (7,27) (8,31) (8,10) (8,18) (8,14) (8,23) (8,33) (8,32) (9,31) (9,10) (9,18) (9,14) (9,23) (9,32) (10,31) (10,18) (10,14) (10,23) (10,33) (10,32) (11,19) (11,21) (11,22) (11,13) (11,28) (11,26) (11,12) (11,16) (11,27) (12,22) (12,13) (12,24) (12,16) (12,25) (12,27) (13,19) (13,22) (13,28) (13,26) (13,24) (13,16) (13,25) (14,31) (14,18) (14,23) (14,33) (14,32) (15,34) (15,30) (16,21) (16,22) (16,25) (16,27) (17,20) (18,31) (18,23) (18,32) (19,21) (19,22) (19,28) (19,26) (19,24) (19,25) (21,22) (21,28) (21,26) (21,24) (21,25) (21,27) (22,28) (22,27) (23,31) (23,33) (23,32) (24,28) (24,26) (24,27) (25,28) (25,26) (25,27) (26,28) (26,27) (30,34) (31,33)\nIs there a path between node 31 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph643-3_18", + "image": "data/connectivity/graph_visual/hard/graph643.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,19) (0,3) (0,23) (0,8) (0,1) (0,28) (0,27) (0,9) (0,11) (0,32) (1,3) (1,26) (1,8) (1,15) (1,28) (1,27) (1,9) (1,11) (1,32) (2,29) (2,20) (2,12) (2,5) (2,33) (2,6) (2,18) (2,21) (2,25) (2,31) (2,14) (2,24) (2,16) (3,19) (3,23) (3,26) (3,8) (3,34) (3,27) (3,11) (3,32) (3,30) (4,20) (4,12) (4,5) (4,6) (4,18) (4,21) (4,7) (4,25) (4,13) (4,14) (4,16) (4,22) (5,29) (5,20) (5,12) (5,6) (5,17) (5,7) (5,25) (5,31) (5,24) (5,22) (6,29) (6,12) (6,33) (6,17) (6,7) (6,25) (6,13) (6,31) (6,24) (6,16) (6,22) (7,29) (7,18) (7,13) (7,14) (7,24) (8,19) (8,23) (8,26) (8,28) (8,9) (8,11) (8,32) (8,30) (9,19) (9,26) (9,34) (9,15) (9,28) (9,27) (9,11) (9,32) (10,29) (10,12) (10,33) (10,21) (10,25) (10,13) (10,31) (10,14) (10,24) (10,16) (11,23) (11,26) (11,34) (11,15) (11,28) (11,27) (11,32) (12,29) (12,20) (12,33) (12,17) (12,18) (12,21) (12,25) (12,13) (12,24) (12,16) (12,22) (13,29) (13,20) (13,33) (13,17) (13,18) (13,25) (13,31) (13,24) (13,16) (14,20) (14,18) (14,21) (14,25) (14,31) (14,24) (14,16) (14,22) (15,19) (15,23) (15,34) (15,28) (15,27) (15,32) (15,30) (16,29) (16,20) (16,33) (16,17) (16,31) (16,24) (17,29) (17,33) (17,18) (17,21) (17,31) (17,24) (17,22) (18,29) (18,20) (18,25) (18,31) (18,24) (18,22) (19,26) (19,34) (19,28) (19,27) (19,32) (19,30) (20,21) (20,25) (20,31) (20,24) (20,22) (21,29) (21,33) (21,31) (21,24) (21,22) (22,29) (22,33) (22,25) (22,31) (22,24) (23,26) (23,28) (23,27) (23,30) (24,33) (24,25) (24,31) (25,29) (25,33) (25,31) (26,34) (26,28) (26,27) (26,30) (27,34) (27,30) (28,32) (28,30) (29,33) (29,31) (30,34) (30,32) (31,33) (32,34)\nIs there a path between node 3 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph414-1_27", + "image": "data/connectivity/graph_visual/hard/graph414.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,2) (0,26) (0,21) (0,6) (0,12) (0,28) (0,15) (0,7) (1,21) (1,14) (1,25) (1,8) (1,18) (1,15) (1,27) (1,7) (2,26) (2,21) (2,14) (2,8) (2,24) (2,16) (2,13) (2,19) (2,28) (2,15) (2,27) (2,7) (3,26) (3,13) (3,18) (3,12) (3,9) (3,15) (3,27) (3,7) (3,4) (4,17) (4,8) (4,16) (4,12) (4,20) (5,14) (5,25) (5,13) (5,18) (5,28) (5,27) (5,32) (6,17) (6,25) (6,16) (6,9) (6,32) (6,11) (7,21) (7,24) (7,18) (7,12) (7,28) (7,15) (7,31) (8,25) (8,24) (8,9) (8,15) (8,31) (8,27) (8,32) (9,17) (9,16) (9,19) (9,12) (9,28) (9,15) (9,27) (10,22) (11,13) (11,18) (11,19) (11,12) (11,31) (11,27) (12,21) (12,25) (12,24) (12,16) (12,15) (12,32) (13,17) (13,14) (13,24) (13,18) (13,15) (13,20) (13,32) (14,24) (14,19) (14,28) (14,15) (14,20) (14,32) (15,28) (16,24) (16,18) (17,25) (17,28) (17,27) (18,21) (19,25) (19,28) (20,24) (20,32) (21,26) (21,25) (22,30) (23,30) (23,29) (24,25) (25,26) (25,28) (25,32) (26,31) (27,28) (27,31) (28,31) (28,32)\nIs there a path between node 1 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph78-17_11", + "image": "data/connectivity/graph_visual/hard/graph78.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,7) (0,24) (0,8) (1,10) (1,22) (1,4) (1,5) (1,11) (1,13) (1,12) (1,14) (1,18) (1,20) (1,25) (1,6) (1,15) (1,26) (1,3) (2,10) (2,22) (2,4) (2,5) (2,11) (2,21) (2,12) (2,14) (2,18) (2,20) (2,25) (2,23) (2,6) (2,15) (2,26) (2,3) (3,19) (3,16) (3,22) (3,4) (3,5) (3,11) (3,25) (3,23) (3,15) (3,26) (4,19) (4,16) (4,22) (4,5) (4,11) (4,13) (4,12) (4,14) (4,15) (4,26) (5,19) (5,10) (5,16) (5,21) (5,13) (5,14) (5,18) (5,20) (5,25) (5,23) (5,6) (6,19) (6,10) (6,16) (6,22) (6,18) (6,20) (6,25) (6,23) (6,15) (7,17) (7,9) (7,24) (7,8) (8,17) (8,9) (9,17) (9,24) (10,19) (10,16) (10,22) (10,11) (10,21) (10,13) (10,12) (10,18) (10,20) (10,23) (10,15) (11,19) (11,16) (11,13) (11,12) (11,14) (11,18) (11,20) (11,25) (11,23) (12,19) (12,16) (12,21) (12,13) (12,14) (12,20) (12,25) (12,23) (13,19) (13,16) (13,22) (13,18) (13,20) (13,15) (13,26) (14,19) (14,22) (14,21) (14,18) (14,20) (14,15) (15,16) (15,22) (15,21) (15,20) (15,23) (15,26) (16,19) (16,21) (16,18) (16,20) (16,25) (16,23) (16,26) (17,24) (18,19) (18,22) (18,21) (18,20) (18,23) (19,22) (19,21) (19,20) (19,25) (19,23) (20,22) (20,21) (20,25) (20,23) (20,26) (21,22) (21,23) (22,25) (22,23) (22,26) (23,26) (25,26)\nIs there a path between node 17 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph431-9_28", + "image": "data/connectivity/graph_visual/hard/graph431.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,3) (0,7) (0,5) (0,9) (0,25) (0,26) (0,15) (0,22) (0,13) (0,31) (0,1) (0,20) (1,3) (1,7) (1,5) (1,28) (1,9) (1,15) (1,22) (1,31) (1,30) (2,16) (2,17) (2,6) (2,14) (2,21) (2,32) (2,24) (2,8) (2,27) (2,10) (2,29) (2,19) (3,23) (3,18) (3,5) (3,28) (3,9) (3,25) (3,20) (3,30) (4,16) (4,17) (4,14) (4,21) (4,32) (4,12) (4,24) (4,8) (4,27) (4,10) (4,29) (4,11) (4,19) (5,23) (5,18) (5,7) (5,28) (5,9) (5,25) (5,26) (5,15) (5,22) (5,20) (5,30) (6,17) (6,14) (6,32) (6,12) (6,24) (6,8) (6,27) (6,19) (7,18) (7,9) (7,25) (7,26) (7,22) (7,13) (7,31) (7,20) (8,16) (8,17) (8,14) (8,32) (8,24) (8,27) (8,29) (8,19) (9,23) (9,18) (9,28) (9,25) (9,15) (9,22) (9,13) (9,31) (9,20) (10,16) (10,17) (10,21) (10,32) (10,12) (10,19) (11,16) (11,14) (11,21) (11,12) (11,24) (11,27) (11,29) (11,19) (12,16) (12,17) (12,14) (12,32) (12,27) (12,29) (12,19) (13,23) (13,18) (13,26) (13,15) (13,20) (13,30) (14,16) (14,32) (14,24) (14,27) (14,19) (15,23) (15,18) (15,28) (15,25) (15,26) (15,22) (15,31) (15,20) (16,17) (16,21) (16,32) (16,29) (17,21) (17,32) (17,24) (17,27) (17,29) (17,19) (18,25) (18,26) (18,22) (18,31) (18,30) (19,21) (19,32) (19,24) (19,27) (19,29) (20,28) (20,25) (20,26) (20,22) (20,31) (21,32) (21,24) (21,27) (22,23) (22,28) (22,25) (22,30) (23,28) (23,31) (23,30) (24,32) (24,29) (25,28) (25,26) (26,28) (26,30) (27,32) (27,29) (28,31) (28,30) (29,32)\nIs there a path between node 9 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph699-23_14", + "image": "data/connectivity/graph_visual/hard/graph699.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,22) (0,23) (0,24) (0,19) (0,4) (0,7) (0,10) (0,3) (0,20) (0,28) (0,2) (0,26) (0,29) (0,21) (1,17) (1,5) (1,14) (1,30) (1,16) (2,13) (2,27) (2,23) (2,24) (2,34) (2,32) (2,10) (2,33) (2,20) (2,26) (2,9) (3,13) (3,27) (3,6) (3,23) (3,24) (3,19) (3,34) (3,10) (3,33) (3,20) (3,28) (3,26) (3,9) (3,29) (3,21) (4,13) (4,27) (4,22) (4,24) (4,19) (4,7) (4,10) (4,33) (4,20) (4,28) (4,26) (4,9) (4,29) (4,21) (5,17) (5,14) (5,15) (5,12) (5,30) (5,18) (5,16) (6,13) (6,22) (6,23) (6,34) (6,32) (6,10) (6,20) (6,26) (6,9) (6,8) (7,13) (7,23) (7,24) (7,19) (7,34) (7,10) (7,33) (7,20) (7,28) (7,8) (7,29) (7,21) (8,27) (8,23) (8,24) (8,34) (8,10) (8,28) (8,9) (8,29) (8,21) (9,13) (9,27) (9,22) (9,23) (9,34) (9,32) (9,10) (9,20) (9,28) (9,26) (9,21) (10,13) (10,27) (10,22) (10,24) (10,19) (10,34) (10,32) (10,33) (10,20) (10,26) (10,29) (10,21) (11,17) (11,31) (11,14) (11,15) (11,18) (11,16) (12,31) (12,15) (12,30) (12,18) (13,27) (13,22) (13,24) (13,32) (13,33) (13,20) (13,28) (13,26) (13,21) (14,17) (14,31) (14,15) (14,30) (14,18) (14,16) (15,17) (15,30) (15,18) (15,16) (16,17) (16,31) (16,30) (16,18) (17,31) (17,18) (18,31) (18,30) (19,22) (19,23) (19,24) (19,34) (19,32) (19,33) (19,20) (19,28) (19,26) (19,29) (19,21) (20,22) (20,23) (20,34) (20,21) (21,27) (21,22) (21,23) (21,34) (21,32) (21,33) (21,28) (21,26) (21,29) (22,27) (22,24) (22,33) (22,28) (22,26) (22,29) (23,27) (23,32) (23,33) (23,26) (23,29) (24,27) (24,34) (24,33) (24,28) (24,26) (24,29) (26,27) (26,34) (26,32) (26,29) (27,34) (27,32) (27,33) (27,28) (27,29) (28,32) (28,33) (28,29) (29,34) (29,32) (32,34) (32,33)\nIs there a path between node 23 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph86-15_0", + "image": "data/connectivity/graph_visual/hard/graph86.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,25) (0,5) (0,14) (0,24) (1,7) (1,23) (1,18) (1,15) (1,26) (1,9) (1,22) (1,2) (1,3) (2,12) (2,16) (2,7) (2,15) (2,26) (2,9) (2,22) (2,3) (3,12) (3,16) (3,23) (3,8) (3,18) (3,26) (3,9) (3,22) (3,19) (4,10) (4,25) (4,20) (4,11) (4,14) (4,24) (4,13) (5,25) (5,14) (6,10) (6,21) (6,20) (6,13) (7,16) (7,23) (7,15) (7,26) (7,9) (7,22) (7,17) (7,19) (8,12) (8,16) (8,23) (8,18) (8,15) (8,26) (8,9) (8,22) (8,17) (8,19) (9,16) (9,18) (9,15) (9,26) (10,21) (10,20) (10,11) (10,14) (10,13) (11,21) (11,25) (11,20) (11,13) (12,16) (12,23) (12,15) (12,26) (12,22) (12,19) (13,21) (13,25) (13,20) (13,14) (13,24) (14,25) (15,16) (15,23) (15,18) (15,22) (15,17) (16,23) (16,26) (16,17) (16,19) (17,23) (17,18) (17,26) (17,22) (17,19) (18,23) (18,26) (18,22) (19,23) (19,26) (19,22) (20,21) (20,25) (20,24) (21,25) (21,24) (22,23) (22,26) (23,26) (24,25)\nIs there a path between node 15 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph500-30_28", + "image": "data/connectivity/graph_visual/hard/graph500.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,24) (0,14) (0,1) (0,12) (0,7) (1,15) (1,10) (1,12) (1,25) (3,9) (3,13) (3,23) (3,7) (4,14) (4,20) (4,23) (4,12) (4,16) (4,8) (4,6) (5,18) (6,24) (6,15) (6,14) (6,12) (7,15) (7,20) (7,12) (7,25) (7,16) (7,27) (8,24) (8,10) (8,14) (8,9) (8,13) (8,23) (8,12) (8,16) (8,27) (9,20) (9,12) (9,25) (9,16) (10,14) (10,12) (10,16) (10,27) (12,23) (13,24) (13,15) (13,20) (13,33) (14,24) (14,20) (14,23) (14,33) (14,16) (14,27) (15,24) (15,25) (16,24) (19,31) (20,33) (20,27) (23,25) (26,29) (28,32)\nIs there a path between node 30 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph99-11_8", + "image": "data/connectivity/graph_visual/hard/graph99.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,1) (0,13) (0,22) (0,23) (0,9) (0,18) (0,7) (0,2) (0,15) (0,10) (0,16) (0,21) (0,4) (0,25) (0,27) (1,8) (1,13) (1,14) (1,22) (1,6) (1,24) (1,9) (1,18) (1,7) (1,2) (1,15) (1,26) (1,10) (1,12) (1,16) (1,11) (1,4) (1,5) (2,13) (2,14) (2,23) (2,6) (2,24) (2,9) (2,12) (2,16) (2,21) (2,11) (2,4) (2,25) (3,19) (4,8) (4,13) (4,14) (4,22) (4,6) (4,24) (4,18) (4,7) (4,15) (4,20) (4,16) (4,21) (4,11) (4,17) (4,27) (5,8) (5,13) (5,14) (5,23) (5,6) (5,9) (5,18) (5,7) (5,15) (5,26) (5,20) (5,12) (5,16) (5,21) (6,8) (6,13) (6,14) (6,22) (6,24) (6,9) (6,18) (6,7) (6,15) (6,26) (6,20) (6,10) (6,25) (6,17) (6,27) (7,8) (7,13) (7,14) (7,22) (7,24) (7,9) (7,15) (7,26) (7,10) (7,11) (7,25) (7,17) (8,13) (8,14) (8,22) (8,23) (8,24) (8,9) (8,26) (8,10) (8,12) (8,11) (8,25) (8,17) (9,14) (9,22) (9,23) (9,24) (9,18) (9,15) (9,26) (9,16) (9,21) (9,11) (9,25) (10,23) (10,24) (10,18) (10,15) (10,12) (10,21) (10,25) (10,17) (10,27) (11,14) (11,22) (11,15) (11,26) (11,20) (11,12) (11,21) (11,25) (11,17) (11,27) (12,13) (12,14) (12,22) (12,23) (12,24) (12,18) (12,15) (12,26) (12,16) (12,21) (12,17) (13,14) (13,22) (13,24) (13,26) (13,20) (13,16) (13,25) (13,17) (13,27) (14,22) (14,18) (14,15) (14,26) (14,20) (14,16) (14,25) (15,23) (15,24) (15,18) (15,26) (15,20) (15,16) (15,21) (15,25) (15,17) (15,27) (16,22) (16,26) (16,20) (16,21) (16,25) (16,17) (16,27) (17,22) (17,23) (17,25) (18,22) (18,23) (18,24) (18,26) (18,21) (18,25) (20,26) (20,21) (21,23) (21,26) (21,25) (21,27) (22,23) (22,26) (22,27) (23,24) (23,27) (24,26) (24,27) (25,27) (26,27)\nIs there a path between node 11 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph364-15_13", + "image": "data/connectivity/graph_visual/hard/graph364.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,15) (0,25) (0,4) (0,27) (0,9) (0,10) (0,1) (0,7) (0,3) (0,31) (0,24) (0,20) (0,23) (1,15) (1,12) (1,25) (1,4) (1,27) (1,9) (1,30) (1,13) (1,8) (1,7) (1,3) (1,2) (1,20) (1,23) (2,15) (2,12) (2,25) (2,26) (2,9) (2,13) (2,8) (2,10) (2,22) (2,7) (2,3) (2,31) (2,19) (2,20) (2,23) (3,4) (3,27) (3,9) (3,13) (3,22) (3,7) (3,16) (3,24) (3,19) (3,20) (3,23) (4,12) (4,25) (4,27) (4,9) (4,13) (4,8) (4,10) (4,22) (4,31) (4,24) (4,23) (5,14) (5,17) (6,18) (6,21) (6,29) (6,28) (7,12) (7,25) (7,26) (7,9) (7,13) (7,8) (7,10) (7,22) (7,31) (7,16) (7,24) (7,19) (7,20) (7,23) (8,15) (8,25) (8,27) (8,30) (8,13) (8,10) (8,24) (8,19) (9,26) (9,27) (9,30) (9,22) (9,16) (9,20) (9,23) (10,12) (10,25) (10,30) (10,13) (10,22) (10,31) (10,24) (10,20) (10,23) (11,18) (11,21) (11,28) (12,25) (12,30) (12,13) (12,31) (12,16) (12,24) (12,20) (13,15) (13,25) (13,26) (13,27) (13,22) (13,24) (13,19) (13,20) (13,23) (14,17) (15,16) (15,19) (16,25) (16,27) (16,30) (16,22) (16,31) (16,19) (16,20) (16,23) (18,29) (19,25) (19,22) (19,31) (19,24) (19,20) (19,23) (20,26) (20,27) (20,30) (20,22) (20,31) (20,24) (20,23) (21,29) (21,28) (22,25) (22,26) (22,27) (22,30) (22,31) (22,24) (22,23) (23,25) (23,27) (23,30) (24,25) (24,26) (24,31) (25,26) (25,27) (25,30) (26,27) (26,30) (27,30) (27,31) (30,31)\nIs there a path between node 15 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph358-4_31", + "image": "data/connectivity/graph_visual/hard/graph358.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,7) (0,1) (0,10) (0,13) (0,26) (0,12) (1,11) (1,4) (1,10) (1,13) (1,24) (1,22) (1,17) (2,8) (2,29) (2,7) (2,4) (2,10) (2,19) (2,30) (3,6) (3,11) (3,29) (3,7) (3,26) (3,22) (4,14) (4,29) (4,7) (4,13) (4,12) (4,22) (5,6) (5,8) (5,11) (5,7) (5,15) (5,12) (5,22) (5,17) (6,8) (6,29) (6,15) (6,10) (6,13) (6,19) (6,22) (6,17) (7,14) (7,28) (7,11) (7,13) (7,26) (7,24) (7,19) (7,21) (7,30) (8,28) (8,20) (8,11) (8,25) (8,27) (8,15) (8,10) (8,26) (8,12) (8,24) (8,22) (8,21) (10,18) (10,27) (10,15) (10,24) (11,14) (11,18) (11,19) (11,22) (11,21) (11,17) (11,30) (12,14) (12,20) (12,29) (12,27) (12,13) (12,26) (12,19) (13,14) (13,20) (13,18) (13,25) (14,28) (14,25) (14,27) (14,24) (14,22) (15,28) (15,20) (15,26) (15,30) (16,23) (17,28) (17,20) (17,27) (17,19) (17,22) (18,24) (18,22) (18,30) (19,20) (19,29) (19,25) (19,27) (19,30) (20,30) (21,29) (21,27) (21,26) (21,24) (21,22) (21,30) (22,28) (22,29) (22,26) (22,30) (24,25) (25,29) (27,28) (27,29) (27,30)\nIs there a path between node 4 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph674-12_19", + "image": "data/connectivity/graph_visual/hard/graph674.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,6) (0,23) (0,25) (0,8) (0,29) (1,19) (1,30) (2,7) (2,4) (2,3) (2,31) (2,8) (2,34) (3,23) (4,9) (4,17) (4,8) (4,13) (4,34) (5,15) (5,24) (6,9) (6,7) (6,12) (6,23) (6,31) (7,10) (7,23) (7,22) (7,29) (9,10) (9,22) (9,29) (10,12) (10,22) (11,23) (11,22) (12,22) (12,17) (12,13) (12,34) (13,31) (13,17) (14,16) (15,21) (15,19) (15,27) (17,26) (17,25) (17,31) (18,20) (18,33) (19,21) (19,30) (19,32) (19,27) (20,28) (20,33) (21,24) (21,30) (21,27) (22,34) (25,26) (25,34) (26,31) (27,32) (30,32)\nIs there a path between node 12 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph596-11_25", + "image": "data/connectivity/graph_visual/hard/graph596.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,27) (0,9) (0,11) (0,17) (0,29) (0,3) (0,21) (0,24) (0,23) (0,19) (0,22) (0,4) (0,33) (1,6) (1,31) (1,2) (1,12) (1,14) (1,16) (1,15) (1,13) (1,5) (2,26) (2,6) (2,31) (2,12) (2,10) (2,32) (2,14) (2,16) (2,15) (2,13) (2,5) (3,9) (3,11) (3,8) (3,17) (3,29) (3,21) (3,23) (3,19) (3,22) (3,4) (3,33) (4,11) (4,17) (4,29) (4,21) (4,24) (4,23) (4,19) (4,22) (4,20) (5,26) (5,6) (5,31) (5,12) (5,10) (5,32) (5,15) (6,26) (6,12) (6,10) (6,32) (6,14) (6,16) (6,15) (7,9) (7,11) (7,8) (7,17) (7,29) (7,24) (7,19) (7,22) (7,20) (7,33) (8,29) (8,21) (8,24) (8,23) (8,22) (8,28) (8,33) (9,27) (9,11) (9,17) (9,29) (9,21) (9,24) (9,28) (9,20) (10,26) (10,12) (10,14) (10,16) (10,13) (11,27) (11,29) (11,19) (11,22) (11,20) (12,31) (12,32) (12,16) (12,13) (13,26) (13,32) (13,16) (13,15) (14,26) (14,31) (14,16) (14,15) (15,31) (15,32) (15,16) (16,26) (16,31) (17,27) (17,29) (17,21) (17,23) (17,19) (17,22) (17,33) (18,25) (18,30) (19,29) (19,24) (19,28) (19,33) (20,27) (20,29) (20,21) (20,28) (20,33) (21,29) (21,24) (21,22) (21,33) (22,29) (22,24) (22,23) (22,28) (22,33) (24,29) (24,28) (24,33) (25,30) (26,32) (27,29) (27,28) (27,33) (28,29) (29,33) (31,32)\nIs there a path between node 11 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph336-16_24", + "image": "data/connectivity/graph_visual/hard/graph336.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,22) (0,14) (0,4) (0,15) (0,20) (0,3) (0,18) (0,26) (1,7) (1,19) (1,6) (1,27) (1,11) (1,12) (1,31) (1,13) (1,24) (1,16) (1,10) (1,29) (2,7) (2,23) (2,6) (2,27) (2,17) (2,12) (2,28) (2,24) (2,10) (2,29) (2,21) (2,8) (3,14) (3,4) (3,20) (3,18) (3,26) (4,22) (4,14) (4,15) (4,20) (4,18) (4,26) (5,30) (5,25) (6,7) (6,27) (6,17) (6,11) (6,31) (6,13) (6,10) (6,8) (7,23) (7,27) (7,17) (7,11) (7,12) (7,31) (7,13) (7,24) (7,16) (7,10) (7,29) (7,8) (8,23) (8,17) (8,11) (8,12) (8,28) (8,31) (8,13) (8,24) (8,16) (8,29) (10,11) (10,12) (10,31) (10,24) (10,16) (10,29) (10,21) (11,23) (11,19) (11,27) (11,17) (11,12) (11,28) (11,13) (11,24) (12,23) (12,17) (12,28) (12,31) (12,16) (12,21) (13,23) (13,19) (13,27) (13,28) (13,31) (13,21) (14,22) (14,15) (14,18) (14,26) (15,20) (15,26) (16,23) (16,27) (16,17) (16,31) (16,24) (16,29) (16,21) (17,23) (17,19) (17,27) (17,28) (17,31) (17,24) (18,22) (18,26) (19,27) (19,31) (19,24) (19,29) (19,21) (20,22) (20,26) (21,27) (21,28) (21,31) (21,29) (22,26) (23,28) (23,31) (23,24) (23,29) (24,27) (24,31) (24,29) (25,30) (27,28) (28,31)\nIs there a path between node 16 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph331-18_27", + "image": "data/connectivity/graph_visual/hard/graph331.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,16) (0,12) (0,23) (0,10) (0,31) (0,3) (0,26) (0,22) (0,6) (0,25) (0,14) (0,24) (0,5) (1,29) (1,7) (1,16) (1,27) (1,12) (1,23) (1,31) (1,3) (1,19) (1,15) (1,9) (1,26) (1,6) (1,28) (1,13) (1,14) (1,24) (1,5) (2,20) (2,4) (2,17) (2,21) (2,30) (3,29) (3,7) (3,16) (3,27) (3,23) (3,31) (3,19) (3,15) (3,26) (3,6) (3,25) (3,28) (3,8) (3,13) (3,14) (3,24) (3,5) (4,20) (4,18) (4,30) (5,29) (5,7) (5,27) (5,12) (5,10) (5,9) (5,11) (5,26) (5,6) (5,28) (5,14) (5,24) (6,7) (6,16) (6,27) (6,23) (6,10) (6,15) (6,11) (6,26) (6,22) (6,25) (6,28) (6,13) (6,14) (7,29) (7,12) (7,23) (7,19) (7,15) (7,26) (7,22) (7,13) (7,14) (7,24) (8,29) (8,27) (8,23) (8,10) (8,19) (8,9) (8,11) (8,26) (8,22) (8,25) (8,14) (9,29) (9,12) (9,23) (9,10) (9,31) (9,19) (9,15) (9,22) (9,13) (9,24) (10,27) (10,12) (10,15) (10,11) (10,26) (10,25) (10,28) (10,13) (10,14) (11,29) (11,16) (11,27) (11,12) (11,23) (11,19) (11,15) (11,26) (11,28) (11,14) (11,24) (12,29) (12,23) (12,31) (12,19) (12,26) (12,22) (12,25) (12,28) (12,13) (12,24) (13,29) (13,16) (13,27) (13,31) (13,19) (13,22) (13,28) (13,14) (13,24) (14,29) (14,16) (14,27) (14,23) (14,31) (14,19) (14,26) (14,22) (14,25) (14,28) (14,24) (15,29) (15,16) (15,31) (15,19) (15,26) (15,22) (15,25) (15,28) (15,24) (16,29) (16,31) (16,26) (16,22) (16,25) (16,28) (16,24) (17,20) (17,18) (17,21) (17,30) (18,21) (18,30) (19,29) (19,27) (19,23) (19,22) (19,25) (20,21) (21,30) (22,29) (22,27) (22,23) (22,31) (22,25) (22,28) (22,24) (23,29) (23,27) (23,31) (23,24) (24,29) (24,27) (24,31) (24,26) (24,25) (24,28) (25,29) (25,27) (25,31) (25,28) (26,29) (26,27) (26,31) (27,29) (27,28) (28,29) (29,31)\nIs there a path between node 18 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph538-30_29", + "image": "data/connectivity/graph_visual/hard/graph538.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,17) (0,4) (0,11) (0,9) (0,3) (0,13) (0,16) (0,31) (0,23) (0,6) (0,14) (0,30) (0,27) (0,5) (0,2) (0,24) (0,10) (0,28) (0,7) (0,26) (1,15) (1,22) (1,8) (2,17) (2,4) (2,3) (2,13) (2,12) (2,16) (2,18) (2,32) (2,31) (2,6) (2,14) (2,19) (2,24) (2,21) (2,10) (2,28) (2,7) (2,26) (2,25) (2,29) (3,17) (3,11) (3,9) (3,12) (3,18) (3,20) (3,32) (3,31) (3,6) (3,14) (3,19) (3,30) (3,5) (3,21) (3,7) (3,25) (4,11) (4,9) (4,16) (4,18) (4,20) (4,31) (4,23) (4,6) (4,14) (4,19) (4,30) (4,27) (4,5) (4,24) (4,21) (4,28) (4,7) (4,25) (4,29) (5,11) (5,9) (5,13) (5,12) (5,16) (5,18) (5,32) (5,31) (5,14) (5,19) (5,28) (5,7) (5,25) (5,29) (6,11) (6,12) (6,16) (6,20) (6,31) (6,23) (6,14) (6,19) (6,30) (6,24) (6,21) (6,10) (6,28) (6,7) (6,25) (6,29) (7,11) (7,13) (7,18) (7,20) (7,32) (7,31) (7,23) (7,14) (7,19) (7,30) (7,27) (7,24) (7,21) (7,10) (7,25) (7,29) (8,15) (9,17) (9,16) (9,32) (9,31) (9,23) (9,14) (9,19) (9,30) (9,27) (9,21) (9,10) (9,28) (9,26) (10,17) (10,11) (10,12) (10,18) (10,20) (10,32) (10,30) (10,24) (10,28) (10,26) (10,25) (11,17) (11,13) (11,12) (11,18) (11,31) (11,23) (11,19) (11,30) (11,27) (11,24) (11,28) (11,26) (11,25) (11,29) (12,17) (12,13) (12,16) (12,20) (12,32) (12,31) (12,23) (12,19) (12,24) (12,21) (12,28) (12,26) (12,25) (12,29) (13,16) (13,18) (13,20) (13,32) (13,31) (13,14) (13,19) (13,30) (13,24) (13,26) (13,29) (14,17) (14,16) (14,18) (14,20) (14,31) (14,19) (14,30) (14,24) (14,21) (14,26) (14,25) (14,29) (15,22) (16,17) (16,18) (16,20) (16,32) (16,31) (16,23) (16,19) (16,30) (16,21) (16,28) (16,26) (16,29) (17,20) (17,23) (17,19) (17,27) (17,24) (17,21) (17,28) (17,29) (18,27) (18,24) (18,28) (18,26) (19,20) (19,31) (19,23) (19,21) (19,28) (19,26) (19,25) (20,32) (20,23) (20,24) (20,21) (20,28) (20,25) (20,29) (21,32) (21,31) (21,23) (21,30) (21,27) (21,24) (21,28) (21,25) (21,29) (22,33) (23,30) (23,27) (23,24) (23,28) (23,25) (24,32) (24,31) (24,30) (24,27) (24,28) (24,26) (24,29) (25,32) (25,30) (25,26) (25,29) (26,32) (26,31) (26,30) (26,27) (27,32) (27,30) (27,28) (27,29) (28,32) (28,31) (28,30) (28,29) (29,32) (30,32) (30,31) (31,32)\nIs there a path between node 30 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph332-12_6", + "image": "data/connectivity/graph_visual/hard/graph332.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,23) (0,2) (0,30) (0,21) (0,10) (0,18) (0,28) (0,12) (0,24) (0,19) (0,3) (0,14) (0,13) (1,26) (1,16) (1,11) (1,20) (1,8) (1,6) (1,25) (2,15) (2,29) (2,23) (2,7) (2,21) (2,10) (2,18) (2,12) (2,24) (2,27) (2,19) (2,14) (2,17) (2,13) (3,29) (3,23) (3,30) (3,7) (3,10) (3,24) (3,27) (3,19) (3,14) (3,31) (3,17) (3,4) (3,13) (4,23) (4,21) (4,10) (4,12) (4,27) (4,19) (4,14) (4,31) (4,17) (4,13) (5,26) (5,16) (5,20) (5,8) (5,6) (5,25) (6,9) (6,16) (6,11) (6,8) (7,29) (7,23) (7,30) (7,21) (7,10) (7,18) (7,28) (7,12) (7,24) (7,27) (7,19) (7,17) (7,22) (7,13) (8,9) (8,26) (8,16) (8,11) (8,20) (8,25) (9,26) (9,11) (9,20) (9,25) (10,15) (10,29) (10,28) (10,12) (10,24) (10,27) (10,31) (10,13) (11,16) (11,20) (11,25) (12,15) (12,29) (12,21) (12,24) (12,27) (12,19) (12,14) (12,31) (12,22) (13,15) (13,23) (13,30) (13,21) (13,18) (13,28) (13,24) (13,27) (13,19) (13,14) (13,22) (14,15) (14,29) (14,30) (14,21) (14,18) (14,24) (14,27) (14,19) (14,31) (14,22) (15,29) (15,23) (15,30) (15,21) (15,24) (15,19) (15,17) (16,26) (16,25) (17,21) (17,18) (17,28) (17,24) (17,27) (17,19) (17,31) (17,22) (18,23) (18,30) (18,21) (18,28) (18,27) (18,19) (18,31) (18,22) (19,23) (19,21) (19,28) (19,24) (19,27) (19,31) (19,22) (20,26) (20,25) (21,29) (21,23) (21,28) (21,24) (21,27) (21,22) (22,29) (22,23) (22,30) (22,24) (22,27) (22,31) (23,28) (23,31) (24,30) (24,27) (24,31) (25,26) (27,29) (27,28) (27,31) (28,29) (28,30) (28,31) (29,30) (29,31)\nIs there a path between node 12 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph188-7_3", + "image": "data/connectivity/graph_visual/hard/graph188.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,21) (0,7) (0,2) (0,6) (0,14) (0,24) (0,23) (0,20) (1,10) (1,28) (1,3) (1,16) (1,24) (1,5) (2,3) (2,7) (2,24) (2,20) (3,25) (3,28) (3,22) (3,21) (3,16) (3,14) (4,28) (4,22) (4,16) (4,18) (4,14) (5,10) (5,7) (5,16) (6,10) (6,22) (6,7) (6,24) (6,23) (7,25) (7,22) (7,21) (7,14) (7,24) (7,20) (8,13) (10,20) (10,11) (11,18) (11,14) (11,23) (12,13) (12,17) (13,17) (13,19) (14,28) (14,23) (16,21) (16,18) (16,26) (18,22) (18,24) (18,20) (21,28) (21,23) (22,24) (23,24) (25,26)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph115-5_9", + "image": "data/connectivity/graph_visual/hard/graph115.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,13) (1,6) (1,12) (1,20) (1,5) (1,27) (1,24) (1,14) (1,16) (2,7) (3,17) (3,21) (3,26) (3,22) (3,10) (3,24) (3,14) (3,16) (4,19) (4,21) (4,6) (4,20) (4,9) (4,5) (4,23) (4,10) (4,14) (4,15) (4,16) (4,8) (5,13) (5,12) (5,27) (6,21) (6,26) (6,16) (6,8) (8,17) (8,26) (8,23) (8,15) (9,27) (9,22) (9,10) (9,24) (10,12) (10,20) (10,27) (10,22) (10,24) (10,15) (10,16) (12,13) (12,24) (12,15) (12,16) (13,22) (13,15) (14,19) (14,20) (14,26) (14,18) (14,23) (14,24) (15,27) (15,23) (15,24) (16,19) (16,21) (16,20) (16,23) (17,20) (17,23) (18,21) (18,23) (19,23) (19,24) (21,22) (21,24) (22,27) (22,23) (23,26) (23,27) (24,27)\nIs there a path between node 5 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph219-17_27", + "image": "data/connectivity/graph_visual/hard/graph219.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,23) (0,2) (0,27) (1,16) (1,7) (1,25) (1,22) (1,24) (1,5) (1,13) (1,21) (1,12) (1,17) (1,20) (1,29) (1,28) (1,10) (1,8) (1,18) (1,6) (1,3) (1,9) (2,27) (2,26) (3,14) (3,4) (3,25) (3,22) (3,24) (3,5) (3,12) (3,19) (3,15) (3,20) (3,11) (3,10) (3,8) (3,18) (3,6) (3,9) (4,14) (4,16) (4,7) (4,25) (4,24) (4,5) (4,13) (4,21) (4,12) (4,19) (4,17) (4,20) (4,29) (4,11) (4,10) (4,8) (4,18) (4,6) (4,9) (5,14) (5,16) (5,25) (5,24) (5,13) (5,21) (5,12) (5,19) (5,15) (5,20) (5,29) (5,28) (5,18) (5,9) (6,14) (6,16) (6,7) (6,25) (6,24) (6,13) (6,21) (6,12) (6,15) (6,29) (6,11) (6,28) (6,8) (6,18) (7,14) (7,25) (7,22) (7,24) (7,13) (7,21) (7,12) (7,19) (7,15) (7,17) (7,20) (7,29) (7,11) (7,28) (7,10) (7,8) (7,18) (7,9) (8,21) (8,12) (8,15) (8,17) (8,20) (8,29) (8,28) (8,18) (8,9) (9,16) (9,25) (9,22) (9,19) (9,17) (9,11) (9,28) (9,10) (9,18) (10,16) (10,25) (10,24) (10,21) (10,15) (10,17) (10,20) (10,29) (10,11) (10,18) (11,14) (11,16) (11,25) (11,22) (11,24) (11,21) (11,15) (11,20) (11,29) (11,28) (12,22) (12,24) (12,21) (12,15) (12,20) (13,14) (13,25) (13,24) (13,21) (13,19) (13,15) (13,17) (13,28) (13,18) (14,16) (14,25) (14,22) (14,24) (14,21) (14,19) (14,15) (14,20) (14,29) (14,28) (14,18) (15,16) (15,25) (15,22) (15,24) (15,21) (15,19) (15,17) (15,20) (15,29) (15,28) (15,18) (16,25) (16,19) (16,17) (16,20) (16,18) (17,25) (17,22) (17,24) (17,21) (17,19) (17,28) (17,18) (18,25) (18,24) (18,21) (18,19) (18,29) (18,28) (19,22) (19,24) (19,21) (19,29) (19,28) (20,22) (20,24) (20,21) (20,28) (21,25) (21,24) (21,29) (22,25) (22,24) (22,28) (23,26) (24,29) (24,28) (26,27) (28,29)\nIs there a path between node 17 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph553-4_9", + "image": "data/connectivity/graph_visual/hard/graph553.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,24) (0,26) (0,31) (0,22) (1,25) (1,28) (1,20) (1,30) (1,14) (1,2) (1,17) (1,5) (2,9) (2,6) (2,33) (2,30) (2,17) (3,24) (3,12) (3,16) (3,29) (4,15) (4,25) (4,28) (4,20) (4,21) (5,15) (5,10) (5,28) (5,6) (5,33) (5,20) (5,13) (5,17) (6,15) (6,9) (6,21) (6,17) (7,15) (7,10) (7,20) (7,14) (7,21) (8,24) (8,26) (8,16) (9,25) (9,13) (9,21) (10,15) (10,32) (10,20) (10,18) (11,27) (12,26) (13,17) (14,30) (14,21) (15,18) (15,17) (16,31) (16,23) (16,29) (17,25) (17,33) (17,32) (17,18) (18,30) (19,27) (22,26) (23,24) (25,33) (25,32) (26,31) (28,32)\nIs there a path between node 4 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph664-4_15", + "image": "data/connectivity/graph_visual/hard/graph664.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,14) (0,16) (0,33) (0,10) (0,7) (0,25) (1,28) (1,2) (1,12) (1,17) (1,13) (1,18) (1,32) (1,20) (1,16) (1,30) (1,7) (1,25) (1,31) (2,17) (2,18) (2,21) (2,33) (2,8) (2,11) (3,24) (3,6) (3,19) (4,6) (4,23) (4,34) (4,26) (5,24) (5,23) (5,26) (6,23) (6,19) (7,28) (7,13) (7,20) (7,22) (8,17) (8,20) (8,16) (8,22) (9,28) (9,18) (9,32) (9,16) (9,30) (9,11) (10,28) (10,14) (10,22) (10,25) (11,28) (11,12) (11,17) (11,18) (11,22) (11,33) (12,28) (12,15) (12,14) (12,16) (12,29) (12,33) (12,25) (13,30) (14,17) (14,18) (14,16) (14,22) (14,31) (15,18) (15,21) (15,16) (15,30) (16,28) (16,21) (16,20) (16,22) (16,31) (17,28) (17,18) (17,32) (17,20) (18,32) (18,21) (18,22) (18,30) (19,23) (19,34) (20,27) (20,25) (20,31) (21,32) (21,29) (21,33) (21,31) (22,31) (25,28) (25,32) (25,27) (26,34) (27,29) (30,31) (31,32) (31,33) (32,33)\nIs there a path between node 4 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph450-4_28", + "image": "data/connectivity/graph_visual/hard/graph450.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (0,25) (0,30) (0,26) (1,24) (2,13) (2,29) (3,15) (3,25) (3,30) (3,28) (3,31) (3,27) (4,19) (4,18) (4,30) (4,32) (4,28) (4,31) (4,27) (5,22) (5,6) (6,14) (7,15) (7,25) (7,10) (7,30) (7,32) (7,21) (8,17) (8,29) (9,25) (9,30) (9,31) (9,26) (9,27) (10,25) (10,11) (10,32) (11,25) (11,19) (11,28) (12,13) (13,29) (15,18) (15,30) (15,21) (15,31) (15,26) (18,28) (19,30) (19,27) (20,23) (20,25) (20,30) (20,32) (20,27) (21,25) (21,32) (21,31) (23,25) (23,30) (23,28) (23,26) (25,32) (25,31) (26,30) (26,28) (27,32)\nIs there a path between node 4 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph556-20_2", + "image": "data/connectivity/graph_visual/hard/graph556.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,2) (0,20) (0,30) (0,26) (0,15) (0,32) (0,13) (1,25) (2,31) (2,3) (2,30) (2,12) (2,11) (2,23) (2,27) (2,15) (2,6) (2,21) (3,31) (3,14) (3,33) (3,18) (3,11) (3,26) (3,23) (3,27) (3,16) (3,32) (3,29) (4,7) (4,25) (5,33) (5,12) (5,29) (5,6) (5,8) (6,33) (6,22) (6,18) (6,19) (6,16) (7,10) (8,22) (8,19) (8,11) (8,15) (8,32) (9,33) (9,19) (9,15) (9,29) (9,13) (11,27) (11,15) (11,32) (11,29) (13,33) (13,22) (13,23) (13,28) (13,21) (14,31) (14,33) (14,22) (14,18) (14,26) (14,15) (14,16) (14,21) (15,33) (15,19) (15,21) (16,20) (16,33) (16,27) (18,22) (18,30) (18,19) (18,32) (18,29) (19,26) (19,23) (19,21) (20,31) (20,30) (20,23) (20,28) (21,31) (21,26) (21,32) (22,26) (22,32) (22,29) (22,28) (23,33) (23,30) (23,27) (26,32) (28,31) (28,30) (28,29) (29,31) (29,32) (30,32) (31,33)\nIs there a path between node 20 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph251-30_12", + "image": "data/connectivity/graph_visual/hard/graph251.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,17) (1,8) (1,29) (1,10) (1,7) (1,11) (1,25) (1,18) (1,14) (1,30) (1,16) (1,5) (1,26) (1,4) (1,23) (1,27) (2,21) (3,21) (4,17) (4,29) (4,9) (4,10) (4,6) (4,7) (4,11) (4,14) (4,22) (4,26) (4,13) (4,24) (4,23) (4,19) (5,17) (5,29) (5,9) (5,10) (5,6) (5,7) (5,11) (5,18) (5,14) (5,30) (5,16) (5,26) (5,15) (5,13) (5,24) (5,19) (5,27) (6,17) (6,9) (6,10) (6,11) (6,18) (6,14) (6,30) (6,16) (6,22) (6,15) (6,24) (6,19) (6,27) (7,17) (7,8) (7,29) (7,9) (7,10) (7,25) (7,18) (7,30) (7,16) (7,22) (7,24) (7,23) (7,19) (7,27) (8,17) (8,11) (8,25) (8,18) (8,14) (8,30) (8,16) (8,15) (8,13) (8,24) (8,19) (8,27) (9,17) (9,29) (9,10) (9,11) (9,25) (9,14) (9,30) (9,16) (9,22) (9,15) (9,13) (9,24) (9,19) (9,27) (10,17) (10,11) (10,25) (10,18) (10,14) (10,30) (10,16) (10,22) (10,15) (10,13) (10,24) (10,23) (10,27) (11,29) (11,25) (11,14) (11,30) (11,16) (11,26) (11,15) (11,13) (11,24) (11,23) (11,19) (11,27) (12,28) (13,29) (13,18) (13,14) (13,30) (13,16) (13,22) (13,26) (13,15) (13,24) (13,19) (13,27) (14,17) (14,25) (14,18) (14,30) (14,16) (14,22) (14,26) (14,15) (14,19) (14,27) (15,17) (15,25) (15,18) (15,30) (15,16) (15,22) (15,26) (15,24) (15,23) (15,19) (15,27) (16,29) (16,25) (16,30) (16,23) (16,27) (17,29) (17,25) (17,18) (17,30) (17,26) (17,19) (17,27) (18,22) (18,26) (18,24) (18,23) (18,19) (19,29) (19,25) (19,22) (19,26) (19,24) (19,23) (19,27) (22,29) (22,25) (22,26) (22,24) (22,23) (22,27) (23,25) (23,30) (23,24) (24,29) (24,25) (24,26) (24,27) (25,29) (25,30) (25,26) (25,27) (26,29) (26,30) (29,30)\nIs there a path between node 30 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph424-15_22", + "image": "data/connectivity/graph_visual/hard/graph424.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,16) (0,10) (0,29) (0,2) (0,12) (0,18) (0,26) (0,8) (1,19) (1,16) (1,24) (1,18) (2,19) (2,17) (2,7) (2,32) (2,24) (2,18) (3,15) (3,14) (4,9) (4,25) (5,30) (5,25) (5,6) (6,9) (6,30) (6,25) (7,19) (7,16) (7,26) (8,27) (8,16) (8,12) (8,32) (8,18) (10,27) (10,19) (10,16) (10,12) (10,32) (11,18) (11,26) (12,27) (12,19) (12,17) (12,28) (12,24) (12,18) (12,26) (13,23) (16,31) (16,29) (17,24) (18,31) (19,28) (19,24) (20,28) (20,24) (21,28) (21,26) (26,28) (27,31) (28,31) (28,29) (31,32)\nIs there a path between node 15 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph82-12_3", + "image": "data/connectivity/graph_visual/hard/graph82.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,6) (0,11) (0,25) (0,15) (0,13) (0,16) (1,12) (1,7) (1,3) (1,9) (1,4) (1,22) (1,23) (1,2) (1,19) (1,18) (1,8) (1,14) (1,20) (2,12) (2,26) (2,7) (2,9) (2,21) (2,22) (2,23) (2,19) (2,18) (2,5) (2,10) (2,8) (2,14) (2,20) (3,9) (3,4) (3,21) (3,23) (3,18) (3,5) (3,10) (3,8) (3,14) (3,20) (4,12) (4,7) (4,21) (4,22) (4,19) (4,18) (4,17) (4,10) (4,8) (4,14) (4,20) (5,12) (5,7) (5,9) (5,21) (5,22) (5,23) (5,10) (5,14) (5,20) (6,11) (6,13) (7,9) (7,21) (7,22) (7,23) (7,19) (7,18) (7,17) (7,14) (7,20) (8,12) (8,26) (8,9) (8,22) (8,23) (8,19) (8,18) (8,17) (8,10) (8,20) (9,12) (9,22) (9,23) (9,19) (9,18) (9,17) (9,10) (9,14) (9,20) (10,12) (10,21) (10,22) (10,23) (10,19) (10,18) (10,17) (10,20) (11,25) (11,15) (11,16) (12,26) (12,21) (12,22) (12,23) (12,19) (12,17) (12,14) (13,25) (13,15) (13,16) (14,26) (14,21) (14,22) (14,23) (14,19) (14,20) (15,16) (17,26) (17,19) (17,20) (18,26) (18,21) (18,22) (18,23) (18,19) (19,26) (19,21) (19,22) (19,20) (20,23) (21,26) (21,23) (22,23) (23,26)\nIs there a path between node 12 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph283-17_14", + "image": "data/connectivity/graph_visual/hard/graph283.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,14) (0,27) (0,23) (0,15) (1,2) (1,20) (1,13) (1,30) (1,16) (1,7) (1,22) (1,26) (2,9) (2,20) (2,13) (2,30) (2,16) (2,7) (2,22) (2,26) (3,29) (3,14) (3,27) (3,24) (3,23) (3,15) (4,21) (4,25) (4,28) (4,5) (4,18) (4,17) (4,8) (5,21) (5,25) (5,28) (5,10) (5,18) (5,17) (5,8) (6,29) (6,14) (6,27) (6,24) (6,23) (6,15) (7,9) (7,13) (7,30) (7,16) (7,26) (8,19) (8,21) (8,25) (8,28) (8,11) (8,10) (8,17) (9,20) (9,13) (9,30) (9,22) (9,26) (10,19) (10,21) (10,25) (10,28) (10,18) (10,17) (11,19) (11,21) (11,25) (11,28) (11,18) (12,29) (12,14) (12,27) (12,24) (12,15) (13,30) (13,16) (13,22) (14,29) (14,27) (14,24) (14,15) (15,29) (15,27) (15,24) (15,23) (16,20) (16,30) (16,26) (17,21) (17,25) (17,28) (17,18) (18,19) (18,21) (18,25) (19,21) (19,25) (20,22) (20,26) (21,25) (22,30) (23,27) (24,29) (24,27)\nIs there a path between node 17 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph292-14_5", + "image": "data/connectivity/graph_visual/hard/graph292.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,29) (0,7) (0,26) (1,20) (1,21) (1,24) (2,13) (3,17) (3,25) (3,26) (4,20) (4,27) (4,24) (5,9) (5,12) (5,8) (6,9) (6,7) (6,26) (6,22) (7,10) (7,9) (7,12) (7,25) (7,22) (8,9) (8,29) (8,22) (9,17) (9,10) (9,25) (10,17) (10,16) (10,29) (10,18) (10,25) (10,22) (11,13) (12,29) (12,26) (13,23) (13,30) (13,28) (13,27) (14,15) (14,19) (15,31) (16,25) (18,26) (18,22) (19,31) (20,27) (20,21) (21,23) (21,30) (21,27) (23,28) (23,27)\nIs there a path between node 14 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph163-21_18", + "image": "data/connectivity/graph_visual/hard/graph163.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,8) (0,11) (0,14) (0,13) (0,3) (1,28) (1,10) (1,21) (1,18) (1,14) (1,13) (2,28) (2,8) (2,27) (2,23) (2,7) (2,4) (2,25) (2,20) (2,26) (2,9) (3,28) (3,6) (3,11) (3,23) (3,21) (3,14) (4,19) (4,23) (4,18) (4,20) (4,9) (5,15) (6,28) (6,8) (6,23) (6,21) (6,25) (6,20) (6,26) (7,27) (7,25) (7,20) (7,13) (7,24) (7,26) (8,28) (8,19) (8,14) (8,26) (8,12) (9,19) (9,21) (9,14) (9,26) (10,14) (10,13) (10,12) (11,28) (11,16) (11,27) (11,14) (11,20) (11,13) (11,24) (11,26) (11,12) (12,20) (13,16) (13,21) (13,18) (14,28) (14,19) (14,23) (14,21) (14,25) (14,24) (15,17) (16,23) (16,24) (18,28) (18,27) (18,26) (19,27) (19,24) (19,26) (20,28) (20,27) (20,23) (21,23) (21,25) (21,26) (23,26) (26,27)\nIs there a path between node 21 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph190-16_17", + "image": "data/connectivity/graph_visual/hard/graph190.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,3) (0,16) (0,26) (0,9) (0,8) (1,28) (1,22) (1,20) (1,26) (1,9) (2,17) (2,28) (2,3) (2,14) (3,15) (3,6) (3,22) (3,26) (3,8) (3,29) (4,12) (4,20) (4,26) (5,7) (5,25) (5,19) (6,22) (6,14) (7,24) (7,23) (7,19) (7,13) (7,10) (8,17) (8,28) (8,18) (8,29) (9,17) (9,15) (9,20) (9,11) (10,24) (11,17) (11,16) (11,26) (12,28) (12,20) (12,26) (12,14) (13,19) (14,17) (15,17) (16,22) (17,20) (17,26) (17,29) (19,25) (20,22) (20,26) (21,27) (22,28) (22,26) (24,25) (25,27) (26,29) (28,29)\nIs there a path between node 16 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph611-17_0", + "image": "data/connectivity/graph_visual/hard/graph611.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,4) (1,32) (1,22) (1,34) (1,7) (1,5) (1,28) (1,11) (1,13) (1,30) (1,31) (1,26) (2,12) (2,3) (2,24) (2,15) (2,18) (2,8) (2,20) (2,25) (2,19) (2,17) (2,16) (3,10) (3,24) (3,15) (3,18) (3,8) (3,20) (3,14) (3,19) (3,21) (4,23) (4,6) (5,32) (5,22) (5,7) (5,33) (5,11) (5,13) (5,27) (5,31) (5,26) (6,23) (7,22) (7,34) (7,28) (7,13) (7,27) (7,30) (7,26) (7,29) (8,10) (8,24) (8,15) (8,18) (8,20) (8,14) (8,17) (8,21) (8,16) (9,32) (9,22) (9,34) (9,28) (9,13) (9,27) (9,31) (9,26) (9,29) (10,12) (10,24) (10,15) (10,18) (10,20) (10,25) (10,17) (11,32) (11,22) (11,34) (11,28) (11,13) (11,27) (11,30) (11,31) (11,26) (12,24) (12,25) (12,14) (12,17) (12,21) (12,16) (13,34) (13,33) (13,27) (13,30) (13,31) (13,29) (14,15) (14,18) (14,20) (14,25) (14,19) (14,17) (14,21) (14,16) (15,24) (15,18) (15,20) (15,17) (15,21) (16,24) (16,20) (16,19) (16,17) (17,24) (17,20) (17,21) (18,20) (18,25) (18,19) (20,24) (20,25) (20,21) (21,25) (22,32) (22,28) (22,27) (22,30) (22,31) (22,26) (24,25) (26,34) (26,33) (26,31) (27,34) (27,33) (27,28) (27,30) (27,31) (27,29) (28,32) (28,33) (28,30) (28,31) (28,29) (29,32) (29,33) (30,32) (31,32) (31,34) (32,34) (32,33) (33,34)\nIs there a path between node 17 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph442-22_3", + "image": "data/connectivity/graph_visual/hard/graph442.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,11) (0,32) (0,29) (0,7) (0,15) (1,30) (1,10) (1,8) (2,27) (2,18) (2,20) (2,7) (2,26) (3,14) (3,9) (4,18) (4,11) (4,13) (4,15) (5,30) (5,21) (6,14) (6,21) (6,17) (7,18) (7,22) (7,31) (7,29) (7,26) (8,14) (8,10) (9,21) (10,12) (10,21) (10,17) (11,19) (11,22) (11,28) (11,32) (11,29) (11,15) (11,26) (12,30) (12,21) (13,27) (13,20) (13,28) (13,31) (14,17) (15,20) (15,31) (15,26) (16,27) (16,32) (17,30) (18,27) (18,28) (18,32) (18,26) (18,24) (18,23) (19,27) (19,20) (19,31) (19,29) (19,26) (19,24) (20,25) (20,28) (20,32) (20,26) (22,31) (22,23) (23,27) (23,28) (23,26) (25,26) (26,27) (26,28) (26,29) (28,32) (28,31) (29,31)\nIs there a path between node 22 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph267-1_21", + "image": "data/connectivity/graph_visual/hard/graph267.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,3) (0,16) (0,21) (0,15) (1,18) (1,11) (1,22) (1,30) (1,12) (2,3) (2,25) (2,7) (3,17) (3,25) (3,19) (4,22) (4,30) (5,28) (7,16) (7,25) (7,14) (7,21) (7,19) (7,27) (8,9) (10,13) (10,30) (10,12) (10,26) (11,18) (11,30) (11,26) (12,29) (12,18) (12,30) (15,17) (15,25) (15,19) (17,25) (18,22) (18,26) (19,27) (20,28) (22,29) (24,26) (26,29)\nIs there a path between node 1 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph249-7_15", + "image": "data/connectivity/graph_visual/hard/graph249.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,22) (0,29) (0,21) (0,1) (0,28) (0,15) (0,7) (0,12) (0,10) (0,19) (0,17) (0,8) (0,6) (1,22) (1,9) (1,21) (1,20) (1,18) (1,7) (1,14) (1,19) (1,17) (1,8) (1,2) (1,23) (2,22) (2,9) (2,29) (2,21) (2,18) (2,30) (2,12) (2,5) (2,19) (2,17) (2,25) (2,8) (2,6) (2,23) (3,4) (3,27) (3,11) (3,26) (4,27) (4,11) (4,26) (5,9) (5,21) (5,18) (5,13) (5,28) (5,30) (5,12) (5,10) (5,19) (5,6) (5,23) (6,29) (6,21) (6,20) (6,18) (6,13) (6,15) (6,7) (6,16) (6,30) (6,12) (6,10) (6,8) (6,23) (7,22) (7,9) (7,29) (7,21) (7,18) (7,28) (7,15) (7,30) (7,10) (7,14) (7,19) (7,17) (7,8) (7,23) (8,22) (8,9) (8,29) (8,21) (8,20) (8,18) (8,13) (8,15) (8,16) (8,30) (8,12) (8,10) (8,14) (8,19) (8,23) (9,22) (9,21) (9,20) (9,18) (9,13) (9,28) (9,30) (9,12) (9,10) (9,14) (9,19) (9,17) (9,25) (10,22) (10,21) (10,20) (10,18) (10,13) (10,28) (10,15) (10,25) (10,23) (11,27) (11,26) (12,22) (12,29) (12,21) (12,28) (12,15) (12,30) (12,19) (12,17) (12,25) (12,23) (13,29) (13,21) (13,20) (13,15) (13,16) (13,14) (13,19) (13,17) (13,25) (13,23) (14,21) (14,28) (14,15) (14,16) (14,30) (14,19) (14,25) (14,23) (15,22) (15,29) (15,20) (15,16) (15,30) (15,19) (15,17) (15,25) (15,23) (16,22) (16,20) (16,18) (16,28) (16,30) (16,19) (16,17) (16,25) (16,23) (17,29) (17,21) (17,18) (17,28) (17,25) (18,22) (18,29) (18,21) (18,20) (18,28) (18,30) (18,19) (18,25) (19,29) (19,20) (19,30) (19,25) (19,23) (20,29) (20,21) (20,28) (20,30) (20,23) (21,22) (21,28) (21,30) (21,25) (21,23) (22,29) (22,28) (22,25) (23,29) (23,28) (25,29) (25,28) (25,30) (26,27) (28,29) (28,30) (29,30)\nIs there a path between node 7 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph593-24_23", + "image": "data/connectivity/graph_visual/hard/graph593.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,3) (0,18) (0,13) (0,17) (0,4) (0,15) (0,28) (0,19) (0,14) (0,31) (0,25) (0,29) (0,30) (0,26) (0,2) (0,23) (0,5) (0,8) (1,3) (1,18) (1,13) (1,17) (1,15) (1,28) (1,19) (1,14) (1,25) (1,2) (1,23) (1,5) (1,8) (2,18) (2,13) (2,17) (2,28) (2,14) (2,29) (2,30) (2,23) (2,5) (2,32) (2,8) (3,13) (3,4) (3,15) (3,28) (3,19) (3,14) (3,31) (3,29) (3,10) (3,30) (3,5) (3,32) (4,18) (4,13) (4,17) (4,15) (4,28) (4,31) (4,25) (4,29) (4,10) (4,30) (4,26) (4,5) (4,22) (4,32) (4,8) (5,13) (5,28) (5,19) (5,14) (5,25) (5,29) (5,10) (5,30) (5,26) (5,23) (5,22) (5,8) (6,16) (6,27) (6,9) (6,21) (6,12) (6,11) (6,20) (7,16) (7,27) (7,33) (7,9) (7,21) (7,12) (7,11) (8,13) (8,17) (8,15) (8,14) (8,25) (8,29) (8,10) (8,30) (8,23) (9,16) (9,27) (9,33) (9,21) (9,12) (9,20) (10,13) (10,17) (10,15) (10,28) (10,14) (10,25) (10,23) (10,22) (10,32) (11,16) (11,27) (11,33) (11,20) (12,16) (12,33) (12,24) (13,18) (13,28) (13,31) (13,25) (13,29) (13,30) (13,26) (13,23) (13,22) (14,18) (14,15) (14,19) (14,31) (14,25) (14,29) (14,23) (14,22) (14,32) (15,18) (15,17) (15,28) (15,31) (15,29) (15,30) (15,26) (15,23) (15,22) (15,32) (16,27) (16,33) (17,18) (17,28) (17,19) (17,31) (17,25) (17,29) (17,26) (17,23) (17,22) (17,32) (18,19) (18,29) (18,22) (19,28) (19,31) (19,25) (19,29) (19,30) (19,26) (19,23) (19,22) (19,32) (20,27) (20,21) (20,24) (21,27) (21,24) (22,28) (22,25) (22,29) (22,30) (22,26) (22,23) (22,32) (23,28) (23,29) (23,30) (23,26) (25,31) (25,26) (26,28) (26,29) (26,30) (27,33) (28,30) (28,32) (29,30) (29,32) (30,31) (30,32) (31,32)\nIs there a path between node 24 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph324-23_5", + "image": "data/connectivity/graph_visual/hard/graph324.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,10) (0,28) (0,11) (0,21) (0,9) (0,12) (0,14) (0,26) (0,19) (0,29) (0,16) (0,25) (0,23) (1,18) (1,10) (1,7) (1,27) (1,13) (1,20) (1,6) (1,5) (1,9) (1,12) (1,19) (1,31) (1,16) (1,23) (2,3) (2,17) (2,24) (2,4) (3,15) (3,17) (3,24) (3,4) (4,15) (4,17) (4,24) (5,13) (5,6) (5,21) (5,12) (5,14) (5,8) (5,26) (5,19) (5,31) (5,16) (5,23) (6,18) (6,10) (6,27) (6,11) (6,12) (6,8) (6,19) (6,29) (6,25) (6,23) (7,18) (7,27) (7,20) (7,11) (7,21) (7,9) (7,12) (7,14) (7,8) (7,19) (7,29) (7,31) (7,23) (8,10) (8,27) (8,28) (8,21) (8,12) (8,14) (8,26) (8,29) (8,31) (8,16) (8,25) (9,18) (9,10) (9,27) (9,21) (9,26) (9,16) (10,27) (10,28) (10,20) (10,11) (10,21) (10,12) (10,14) (10,19) (10,29) (10,31) (10,16) (10,25) (11,18) (11,28) (11,20) (11,21) (11,12) (11,26) (11,19) (11,29) (11,31) (11,16) (11,25) (11,23) (12,18) (12,28) (12,13) (12,21) (12,14) (12,26) (12,19) (12,29) (12,31) (12,16) (12,23) (13,18) (13,27) (13,20) (13,21) (13,14) (13,26) (13,29) (13,16) (13,25) (13,23) (14,27) (14,26) (14,31) (14,16) (14,25) (14,23) (15,17) (15,24) (16,18) (16,27) (16,20) (16,21) (16,26) (16,19) (16,29) (16,31) (17,24) (18,27) (18,28) (18,20) (18,21) (18,26) (18,19) (18,29) (18,31) (18,25) (18,23) (19,27) (19,28) (19,20) (19,21) (19,26) (19,29) (19,31) (19,25) (20,27) (20,21) (20,26) (20,25) (20,23) (21,27) (21,28) (21,29) (21,31) (23,27) (23,29) (23,25) (25,28) (25,26) (25,29) (25,31) (26,27) (26,28) (26,29) (26,31) (27,28) (27,29) (28,29) (28,31) (29,31)\nIs there a path between node 23 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph692-0_6", + "image": "data/connectivity/graph_visual/hard/graph692.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,15) (0,2) (0,33) (0,4) (0,8) (0,23) (0,34) (0,30) (1,22) (1,28) (1,9) (1,29) (1,24) (1,26) (1,7) (1,27) (1,32) (1,19) (1,16) (1,5) (1,10) (2,12) (2,3) (2,15) (2,33) (2,20) (2,8) (2,23) (3,12) (3,11) (3,33) (3,4) (3,8) (3,23) (4,12) (4,11) (4,33) (4,20) (4,23) (5,22) (5,17) (5,28) (5,29) (5,14) (5,31) (5,25) (5,18) (5,24) (5,26) (5,6) (5,27) (5,32) (5,21) (5,19) (5,16) (6,17) (6,28) (6,13) (6,29) (6,14) (6,31) (6,25) (6,24) (6,27) (6,19) (6,16) (6,10) (7,22) (7,17) (7,9) (7,13) (7,29) (7,25) (7,24) (7,26) (7,27) (7,21) (7,19) (7,16) (7,10) (8,12) (8,11) (8,15) (8,33) (8,30) (9,22) (9,28) (9,13) (9,29) (9,14) (9,31) (9,18) (9,24) (9,26) (9,27) (9,32) (9,21) (9,19) (9,16) (9,10) (10,22) (10,17) (10,28) (10,13) (10,29) (10,14) (10,31) (10,25) (10,18) (10,26) (10,32) (10,21) (10,16) (11,33) (11,20) (11,23) (11,30) (12,33) (12,20) (12,34) (12,30) (13,22) (13,17) (13,28) (13,29) (13,14) (13,31) (13,25) (13,18) (13,24) (13,26) (13,32) (13,21) (13,19) (13,16) (14,22) (14,17) (14,28) (14,29) (14,31) (14,25) (14,18) (14,24) (14,26) (14,27) (14,32) (14,21) (14,19) (14,16) (15,33) (15,20) (15,23) (15,34) (15,30) (16,22) (16,17) (16,28) (16,29) (16,31) (16,18) (16,24) (16,26) (16,27) (16,32) (16,21) (17,28) (17,29) (17,31) (17,18) (17,24) (17,27) (17,32) (17,21) (17,19) (18,22) (18,28) (18,29) (18,31) (18,25) (18,27) (18,21) (19,22) (19,28) (19,29) (19,31) (19,25) (19,27) (19,21) (20,33) (20,23) (20,34) (20,30) (21,28) (21,29) (21,31) (21,25) (21,26) (21,32) (22,28) (22,31) (22,25) (22,24) (22,26) (22,27) (22,32) (23,33) (24,28) (24,29) (24,31) (24,26) (24,32) (25,31) (25,27) (25,32) (26,29) (26,31) (26,27) (27,28) (27,29) (27,31) (27,32) (28,29) (28,32) (29,32) (30,33) (30,34) (31,32) (33,34)\nIs there a path between node 0 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph97-4_8", + "image": "data/connectivity/graph_visual/hard/graph97.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,2) (0,8) (0,4) (0,9) (0,16) (0,21) (0,12) (0,23) (0,7) (0,11) (1,25) (1,22) (2,8) (2,26) (2,16) (2,20) (3,10) (3,16) (3,13) (3,14) (3,11) (4,26) (4,21) (4,12) (4,14) (5,10) (5,21) (5,13) (5,23) (5,7) (5,14) (5,15) (6,10) (6,9) (6,13) (6,12) (6,23) (6,14) (6,20) (6,15) (7,9) (7,16) (7,18) (7,23) (7,14) (7,15) (7,17) (8,10) (8,9) (8,16) (8,15) (8,11) (9,10) (9,26) (9,14) (9,17) (10,16) (12,18) (12,13) (13,18) (13,15) (14,21) (14,15) (15,26) (15,20) (16,18) (16,20) (17,20) (19,24) (19,22) (20,26) (20,21) (22,27)\nIs there a path between node 4 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph501-4_7", + "image": "data/connectivity/graph_visual/hard/graph501.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,22) (0,2) (0,17) (0,14) (0,6) (0,28) (0,23) (0,21) (1,22) (1,8) (1,17) (1,14) (1,19) (1,6) (1,10) (1,23) (1,16) (2,22) (2,4) (2,8) (2,18) (2,32) (2,27) (2,16) (3,4) (3,17) (3,14) (3,33) (3,18) (4,7) (4,19) (4,9) (4,18) (4,28) (4,21) (5,25) (5,13) (6,22) (6,14) (6,9) (6,18) (6,10) (6,12) (6,32) (7,17) (7,33) (7,9) (7,32) (8,22) (8,26) (8,9) (8,28) (8,10) (8,31) (8,16) (9,14) (9,18) (9,28) (9,10) (9,12) (9,31) (9,11) (9,27) (9,16) (10,22) (10,26) (10,29) (10,19) (10,23) (10,21) (11,26) (11,18) (11,12) (11,23) (11,32) (11,27) (11,16) (12,22) (12,14) (12,18) (12,31) (12,23) (12,27) (13,24) (14,22) (14,26) (14,29) (14,19) (14,28) (14,32) (14,16) (15,20) (15,24) (16,22) (16,19) (16,32) (17,33) (17,18) (17,28) (17,23) (18,22) (18,27) (19,32) (20,24) (20,30) (22,26) (22,31) (23,32) (24,30) (25,30) (26,29) (26,33) (27,33) (27,28) (27,31) (29,33) (29,32)\nIs there a path between node 4 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph434-13_30", + "image": "data/connectivity/graph_visual/hard/graph434.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (0,5) (0,6) (0,2) (0,23) (0,3) (0,26) (0,7) (1,5) (1,6) (1,24) (1,30) (1,2) (1,3) (1,17) (1,26) (1,18) (1,21) (2,5) (2,6) (2,24) (2,30) (2,13) (2,23) (2,18) (3,5) (3,6) (3,24) (3,30) (3,13) (3,23) (3,17) (3,7) (4,28) (4,27) (4,31) (5,6) (5,30) (5,13) (5,17) (5,26) (6,24) (6,30) (6,13) (6,23) (6,18) (6,7) (7,24) (7,30) (7,23) (7,17) (7,26) (8,22) (8,10) (8,25) (8,12) (8,11) (8,15) (8,16) (8,32) (8,19) (8,9) (8,14) (8,20) (9,10) (9,25) (9,12) (9,11) (9,16) (9,32) (9,19) (9,20) (10,22) (10,25) (10,12) (10,11) (10,15) (10,16) (10,32) (10,20) (11,14) (11,20) (12,22) (12,15) (12,16) (12,20) (13,24) (13,17) (13,26) (13,18) (13,21) (14,25) (14,15) (14,16) (14,32) (14,19) (15,25) (15,16) (15,32) (15,19) (15,20) (16,22) (16,25) (16,19) (16,20) (17,30) (17,23) (17,26) (18,24) (18,30) (18,26) (18,21) (19,22) (19,32) (20,25) (21,24) (21,23) (21,26) (22,25) (22,32) (23,24) (23,30) (24,30) (24,26) (25,32) (26,30) (27,28) (27,31) (28,29) (28,31) (29,31)\nIs there a path between node 13 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph551-3_14", + "image": "data/connectivity/graph_visual/hard/graph551.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,21) (0,30) (0,19) (0,25) (1,24) (1,18) (1,19) (1,31) (1,25) (1,26) (2,22) (2,23) (3,8) (3,13) (3,10) (5,14) (6,24) (6,8) (6,9) (6,13) (6,10) (6,28) (6,15) (7,11) (8,30) (8,9) (8,13) (8,26) (9,24) (9,16) (9,30) (9,10) (9,27) (10,18) (10,28) (10,15) (11,22) (11,29) (13,18) (13,21) (14,17) (15,18) (15,30) (15,19) (15,33) (15,31) (15,27) (15,26) (16,30) (16,19) (16,27) (18,30) (18,19) (18,28) (18,27) (19,24) (19,33) (19,28) (20,22) (20,29) (21,33) (21,25) (21,27) (23,32) (24,30) (24,28) (24,31) (25,31) (26,30) (26,28) (28,30) (31,33)\nIs there a path between node 3 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph339-5_2", + "image": "data/connectivity/graph_visual/hard/graph339.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,4) (0,1) (1,10) (1,14) (2,28) (2,13) (2,30) (2,16) (2,9) (2,8) (2,3) (3,29) (3,23) (3,30) (3,31) (3,17) (3,16) (3,12) (3,9) (5,18) (5,26) (5,15) (5,23) (5,27) (5,24) (5,22) (6,21) (7,19) (7,15) (7,28) (7,31) (7,9) (7,8) (7,11) (8,26) (8,25) (8,24) (8,12) (9,15) (9,27) (9,30) (9,25) (9,16) (9,20) (9,12) (9,22) (11,15) (11,30) (11,16) (12,19) (12,26) (12,29) (12,31) (12,24) (13,19) (13,18) (13,25) (13,17) (15,18) (15,28) (15,30) (15,31) (15,25) (15,16) (15,22) (16,19) (16,18) (16,28) (16,22) (17,19) (17,18) (17,23) (17,31) (18,26) (18,27) (18,24) (19,29) (19,23) (19,27) (19,31) (19,24) (20,29) (20,23) (20,30) (20,25) (20,24) (20,22) (22,30) (23,25) (23,24) (24,27) (24,31) (25,29) (26,28) (27,30) (27,31) (28,30) (28,31)\nIs there a path between node 5 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph346-11_23", + "image": "data/connectivity/graph_visual/hard/graph346.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,29) (0,31) (0,26) (0,27) (0,19) (1,28) (2,30) (4,6) (5,29) (5,31) (6,17) (6,30) (7,24) (7,29) (7,31) (8,21) (8,28) (10,11) (10,15) (12,28) (14,15) (14,20) (15,20) (18,29) (18,26) (20,23) (21,28) (24,26) (24,27)\nIs there a path between node 11 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph195-13_18", + "image": "data/connectivity/graph_visual/hard/graph195.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,28) (0,13) (0,26) (0,17) (0,6) (0,29) (0,18) (0,27) (1,12) (1,9) (1,20) (1,4) (1,7) (1,22) (1,11) (1,15) (2,12) (2,9) (2,23) (2,20) (2,24) (2,22) (2,11) (2,15) (3,8) (3,28) (3,26) (3,17) (3,6) (3,29) (3,25) (3,18) (3,27) (4,12) (4,9) (4,20) (4,24) (4,22) (4,11) (5,10) (5,21) (6,8) (6,28) (6,13) (6,26) (6,17) (6,25) (6,18) (7,24) (7,22) (7,11) (7,15) (8,13) (8,19) (8,29) (8,25) (8,27) (9,23) (9,20) (9,24) (9,22) (10,16) (10,14) (10,21) (11,12) (11,23) (11,20) (11,24) (12,23) (12,20) (12,24) (13,28) (13,26) (13,17) (13,19) (13,29) (13,25) (13,18) (13,27) (14,16) (15,23) (15,20) (15,24) (15,22) (17,28) (17,26) (17,19) (17,29) (17,25) (17,18) (17,27) (18,28) (18,26) (18,19) (18,25) (18,27) (19,28) (19,26) (19,29) (19,25) (20,23) (20,22) (22,23) (22,24) (23,24) (25,26) (25,29) (25,27) (26,28) (26,29) (27,28)\nIs there a path between node 13 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph112-4_7", + "image": "data/connectivity/graph_visual/hard/graph112.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,22) (0,11) (0,10) (0,23) (0,4) (0,9) (0,19) (1,17) (1,27) (1,15) (1,23) (1,24) (1,5) (1,18) (2,15) (2,10) (2,23) (2,5) (2,6) (2,16) (4,17) (4,27) (4,16) (4,25) (5,27) (5,11) (5,24) (5,7) (5,16) (5,25) (5,21) (5,18) (6,17) (6,13) (6,27) (6,11) (6,10) (6,14) (6,16) (6,8) (6,19) (7,20) (7,15) (7,10) (7,24) (7,16) (7,8) (7,19) (7,25) (7,21) (8,20) (8,17) (8,27) (8,11) (8,24) (8,16) (9,20) (9,27) (9,11) (9,16) (9,25) (10,13) (10,27) (10,15) (10,16) (11,20) (11,13) (11,14) (11,24) (11,21) (13,20) (13,14) (13,16) (14,22) (14,15) (14,23) (14,19) (15,24) (15,19) (15,25) (16,22) (16,17) (16,23) (17,22) (17,23) (17,25) (18,19) (18,21) (19,27) (19,24) (19,25) (21,25) (23,27) (25,27)\nIs there a path between node 4 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph262-6_4", + "image": "data/connectivity/graph_visual/hard/graph262.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,23) (1,19) (1,11) (1,16) (1,28) (2,10) (2,13) (2,16) (2,3) (2,4) (2,27) (2,9) (3,14) (3,19) (3,26) (3,8) (3,11) (3,24) (3,27) (4,21) (4,29) (4,16) (4,27) (4,28) (5,7) (5,6) (5,12) (5,23) (6,30) (6,12) (7,23) (7,15) (8,14) (8,26) (8,10) (8,29) (8,27) (8,28) (9,26) (9,21) (9,13) (10,18) (10,27) (11,14) (11,19) (11,26) (11,21) (12,20) (13,19) (13,26) (13,18) (14,21) (14,25) (15,30) (16,24) (16,28) (18,25) (19,26) (19,21) (19,29) (19,28) (20,23) (21,26) (21,24) (22,30) (24,29) (24,28) (25,27) (26,27)\nIs there a path between node 6 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph617-31_10", + "image": "data/connectivity/graph_visual/hard/graph617.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,19) (0,23) (0,18) (0,2) (0,24) (0,14) (0,6) (0,7) (0,33) (0,30) (0,21) (0,11) (0,29) (0,10) (1,25) (1,31) (1,16) (1,34) (1,28) (2,22) (2,23) (2,18) (2,24) (2,32) (2,14) (2,6) (2,33) (2,8) (2,27) (2,21) (2,4) (2,29) (3,9) (3,13) (3,15) (3,5) (3,26) (4,19) (4,23) (4,18) (4,24) (4,12) (4,32) (4,6) (4,7) (4,33) (4,8) (4,27) (4,30) (4,17) (4,10) (5,9) (5,13) (5,15) (5,26) (6,19) (6,12) (6,32) (6,14) (6,33) (6,27) (6,10) (7,22) (7,19) (7,18) (7,24) (7,32) (7,14) (7,27) (7,30) (7,11) (7,10) (8,22) (8,19) (8,23) (8,12) (8,33) (8,30) (8,17) (8,11) (8,29) (8,10) (9,13) (9,15) (9,26) (10,19) (10,18) (10,12) (10,32) (10,33) (10,27) (10,17) (10,11) (10,29) (11,19) (11,23) (11,18) (11,24) (11,32) (11,33) (11,27) (11,21) (11,29) (12,19) (12,23) (12,18) (12,32) (12,14) (12,33) (12,27) (12,30) (12,21) (12,17) (13,26) (14,22) (14,19) (14,23) (14,18) (14,32) (14,30) (14,21) (14,29) (15,26) (16,25) (16,31) (16,34) (16,28) (17,19) (17,23) (17,18) (17,24) (17,33) (17,27) (17,29) (18,22) (18,19) (18,23) (18,33) (18,27) (18,21) (18,29) (19,22) (19,23) (19,33) (19,27) (19,29) (20,25) (20,31) (20,34) (21,22) (21,23) (21,32) (21,33) (21,27) (21,30) (21,29) (22,33) (22,27) (22,30) (23,24) (23,32) (23,33) (23,27) (23,29) (24,32) (24,33) (24,27) (24,30) (24,29) (25,31) (25,34) (27,32) (27,33) (27,29) (29,33) (30,32) (30,33) (31,34) (32,33)\nIs there a path between node 31 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph172-0_5", + "image": "data/connectivity/graph_visual/hard/graph172.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,17) (0,11) (0,6) (0,9) (1,23) (1,21) (1,3) (1,19) (1,15) (1,22) (1,24) (1,5) (1,14) (1,25) (1,27) (1,18) (2,28) (2,13) (2,6) (3,23) (3,21) (3,12) (3,19) (3,15) (3,22) (3,24) (3,10) (3,14) (3,26) (3,25) (3,27) (4,21) (4,12) (4,15) (4,22) (4,24) (4,5) (4,14) (4,26) (4,25) (4,16) (4,27) (5,23) (5,21) (5,19) (5,15) (5,24) (5,10) (5,26) (5,8) (5,27) (6,28) (6,13) (6,17) (6,11) (7,28) (7,13) (7,11) (7,20) (8,21) (8,12) (8,19) (8,15) (8,22) (8,14) (8,26) (8,25) (8,16) (8,27) (9,17) (9,11) (9,20) (10,23) (10,12) (10,15) (10,22) (10,24) (10,14) (10,26) (10,25) (10,16) (10,18) (11,28) (11,13) (11,17) (11,20) (12,23) (12,21) (12,15) (12,22) (12,24) (12,16) (12,18) (13,28) (13,17) (13,20) (14,23) (14,21) (14,19) (14,15) (14,24) (14,25) (14,16) (14,27) (15,23) (15,19) (15,26) (15,25) (15,16) (15,27) (15,18) (16,23) (16,21) (16,19) (16,24) (16,26) (16,27) (16,18) (17,28) (18,23) (18,21) (18,19) (18,22) (18,24) (18,26) (18,25) (19,23) (19,22) (19,24) (19,26) (19,25) (19,27) (20,28) (21,23) (21,22) (21,24) (21,26) (21,25) (21,27) (22,24) (22,25) (23,24) (24,26) (24,25) (24,27)\nIs there a path between node 0 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph481-21_31", + "image": "data/connectivity/graph_visual/hard/graph481.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,17) (0,21) (0,16) (0,23) (0,24) (0,8) (0,28) (0,31) (0,10) (0,32) (0,3) (0,5) (1,23) (1,15) (1,29) (1,28) (1,31) (1,26) (1,30) (1,10) (1,32) (1,3) (1,2) (1,5) (2,17) (2,27) (2,16) (2,23) (2,15) (2,24) (2,8) (2,31) (2,32) (2,3) (2,5) (3,27) (3,16) (3,23) (3,15) (3,8) (3,29) (3,28) (3,26) (3,10) (4,6) (5,17) (5,27) (5,21) (5,16) (5,23) (5,15) (5,8) (5,29) (5,28) (5,26) (5,7) (5,30) (5,10) (6,19) (7,17) (7,21) (7,16) (7,23) (7,24) (7,8) (7,29) (7,28) (7,31) (7,30) (7,32) (8,17) (8,27) (8,23) (8,15) (8,24) (8,28) (8,31) (8,26) (8,30) (8,10) (8,32) (9,13) (9,18) (9,12) (9,20) (9,11) (10,27) (10,16) (10,23) (10,15) (10,24) (10,29) (10,28) (10,26) (10,30) (11,13) (11,18) (11,12) (11,25) (11,14) (11,22) (12,13) (12,18) (12,25) (12,14) (12,20) (13,18) (13,14) (13,20) (13,22) (14,18) (14,22) (15,17) (15,24) (15,28) (15,31) (15,26) (15,30) (15,32) (16,27) (16,21) (16,23) (16,29) (16,28) (16,31) (16,30) (17,23) (17,24) (17,29) (17,28) (17,30) (17,32) (18,20) (20,22) (21,23) (21,24) (21,29) (21,31) (21,26) (21,30) (21,32) (22,25) (23,29) (23,31) (23,32) (24,27) (24,29) (26,27) (26,29) (26,31) (26,30) (26,32) (27,28) (27,31) (27,32) (28,29) (28,30) (28,32) (29,31) (29,32) (30,31) (31,32)\nIs there a path between node 21 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph255-21_8", + "image": "data/connectivity/graph_visual/hard/graph255.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,6) (0,2) (0,10) (0,29) (0,19) (0,5) (0,3) (1,30) (1,8) (1,28) (2,3) (3,6) (3,19) (4,14) (5,25) (6,19) (7,13) (7,30) (7,21) (7,8) (7,11) (8,13) (8,16) (8,30) (9,18) (12,19) (13,20) (13,28) (14,24) (14,18) (14,23) (15,30) (16,22) (16,28) (17,29) (17,19) (18,23) (19,25) (20,30) (20,28)\nIs there a path between node 21 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph334-0_7", + "image": "data/connectivity/graph_visual/hard/graph334.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,28) (0,16) (0,30) (0,27) (0,22) (0,18) (1,4) (1,29) (1,2) (1,8) (1,21) (1,6) (1,23) (1,17) (1,11) (1,15) (1,10) (1,12) (1,3) (1,31) (1,25) (1,14) (2,29) (2,8) (2,21) (2,11) (2,15) (2,10) (2,12) (2,3) (2,31) (2,9) (2,19) (3,4) (3,29) (3,8) (3,21) (3,6) (3,17) (3,20) (3,11) (3,12) (3,31) (3,19) (3,14) (4,29) (4,21) (4,23) (4,17) (4,20) (4,11) (4,15) (4,10) (4,12) (4,31) (4,9) (4,19) (4,14) (5,29) (5,8) (5,21) (5,6) (5,23) (5,17) (5,20) (5,11) (5,15) (5,10) (5,12) (5,31) (5,25) (5,19) (5,14) (6,8) (6,21) (6,23) (6,20) (6,11) (6,10) (6,12) (6,31) (6,25) (7,16) (7,30) (7,24) (7,22) (7,18) (8,29) (8,23) (8,17) (8,11) (8,15) (8,10) (8,12) (8,31) (8,25) (8,9) (8,14) (9,29) (9,20) (9,11) (9,15) (9,10) (9,31) (9,19) (9,14) (10,29) (10,23) (10,20) (10,11) (10,15) (10,19) (11,29) (11,23) (11,17) (11,20) (11,12) (11,25) (11,19) (11,14) (12,21) (12,23) (12,17) (12,20) (12,31) (12,19) (12,14) (13,26) (13,28) (13,16) (13,30) (13,18) (14,29) (14,21) (14,23) (14,17) (14,20) (14,15) (14,31) (15,21) (15,20) (15,31) (15,19) (16,30) (16,24) (16,27) (16,22) (16,18) (17,29) (17,21) (17,23) (17,20) (17,31) (17,25) (18,28) (18,24) (18,27) (18,22) (19,29) (19,21) (19,23) (19,20) (19,31) (19,25) (20,23) (20,31) (20,25) (21,29) (22,26) (22,28) (22,30) (22,24) (23,29) (23,31) (24,26) (24,28) (24,27) (25,31) (26,28) (27,30) (28,30) (29,31)\nIs there a path between node 0 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph96-22_12", + "image": "data/connectivity/graph_visual/hard/graph96.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,20) (0,8) (0,13) (0,11) (0,22) (0,15) (1,24) (2,3) (3,24) (4,18) (5,13) (5,27) (5,11) (5,7) (5,21) (6,11) (6,22) (6,17) (7,25) (7,8) (7,23) (7,11) (7,12) (7,22) (7,17) (8,20) (8,10) (8,12) (8,21) (10,20) (10,25) (10,13) (10,22) (10,16) (10,21) (11,20) (11,25) (11,16) (11,15) (12,23) (12,16) (12,21) (13,20) (13,23) (13,22) (13,17) (13,15) (15,26) (15,25) (15,22) (16,27) (17,26) (17,23) (17,27) (20,26) (20,22) (21,25) (22,25) (23,25) (25,26) (26,27)\nIs there a path between node 22 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph278-5_14", + "image": "data/connectivity/graph_visual/hard/graph278.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,10) (0,1) (0,15) (0,17) (0,12) (0,8) (1,16) (1,10) (1,18) (1,15) (1,2) (1,17) (1,28) (2,12) (2,8) (3,29) (3,24) (3,25) (3,6) (3,27) (3,19) (3,11) (3,4) (3,5) (4,9) (4,30) (4,22) (4,11) (5,29) (5,24) (5,23) (5,9) (5,25) (5,30) (5,6) (5,22) (5,19) (5,11) (6,29) (6,24) (6,23) (6,25) (6,30) (6,27) (6,22) (6,11) (7,20) (7,21) (7,13) (7,26) (7,14) (8,16) (8,10) (8,18) (8,15) (8,17) (8,12) (8,28) (9,29) (9,23) (9,30) (9,27) (9,22) (9,19) (10,16) (10,18) (10,15) (10,17) (10,12) (10,28) (11,29) (11,25) (11,22) (12,16) (12,15) (12,17) (13,26) (13,14) (14,20) (14,21) (15,16) (15,18) (15,28) (16,18) (16,17) (16,28) (17,18) (17,28) (18,28) (19,29) (19,23) (19,25) (19,30) (19,22) (20,21) (22,29) (22,24) (22,25) (22,30) (23,24) (23,25) (23,27) (24,25) (25,29) (25,30) (25,27) (27,29) (29,30)\nIs there a path between node 5 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph51-17_20", + "image": "data/connectivity/graph_visual/hard/graph51.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,4) (0,11) (0,16) (2,19) (2,4) (2,11) (3,4) (3,11) (5,8) (5,20) (5,25) (6,8) (6,22) (6,7) (6,18) (6,25) (7,22) (8,18) (8,24) (8,20) (8,21) (10,20) (10,26) (10,13) (11,19) (11,23) (13,22) (13,25) (15,24) (15,20) (15,25) (15,21) (16,23) (18,26) (19,23) (21,24) (21,25) (22,25) (22,26) (24,26)\nIs there a path between node 17 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph616-22_24", + "image": "data/connectivity/graph_visual/hard/graph616.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,33) (0,24) (0,27) (0,12) (0,16) (0,20) (0,5) (0,14) (0,17) (0,34) (0,29) (0,23) (0,22) (0,10) (0,28) (0,2) (0,15) (0,11) (0,8) (1,3) (1,6) (1,33) (1,27) (1,16) (1,20) (1,5) (1,26) (1,7) (1,19) (1,34) (1,29) (1,23) (1,22) (1,10) (1,28) (1,2) (1,9) (1,15) (1,11) (1,31) (1,8) (2,13) (2,33) (2,27) (2,12) (2,20) (2,7) (2,14) (2,19) (2,34) (2,29) (2,15) (2,11) (2,31) (3,6) (3,33) (3,12) (3,20) (3,5) (3,21) (3,7) (3,14) (3,17) (3,34) (3,29) (3,23) (3,22) (3,10) (3,28) (3,15) (3,11) (3,31) (3,8) (4,32) (4,30) (4,18) (5,13) (5,6) (5,33) (5,24) (5,12) (5,16) (5,20) (5,21) (5,26) (5,7) (5,14) (5,19) (5,17) (5,34) (5,29) (5,23) (5,22) (5,10) (5,28) (5,9) (5,15) (5,11) (6,13) (6,33) (6,27) (6,12) (6,20) (6,21) (6,26) (6,7) (6,14) (6,34) (6,23) (6,22) (6,10) (6,15) (6,31) (6,8) (7,13) (7,33) (7,24) (7,27) (7,16) (7,20) (7,21) (7,14) (7,19) (7,17) (7,29) (7,23) (7,10) (7,28) (7,9) (7,15) (7,11) (7,31) (7,8) (8,33) (8,24) (8,27) (8,26) (8,34) (8,29) (8,23) (8,10) (8,28) (8,9) (8,15) (8,11) (8,31) (9,13) (9,33) (9,24) (9,27) (9,16) (9,20) (9,21) (9,26) (9,14) (9,19) (9,17) (9,34) (9,22) (9,15) (9,11) (9,31) (10,13) (10,33) (10,24) (10,20) (10,14) (10,19) (10,17) (10,34) (10,29) (10,23) (10,28) (10,11) (10,31) (11,13) (11,33) (11,24) (11,27) (11,12) (11,16) (11,20) (11,21) (11,26) (11,19) (11,29) (11,22) (12,13) (12,24) (12,27) (12,16) (12,20) (12,21) (12,26) (12,14) (12,19) (12,34) (12,23) (12,22) (12,28) (12,15) (12,31) (13,24) (13,27) (13,16) (13,20) (13,21) (13,14) (13,19) (13,17) (13,34) (13,23) (13,22) (13,28) (13,15) (13,31) (14,24) (14,27) (14,16) (14,20) (14,26) (14,17) (14,34) (14,22) (14,28) (15,33) (15,24) (15,16) (15,26) (15,17) (15,34) (15,29) (15,22) (15,28) (15,31) (16,33) (16,24) (16,20) (16,21) (16,17) (16,34) (16,29) (16,31) (17,33) (17,24) (17,27) (17,20) (17,26) (17,19) (17,34) (17,29) (17,23) (17,22) (17,28) (17,31) (18,32) (18,25) (19,33) (19,24) (19,20) (19,21) (19,26) (19,29) (19,23) (19,31) (20,33) (20,24) (20,27) (20,21) (20,26) (20,34) (20,29) (20,23) (20,22) (20,28) (20,31) (21,33) (21,24) (21,27) (21,26) (21,23) (21,22) (21,28) (21,31) (22,33) (22,24) (22,27) (22,26) (22,34) (22,29) (22,23) (22,28) (22,31) (23,33) (23,27) (23,26) (23,34) (23,29) (23,28) (23,31) (24,33) (24,27) (24,34) (24,31) (25,32) (25,30) (26,33) (26,27) (26,34) (26,29) (26,28) (26,31) (27,33) (27,28) (27,31) (28,33) (28,34) (29,33) (29,34) (29,31) (30,32) (31,33) (31,34)\nIs there a path between node 22 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph123-9_22", + "image": "data/connectivity/graph_visual/hard/graph123.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,13) (0,26) (0,21) (0,20) (0,25) (0,16) (0,22) (0,14) (0,2) (0,27) (0,3) (0,5) (0,4) (0,7) (0,11) (0,24) (0,12) (0,1) (0,6) (0,23) (1,13) (1,26) (1,21) (1,25) (1,16) (1,22) (1,14) (1,2) (1,8) (1,27) (1,3) (1,5) (1,7) (1,11) (1,24) (1,12) (1,6) (1,23) (2,21) (2,25) (2,16) (2,10) (2,14) (2,8) (2,27) (2,3) (2,5) (2,4) (2,7) (2,11) (2,24) (2,12) (3,26) (3,21) (3,25) (3,10) (3,8) (3,4) (3,7) (3,11) (3,24) (3,12) (3,23) (4,13) (4,21) (4,20) (4,16) (4,10) (4,22) (4,8) (4,27) (4,7) (4,11) (4,24) (4,6) (5,21) (5,20) (5,25) (5,10) (5,8) (5,27) (5,11) (5,12) (5,6) (5,23) (6,13) (6,26) (6,21) (6,16) (6,10) (6,22) (6,14) (6,8) (6,11) (6,24) (6,12) (6,23) (7,13) (7,26) (7,21) (7,22) (7,14) (7,8) (7,24) (7,12) (7,23) (8,13) (8,21) (8,20) (8,25) (8,16) (8,22) (8,14) (8,23) (9,17) (9,18) (10,13) (10,26) (10,21) (10,20) (10,16) (10,14) (10,27) (10,11) (10,12) (10,23) (11,26) (11,25) (11,22) (11,27) (11,24) (11,12) (12,13) (12,21) (12,20) (12,16) (12,22) (12,14) (12,27) (12,24) (12,23) (13,26) (13,21) (13,20) (13,16) (13,22) (13,14) (13,27) (13,24) (13,23) (14,26) (14,21) (14,20) (14,25) (14,16) (14,22) (14,27) (14,24) (14,23) (15,18) (15,19) (16,26) (16,21) (16,27) (16,23) (17,18) (17,19) (18,19) (20,26) (20,21) (20,27) (20,24) (20,23) (21,26) (21,22) (21,27) (22,26) (22,25) (22,24) (22,23) (23,25) (23,24) (24,26) (24,25) (24,27)\nIs there a path between node 9 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph99-9_22", + "image": "data/connectivity/graph_visual/hard/graph99.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,1) (0,13) (0,22) (0,23) (0,9) (0,18) (0,7) (0,2) (0,15) (0,10) (0,16) (0,21) (0,4) (0,25) (0,27) (1,8) (1,13) (1,14) (1,22) (1,6) (1,24) (1,9) (1,18) (1,7) (1,2) (1,15) (1,26) (1,10) (1,12) (1,16) (1,11) (1,4) (1,5) (2,13) (2,14) (2,23) (2,6) (2,24) (2,9) (2,12) (2,16) (2,21) (2,11) (2,4) (2,25) (3,19) (4,8) (4,13) (4,14) (4,22) (4,6) (4,24) (4,18) (4,7) (4,15) (4,20) (4,16) (4,21) (4,11) (4,17) (4,27) (5,8) (5,13) (5,14) (5,23) (5,6) (5,9) (5,18) (5,7) (5,15) (5,26) (5,20) (5,12) (5,16) (5,21) (6,8) (6,13) (6,14) (6,22) (6,24) (6,9) (6,18) (6,7) (6,15) (6,26) (6,20) (6,10) (6,25) (6,17) (6,27) (7,8) (7,13) (7,14) (7,22) (7,24) (7,9) (7,15) (7,26) (7,10) (7,11) (7,25) (7,17) (8,13) (8,14) (8,22) (8,23) (8,24) (8,9) (8,26) (8,10) (8,12) (8,11) (8,25) (8,17) (9,14) (9,22) (9,23) (9,24) (9,18) (9,15) (9,26) (9,16) (9,21) (9,11) (9,25) (10,23) (10,24) (10,18) (10,15) (10,12) (10,21) (10,25) (10,17) (10,27) (11,14) (11,22) (11,15) (11,26) (11,20) (11,12) (11,21) (11,25) (11,17) (11,27) (12,13) (12,14) (12,22) (12,23) (12,24) (12,18) (12,15) (12,26) (12,16) (12,21) (12,17) (13,14) (13,22) (13,24) (13,26) (13,20) (13,16) (13,25) (13,17) (13,27) (14,22) (14,18) (14,15) (14,26) (14,20) (14,16) (14,25) (15,23) (15,24) (15,18) (15,26) (15,20) (15,16) (15,21) (15,25) (15,17) (15,27) (16,22) (16,26) (16,20) (16,21) (16,25) (16,17) (16,27) (17,22) (17,23) (17,25) (18,22) (18,23) (18,24) (18,26) (18,21) (18,25) (20,26) (20,21) (21,23) (21,26) (21,25) (21,27) (22,23) (22,26) (22,27) (23,24) (23,27) (24,26) (24,27) (25,27) (26,27)\nIs there a path between node 9 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph38-11_19", + "image": "data/connectivity/graph_visual/hard/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,7) (0,4) (0,24) (0,15) (1,2) (1,19) (1,6) (1,23) (1,13) (1,5) (1,20) (1,16) (1,25) (1,9) (1,21) (2,3) (2,6) (2,12) (2,23) (2,13) (2,5) (2,20) (2,16) (2,25) (2,9) (2,21) (2,8) (3,10) (3,22) (3,19) (3,6) (3,12) (3,14) (3,23) (3,13) (3,5) (3,20) (3,25) (3,9) (3,8) (4,11) (4,15) (5,6) (5,12) (5,23) (5,20) (5,17) (5,8) (6,22) (6,19) (6,14) (6,23) (6,13) (6,25) (6,17) (6,9) (7,15) (8,10) (8,22) (8,12) (8,13) (8,20) (8,16) (8,25) (8,9) (8,21) (9,22) (9,19) (9,12) (9,14) (9,23) (9,16) (9,25) (9,21) (10,12) (10,14) (10,20) (10,16) (10,25) (11,24) (11,15) (12,22) (12,16) (12,25) (12,17) (12,21) (13,22) (13,19) (13,14) (13,23) (13,20) (13,16) (13,17) (14,22) (14,19) (14,23) (14,25) (14,21) (15,18) (16,22) (16,23) (16,20) (16,25) (17,22) (17,19) (17,23) (17,20) (18,24) (19,22) (19,21) (20,23) (20,25) (21,22) (21,25) (22,25) (23,25)\nIs there a path between node 11 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph660-24_19", + "image": "data/connectivity/graph_visual/hard/graph660.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,31) (0,28) (0,12) (0,20) (0,22) (0,16) (0,7) (1,25) (1,28) (1,27) (1,29) (1,20) (1,16) (1,17) (2,31) (2,18) (2,12) (2,24) (2,29) (2,13) (2,19) (2,26) (2,16) (3,14) (3,28) (3,27) (3,29) (3,19) (3,22) (4,21) (4,31) (4,25) (4,28) (4,18) (4,11) (4,8) (4,10) (5,6) (6,9) (6,33) (7,23) (7,31) (7,24) (7,29) (7,13) (7,20) (8,21) (8,31) (8,14) (8,27) (8,12) (8,29) (8,20) (9,33) (10,23) (10,14) (10,27) (10,29) (10,19) (10,11) (10,26) (11,23) (11,31) (11,14) (11,28) (11,27) (11,18) (11,12) (11,29) (11,20) (11,16) (12,15) (12,28) (12,18) (12,13) (12,20) (13,31) (13,25) (13,15) (13,28) (13,22) (13,26) (13,32) (13,16) (13,17) (14,31) (14,15) (14,28) (14,27) (15,23) (15,25) (15,27) (15,18) (15,30) (15,26) (15,32) (16,25) (16,27) (16,24) (16,29) (16,20) (16,26) (17,23) (17,25) (17,27) (17,30) (17,32) (18,25) (18,28) (18,24) (18,20) (18,30) (18,32) (19,24) (19,29) (19,26) (20,21) (20,31) (20,22) (21,25) (21,29) (22,24) (23,26) (24,31) (24,25) (24,27) (24,32) (27,30) (28,29) (28,32)\nIs there a path between node 24 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph62-9_4", + "image": "data/connectivity/graph_visual/hard/graph62.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,5) (0,23) (0,20) (0,12) (1,9) (1,17) (1,16) (1,13) (2,9) (2,12) (3,10) (3,24) (3,21) (5,23) (6,10) (6,24) (7,10) (7,22) (7,25) (8,23) (8,17) (8,20) (9,17) (9,20) (9,26) (9,12) (10,18) (10,14) (12,23) (12,20) (12,26) (12,16) (12,19) (13,20) (14,22) (15,17) (15,20) (16,19) (17,23) (17,26) (17,19) (18,24) (18,21) (20,23) (20,26) (21,22) (21,24) (22,25)\nIs there a path between node 9 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph95-20_10", + "image": "data/connectivity/graph_visual/hard/graph95.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,21) (1,10) (1,6) (1,19) (1,13) (1,23) (1,5) (2,19) (2,13) (2,23) (2,20) (2,18) (3,12) (3,27) (3,13) (3,23) (3,11) (3,26) (3,16) (3,5) (4,27) (4,20) (4,18) (5,24) (5,13) (5,16) (6,23) (6,11) (6,18) (8,9) (8,10) (8,17) (8,27) (8,23) (9,24) (9,17) (9,14) (9,26) (9,18) (10,21) (10,12) (10,19) (10,26) (10,20) (10,18) (11,25) (11,17) (11,13) (11,23) (11,26) (11,20) (12,24) (12,20) (12,18) (14,27) (14,19) (14,23) (14,20) (14,18) (15,22) (16,27) (16,19) (16,23) (16,26) (16,20) (17,24) (17,19) (17,26) (17,20) (18,21) (18,19) (18,26) (20,25) (20,21) (20,27) (20,23) (20,26) (21,24) (23,26)\nIs there a path between node 20 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph307-16_23", + "image": "data/connectivity/graph_visual/hard/graph307.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,19) (0,9) (1,14) (1,21) (1,6) (1,12) (1,22) (1,3) (2,11) (2,5) (3,24) (3,30) (3,13) (3,19) (3,9) (3,22) (4,6) (5,28) (5,26) (6,14) (6,24) (6,18) (6,22) (8,24) (8,21) (8,12) (8,20) (8,19) (8,22) (9,21) (9,20) (11,25) (12,24) (12,13) (13,24) (13,21) (13,30) (14,21) (14,30) (14,19) (16,17) (16,31) (17,25) (18,30) (18,27) (19,21) (19,27) (20,27) (21,24) (21,27) (22,30) (23,25) (25,28) (26,29) (26,31) (28,29)\nIs there a path between node 16 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph167-17_27", + "image": "data/connectivity/graph_visual/hard/graph167.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,15) (0,8) (0,7) (0,4) (0,28) (0,18) (1,21) (1,15) (1,19) (1,25) (1,10) (1,4) (1,27) (1,5) (2,6) (2,14) (2,12) (2,8) (2,4) (2,11) (2,17) (3,21) (3,15) (3,6) (3,20) (3,23) (3,10) (3,7) (3,16) (3,28) (3,5) (3,18) (4,15) (4,14) (4,24) (4,20) (4,10) (4,11) (5,8) (5,27) (5,16) (5,11) (6,20) (6,16) (6,26) (6,18) (7,14) (7,19) (7,25) (7,12) (7,23) (7,8) (7,17) (7,13) (8,20) (8,16) (8,13) (10,25) (10,11) (10,26) (11,20) (11,28) (11,17) (11,18) (12,20) (12,28) (13,19) (13,27) (13,18) (14,21) (14,15) (14,23) (15,21) (15,19) (15,24) (15,16) (16,21) (16,20) (16,23) (16,26) (17,24) (17,20) (17,27) (18,19) (18,28) (19,21) (19,27) (19,28) (19,26) (20,28) (23,25) (24,25) (24,28) (25,28)\nIs there a path between node 17 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph2-21_24", + "image": "data/connectivity/graph_visual/hard/graph2.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,24) (0,1) (0,6) (0,14) (1,10) (2,25) (2,5) (2,20) (2,18) (3,22) (3,6) (3,19) (3,23) (4,9) (4,18) (5,15) (5,25) (5,17) (5,20) (6,11) (6,24) (6,14) (6,7) (6,21) (7,24) (8,25) (8,17) (8,20) (8,18) (9,25) (10,24) (10,22) (10,21) (11,22) (11,19) (11,23) (12,15) (12,16) (12,17) (13,19) (13,14) (14,22) (14,19) (15,16) (15,18) (16,17) (17,20) (18,25) (19,24) (19,22) (20,25) (21,23) (22,24) (22,23)\nIs there a path between node 21 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph52-3_5", + "image": "data/connectivity/graph_visual/hard/graph52.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,26) (0,19) (0,14) (0,23) (0,10) (1,21) (1,6) (1,19) (2,16) (3,13) (5,25) (5,15) (6,14) (7,13) (8,24) (8,17) (8,13) (8,15) (9,12) (9,20) (9,19) (10,26) (10,19) (12,20) (13,25) (13,15) (14,21) (14,26) (15,24) (18,22) (18,25) (19,26) (22,24)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph651-14_13", + "image": "data/connectivity/graph_visual/hard/graph651.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,5) (0,7) (0,9) (0,30) (0,26) (0,11) (0,28) (0,22) (0,34) (0,14) (0,20) (0,17) (0,29) (0,21) (0,25) (0,24) (1,5) (1,10) (1,9) (1,30) (1,26) (1,18) (1,11) (1,28) (1,22) (1,4) (1,34) (1,32) (1,17) (1,16) (1,29) (1,19) (1,21) (1,23) (1,24) (2,7) (2,10) (2,9) (2,26) (2,33) (2,18) (2,11) (2,28) (2,3) (2,22) (2,4) (2,34) (2,6) (2,8) (2,31) (2,12) (2,20) (2,17) (2,16) (2,29) (2,19) (2,25) (2,24) (3,5) (3,7) (3,10) (3,9) (3,30) (3,26) (3,33) (3,18) (3,11) (3,28) (3,22) (3,34) (3,6) (3,8) (3,32) (3,31) (3,14) (3,12) (3,17) (3,16) (3,29) (3,25) (3,23) (4,10) (4,26) (4,33) (4,18) (4,28) (4,22) (4,34) (4,6) (4,32) (4,14) (4,12) (4,20) (4,17) (4,16) (4,29) (4,19) (4,21) (4,25) (4,24) (5,10) (5,9) (5,30) (5,18) (5,11) (5,28) (5,34) (5,6) (5,8) (5,32) (5,14) (5,20) (5,16) (5,19) (5,21) (5,25) (5,23) (6,7) (6,10) (6,9) (6,33) (6,18) (6,11) (6,28) (6,22) (6,8) (6,17) (6,29) (6,19) (6,21) (6,25) (6,24) (7,10) (7,9) (7,33) (7,18) (7,11) (7,28) (7,22) (7,34) (7,32) (7,31) (7,14) (7,12) (7,17) (7,16) (7,29) (7,21) (7,25) (7,23) (7,24) (8,10) (8,9) (8,30) (8,26) (8,33) (8,18) (8,34) (8,14) (8,12) (8,16) (8,19) (8,21) (8,23) (9,10) (9,30) (9,26) (9,33) (9,18) (9,11) (9,28) (9,22) (9,34) (9,32) (9,14) (9,20) (9,17) (9,29) (9,19) (9,21) (9,25) (9,23) (9,24) (10,26) (10,18) (10,11) (10,28) (10,34) (10,32) (10,31) (10,14) (10,20) (10,29) (10,19) (10,21) (10,25) (10,23) (10,24) (11,26) (11,33) (11,18) (11,28) (11,22) (11,34) (11,31) (11,14) (11,20) (11,16) (11,29) (11,21) (11,25) (11,24) (12,30) (12,26) (12,33) (12,28) (12,22) (12,31) (12,14) (12,20) (12,19) (12,25) (12,23) (12,24) (13,15) (13,27) (14,30) (14,26) (14,28) (14,34) (14,31) (14,17) (14,29) (14,25) (15,27) (16,30) (16,26) (16,18) (16,22) (16,34) (16,31) (16,17) (16,29) (16,19) (16,21) (16,25) (16,23) (16,24) (17,30) (17,26) (17,33) (17,18) (17,28) (17,31) (17,20) (17,29) (17,19) (17,21) (17,25) (17,23) (17,24) (18,30) (18,26) (18,33) (18,28) (18,32) (18,31) (18,29) (18,21) (18,25) (18,23) (18,24) (19,30) (19,33) (19,32) (19,20) (19,29) (19,21) (19,23) (19,24) (20,30) (20,26) (20,33) (20,28) (20,22) (20,34) (20,32) (20,31) (20,21) (20,25) (20,23) (20,24) (21,26) (21,33) (21,28) (21,22) (21,34) (21,31) (21,29) (21,25) (21,24) (22,26) (22,33) (22,28) (22,32) (22,31) (22,23) (22,24) (23,26) (23,28) (23,32) (23,31) (23,29) (24,30) (24,26) (24,33) (24,28) (24,34) (24,32) (24,31) (24,29) (24,25) (25,30) (25,26) (25,33) (25,28) (25,31) (25,29) (26,33) (26,28) (26,34) (26,32) (26,29) (28,34) (28,31) (29,33) (29,32) (29,31) (30,33) (30,34) (30,32) (30,31) (31,34) (31,32) (32,33) (33,34)\nIs there a path between node 14 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph101-8_21", + "image": "data/connectivity/graph_visual/hard/graph101.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,14) (0,21) (0,23) (0,9) (0,6) (0,17) (0,2) (0,10) (0,25) (0,7) (0,27) (0,26) (0,8) (0,5) (1,22) (1,24) (1,20) (1,4) (1,15) (1,12) (2,21) (2,9) (2,6) (2,17) (2,18) (2,3) (2,27) (2,26) (2,5) (3,23) (3,9) (3,6) (3,17) (3,19) (3,16) (3,18) (3,11) (3,10) (3,7) (3,26) (3,8) (3,5) (4,22) (4,20) (4,13) (4,15) (5,14) (5,23) (5,9) (5,6) (5,17) (5,16) (5,18) (5,11) (5,10) (5,25) (5,7) (5,27) (5,26) (5,8) (6,14) (6,21) (6,23) (6,9) (6,17) (6,19) (6,16) (6,18) (6,10) (6,7) (6,27) (6,8) (7,14) (7,21) (7,23) (7,9) (7,17) (7,19) (7,18) (7,11) (7,10) (7,25) (7,26) (7,8) (8,14) (8,21) (8,23) (8,9) (8,17) (8,19) (8,18) (8,11) (8,10) (8,25) (8,27) (8,26) (9,21) (9,19) (9,10) (9,25) (9,27) (9,26) (10,21) (10,19) (10,11) (10,25) (10,27) (10,26) (11,14) (11,21) (11,23) (11,17) (11,19) (11,16) (11,18) (11,25) (12,22) (12,24) (12,13) (13,22) (13,24) (13,20) (14,21) (14,23) (14,17) (14,19) (14,16) (14,18) (14,25) (14,26) (15,22) (15,20) (16,21) (16,23) (16,17) (16,19) (16,18) (16,26) (17,21) (17,23) (17,25) (17,27) (17,26) (18,21) (18,23) (19,21) (19,23) (19,25) (19,27) (19,26) (20,22) (20,24) (21,23) (21,25) (22,24) (23,25) (25,27) (25,26) (26,27)\nIs there a path between node 8 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph680-32_15", + "image": "data/connectivity/graph_visual/hard/graph680.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,21) (0,4) (0,30) (0,19) (0,26) (1,27) (1,21) (1,32) (1,8) (1,34) (1,3) (2,27) (2,11) (2,7) (2,30) (2,9) (2,13) (2,26) (3,32) (3,4) (3,18) (3,8) (3,30) (3,31) (3,33) (3,26) (4,11) (4,21) (4,32) (4,8) (4,30) (4,9) (4,13) (5,29) (5,23) (5,17) (6,25) (6,29) (6,23) (6,22) (7,28) (7,8) (7,31) (7,26) (8,15) (8,28) (8,18) (8,33) (8,26) (9,27) (9,21) (9,24) (9,19) (9,33) (10,14) (11,31) (11,13) (11,20) (12,14) (12,23) (13,16) (13,34) (13,31) (14,25) (14,29) (14,23) (15,28) (15,30) (16,21) (16,32) (16,18) (16,34) (16,33) (17,25) (18,21) (18,32) (18,30) (18,19) (19,28) (19,31) (20,27) (20,30) (20,34) (20,31) (20,33) (21,27) (21,30) (21,31) (21,33) (24,28) (26,32) (26,34) (26,31) (27,28) (27,30) (27,33) (28,30) (28,34) (28,33) (31,33) (32,34) (32,33) (33,34)\nIs there a path between node 32 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph175-4_15", + "image": "data/connectivity/graph_visual/hard/graph175.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,5) (0,7) (0,6) (0,26) (0,24) (0,15) (0,22) (0,18) (1,2) (1,28) (1,3) (1,13) (1,9) (1,8) (1,4) (2,27) (2,11) (2,14) (2,17) (2,16) (2,28) (2,3) (2,9) (2,4) (3,27) (3,11) (3,25) (3,28) (3,13) (3,9) (3,8) (3,23) (3,12) (4,10) (4,11) (4,25) (4,14) (4,17) (4,16) (4,28) (4,13) (4,23) (5,21) (5,6) (5,26) (5,20) (5,19) (5,15) (5,22) (5,18) (6,7) (6,24) (6,20) (6,19) (6,22) (6,18) (7,21) (7,26) (7,20) (7,15) (8,27) (8,10) (8,11) (8,25) (8,14) (8,16) (8,23) (8,12) (9,27) (9,16) (9,28) (9,13) (9,23) (9,12) (10,27) (10,11) (10,25) (10,14) (10,17) (10,28) (10,13) (10,23) (10,12) (11,14) (11,16) (11,13) (11,12) (12,27) (12,14) (12,17) (12,28) (12,13) (13,27) (13,25) (13,14) (13,17) (13,16) (13,28) (13,23) (14,27) (14,17) (14,16) (14,28) (14,23) (15,21) (15,26) (15,24) (15,20) (15,22) (16,27) (16,25) (16,17) (16,28) (16,23) (17,27) (17,28) (18,21) (18,26) (18,20) (18,19) (19,26) (20,21) (20,26) (20,24) (21,26) (21,24) (22,26) (22,24) (23,27) (23,25) (25,28) (27,28)\nIs there a path between node 4 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph28-23_12", + "image": "data/connectivity/graph_visual/hard/graph28.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,1) (0,11) (1,18) (1,17) (1,2) (4,16) (4,18) (4,22) (5,13) (5,24) (5,10) (7,12) (8,16) (8,11) (9,13) (9,14) (10,15) (10,14) (11,18) (13,14) (14,15) (15,24) (16,19) (16,22) (17,18) (18,20) (18,21) (18,25) (19,20) (19,21) (19,22) (20,21) (22,25) (23,24)\nIs there a path between node 23 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph141-4_17", + "image": "data/connectivity/graph_visual/hard/graph141.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,4) (0,12) (0,17) (0,3) (0,24) (0,10) (1,16) (1,24) (1,7) (1,2) (2,14) (2,11) (2,22) (2,15) (3,11) (3,24) (3,10) (4,17) (4,24) (4,10) (5,27) (5,23) (6,18) (7,22) (7,17) (7,15) (7,24) (9,27) (9,25) (10,14) (10,12) (10,15) (11,14) (11,12) (13,19) (14,16) (14,17) (15,22) (15,16) (16,17) (17,24) (19,26) (21,27) (23,27) (23,25) (25,28)\nIs there a path between node 4 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph683-25_9", + "image": "data/connectivity/graph_visual/hard/graph683.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,10) (0,15) (0,21) (0,1) (0,7) (0,29) (0,24) (0,16) (0,23) (0,17) (1,26) (1,10) (1,15) (1,7) (1,28) (1,29) (1,12) (1,24) (1,16) (1,3) (1,23) (2,14) (2,27) (2,34) (3,26) (3,32) (3,15) (3,21) (3,7) (3,28) (3,29) (3,12) (3,24) (3,23) (3,17) (4,9) (4,14) (4,27) (4,31) (5,19) (5,22) (5,13) (5,20) (5,25) (5,30) (5,8) (5,33) (6,9) (6,27) (6,34) (6,31) (7,26) (7,32) (7,10) (7,15) (7,21) (7,29) (7,12) (7,24) (7,16) (7,23) (7,17) (8,19) (8,22) (8,13) (8,20) (8,25) (8,18) (8,30) (8,33) (9,14) (9,34) (10,32) (10,15) (10,21) (10,29) (10,24) (10,23) (10,17) (11,19) (11,22) (11,13) (11,25) (11,18) (11,30) (12,26) (12,32) (12,15) (12,21) (12,24) (12,16) (12,23) (13,19) (13,20) (13,25) (13,18) (13,33) (14,27) (14,31) (15,26) (15,21) (15,28) (15,24) (15,16) (15,23) (15,17) (16,26) (16,32) (16,23) (16,17) (17,26) (17,32) (17,21) (17,28) (17,24) (18,19) (18,22) (18,20) (18,30) (19,22) (19,20) (19,25) (19,30) (20,25) (20,30) (20,33) (21,26) (21,32) (21,28) (21,29) (22,25) (22,30) (22,33) (23,32) (23,28) (23,29) (23,24) (24,32) (24,28) (25,30) (25,33) (26,32) (26,28) (27,31) (28,29) (30,33)\nIs there a path between node 25 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph567-25_27", + "image": "data/connectivity/graph_visual/hard/graph567.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,5) (0,1) (0,21) (0,24) (0,33) (0,22) (1,10) (1,20) (1,18) (1,14) (1,13) (1,22) (2,7) (2,12) (2,6) (2,28) (2,31) (3,17) (3,16) (3,30) (3,28) (3,25) (5,8) (5,29) (5,19) (5,18) (5,24) (5,22) (6,26) (6,16) (6,30) (6,25) (7,12) (7,17) (7,26) (8,19) (8,24) (8,23) (9,18) (9,32) (9,22) (10,13) (10,22) (11,29) (11,20) (11,14) (11,23) (11,13) (11,32) (11,22) (12,30) (13,24) (13,23) (13,15) (14,29) (14,18) (14,24) (15,20) (15,23) (15,32) (15,22) (16,30) (16,25) (16,31) (17,25) (18,20) (18,21) (18,24) (18,27) (19,33) (19,27) (19,32) (19,22) (20,29) (20,21) (20,24) (20,23) (21,29) (22,33) (22,23) (23,29) (24,27) (25,30) (25,31) (26,28) (27,32)\nIs there a path between node 25 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph100-14_6", + "image": "data/connectivity/graph_visual/hard/graph100.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,11) (0,20) (1,12) (1,5) (1,2) (1,16) (1,17) (1,25) (1,6) (1,21) (1,7) (1,3) (1,15) (1,23) (1,4) (1,24) (1,9) (1,27) (1,10) (2,8) (2,26) (2,5) (2,19) (2,18) (2,16) (2,6) (2,21) (2,7) (2,3) (2,23) (2,24) (2,9) (2,10) (3,8) (3,26) (3,12) (3,5) (3,22) (3,19) (3,18) (3,17) (3,6) (3,21) (3,7) (3,15) (3,23) (3,4) (3,24) (3,9) (3,27) (3,10) (4,14) (4,26) (4,12) (4,5) (4,22) (4,19) (4,18) (4,16) (4,17) (4,25) (4,6) (4,21) (4,7) (4,15) (4,23) (4,24) (4,9) (4,27) (5,14) (5,26) (5,12) (5,19) (5,16) (5,17) (5,6) (5,21) (5,7) (5,15) (5,23) (5,24) (5,9) (5,27) (6,8) (6,26) (6,12) (6,19) (6,16) (6,17) (6,25) (6,21) (6,7) (6,15) (6,24) (6,9) (6,27) (7,14) (7,26) (7,22) (7,19) (7,18) (7,16) (7,17) (7,25) (7,21) (7,15) (7,23) (7,24) (7,9) (7,27) (8,14) (8,12) (8,22) (8,19) (8,18) (8,16) (8,17) (8,25) (8,21) (8,15) (8,23) (8,24) (8,9) (8,27) (8,10) (9,14) (9,26) (9,12) (9,22) (9,19) (9,18) (9,16) (9,21) (9,15) (9,23) (9,24) (9,27) (9,10) (10,14) (10,26) (10,22) (10,19) (10,18) (10,16) (10,17) (10,25) (10,21) (10,15) (10,23) (10,24) (10,27) (11,20) (11,13) (12,14) (12,26) (12,22) (12,19) (12,18) (12,16) (12,17) (12,25) (12,21) (12,15) (12,23) (13,20) (14,26) (14,22) (14,16) (14,17) (14,15) (14,23) (14,27) (15,26) (15,22) (15,18) (15,16) (15,25) (15,24) (16,26) (16,18) (16,17) (16,23) (16,27) (17,26) (17,19) (17,25) (17,24) (17,27) (18,26) (18,19) (18,25) (18,21) (18,23) (18,24) (18,27) (19,26) (19,25) (19,24) (21,26) (21,22) (21,25) (21,24) (21,27) (22,26) (22,24) (22,27) (23,24) (24,25) (24,27) (25,26) (25,27) (26,27)\nIs there a path between node 14 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph33-9_16", + "image": "data/connectivity/graph_visual/hard/graph33.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,22) (0,7) (0,18) (0,14) (0,20) (0,13) (0,24) (0,17) (1,25) (1,9) (1,21) (1,15) (1,23) (1,19) (1,16) (1,8) (2,9) (2,21) (2,23) (2,19) (2,6) (2,3) (2,8) (2,5) (3,25) (3,21) (3,15) (3,23) (3,4) (3,19) (4,25) (4,10) (4,9) (4,21) (4,23) (4,19) (4,6) (4,5) (5,25) (5,10) (5,9) (5,23) (5,16) (5,8) (6,9) (6,21) (6,15) (6,19) (6,16) (7,22) (7,14) (7,13) (7,24) (7,17) (8,25) (8,10) (8,9) (8,21) (8,15) (8,23) (8,19) (8,16) (9,10) (9,15) (9,19) (9,16) (10,23) (10,16) (11,22) (11,18) (11,14) (11,20) (11,12) (11,13) (11,24) (11,17) (12,22) (12,18) (12,20) (12,24) (12,17) (13,18) (13,14) (13,20) (13,24) (13,17) (14,22) (14,18) (14,20) (14,24) (14,17) (15,25) (15,21) (15,19) (15,16) (16,25) (16,21) (16,23) (17,18) (17,20) (17,24) (18,22) (18,20) (18,24) (19,25) (19,21) (20,22) (20,24) (21,25) (21,23) (23,25)\nIs there a path between node 9 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph709-9_2", + "image": "data/connectivity/graph_visual/hard/graph709.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,10) (0,2) (0,34) (0,21) (1,18) (1,31) (1,3) (1,4) (1,8) (1,20) (1,23) (1,14) (1,26) (1,16) (1,5) (1,17) (1,27) (1,9) (1,19) (1,15) (1,33) (2,10) (3,31) (3,29) (3,22) (3,12) (3,7) (3,4) (3,28) (3,8) (3,6) (3,20) (3,23) (3,14) (3,16) (3,13) (3,17) (3,24) (3,27) (3,15) (4,29) (4,22) (4,12) (4,11) (4,28) (4,20) (4,23) (4,14) (4,26) (4,16) (4,5) (4,13) (4,24) (4,27) (4,19) (4,33) (5,18) (5,31) (5,29) (5,12) (5,11) (5,7) (5,28) (5,8) (5,6) (5,20) (5,32) (5,23) (5,26) (5,16) (5,13) (5,17) (5,24) (5,9) (5,15) (5,33) (6,18) (6,31) (6,22) (6,12) (6,11) (6,7) (6,20) (6,23) (6,14) (6,16) (6,17) (6,27) (6,9) (6,19) (6,15) (7,18) (7,22) (7,12) (7,11) (7,8) (7,20) (7,14) (7,26) (7,16) (7,13) (7,17) (7,24) (7,9) (7,15) (7,33) (8,18) (8,29) (8,12) (8,11) (8,28) (8,20) (8,32) (8,23) (8,26) (8,17) (8,24) (8,27) (8,9) (8,19) (8,15) (8,33) (9,31) (9,22) (9,12) (9,28) (9,20) (9,32) (9,23) (9,14) (9,16) (9,13) (9,17) (9,24) (9,15) (10,30) (10,25) (10,34) (11,18) (11,31) (11,22) (11,12) (11,28) (11,20) (11,32) (11,23) (11,26) (11,13) (11,17) (11,24) (11,27) (11,19) (11,15) (12,18) (12,31) (12,29) (12,22) (12,20) (12,23) (12,14) (12,26) (12,17) (12,27) (12,19) (12,15) (12,33) (13,18) (13,29) (13,28) (13,20) (13,32) (13,23) (13,26) (13,16) (13,24) (13,15) (14,29) (14,22) (14,20) (14,32) (14,23) (14,16) (14,17) (14,27) (14,19) (15,18) (15,31) (15,29) (15,22) (15,28) (15,32) (15,23) (15,26) (15,16) (15,17) (15,24) (15,19) (15,33) (16,18) (16,31) (16,22) (16,28) (16,26) (16,27) (16,33) (17,28) (17,32) (17,23) (17,24) (17,27) (17,19) (18,31) (18,29) (18,22) (18,32) (18,26) (18,24) (18,19) (18,33) (19,31) (19,28) (19,20) (19,23) (19,33) (20,31) (20,32) (20,26) (21,25) (21,34) (22,29) (22,28) (22,32) (22,23) (22,27) (22,33) (23,31) (23,29) (23,28) (23,32) (23,26) (23,24) (23,27) (24,28) (24,26) (24,27) (24,33) (25,30) (26,31) (26,29) (26,28) (26,33) (27,31) (27,28) (27,32) (27,33) (28,29) (28,32) (29,32) (29,33) (31,33) (32,33)\nIs there a path between node 9 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph287-29_30", + "image": "data/connectivity/graph_visual/hard/graph287.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,16) (0,19) (1,31) (1,27) (1,7) (2,26) (2,12) (2,4) (2,7) (2,23) (3,28) (3,10) (3,14) (3,19) (3,11) (3,25) (4,27) (4,24) (4,17) (5,20) (5,13) (5,10) (5,14) (5,19) (6,31) (6,15) (6,27) (6,21) (8,13) (9,13) (9,11) (9,18) (10,28) (10,14) (10,16) (10,19) (10,11) (10,18) (11,20) (11,22) (11,14) (11,16) (11,18) (12,31) (12,30) (12,27) (12,24) (12,23) (13,22) (13,14) (13,25) (14,22) (14,25) (14,18) (15,31) (15,26) (15,24) (16,18) (17,31) (17,26) (17,23) (18,19) (19,22) (20,25) (21,31) (21,24) (21,29) (21,23) (22,28) (22,25) (23,27) (23,29) (24,30) (26,27) (29,31)\nIs there a path between node 29 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph627-30_1", + "image": "data/connectivity/graph_visual/hard/graph627.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,5) (0,24) (0,14) (0,29) (0,28) (0,32) (0,22) (0,23) (1,4) (1,30) (1,6) (1,14) (1,2) (1,28) (2,4) (2,26) (2,6) (2,17) (2,9) (2,32) (2,10) (3,26) (3,13) (3,6) (3,31) (3,32) (3,20) (3,21) (3,10) (4,26) (4,5) (4,17) (4,21) (4,10) (5,30) (5,26) (5,6) (5,31) (5,22) (5,34) (5,21) (6,19) (6,29) (6,28) (6,9) (6,32) (6,20) (7,12) (7,18) (7,11) (8,12) (8,18) (8,11) (9,19) (9,24) (9,13) (9,32) (9,21) (10,19) (10,24) (10,28) (10,23) (11,12) (11,27) (12,18) (13,26) (13,14) (13,28) (13,31) (13,23) (14,19) (14,24) (14,29) (14,22) (14,34) (14,21) (14,23) (15,25) (17,30) (17,19) (17,24) (17,29) (17,31) (17,32) (17,22) (18,27) (19,24) (19,32) (19,34) (19,33) (20,26) (20,28) (20,21) (20,23) (20,33) (21,30) (21,24) (21,31) (21,34) (21,23) (22,30) (22,26) (22,31) (22,23) (22,33) (23,34) (24,29) (24,33) (26,29) (26,28) (26,32) (28,30) (28,34) (30,31)\nIs there a path between node 30 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph282-24_12", + "image": "data/connectivity/graph_visual/hard/graph282.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,13) (0,28) (0,2) (0,25) (0,9) (0,3) (0,1) (0,19) (0,23) (0,29) (0,16) (0,8) (0,27) (0,14) (0,22) (1,28) (1,2) (1,25) (1,9) (1,11) (1,3) (1,10) (1,20) (1,19) (1,29) (1,16) (1,8) (1,14) (1,26) (1,22) (1,4) (2,28) (2,25) (2,11) (2,10) (2,20) (2,19) (2,23) (2,29) (2,8) (2,21) (2,22) (3,13) (3,25) (3,9) (3,11) (3,20) (3,23) (3,29) (3,27) (3,26) (3,21) (3,22) (3,4) (4,25) (4,9) (4,11) (4,10) (4,20) (4,23) (4,29) (4,16) (4,14) (4,21) (4,22) (5,24) (6,12) (6,15) (6,18) (7,12) (7,18) (8,13) (8,28) (8,25) (8,9) (8,11) (8,10) (8,20) (8,23) (8,29) (8,16) (8,27) (8,26) (9,13) (9,28) (9,25) (9,10) (9,20) (9,19) (9,23) (9,29) (9,16) (9,27) (9,14) (9,26) (9,21) (9,22) (10,13) (10,28) (10,25) (10,11) (10,20) (10,19) (10,23) (10,29) (10,16) (10,27) (10,14) (10,21) (10,22) (11,13) (11,25) (11,20) (11,19) (11,23) (11,29) (11,16) (11,27) (11,14) (11,26) (11,21) (11,22) (12,15) (12,18) (13,28) (13,25) (13,20) (13,19) (13,29) (13,14) (13,26) (13,22) (14,20) (14,19) (14,23) (14,29) (14,27) (14,26) (14,22) (15,18) (16,28) (16,25) (16,20) (16,23) (16,27) (16,26) (16,22) (17,30) (17,24) (19,28) (19,25) (19,23) (19,27) (19,26) (19,21) (19,22) (20,28) (20,25) (20,29) (20,26) (20,21) (20,22) (21,25) (21,23) (21,27) (21,22) (22,28) (22,29) (22,27) (22,26) (23,28) (23,25) (23,29) (23,27) (24,30) (25,28) (25,29) (25,27) (25,26) (26,28) (26,29) (27,28) (27,29) (28,29)\nIs there a path between node 24 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph387-20_0", + "image": "data/connectivity/graph_visual/hard/graph387.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,27) (0,28) (0,29) (0,22) (0,23) (0,8) (0,19) (0,6) (0,16) (0,7) (0,15) (0,26) (0,1) (1,3) (1,27) (1,20) (1,22) (1,23) (1,8) (1,19) (1,18) (1,6) (1,5) (1,16) (1,10) (1,7) (1,26) (2,31) (2,21) (2,11) (2,17) (2,12) (3,22) (3,8) (3,19) (3,6) (3,16) (3,10) (3,7) (3,15) (4,31) (4,14) (4,11) (4,17) (4,25) (4,24) (4,13) (4,12) (4,30) (5,28) (5,29) (5,23) (5,19) (5,18) (5,10) (5,15) (5,26) (6,27) (6,29) (6,20) (6,23) (6,8) (6,18) (6,16) (6,10) (6,15) (6,26) (7,27) (7,28) (7,20) (7,22) (7,23) (7,8) (7,19) (7,18) (7,16) (7,15) (7,26) (8,27) (8,28) (8,29) (8,20) (8,22) (8,23) (8,18) (8,16) (9,31) (9,21) (9,11) (9,17) (9,25) (9,24) (9,12) (10,27) (10,28) (10,29) (10,20) (10,22) (10,23) (10,19) (10,16) (10,15) (10,26) (11,31) (11,21) (11,25) (11,24) (11,12) (12,31) (12,21) (12,14) (12,17) (12,25) (12,24) (12,30) (13,21) (13,25) (13,24) (13,30) (14,31) (14,17) (14,25) (14,24) (14,30) (15,29) (15,20) (15,22) (15,23) (15,19) (15,18) (15,26) (16,27) (16,28) (16,29) (16,20) (16,22) (16,18) (16,26) (17,31) (17,21) (17,25) (17,24) (17,30) (18,28) (18,29) (18,20) (18,22) (18,19) (19,27) (19,28) (19,29) (19,20) (19,22) (19,23) (19,26) (20,27) (20,28) (20,29) (20,22) (20,23) (21,25) (22,27) (22,28) (22,29) (23,28) (24,25) (24,30) (25,31) (25,30) (26,27) (26,28) (26,29) (27,28) (27,29) (28,29) (30,31)\nIs there a path between node 20 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph212-5_4", + "image": "data/connectivity/graph_visual/hard/graph212.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,11) (0,28) (0,27) (0,2) (0,18) (1,25) (1,20) (1,28) (1,6) (1,4) (2,3) (2,25) (2,22) (2,14) (2,24) (2,4) (3,19) (3,28) (3,27) (3,6) (3,14) (4,7) (4,19) (4,20) (4,26) (4,18) (4,17) (4,21) (5,29) (5,15) (6,25) (6,22) (6,20) (6,18) (7,25) (7,19) (7,20) (7,14) (7,18) (7,24) (7,21) (8,16) (8,10) (8,23) (8,15) (9,13) (10,29) (11,24) (12,16) (12,23) (13,23) (14,19) (14,17) (15,23) (16,23) (18,25) (19,26) (19,24) (19,21) (20,24) (22,25) (22,26) (25,27) (26,28)\nIs there a path between node 5 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph516-16_32", + "image": "data/connectivity/graph_visual/hard/graph516.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,4) (1,33) (1,21) (1,17) (2,10) (2,30) (2,23) (3,10) (3,16) (3,30) (3,23) (5,26) (6,22) (6,25) (6,10) (6,13) (6,30) (6,11) (6,15) (6,29) (6,20) (7,8) (7,13) (7,33) (7,27) (7,14) (7,29) (8,10) (8,33) (8,15) (9,10) (9,12) (9,11) (9,15) (9,17) (10,22) (10,31) (10,16) (10,33) (10,27) (10,20) (11,25) (11,31) (11,12) (11,27) (11,14) (12,22) (12,31) (12,30) (12,33) (12,21) (12,27) (12,17) (12,14) (13,25) (13,31) (13,29) (14,33) (14,23) (14,20) (15,33) (15,20) (16,25) (16,33) (16,21) (16,17) (16,20) (17,29) (19,24) (20,25) (20,31) (20,30) (21,29) (22,25) (23,25) (23,33) (25,27) (27,29) (29,31) (31,33)\nIs there a path between node 16 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph168-22_5", + "image": "data/connectivity/graph_visual/hard/graph168.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,3) (1,12) (2,16) (2,13) (2,23) (4,5) (5,19) (5,20) (6,27) (6,13) (6,7) (7,28) (7,22) (7,23) (7,26) (8,9) (8,26) (9,27) (9,28) (9,23) (9,25) (9,24) (10,16) (10,27) (10,23) (10,25) (11,19) (11,17) (13,16) (13,27) (13,21) (13,22) (14,22) (15,16) (15,27) (15,28) (15,22) (15,24) (16,27) (16,28) (16,26) (17,18) (17,19) (18,20) (19,20) (22,23) (23,28) (23,26) (23,24) (24,25) (25,27) (25,26)\nIs there a path between node 22 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph515-26_29", + "image": "data/connectivity/graph_visual/hard/graph515.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,4) (0,20) (0,31) (0,15) (0,28) (0,12) (0,18) (1,4) (1,10) (1,8) (1,16) (1,29) (1,15) (1,28) (1,23) (1,32) (1,6) (1,26) (2,14) (2,11) (3,17) (4,8) (4,23) (4,12) (4,32) (4,26) (5,10) (5,16) (5,29) (5,23) (5,12) (5,32) (6,8) (6,29) (6,12) (6,18) (6,26) (7,10) (7,8) (7,29) (7,15) (7,28) (8,29) (8,28) (8,12) (9,10) (9,31) (9,15) (9,23) (9,12) (9,18) (9,24) (9,32) (9,26) (10,20) (10,31) (10,23) (10,26) (11,14) (12,23) (12,18) (14,33) (14,25) (15,31) (15,29) (15,23) (15,18) (16,20) (16,28) (16,24) (17,19) (17,30) (17,27) (18,20) (18,29) (18,32) (20,29) (20,28) (20,23) (21,22) (22,25) (23,31) (23,29) (23,28) (24,32) (24,26) (26,31) (31,32)\nIs there a path between node 26 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph185-3_28", + "image": "data/connectivity/graph_visual/hard/graph185.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,3) (0,18) (0,24) (0,5) (0,12) (0,26) (0,14) (0,16) (0,21) (0,9) (0,1) (0,28) (0,25) (1,3) (1,18) (1,24) (1,5) (1,12) (1,26) (1,14) (1,16) (1,21) (1,2) (1,23) (1,20) (1,28) (1,25) (2,3) (2,18) (2,10) (2,24) (2,5) (2,12) (2,26) (2,14) (2,16) (2,9) (2,23) (2,20) (2,28) (2,7) (2,25) (2,22) (2,13) (3,18) (3,24) (3,12) (3,26) (3,16) (3,9) (3,19) (3,7) (3,25) (3,22) (4,11) (4,27) (4,17) (4,15) (4,8) (5,18) (5,24) (5,12) (5,26) (5,14) (5,16) (5,21) (5,9) (5,23) (5,19) (5,20) (5,7) (5,13) (6,11) (6,27) (6,29) (6,15) (6,8) (7,18) (7,10) (7,12) (7,26) (7,14) (7,16) (7,21) (7,9) (7,20) (7,25) (7,22) (7,13) (8,11) (8,27) (8,29) (8,17) (8,15) (9,18) (9,10) (9,24) (9,16) (9,21) (9,19) (9,20) (9,28) (9,25) (9,13) (10,18) (10,24) (10,12) (10,26) (10,14) (10,16) (10,23) (10,20) (10,28) (10,25) (10,22) (10,13) (11,27) (11,29) (12,18) (12,24) (12,16) (12,21) (12,23) (12,20) (12,28) (12,22) (12,13) (13,18) (13,24) (13,26) (13,14) (13,16) (13,21) (13,23) (13,20) (13,28) (13,25) (13,22) (14,26) (14,16) (14,21) (14,23) (14,19) (14,20) (14,28) (14,25) (15,27) (15,17) (16,18) (16,24) (16,26) (16,20) (16,25) (16,22) (17,29) (18,24) (18,26) (18,23) (18,19) (18,20) (18,25) (18,22) (19,21) (19,23) (19,28) (19,25) (20,26) (20,23) (20,28) (20,25) (20,22) (21,26) (21,23) (21,28) (21,22) (22,26) (22,23) (22,25) (23,24) (23,26) (24,26) (24,28) (25,26)\nIs there a path between node 3 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph0-18_7", + "image": "data/connectivity/graph_visual/hard/graph0.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,9) (1,18) (1,8) (1,4) (2,15) (2,18) (2,11) (2,23) (2,4) (3,12) (3,5) (4,23) (4,25) (5,12) (5,17) (6,22) (6,13) (7,18) (7,23) (7,8) (9,17) (10,19) (10,17) (11,15) (12,24) (14,20) (14,22) (15,18) (16,20) (16,22) (20,22) (21,22) (23,25)\nIs there a path between node 18 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph480-1_24", + "image": "data/connectivity/graph_visual/hard/graph480.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,28) (0,10) (0,15) (0,27) (0,11) (0,31) (0,4) (0,30) (0,5) (0,26) (0,24) (0,17) (0,21) (0,25) (0,9) (0,19) (0,18) (0,7) (0,14) (0,22) (0,6) (1,32) (1,12) (1,29) (2,28) (2,10) (2,15) (2,16) (2,31) (2,4) (2,5) (2,26) (2,24) (2,17) (2,21) (2,25) (2,9) (2,19) (2,18) (2,7) (2,14) (2,23) (2,3) (2,6) (3,28) (3,27) (3,11) (3,16) (3,31) (3,30) (3,8) (3,5) (3,26) (3,24) (3,17) (3,21) (3,25) (3,19) (3,18) (3,14) (3,23) (3,20) (3,22) (3,6) (4,28) (4,10) (4,15) (4,11) (4,16) (4,31) (4,30) (4,8) (4,5) (4,26) (4,24) (4,17) (4,21) (4,9) (4,18) (4,7) (4,14) (4,23) (4,20) (4,22) (4,6) (5,28) (5,10) (5,15) (5,27) (5,11) (5,16) (5,30) (5,8) (5,26) (5,17) (5,21) (5,25) (5,19) (5,18) (5,7) (5,23) (5,20) (5,6) (6,28) (6,10) (6,27) (6,16) (6,8) (6,26) (6,24) (6,17) (6,21) (6,25) (6,18) (6,7) (6,14) (7,28) (7,15) (7,27) (7,11) (7,16) (7,31) (7,30) (7,8) (7,26) (7,24) (7,17) (7,21) (7,25) (7,19) (7,14) (7,23) (7,22) (8,28) (8,11) (8,31) (8,26) (8,24) (8,17) (8,21) (8,9) (8,19) (8,18) (8,20) (8,22) (9,28) (9,10) (9,15) (9,11) (9,16) (9,31) (9,30) (9,26) (9,24) (9,17) (9,19) (9,14) (9,20) (9,22) (10,28) (10,15) (10,11) (10,31) (10,30) (10,26) (10,24) (10,17) (10,21) (10,19) (10,18) (10,14) (10,23) (10,20) (10,22) (11,27) (11,16) (11,31) (11,30) (11,26) (11,24) (11,21) (11,25) (11,14) (11,20) (11,22) (12,13) (13,32) (13,29) (14,28) (14,27) (14,16) (14,31) (14,30) (14,26) (14,24) (14,17) (14,21) (14,19) (14,23) (14,20) (14,22) (15,27) (15,31) (15,24) (15,17) (15,21) (15,25) (15,19) (15,23) (15,20) (15,22) (16,28) (16,30) (16,26) (16,24) (16,17) (16,25) (16,23) (16,20) (16,22) (17,31) (17,30) (17,26) (17,24) (17,25) (17,18) (18,28) (18,27) (18,31) (18,30) (18,26) (18,24) (18,21) (18,25) (18,19) (18,23) (18,22) (19,27) (19,31) (19,30) (19,24) (19,21) (19,25) (19,20) (20,27) (20,31) (20,30) (20,26) (20,24) (20,25) (20,23) (20,22) (21,28) (21,27) (21,31) (21,30) (21,26) (21,25) (21,23) (21,22) (22,27) (22,31) (22,26) (22,25) (23,28) (23,27) (23,31) (23,26) (23,24) (24,31) (24,26) (24,25) (25,28) (25,27) (25,31) (25,30) (25,26) (26,28) (26,27) (26,31) (26,30) (27,28) (27,31) (27,30) (28,30) (29,32)\nIs there a path between node 1 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph19-20_0", + "image": "data/connectivity/graph_visual/hard/graph19.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,21) (0,9) (0,6) (0,8) (1,21) (1,19) (1,13) (1,9) (1,3) (2,17) (3,21) (3,16) (3,19) (3,13) (3,8) (4,12) (4,13) (4,6) (4,7) (6,12) (6,16) (6,20) (6,13) (6,18) (6,11) (6,7) (7,20) (7,9) (8,12) (8,16) (8,20) (8,18) (8,11) (9,21) (10,25) (10,24) (11,20) (12,19) (12,13) (13,21) (13,19) (15,23) (18,21) (18,20) (19,20) (23,24)\nIs there a path between node 20 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph279-6_2", + "image": "data/connectivity/graph_visual/hard/graph279.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,7) (0,22) (0,14) (0,1) (0,12) (0,23) (1,8) (1,14) (1,12) (1,2) (1,23) (2,7) (2,22) (2,19) (2,12) (2,23) (3,13) (3,26) (3,21) (3,20) (3,6) (3,10) (3,11) (3,4) (3,17) (3,27) (3,24) (3,28) (3,30) (4,29) (4,21) (4,18) (4,20) (4,6) (4,16) (4,17) (4,27) (4,28) (4,9) (4,30) (5,25) (5,13) (5,26) (5,21) (5,20) (5,6) (5,10) (5,11) (5,15) (5,16) (5,17) (5,27) (5,24) (5,28) (6,25) (6,13) (6,29) (6,26) (6,21) (6,18) (6,11) (6,15) (6,16) (6,17) (6,27) (6,24) (6,28) (7,8) (7,22) (7,19) (7,14) (7,12) (7,23) (8,19) (8,12) (8,23) (9,25) (9,13) (9,26) (9,21) (9,18) (9,11) (9,16) (9,27) (10,25) (10,26) (10,18) (10,15) (10,17) (10,24) (10,30) (11,29) (11,21) (11,18) (11,20) (11,15) (11,17) (11,27) (11,24) (11,28) (12,22) (12,14) (12,23) (13,25) (13,26) (13,18) (13,20) (13,15) (13,16) (13,24) (13,28) (13,30) (14,22) (14,23) (15,25) (15,29) (15,26) (15,21) (15,18) (15,16) (15,27) (15,28) (15,30) (16,25) (16,29) (16,26) (16,20) (16,17) (16,30) (17,29) (17,21) (17,18) (17,20) (17,27) (18,25) (18,29) (18,26) (18,21) (18,20) (18,28) (18,30) (19,22) (20,25) (20,29) (20,26) (20,21) (20,24) (20,28) (21,25) (21,26) (21,27) (21,24) (21,28) (21,30) (24,29) (24,26) (24,27) (24,28) (24,30) (25,29) (25,26) (25,28) (25,30) (26,29) (26,27) (26,30) (27,29) (27,28) (29,30)\nIs there a path between node 6 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph498-20_31", + "image": "data/connectivity/graph_visual/hard/graph498.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,13) (0,29) (0,24) (0,31) (0,12) (0,10) (1,11) (1,21) (2,23) (2,29) (2,32) (2,24) (2,12) (2,9) (2,6) (2,4) (2,20) (3,33) (3,18) (3,22) (3,31) (3,12) (3,8) (3,9) (3,26) (3,6) (4,18) (4,22) (4,15) (4,8) (4,20) (5,11) (5,28) (5,14) (5,27) (6,33) (6,13) (6,19) (6,18) (6,22) (6,31) (6,26) (6,10) (7,16) (7,25) (8,24) (9,18) (9,22) (10,13) (10,29) (10,18) (10,17) (10,26) (10,20) (11,25) (12,13) (12,29) (12,24) (12,15) (12,20) (13,29) (13,19) (13,18) (13,24) (14,28) (14,16) (14,27) (15,33) (15,23) (15,29) (16,30) (17,29) (17,19) (17,26) (18,33) (18,23) (18,29) (18,24) (18,31) (19,31) (19,26) (20,32) (21,30) (21,27) (22,29) (24,33) (25,28) (25,30) (25,27) (26,32) (29,31) (31,32)\nIs there a path between node 20 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph399-20_3", + "image": "data/connectivity/graph_visual/hard/graph399.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,4) (0,12) (0,11) (0,10) (0,3) (0,17) (0,21) (0,27) (0,15) (0,23) (0,31) (0,29) (0,2) (0,8) (0,9) (0,14) (0,18) (1,5) (1,26) (1,13) (1,20) (1,32) (1,7) (2,19) (2,4) (2,28) (2,22) (2,16) (2,12) (2,10) (2,3) (2,17) (2,21) (2,27) (2,15) (2,23) (2,31) (2,29) (2,8) (2,9) (2,14) (2,18) (3,4) (3,22) (3,16) (3,12) (3,10) (3,17) (3,21) (3,27) (3,23) (3,31) (3,29) (3,6) (3,9) (3,14) (3,18) (4,16) (4,12) (4,11) (4,17) (4,21) (4,15) (4,30) (4,23) (4,29) (4,6) (4,8) (4,9) (4,18) (5,26) (5,13) (5,25) (5,24) (5,32) (5,7) (6,19) (6,22) (6,12) (6,11) (6,10) (6,17) (6,21) (6,27) (6,15) (6,30) (6,23) (6,31) (6,29) (6,9) (6,14) (7,26) (7,25) (7,32) (8,19) (8,28) (8,10) (8,17) (8,27) (8,15) (8,30) (8,23) (9,19) (9,28) (9,22) (9,16) (9,12) (9,10) (9,17) (9,21) (9,15) (9,30) (9,23) (9,29) (9,18) (10,19) (10,28) (10,22) (10,12) (10,11) (10,17) (10,21) (10,27) (10,15) (10,30) (10,23) (10,31) (10,29) (10,14) (10,18) (11,16) (11,12) (11,17) (11,21) (11,27) (11,15) (11,30) (11,31) (11,29) (11,14) (11,18) (12,19) (12,28) (12,22) (12,17) (12,27) (12,15) (12,30) (12,23) (12,31) (12,29) (12,14) (12,18) (13,26) (13,25) (13,20) (13,32) (14,28) (14,16) (14,17) (14,21) (14,27) (14,15) (14,31) (14,29) (14,18) (15,19) (15,22) (15,16) (15,17) (15,21) (15,27) (15,30) (15,23) (15,31) (15,29) (15,18) (16,19) (16,28) (16,22) (16,17) (16,21) (16,27) (16,30) (16,31) (16,18) (17,22) (17,21) (17,30) (17,31) (17,29) (17,18) (18,19) (18,28) (18,22) (18,21) (18,27) (18,29) (19,28) (19,22) (19,21) (19,30) (19,31) (19,29) (20,32) (21,28) (21,22) (21,27) (21,29) (22,28) (22,30) (22,23) (22,31) (22,29) (23,28) (23,27) (23,30) (23,31) (23,29) (24,26) (24,25) (25,26) (25,32) (26,32) (27,28) (27,30) (27,29) (28,30) (28,31) (28,29) (29,30) (29,31)\nIs there a path between node 20 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph645-16_29", + "image": "data/connectivity/graph_visual/hard/graph645.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,16) (0,18) (0,5) (0,29) (0,21) (0,22) (0,7) (0,2) (0,13) (0,27) (0,26) (0,14) (0,33) (0,8) (0,10) (1,32) (1,16) (1,18) (1,29) (1,17) (1,2) (1,13) (1,26) (1,14) (1,31) (1,33) (1,10) (2,23) (2,32) (2,16) (2,18) (2,5) (2,29) (2,17) (2,21) (2,7) (2,13) (2,27) (2,9) (2,31) (2,33) (2,8) (3,12) (3,15) (3,19) (3,20) (3,34) (3,4) (3,11) (4,12) (4,28) (4,6) (4,15) (4,19) (4,34) (4,30) (4,11) (5,16) (5,18) (5,17) (5,21) (5,22) (5,13) (5,24) (5,9) (5,26) (5,31) (5,33) (5,10) (6,12) (6,28) (6,15) (6,19) (6,20) (6,30) (6,11) (6,25) (7,32) (7,16) (7,18) (7,22) (7,13) (7,24) (7,27) (7,9) (7,26) (7,14) (7,31) (7,33) (7,8) (7,10) (8,23) (8,16) (8,18) (8,29) (8,17) (8,21) (8,22) (8,13) (8,24) (8,26) (8,14) (8,31) (8,33) (8,10) (9,23) (9,32) (9,16) (9,18) (9,17) (9,21) (9,22) (9,13) (9,24) (9,27) (9,26) (9,14) (9,31) (9,33) (9,10) (10,23) (10,32) (10,16) (10,18) (10,17) (10,21) (10,13) (10,24) (10,27) (10,26) (10,14) (11,28) (11,15) (11,34) (11,30) (11,25) (12,28) (12,15) (12,20) (12,30) (12,25) (13,23) (13,32) (13,16) (13,18) (13,29) (13,17) (13,22) (13,24) (13,27) (13,26) (13,14) (13,33) (14,23) (14,29) (14,17) (14,21) (14,22) (14,27) (14,26) (15,20) (15,30) (16,23) (16,29) (16,17) (16,21) (16,22) (16,24) (16,27) (16,26) (16,31) (17,23) (17,32) (17,18) (17,21) (17,24) (17,27) (17,31) (18,23) (18,29) (18,21) (18,27) (18,26) (18,31) (18,33) (19,20) (19,34) (19,30) (19,25) (20,28) (20,34) (20,30) (20,25) (21,32) (21,22) (21,24) (21,27) (21,26) (21,31) (22,23) (22,32) (22,29) (22,24) (22,26) (22,31) (22,33) (23,32) (23,29) (23,24) (23,26) (23,31) (24,29) (24,27) (24,26) (24,33) (25,28) (25,34) (25,30) (26,32) (26,29) (27,29) (27,33) (28,30) (29,32) (30,34) (31,32) (32,33)\nIs there a path between node 16 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph557-2_18", + "image": "data/connectivity/graph_visual/hard/graph557.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,10) (0,11) (1,18) (4,10) (4,11) (4,24) (4,12) (5,30) (5,9) (5,32) (5,26) (5,8) (6,30) (6,19) (7,28) (8,19) (8,15) (8,13) (9,19) (9,13) (10,11) (10,31) (10,17) (10,12) (11,14) (11,22) (12,23) (12,16) (13,15) (14,24) (14,16) (15,26) (15,29) (16,22) (16,17) (17,22) (17,23) (19,26) (20,28) (21,23) (22,23) (22,31) (23,31) (29,32)\nIs there a path between node 2 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph594-13_8", + "image": "data/connectivity/graph_visual/hard/graph594.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,3) (0,26) (0,7) (0,22) (0,17) (0,18) (0,8) (1,20) (1,33) (1,14) (1,30) (1,25) (1,12) (1,24) (1,19) (1,28) (1,9) (1,32) (1,21) (1,13) (1,2) (1,16) (2,33) (2,14) (2,23) (2,25) (2,27) (2,4) (2,19) (2,28) (2,9) (2,32) (2,21) (2,16) (3,6) (3,5) (3,26) (3,7) (3,11) (3,22) (3,17) (3,31) (3,15) (3,18) (3,29) (3,8) (3,10) (4,33) (4,14) (4,23) (4,30) (4,27) (4,24) (4,28) (4,9) (4,32) (4,21) (4,13) (4,16) (5,6) (5,11) (5,22) (5,17) (5,31) (5,15) (5,18) (5,29) (5,10) (6,26) (6,11) (6,22) (6,17) (6,31) (6,15) (6,8) (6,10) (7,26) (7,11) (7,22) (7,31) (7,15) (7,18) (7,29) (7,8) (8,26) (8,11) (8,22) (8,31) (8,15) (8,10) (9,20) (9,33) (9,14) (9,23) (9,12) (9,27) (9,24) (9,19) (9,21) (9,13) (9,16) (10,11) (10,17) (10,31) (10,15) (10,18) (11,17) (11,31) (11,18) (11,29) (12,20) (12,23) (12,25) (12,27) (12,19) (12,28) (12,32) (12,21) (12,13) (13,33) (13,14) (13,23) (13,30) (13,27) (13,24) (13,19) (13,32) (13,21) (13,16) (14,23) (14,30) (14,27) (14,19) (14,32) (14,16) (15,22) (15,31) (15,18) (15,29) (16,20) (16,23) (16,25) (16,19) (16,28) (16,32) (16,21) (17,26) (17,22) (17,31) (17,18) (17,29) (18,31) (18,29) (19,33) (19,25) (19,27) (19,28) (19,21) (20,33) (20,30) (20,25) (20,28) (20,32) (21,23) (21,30) (21,25) (21,27) (21,24) (22,31) (22,29) (23,30) (23,25) (23,27) (23,24) (23,28) (24,33) (24,27) (24,28) (24,32) (25,30) (25,27) (25,28) (25,32) (26,31) (26,29) (27,32) (28,33) (29,31) (30,32) (32,33)\nIs there a path between node 13 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph11-12_21", + "image": "data/connectivity/graph_visual/hard/graph11.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,15) (0,2) (0,1) (0,23) (0,8) (0,24) (0,6) (0,22) (0,4) (0,11) (1,15) (1,14) (1,2) (1,8) (1,12) (1,17) (1,19) (2,15) (2,14) (2,23) (2,8) (2,20) (2,6) (2,22) (2,4) (2,17) (2,11) (2,19) (2,7) (3,18) (3,9) (3,10) (3,21) (3,13) (3,16) (4,15) (4,14) (4,5) (4,23) (4,24) (4,12) (4,17) (4,11) (4,19) (4,7) (5,15) (5,14) (5,8) (5,20) (5,6) (5,22) (5,12) (5,17) (5,11) (5,19) (5,7) (6,15) (6,14) (6,23) (6,8) (6,20) (6,22) (6,12) (6,11) (6,19) (7,15) (7,23) (7,22) (7,12) (7,17) (7,19) (8,15) (8,14) (8,23) (8,24) (8,12) (8,17) (9,18) (9,21) (9,13) (9,16) (10,25) (10,16) (11,15) (11,14) (11,23) (11,24) (11,17) (11,19) (12,14) (12,22) (12,19) (13,25) (13,18) (13,21) (13,16) (14,15) (14,23) (14,22) (14,17) (14,19) (15,23) (15,24) (15,20) (15,22) (15,17) (15,19) (16,18) (17,23) (17,24) (17,19) (18,25) (18,21) (19,23) (19,24) (19,20) (20,23) (20,22) (21,25) (23,24)\nIs there a path between node 12 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph255-13_22", + "image": "data/connectivity/graph_visual/hard/graph255.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,6) (0,2) (0,10) (0,29) (0,19) (0,5) (0,3) (1,30) (1,8) (1,28) (2,3) (3,6) (3,19) (4,14) (5,25) (6,19) (7,13) (7,30) (7,21) (7,8) (7,11) (8,13) (8,16) (8,30) (9,18) (12,19) (13,20) (13,28) (14,24) (14,18) (14,23) (15,30) (16,22) (16,28) (17,29) (17,19) (18,23) (19,25) (20,30) (20,28)\nIs there a path between node 13 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph388-22_8", + "image": "data/connectivity/graph_visual/hard/graph388.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,17) (0,10) (0,28) (0,30) (0,29) (0,3) (1,14) (1,2) (2,25) (2,20) (2,7) (2,32) (2,22) (3,24) (3,19) (3,23) (3,4) (3,12) (3,29) (4,26) (4,24) (4,23) (4,8) (4,13) (5,26) (5,19) (5,23) (5,8) (5,15) (5,21) (6,14) (7,32) (8,16) (8,12) (8,29) (9,26) (9,13) (9,18) (9,29) (9,31) (10,17) (10,11) (10,30) (10,23) (10,13) (11,16) (11,17) (11,19) (11,28) (11,23) (12,26) (12,24) (12,21) (13,26) (13,17) (13,19) (13,30) (13,31) (14,25) (14,22) (15,16) (15,17) (15,23) (15,18) (15,29) (16,26) (16,24) (16,18) (16,21) (17,24) (17,19) (17,28) (17,30) (17,23) (18,24) (18,21) (19,26) (19,24) (19,28) (19,23) (20,32) (22,32) (22,27) (24,26) (24,30) (26,29) (28,29)\nIs there a path between node 22 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph252-22_14", + "image": "data/connectivity/graph_visual/hard/graph252.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,20) (0,13) (0,30) (0,1) (0,4) (0,2) (0,22) (1,30) (1,17) (1,5) (1,4) (1,25) (1,29) (2,3) (2,5) (2,23) (3,28) (3,24) (3,4) (3,6) (3,8) (3,12) (4,15) (4,24) (4,25) (4,7) (4,6) (4,29) (5,21) (5,23) (5,7) (5,12) (6,20) (6,28) (6,23) (7,13) (7,15) (7,16) (7,8) (7,12) (8,20) (8,30) (8,24) (8,17) (8,23) (10,19) (11,19) (11,26) (12,20) (12,16) (12,25) (12,18) (13,28) (13,18) (14,20) (15,28) (15,24) (15,23) (16,20) (16,30) (16,24) (16,29) (17,21) (17,28) (17,25) (18,21) (18,23) (18,29) (20,24) (20,23) (20,22) (20,29) (21,25) (21,23) (21,22) (22,25) (23,24) (23,29) (24,28) (24,29) (25,28) (26,27) (29,30)\nIs there a path between node 22 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph206-24_23", + "image": "data/connectivity/graph_visual/hard/graph206.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,23) (0,26) (0,24) (0,27) (1,4) (1,16) (1,15) (1,10) (1,29) (1,17) (1,11) (2,9) (2,7) (2,6) (2,27) (3,13) (3,28) (3,16) (3,18) (3,29) (3,21) (4,20) (4,16) (4,5) (4,15) (4,18) (4,14) (4,25) (5,28) (5,16) (5,15) (5,18) (5,14) (5,29) (5,19) (5,17) (5,11) (7,23) (7,26) (7,27) (8,26) (10,29) (10,19) (11,13) (11,28) (11,15) (11,17) (13,20) (13,28) (13,19) (14,16) (14,15) (14,29) (14,19) (14,21) (15,20) (15,28) (15,29) (15,19) (16,28) (16,25) (16,17) (17,19) (18,20) (18,21) (20,21) (21,29) (21,25) (22,28) (23,24) (26,27) (28,29)\nIs there a path between node 24 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph286-19_4", + "image": "data/connectivity/graph_visual/hard/graph286.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,1) (0,20) (0,8) (0,31) (0,22) (1,4) (1,24) (1,19) (1,16) (1,5) (1,2) (1,8) (1,18) (1,27) (2,4) (2,19) (2,12) (2,17) (2,21) (2,31) (2,22) (3,25) (3,20) (3,14) (3,31) (3,22) (3,27) (4,7) (4,21) (4,26) (4,27) (5,11) (5,24) (5,20) (5,19) (5,12) (5,16) (5,17) (5,21) (5,9) (5,22) (6,15) (7,24) (7,20) (7,19) (7,16) (7,29) (7,17) (7,21) (7,14) (7,9) (7,8) (7,18) (7,22) (7,30) (8,20) (8,12) (8,14) (9,20) (9,16) (9,14) (9,18) (9,26) (9,23) (10,15) (11,25) (11,28) (11,20) (11,21) (11,26) (12,28) (12,24) (12,20) (12,29) (12,14) (12,18) (12,26) (12,22) (12,27) (12,23) (14,24) (14,16) (14,18) (14,31) (16,25) (16,26) (16,31) (16,23) (17,31) (17,27) (18,25) (18,28) (18,24) (18,21) (18,26) (18,27) (19,29) (19,21) (19,22) (20,25) (20,21) (20,26) (21,24) (21,29) (21,31) (21,23) (22,29) (22,26) (22,23) (23,25) (23,26) (24,25) (24,26) (24,30) (25,29) (25,31) (26,29) (26,31) (27,28) (27,31) (28,29) (29,31) (29,30) (30,31)\nIs there a path between node 19 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph321-11_28", + "image": "data/connectivity/graph_visual/hard/graph321.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,5) (0,21) (0,7) (0,6) (0,3) (0,17) (0,20) (0,22) (0,16) (0,23) (0,25) (0,27) (1,5) (1,21) (1,4) (1,7) (1,15) (1,18) (1,2) (1,24) (1,20) (1,11) (1,16) (1,25) (1,27) (2,14) (2,5) (2,21) (2,4) (2,15) (2,24) (2,22) (2,11) (2,23) (2,25) (2,27) (3,14) (3,13) (3,21) (3,7) (3,15) (3,6) (3,17) (3,24) (3,22) (3,11) (3,16) (3,23) (4,14) (4,13) (4,5) (4,19) (4,7) (4,18) (4,17) (4,22) (4,11) (4,23) (4,25) (4,27) (5,13) (5,19) (5,15) (5,18) (5,24) (5,20) (5,22) (5,11) (5,23) (5,27) (6,14) (6,21) (6,19) (6,7) (6,15) (6,18) (6,17) (6,24) (6,20) (6,11) (6,16) (6,25) (6,27) (7,14) (7,13) (7,21) (7,19) (7,15) (7,18) (7,17) (7,20) (7,22) (7,11) (7,23) (7,27) (8,30) (8,28) (9,31) (9,10) (9,26) (9,29) (10,31) (10,26) (10,29) (11,13) (11,21) (11,19) (11,15) (11,24) (11,22) (11,25) (11,27) (12,28) (13,14) (13,21) (13,15) (13,18) (13,17) (13,24) (13,20) (13,16) (13,23) (13,25) (13,27) (14,21) (14,19) (14,24) (14,20) (14,22) (14,16) (14,23) (14,25) (15,21) (15,18) (15,17) (15,24) (15,20) (15,22) (15,16) (15,25) (15,27) (16,21) (16,18) (16,17) (16,24) (16,20) (16,22) (16,25) (17,21) (17,19) (17,18) (17,24) (17,20) (17,22) (17,23) (17,25) (17,27) (18,21) (18,24) (18,20) (18,25) (18,27) (19,21) (19,20) (19,22) (19,27) (20,21) (20,24) (20,22) (20,23) (20,27) (21,24) (21,22) (21,25) (21,27) (22,25) (23,25) (23,27) (25,27) (26,31) (26,29) (29,31)\nIs there a path between node 11 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph457-12_1", + "image": "data/connectivity/graph_visual/hard/graph457.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,32) (0,31) (0,29) (0,28) (0,7) (1,6) (1,16) (1,25) (1,15) (2,5) (2,17) (2,22) (2,14) (2,13) (2,28) (2,21) (2,3) (2,24) (2,27) (3,17) (3,21) (4,6) (4,16) (5,31) (5,17) (5,24) (5,7) (5,27) (6,18) (6,16) (6,30) (7,29) (7,14) (7,13) (7,28) (7,24) (8,15) (9,10) (9,26) (9,16) (9,25) (9,30) (10,16) (10,15) (11,18) (11,16) (11,25) (11,19) (11,30) (12,18) (12,16) (12,15) (12,23) (13,28) (13,27) (14,27) (16,19) (16,23) (17,32) (18,26) (18,19) (18,30) (18,20) (19,30) (19,23) (20,23) (22,32) (22,31) (22,28) (22,24) (24,31) (24,27) (27,31) (28,29)\nIs there a path between node 12 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph200-18_8", + "image": "data/connectivity/graph_visual/hard/graph200.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,26) (0,1) (0,17) (0,6) (0,27) (0,11) (0,2) (1,16) (1,26) (1,17) (1,6) (1,27) (1,11) (1,2) (2,17) (2,27) (2,11) (3,5) (3,23) (3,22) (3,4) (4,23) (4,14) (5,23) (5,14) (5,18) (6,16) (6,17) (6,27) (7,8) (7,24) (7,19) (7,10) (7,9) (7,12) (7,21) (7,25) (7,28) (7,15) (8,24) (8,19) (8,10) (8,9) (8,21) (8,13) (8,28) (8,15) (9,24) (9,19) (9,10) (9,20) (9,12) (9,13) (9,29) (9,15) (10,24) (10,19) (10,20) (10,21) (10,25) (10,29) (10,28) (10,15) (11,16) (11,26) (11,27) (12,24) (12,19) (12,20) (12,21) (12,25) (12,29) (12,28) (13,19) (13,20) (13,21) (13,25) (13,28) (13,15) (14,23) (14,18) (15,24) (15,19) (15,25) (15,28) (16,26) (16,17) (16,27) (17,27) (18,22) (19,24) (19,20) (19,29) (19,28) (20,24) (20,29) (20,28) (21,24) (21,25) (21,29) (21,28) (22,23) (24,25) (24,29) (24,28) (25,28) (26,27) (28,29)\nIs there a path between node 18 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph108-20_5", + "image": "data/connectivity/graph_visual/hard/graph108.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,27) (0,23) (0,5) (0,1) (1,13) (1,27) (2,13) (2,16) (2,26) (3,19) (3,18) (3,12) (3,10) (3,8) (4,13) (4,27) (4,7) (5,24) (5,26) (5,11) (6,15) (6,19) (6,18) (6,12) (7,13) (7,16) (7,26) (8,12) (8,17) (8,10) (9,25) (10,12) (11,27) (11,23) (11,16) (11,25) (11,24) (12,17) (13,27) (13,23) (13,26) (13,21) (14,19) (14,20) (15,20) (15,17) (16,27) (17,20) (17,18) (18,19) (21,22) (21,23) (22,23) (22,24) (24,27) (24,25)\nIs there a path between node 20 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph236-6_27", + "image": "data/connectivity/graph_visual/hard/graph236.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,2) (1,26) (2,26) (2,30) (2,6) (3,19) (4,29) (4,8) (4,11) (4,9) (5,25) (6,30) (6,19) (6,13) (6,25) (7,23) (7,29) (7,10) (7,28) (7,14) (8,23) (8,15) (8,27) (8,18) (8,11) (8,28) (8,9) (9,23) (9,29) (9,15) (9,18) (9,12) (10,15) (11,29) (11,27) (11,28) (11,14) (12,27) (13,16) (13,26) (14,17) (15,29) (15,21) (15,28) (16,25) (17,23) (17,29) (17,18) (19,20) (19,22) (20,22) (21,27) (21,28) (22,26) (23,29) (23,28) (24,26) (24,30) (25,26) (25,30) (27,28)\nIs there a path between node 6 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph429-9_17", + "image": "data/connectivity/graph_visual/hard/graph429.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,30) (0,15) (0,16) (0,27) (0,1) (0,13) (1,14) (1,30) (1,27) (1,13) (2,9) (2,25) (2,22) (2,8) (2,5) (2,26) (2,20) (2,10) (2,6) (2,31) (2,32) (2,19) (2,17) (2,18) (2,23) (2,4) (2,11) (3,9) (3,25) (3,22) (3,8) (3,26) (3,20) (3,24) (3,10) (3,6) (3,31) (3,17) (3,18) (3,12) (3,23) (3,4) (4,25) (4,22) (4,8) (4,5) (4,20) (4,31) (4,32) (4,19) (4,17) (4,23) (4,11) (5,9) (5,25) (5,22) (5,8) (5,10) (5,6) (5,32) (5,19) (5,18) (5,12) (5,23) (5,11) (6,9) (6,25) (6,22) (6,26) (6,24) (6,31) (6,32) (6,19) (6,17) (6,18) (7,29) (7,28) (8,22) (8,26) (8,20) (8,10) (8,31) (8,19) (8,18) (8,11) (9,25) (9,22) (9,26) (9,20) (9,24) (9,31) (9,32) (9,19) (9,17) (9,12) (9,23) (10,25) (10,22) (10,20) (10,24) (10,31) (10,32) (10,19) (10,17) (10,18) (10,12) (10,23) (10,11) (11,26) (11,20) (11,24) (11,31) (11,19) (11,17) (12,25) (12,26) (12,20) (12,24) (12,31) (12,32) (12,19) (13,14) (13,30) (13,27) (14,30) (14,15) (14,16) (15,16) (17,25) (17,22) (17,26) (17,20) (17,24) (17,31) (17,32) (17,23) (18,25) (18,22) (18,26) (18,32) (19,25) (19,22) (19,26) (19,20) (19,32) (19,23) (20,25) (20,22) (20,26) (20,24) (20,31) (21,29) (22,25) (22,26) (22,24) (22,32) (23,25) (23,26) (23,24) (23,31) (24,26) (24,31) (24,32) (25,26) (25,31) (25,32) (27,30) (28,29)\nIs there a path between node 9 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph264-11_27", + "image": "data/connectivity/graph_visual/hard/graph264.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,14) (0,8) (0,20) (0,23) (0,29) (0,15) (0,25) (0,24) (0,18) (1,2) (2,21) (3,8) (3,17) (3,20) (3,12) (3,10) (3,5) (4,26) (4,14) (4,22) (4,8) (4,12) (4,7) (4,10) (4,5) (5,22) (5,13) (5,8) (5,19) (5,17) (5,12) (5,6) (5,7) (5,24) (6,26) (6,22) (6,29) (6,24) (7,26) (7,11) (7,17) (7,20) (7,23) (7,15) (7,10) (7,24) (8,11) (8,13) (8,19) (8,17) (8,29) (8,15) (8,10) (8,25) (9,21) (10,26) (10,28) (10,17) (10,15) (10,25) (10,18) (11,22) (11,28) (11,20) (11,12) (11,29) (11,18) (12,14) (12,13) (12,28) (12,15) (12,25) (13,19) (13,25) (13,18) (14,20) (14,15) (14,25) (15,25) (16,30) (16,21) (17,19) (17,23) (17,29) (17,24) (17,18) (18,22) (18,23) (18,29) (18,25) (18,24) (19,24) (20,22) (20,23) (20,25) (22,26) (22,28) (23,24) (24,26) (25,29) (26,29)\nIs there a path between node 11 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph412-32_8", + "image": "data/connectivity/graph_visual/hard/graph412.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,16) (0,14) (0,20) (1,32) (1,25) (1,21) (1,22) (1,23) (1,26) (2,9) (2,20) (3,32) (3,28) (4,9) (4,5) (4,17) (4,31) (5,13) (5,31) (5,11) (6,32) (6,26) (7,32) (7,27) (7,25) (7,28) (7,22) (7,23) (8,30) (8,31) (8,20) (9,24) (9,12) (9,11) (10,18) (10,29) (10,25) (10,28) (10,26) (11,17) (11,14) (12,14) (12,20) (13,16) (13,17) (14,24) (14,16) (14,20) (15,32) (15,25) (15,28) (15,23) (16,17) (16,20) (17,30) (18,29) (18,21) (18,28) (18,22) (19,28) (19,26) (20,30) (21,25) (21,23) (21,26) (22,25) (22,28) (22,26) (25,27) (25,29) (25,28) (27,28)\nIs there a path between node 32 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph38-24_11", + "image": "data/connectivity/graph_visual/hard/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,7) (0,4) (0,24) (0,15) (1,2) (1,19) (1,6) (1,23) (1,13) (1,5) (1,20) (1,16) (1,25) (1,9) (1,21) (2,3) (2,6) (2,12) (2,23) (2,13) (2,5) (2,20) (2,16) (2,25) (2,9) (2,21) (2,8) (3,10) (3,22) (3,19) (3,6) (3,12) (3,14) (3,23) (3,13) (3,5) (3,20) (3,25) (3,9) (3,8) (4,11) (4,15) (5,6) (5,12) (5,23) (5,20) (5,17) (5,8) (6,22) (6,19) (6,14) (6,23) (6,13) (6,25) (6,17) (6,9) (7,15) (8,10) (8,22) (8,12) (8,13) (8,20) (8,16) (8,25) (8,9) (8,21) (9,22) (9,19) (9,12) (9,14) (9,23) (9,16) (9,25) (9,21) (10,12) (10,14) (10,20) (10,16) (10,25) (11,24) (11,15) (12,22) (12,16) (12,25) (12,17) (12,21) (13,22) (13,19) (13,14) (13,23) (13,20) (13,16) (13,17) (14,22) (14,19) (14,23) (14,25) (14,21) (15,18) (16,22) (16,23) (16,20) (16,25) (17,22) (17,19) (17,23) (17,20) (18,24) (19,22) (19,21) (20,23) (20,25) (21,22) (21,25) (22,25) (23,25)\nIs there a path between node 24 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph583-17_15", + "image": "data/connectivity/graph_visual/hard/graph583.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,19) (0,16) (0,14) (0,22) (0,3) (0,21) (0,28) (0,1) (0,10) (0,8) (0,30) (0,18) (0,4) (0,25) (0,26) (0,23) (0,6) (0,24) (0,20) (0,11) (0,29) (0,33) (1,16) (1,14) (1,3) (1,21) (1,8) (1,30) (1,18) (1,4) (1,26) (1,23) (1,6) (1,24) (1,20) (1,32) (1,11) (1,29) (1,33) (1,12) (2,19) (2,14) (2,22) (2,28) (2,10) (2,8) (2,30) (2,18) (2,4) (2,25) (2,5) (2,26) (2,23) (2,6) (2,24) (2,20) (2,32) (2,29) (2,33) (2,9) (2,12) (3,19) (3,16) (3,10) (3,8) (3,30) (3,18) (3,4) (3,25) (3,5) (3,26) (3,23) (3,6) (3,32) (3,11) (3,29) (4,16) (4,22) (4,21) (4,28) (4,10) (4,18) (4,25) (4,26) (4,20) (4,11) (4,29) (4,33) (4,9) (4,12) (5,19) (5,16) (5,14) (5,22) (5,21) (5,28) (5,10) (5,8) (5,30) (5,18) (5,25) (5,26) (5,6) (5,24) (5,20) (5,32) (5,11) (5,33) (5,9) (5,12) (6,16) (6,14) (6,21) (6,10) (6,30) (6,18) (6,25) (6,24) (6,20) (6,32) (6,11) (6,12) (7,17) (7,13) (8,19) (8,16) (8,22) (8,10) (8,18) (8,23) (8,24) (8,32) (8,11) (8,29) (8,33) (8,9) (9,16) (9,14) (9,28) (9,10) (9,30) (9,18) (9,25) (9,26) (9,11) (9,29) (9,33) (10,19) (10,16) (10,14) (10,22) (10,28) (10,30) (10,18) (10,25) (10,26) (10,32) (10,11) (10,29) (10,12) (11,19) (11,16) (11,22) (11,21) (11,28) (11,18) (11,26) (11,23) (11,24) (11,20) (11,32) (11,29) (11,12) (12,16) (12,14) (12,22) (12,21) (12,28) (12,30) (12,18) (12,25) (12,23) (12,24) (12,32) (12,33) (14,16) (14,22) (14,21) (14,28) (14,18) (14,25) (14,26) (14,20) (14,32) (14,33) (15,31) (15,27) (16,19) (16,22) (16,28) (16,30) (16,18) (16,26) (16,23) (16,24) (16,20) (16,32) (16,33) (18,19) (18,22) (18,21) (18,28) (18,25) (18,26) (18,20) (18,32) (18,33) (19,22) (19,21) (19,28) (19,30) (19,25) (19,26) (19,20) (19,33) (20,22) (20,28) (20,25) (20,26) (20,24) (20,32) (20,33) (21,22) (21,28) (21,30) (21,25) (21,26) (21,24) (21,32) (21,29) (21,33) (22,26) (22,23) (22,24) (22,32) (23,30) (23,25) (23,24) (23,29) (23,33) (24,28) (24,32) (24,29) (25,28) (25,26) (25,33) (26,30) (26,29) (26,33) (27,31) (28,30) (28,32) (28,29) (29,30) (30,32)\nIs there a path between node 17 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph30-11_1", + "image": "data/connectivity/graph_visual/hard/graph30.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,16) (0,14) (0,10) (0,24) (0,2) (0,12) (0,19) (0,3) (0,17) (0,25) (0,23) (0,15) (1,18) (1,11) (1,8) (2,14) (2,10) (2,24) (2,7) (2,3) (2,21) (2,25) (2,23) (2,6) (3,14) (3,24) (3,12) (3,19) (3,17) (3,25) (3,23) (3,6) (3,15) (4,18) (4,8) (5,18) (5,11) (5,8) (6,16) (6,14) (6,10) (6,12) (6,7) (6,19) (6,21) (6,25) (6,23) (6,9) (6,15) (7,16) (7,10) (7,24) (7,12) (7,19) (7,17) (7,25) (7,9) (7,15) (8,18) (8,11) (9,16) (9,14) (9,10) (9,24) (9,12) (9,19) (9,17) (9,21) (9,23) (9,15) (10,16) (10,14) (10,19) (10,21) (10,25) (10,23) (10,15) (11,18) (12,16) (12,14) (12,24) (12,19) (12,17) (12,21) (12,25) (12,23) (12,15) (13,20) (14,16) (14,24) (14,17) (14,21) (14,25) (14,23) (14,15) (15,16) (15,24) (15,23) (16,21) (16,25) (16,23) (17,21) (17,23) (19,21) (19,25) (21,24) (21,25) (21,23) (23,25) (24,25)\nIs there a path between node 11 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph14-16_2", + "image": "data/connectivity/graph_visual/hard/graph14.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,11) (0,13) (0,25) (0,21) (0,14) (0,4) (0,1) (1,3) (1,11) (1,13) (1,21) (1,14) (1,4) (2,6) (2,19) (2,12) (2,8) (2,9) (2,24) (2,17) (2,10) (2,7) (2,22) (2,16) (2,18) (3,5) (3,11) (3,13) (3,25) (3,21) (3,4) (4,5) (4,11) (4,13) (4,25) (4,21) (5,11) (5,25) (5,14) (6,19) (6,12) (6,8) (6,20) (6,9) (6,24) (6,17) (6,7) (6,22) (6,15) (6,18) (7,19) (7,12) (7,8) (7,23) (7,20) (7,24) (7,17) (7,22) (7,15) (7,16) (7,18) (8,12) (8,23) (8,20) (8,9) (8,24) (8,17) (8,22) (8,15) (8,16) (9,23) (9,20) (9,10) (9,22) (9,16) (10,19) (10,12) (10,23) (10,24) (10,17) (11,13) (11,25) (12,17) (12,22) (12,16) (13,25) (14,21) (15,19) (15,23) (15,20) (15,17) (15,16) (16,17) (16,22) (16,18) (17,20) (17,22) (18,23) (18,20) (18,24) (18,22) (19,23) (19,24) (19,22) (20,23) (20,24) (20,22) (21,25) (22,23) (22,24) (23,24)\nIs there a path between node 16 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph320-4_8", + "image": "data/connectivity/graph_visual/hard/graph320.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,6) (0,28) (1,30) (1,7) (1,26) (1,29) (1,8) (2,19) (2,22) (2,9) (2,20) (3,13) (3,23) (3,26) (3,17) (3,8) (3,4) (4,5) (4,28) (4,17) (5,10) (5,27) (5,26) (5,6) (6,15) (6,7) (6,27) (6,21) (6,23) (6,29) (6,28) (7,30) (7,10) (7,23) (7,26) (7,29) (8,15) (8,30) (8,29) (8,28) (9,18) (10,15) (10,27) (10,23) (10,26) (10,28) (11,14) (11,16) (11,18) (12,19) (12,20) (13,17) (14,19) (14,24) (14,25) (14,31) (15,21) (15,28) (16,22) (16,24) (17,30) (17,23) (17,29) (18,19) (18,22) (18,31) (19,31) (20,24) (21,30) (21,28) (26,30) (26,29) (28,30)\nIs there a path between node 4 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph333-3_11", + "image": "data/connectivity/graph_visual/hard/graph333.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,19) (0,14) (0,10) (1,12) (1,13) (1,17) (1,25) (2,24) (2,12) (2,13) (2,25) (3,27) (3,15) (3,9) (3,18) (3,23) (3,31) (3,28) (3,21) (4,6) (4,14) (4,10) (5,16) (5,26) (5,8) (5,7) (6,19) (6,14) (7,16) (7,20) (7,8) (8,16) (8,20) (9,15) (9,18) (9,29) (9,30) (9,23) (9,31) (9,28) (9,21) (10,14) (11,17) (11,25) (12,13) (12,17) (13,24) (13,17) (13,25) (14,19) (15,27) (15,18) (15,29) (15,22) (15,30) (15,23) (15,31) (15,28) (15,21) (16,26) (17,24) (17,25) (18,29) (18,30) (18,23) (18,31) (18,21) (20,26) (21,27) (21,29) (21,22) (21,30) (21,23) (21,31) (21,28) (22,27) (22,29) (22,30) (22,23) (22,28) (23,27) (23,29) (23,30) (23,28) (24,25) (27,29) (27,30) (27,31) (27,28) (28,29) (28,30) (28,31) (29,30) (29,31) (30,31)\nIs there a path between node 3 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph103-7_14", + "image": "data/connectivity/graph_visual/hard/graph103.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,20) (0,2) (0,21) (0,26) (0,24) (0,9) (0,18) (0,8) (0,23) (0,5) (0,4) (0,7) (0,14) (0,17) (0,12) (0,10) (0,25) (0,27) (2,20) (2,21) (2,24) (2,9) (2,18) (2,8) (2,6) (2,23) (2,4) (2,11) (2,7) (2,14) (2,17) (2,12) (2,10) (2,25) (2,13) (2,27) (4,20) (4,22) (4,21) (4,24) (4,9) (4,8) (4,6) (4,23) (4,5) (4,11) (4,14) (4,15) (4,12) (4,10) (4,25) (4,13) (4,16) (4,27) (5,22) (5,21) (5,26) (5,6) (5,23) (5,7) (5,14) (5,15) (5,10) (5,13) (6,20) (6,22) (6,24) (6,11) (6,7) (6,17) (6,12) (6,25) (6,13) (6,16) (7,20) (7,22) (7,21) (7,9) (7,23) (7,14) (7,17) (7,10) (7,25) (7,13) (7,16) (8,20) (8,22) (8,26) (8,18) (8,23) (8,11) (8,14) (8,15) (8,17) (8,12) (8,13) (8,16) (9,20) (9,22) (9,21) (9,24) (9,18) (9,23) (9,14) (9,15) (9,17) (9,10) (9,25) (9,13) (9,16) (10,20) (10,21) (10,26) (10,23) (10,11) (10,14) (10,15) (10,17) (10,12) (10,25) (10,13) (10,16) (10,27) (11,21) (11,26) (11,18) (11,23) (11,14) (11,15) (11,17) (11,12) (11,25) (11,13) (11,27) (12,20) (12,21) (12,26) (12,18) (12,23) (12,14) (12,15) (12,25) (12,13) (12,16) (13,20) (13,21) (13,24) (13,18) (13,14) (13,15) (13,17) (13,27) (14,20) (14,22) (14,21) (14,26) (14,24) (14,23) (14,25) (14,27) (15,20) (15,22) (15,21) (15,26) (15,25) (15,16) (15,27) (16,20) (16,22) (16,21) (16,26) (16,24) (16,18) (16,23) (16,17) (17,20) (17,22) (17,21) (17,26) (17,24) (17,18) (17,23) (17,25) (17,27) (18,20) (18,26) (18,24) (18,23) (20,22) (20,21) (20,26) (20,24) (20,25) (20,27) (21,26) (21,24) (21,23) (21,25) (22,26) (22,24) (22,23) (22,25) (23,26) (23,24) (23,25) (23,27) (24,26) (24,25) (24,27)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph116-6_1", + "image": "data/connectivity/graph_visual/hard/graph116.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,21) (0,18) (0,16) (0,12) (1,15) (1,2) (1,24) (1,20) (2,10) (2,15) (2,9) (2,24) (2,14) (3,6) (3,8) (3,24) (3,20) (3,14) (4,22) (4,10) (4,15) (4,8) (4,5) (4,23) (5,22) (5,15) (5,19) (5,17) (5,23) (6,15) (6,17) (6,23) (7,9) (7,19) (7,17) (7,23) (8,23) (9,15) (9,19) (9,23) (10,20) (10,17) (11,27) (11,25) (12,21) (12,26) (12,16) (12,13) (13,27) (14,15) (14,19) (15,19) (15,17) (17,22) (17,20) (18,27) (18,26) (19,20) (20,22) (20,24) (21,27) (22,24) (22,23) (25,26)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph64-21_6", + "image": "data/connectivity/graph_visual/hard/graph64.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,15) (0,8) (0,25) (0,1) (1,4) (1,8) (2,16) (2,5) (2,24) (2,22) (4,23) (4,7) (4,17) (5,9) (5,19) (5,20) (6,9) (6,20) (7,14) (7,17) (8,18) (8,17) (9,24) (9,22) (10,19) (10,20) (10,24) (11,16) (12,14) (12,26) (14,23) (14,18) (14,25) (14,17) (15,18) (16,22) (18,26) (19,24) (19,22) (21,23) (22,24) (25,26)\nIs there a path between node 21 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph200-24_21", + "image": "data/connectivity/graph_visual/hard/graph200.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,26) (0,1) (0,17) (0,6) (0,27) (0,11) (0,2) (1,16) (1,26) (1,17) (1,6) (1,27) (1,11) (1,2) (2,17) (2,27) (2,11) (3,5) (3,23) (3,22) (3,4) (4,23) (4,14) (5,23) (5,14) (5,18) (6,16) (6,17) (6,27) (7,8) (7,24) (7,19) (7,10) (7,9) (7,12) (7,21) (7,25) (7,28) (7,15) (8,24) (8,19) (8,10) (8,9) (8,21) (8,13) (8,28) (8,15) (9,24) (9,19) (9,10) (9,20) (9,12) (9,13) (9,29) (9,15) (10,24) (10,19) (10,20) (10,21) (10,25) (10,29) (10,28) (10,15) (11,16) (11,26) (11,27) (12,24) (12,19) (12,20) (12,21) (12,25) (12,29) (12,28) (13,19) (13,20) (13,21) (13,25) (13,28) (13,15) (14,23) (14,18) (15,24) (15,19) (15,25) (15,28) (16,26) (16,17) (16,27) (17,27) (18,22) (19,24) (19,20) (19,29) (19,28) (20,24) (20,29) (20,28) (21,24) (21,25) (21,29) (21,28) (22,23) (24,25) (24,29) (24,28) (25,28) (26,27) (28,29)\nIs there a path between node 24 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph421-8_22", + "image": "data/connectivity/graph_visual/hard/graph421.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,20) (0,5) (0,28) (2,16) (2,6) (2,4) (2,17) (2,9) (3,16) (3,6) (3,21) (3,31) (4,17) (4,21) (4,25) (6,22) (6,14) (6,30) (6,9) (6,25) (7,11) (7,15) (7,24) (9,22) (9,14) (9,17) (9,25) (10,28) (11,12) (11,24) (12,24) (13,18) (13,17) (13,21) (13,25) (14,22) (15,32) (15,28) (16,30) (16,17) (17,22) (17,30) (17,25) (18,30) (21,22) (21,31) (21,25) (22,30) (24,26) (25,31) (26,28) (27,28)\nIs there a path between node 8 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph527-10_26", + "image": "data/connectivity/graph_visual/hard/graph527.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,33) (0,21) (0,2) (0,19) (1,11) (2,17) (3,18) (3,10) (4,12) (4,7) (4,13) (5,14) (5,32) (6,10) (6,14) (7,12) (7,21) (8,14) (8,28) (10,32) (10,28) (12,33) (12,17) (12,19) (13,21) (13,29) (14,18) (14,32) (16,21) (16,19) (17,29) (18,26) (19,33) (19,29) (20,23) (23,31) (24,32) (25,30) (26,32) (26,28)\nIs there a path between node 10 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph37-10_17", + "image": "data/connectivity/graph_visual/hard/graph37.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,20) (1,10) (1,8) (1,16) (1,6) (1,23) (1,24) (1,18) (1,13) (1,17) (1,3) (1,4) (1,25) (1,14) (1,7) (1,22) (2,12) (2,21) (3,5) (3,10) (3,9) (3,11) (3,8) (3,16) (3,6) (3,24) (3,19) (3,17) (3,25) (3,14) (3,7) (3,22) (4,5) (4,11) (4,8) (4,16) (4,6) (4,23) (4,24) (4,18) (4,19) (4,15) (4,17) (4,25) (4,14) (4,7) (5,10) (5,11) (5,8) (5,6) (5,23) (5,24) (5,18) (5,15) (5,17) (5,25) (5,7) (5,22) (6,10) (6,9) (6,11) (6,8) (6,23) (6,24) (6,19) (6,13) (6,17) (6,25) (6,14) (7,10) (7,11) (7,23) (7,19) (7,15) (7,17) (7,25) (7,14) (8,10) (8,9) (8,11) (8,18) (8,19) (8,13) (8,15) (8,17) (8,25) (8,22) (9,10) (9,11) (9,16) (9,23) (9,24) (9,18) (9,19) (9,13) (9,15) (9,17) (9,25) (9,14) (10,11) (10,16) (10,24) (10,18) (10,19) (10,13) (10,15) (10,17) (10,14) (10,22) (11,16) (11,23) (11,24) (11,18) (11,19) (11,13) (11,15) (11,17) (11,25) (11,14) (11,22) (12,21) (13,16) (13,15) (13,17) (13,25) (13,14) (13,22) (14,16) (14,23) (14,24) (14,18) (14,19) (14,17) (14,25) (15,16) (15,23) (15,24) (15,18) (15,19) (15,17) (15,25) (16,23) (16,18) (16,25) (17,23) (17,24) (17,18) (17,19) (17,25) (17,22) (18,23) (18,24) (18,19) (18,25) (19,23) (19,24) (19,25) (22,24) (22,25) (23,24) (23,25)\nIs there a path between node 10 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph229-20_16", + "image": "data/connectivity/graph_visual/hard/graph229.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,26) (0,13) (1,23) (1,10) (1,16) (1,11) (1,19) (1,8) (1,2) (1,14) (1,29) (1,25) (1,9) (1,17) (1,28) (2,24) (2,23) (2,10) (2,16) (2,11) (2,19) (2,20) (2,21) (2,14) (2,25) (2,9) (2,4) (2,17) (2,28) (3,5) (3,15) (3,6) (3,7) (4,24) (4,16) (4,11) (4,19) (4,8) (4,18) (4,14) (4,29) (4,25) (4,22) (4,17) (4,28) (5,27) (5,15) (5,6) (6,27) (7,27) (7,15) (8,24) (8,23) (8,10) (8,19) (8,20) (8,18) (8,29) (8,25) (8,17) (8,28) (9,24) (9,23) (9,10) (9,19) (9,18) (9,29) (9,25) (9,22) (9,17) (10,24) (10,23) (10,16) (10,11) (10,19) (10,20) (10,21) (10,18) (10,29) (10,25) (10,22) (10,17) (10,28) (11,24) (11,23) (11,16) (11,19) (11,21) (11,18) (11,14) (11,29) (11,22) (11,28) (12,26) (13,26) (14,24) (14,16) (14,20) (14,21) (14,18) (14,29) (14,25) (14,22) (15,27) (16,23) (16,20) (16,18) (16,29) (16,25) (17,23) (17,20) (17,29) (17,22) (17,28) (18,23) (18,19) (18,20) (18,21) (18,29) (18,25) (18,28) (19,24) (19,21) (19,29) (19,25) (19,22) (19,28) (20,24) (20,21) (20,25) (20,22) (20,28) (21,23) (21,29) (21,22) (22,23) (22,29) (23,29) (23,25) (23,28) (24,25) (25,28) (28,29)\nIs there a path between node 20 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph139-2_22", + "image": "data/connectivity/graph_visual/hard/graph139.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,9) (2,8) (2,6) (3,10) (3,16) (3,23) (4,28) (4,8) (5,7) (5,13) (5,18) (5,8) (5,6) (6,7) (6,13) (6,24) (6,18) (6,28) (7,13) (7,11) (8,24) (8,28) (8,22) (9,10) (9,16) (9,15) (10,23) (11,24) (11,18) (12,21) (13,28) (13,22) (14,27) (14,20) (15,27) (15,16) (16,19) (17,19) (19,27) (20,27) (22,28) (23,27) (25,26)\nIs there a path between node 2 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph266-7_14", + "image": "data/connectivity/graph_visual/hard/graph266.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,20) (0,12) (0,25) (0,2) (0,23) (0,17) (0,28) (0,5) (0,10) (0,19) (1,30) (1,9) (1,15) (1,6) (1,10) (1,18) (2,20) (2,12) (2,8) (2,21) (2,28) (2,22) (2,10) (2,3) (2,4) (2,18) (3,25) (3,13) (3,21) (3,28) (3,29) (3,4) (3,18) (4,25) (4,30) (4,13) (4,23) (4,17) (4,28) (4,5) (4,15) (4,14) (4,7) (4,18) (5,20) (5,12) (5,30) (5,13) (5,9) (5,28) (5,16) (5,14) (5,11) (6,12) (6,25) (6,13) (6,21) (6,29) (6,19) (7,13) (7,8) (7,23) (7,28) (7,29) (8,27) (8,21) (8,23) (8,28) (8,22) (8,18) (9,20) (9,12) (9,18) (10,13) (10,22) (10,14) (10,29) (11,20) (11,13) (11,17) (11,15) (12,25) (12,23) (12,28) (12,18) (13,30) (13,27) (13,21) (13,16) (13,14) (14,30) (14,21) (14,16) (14,29) (14,19) (15,20) (15,30) (15,23) (16,20) (16,25) (16,21) (16,28) (17,20) (17,30) (17,28) (18,30) (18,27) (18,23) (18,22) (18,29) (19,23) (19,29) (20,30) (20,23) (20,29) (21,28) (22,29) (23,25) (23,30) (23,28) (25,29) (27,28) (28,30) (29,30)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph427-13_0", + "image": "data/connectivity/graph_visual/hard/graph427.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,4) (0,30) (0,24) (0,13) (0,20) (0,16) (0,15) (0,25) (0,3) (1,5) (1,17) (1,6) (2,12) (2,22) (2,8) (2,11) (2,9) (2,14) (2,32) (2,21) (2,27) (3,20) (3,15) (4,30) (4,24) (4,13) (4,20) (4,16) (4,15) (4,25) (5,26) (5,17) (5,31) (5,7) (5,6) (6,26) (6,18) (6,31) (6,7) (7,26) (7,18) (7,31) (8,12) (8,22) (8,11) (8,21) (8,28) (8,27) (9,22) (9,14) (9,32) (9,10) (9,28) (10,22) (10,11) (10,19) (10,14) (10,32) (10,21) (10,28) (10,27) (11,12) (11,22) (11,14) (11,32) (11,21) (11,27) (12,22) (12,32) (12,21) (12,28) (12,27) (13,30) (13,24) (13,20) (13,15) (13,25) (14,19) (14,32) (14,21) (15,20) (15,25) (16,24) (16,20) (16,25) (17,18) (17,31) (18,26) (18,31) (19,21) (19,28) (20,24) (20,25) (21,22) (21,32) (21,28) (21,27) (22,32) (22,28) (22,27) (24,25) (25,30) (26,31) (27,28) (28,32)\nIs there a path between node 13 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph157-10_23", + "image": "data/connectivity/graph_visual/hard/graph157.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,24) (0,7) (1,14) (1,10) (1,28) (1,4) (2,11) (2,24) (2,7) (2,18) (2,27) (2,3) (2,19) (3,12) (3,27) (3,19) (4,16) (4,13) (5,14) (5,22) (5,10) (5,9) (7,11) (7,24) (7,18) (7,27) (7,19) (8,12) (8,19) (9,17) (9,10) (9,15) (10,21) (11,26) (12,24) (12,26) (13,14) (13,28) (14,17) (14,22) (14,21) (14,15) (15,17) (15,22) (16,22) (17,28) (18,25) (18,26) (19,23) (20,23) (21,28) (23,24) (23,27)\nIs there a path between node 10 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph316-24_15", + "image": "data/connectivity/graph_visual/hard/graph316.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,19) (0,31) (0,15) (0,18) (1,24) (1,19) (1,31) (1,5) (2,30) (2,23) (2,4) (2,17) (3,30) (3,23) (3,12) (3,17) (5,28) (5,6) (5,14) (5,9) (5,31) (5,18) (6,10) (6,13) (6,19) (6,31) (6,21) (6,18) (7,28) (7,14) (7,25) (7,20) (8,26) (8,23) (8,12) (8,17) (9,22) (9,13) (9,29) (9,31) (9,15) (9,21) (9,18) (10,13) (10,19) (10,14) (10,15) (10,18) (11,12) (11,16) (12,30) (12,17) (13,28) (13,29) (13,15) (13,21) (13,20) (13,18) (14,22) (14,24) (14,29) (15,29) (15,25) (16,26) (17,30) (18,25) (18,20) (19,29) (19,21) (19,20) (20,22) (20,28) (20,29) (20,25) (21,27) (21,31) (22,28) (22,29) (23,30) (23,26) (24,29) (24,31) (27,31)\nIs there a path between node 24 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph311-18_10", + "image": "data/connectivity/graph_visual/hard/graph311.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,21) (1,6) (1,16) (2,5) (2,29) (4,14) (4,8) (4,28) (4,19) (5,23) (5,8) (5,15) (5,11) (5,9) (6,26) (7,23) (7,8) (7,19) (7,30) (8,14) (9,10) (9,19) (9,15) (9,22) (10,23) (10,14) (10,28) (10,25) (10,30) (11,23) (11,29) (12,31) (12,13) (13,18) (14,27) (15,23) (15,25) (19,28) (20,24) (22,23) (23,30) (23,29) (24,26) (28,29) (29,30)\nIs there a path between node 18 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph378-0_24", + "image": "data/connectivity/graph_visual/hard/graph378.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,25) (0,4) (0,14) (0,12) (0,9) (0,30) (0,20) (0,2) (0,24) (0,13) (0,10) (0,27) (1,11) (1,8) (1,17) (1,28) (1,26) (1,19) (1,15) (2,25) (2,29) (2,4) (2,14) (2,12) (2,9) (2,30) (2,20) (2,6) (2,10) (2,31) (2,27) (3,11) (3,8) (3,17) (3,28) (3,19) (3,15) (3,23) (4,25) (4,14) (4,12) (4,30) (4,24) (4,13) (4,6) (4,21) (4,16) (5,11) (5,8) (5,18) (5,17) (5,26) (5,15) (5,23) (6,14) (6,12) (6,9) (6,30) (6,20) (6,13) (6,21) (6,7) (6,16) (6,10) (6,27) (7,25) (7,29) (7,14) (7,12) (7,9) (7,30) (7,20) (7,13) (7,10) (7,27) (8,11) (8,17) (8,28) (8,26) (8,19) (8,15) (8,23) (9,25) (9,29) (9,14) (9,12) (9,30) (9,24) (9,13) (9,21) (9,10) (9,31) (10,25) (10,14) (10,12) (10,30) (10,13) (10,21) (10,16) (10,31) (10,27) (11,18) (11,17) (11,28) (11,26) (11,15) (11,23) (11,22) (12,25) (12,29) (12,20) (12,24) (12,13) (12,21) (12,16) (12,31) (12,27) (13,25) (13,29) (13,30) (13,20) (13,24) (13,21) (14,25) (14,29) (14,30) (14,20) (14,21) (14,16) (14,31) (15,17) (15,28) (15,23) (15,22) (16,25) (16,29) (16,30) (16,20) (16,24) (16,21) (16,31) (16,27) (17,18) (17,19) (17,23) (18,28) (18,23) (19,28) (19,26) (19,23) (19,22) (20,29) (20,30) (20,24) (20,21) (20,31) (20,27) (21,25) (21,29) (21,30) (21,31) (21,27) (22,28) (22,26) (23,28) (23,26) (24,30) (24,27) (25,29) (25,30) (26,28) (27,29) (27,30) (27,31) (29,30) (29,31) (30,31)\nIs there a path between node 0 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph92-13_26", + "image": "data/connectivity/graph_visual/hard/graph92.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,11) (0,1) (0,5) (0,24) (0,22) (0,12) (0,19) (0,25) (0,26) (1,3) (1,24) (1,22) (1,20) (1,26) (2,3) (2,14) (2,9) (2,25) (3,15) (3,12) (3,19) (3,20) (3,16) (4,21) (4,8) (5,27) (5,19) (5,16) (6,24) (6,9) (6,20) (6,16) (7,8) (7,23) (8,13) (8,18) (9,27) (9,11) (9,15) (9,22) (10,24) (10,12) (10,16) (11,12) (11,25) (11,16) (12,25) (12,16) (12,26) (13,21) (14,27) (14,24) (14,22) (14,25) (14,16) (14,26) (15,16) (16,27) (16,25) (16,26) (17,18) (18,21) (18,23) (19,27) (19,26) (20,27) (20,22) (24,27) (24,25) (25,27) (25,26)\nIs there a path between node 13 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph428-4_29", + "image": "data/connectivity/graph_visual/hard/graph428.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,30) (0,7) (0,26) (0,13) (0,21) (0,22) (0,1) (1,24) (1,7) (1,26) (1,11) (2,32) (2,18) (2,9) (2,8) (2,12) (2,29) (2,14) (2,16) (2,10) (2,3) (2,5) (2,17) (2,28) (3,27) (3,32) (3,18) (3,9) (3,8) (3,12) (3,29) (3,16) (3,4) (3,23) (3,5) (3,31) (3,17) (3,15) (3,28) (4,18) (4,9) (4,29) (4,16) (4,10) (4,23) (4,5) (4,17) (4,15) (5,27) (5,32) (5,18) (5,20) (5,9) (5,16) (5,10) (5,17) (5,15) (5,28) (6,25) (6,19) (7,24) (7,30) (7,13) (7,21) (7,22) (8,27) (8,32) (8,18) (8,20) (8,9) (8,29) (8,14) (8,16) (8,10) (8,23) (8,31) (8,17) (8,15) (8,28) (9,27) (9,32) (9,20) (9,12) (9,14) (9,10) (9,23) (9,17) (9,15) (9,28) (10,32) (10,18) (10,20) (10,12) (10,29) (10,16) (10,31) (10,15) (10,28) (11,24) (11,30) (11,26) (11,22) (12,32) (12,18) (12,14) (12,16) (12,23) (12,31) (12,15) (12,28) (13,24) (13,30) (13,26) (14,27) (14,32) (14,18) (14,20) (14,29) (14,17) (14,28) (15,27) (15,32) (15,20) (15,23) (15,31) (15,17) (15,28) (16,27) (16,32) (16,18) (16,20) (16,23) (16,31) (16,28) (17,32) (17,20) (17,29) (17,23) (17,28) (18,27) (18,32) (18,20) (18,29) (18,31) (20,27) (20,32) (20,29) (20,23) (20,31) (20,28) (21,24) (21,30) (21,26) (21,22) (22,30) (22,26) (23,29) (23,31) (24,26) (26,30) (27,32) (28,29) (28,31) (31,32)\nIs there a path between node 4 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph218-1_8", + "image": "data/connectivity/graph_visual/hard/graph218.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,7) (0,15) (0,18) (0,27) (0,9) (0,13) (0,25) (0,3) (1,8) (1,5) (1,26) (1,12) (1,2) (1,16) (1,14) (2,8) (2,26) (2,12) (2,16) (2,14) (3,7) (3,4) (3,15) (3,18) (3,27) (3,13) (4,7) (4,15) (4,18) (4,27) (4,13) (5,8) (5,12) (5,11) (5,16) (5,14) (5,20) (6,17) (6,21) (6,29) (6,28) (7,15) (7,18) (7,27) (7,9) (7,13) (8,26) (8,23) (8,16) (8,14) (9,15) (10,29) (10,24) (11,12) (11,16) (11,14) (11,20) (12,22) (12,23) (12,14) (12,20) (13,18) (13,27) (14,26) (14,22) (14,23) (14,20) (15,18) (15,27) (15,25) (16,26) (16,22) (16,23) (16,20) (17,21) (17,19) (17,24) (17,28) (19,21) (19,29) (19,24) (19,28) (20,26) (20,22) (20,23) (21,29) (21,24) (22,26) (22,23) (24,29) (24,28) (25,27)\nIs there a path between node 1 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph437-20_15", + "image": "data/connectivity/graph_visual/hard/graph437.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (0,30) (0,13) (0,2) (0,23) (0,28) (0,8) (0,26) (0,25) (0,21) (0,15) (0,14) (0,31) (1,16) (1,5) (1,20) (1,6) (1,30) (1,13) (1,2) (1,28) (1,8) (1,25) (1,7) (1,15) (1,4) (1,17) (2,16) (2,20) (2,6) (2,30) (2,23) (2,28) (2,3) (2,26) (2,4) (2,17) (2,14) (2,22) (2,31) (3,16) (3,20) (3,30) (3,13) (3,23) (3,28) (3,21) (3,15) (3,14) (3,31) (4,16) (4,5) (4,6) (4,30) (4,13) (4,23) (4,28) (4,8) (4,26) (4,25) (4,21) (4,7) (4,15) (4,17) (4,14) (4,22) (5,16) (5,30) (5,23) (5,28) (5,8) (5,26) (5,15) (5,17) (5,22) (5,31) (6,16) (6,20) (6,30) (6,13) (6,23) (6,28) (6,26) (6,25) (6,21) (6,7) (6,14) (6,22) (6,31) (7,16) (7,30) (7,13) (7,28) (7,26) (7,25) (7,21) (7,14) (8,20) (8,13) (8,28) (8,21) (8,14) (8,22) (9,29) (9,10) (9,27) (9,19) (9,11) (9,18) (10,12) (10,29) (10,27) (10,18) (11,12) (11,29) (11,32) (12,29) (12,27) (12,32) (12,19) (12,18) (13,16) (13,20) (13,30) (13,28) (13,21) (13,15) (13,17) (13,22) (13,31) (14,16) (14,23) (14,28) (14,26) (14,25) (14,15) (14,17) (14,22) (14,31) (15,16) (15,30) (15,23) (15,28) (15,26) (15,25) (15,21) (15,17) (15,22) (15,31) (16,30) (16,23) (16,28) (16,17) (16,22) (16,31) (17,20) (17,30) (17,23) (17,28) (17,22) (17,31) (18,29) (18,27) (18,32) (19,32) (20,30) (20,23) (20,28) (20,26) (20,25) (20,21) (20,22) (20,31) (21,30) (21,28) (21,26) (21,22) (22,23) (22,25) (23,30) (23,26) (23,25) (25,30) (25,28) (25,26) (26,31) (27,29) (27,32) (28,30) (29,32) (30,31)\nIs there a path between node 20 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph270-13_5", + "image": "data/connectivity/graph_visual/hard/graph270.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,20) (0,14) (0,18) (0,16) (1,27) (1,28) (1,9) (1,22) (1,21) (1,19) (1,10) (1,23) (1,7) (1,2) (2,26) (2,25) (2,6) (2,9) (2,22) (2,21) (2,10) (2,23) (2,7) (2,30) (2,12) (3,5) (3,15) (3,11) (3,29) (3,4) (4,5) (4,15) (4,11) (5,15) (5,24) (5,29) (5,8) (6,25) (6,22) (6,17) (6,21) (6,19) (6,10) (6,23) (6,7) (6,30) (7,26) (7,25) (7,9) (7,22) (7,17) (7,21) (7,19) (7,10) (7,23) (7,12) (8,24) (9,27) (9,26) (9,22) (9,21) (9,19) (9,23) (9,30) (9,12) (10,28) (10,26) (10,22) (10,17) (10,21) (10,23) (10,30) (10,12) (11,15) (11,24) (11,29) (12,27) (12,28) (12,26) (12,25) (12,17) (12,21) (12,19) (12,23) (12,30) (13,14) (13,16) (14,18) (14,16) (15,24) (15,29) (16,20) (16,18) (17,27) (17,26) (17,22) (17,19) (17,30) (18,20) (19,27) (19,26) (19,22) (19,23) (19,30) (21,28) (21,26) (21,25) (21,22) (21,23) (21,30) (22,27) (22,28) (22,25) (22,23) (22,30) (23,27) (23,28) (23,26) (23,25) (23,30) (24,29) (25,26) (26,27) (26,28) (26,30) (27,28) (27,30) (28,30)\nIs there a path between node 13 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph665-11_0", + "image": "data/connectivity/graph_visual/hard/graph665.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,3) (0,29) (0,7) (0,32) (0,4) (0,17) (0,9) (1,12) (1,14) (1,7) (1,28) (1,23) (1,9) (1,33) (1,30) (1,6) (1,8) (2,14) (2,29) (2,32) (2,15) (2,30) (2,6) (2,10) (3,12) (3,14) (3,4) (3,23) (3,9) (3,31) (3,30) (3,20) (4,27) (4,19) (4,17) (4,15) (4,31) (4,30) (5,34) (5,18) (5,13) (6,7) (6,16) (6,23) (6,22) (6,30) (7,12) (7,15) (7,11) (7,31) (7,30) (7,24) (7,10) (8,29) (8,32) (8,16) (8,27) (8,23) (8,20) (9,28) (9,15) (9,33) (9,31) (9,30) (9,24) (9,10) (10,12) (10,19) (10,17) (10,33) (10,22) (10,20) (11,32) (11,16) (11,19) (11,17) (11,22) (12,32) (12,28) (12,23) (12,33) (14,32) (14,30) (14,20) (15,17) (15,30) (16,19) (16,17) (16,23) (16,33) (16,30) (17,29) (17,27) (17,30) (17,24) (17,20) (18,25) (19,32) (19,28) (19,30) (19,20) (20,28) (20,23) (20,30) (22,28) (22,33) (23,29) (23,31) (24,31) (26,34) (28,29) (28,33) (29,31) (30,33)\nIs there a path between node 11 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph215-8_0", + "image": "data/connectivity/graph_visual/hard/graph215.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,11) (0,27) (0,29) (1,16) (1,11) (1,20) (1,14) (2,8) (2,18) (2,15) (2,11) (2,27) (2,19) (2,25) (2,29) (3,5) (4,8) (4,24) (4,23) (4,26) (4,13) (4,7) (4,28) (4,6) (4,20) (4,19) (6,15) (6,27) (6,25) (7,22) (7,24) (7,23) (7,26) (7,13) (7,28) (7,29) (8,18) (8,26) (8,12) (9,17) (11,22) (11,24) (11,28) (11,20) (12,22) (12,15) (12,28) (12,27) (12,20) (12,29) (13,16) (13,23) (13,28) (13,27) (13,20) (13,19) (14,19) (15,28) (15,25) (16,26) (16,25) (18,20) (18,29) (19,23) (19,20) (20,24) (20,26) (20,28) (20,27) (20,25) (22,23) (22,28) (22,29) (23,24) (23,26) (23,29) (24,27) (25,27) (26,29) (27,28)\nIs there a path between node 8 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph698-4_8", + "image": "data/connectivity/graph_visual/hard/graph698.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,16) (0,9) (0,7) (0,30) (0,29) (1,34) (1,19) (1,6) (1,18) (2,8) (2,15) (2,31) (2,24) (2,12) (2,20) (2,14) (2,3) (2,25) (2,32) (2,4) (2,23) (2,28) (3,8) (3,33) (3,15) (3,12) (3,5) (3,14) (3,26) (3,25) (3,17) (3,22) (3,11) (4,8) (4,24) (4,12) (4,20) (4,5) (4,14) (4,26) (4,25) (4,32) (4,17) (4,23) (4,28) (4,11) (5,8) (5,15) (5,31) (5,14) (5,26) (5,25) (5,32) (5,10) (5,28) (5,11) (6,13) (6,19) (6,18) (7,16) (7,9) (7,30) (7,21) (7,29) (8,33) (8,15) (8,31) (8,24) (8,12) (8,20) (8,14) (8,26) (8,25) (8,32) (8,17) (8,22) (8,23) (8,28) (9,16) (9,30) (10,33) (10,15) (10,31) (10,24) (10,12) (10,14) (10,26) (10,25) (10,17) (10,22) (10,23) (10,28) (11,33) (11,15) (11,24) (11,12) (11,26) (11,25) (11,32) (11,22) (11,23) (11,28) (11,27) (12,15) (12,24) (12,20) (12,14) (12,26) (12,25) (12,32) (12,17) (12,22) (13,34) (13,19) (13,18) (14,33) (14,15) (14,31) (14,24) (14,26) (14,25) (14,32) (14,17) (14,22) (14,28) (14,27) (15,31) (15,24) (15,20) (15,25) (15,32) (15,17) (15,28) (15,27) (17,31) (17,24) (17,20) (17,25) (17,32) (17,23) (17,27) (18,34) (18,19) (19,34) (20,31) (20,24) (20,26) (20,25) (20,22) (20,23) (20,28) (20,27) (21,29) (22,33) (22,31) (22,24) (22,26) (22,32) (22,23) (22,28) (22,27) (23,33) (23,31) (23,24) (23,26) (23,25) (23,32) (23,27) (24,33) (24,26) (24,25) (24,32) (24,27) (25,31) (25,32) (25,28) (25,27) (26,33) (26,31) (26,32) (26,28) (26,27) (27,31) (27,32) (27,28) (28,33) (28,31) (28,32) (29,30) (31,33) (31,32) (32,33)\nIs there a path between node 4 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph536-21_15", + "image": "data/connectivity/graph_visual/hard/graph536.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,28) (0,24) (0,10) (0,2) (0,16) (0,15) (0,19) (0,23) (0,27) (0,12) (0,20) (0,11) (0,18) (0,3) (0,8) (1,17) (1,26) (1,28) (1,24) (1,10) (1,2) (1,16) (1,33) (1,19) (1,27) (1,12) (1,25) (1,11) (1,18) (2,17) (2,26) (2,28) (2,24) (2,10) (2,13) (2,33) (2,15) (2,19) (2,6) (2,7) (2,23) (2,27) (2,20) (2,25) (2,18) (2,3) (2,8) (3,17) (3,24) (3,16) (3,15) (3,19) (3,23) (3,27) (3,12) (3,25) (3,11) (3,18) (4,31) (4,14) (4,30) (4,32) (4,21) (5,30) (5,9) (5,32) (5,21) (5,29) (6,17) (6,26) (6,10) (6,16) (6,33) (6,19) (6,23) (6,22) (6,27) (6,12) (6,20) (6,25) (6,11) (6,18) (6,8) (7,26) (7,24) (7,10) (7,16) (7,13) (7,33) (7,15) (7,19) (7,27) (7,12) (7,20) (7,25) (7,11) (7,18) (7,8) (8,28) (8,10) (8,13) (8,33) (8,15) (8,19) (8,22) (8,27) (8,12) (8,20) (8,18) (9,31) (9,14) (9,32) (9,21) (9,29) (10,26) (10,16) (10,13) (10,33) (10,19) (10,23) (10,27) (10,11) (11,17) (11,28) (11,24) (11,16) (11,13) (11,33) (11,19) (11,12) (11,20) (11,25) (11,18) (12,17) (12,26) (12,24) (12,16) (12,13) (12,33) (12,15) (12,23) (12,27) (13,17) (13,28) (13,16) (13,33) (13,19) (13,23) (13,22) (13,20) (13,25) (13,18) (14,30) (15,17) (15,26) (15,16) (15,19) (15,27) (15,20) (15,25) (15,18) (16,17) (16,28) (16,33) (16,22) (16,27) (16,20) (16,25) (17,26) (17,24) (17,33) (17,19) (17,23) (17,22) (17,27) (17,25) (18,33) (18,19) (18,25) (19,26) (19,28) (19,33) (19,22) (19,27) (19,20) (20,28) (20,24) (20,33) (20,23) (20,22) (20,27) (21,31) (21,30) (21,32) (21,29) (22,23) (22,27) (23,26) (23,24) (23,33) (23,27) (24,26) (24,28) (24,33) (24,25) (25,28) (25,33) (25,27) (26,33) (27,28) (29,31) (29,30) (29,32) (30,31) (30,32) (31,32)\nIs there a path between node 21 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph485-29_4", + "image": "data/connectivity/graph_visual/hard/graph485.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,7) (0,31) (0,25) (0,22) (0,24) (0,23) (0,5) (0,9) (0,21) (0,30) (1,26) (1,14) (1,7) (1,6) (1,31) (1,24) (1,23) (1,9) (1,21) (1,30) (2,27) (2,20) (2,12) (2,19) (2,32) (2,28) (2,13) (2,17) (3,26) (3,11) (3,18) (3,7) (3,31) (3,25) (3,22) (3,23) (3,5) (3,9) (3,21) (3,30) (4,27) (4,20) (4,12) (4,19) (4,28) (4,17) (4,29) (5,26) (5,11) (5,14) (5,18) (5,7) (5,6) (5,31) (5,22) (5,24) (5,23) (5,21) (5,30) (6,26) (6,11) (6,18) (6,7) (6,31) (6,25) (6,22) (6,23) (7,11) (7,18) (7,31) (7,25) (7,22) (7,23) (7,9) (8,16) (8,10) (8,15) (9,26) (9,11) (9,18) (9,25) (9,24) (9,23) (9,21) (9,30) (10,16) (11,26) (11,14) (11,31) (11,25) (11,23) (11,21) (11,30) (12,19) (12,28) (12,13) (12,17) (12,29) (13,27) (13,19) (13,32) (13,28) (13,17) (13,29) (14,18) (14,25) (14,22) (14,24) (14,23) (14,21) (14,30) (17,27) (17,19) (17,32) (17,28) (17,29) (18,31) (18,25) (18,22) (18,23) (18,21) (19,27) (19,32) (19,28) (19,29) (20,27) (20,32) (20,28) (20,29) (21,22) (21,24) (21,23) (22,26) (22,31) (22,24) (22,23) (22,30) (23,26) (23,31) (23,25) (24,31) (24,25) (25,26) (26,31) (27,32) (27,29) (29,32)\nIs there a path between node 29 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph187-15_12", + "image": "data/connectivity/graph_visual/hard/graph187.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,20) (1,9) (1,25) (1,14) (1,8) (1,7) (1,27) (1,3) (1,13) (2,4) (2,10) (3,14) (3,7) (3,21) (3,13) (4,5) (5,18) (6,9) (6,16) (6,28) (6,8) (6,17) (6,7) (6,15) (6,24) (6,22) (6,13) (7,29) (7,17) (8,28) (8,23) (8,29) (8,17) (8,27) (9,14) (9,15) (10,20) (10,18) (11,15) (11,24) (11,22) (13,25) (13,23) (13,21) (14,28) (14,23) (14,29) (14,24) (15,16) (15,28) (15,29) (15,27) (15,22) (16,29) (16,27) (17,25) (17,29) (17,27) (21,25) (21,28) (22,25) (23,28) (23,29) (27,29)\nIs there a path between node 15 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph525-13_21", + "image": "data/connectivity/graph_visual/hard/graph525.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,12) (0,30) (0,8) (0,15) (1,20) (1,21) (1,29) (1,19) (1,5) (1,16) (2,32) (2,4) (2,27) (2,24) (2,19) (2,18) (2,16) (3,20) (3,18) (3,16) (4,20) (4,21) (4,14) (4,5) (4,16) (5,20) (5,17) (5,31) (6,28) (6,30) (7,29) (7,31) (8,30) (8,15) (9,21) (9,27) (9,14) (9,29) (10,25) (13,22) (13,28) (14,21) (14,27) (14,17) (16,32) (16,20) (16,24) (16,29) (17,21) (17,27) (17,31) (18,20) (18,21) (18,24) (19,24) (20,21) (20,24) (20,31) (21,24) (21,29) (21,31) (27,29)\nIs there a path between node 13 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph112-4_11", + "image": "data/connectivity/graph_visual/hard/graph112.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,22) (0,11) (0,10) (0,23) (0,4) (0,9) (0,19) (1,17) (1,27) (1,15) (1,23) (1,24) (1,5) (1,18) (2,15) (2,10) (2,23) (2,5) (2,6) (2,16) (4,17) (4,27) (4,16) (4,25) (5,27) (5,11) (5,24) (5,7) (5,16) (5,25) (5,21) (5,18) (6,17) (6,13) (6,27) (6,11) (6,10) (6,14) (6,16) (6,8) (6,19) (7,20) (7,15) (7,10) (7,24) (7,16) (7,8) (7,19) (7,25) (7,21) (8,20) (8,17) (8,27) (8,11) (8,24) (8,16) (9,20) (9,27) (9,11) (9,16) (9,25) (10,13) (10,27) (10,15) (10,16) (11,20) (11,13) (11,14) (11,24) (11,21) (13,20) (13,14) (13,16) (14,22) (14,15) (14,23) (14,19) (15,24) (15,19) (15,25) (16,22) (16,17) (16,23) (17,22) (17,23) (17,25) (18,19) (18,21) (19,27) (19,24) (19,25) (21,25) (23,27) (25,27)\nIs there a path between node 4 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph634-31_24", + "image": "data/connectivity/graph_visual/hard/graph634.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,6) (0,1) (0,8) (0,13) (0,32) (0,2) (1,33) (1,34) (1,30) (1,8) (1,10) (1,19) (1,31) (1,2) (2,15) (2,34) (2,18) (2,8) (2,3) (2,16) (2,32) (2,4) (3,5) (3,26) (3,15) (3,11) (3,16) (3,4) (3,14) (4,5) (4,26) (4,12) (4,33) (4,34) (4,30) (4,13) (4,19) (5,34) (5,21) (5,6) (5,8) (5,19) (5,32) (5,31) (6,33) (6,15) (6,34) (6,13) (6,31) (7,23) (7,20) (8,33) (8,15) (8,34) (8,21) (8,11) (9,24) (10,33) (10,21) (10,27) (10,13) (10,11) (10,19) (11,26) (11,33) (11,13) (11,32) (12,30) (12,16) (13,33) (13,34) (13,19) (13,14) (15,33) (15,34) (15,27) (16,34) (16,30) (16,27) (16,32) (17,29) (18,27) (18,32) (19,30) (19,21) (19,32) (20,28) (21,27) (21,32) (26,33) (26,30) (26,31) (27,34)\nIs there a path between node 31 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph296-10_12", + "image": "data/connectivity/graph_visual/hard/graph296.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,1) (0,24) (0,3) (0,16) (0,17) (0,30) (0,27) (0,19) (0,11) (0,23) (0,31) (1,10) (1,24) (1,2) (1,17) (1,30) (1,29) (1,4) (1,27) (1,21) (1,11) (2,10) (2,18) (2,3) (2,15) (2,17) (2,29) (2,27) (2,19) (2,21) (2,26) (2,31) (3,10) (3,18) (3,24) (3,16) (3,17) (3,29) (3,4) (3,19) (3,21) (3,26) (3,31) (4,18) (4,15) (4,16) (4,17) (4,30) (4,27) (4,19) (4,21) (4,31) (6,22) (7,12) (7,8) (7,28) (7,20) (7,9) (8,13) (8,12) (8,20) (8,9) (9,13) (9,12) (9,25) (9,28) (10,18) (10,24) (10,15) (10,17) (10,30) (10,27) (10,19) (10,21) (10,11) (10,23) (10,31) (11,18) (11,24) (11,15) (11,16) (11,30) (11,27) (11,19) (11,21) (11,23) (11,26) (11,31) (12,13) (12,25) (12,28) (13,25) (13,28) (13,20) (15,17) (15,29) (15,27) (15,19) (15,23) (15,31) (16,24) (16,17) (16,29) (16,19) (16,21) (16,23) (16,26) (17,18) (17,24) (17,30) (17,29) (17,27) (17,19) (17,23) (17,26) (17,31) (18,24) (18,30) (18,27) (18,19) (18,23) (19,30) (19,29) (19,27) (19,21) (19,23) (19,26) (20,28) (21,29) (21,27) (21,26) (21,31) (23,24) (23,26) (23,31) (24,30) (24,27) (24,26) (25,28) (26,30) (26,29) (26,27) (26,31) (27,30) (27,31) (29,30) (29,31) (30,31)\nIs there a path between node 10 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph180-16_26", + "image": "data/connectivity/graph_visual/hard/graph180.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,6) (0,15) (0,9) (0,19) (0,26) (0,21) (0,13) (0,24) (0,11) (0,2) (0,25) (0,3) (0,12) (0,23) (0,27) (0,4) (1,28) (1,16) (1,7) (1,10) (2,8) (2,6) (2,15) (2,26) (2,17) (2,21) (2,13) (2,11) (2,14) (2,18) (2,5) (2,12) (2,4) (3,8) (3,22) (3,6) (3,15) (3,9) (3,19) (3,17) (3,21) (3,24) (3,11) (3,25) (3,14) (3,23) (3,4) (4,22) (4,15) (4,9) (4,19) (4,17) (4,13) (4,24) (4,25) (4,14) (4,18) (4,5) (4,23) (4,27) (5,8) (5,15) (5,9) (5,26) (5,17) (5,13) (5,24) (5,25) (5,12) (5,23) (5,27) (6,15) (6,19) (6,26) (6,17) (6,21) (6,13) (6,14) (6,12) (6,23) (6,27) (7,16) (7,20) (8,22) (8,9) (8,19) (8,17) (8,13) (8,24) (8,14) (8,18) (8,23) (8,27) (9,22) (9,19) (9,17) (9,21) (9,24) (9,11) (9,25) (9,14) (9,18) (9,12) (9,23) (9,27) (10,28) (10,16) (10,20) (11,22) (11,19) (11,26) (11,21) (11,24) (11,14) (11,18) (11,12) (11,23) (11,27) (12,22) (12,19) (12,26) (12,21) (12,13) (12,24) (12,14) (12,18) (12,27) (13,22) (13,15) (13,26) (13,21) (13,25) (13,14) (13,18) (13,27) (14,22) (14,15) (14,19) (14,26) (14,17) (14,21) (14,24) (14,18) (14,23) (14,27) (15,22) (15,19) (15,17) (15,21) (15,24) (15,25) (15,18) (15,27) (16,28) (17,22) (17,26) (17,21) (17,24) (17,25) (17,23) (17,27) (18,19) (18,26) (18,21) (18,23) (18,27) (19,22) (19,24) (20,28) (21,22) (21,26) (21,23) (21,27) (22,26) (22,24) (22,27) (23,26) (23,24) (23,25) (23,27) (24,25) (24,27) (25,26) (26,27)\nIs there a path between node 16 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph111-0_19", + "image": "data/connectivity/graph_visual/hard/graph111.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,16) (0,20) (0,1) (0,19) (0,18) (0,7) (0,17) (0,11) (0,13) (0,5) (0,3) (1,16) (1,9) (1,27) (1,19) (1,18) (1,2) (2,20) (2,10) (2,24) (2,23) (3,10) (3,13) (3,12) (4,9) (4,8) (4,14) (4,19) (4,18) (4,7) (4,17) (4,13) (4,5) (4,12) (4,23) (5,16) (5,6) (5,8) (5,19) (5,24) (5,17) (5,26) (6,20) (6,10) (6,18) (6,7) (6,11) (6,25) (7,8) (7,18) (7,17) (8,19) (8,24) (8,11) (8,13) (9,19) (9,11) (9,25) (10,27) (10,19) (10,18) (10,17) (11,14) (11,18) (11,25) (12,16) (12,14) (13,24) (13,25) (14,25) (15,22) (16,19) (16,24) (16,25) (17,19) (17,25) (18,19) (19,20) (24,27)\nIs there a path between node 0 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph379-7_2", + "image": "data/connectivity/graph_visual/hard/graph379.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,2) (0,18) (0,15) (0,10) (0,24) (0,26) (0,5) (0,11) (0,30) (1,12) (1,6) (1,9) (1,25) (1,4) (1,20) (1,19) (1,22) (1,8) (1,28) (1,17) (2,18) (2,14) (2,10) (2,24) (2,26) (2,23) (2,29) (2,31) (2,30) (3,12) (3,13) (3,6) (3,9) (3,4) (3,20) (3,22) (3,8) (3,28) (4,12) (4,27) (4,25) (4,19) (4,22) (4,8) (4,7) (4,17) (4,16) (5,18) (5,15) (5,14) (5,10) (5,24) (5,23) (5,29) (5,31) (5,30) (6,12) (6,13) (6,27) (6,25) (6,20) (6,19) (6,21) (6,28) (6,7) (6,17) (7,13) (7,27) (7,20) (7,19) (7,21) (7,28) (7,17) (7,16) (8,12) (8,13) (8,27) (8,20) (8,19) (8,21) (8,22) (8,28) (8,16) (9,12) (9,13) (9,27) (9,25) (9,20) (9,21) (9,22) (9,28) (9,17) (9,16) (10,18) (10,15) (10,14) (10,24) (10,23) (10,29) (10,11) (10,30) (11,15) (11,23) (11,29) (11,31) (12,25) (12,19) (12,21) (12,22) (12,28) (12,17) (12,16) (13,27) (13,19) (13,21) (13,28) (13,17) (13,16) (14,18) (14,24) (14,26) (14,23) (14,29) (14,31) (14,30) (15,18) (15,24) (15,26) (15,23) (15,29) (15,31) (15,30) (16,27) (16,25) (16,20) (16,19) (16,21) (16,17) (17,27) (17,25) (17,19) (17,22) (17,28) (18,24) (18,29) (18,30) (19,27) (19,25) (19,20) (19,22) (19,28) (20,27) (20,25) (20,21) (20,22) (20,28) (21,25) (21,22) (21,28) (22,27) (22,25) (23,26) (23,29) (23,31) (23,30) (26,29) (26,31) (26,30) (27,28) (29,31) (29,30) (30,31)\nIs there a path between node 7 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph40-14_24", + "image": "data/connectivity/graph_visual/hard/graph40.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,11) (0,13) (0,8) (0,3) (0,23) (0,4) (0,12) (0,7) (1,25) (1,14) (1,9) (2,20) (2,22) (2,21) (2,6) (2,15) (2,17) (2,19) (3,11) (3,13) (3,23) (3,18) (3,5) (3,16) (3,7) (4,11) (4,13) (4,8) (4,23) (4,18) (4,5) (4,16) (4,7) (5,11) (5,13) (5,23) (5,18) (5,16) (5,12) (5,7) (6,20) (6,22) (6,10) (6,21) (6,15) (6,17) (6,19) (7,11) (7,13) (7,8) (7,18) (7,12) (8,11) (8,13) (8,23) (8,18) (8,16) (8,12) (9,14) (10,20) (10,22) (10,17) (10,19) (11,23) (11,18) (11,16) (11,12) (12,13) (12,16) (13,16) (15,22) (15,21) (15,17) (15,19) (16,23) (16,18) (17,20) (17,22) (17,19) (18,23) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22) (24,25)\nIs there a path between node 14 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph625-2_8", + "image": "data/connectivity/graph_visual/hard/graph625.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,30) (0,9) (0,23) (0,3) (2,19) (2,6) (2,31) (2,21) (2,18) (2,11) (3,7) (3,10) (3,34) (3,27) (3,23) (4,16) (4,14) (4,21) (4,18) (4,11) (4,33) (5,17) (6,21) (7,15) (7,13) (7,9) (8,16) (8,31) (8,11) (9,10) (9,15) (9,26) (9,27) (9,23) (10,34) (10,13) (10,28) (11,16) (11,19) (11,31) (12,34) (12,13) (12,30) (12,27) (12,23) (13,26) (13,27) (13,28) (14,31) (14,21) (14,32) (15,27) (15,22) (16,19) (16,25) (17,20) (18,21) (18,33) (18,32) (19,29) (19,21) (19,32) (21,29) (21,25) (21,32) (22,24) (22,28) (23,30) (23,28) (24,34) (24,30) (24,28) (25,31) (26,30) (29,31) (29,33) (29,32) (30,34) (31,33)\nIs there a path between node 2 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph52-19_12", + "image": "data/connectivity/graph_visual/hard/graph52.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,26) (0,19) (0,14) (0,23) (0,10) (1,21) (1,6) (1,19) (2,16) (3,13) (5,25) (5,15) (6,14) (7,13) (8,24) (8,17) (8,13) (8,15) (9,12) (9,20) (9,19) (10,26) (10,19) (12,20) (13,25) (13,15) (14,21) (14,26) (15,24) (18,22) (18,25) (19,26) (22,24)\nIs there a path between node 19 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph340-0_7", + "image": "data/connectivity/graph_visual/hard/graph340.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,14) (0,13) (0,27) (1,21) (1,24) (1,13) (1,5) (2,19) (3,30) (3,26) (3,10) (3,25) (5,15) (5,9) (5,27) (5,19) (6,22) (6,29) (6,16) (7,15) (7,24) (7,9) (7,19) (9,21) (9,15) (9,24) (10,31) (10,11) (10,23) (11,23) (11,26) (11,17) (12,22) (12,29) (12,16) (13,14) (13,24) (14,21) (14,24) (14,27) (15,21) (16,29) (17,23) (17,25) (18,20) (18,29) (20,22) (21,27) (24,27) (25,28)\nIs there a path between node 0 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph494-15_32", + "image": "data/connectivity/graph_visual/hard/graph494.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,12) (0,13) (0,2) (0,14) (0,23) (0,8) (0,1) (0,25) (0,27) (0,10) (1,29) (1,13) (1,19) (1,28) (1,23) (1,30) (1,25) (1,24) (2,12) (2,5) (2,14) (2,17) (2,23) (3,7) (3,12) (3,19) (3,23) (3,8) (3,30) (3,25) (3,24) (4,33) (5,20) (5,23) (5,30) (6,15) (6,11) (7,32) (7,17) (7,23) (7,8) (7,10) (8,29) (8,12) (8,32) (8,20) (8,19) (8,17) (8,30) (9,29) (9,28) (9,30) (9,24) (10,13) (10,20) (10,14) (10,22) (11,31) (12,13) (12,23) (12,27) (12,26) (13,29) (13,32) (13,14) (13,28) (13,30) (13,24) (14,17) (14,30) (14,22) (14,27) (15,16) (15,31) (15,33) (17,32) (17,20) (17,19) (17,27) (17,24) (17,26) (18,21) (20,28) (20,30) (20,25) (21,31) (22,32) (22,28) (22,30) (23,28) (23,25) (23,27) (24,29) (24,28) (24,26) (25,32) (26,29) (26,27) (27,32) (27,30) (28,32) (28,30)\nIs there a path between node 15 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph87-12_21", + "image": "data/connectivity/graph_visual/hard/graph87.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,14) (0,20) (0,2) (0,6) (0,11) (0,8) (0,12) (0,9) (0,5) (0,26) (0,24) (0,17) (1,14) (1,20) (1,6) (1,11) (1,8) (1,12) (1,9) (1,7) (1,13) (1,5) (1,19) (1,16) (1,24) (1,17) (1,25) (2,12) (2,9) (2,7) (2,5) (2,19) (2,16) (2,26) (2,24) (2,17) (2,25) (3,21) (3,4) (3,15) (3,18) (3,22) (3,23) (4,21) (4,15) (4,18) (4,23) (4,10) (5,14) (5,11) (5,8) (5,7) (5,19) (5,16) (5,24) (5,17) (6,20) (6,11) (6,8) (6,12) (6,7) (6,13) (6,19) (6,16) (6,26) (6,17) (7,14) (7,20) (7,11) (7,8) (7,12) (7,9) (7,13) (7,19) (7,16) (7,26) (7,24) (7,17) (7,25) (8,14) (8,20) (8,11) (8,9) (8,19) (8,16) (8,26) (8,24) (9,20) (9,13) (9,19) (9,16) (9,24) (9,17) (10,15) (10,22) (10,23) (11,20) (11,13) (11,19) (12,14) (12,20) (12,13) (12,19) (12,16) (12,24) (12,17) (12,25) (13,20) (13,19) (13,26) (13,24) (13,25) (14,19) (14,16) (14,26) (14,24) (14,17) (15,21) (15,18) (15,23) (16,20) (16,19) (16,26) (16,24) (16,17) (17,20) (17,19) (17,26) (17,24) (17,25) (18,21) (18,22) (19,20) (19,26) (19,24) (19,25) (20,26) (20,24) (21,22) (21,23) (22,23)\nIs there a path between node 12 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph363-20_19", + "image": "data/connectivity/graph_visual/hard/graph363.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,3) (0,18) (0,25) (0,19) (0,16) (0,22) (0,8) (0,10) (0,31) (0,13) (0,5) (0,14) (0,24) (0,27) (0,1) (0,15) (0,23) (1,9) (1,30) (1,25) (1,19) (1,16) (1,17) (1,22) (1,8) (1,21) (1,4) (1,31) (1,13) (1,14) (1,24) (1,12) (1,27) (1,15) (2,11) (2,28) (2,29) (2,7) (3,9) (3,18) (3,25) (3,19) (3,16) (3,22) (3,10) (3,4) (3,31) (3,13) (3,5) (3,14) (3,24) (3,12) (3,20) (3,27) (3,15) (3,23) (4,18) (4,30) (4,19) (4,22) (4,8) (4,21) (4,31) (4,5) (4,24) (4,12) (4,27) (4,23) (5,18) (5,30) (5,25) (5,19) (5,17) (5,10) (5,21) (5,31) (5,12) (5,20) (5,15) (5,23) (6,28) (6,29) (6,7) (6,26) (7,28) (8,9) (8,25) (8,19) (8,16) (8,22) (8,10) (8,13) (8,14) (8,24) (8,12) (8,27) (8,15) (8,23) (9,18) (9,30) (9,19) (9,16) (9,17) (9,22) (9,10) (9,31) (9,13) (9,27) (9,15) (9,23) (10,18) (10,30) (10,25) (10,16) (10,22) (10,21) (10,31) (10,14) (10,24) (10,12) (10,20) (10,15) (11,28) (11,26) (12,19) (12,22) (12,21) (12,13) (12,24) (12,15) (12,23) (13,25) (13,19) (13,16) (13,17) (13,22) (13,31) (13,14) (13,27) (14,30) (14,25) (14,16) (14,17) (14,22) (14,31) (14,24) (14,20) (14,15) (14,23) (15,18) (15,30) (15,25) (15,19) (15,16) (15,22) (15,31) (15,24) (16,18) (16,30) (16,22) (16,21) (16,31) (16,20) (16,27) (17,18) (17,30) (17,25) (17,19) (17,22) (17,21) (17,31) (17,24) (17,27) (17,23) (18,30) (18,25) (18,19) (18,22) (18,21) (18,31) (18,24) (18,27) (18,23) (19,30) (19,25) (19,21) (19,24) (19,20) (19,27) (19,23) (20,21) (20,31) (20,24) (20,27) (20,23) (21,25) (21,22) (21,31) (21,24) (21,27) (21,23) (22,30) (22,31) (22,24) (22,23) (23,30) (23,25) (23,24) (23,27) (24,30) (24,25) (24,31) (24,27) (25,30) (25,27) (26,28) (27,30) (27,31) (28,29) (30,31)\nIs there a path between node 20 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph387-10_7", + "image": "data/connectivity/graph_visual/hard/graph387.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,27) (0,28) (0,29) (0,22) (0,23) (0,8) (0,19) (0,6) (0,16) (0,7) (0,15) (0,26) (0,1) (1,3) (1,27) (1,20) (1,22) (1,23) (1,8) (1,19) (1,18) (1,6) (1,5) (1,16) (1,10) (1,7) (1,26) (2,31) (2,21) (2,11) (2,17) (2,12) (3,22) (3,8) (3,19) (3,6) (3,16) (3,10) (3,7) (3,15) (4,31) (4,14) (4,11) (4,17) (4,25) (4,24) (4,13) (4,12) (4,30) (5,28) (5,29) (5,23) (5,19) (5,18) (5,10) (5,15) (5,26) (6,27) (6,29) (6,20) (6,23) (6,8) (6,18) (6,16) (6,10) (6,15) (6,26) (7,27) (7,28) (7,20) (7,22) (7,23) (7,8) (7,19) (7,18) (7,16) (7,15) (7,26) (8,27) (8,28) (8,29) (8,20) (8,22) (8,23) (8,18) (8,16) (9,31) (9,21) (9,11) (9,17) (9,25) (9,24) (9,12) (10,27) (10,28) (10,29) (10,20) (10,22) (10,23) (10,19) (10,16) (10,15) (10,26) (11,31) (11,21) (11,25) (11,24) (11,12) (12,31) (12,21) (12,14) (12,17) (12,25) (12,24) (12,30) (13,21) (13,25) (13,24) (13,30) (14,31) (14,17) (14,25) (14,24) (14,30) (15,29) (15,20) (15,22) (15,23) (15,19) (15,18) (15,26) (16,27) (16,28) (16,29) (16,20) (16,22) (16,18) (16,26) (17,31) (17,21) (17,25) (17,24) (17,30) (18,28) (18,29) (18,20) (18,22) (18,19) (19,27) (19,28) (19,29) (19,20) (19,22) (19,23) (19,26) (20,27) (20,28) (20,29) (20,22) (20,23) (21,25) (22,27) (22,28) (22,29) (23,28) (24,25) (24,30) (25,31) (25,30) (26,27) (26,28) (26,29) (27,28) (27,29) (28,29) (30,31)\nIs there a path between node 10 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph260-15_27", + "image": "data/connectivity/graph_visual/hard/graph260.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,18) (0,28) (0,30) (0,24) (0,14) (1,13) (1,12) (2,10) (2,22) (2,12) (3,9) (4,20) (4,6) (4,7) (4,18) (4,30) (4,25) (4,14) (5,21) (5,26) (6,11) (6,15) (6,25) (6,14) (7,20) (7,18) (7,11) (7,28) (7,24) (7,17) (7,15) (7,14) (8,30) (8,24) (8,25) (8,14) (9,26) (11,28) (11,14) (13,16) (13,22) (14,20) (14,28) (14,17) (14,25) (15,25) (16,22) (16,23) (17,28) (17,24) (17,25) (18,19) (19,25) (20,28) (20,30) (20,25) (21,27) (21,26) (22,23) (27,29)\nIs there a path between node 15 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph686-11_27", + "image": "data/connectivity/graph_visual/hard/graph686.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,24) (0,27) (0,32) (0,33) (0,29) (0,9) (0,21) (0,5) (0,31) (0,14) (0,12) (0,26) (0,11) (0,17) (0,16) (0,34) (0,23) (0,30) (0,7) (0,6) (1,24) (1,32) (1,4) (1,20) (1,9) (1,21) (1,22) (1,12) (1,26) (1,25) (1,11) (1,17) (1,34) (1,23) (1,7) (1,6) (1,8) (2,27) (2,4) (2,29) (2,9) (2,21) (2,5) (2,15) (2,31) (2,22) (2,12) (2,26) (2,25) (2,11) (2,17) (2,18) (2,34) (2,23) (2,30) (3,24) (3,27) (3,32) (3,33) (3,4) (3,20) (3,5) (3,15) (3,31) (3,14) (3,22) (3,25) (3,11) (3,17) (3,16) (3,18) (3,34) (3,30) (3,7) (3,28) (3,6) (3,8) (4,24) (4,27) (4,33) (4,29) (4,20) (4,9) (4,21) (4,5) (4,15) (4,31) (4,14) (4,22) (4,12) (4,25) (4,17) (4,16) (4,18) (4,30) (4,28) (4,6) (4,8) (5,27) (5,29) (5,20) (5,21) (5,15) (5,31) (5,14) (5,12) (5,26) (5,25) (5,11) (5,17) (5,16) (5,30) (5,7) (5,28) (5,8) (6,24) (6,32) (6,33) (6,29) (6,20) (6,9) (6,21) (6,15) (6,14) (6,22) (6,12) (6,26) (6,25) (6,11) (6,16) (6,18) (6,7) (6,28) (6,8) (7,24) (7,27) (7,33) (7,9) (7,21) (7,15) (7,31) (7,14) (7,22) (7,12) (7,26) (7,25) (7,18) (7,23) (7,28) (7,8) (8,24) (8,32) (8,20) (8,9) (8,15) (8,31) (8,14) (8,22) (8,12) (8,17) (8,16) (8,34) (8,23) (8,30) (8,28) (9,27) (9,32) (9,33) (9,29) (9,20) (9,21) (9,31) (9,14) (9,12) (9,26) (9,16) (9,34) (9,23) (9,30) (9,28) (10,19) (10,13) (11,24) (11,32) (11,29) (11,20) (11,21) (11,15) (11,14) (11,22) (11,12) (11,26) (11,17) (11,18) (11,34) (11,23) (11,30) (11,28) (12,24) (12,27) (12,32) (12,33) (12,20) (12,21) (12,31) (12,22) (12,26) (12,25) (12,17) (12,16) (12,18) (12,34) (12,30) (12,28) (13,19) (14,32) (14,29) (14,21) (14,31) (14,26) (14,25) (14,17) (14,16) (14,18) (14,23) (14,30) (15,24) (15,27) (15,32) (15,33) (15,20) (15,31) (15,22) (15,26) (15,25) (15,17) (15,16) (15,34) (15,23) (15,30) (16,27) (16,33) (16,29) (16,20) (16,21) (16,31) (16,22) (16,26) (16,25) (16,17) (16,18) (16,34) (16,23) (16,30) (17,24) (17,32) (17,33) (17,29) (17,20) (17,31) (17,22) (17,26) (17,25) (17,34) (17,23) (17,28) (18,24) (18,32) (18,33) (18,20) (18,31) (18,22) (18,26) (18,34) (18,23) (18,28) (20,24) (20,33) (20,29) (20,31) (20,22) (20,26) (20,34) (20,23) (20,30) (20,28) (21,24) (21,32) (21,26) (21,25) (21,34) (21,23) (21,30) (21,28) (22,24) (22,32) (22,33) (22,29) (22,31) (22,26) (22,25) (22,34) (22,28) (23,27) (23,32) (23,33) (23,29) (23,31) (23,34) (23,30) (23,28) (24,27) (24,33) (24,29) (24,31) (24,26) (24,25) (24,34) (24,30) (24,28) (25,27) (25,32) (25,33) (25,29) (25,26) (25,34) (25,30) (25,28) (26,27) (26,32) (26,33) (26,29) (26,31) (26,28) (27,32) (27,33) (27,29) (27,31) (27,30) (28,32) (28,31) (28,34) (28,30) (29,32) (29,33) (29,34) (30,32) (30,31) (30,34) (31,32) (31,33) (32,33) (32,34) (33,34)\nIs there a path between node 11 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph97-10_3", + "image": "data/connectivity/graph_visual/hard/graph97.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,2) (0,8) (0,4) (0,9) (0,16) (0,21) (0,12) (0,23) (0,7) (0,11) (1,25) (1,22) (2,8) (2,26) (2,16) (2,20) (3,10) (3,16) (3,13) (3,14) (3,11) (4,26) (4,21) (4,12) (4,14) (5,10) (5,21) (5,13) (5,23) (5,7) (5,14) (5,15) (6,10) (6,9) (6,13) (6,12) (6,23) (6,14) (6,20) (6,15) (7,9) (7,16) (7,18) (7,23) (7,14) (7,15) (7,17) (8,10) (8,9) (8,16) (8,15) (8,11) (9,10) (9,26) (9,14) (9,17) (10,16) (12,18) (12,13) (13,18) (13,15) (14,21) (14,15) (15,26) (15,20) (16,18) (16,20) (17,20) (19,24) (19,22) (20,26) (20,21) (22,27)\nIs there a path between node 10 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph174-4_7", + "image": "data/connectivity/graph_visual/hard/graph174.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,1) (0,25) (0,17) (0,8) (0,9) (0,7) (0,10) (0,11) (0,6) (0,15) (0,27) (0,16) (0,24) (1,25) (1,17) (1,8) (1,10) (1,11) (1,15) (1,27) (1,16) (1,24) (2,18) (2,21) (2,23) (2,5) (2,26) (2,3) (3,21) (3,23) (4,22) (4,20) (4,28) (4,12) (4,14) (5,18) (5,19) (6,25) (6,17) (6,8) (6,7) (6,11) (6,16) (6,24) (6,13) (7,8) (7,9) (7,10) (7,27) (7,16) (7,24) (8,25) (8,17) (8,10) (8,27) (8,24) (9,25) (9,17) (9,10) (9,11) (9,15) (9,27) (9,16) (9,24) (9,13) (10,25) (10,16) (10,24) (10,13) (11,25) (11,15) (11,27) (11,16) (11,13) (12,22) (13,25) (13,17) (13,27) (13,16) (13,24) (14,22) (14,20) (14,28) (15,17) (15,27) (15,16) (15,24) (16,25) (16,17) (17,25) (17,27) (18,23) (18,19) (18,26) (19,21) (19,23) (20,22) (21,23) (21,26) (22,28) (24,25) (24,27) (25,27)\nIs there a path between node 4 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph465-16_15", + "image": "data/connectivity/graph_visual/hard/graph465.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (1,5) (1,31) (1,4) (1,3) (1,30) (1,13) (2,22) (2,5) (2,31) (2,23) (2,3) (2,20) (2,30) (3,22) (3,31) (3,19) (4,22) (4,5) (4,23) (4,20) (5,7) (5,23) (5,19) (5,6) (6,28) (6,23) (6,19) (7,20) (7,13) (8,24) (8,21) (8,15) (8,25) (8,12) (10,26) (10,15) (10,14) (11,32) (11,27) (11,12) (12,29) (12,17) (13,20) (13,19) (14,21) (14,16) (14,17) (15,21) (15,17) (16,24) (16,32) (16,17) (17,24) (17,29) (19,28) (19,20) (19,30) (20,23) (22,30) (24,32) (24,29) (25,29) (27,29) (28,31) (28,30)\nIs there a path between node 16 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph553-23_31", + "image": "data/connectivity/graph_visual/hard/graph553.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,24) (0,26) (0,31) (0,22) (1,25) (1,28) (1,20) (1,30) (1,14) (1,2) (1,17) (1,5) (2,9) (2,6) (2,33) (2,30) (2,17) (3,24) (3,12) (3,16) (3,29) (4,15) (4,25) (4,28) (4,20) (4,21) (5,15) (5,10) (5,28) (5,6) (5,33) (5,20) (5,13) (5,17) (6,15) (6,9) (6,21) (6,17) (7,15) (7,10) (7,20) (7,14) (7,21) (8,24) (8,26) (8,16) (9,25) (9,13) (9,21) (10,15) (10,32) (10,20) (10,18) (11,27) (12,26) (13,17) (14,30) (14,21) (15,18) (15,17) (16,31) (16,23) (16,29) (17,25) (17,33) (17,32) (17,18) (18,30) (19,27) (22,26) (23,24) (25,33) (25,32) (26,31) (28,32)\nIs there a path between node 23 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph153-14_8", + "image": "data/connectivity/graph_visual/hard/graph153.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,1) (0,21) (0,2) (0,3) (0,10) (0,4) (0,28) (0,26) (0,19) (0,23) (0,18) (0,25) (0,22) (0,16) (0,20) (0,7) (0,27) (0,15) (0,24) (0,12) (0,14) (1,6) (1,21) (1,13) (1,2) (1,3) (1,10) (1,4) (1,9) (1,28) (1,18) (1,25) (1,20) (1,17) (1,27) (1,15) (1,12) (1,14) (2,6) (2,13) (2,3) (2,10) (2,4) (2,9) (2,28) (2,26) (2,19) (2,23) (2,18) (2,22) (2,16) (2,20) (2,27) (2,15) (2,24) (2,12) (2,14) (3,11) (3,6) (3,13) (3,10) (3,4) (3,9) (3,26) (3,23) (3,25) (3,22) (3,16) (3,20) (3,7) (3,15) (3,14) (4,11) (4,21) (4,13) (4,10) (4,9) (4,28) (4,26) (4,23) (4,22) (4,16) (4,17) (4,7) (4,27) (4,15) (4,24) (5,8) (6,11) (6,28) (6,19) (6,23) (6,18) (6,22) (6,20) (6,7) (6,27) (6,15) (7,11) (7,21) (7,13) (7,10) (7,9) (7,28) (7,26) (7,19) (7,18) (7,22) (7,16) (7,17) (7,15) (7,24) (7,14) (9,11) (9,21) (9,10) (9,28) (9,26) (9,23) (9,18) (9,25) (9,22) (9,16) (9,27) (9,24) (9,12) (10,11) (10,13) (10,28) (10,26) (10,19) (10,23) (10,18) (10,25) (10,16) (10,20) (10,17) (10,27) (10,15) (10,24) (10,12) (10,14) (11,19) (11,23) (11,18) (11,25) (11,22) (11,17) (11,24) (11,12) (11,14) (12,21) (12,26) (12,19) (12,23) (12,18) (12,22) (12,20) (12,17) (12,14) (13,21) (13,28) (13,19) (13,23) (13,25) (13,22) (13,16) (13,20) (13,17) (13,27) (13,15) (13,14) (14,21) (14,26) (14,19) (14,23) (14,18) (14,25) (14,16) (14,20) (14,17) (14,27) (15,21) (15,26) (15,18) (15,25) (15,22) (15,16) (15,20) (15,24) (16,21) (16,28) (16,26) (16,23) (16,18) (16,22) (16,17) (16,24) (17,28) (17,19) (17,18) (17,20) (17,27) (17,24) (18,21) (18,19) (18,23) (18,22) (18,20) (19,21) (19,28) (19,26) (19,23) (19,25) (19,22) (19,20) (19,27) (19,24) (20,21) (20,28) (20,25) (20,24) (21,28) (21,26) (21,23) (21,25) (21,22) (21,27) (21,24) (22,28) (22,26) (22,23) (22,25) (23,26) (23,25) (23,27) (24,25) (25,26) (26,28) (27,28)\nIs there a path between node 14 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph522-5_27", + "image": "data/connectivity/graph_visual/hard/graph522.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,11) (0,33) (0,7) (0,13) (1,25) (1,30) (1,27) (2,6) (2,5) (2,13) (3,30) (3,17) (3,15) (3,32) (3,14) (3,21) (3,8) (3,12) (3,4) (3,24) (4,25) (4,17) (4,32) (4,12) (5,9) (7,16) (7,33) (8,28) (8,25) (8,32) (8,26) (8,21) (8,27) (8,20) (9,11) (9,16) (9,13) (10,28) (10,15) (10,26) (10,27) (10,24) (10,18) (11,16) (11,33) (12,28) (12,25) (12,24) (13,33) (14,27) (15,27) (15,29) (15,24) (17,25) (17,21) (18,25) (18,31) (18,21) (18,27) (20,25) (20,32) (20,22) (20,21) (20,27) (20,29) (20,24) (21,28) (21,29) (21,24) (22,24) (24,30) (24,31) (24,26) (25,31) (25,32) (25,26) (25,27) (26,30) (27,31) (28,29) (30,32)\nIs there a path between node 5 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph142-17_10", + "image": "data/connectivity/graph_visual/hard/graph142.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,7) (0,23) (0,27) (0,25) (0,3) (1,2) (1,21) (1,25) (1,22) (1,9) (2,10) (2,25) (2,3) (2,8) (3,23) (3,12) (3,25) (3,9) (3,26) (4,20) (4,5) (4,24) (4,18) (5,19) (5,20) (5,17) (6,21) (6,27) (6,22) (6,16) (6,26) (7,23) (7,21) (7,10) (7,22) (7,26) (7,8) (8,21) (8,15) (8,22) (8,16) (9,21) (9,12) (10,13) (10,21) (10,25) (11,18) (12,13) (12,21) (12,27) (12,25) (12,22) (13,21) (14,18) (15,27) (15,22) (16,21) (16,28) (16,26) (17,19) (17,20) (17,18) (19,24) (21,23) (21,25) (21,28) (22,25) (23,28) (27,28)\nIs there a path between node 17 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph454-15_5", + "image": "data/connectivity/graph_visual/hard/graph454.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,7) (0,4) (0,23) (0,21) (0,18) (1,10) (1,19) (1,24) (1,18) (1,5) (2,11) (2,14) (2,22) (2,23) (2,13) (2,15) (2,31) (2,20) (3,11) (3,22) (3,16) (3,30) (3,13) (3,20) (3,18) (4,11) (4,14) (4,6) (4,23) (4,24) (4,31) (4,32) (4,18) (4,5) (5,19) (5,11) (5,7) (5,23) (5,15) (5,31) (6,19) (6,7) (6,13) (6,8) (7,11) (7,22) (7,28) (7,30) (7,21) (7,31) (8,10) (8,12) (8,14) (8,16) (8,30) (8,21) (9,17) (10,12) (10,24) (10,21) (10,32) (10,20) (11,22) (11,23) (11,13) (11,15) (11,18) (12,22) (12,31) (12,18) (13,16) (13,30) (13,23) (13,21) (13,15) (13,32) (14,19) (14,30) (14,23) (14,31) (15,30) (15,31) (15,32) (15,20) (16,30) (16,24) (16,21) (16,32) (17,25) (18,19) (18,28) (18,24) (19,21) (20,22) (20,21) (22,30) (22,23) (22,32) (24,28) (24,31) (24,32) (25,26) (25,27)\nIs there a path between node 15 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph114-13_23", + "image": "data/connectivity/graph_visual/hard/graph114.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,11) (0,16) (1,13) (2,27) (2,10) (2,5) (2,25) (2,16) (2,4) (3,10) (3,21) (3,7) (4,5) (4,22) (4,25) (4,21) (4,16) (4,6) (4,14) (5,10) (5,22) (5,25) (5,21) (5,11) (5,16) (5,19) (6,21) (6,19) (7,10) (7,21) (7,14) (7,19) (8,15) (9,13) (9,20) (9,23) (10,22) (10,11) (10,16) (10,19) (11,25) (12,15) (13,20) (14,16) (14,19) (15,24) (15,20) (16,27) (16,22) (16,25) (17,27) (17,22) (17,25) (19,27) (19,26) (20,23) (21,25) (21,26) (25,27) (26,27)\nIs there a path between node 13 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph100-14_0", + "image": "data/connectivity/graph_visual/hard/graph100.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,11) (0,20) (1,12) (1,5) (1,2) (1,16) (1,17) (1,25) (1,6) (1,21) (1,7) (1,3) (1,15) (1,23) (1,4) (1,24) (1,9) (1,27) (1,10) (2,8) (2,26) (2,5) (2,19) (2,18) (2,16) (2,6) (2,21) (2,7) (2,3) (2,23) (2,24) (2,9) (2,10) (3,8) (3,26) (3,12) (3,5) (3,22) (3,19) (3,18) (3,17) (3,6) (3,21) (3,7) (3,15) (3,23) (3,4) (3,24) (3,9) (3,27) (3,10) (4,14) (4,26) (4,12) (4,5) (4,22) (4,19) (4,18) (4,16) (4,17) (4,25) (4,6) (4,21) (4,7) (4,15) (4,23) (4,24) (4,9) (4,27) (5,14) (5,26) (5,12) (5,19) (5,16) (5,17) (5,6) (5,21) (5,7) (5,15) (5,23) (5,24) (5,9) (5,27) (6,8) (6,26) (6,12) (6,19) (6,16) (6,17) (6,25) (6,21) (6,7) (6,15) (6,24) (6,9) (6,27) (7,14) (7,26) (7,22) (7,19) (7,18) (7,16) (7,17) (7,25) (7,21) (7,15) (7,23) (7,24) (7,9) (7,27) (8,14) (8,12) (8,22) (8,19) (8,18) (8,16) (8,17) (8,25) (8,21) (8,15) (8,23) (8,24) (8,9) (8,27) (8,10) (9,14) (9,26) (9,12) (9,22) (9,19) (9,18) (9,16) (9,21) (9,15) (9,23) (9,24) (9,27) (9,10) (10,14) (10,26) (10,22) (10,19) (10,18) (10,16) (10,17) (10,25) (10,21) (10,15) (10,23) (10,24) (10,27) (11,20) (11,13) (12,14) (12,26) (12,22) (12,19) (12,18) (12,16) (12,17) (12,25) (12,21) (12,15) (12,23) (13,20) (14,26) (14,22) (14,16) (14,17) (14,15) (14,23) (14,27) (15,26) (15,22) (15,18) (15,16) (15,25) (15,24) (16,26) (16,18) (16,17) (16,23) (16,27) (17,26) (17,19) (17,25) (17,24) (17,27) (18,26) (18,19) (18,25) (18,21) (18,23) (18,24) (18,27) (19,26) (19,25) (19,24) (21,26) (21,22) (21,25) (21,24) (21,27) (22,26) (22,24) (22,27) (23,24) (24,25) (24,27) (25,26) (25,27) (26,27)\nIs there a path between node 14 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph692-24_21", + "image": "data/connectivity/graph_visual/hard/graph692.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,15) (0,2) (0,33) (0,4) (0,8) (0,23) (0,34) (0,30) (1,22) (1,28) (1,9) (1,29) (1,24) (1,26) (1,7) (1,27) (1,32) (1,19) (1,16) (1,5) (1,10) (2,12) (2,3) (2,15) (2,33) (2,20) (2,8) (2,23) (3,12) (3,11) (3,33) (3,4) (3,8) (3,23) (4,12) (4,11) (4,33) (4,20) (4,23) (5,22) (5,17) (5,28) (5,29) (5,14) (5,31) (5,25) (5,18) (5,24) (5,26) (5,6) (5,27) (5,32) (5,21) (5,19) (5,16) (6,17) (6,28) (6,13) (6,29) (6,14) (6,31) (6,25) (6,24) (6,27) (6,19) (6,16) (6,10) (7,22) (7,17) (7,9) (7,13) (7,29) (7,25) (7,24) (7,26) (7,27) (7,21) (7,19) (7,16) (7,10) (8,12) (8,11) (8,15) (8,33) (8,30) (9,22) (9,28) (9,13) (9,29) (9,14) (9,31) (9,18) (9,24) (9,26) (9,27) (9,32) (9,21) (9,19) (9,16) (9,10) (10,22) (10,17) (10,28) (10,13) (10,29) (10,14) (10,31) (10,25) (10,18) (10,26) (10,32) (10,21) (10,16) (11,33) (11,20) (11,23) (11,30) (12,33) (12,20) (12,34) (12,30) (13,22) (13,17) (13,28) (13,29) (13,14) (13,31) (13,25) (13,18) (13,24) (13,26) (13,32) (13,21) (13,19) (13,16) (14,22) (14,17) (14,28) (14,29) (14,31) (14,25) (14,18) (14,24) (14,26) (14,27) (14,32) (14,21) (14,19) (14,16) (15,33) (15,20) (15,23) (15,34) (15,30) (16,22) (16,17) (16,28) (16,29) (16,31) (16,18) (16,24) (16,26) (16,27) (16,32) (16,21) (17,28) (17,29) (17,31) (17,18) (17,24) (17,27) (17,32) (17,21) (17,19) (18,22) (18,28) (18,29) (18,31) (18,25) (18,27) (18,21) (19,22) (19,28) (19,29) (19,31) (19,25) (19,27) (19,21) (20,33) (20,23) (20,34) (20,30) (21,28) (21,29) (21,31) (21,25) (21,26) (21,32) (22,28) (22,31) (22,25) (22,24) (22,26) (22,27) (22,32) (23,33) (24,28) (24,29) (24,31) (24,26) (24,32) (25,31) (25,27) (25,32) (26,29) (26,31) (26,27) (27,28) (27,29) (27,31) (27,32) (28,29) (28,32) (29,32) (30,33) (30,34) (31,32) (33,34)\nIs there a path between node 24 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph685-30_21", + "image": "data/connectivity/graph_visual/hard/graph685.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,1) (0,2) (0,11) (0,31) (0,24) (0,20) (0,26) (0,7) (0,23) (1,21) (1,2) (1,11) (1,31) (1,14) (1,24) (1,26) (1,19) (1,23) (1,15) (2,32) (2,21) (2,11) (2,8) (2,31) (2,14) (2,24) (2,20) (2,26) (2,19) (2,15) (3,16) (3,29) (3,17) (3,6) (3,13) (3,33) (3,18) (3,27) (3,25) (3,34) (3,9) (4,22) (4,5) (5,30) (5,22) (6,16) (6,12) (6,13) (6,33) (6,18) (6,25) (6,34) (6,9) (7,32) (7,11) (7,8) (7,14) (7,19) (7,23) (8,32) (8,11) (8,14) (8,24) (8,15) (9,29) (9,12) (9,17) (9,33) (9,18) (9,25) (9,10) (9,34) (10,29) (10,13) (10,33) (10,27) (10,25) (10,28) (11,21) (11,31) (11,14) (11,24) (11,26) (11,19) (11,23) (11,15) (12,16) (12,29) (12,13) (12,18) (12,27) (12,25) (12,34) (12,28) (13,16) (13,29) (13,17) (13,33) (13,28) (14,32) (14,21) (14,31) (14,24) (14,20) (14,26) (14,19) (14,23) (15,21) (15,31) (15,24) (15,20) (15,26) (15,23) (16,17) (16,33) (16,18) (16,27) (16,25) (16,34) (16,28) (17,33) (17,27) (17,34) (17,28) (18,29) (18,27) (18,25) (18,34) (18,28) (19,21) (19,24) (19,20) (20,32) (20,21) (20,31) (20,26) (20,23) (21,32) (21,31) (21,24) (21,26) (21,23) (22,30) (23,24) (23,26) (24,32) (24,31) (24,26) (25,33) (25,34) (25,28) (26,32) (27,28) (28,33) (28,34) (29,33) (31,32) (33,34)\nIs there a path between node 30 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph52-21_9", + "image": "data/connectivity/graph_visual/hard/graph52.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,26) (0,19) (0,14) (0,23) (0,10) (1,21) (1,6) (1,19) (2,16) (3,13) (5,25) (5,15) (6,14) (7,13) (8,24) (8,17) (8,13) (8,15) (9,12) (9,20) (9,19) (10,26) (10,19) (12,20) (13,25) (13,15) (14,21) (14,26) (15,24) (18,22) (18,25) (19,26) (22,24)\nIs there a path between node 21 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph622-22_11", + "image": "data/connectivity/graph_visual/hard/graph622.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,25) (0,13) (1,16) (1,27) (1,32) (1,4) (1,31) (1,34) (2,16) (2,27) (2,32) (2,6) (2,19) (2,9) (3,25) (3,28) (3,7) (3,18) (3,21) (4,29) (4,33) (4,23) (4,12) (4,9) (4,34) (5,27) (5,11) (5,19) (5,9) (6,33) (6,27) (6,34) (7,25) (7,18) (8,10) (9,16) (9,19) (9,34) (10,30) (11,29) (11,16) (11,19) (11,31) (11,14) (11,12) (12,33) (12,26) (12,19) (12,34) (13,25) (13,28) (14,32) (15,30) (16,29) (16,27) (16,32) (18,21) (20,24) (21,25) (22,25) (22,28) (23,27) (26,33) (26,27) (26,34) (27,29) (27,33) (27,34) (29,33)\nIs there a path between node 22 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph129-17_20", + "image": "data/connectivity/graph_visual/hard/graph129.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,6) (0,7) (0,19) (0,18) (0,12) (0,17) (0,13) (0,24) (0,3) (0,1) (0,15) (0,11) (0,27) (0,16) (1,6) (1,8) (1,26) (1,7) (1,10) (1,19) (1,18) (1,24) (1,3) (1,9) (1,15) (1,11) (1,27) (2,20) (2,25) (2,14) (2,21) (3,6) (3,8) (3,26) (3,7) (3,10) (3,19) (3,18) (3,12) (3,17) (3,24) (3,9) (3,15) (3,11) (4,22) (5,23) (5,20) (5,25) (6,8) (6,26) (6,19) (6,18) (6,12) (6,17) (6,13) (6,24) (6,15) (6,11) (6,27) (6,16) (7,10) (7,19) (7,18) (7,17) (7,13) (7,24) (7,9) (7,16) (8,26) (8,19) (8,18) (8,12) (8,17) (8,13) (8,24) (8,9) (8,15) (8,27) (8,16) (9,26) (9,10) (9,18) (9,12) (9,17) (9,13) (9,15) (9,27) (9,16) (10,26) (10,19) (10,17) (10,13) (10,15) (10,16) (11,26) (11,19) (11,18) (11,12) (11,17) (11,15) (12,26) (12,19) (12,18) (12,13) (12,24) (13,18) (13,24) (13,27) (13,16) (14,23) (14,20) (14,21) (15,26) (15,19) (15,18) (15,17) (15,16) (16,26) (16,19) (16,24) (16,27) (17,26) (17,24) (17,27) (18,26) (18,19) (18,27) (19,26) (19,27) (20,25) (21,23) (21,25)\nIs there a path between node 17 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph435-24_8", + "image": "data/connectivity/graph_visual/hard/graph435.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,13) (0,31) (0,30) (0,8) (0,27) (0,6) (0,7) (0,1) (0,9) (0,2) (0,12) (0,11) (0,24) (0,29) (0,4) (0,14) (0,3) (0,15) (1,13) (1,31) (1,30) (1,5) (1,8) (1,6) (1,10) (1,32) (1,2) (1,12) (1,22) (1,19) (1,24) (1,16) (1,29) (1,4) (1,15) (2,31) (2,30) (2,6) (2,10) (2,32) (2,7) (2,9) (2,12) (2,22) (2,11) (2,16) (2,26) (2,29) (2,4) (2,14) (2,3) (2,15) (3,13) (3,30) (3,5) (3,8) (3,27) (3,6) (3,10) (3,7) (3,12) (3,22) (3,24) (3,26) (3,29) (3,4) (3,18) (3,14) (3,15) (4,13) (4,31) (4,5) (4,8) (4,27) (4,6) (4,10) (4,32) (4,12) (4,11) (4,19) (4,24) (4,16) (4,26) (4,29) (4,18) (4,15) (5,31) (5,30) (5,8) (5,32) (5,7) (5,9) (5,12) (5,11) (5,19) (5,16) (5,26) (5,18) (5,14) (5,15) (6,13) (6,31) (6,30) (6,8) (6,27) (6,10) (6,32) (6,7) (6,9) (6,22) (6,11) (6,24) (6,16) (6,15) (7,13) (7,30) (7,27) (7,32) (7,9) (7,22) (7,19) (7,16) (7,26) (7,14) (7,15) (8,13) (8,27) (8,32) (8,9) (8,22) (8,19) (8,24) (8,16) (8,26) (8,29) (8,18) (8,14) (8,15) (9,13) (9,31) (9,30) (9,10) (9,32) (9,22) (9,11) (9,19) (9,16) (9,26) (9,29) (9,18) (9,14) (9,15) (10,30) (10,27) (10,12) (10,11) (10,19) (10,24) (10,29) (10,18) (10,14) (10,15) (11,31) (11,27) (11,32) (11,12) (11,22) (11,24) (11,16) (11,26) (11,29) (11,18) (11,14) (11,15) (12,30) (12,27) (12,32) (12,22) (12,19) (12,24) (12,16) (12,26) (12,29) (12,18) (12,14) (12,15) (13,31) (13,30) (13,32) (13,22) (13,24) (13,16) (13,26) (13,29) (13,14) (14,30) (14,27) (14,32) (14,22) (14,19) (14,24) (14,16) (14,26) (14,15) (15,31) (15,30) (15,27) (15,19) (15,24) (15,16) (15,26) (15,29) (16,31) (16,27) (16,22) (16,19) (16,24) (16,26) (18,31) (18,30) (18,27) (18,22) (18,24) (18,26) (18,29) (19,31) (19,30) (19,27) (19,32) (19,22) (19,29) (20,23) (20,25) (22,31) (22,30) (22,24) (22,26) (23,25) (24,31) (24,27) (24,32) (24,26) (24,29) (26,31) (26,30) (26,27) (27,31) (27,30) (29,30) (29,32) (30,32) (31,32)\nIs there a path between node 24 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph39-10_17", + "image": "data/connectivity/graph_visual/hard/graph39.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,10) (0,2) (0,25) (0,7) (0,19) (0,4) (0,15) (0,17) (0,8) (0,6) (0,20) (0,14) (0,12) (0,21) (1,10) (1,24) (1,2) (1,25) (1,7) (1,4) (1,18) (1,15) (1,13) (1,8) (1,6) (1,12) (1,3) (1,21) (2,11) (2,25) (2,7) (2,19) (2,18) (2,15) (2,9) (2,13) (2,8) (2,6) (2,14) (2,3) (2,21) (3,24) (3,25) (3,7) (3,19) (3,4) (3,18) (3,9) (3,17) (3,8) (3,14) (3,12) (3,21) (4,11) (4,10) (4,24) (4,25) (4,19) (4,15) (4,13) (4,17) (4,8) (4,6) (4,20) (4,12) (5,16) (5,22) (5,23) (6,11) (6,24) (6,25) (6,7) (6,18) (6,15) (6,9) (6,17) (6,8) (6,20) (6,14) (6,12) (6,21) (7,10) (7,24) (7,25) (7,19) (7,18) (7,15) (7,13) (7,17) (7,8) (7,20) (7,14) (8,11) (8,10) (8,15) (8,9) (8,17) (8,20) (8,14) (8,12) (9,11) (9,10) (9,24) (9,25) (9,19) (9,15) (9,13) (9,17) (9,20) (9,14) (9,12) (9,21) (10,11) (10,25) (10,19) (10,18) (10,15) (10,13) (10,17) (10,20) (10,12) (10,21) (11,24) (11,25) (11,18) (11,13) (11,17) (11,20) (11,12) (12,25) (12,19) (12,18) (12,15) (12,13) (12,17) (12,20) (12,21) (13,24) (13,25) (13,19) (13,18) (13,15) (13,17) (13,20) (13,21) (14,24) (14,19) (14,18) (14,15) (14,20) (15,24) (15,25) (15,19) (15,17) (15,20) (15,21) (16,22) (16,23) (17,24) (17,19) (17,18) (17,21) (18,25) (18,20) (19,24) (19,25) (20,24) (20,25) (20,21) (21,25) (24,25)\nIs there a path between node 10 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph422-16_22", + "image": "data/connectivity/graph_visual/hard/graph422.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,21) (0,6) (0,13) (0,26) (1,27) (1,28) (1,6) (1,17) (1,13) (1,24) (1,10) (1,15) (2,9) (2,31) (2,19) (2,17) (2,29) (3,16) (3,9) (3,18) (3,26) (3,29) (4,20) (4,16) (4,9) (4,17) (4,18) (4,24) (6,27) (6,20) (6,9) (6,14) (6,13) (6,26) (6,24) (7,28) (7,9) (7,31) (7,30) (7,19) (7,17) (7,22) (7,29) (8,32) (9,16) (9,21) (9,30) (9,17) (9,22) (9,18) (10,20) (10,16) (10,14) (10,21) (10,18) (10,15) (13,20) (13,17) (13,26) (13,29) (14,28) (14,21) (14,19) (14,18) (15,17) (15,18) (15,29) (16,20) (16,31) (16,17) (16,18) (16,29) (17,27) (17,28) (17,20) (17,18) (17,26) (18,31) (19,21) (19,30) (19,22) (20,27) (20,28) (21,27) (21,31) (21,30) (22,30) (24,28) (24,29) (26,27) (26,29) (27,31) (27,30) (29,31) (29,30)\nIs there a path between node 16 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph446-28_9", + "image": "data/connectivity/graph_visual/hard/graph446.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (0,27) (0,21) (0,12) (0,24) (0,16) (0,13) (0,20) (0,23) (0,22) (0,31) (0,29) (1,32) (2,25) (3,5) (3,24) (3,19) (3,13) (3,18) (3,15) (3,10) (3,22) (3,7) (3,17) (4,5) (4,13) (4,18) (4,15) (4,31) (4,17) (4,26) (5,21) (5,14) (5,19) (5,15) (5,22) (5,26) (6,28) (7,19) (7,13) (7,18) (7,10) (7,29) (7,17) (8,12) (8,24) (8,20) (8,18) (8,15) (8,26) (9,27) (9,24) (9,16) (9,13) (9,20) (9,18) (9,10) (9,26) (10,27) (10,12) (10,19) (10,18) (10,15) (10,23) (10,22) (10,11) (10,31) (10,29) (10,30) (11,27) (11,12) (11,24) (11,16) (11,20) (11,18) (11,22) (11,30) (12,18) (12,15) (12,31) (12,29) (12,17) (13,19) (13,16) (13,20) (13,23) (14,21) (14,16) (14,15) (14,30) (15,18) (15,22) (15,30) (15,26) (16,19) (16,29) (16,30) (17,18) (18,24) (18,23) (18,22) (19,20) (19,23) (20,24) (20,22) (21,27) (21,23) (21,30) (22,23) (23,31) (23,26) (24,27) (24,26) (25,28) (29,31)\nIs there a path between node 28 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph304-5_13", + "image": "data/connectivity/graph_visual/hard/graph304.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,5) (0,17) (0,24) (1,11) (1,9) (1,3) (2,19) (2,29) (2,27) (3,7) (3,20) (4,23) (4,25) (5,17) (6,22) (7,29) (7,27) (7,9) (8,16) (8,30) (8,26) (8,18) (8,31) (9,11) (9,27) (10,13) (10,12) (11,19) (11,27) (12,26) (12,18) (14,28) (15,27) (16,30) (17,23) (18,26) (19,28) (20,29) (21,22) (23,24) (24,25) (27,28) (30,31)\nIs there a path between node 5 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph584-6_3", + "image": "data/connectivity/graph_visual/hard/graph584.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,20) (0,12) (0,16) (1,29) (1,2) (1,14) (1,15) (1,5) (1,6) (1,13) (2,3) (2,6) (2,13) (3,29) (3,13) (4,20) (4,21) (4,7) (4,25) (4,26) (4,31) (5,14) (5,6) (6,14) (7,20) (7,16) (7,24) (7,25) (8,23) (8,30) (8,32) (8,27) (8,22) (8,9) (8,33) (8,11) (8,28) (9,23) (9,19) (9,30) (9,17) (9,10) (9,27) (9,18) (9,22) (9,33) (9,11) (9,28) (10,19) (10,30) (10,27) (10,18) (10,22) (10,33) (10,11) (10,28) (11,23) (11,19) (11,30) (11,17) (11,32) (11,27) (11,18) (11,22) (11,33) (11,28) (12,20) (12,21) (12,16) (12,24) (12,25) (12,26) (12,31) (13,29) (14,29) (14,15) (15,29) (16,20) (16,21) (16,24) (16,26) (16,31) (17,23) (17,30) (17,18) (17,22) (17,28) (18,23) (18,19) (18,30) (18,32) (18,27) (18,22) (18,33) (18,28) (19,23) (19,30) (19,32) (19,27) (19,33) (19,28) (20,21) (20,24) (20,25) (20,31) (21,24) (21,25) (21,31) (22,23) (22,30) (22,27) (22,33) (22,28) (23,30) (23,32) (23,28) (24,26) (24,31) (25,31) (26,31) (27,32) (27,33) (27,28) (28,30) (28,33) (30,32) (30,33) (32,33)\nIs there a path between node 6 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph16-21_16", + "image": "data/connectivity/graph_visual/hard/graph16.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (1,4) (1,11) (2,21) (2,20) (2,24) (3,24) (4,13) (4,15) (4,8) (5,19) (5,24) (6,20) (6,24) (7,25) (7,21) (8,17) (8,15) (8,12) (9,13) (9,12) (10,16) (11,13) (11,18) (11,23) (11,14) (11,12) (13,17) (14,23) (15,18) (15,23) (18,23) (19,25) (19,24) (20,21) (21,25) (24,25)\nIs there a path between node 21 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph257-29_18", + "image": "data/connectivity/graph_visual/hard/graph257.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,10) (0,8) (0,15) (0,12) (0,27) (0,23) (0,29) (1,20) (1,7) (1,27) (1,4) (1,2) (1,3) (1,5) (1,29) (2,15) (2,7) (2,27) (2,17) (2,26) (2,30) (3,27) (3,25) (3,13) (3,26) (3,29) (3,30) (4,7) (4,27) (4,23) (4,5) (4,29) (5,20) (5,8) (5,14) (5,12) (5,26) (5,21) (5,30) (6,16) (6,28) (6,22) (7,8) (7,27) (7,9) (7,17) (7,29) (7,30) (8,20) (8,23) (8,25) (8,13) (8,26) (9,12) (9,27) (10,14) (10,23) (11,24) (11,16) (12,27) (12,13) (13,14) (13,21) (13,29) (14,20) (14,27) (14,23) (15,23) (15,26) (16,24) (16,18) (17,23) (17,26) (18,28) (18,22) (19,22) (21,23) (23,26) (25,27) (25,26) (26,27) (26,29) (27,30)\nIs there a path between node 29 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph268-30_13", + "image": "data/connectivity/graph_visual/hard/graph268.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,5) (0,11) (0,22) (0,30) (0,25) (0,19) (0,12) (0,13) (0,10) (0,29) (1,17) (1,4) (1,18) (1,7) (1,27) (1,2) (1,3) (1,9) (1,23) (1,28) (2,4) (2,21) (2,26) (2,7) (2,27) (2,9) (2,23) (2,28) (3,17) (3,4) (3,21) (3,26) (3,18) (3,7) (3,27) (3,14) (3,9) (3,23) (3,28) (3,24) (4,17) (4,21) (4,26) (4,18) (4,14) (4,9) (4,28) (4,24) (5,11) (5,22) (5,20) (5,25) (5,29) (6,8) (7,21) (7,26) (7,18) (7,27) (7,23) (7,28) (7,24) (9,21) (9,26) (9,18) (9,27) (9,14) (9,23) (9,28) (9,24) (10,11) (10,22) (10,20) (10,30) (10,25) (10,16) (10,19) (10,15) (10,13) (10,29) (11,22) (11,20) (11,30) (11,25) (11,16) (11,19) (11,12) (11,15) (11,13) (11,29) (12,22) (12,20) (12,30) (12,16) (12,15) (12,13) (13,22) (13,20) (13,30) (13,25) (13,16) (13,19) (13,15) (13,29) (14,26) (14,18) (14,23) (14,28) (14,24) (15,22) (15,30) (15,16) (15,19) (15,29) (16,22) (16,30) (16,25) (16,19) (16,29) (17,26) (17,18) (17,27) (17,23) (17,28) (18,21) (18,26) (18,27) (18,24) (19,20) (19,30) (19,25) (19,29) (20,22) (20,25) (20,29) (21,26) (21,27) (21,28) (21,24) (22,30) (22,29) (23,26) (23,27) (23,28) (23,24) (24,27) (24,28) (25,29) (26,27) (27,28) (29,30)\nIs there a path between node 30 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph460-7_14", + "image": "data/connectivity/graph_visual/hard/graph460.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (0,16) (0,12) (0,2) (0,27) (0,30) (0,19) (0,28) (0,21) (0,13) (0,18) (1,5) (1,7) (1,4) (1,30) (1,24) (1,3) (2,5) (2,6) (2,22) (2,29) (2,19) (2,24) (2,21) (2,3) (3,31) (3,5) (3,16) (3,6) (3,12) (3,22) (3,29) (3,28) (3,24) (3,21) (3,18) (4,31) (4,16) (4,7) (4,23) (5,17) (5,22) (5,13) (6,32) (6,25) (6,19) (6,23) (6,15) (7,31) (7,25) (7,21) (7,13) (7,18) (8,26) (8,11) (10,12) (10,19) (10,13) (10,18) (11,20) (12,16) (12,27) (12,22) (12,30) (12,28) (12,21) (12,13) (12,15) (13,25) (13,27) (13,30) (13,19) (13,24) (13,18) (15,16) (15,22) (15,21) (15,18) (16,31) (16,32) (16,25) (16,22) (16,29) (16,24) (17,32) (17,19) (17,28) (17,21) (17,23) (18,32) (18,22) (18,19) (18,28) (18,21) (19,31) (19,27) (19,22) (19,29) (19,24) (19,21) (20,26) (21,32) (21,24) (22,31) (22,32) (23,31) (23,25) (23,27) (23,29) (24,25) (28,30) (31,32)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph338-22_12", + "image": "data/connectivity/graph_visual/hard/graph338.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (1,11) (1,9) (1,19) (1,31) (1,20) (2,15) (2,11) (2,27) (2,29) (2,16) (2,31) (3,8) (3,4) (3,12) (3,18) (3,17) (3,10) (3,25) (3,31) (3,20) (4,30) (4,24) (4,19) (5,26) (5,23) (6,13) (7,15) (7,9) (7,30) (7,12) (7,16) (7,19) (7,10) (7,25) (8,15) (8,11) (8,30) (8,24) (8,10) (8,31) (9,11) (9,30) (9,27) (9,29) (9,10) (10,15) (10,30) (10,12) (10,18) (10,19) (10,17) (10,14) (11,30) (11,29) (11,19) (12,15) (12,19) (12,14) (12,20) (13,28) (14,27) (14,24) (14,20) (15,27) (15,18) (15,25) (15,20) (16,29) (16,24) (16,19) (17,29) (17,19) (17,31) (18,30) (18,24) (18,19) (18,31) (19,30) (19,25) (21,28) (21,23) (22,23) (25,27) (25,31) (26,28) (29,31)\nIs there a path between node 22 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph420-20_6", + "image": "data/connectivity/graph_visual/hard/graph420.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,12) (0,5) (0,20) (0,28) (1,14) (1,27) (2,21) (2,16) (3,29) (3,31) (3,22) (3,17) (4,13) (4,9) (5,12) (5,32) (5,11) (6,14) (6,12) (6,32) (6,28) (7,10) (7,20) (7,27) (8,21) (8,15) (9,26) (9,31) (9,30) (9,17) (10,20) (10,28) (11,14) (11,12) (12,20) (12,32) (12,28) (13,29) (13,31) (13,22) (14,28) (15,16) (15,24) (16,19) (17,26) (17,18) (20,23) (21,24) (22,26) (22,31) (26,30)\nIs there a path between node 20 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph431-8_28", + "image": "data/connectivity/graph_visual/hard/graph431.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,3) (0,7) (0,5) (0,9) (0,25) (0,26) (0,15) (0,22) (0,13) (0,31) (0,1) (0,20) (1,3) (1,7) (1,5) (1,28) (1,9) (1,15) (1,22) (1,31) (1,30) (2,16) (2,17) (2,6) (2,14) (2,21) (2,32) (2,24) (2,8) (2,27) (2,10) (2,29) (2,19) (3,23) (3,18) (3,5) (3,28) (3,9) (3,25) (3,20) (3,30) (4,16) (4,17) (4,14) (4,21) (4,32) (4,12) (4,24) (4,8) (4,27) (4,10) (4,29) (4,11) (4,19) (5,23) (5,18) (5,7) (5,28) (5,9) (5,25) (5,26) (5,15) (5,22) (5,20) (5,30) (6,17) (6,14) (6,32) (6,12) (6,24) (6,8) (6,27) (6,19) (7,18) (7,9) (7,25) (7,26) (7,22) (7,13) (7,31) (7,20) (8,16) (8,17) (8,14) (8,32) (8,24) (8,27) (8,29) (8,19) (9,23) (9,18) (9,28) (9,25) (9,15) (9,22) (9,13) (9,31) (9,20) (10,16) (10,17) (10,21) (10,32) (10,12) (10,19) (11,16) (11,14) (11,21) (11,12) (11,24) (11,27) (11,29) (11,19) (12,16) (12,17) (12,14) (12,32) (12,27) (12,29) (12,19) (13,23) (13,18) (13,26) (13,15) (13,20) (13,30) (14,16) (14,32) (14,24) (14,27) (14,19) (15,23) (15,18) (15,28) (15,25) (15,26) (15,22) (15,31) (15,20) (16,17) (16,21) (16,32) (16,29) (17,21) (17,32) (17,24) (17,27) (17,29) (17,19) (18,25) (18,26) (18,22) (18,31) (18,30) (19,21) (19,32) (19,24) (19,27) (19,29) (20,28) (20,25) (20,26) (20,22) (20,31) (21,32) (21,24) (21,27) (22,23) (22,28) (22,25) (22,30) (23,28) (23,31) (23,30) (24,32) (24,29) (25,28) (25,26) (26,28) (26,30) (27,32) (27,29) (28,31) (28,30) (29,32)\nIs there a path between node 8 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph438-18_31", + "image": "data/connectivity/graph_visual/hard/graph438.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,27) (0,10) (0,6) (0,24) (0,30) (0,18) (0,19) (0,31) (0,16) (0,12) (1,25) (1,15) (1,17) (1,22) (1,2) (1,7) (1,3) (1,13) (1,9) (2,32) (2,25) (2,15) (2,17) (2,20) (2,29) (2,3) (2,11) (2,13) (2,9) (3,25) (3,15) (3,21) (3,4) (3,17) (3,20) (3,22) (3,29) (3,11) (4,32) (4,25) (4,20) (4,11) (4,13) (4,9) (6,27) (6,10) (6,30) (6,18) (6,31) (6,12) (6,8) (6,26) (6,28) (7,32) (7,25) (7,20) (7,29) (7,11) (7,13) (7,9) (8,27) (8,10) (8,24) (8,30) (8,18) (8,31) (8,12) (8,26) (9,25) (9,21) (9,17) (9,22) (9,29) (9,11) (9,13) (10,30) (10,31) (10,23) (10,12) (10,28) (11,32) (11,25) (11,15) (11,21) (11,17) (11,20) (11,22) (11,29) (11,13) (12,27) (12,24) (12,30) (12,19) (12,16) (12,23) (12,26) (12,28) (13,32) (13,25) (13,15) (13,21) (13,20) (13,29) (15,32) (15,25) (15,21) (15,17) (15,29) (16,24) (16,30) (16,18) (16,19) (16,31) (16,23) (16,26) (16,28) (17,21) (17,22) (17,29) (18,27) (18,24) (18,30) (18,31) (18,23) (19,24) (19,31) (19,23) (19,28) (20,32) (20,25) (20,21) (20,22) (21,32) (21,25) (21,22) (22,25) (23,24) (23,31) (23,28) (24,27) (24,31) (24,26) (24,28) (25,29) (26,30) (27,30) (27,31) (27,28) (28,31) (29,32) (30,31)\nIs there a path between node 18 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph669-27_33", + "image": "data/connectivity/graph_visual/hard/graph669.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,17) (0,33) (0,14) (1,18) (1,14) (2,28) (2,24) (2,25) (2,20) (2,31) (2,22) (2,8) (3,30) (3,23) (3,17) (3,29) (3,21) (4,7) (4,11) (4,31) (4,22) (4,8) (5,28) (5,9) (5,34) (5,22) (6,20) (6,9) (6,15) (6,8) (7,11) (7,16) (8,25) (8,20) (8,9) (8,31) (8,15) (8,22) (8,19) (9,28) (9,32) (9,11) (9,31) (10,32) (10,20) (10,15) (10,22) (10,19) (11,28) (11,31) (11,15) (11,34) (12,18) (12,23) (12,13) (13,23) (13,29) (13,33) (14,26) (14,17) (14,29) (14,33) (16,24) (16,32) (16,22) (17,30) (17,23) (18,26) (18,23) (18,29) (18,21) (21,26) (21,23) (22,34) (23,26) (24,28) (24,32) (25,28) (25,34) (28,32) (29,30)\nIs there a path between node 27 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph137-0_17", + "image": "data/connectivity/graph_visual/hard/graph137.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,16) (0,13) (0,1) (0,9) (0,5) (0,7) (0,3) (0,10) (0,23) (0,26) (0,27) (0,8) (0,14) (0,22) (0,20) (0,15) (0,4) (0,2) (1,25) (1,11) (1,21) (1,13) (1,9) (1,3) (1,10) (1,23) (1,26) (1,27) (1,14) (1,20) (1,15) (1,2) (1,28) (2,25) (2,11) (2,16) (2,21) (2,6) (2,13) (2,9) (2,7) (2,23) (2,26) (2,8) (2,20) (2,15) (3,25) (3,6) (3,13) (3,9) (3,10) (3,27) (3,20) (3,15) (3,4) (3,28) (4,11) (4,16) (4,6) (4,13) (4,10) (4,23) (4,26) (4,27) (4,8) (4,14) (4,22) (4,15) (4,28) (5,25) (5,16) (5,21) (5,6) (5,13) (5,9) (5,7) (5,26) (5,8) (5,22) (5,15) (5,28) (6,11) (6,16) (6,21) (6,13) (6,9) (6,7) (6,10) (6,27) (6,22) (6,20) (6,15) (7,25) (7,16) (7,21) (7,9) (7,10) (7,27) (7,8) (7,14) (7,22) (7,20) (7,15) (7,28) (8,25) (8,13) (8,23) (8,26) (8,27) (8,14) (8,20) (8,28) (9,25) (9,11) (9,16) (9,21) (9,10) (9,23) (9,26) (9,27) (9,22) (9,20) (9,28) (10,11) (10,16) (10,21) (10,13) (10,23) (10,26) (10,27) (10,14) (10,22) (10,20) (10,15) (10,28) (11,25) (11,16) (11,21) (11,13) (11,23) (11,26) (11,27) (11,14) (11,22) (11,20) (12,24) (12,19) (13,25) (13,16) (13,14) (13,22) (13,15) (13,28) (14,25) (14,21) (14,23) (14,26) (14,20) (14,15) (15,16) (15,21) (15,26) (15,27) (15,22) (15,28) (16,21) (16,23) (16,26) (16,27) (16,28) (17,18) (20,25) (20,23) (20,26) (20,27) (20,22) (20,28) (21,25) (21,23) (21,26) (21,22) (22,25) (22,23) (22,27) (23,25) (23,26) (23,27) (23,28) (25,26) (25,27) (26,27) (27,28)\nIs there a path between node 0 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph234-22_30", + "image": "data/connectivity/graph_visual/hard/graph234.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,9) (0,30) (0,6) (0,12) (1,15) (2,17) (2,4) (3,25) (3,30) (3,12) (4,18) (4,16) (4,20) (4,22) (4,28) (4,8) (4,17) (5,12) (5,11) (6,19) (7,9) (7,10) (8,22) (8,28) (8,21) (9,23) (10,12) (10,11) (11,30) (11,19) (11,12) (12,25) (12,19) (13,27) (13,26) (15,26) (16,18) (16,29) (16,20) (16,24) (16,22) (16,28) (16,17) (17,22) (17,28) (17,21) (18,29) (18,20) (18,24) (18,22) (19,30) (20,22) (20,28) (21,24) (24,28) (25,30)\nIs there a path between node 22 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph194-18_26", + "image": "data/connectivity/graph_visual/hard/graph194.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,28) (0,1) (0,22) (0,20) (0,15) (0,18) (0,2) (0,5) (0,10) (0,8) (0,14) (0,6) (1,27) (1,12) (1,19) (1,28) (1,25) (1,29) (1,22) (1,4) (1,7) (1,15) (1,18) (1,3) (1,2) (1,24) (1,5) (1,11) (1,14) (1,13) (1,6) (2,12) (2,19) (2,28) (2,29) (2,4) (2,15) (2,16) (2,18) (2,3) (2,10) (2,13) (2,21) (2,6) (3,27) (3,19) (3,28) (3,20) (3,4) (3,7) (3,16) (3,18) (3,9) (3,24) (3,5) (3,11) (3,10) (3,8) (3,14) (3,23) (3,21) (3,6) (4,27) (4,12) (4,19) (4,28) (4,25) (4,20) (4,7) (4,15) (4,16) (4,5) (4,8) (4,14) (4,13) (4,21) (4,6) (5,27) (5,12) (5,19) (5,28) (5,25) (5,29) (5,22) (5,20) (5,7) (5,15) (5,16) (5,24) (5,11) (5,10) (5,8) (5,14) (5,23) (5,13) (5,21) (5,6) (6,27) (6,12) (6,28) (6,25) (6,29) (6,22) (6,20) (6,7) (6,16) (6,18) (6,9) (6,24) (6,8) (6,14) (6,21) (7,19) (7,25) (7,29) (7,22) (7,20) (7,15) (7,16) (7,24) (7,11) (7,10) (7,14) (7,23) (7,21) (8,27) (8,12) (8,19) (8,29) (8,22) (8,20) (8,15) (8,16) (8,9) (8,24) (8,11) (8,10) (8,14) (8,13) (9,12) (9,19) (9,25) (9,22) (9,20) (9,18) (9,24) (9,11) (9,10) (9,14) (9,23) (9,13) (9,21) (10,27) (10,12) (10,19) (10,28) (10,25) (10,29) (10,16) (10,18) (10,24) (10,14) (10,23) (10,13) (10,21) (11,27) (11,12) (11,25) (11,22) (11,20) (11,18) (11,24) (12,19) (12,28) (12,29) (12,22) (12,15) (12,16) (12,18) (12,14) (12,23) (12,13) (12,21) (13,27) (13,28) (13,25) (13,29) (13,22) (13,20) (13,15) (13,18) (13,24) (14,19) (14,28) (14,25) (14,29) (14,15) (14,16) (14,18) (14,24) (14,23) (15,27) (15,28) (15,25) (15,29) (15,20) (15,18) (15,23) (15,21) (16,27) (16,19) (16,28) (16,25) (16,29) (16,22) (16,20) (16,18) (16,24) (16,21) (18,19) (18,28) (18,29) (18,22) (18,20) (18,24) (18,23) (18,21) (19,27) (19,28) (19,25) (19,29) (19,22) (19,20) (19,24) (19,23) (19,21) (20,27) (20,28) (20,29) (20,22) (20,23) (20,21) (21,27) (21,28) (21,24) (21,23) (22,27) (22,28) (22,29) (22,23) (23,27) (23,28) (23,25) (23,29) (24,27) (24,28) (24,25) (24,29) (25,27) (25,29) (27,28) (27,29)\nIs there a path between node 18 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph304-20_28", + "image": "data/connectivity/graph_visual/hard/graph304.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,5) (0,17) (0,24) (1,11) (1,9) (1,3) (2,19) (2,29) (2,27) (3,7) (3,20) (4,23) (4,25) (5,17) (6,22) (7,29) (7,27) (7,9) (8,16) (8,30) (8,26) (8,18) (8,31) (9,11) (9,27) (10,13) (10,12) (11,19) (11,27) (12,26) (12,18) (14,28) (15,27) (16,30) (17,23) (18,26) (19,28) (20,29) (21,22) (23,24) (24,25) (27,28) (30,31)\nIs there a path between node 20 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph579-7_2", + "image": "data/connectivity/graph_visual/hard/graph579.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,29) (0,12) (0,5) (0,30) (0,19) (0,21) (0,28) (1,17) (1,31) (1,6) (1,16) (1,2) (1,32) (1,4) (1,3) (1,18) (2,23) (2,17) (2,8) (2,6) (2,24) (2,16) (2,33) (2,13) (2,22) (2,3) (3,23) (3,17) (3,31) (3,8) (3,6) (3,24) (3,16) (3,33) (3,4) (3,18) (4,23) (4,17) (4,31) (4,6) (4,24) (4,33) (4,32) (5,29) (5,12) (5,21) (5,28) (5,11) (6,23) (6,17) (6,31) (6,8) (6,24) (6,16) (6,33) (6,13) (6,22) (6,32) (7,20) (7,26) (7,15) (7,14) (7,27) (7,25) (8,17) (8,31) (8,24) (8,33) (8,13) (8,22) (8,32) (8,18) (9,26) (9,15) (9,10) (9,14) (9,27) (9,25) (10,20) (10,26) (10,27) (10,25) (11,29) (11,12) (11,19) (11,28) (12,29) (12,30) (12,19) (12,21) (12,28) (13,23) (13,17) (13,31) (13,24) (13,16) (13,33) (13,22) (14,20) (14,15) (14,27) (14,25) (15,20) (15,26) (15,27) (15,25) (16,31) (16,33) (16,32) (16,18) (17,33) (18,23) (18,33) (18,22) (18,32) (19,29) (19,30) (19,21) (21,30) (22,31) (22,24) (22,33) (22,32) (23,31) (23,24) (23,33) (24,31) (24,33) (24,32) (25,26) (25,27) (26,27) (28,29) (29,30) (31,33) (31,32)\nIs there a path between node 7 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph605-16_19", + "image": "data/connectivity/graph_visual/hard/graph605.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,3) (0,18) (0,9) (1,3) (1,31) (1,23) (2,22) (2,5) (3,27) (3,20) (4,12) (4,22) (4,33) (4,10) (4,26) (5,22) (5,17) (5,33) (5,14) (6,32) (6,29) (7,26) (8,28) (8,25) (8,17) (9,34) (9,13) (10,28) (10,17) (10,16) (11,18) (11,13) (11,19) (12,24) (12,22) (12,17) (12,16) (13,31) (13,20) (14,28) (14,30) (14,17) (15,25) (15,30) (15,17) (16,30) (16,26) (18,27) (18,20) (20,23) (22,25) (22,30) (22,33) (22,26) (23,27) (25,28) (26,28) (28,33)\nIs there a path between node 16 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph351-16_1", + "image": "data/connectivity/graph_visual/hard/graph351.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,31) (0,26) (0,30) (0,17) (0,9) (0,11) (0,2) (0,12) (1,10) (1,31) (1,26) (1,17) (1,28) (1,3) (1,21) (2,20) (2,17) (2,3) (2,18) (2,21) (3,20) (3,19) (3,31) (3,26) (3,28) (4,29) (4,19) (4,26) (4,11) (4,28) (4,18) (4,12) (4,27) (5,19) (5,11) (5,28) (5,21) (5,27) (6,20) (6,19) (6,14) (6,16) (6,25) (6,26) (6,30) (7,10) (7,20) (7,14) (7,31) (7,30) (7,17) (7,28) (7,21) (7,27) (9,10) (9,16) (9,25) (9,17) (9,12) (10,20) (10,16) (10,30) (10,22) (10,11) (10,27) (11,29) (11,30) (12,29) (12,16) (12,22) (13,20) (13,14) (13,31) (13,27) (14,30) (14,17) (16,20) (16,19) (16,31) (17,29) (17,20) (17,26) (18,19) (18,31) (18,30) (18,28) (19,29) (19,22) (20,30) (20,22) (21,30) (21,27) (22,28) (25,28) (26,29) (27,28) (28,31) (28,30) (29,30) (30,31)\nIs there a path between node 16 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph572-23_8", + "image": "data/connectivity/graph_visual/hard/graph572.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,10) (0,4) (1,15) (1,11) (1,24) (1,5) (2,6) (2,7) (2,9) (2,30) (3,9) (3,20) (3,14) (3,23) (3,18) (4,10) (4,6) (4,29) (4,9) (4,17) (4,8) (4,23) (4,18) (4,30) (5,15) (5,22) (5,24) (6,10) (6,7) (6,14) (6,21) (6,30) (7,28) (7,29) (7,9) (7,27) (7,17) (7,21) (7,30) (8,10) (8,9) (8,27) (8,14) (8,23) (8,21) (9,10) (9,28) (9,27) (9,17) (10,28) (10,29) (10,18) (12,16) (12,31) (12,33) (13,19) (14,27) (14,17) (14,18) (15,24) (16,31) (16,33) (16,24) (17,29) (18,28) (18,30) (19,22) (20,27) (20,21) (21,28) (22,33) (22,24) (24,31) (24,33) (25,26)\nIs there a path between node 23 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph216-24_17", + "image": "data/connectivity/graph_visual/hard/graph216.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,8) (1,27) (1,21) (1,29) (1,26) (1,19) (1,10) (1,5) (2,4) (2,28) (2,13) (2,25) (2,17) (2,5) (3,6) (3,28) (3,15) (3,13) (3,18) (3,22) (3,7) (3,19) (3,17) (3,5) (3,16) (4,12) (4,6) (4,15) (4,21) (4,10) (4,5) (4,14) (4,16) (5,28) (5,27) (5,23) (5,22) (5,25) (5,10) (6,9) (6,15) (6,20) (6,18) (6,25) (6,17) (6,14) (7,15) (7,13) (7,18) (7,23) (7,25) (7,26) (7,19) (9,15) (9,27) (9,18) (9,23) (9,22) (9,26) (9,10) (10,15) (10,20) (10,27) (10,21) (10,22) (10,25) (10,19) (10,17) (10,14) (12,28) (12,18) (12,22) (12,14) (13,20) (13,27) (13,18) (13,23) (13,19) (13,17) (13,16) (14,18) (14,21) (14,19) (15,27) (15,19) (15,17) (16,27) (16,23) (16,25) (17,28) (17,18) (17,23) (17,21) (17,22) (17,29) (18,27) (18,26) (19,28) (20,28) (20,22) (20,29) (21,29) (21,25) (23,28) (23,27) (23,26) (25,28) (25,29) (26,27) (27,29) (28,29)\nIs there a path between node 24 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph386-6_20", + "image": "data/connectivity/graph_visual/hard/graph386.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,16) (0,20) (0,21) (0,24) (0,6) (0,31) (0,26) (0,2) (0,7) (0,14) (0,27) (0,11) (0,1) (1,16) (1,21) (1,24) (1,31) (1,18) (1,25) (1,26) (1,2) (1,7) (1,14) (1,27) (1,11) (1,10) (2,16) (2,20) (2,21) (2,24) (2,6) (2,31) (2,14) (2,27) (2,10) (3,15) (3,29) (3,4) (3,13) (3,8) (3,19) (3,5) (3,22) (4,30) (4,12) (4,17) (4,29) (4,13) (4,5) (4,22) (5,30) (5,12) (5,15) (5,28) (5,29) (5,19) (5,22) (5,23) (6,9) (6,16) (6,24) (6,31) (6,25) (6,7) (6,27) (6,11) (7,16) (7,21) (7,24) (7,18) (7,14) (7,11) (7,10) (8,12) (8,17) (8,15) (8,13) (8,19) (8,22) (8,23) (9,20) (9,21) (9,24) (9,31) (9,18) (9,26) (9,14) (10,21) (10,31) (10,18) (10,25) (10,26) (10,14) (10,27) (10,11) (11,16) (11,20) (11,21) (11,31) (11,18) (11,25) (11,26) (11,14) (12,28) (12,29) (12,13) (12,23) (13,30) (13,17) (13,15) (13,28) (13,19) (13,23) (14,20) (14,21) (14,31) (14,18) (14,25) (14,26) (14,27) (15,17) (15,28) (15,19) (15,23) (16,20) (16,21) (16,24) (16,18) (16,26) (17,30) (17,22) (17,23) (18,21) (18,31) (18,25) (18,27) (19,30) (19,28) (19,22) (19,23) (20,21) (20,31) (20,26) (20,27) (21,24) (21,31) (21,25) (21,26) (21,27) (22,30) (22,29) (23,30) (23,28) (23,29) (24,31) (24,25) (24,26) (25,31) (25,26) (25,27) (26,27) (27,31) (28,30) (28,29)\nIs there a path between node 6 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph50-10_0", + "image": "data/connectivity/graph_visual/hard/graph50.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,14) (0,17) (0,12) (0,9) (0,8) (1,11) (1,24) (1,15) (1,10) (1,13) (2,14) (2,17) (2,8) (2,3) (3,12) (4,15) (4,25) (4,6) (5,17) (5,12) (5,23) (6,11) (6,24) (6,20) (7,24) (7,20) (7,15) (7,18) (7,26) (8,9) (9,12) (10,20) (10,13) (11,24) (11,26) (11,13) (12,16) (13,26) (15,24) (15,20) (15,25) (15,22) (16,19) (16,21) (17,19) (17,23) (22,26) (24,25)\nIs there a path between node 10 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph171-10_12", + "image": "data/connectivity/graph_visual/hard/graph171.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,2) (0,24) (0,19) (0,5) (0,8) (0,9) (0,23) (0,22) (0,13) (0,20) (0,7) (1,11) (1,24) (1,6) (1,14) (1,17) (1,8) (1,9) (1,23) (1,22) (1,13) (1,20) (1,26) (2,21) (2,3) (2,11) (2,24) (2,6) (2,14) (2,23) (2,13) (2,28) (2,20) (2,15) (2,18) (3,21) (3,11) (3,24) (3,6) (3,14) (3,17) (3,8) (3,9) (3,23) (3,25) (3,28) (3,15) (3,18) (3,7) (5,21) (5,11) (5,24) (5,6) (5,14) (5,19) (5,8) (5,9) (5,13) (5,28) (5,15) (5,18) (5,7) (6,11) (6,24) (6,14) (6,19) (6,17) (6,23) (6,22) (6,13) (6,25) (6,28) (6,18) (6,7) (6,26) (7,21) (7,24) (7,14) (7,19) (7,17) (7,9) (7,23) (7,13) (7,25) (7,28) (7,20) (7,15) (8,21) (8,14) (8,19) (8,17) (8,9) (8,23) (8,22) (8,13) (8,25) (8,18) (8,26) (9,21) (9,24) (9,14) (9,19) (9,17) (9,23) (9,22) (9,25) (9,15) (9,18) (9,26) (10,16) (10,27) (11,21) (11,24) (11,14) (11,17) (11,23) (11,13) (11,25) (11,28) (11,15) (11,18) (11,26) (13,21) (13,14) (13,17) (13,22) (13,28) (13,20) (13,18) (13,26) (14,21) (14,23) (14,25) (14,20) (14,18) (15,21) (15,24) (15,19) (15,17) (15,23) (15,22) (15,25) (15,18) (15,26) (17,21) (17,24) (17,23) (17,22) (17,25) (17,28) (17,20) (17,18) (18,21) (18,24) (18,19) (18,23) (18,22) (18,25) (18,28) (18,20) (18,26) (19,21) (19,24) (19,23) (19,22) (19,25) (19,28) (19,20) (20,24) (20,23) (20,22) (20,25) (20,28) (20,26) (21,23) (21,22) (21,28) (21,26) (22,24) (22,23) (22,25) (22,26) (23,24) (23,25) (23,28) (23,26) (24,25) (24,26) (25,28) (25,26) (26,28)\nIs there a path between node 10 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph372-12_27", + "image": "data/connectivity/graph_visual/hard/graph372.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,15) (0,8) (0,20) (0,14) (0,1) (0,9) (0,29) (0,22) (0,28) (0,17) (0,5) (0,16) (0,2) (0,11) (0,6) (0,10) (0,31) (0,19) (1,13) (1,15) (1,8) (1,20) (1,9) (1,29) (1,7) (1,22) (1,28) (1,25) (1,12) (1,17) (1,21) (1,5) (1,16) (1,2) (1,18) (1,30) (1,11) (1,10) (1,31) (1,19) (2,13) (2,14) (2,9) (2,29) (2,22) (2,28) (2,25) (2,12) (2,27) (2,21) (2,5) (2,16) (2,18) (2,30) (2,11) (2,6) (2,10) (2,26) (2,31) (3,24) (4,13) (4,15) (4,8) (4,20) (4,14) (4,9) (4,29) (4,7) (4,22) (4,25) (4,27) (4,17) (4,16) (4,30) (4,11) (4,6) (4,10) (4,26) (5,13) (5,15) (5,20) (5,14) (5,9) (5,29) (5,7) (5,22) (5,28) (5,25) (5,12) (5,27) (5,17) (5,16) (5,18) (5,30) (5,6) (5,10) (5,26) (5,31) (5,19) (6,13) (6,15) (6,8) (6,20) (6,14) (6,9) (6,29) (6,7) (6,22) (6,28) (6,25) (6,12) (6,27) (6,17) (6,21) (6,10) (6,26) (6,19) (7,13) (7,15) (7,8) (7,28) (7,25) (7,12) (7,17) (7,18) (7,11) (7,10) (7,26) (7,31) (7,19) (8,9) (8,29) (8,22) (8,28) (8,25) (8,17) (8,21) (8,16) (8,18) (8,30) (8,11) (8,19) (9,13) (9,20) (9,14) (9,29) (9,22) (9,28) (9,25) (9,12) (9,17) (9,16) (9,30) (9,11) (9,10) (9,26) (10,13) (10,20) (10,14) (10,22) (10,28) (10,25) (10,12) (10,27) (10,17) (10,21) (10,16) (10,18) (10,11) (10,26) (10,31) (11,15) (11,14) (11,29) (11,22) (11,28) (11,25) (11,12) (11,27) (11,21) (11,16) (11,18) (11,26) (11,31) (11,19) (12,13) (12,15) (12,14) (12,29) (12,22) (12,28) (12,17) (12,16) (12,30) (12,26) (12,31) (12,19) (13,15) (13,20) (13,14) (13,29) (13,28) (13,25) (13,27) (13,16) (13,18) (13,30) (13,19) (14,29) (14,28) (14,25) (14,17) (14,21) (14,16) (14,18) (14,30) (14,26) (14,31) (14,19) (15,20) (15,29) (15,22) (15,28) (15,25) (15,27) (15,17) (15,16) (15,18) (15,31) (15,19) (16,29) (16,22) (16,28) (16,25) (16,27) (16,17) (16,21) (16,18) (16,30) (16,26) (16,31) (16,19) (17,20) (17,22) (17,28) (17,25) (17,27) (17,21) (17,18) (17,31) (18,20) (18,29) (18,22) (18,28) (18,25) (18,27) (18,21) (18,26) (18,31) (19,20) (19,29) (19,22) (19,28) (19,25) (19,27) (19,30) (19,26) (20,22) (20,28) (20,25) (20,27) (20,21) (20,30) (20,26) (20,31) (21,22) (21,28) (21,27) (21,30) (21,31) (22,29) (22,25) (22,30) (22,26) (23,24) (25,27) (25,26) (26,29) (26,30) (26,31) (27,29) (27,28) (27,30) (27,31) (28,30) (28,31) (29,30) (30,31)\nIs there a path between node 12 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph263-10_23", + "image": "data/connectivity/graph_visual/hard/graph263.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,5) (0,9) (0,3) (0,18) (0,26) (0,17) (0,4) (0,1) (0,10) (0,7) (0,22) (0,28) (0,15) (0,27) (1,11) (1,3) (1,29) (1,4) (1,7) (1,15) (1,27) (3,18) (3,6) (3,10) (3,25) (4,5) (4,11) (5,11) (5,20) (5,26) (5,10) (5,16) (5,15) (5,25) (6,19) (6,26) (6,14) (6,29) (6,30) (6,7) (6,22) (6,16) (6,15) (7,11) (7,20) (7,9) (7,18) (7,17) (7,29) (7,24) (7,30) (7,22) (7,27) (9,11) (9,26) (9,29) (9,16) (10,19) (10,26) (10,17) (10,27) (11,18) (11,26) (11,14) (11,27) (13,29) (13,25) (14,22) (14,25) (15,18) (15,22) (15,16) (15,25) (16,19) (16,17) (16,29) (16,30) (16,22) (16,28) (17,20) (17,18) (17,26) (17,24) (17,28) (17,25) (18,30) (18,22) (18,28) (18,25) (19,20) (19,24) (19,30) (20,22) (20,28) (22,30) (22,28) (24,30) (24,27) (25,28) (26,30) (27,29)\nIs there a path between node 10 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph264-14_13", + "image": "data/connectivity/graph_visual/hard/graph264.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,14) (0,8) (0,20) (0,23) (0,29) (0,15) (0,25) (0,24) (0,18) (1,2) (2,21) (3,8) (3,17) (3,20) (3,12) (3,10) (3,5) (4,26) (4,14) (4,22) (4,8) (4,12) (4,7) (4,10) (4,5) (5,22) (5,13) (5,8) (5,19) (5,17) (5,12) (5,6) (5,7) (5,24) (6,26) (6,22) (6,29) (6,24) (7,26) (7,11) (7,17) (7,20) (7,23) (7,15) (7,10) (7,24) (8,11) (8,13) (8,19) (8,17) (8,29) (8,15) (8,10) (8,25) (9,21) (10,26) (10,28) (10,17) (10,15) (10,25) (10,18) (11,22) (11,28) (11,20) (11,12) (11,29) (11,18) (12,14) (12,13) (12,28) (12,15) (12,25) (13,19) (13,25) (13,18) (14,20) (14,15) (14,25) (15,25) (16,30) (16,21) (17,19) (17,23) (17,29) (17,24) (17,18) (18,22) (18,23) (18,29) (18,25) (18,24) (19,24) (20,22) (20,23) (20,25) (22,26) (22,28) (23,24) (24,26) (25,29) (26,29)\nIs there a path between node 14 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph220-11_14", + "image": "data/connectivity/graph_visual/hard/graph220.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,16) (0,5) (0,6) (0,8) (0,4) (0,18) (0,9) (1,14) (1,11) (1,29) (1,26) (1,19) (1,27) (1,13) (1,22) (1,21) (1,15) (2,25) (2,10) (2,12) (2,20) (2,17) (2,7) (3,25) (3,10) (3,24) (3,12) (3,20) (4,28) (4,16) (4,6) (4,8) (4,18) (5,28) (5,16) (5,6) (5,8) (5,18) (5,9) (6,28) (6,16) (6,8) (6,18) (6,9) (7,25) (7,24) (7,12) (7,20) (7,17) (8,28) (8,9) (9,16) (9,18) (10,25) (10,24) (10,12) (10,20) (11,14) (11,29) (11,26) (11,27) (11,13) (11,22) (11,21) (11,15) (12,25) (12,17) (13,14) (13,26) (13,19) (13,27) (13,23) (13,21) (13,15) (14,19) (14,22) (14,21) (14,15) (15,26) (15,27) (15,22) (16,18) (17,25) (17,20) (19,29) (19,26) (19,23) (19,21) (20,25) (20,24) (21,29) (21,26) (21,23) (22,26) (22,27) (22,23) (23,29) (23,27) (24,25) (26,29)\nIs there a path between node 11 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph632-31_13", + "image": "data/connectivity/graph_visual/hard/graph632.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,24) (0,12) (0,2) (2,30) (2,22) (3,7) (3,23) (3,15) (3,30) (3,24) (4,11) (4,28) (5,19) (5,31) (5,24) (5,25) (6,19) (6,31) (6,22) (6,17) (7,18) (7,24) (8,14) (8,32) (8,33) (9,14) (10,32) (12,30) (13,19) (13,30) (13,31) (15,18) (15,19) (15,17) (16,29) (17,30) (17,31) (17,24) (17,25) (18,24) (18,22) (19,30) (20,26) (22,23) (22,31) (25,30) (26,27) (30,31)\nIs there a path between node 31 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph196-27_22", + "image": "data/connectivity/graph_visual/hard/graph196.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,29) (0,15) (0,3) (0,14) (0,27) (0,1) (0,25) (0,12) (0,26) (1,22) (1,15) (1,3) (1,14) (1,27) (1,16) (1,5) (1,12) (2,10) (2,23) (3,29) (3,22) (3,15) (3,14) (3,25) (3,5) (3,12) (4,19) (4,11) (4,18) (4,28) (4,17) (5,7) (5,25) (5,16) (5,12) (6,9) (6,18) (6,20) (6,28) (6,13) (7,29) (7,22) (7,15) (7,25) (7,16) (7,26) (8,24) (8,10) (9,21) (9,20) (9,17) (10,23) (11,19) (11,20) (11,28) (12,29) (12,22) (12,14) (12,27) (12,25) (12,26) (13,21) (13,18) (13,17) (14,29) (14,22) (14,15) (14,27) (14,25) (14,16) (14,26) (15,29) (15,25) (15,16) (15,26) (16,29) (16,25) (17,18) (17,28) (18,19) (18,21) (18,20) (19,21) (20,21) (21,28) (22,25) (22,26) (23,24) (25,27) (25,26) (26,29) (26,27) (27,29)\nIs there a path between node 27 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph323-26_9", + "image": "data/connectivity/graph_visual/hard/graph323.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,16) (0,1) (0,21) (0,27) (0,20) (0,7) (0,25) (0,23) (0,15) (0,17) (0,10) (0,2) (0,6) (0,11) (0,19) (0,4) (0,14) (0,9) (0,30) (0,29) (0,13) (1,16) (1,26) (1,21) (1,12) (1,27) (1,20) (1,7) (1,17) (1,10) (1,2) (1,6) (1,11) (1,4) (1,8) (1,14) (1,29) (1,13) (2,18) (2,16) (2,26) (2,21) (2,24) (2,12) (2,27) (2,20) (2,7) (2,22) (2,23) (2,15) (2,17) (2,11) (2,19) (2,4) (2,8) (2,14) (2,9) (2,29) (2,13) (3,31) (4,18) (4,16) (4,26) (4,21) (4,27) (4,7) (4,25) (4,22) (4,15) (4,10) (4,28) (4,11) (4,19) (4,14) (4,9) (4,30) (4,29) (6,18) (6,16) (6,12) (6,20) (6,25) (6,23) (6,15) (6,17) (6,10) (6,28) (6,11) (6,19) (6,14) (6,9) (6,29) (7,16) (7,26) (7,21) (7,24) (7,12) (7,27) (7,20) (7,25) (7,22) (7,23) (7,15) (7,10) (7,28) (7,11) (7,19) (7,8) (7,9) (7,30) (7,13) (8,16) (8,21) (8,27) (8,20) (8,25) (8,23) (8,15) (8,17) (8,10) (8,11) (8,14) (8,29) (8,13) (9,18) (9,16) (9,21) (9,24) (9,27) (9,22) (9,23) (9,17) (9,10) (9,28) (9,19) (9,14) (9,30) (9,29) (9,13) (10,18) (10,16) (10,26) (10,21) (10,12) (10,27) (10,20) (10,25) (10,22) (10,23) (10,15) (10,11) (10,19) (10,29) (10,13) (11,18) (11,16) (11,26) (11,21) (11,24) (11,12) (11,20) (11,22) (11,23) (11,15) (11,17) (11,30) (11,13) (12,18) (12,16) (12,26) (12,21) (12,24) (12,27) (12,20) (12,25) (12,22) (12,23) (12,17) (12,28) (12,19) (12,30) (12,29) (12,13) (13,18) (13,16) (13,21) (13,24) (13,20) (13,25) (13,22) (13,23) (13,15) (13,17) (13,28) (13,19) (13,30) (13,29) (14,18) (14,16) (14,26) (14,24) (14,27) (14,20) (14,25) (14,23) (14,15) (14,17) (14,28) (14,19) (14,30) (14,29) (15,18) (15,26) (15,21) (15,24) (15,27) (15,20) (15,25) (15,23) (15,28) (15,30) (16,18) (16,26) (16,24) (16,27) (16,20) (16,25) (16,22) (16,23) (16,28) (16,30) (16,29) (17,18) (17,21) (17,24) (17,27) (17,25) (17,23) (17,28) (17,30) (18,26) (18,27) (18,20) (18,23) (18,28) (18,19) (18,30) (18,29) (19,26) (19,24) (19,27) (19,20) (19,25) (19,22) (19,23) (19,28) (19,30) (19,29) (20,26) (20,25) (20,22) (20,23) (20,28) (20,30) (20,29) (21,26) (21,24) (21,23) (21,28) (21,29) (22,26) (22,24) (22,27) (22,25) (22,23) (22,28) (22,30) (22,29) (23,26) (23,27) (23,25) (23,28) (23,30) (24,26) (24,25) (25,26) (25,27) (25,28) (25,29) (26,27) (26,28) (26,30) (26,29) (27,30) (27,29) (28,29)\nIs there a path between node 26 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph485-23_31", + "image": "data/connectivity/graph_visual/hard/graph485.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,7) (0,31) (0,25) (0,22) (0,24) (0,23) (0,5) (0,9) (0,21) (0,30) (1,26) (1,14) (1,7) (1,6) (1,31) (1,24) (1,23) (1,9) (1,21) (1,30) (2,27) (2,20) (2,12) (2,19) (2,32) (2,28) (2,13) (2,17) (3,26) (3,11) (3,18) (3,7) (3,31) (3,25) (3,22) (3,23) (3,5) (3,9) (3,21) (3,30) (4,27) (4,20) (4,12) (4,19) (4,28) (4,17) (4,29) (5,26) (5,11) (5,14) (5,18) (5,7) (5,6) (5,31) (5,22) (5,24) (5,23) (5,21) (5,30) (6,26) (6,11) (6,18) (6,7) (6,31) (6,25) (6,22) (6,23) (7,11) (7,18) (7,31) (7,25) (7,22) (7,23) (7,9) (8,16) (8,10) (8,15) (9,26) (9,11) (9,18) (9,25) (9,24) (9,23) (9,21) (9,30) (10,16) (11,26) (11,14) (11,31) (11,25) (11,23) (11,21) (11,30) (12,19) (12,28) (12,13) (12,17) (12,29) (13,27) (13,19) (13,32) (13,28) (13,17) (13,29) (14,18) (14,25) (14,22) (14,24) (14,23) (14,21) (14,30) (17,27) (17,19) (17,32) (17,28) (17,29) (18,31) (18,25) (18,22) (18,23) (18,21) (19,27) (19,32) (19,28) (19,29) (20,27) (20,32) (20,28) (20,29) (21,22) (21,24) (21,23) (22,26) (22,31) (22,24) (22,23) (22,30) (23,26) (23,31) (23,25) (24,31) (24,25) (25,26) (26,31) (27,32) (27,29) (29,32)\nIs there a path between node 23 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph365-31_13", + "image": "data/connectivity/graph_visual/hard/graph365.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,29) (0,27) (0,31) (0,21) (0,10) (0,5) (0,11) (0,19) (0,18) (0,6) (0,20) (0,26) (1,14) (1,22) (1,23) (1,9) (1,28) (1,25) (1,12) (1,13) (1,2) (1,30) (2,23) (2,9) (2,28) (2,25) (2,12) (2,13) (3,15) (3,7) (3,17) (3,16) (4,29) (4,27) (4,31) (4,10) (4,5) (4,11) (4,20) (4,26) (5,29) (5,27) (5,24) (5,31) (5,19) (5,18) (5,26) (6,29) (6,27) (6,24) (6,31) (6,21) (6,11) (6,19) (6,18) (6,20) (7,15) (7,16) (8,15) (8,17) (8,16) (9,22) (9,23) (9,28) (9,25) (9,12) (9,13) (9,30) (10,29) (10,24) (10,31) (10,11) (10,19) (10,20) (11,29) (11,27) (11,24) (11,31) (11,18) (11,20) (12,14) (12,22) (12,13) (12,30) (13,22) (13,23) (13,28) (13,25) (13,30) (14,22) (14,28) (14,25) (14,30) (16,17) (18,29) (18,27) (18,24) (18,31) (18,19) (19,29) (19,24) (19,31) (19,21) (19,20) (19,26) (20,27) (20,24) (20,31) (20,21) (21,29) (21,27) (21,24) (21,26) (23,25) (24,27) (24,26) (25,30) (26,29) (26,27) (26,31) (27,29) (27,31) (28,30) (29,31)\nIs there a path between node 31 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph112-10_9", + "image": "data/connectivity/graph_visual/hard/graph112.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,22) (0,11) (0,10) (0,23) (0,4) (0,9) (0,19) (1,17) (1,27) (1,15) (1,23) (1,24) (1,5) (1,18) (2,15) (2,10) (2,23) (2,5) (2,6) (2,16) (4,17) (4,27) (4,16) (4,25) (5,27) (5,11) (5,24) (5,7) (5,16) (5,25) (5,21) (5,18) (6,17) (6,13) (6,27) (6,11) (6,10) (6,14) (6,16) (6,8) (6,19) (7,20) (7,15) (7,10) (7,24) (7,16) (7,8) (7,19) (7,25) (7,21) (8,20) (8,17) (8,27) (8,11) (8,24) (8,16) (9,20) (9,27) (9,11) (9,16) (9,25) (10,13) (10,27) (10,15) (10,16) (11,20) (11,13) (11,14) (11,24) (11,21) (13,20) (13,14) (13,16) (14,22) (14,15) (14,23) (14,19) (15,24) (15,19) (15,25) (16,22) (16,17) (16,23) (17,22) (17,23) (17,25) (18,19) (18,21) (19,27) (19,24) (19,25) (21,25) (23,27) (25,27)\nIs there a path between node 10 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph432-28_31", + "image": "data/connectivity/graph_visual/hard/graph432.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (0,28) (0,2) (0,26) (0,6) (0,8) (0,10) (0,16) (0,5) (0,21) (0,7) (0,24) (0,27) (1,9) (1,15) (1,17) (1,30) (1,3) (1,31) (1,25) (2,23) (2,28) (2,26) (2,6) (2,8) (2,18) (2,10) (2,16) (2,21) (2,7) (2,24) (3,13) (3,9) (3,15) (3,17) (3,12) (3,30) (3,31) (3,25) (4,20) (4,32) (4,29) (4,22) (4,14) (4,11) (5,28) (5,6) (5,18) (5,24) (5,27) (6,23) (6,28) (6,8) (6,18) (6,16) (6,7) (6,24) (6,27) (7,23) (7,28) (7,26) (7,8) (7,10) (7,21) (7,24) (7,27) (8,26) (8,18) (8,16) (8,21) (8,24) (8,27) (9,17) (9,12) (9,30) (9,31) (10,23) (10,26) (10,18) (10,16) (10,21) (11,29) (11,22) (11,14) (12,13) (12,17) (12,30) (12,31) (13,15) (13,17) (13,25) (14,20) (14,32) (14,29) (14,19) (14,22) (15,17) (15,31) (15,25) (16,23) (16,21) (16,24) (17,30) (17,31) (17,25) (18,23) (18,28) (18,26) (18,21) (18,24) (18,27) (19,20) (19,32) (19,29) (19,22) (20,29) (20,22) (21,26) (22,32) (22,29) (23,28) (23,26) (23,27) (24,28) (24,26) (24,27) (25,30) (25,31) (26,27) (27,28) (29,32)\nIs there a path between node 28 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph461-5_14", + "image": "data/connectivity/graph_visual/hard/graph461.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,10) (0,23) (0,27) (0,9) (1,16) (1,3) (1,4) (1,21) (1,26) (1,2) (2,31) (2,16) (2,15) (2,6) (2,17) (3,24) (3,8) (3,19) (3,16) (3,30) (3,5) (3,4) (3,15) (3,7) (3,11) (4,24) (4,8) (4,30) (4,21) (4,12) (4,26) (4,7) (4,11) (5,21) (5,6) (5,26) (6,30) (6,21) (6,11) (7,24) (8,31) (8,24) (8,19) (8,12) (9,27) (10,18) (10,23) (10,14) (11,31) (11,24) (11,21) (12,24) (12,19) (12,30) (12,15) (12,21) (13,32) (13,18) (13,29) (14,32) (14,23) (15,19) (15,16) (16,24) (16,19) (17,19) (18,32) (18,23) (18,28) (19,24) (19,30) (19,26) (21,31) (21,30) (21,26) (26,30) (27,32) (28,32) (30,31)\nIs there a path between node 5 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph551-29_11", + "image": "data/connectivity/graph_visual/hard/graph551.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,21) (0,30) (0,19) (0,25) (1,24) (1,18) (1,19) (1,31) (1,25) (1,26) (2,22) (2,23) (3,8) (3,13) (3,10) (5,14) (6,24) (6,8) (6,9) (6,13) (6,10) (6,28) (6,15) (7,11) (8,30) (8,9) (8,13) (8,26) (9,24) (9,16) (9,30) (9,10) (9,27) (10,18) (10,28) (10,15) (11,22) (11,29) (13,18) (13,21) (14,17) (15,18) (15,30) (15,19) (15,33) (15,31) (15,27) (15,26) (16,30) (16,19) (16,27) (18,30) (18,19) (18,28) (18,27) (19,24) (19,33) (19,28) (20,22) (20,29) (21,33) (21,25) (21,27) (23,32) (24,30) (24,28) (24,31) (25,31) (26,30) (26,28) (28,30) (31,33)\nIs there a path between node 29 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph235-21_17", + "image": "data/connectivity/graph_visual/hard/graph235.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,29) (0,27) (0,23) (0,4) (0,20) (0,17) (0,6) (1,5) (1,22) (1,11) (1,19) (1,24) (1,2) (1,15) (1,8) (1,30) (1,9) (1,28) (1,18) (2,5) (2,22) (2,24) (2,15) (2,8) (2,30) (2,9) (2,28) (2,18) (3,26) (3,13) (4,21) (4,29) (4,23) (4,20) (4,17) (4,6) (5,22) (5,19) (5,24) (5,14) (5,30) (5,28) (5,18) (6,21) (6,29) (6,27) (6,23) (6,20) (6,17) (7,26) (7,10) (7,13) (7,16) (7,12) (8,11) (8,24) (8,14) (8,30) (8,9) (8,28) (8,18) (9,22) (9,11) (9,19) (9,15) (9,28) (10,16) (10,12) (11,15) (11,30) (11,28) (11,18) (12,13) (12,16) (13,26) (13,16) (13,25) (14,22) (14,19) (14,15) (14,30) (15,19) (15,30) (15,28) (15,18) (16,26) (16,25) (17,29) (17,23) (18,19) (18,24) (18,28) (19,30) (19,28) (20,21) (20,27) (21,29) (21,27) (21,23) (22,24) (22,28) (23,27) (24,30) (24,28) (25,26) (28,30)\nIs there a path between node 21 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph613-24_30", + "image": "data/connectivity/graph_visual/hard/graph613.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,13) (0,19) (0,6) (0,21) (0,10) (0,31) (0,16) (0,7) (0,20) (0,8) (0,17) (0,12) (0,3) (0,11) (0,23) (0,2) (0,22) (0,1) (0,18) (1,33) (1,32) (1,13) (1,19) (1,29) (1,26) (1,27) (1,6) (1,21) (1,10) (1,31) (1,16) (1,28) (1,7) (1,20) (1,8) (1,17) (1,12) (1,3) (1,2) (1,14) (1,22) (1,18) (1,5) (2,33) (2,13) (2,19) (2,29) (2,26) (2,27) (2,6) (2,10) (2,31) (2,16) (2,28) (2,7) (2,20) (2,24) (2,8) (2,17) (2,12) (2,22) (2,18) (3,32) (3,29) (3,27) (3,6) (3,21) (3,31) (3,16) (3,28) (3,7) (3,20) (3,8) (3,12) (3,23) (3,14) (3,22) (3,18) (3,5) (4,25) (4,34) (5,33) (5,32) (5,13) (5,19) (5,29) (5,26) (5,27) (5,6) (5,21) (5,10) (5,31) (5,16) (5,28) (5,20) (5,8) (5,12) (5,11) (5,23) (5,14) (5,22) (5,18) (6,32) (6,13) (6,19) (6,26) (6,27) (6,21) (6,10) (6,16) (6,28) (6,7) (6,20) (6,17) (6,12) (6,11) (6,23) (6,14) (6,22) (6,18) (7,32) (7,13) (7,29) (7,27) (7,21) (7,10) (7,16) (7,28) (7,20) (7,24) (7,17) (7,12) (7,11) (7,23) (7,14) (7,22) (7,18) (8,33) (8,32) (8,13) (8,19) (8,29) (8,26) (8,21) (8,10) (8,31) (8,16) (8,28) (8,20) (8,24) (8,17) (8,12) (8,11) (8,23) (8,14) (8,22) (8,18) (9,25) (9,34) (9,15) (9,30) (10,33) (10,32) (10,13) (10,19) (10,29) (10,26) (10,27) (10,16) (10,28) (10,12) (10,11) (10,14) (10,22) (11,33) (11,32) (11,13) (11,19) (11,29) (11,21) (11,28) (11,20) (11,24) (11,17) (11,12) (11,23) (11,14) (11,22) (11,18) (12,33) (12,32) (12,13) (12,19) (12,29) (12,26) (12,31) (12,16) (12,28) (12,20) (12,23) (12,18) (13,33) (13,32) (13,19) (13,29) (13,26) (13,27) (13,21) (13,31) (13,16) (13,28) (13,20) (13,17) (13,23) (13,14) (13,18) (14,33) (14,32) (14,19) (14,29) (14,26) (14,27) (14,21) (14,31) (14,16) (14,28) (14,20) (14,17) (14,22) (15,25) (15,30) (16,33) (16,32) (16,19) (16,29) (16,26) (16,27) (16,21) (16,31) (16,28) (16,20) (16,24) (16,17) (16,23) (16,22) (17,33) (17,32) (17,19) (17,29) (17,21) (17,28) (17,20) (17,24) (17,23) (17,22) (17,18) (18,32) (18,19) (18,29) (18,26) (18,27) (18,21) (18,31) (18,28) (18,24) (18,23) (18,22) (19,29) (19,27) (19,21) (19,31) (19,28) (19,20) (19,23) (20,33) (20,29) (20,26) (20,31) (20,28) (20,22) (21,33) (21,32) (21,29) (21,31) (21,24) (21,23) (22,29) (22,31) (22,24) (23,29) (23,26) (23,27) (23,31) (23,28) (23,24) (24,32) (24,26) (24,27) (24,31) (25,34) (26,32) (26,29) (26,27) (26,31) (26,28) (27,33) (27,29) (27,31) (28,33) (28,31) (29,33) (29,32) (30,34) (31,33) (31,32) (32,33)\nIs there a path between node 24 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph174-25_5", + "image": "data/connectivity/graph_visual/hard/graph174.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,1) (0,25) (0,17) (0,8) (0,9) (0,7) (0,10) (0,11) (0,6) (0,15) (0,27) (0,16) (0,24) (1,25) (1,17) (1,8) (1,10) (1,11) (1,15) (1,27) (1,16) (1,24) (2,18) (2,21) (2,23) (2,5) (2,26) (2,3) (3,21) (3,23) (4,22) (4,20) (4,28) (4,12) (4,14) (5,18) (5,19) (6,25) (6,17) (6,8) (6,7) (6,11) (6,16) (6,24) (6,13) (7,8) (7,9) (7,10) (7,27) (7,16) (7,24) (8,25) (8,17) (8,10) (8,27) (8,24) (9,25) (9,17) (9,10) (9,11) (9,15) (9,27) (9,16) (9,24) (9,13) (10,25) (10,16) (10,24) (10,13) (11,25) (11,15) (11,27) (11,16) (11,13) (12,22) (13,25) (13,17) (13,27) (13,16) (13,24) (14,22) (14,20) (14,28) (15,17) (15,27) (15,16) (15,24) (16,25) (16,17) (17,25) (17,27) (18,23) (18,19) (18,26) (19,21) (19,23) (20,22) (21,23) (21,26) (22,28) (24,25) (24,27) (25,27)\nIs there a path between node 25 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph220-13_3", + "image": "data/connectivity/graph_visual/hard/graph220.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,16) (0,5) (0,6) (0,8) (0,4) (0,18) (0,9) (1,14) (1,11) (1,29) (1,26) (1,19) (1,27) (1,13) (1,22) (1,21) (1,15) (2,25) (2,10) (2,12) (2,20) (2,17) (2,7) (3,25) (3,10) (3,24) (3,12) (3,20) (4,28) (4,16) (4,6) (4,8) (4,18) (5,28) (5,16) (5,6) (5,8) (5,18) (5,9) (6,28) (6,16) (6,8) (6,18) (6,9) (7,25) (7,24) (7,12) (7,20) (7,17) (8,28) (8,9) (9,16) (9,18) (10,25) (10,24) (10,12) (10,20) (11,14) (11,29) (11,26) (11,27) (11,13) (11,22) (11,21) (11,15) (12,25) (12,17) (13,14) (13,26) (13,19) (13,27) (13,23) (13,21) (13,15) (14,19) (14,22) (14,21) (14,15) (15,26) (15,27) (15,22) (16,18) (17,25) (17,20) (19,29) (19,26) (19,23) (19,21) (20,25) (20,24) (21,29) (21,26) (21,23) (22,26) (22,27) (22,23) (23,29) (23,27) (24,25) (26,29)\nIs there a path between node 13 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph518-1_0", + "image": "data/connectivity/graph_visual/hard/graph518.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,7) (0,25) (0,10) (0,9) (0,17) (0,16) (0,1) (0,15) (1,28) (1,8) (1,16) (1,3) (1,29) (1,31) (2,5) (2,4) (3,28) (3,32) (3,15) (3,20) (4,21) (4,14) (5,21) (5,14) (6,7) (6,28) (6,24) (6,19) (6,33) (6,23) (6,8) (6,29) (6,31) (7,25) (7,22) (7,15) (8,28) (8,25) (8,33) (8,10) (8,22) (8,17) (8,23) (8,26) (8,15) (9,28) (9,33) (9,10) (9,32) (9,17) (9,12) (9,29) (10,11) (10,25) (10,18) (10,19) (10,17) (10,26) (10,12) (10,20) (10,29) (10,31) (11,30) (11,20) (12,22) (12,32) (12,15) (12,20) (12,31) (13,14) (15,32) (15,17) (15,29) (16,19) (16,33) (16,17) (16,20) (16,29) (17,25) (17,18) (17,32) (18,33) (18,32) (18,29) (19,28) (19,30) (19,23) (19,29) (19,31) (20,30) (22,28) (22,30) (23,28) (23,25) (23,31) (24,28) (24,30) (25,28) (25,33) (25,29) (28,32) (29,33) (29,31) (31,33)\nIs there a path between node 1 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph529-2_20", + "image": "data/connectivity/graph_visual/hard/graph529.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,5) (1,21) (2,26) (2,15) (2,14) (2,20) (2,28) (2,12) (3,29) (3,19) (3,22) (3,21) (4,33) (4,32) (4,9) (4,20) (4,28) (4,7) (4,27) (5,23) (5,17) (5,6) (6,25) (7,32) (7,15) (7,9) (7,11) (7,18) (8,19) (8,22) (8,16) (9,28) (9,27) (10,30) (10,33) (10,32) (10,20) (11,13) (11,12) (12,30) (12,13) (12,33) (12,32) (12,15) (12,28) (12,31) (12,27) (12,18) (13,33) (13,32) (13,20) (14,26) (14,20) (15,26) (15,27) (15,18) (16,29) (16,22) (17,23) (17,24) (18,20) (18,28) (18,31) (19,22) (19,21) (20,33) (20,31) (20,27) (23,24) (26,33) (26,31) (26,27) (27,33) (28,33) (28,31) (30,33) (32,33)\nIs there a path between node 2 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph631-15_1", + "image": "data/connectivity/graph_visual/hard/graph631.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,16) (1,33) (1,17) (1,12) (1,25) (1,7) (1,18) (1,32) (1,11) (1,10) (1,15) (1,9) (1,5) (1,26) (1,4) (2,19) (2,33) (2,18) (2,30) (3,34) (3,31) (3,14) (3,6) (3,17) (3,11) (3,22) (3,29) (3,15) (3,24) (3,30) (4,16) (4,6) (4,12) (4,32) (4,24) (5,31) (5,16) (5,8) (5,23) (5,24) (5,21) (6,19) (6,33) (6,25) (6,11) (6,10) (6,24) (6,30) (7,12) (7,15) (7,9) (7,30) (8,17) (8,12) (8,32) (8,22) (8,29) (8,24) (8,30) (9,16) (9,14) (9,12) (9,25) (9,18) (9,23) (9,26) (10,31) (10,14) (10,19) (10,25) (10,32) (10,22) (10,23) (10,21) (11,34) (11,14) (11,17) (11,27) (11,25) (11,18) (11,26) (14,19) (14,33) (14,25) (14,18) (14,30) (14,26) (14,21) (15,34) (15,31) (15,33) (15,32) (15,24) (15,26) (15,21) (16,34) (16,22) (16,29) (16,24) (16,26) (17,31) (17,18) (17,23) (17,26) (18,22) (18,26) (19,33) (19,27) (19,25) (19,29) (19,26) (21,34) (21,31) (21,33) (21,25) (21,22) (21,24) (21,30) (22,34) (22,29) (22,24) (23,33) (23,27) (23,32) (24,33) (24,27) (24,32) (25,34) (25,31) (26,29) (27,34) (27,33) (29,31) (29,33) (29,30) (30,31) (31,34)\nIs there a path between node 15 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph215-16_24", + "image": "data/connectivity/graph_visual/hard/graph215.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,11) (0,27) (0,29) (1,16) (1,11) (1,20) (1,14) (2,8) (2,18) (2,15) (2,11) (2,27) (2,19) (2,25) (2,29) (3,5) (4,8) (4,24) (4,23) (4,26) (4,13) (4,7) (4,28) (4,6) (4,20) (4,19) (6,15) (6,27) (6,25) (7,22) (7,24) (7,23) (7,26) (7,13) (7,28) (7,29) (8,18) (8,26) (8,12) (9,17) (11,22) (11,24) (11,28) (11,20) (12,22) (12,15) (12,28) (12,27) (12,20) (12,29) (13,16) (13,23) (13,28) (13,27) (13,20) (13,19) (14,19) (15,28) (15,25) (16,26) (16,25) (18,20) (18,29) (19,23) (19,20) (20,24) (20,26) (20,28) (20,27) (20,25) (22,23) (22,28) (22,29) (23,24) (23,26) (23,29) (24,27) (25,27) (26,29) (27,28)\nIs there a path between node 16 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph618-29_22", + "image": "data/connectivity/graph_visual/hard/graph618.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,34) (0,19) (0,17) (0,16) (0,31) (0,2) (0,7) (0,25) (0,22) (0,14) (1,28) (1,19) (1,16) (1,31) (1,8) (1,2) (1,7) (1,25) (1,14) (1,15) (2,28) (2,19) (2,17) (2,3) (2,31) (2,8) (2,7) (2,25) (2,20) (2,22) (2,14) (3,34) (3,19) (3,17) (3,16) (3,31) (3,7) (3,25) (3,22) (3,14) (4,18) (4,10) (4,24) (4,11) (4,6) (4,12) (4,26) (4,27) (4,13) (4,30) (4,21) (4,29) (5,18) (5,9) (5,11) (5,6) (5,26) (5,27) (5,30) (5,29) (6,18) (6,9) (6,24) (6,33) (6,12) (6,23) (6,27) (6,30) (7,34) (7,19) (7,16) (7,31) (7,8) (7,20) (7,14) (7,15) (8,28) (8,17) (8,16) (8,31) (8,25) (8,15) (9,18) (9,10) (9,24) (9,11) (9,33) (9,12) (9,32) (9,23) (9,13) (9,30) (9,29) (10,18) (10,24) (10,11) (10,33) (10,12) (10,32) (10,13) (10,30) (10,21) (10,29) (11,18) (11,12) (11,32) (11,23) (11,26) (11,27) (11,13) (11,30) (11,21) (12,18) (12,24) (12,33) (12,32) (12,23) (12,26) (12,27) (12,13) (12,21) (12,29) (13,18) (13,24) (13,33) (13,32) (13,23) (13,26) (13,27) (13,29) (14,34) (14,28) (14,19) (14,25) (14,22) (14,15) (15,34) (15,28) (15,19) (15,17) (15,16) (15,25) (15,20) (16,28) (16,31) (16,25) (16,22) (17,28) (17,19) (17,31) (17,25) (17,20) (17,22) (18,33) (18,32) (18,23) (18,26) (18,27) (19,34) (19,31) (19,22) (20,34) (20,31) (20,25) (20,22) (21,24) (21,33) (21,32) (21,27) (21,30) (21,29) (22,28) (22,31) (22,25) (23,24) (23,33) (23,32) (23,26) (23,27) (23,30) (24,32) (24,27) (24,30) (24,29) (25,28) (26,32) (26,27) (26,29) (28,34) (28,31) (29,32) (29,30) (30,33) (30,32) (31,34) (32,33)\nIs there a path between node 29 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph66-12_7", + "image": "data/connectivity/graph_visual/hard/graph66.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,23) (0,10) (0,15) (0,1) (0,24) (1,17) (1,11) (1,23) (1,18) (1,13) (1,6) (1,24) (2,25) (3,21) (3,18) (3,10) (3,13) (3,20) (3,24) (5,21) (5,12) (5,23) (5,15) (5,6) (5,24) (6,7) (6,17) (6,13) (6,19) (6,24) (7,16) (7,15) (7,19) (7,24) (8,25) (8,26) (9,26) (10,13) (11,23) (12,21) (12,18) (13,17) (13,15) (13,22) (13,19) (15,20) (16,22) (17,18) (17,22) (19,20) (19,24) (20,21) (21,22) (23,24)\nIs there a path between node 12 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph562-31_19", + "image": "data/connectivity/graph_visual/hard/graph562.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,27) (0,10) (0,8) (0,23) (1,2) (1,21) (1,17) (1,31) (2,6) (2,33) (2,9) (2,3) (2,21) (2,7) (2,16) (3,17) (3,24) (3,5) (4,32) (4,22) (4,12) (5,33) (5,28) (6,24) (6,26) (6,19) (6,16) (6,28) (7,33) (7,24) (7,13) (8,27) (9,31) (9,16) (9,13) (10,27) (10,29) (10,20) (10,12) (11,32) (12,29) (12,22) (13,15) (13,21) (13,26) (13,19) (13,18) (15,21) (16,24) (16,26) (16,18) (17,21) (17,28) (18,33) (18,21) (18,26) (19,21) (19,28) (20,25) (20,22) (21,26) (21,28) (22,30) (22,29) (22,23) (23,29) (23,25) (24,33) (25,29) (26,28) (28,33) (28,31) (29,32) (30,32)\nIs there a path between node 31 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph294-14_18", + "image": "data/connectivity/graph_visual/hard/graph294.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,22) (0,13) (0,31) (0,25) (1,23) (2,17) (3,8) (3,11) (3,19) (5,16) (5,17) (5,9) (6,22) (6,26) (6,19) (6,31) (8,28) (8,12) (8,13) (9,23) (10,22) (10,25) (11,28) (11,26) (11,12) (11,19) (12,22) (12,26) (12,25) (13,28) (13,26) (13,31) (14,30) (15,22) (15,28) (15,26) (15,29) (15,31) (15,25) (16,21) (16,18) (17,18) (18,23) (18,21) (19,28) (19,26) (19,29) (19,27) (19,31) (20,30) (20,24) (22,28) (22,26) (22,29) (24,30) (25,26) (26,29) (26,31) (27,28) (29,31)\nIs there a path between node 14 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph238-2_3", + "image": "data/connectivity/graph_visual/hard/graph238.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,13) (0,4) (0,26) (1,6) (1,15) (1,30) (1,24) (2,3) (2,20) (2,25) (2,26) (3,12) (3,10) (3,25) (4,12) (4,13) (4,10) (4,7) (4,25) (4,26) (5,29) (5,20) (5,11) (5,25) (5,26) (6,14) (6,30) (6,28) (6,17) (7,29) (7,12) (7,13) (7,10) (7,20) (7,25) (7,26) (8,19) (8,27) (8,24) (9,22) (9,11) (9,25) (10,22) (10,29) (10,12) (10,13) (10,25) (10,26) (11,22) (11,23) (11,20) (12,29) (12,23) (14,27) (14,28) (14,24) (15,21) (15,19) (16,30) (16,24) (17,19) (17,28) (17,24) (18,20) (18,25) (20,22) (20,29) (20,25) (21,30) (21,24) (22,23) (22,25) (22,26) (23,29) (25,29) (25,26) (26,29) (28,30)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph91-15_25", + "image": "data/connectivity/graph_visual/hard/graph91.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,5) (0,3) (0,13) (1,26) (2,19) (3,22) (3,19) (4,9) (4,27) (4,6) (4,23) (5,7) (6,12) (6,27) (6,16) (6,8) (6,11) (7,19) (8,25) (8,24) (8,16) (8,11) (9,27) (9,21) (9,23) (11,25) (11,14) (11,24) (11,12) (11,23) (12,24) (12,27) (15,24) (15,20) (16,21) (16,23) (18,26) (20,25) (20,21) (21,27) (23,25)\nIs there a path between node 15 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph621-29_15", + "image": "data/connectivity/graph_visual/hard/graph621.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,9) (0,26) (0,24) (0,27) (0,11) (1,3) (1,2) (1,20) (1,6) (1,31) (2,3) (2,33) (2,30) (2,32) (2,19) (2,7) (3,31) (3,5) (4,33) (4,9) (4,30) (4,16) (4,25) (4,24) (5,30) (5,26) (5,27) (5,15) (6,33) (6,20) (6,24) (6,27) (6,11) (6,7) (7,33) (7,23) (7,30) (9,26) (9,29) (9,24) (9,31) (9,15) (10,28) (10,13) (10,22) (10,21) (11,16) (11,24) (12,15) (13,14) (13,17) (15,23) (15,20) (15,31) (16,20) (16,24) (16,19) (17,21) (19,33) (19,23) (19,25) (19,32) (20,33) (20,23) (20,32) (20,24) (20,27) (21,28) (23,33) (23,32) (24,30) (24,32) (24,29) (25,30) (25,32) (25,29) (25,27) (26,30) (26,32) (26,29) (27,33) (27,30) (29,30) (29,31) (30,32) (31,32)\nIs there a path between node 29 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph532-28_13", + "image": "data/connectivity/graph_visual/hard/graph532.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,16) (0,2) (1,20) (1,25) (1,8) (1,29) (1,19) (1,12) (1,33) (1,9) (1,30) (1,11) (1,7) (1,13) (1,4) (1,26) (1,10) (1,24) (1,5) (3,6) (3,22) (3,27) (3,15) (3,32) (4,20) (4,25) (4,8) (4,29) (4,19) (4,23) (4,21) (4,12) (4,28) (4,33) (4,31) (4,9) (4,13) (4,18) (4,14) (4,26) (5,20) (5,25) (5,8) (5,19) (5,21) (5,17) (5,33) (5,31) (5,9) (5,30) (5,11) (5,7) (5,13) (5,10) (5,24) (6,27) (6,15) (6,32) (7,8) (7,29) (7,19) (7,23) (7,12) (7,17) (7,28) (7,33) (7,9) (7,11) (7,18) (7,24) (8,20) (8,29) (8,23) (8,21) (8,17) (8,28) (8,9) (8,13) (8,18) (8,14) (8,10) (9,25) (9,29) (9,19) (9,23) (9,17) (9,33) (9,31) (9,30) (9,11) (9,14) (9,26) (9,10) (9,24) (10,20) (10,25) (10,29) (10,19) (10,23) (10,21) (10,12) (10,17) (10,31) (10,30) (10,11) (10,13) (10,18) (10,14) (10,26) (10,24) (11,20) (11,25) (11,29) (11,19) (11,12) (11,17) (11,33) (11,31) (11,30) (11,13) (11,18) (11,14) (11,26) (12,20) (12,29) (12,23) (12,17) (12,28) (12,33) (12,31) (12,30) (12,13) (12,18) (12,14) (12,26) (12,24) (13,20) (13,25) (13,29) (13,23) (13,21) (13,28) (13,33) (13,30) (13,18) (13,26) (13,24) (14,20) (14,29) (14,21) (14,28) (14,33) (14,31) (14,30) (14,24) (15,22) (17,25) (17,19) (17,21) (17,28) (17,33) (17,31) (17,30) (17,18) (17,26) (17,24) (18,20) (18,25) (18,19) (18,33) (18,31) (18,30) (18,26) (18,24) (19,25) (19,29) (19,23) (19,33) (19,30) (19,26) (20,29) (20,28) (20,31) (20,30) (20,26) (21,25) (21,29) (21,23) (21,33) (21,31) (23,25) (23,33) (23,31) (23,30) (23,26) (24,28) (24,33) (24,31) (24,30) (24,26) (25,29) (25,28) (25,31) (26,29) (26,28) (26,33) (26,31) (28,29) (28,33) (28,31) (29,33) (29,30) (30,33) (31,33)\nIs there a path between node 28 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph110-21_10", + "image": "data/connectivity/graph_visual/hard/graph110.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,1) (0,14) (0,9) (0,27) (1,26) (1,14) (1,4) (1,15) (1,7) (3,22) (4,21) (4,10) (4,11) (4,5) (4,20) (4,24) (4,15) (4,8) (5,18) (5,14) (5,13) (5,12) (5,24) (6,17) (6,27) (6,24) (6,15) (7,21) (7,18) (7,13) (7,23) (7,12) (8,18) (8,13) (8,23) (8,15) (8,25) (9,21) (9,14) (9,20) (10,18) (10,17) (10,20) (11,26) (11,23) (11,19) (11,27) (11,24) (12,18) (12,13) (12,23) (12,19) (12,17) (12,20) (12,25) (13,18) (13,23) (13,27) (14,21) (14,23) (14,19) (14,25) (15,21) (15,23) (15,20) (16,22) (17,21) (18,19) (18,20) (18,27) (18,24) (19,21) (19,20) (19,27) (20,26) (20,21) (20,24) (21,25) (23,25) (24,25) (25,26) (25,27)\nIs there a path between node 21 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph365-20_4", + "image": "data/connectivity/graph_visual/hard/graph365.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,29) (0,27) (0,31) (0,21) (0,10) (0,5) (0,11) (0,19) (0,18) (0,6) (0,20) (0,26) (1,14) (1,22) (1,23) (1,9) (1,28) (1,25) (1,12) (1,13) (1,2) (1,30) (2,23) (2,9) (2,28) (2,25) (2,12) (2,13) (3,15) (3,7) (3,17) (3,16) (4,29) (4,27) (4,31) (4,10) (4,5) (4,11) (4,20) (4,26) (5,29) (5,27) (5,24) (5,31) (5,19) (5,18) (5,26) (6,29) (6,27) (6,24) (6,31) (6,21) (6,11) (6,19) (6,18) (6,20) (7,15) (7,16) (8,15) (8,17) (8,16) (9,22) (9,23) (9,28) (9,25) (9,12) (9,13) (9,30) (10,29) (10,24) (10,31) (10,11) (10,19) (10,20) (11,29) (11,27) (11,24) (11,31) (11,18) (11,20) (12,14) (12,22) (12,13) (12,30) (13,22) (13,23) (13,28) (13,25) (13,30) (14,22) (14,28) (14,25) (14,30) (16,17) (18,29) (18,27) (18,24) (18,31) (18,19) (19,29) (19,24) (19,31) (19,21) (19,20) (19,26) (20,27) (20,24) (20,31) (20,21) (21,29) (21,27) (21,24) (21,26) (23,25) (24,27) (24,26) (25,30) (26,29) (26,27) (26,31) (27,29) (27,31) (28,30) (29,31)\nIs there a path between node 20 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph360-21_2", + "image": "data/connectivity/graph_visual/hard/graph360.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,28) (0,24) (0,31) (0,30) (0,27) (0,20) (1,21) (1,6) (1,19) (1,12) (1,22) (1,4) (1,17) (1,13) (1,30) (2,23) (2,3) (2,14) (3,25) (4,5) (4,17) (4,27) (5,17) (5,31) (5,20) (6,26) (6,16) (6,28) (6,10) (6,19) (6,12) (6,22) (6,13) (7,21) (7,28) (7,19) (7,17) (7,13) (7,18) (7,27) (8,23) (8,11) (8,25) (10,26) (10,28) (10,22) (10,31) (10,18) (11,23) (12,30) (13,21) (13,19) (13,31) (15,26) (15,16) (15,17) (15,18) (15,20) (16,21) (16,28) (16,19) (16,30) (16,27) (16,20) (17,24) (17,22) (17,18) (18,22) (19,22) (19,31) (19,20) (20,28) (21,22) (21,31) (22,30) (24,31) (27,28) (28,31)\nIs there a path between node 21 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph616-4_16", + "image": "data/connectivity/graph_visual/hard/graph616.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,33) (0,24) (0,27) (0,12) (0,16) (0,20) (0,5) (0,14) (0,17) (0,34) (0,29) (0,23) (0,22) (0,10) (0,28) (0,2) (0,15) (0,11) (0,8) (1,3) (1,6) (1,33) (1,27) (1,16) (1,20) (1,5) (1,26) (1,7) (1,19) (1,34) (1,29) (1,23) (1,22) (1,10) (1,28) (1,2) (1,9) (1,15) (1,11) (1,31) (1,8) (2,13) (2,33) (2,27) (2,12) (2,20) (2,7) (2,14) (2,19) (2,34) (2,29) (2,15) (2,11) (2,31) (3,6) (3,33) (3,12) (3,20) (3,5) (3,21) (3,7) (3,14) (3,17) (3,34) (3,29) (3,23) (3,22) (3,10) (3,28) (3,15) (3,11) (3,31) (3,8) (4,32) (4,30) (4,18) (5,13) (5,6) (5,33) (5,24) (5,12) (5,16) (5,20) (5,21) (5,26) (5,7) (5,14) (5,19) (5,17) (5,34) (5,29) (5,23) (5,22) (5,10) (5,28) (5,9) (5,15) (5,11) (6,13) (6,33) (6,27) (6,12) (6,20) (6,21) (6,26) (6,7) (6,14) (6,34) (6,23) (6,22) (6,10) (6,15) (6,31) (6,8) (7,13) (7,33) (7,24) (7,27) (7,16) (7,20) (7,21) (7,14) (7,19) (7,17) (7,29) (7,23) (7,10) (7,28) (7,9) (7,15) (7,11) (7,31) (7,8) (8,33) (8,24) (8,27) (8,26) (8,34) (8,29) (8,23) (8,10) (8,28) (8,9) (8,15) (8,11) (8,31) (9,13) (9,33) (9,24) (9,27) (9,16) (9,20) (9,21) (9,26) (9,14) (9,19) (9,17) (9,34) (9,22) (9,15) (9,11) (9,31) (10,13) (10,33) (10,24) (10,20) (10,14) (10,19) (10,17) (10,34) (10,29) (10,23) (10,28) (10,11) (10,31) (11,13) (11,33) (11,24) (11,27) (11,12) (11,16) (11,20) (11,21) (11,26) (11,19) (11,29) (11,22) (12,13) (12,24) (12,27) (12,16) (12,20) (12,21) (12,26) (12,14) (12,19) (12,34) (12,23) (12,22) (12,28) (12,15) (12,31) (13,24) (13,27) (13,16) (13,20) (13,21) (13,14) (13,19) (13,17) (13,34) (13,23) (13,22) (13,28) (13,15) (13,31) (14,24) (14,27) (14,16) (14,20) (14,26) (14,17) (14,34) (14,22) (14,28) (15,33) (15,24) (15,16) (15,26) (15,17) (15,34) (15,29) (15,22) (15,28) (15,31) (16,33) (16,24) (16,20) (16,21) (16,17) (16,34) (16,29) (16,31) (17,33) (17,24) (17,27) (17,20) (17,26) (17,19) (17,34) (17,29) (17,23) (17,22) (17,28) (17,31) (18,32) (18,25) (19,33) (19,24) (19,20) (19,21) (19,26) (19,29) (19,23) (19,31) (20,33) (20,24) (20,27) (20,21) (20,26) (20,34) (20,29) (20,23) (20,22) (20,28) (20,31) (21,33) (21,24) (21,27) (21,26) (21,23) (21,22) (21,28) (21,31) (22,33) (22,24) (22,27) (22,26) (22,34) (22,29) (22,23) (22,28) (22,31) (23,33) (23,27) (23,26) (23,34) (23,29) (23,28) (23,31) (24,33) (24,27) (24,34) (24,31) (25,32) (25,30) (26,33) (26,27) (26,34) (26,29) (26,28) (26,31) (27,33) (27,28) (27,31) (28,33) (28,34) (29,33) (29,34) (29,31) (30,32) (31,33) (31,34)\nIs there a path between node 4 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph697-21_26", + "image": "data/connectivity/graph_visual/hard/graph697.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,18) (0,11) (0,9) (0,15) (0,17) (0,12) (1,33) (1,16) (1,24) (1,32) (1,34) (1,22) (1,26) (1,20) (1,2) (1,19) (1,23) (1,29) (1,7) (2,33) (2,16) (2,32) (2,34) (2,22) (2,20) (2,14) (2,7) (3,27) (3,6) (3,10) (4,8) (4,13) (5,18) (5,11) (5,28) (5,17) (5,12) (6,27) (7,25) (7,16) (7,32) (7,22) (7,21) (7,20) (7,14) (7,19) (7,23) (7,29) (8,30) (9,18) (9,11) (9,28) (9,15) (9,17) (9,12) (10,27) (11,28) (11,17) (12,18) (12,17) (13,30) (13,31) (14,25) (14,16) (14,32) (14,34) (14,26) (14,20) (14,23) (14,29) (15,18) (15,28) (15,17) (16,33) (16,25) (16,24) (16,32) (16,34) (16,22) (16,21) (16,26) (16,20) (16,19) (17,28) (18,28) (19,33) (19,25) (19,24) (19,32) (19,34) (19,22) (19,21) (19,26) (19,20) (19,23) (19,29) (20,25) (20,24) (20,32) (20,21) (20,26) (20,23) (20,29) (21,33) (21,25) (21,24) (21,34) (21,22) (21,26) (21,23) (22,25) (22,24) (22,32) (22,26) (22,23) (23,33) (23,24) (23,34) (23,26) (23,29) (24,25) (24,26) (24,29) (25,33) (25,34) (25,26) (25,29) (26,33) (26,29) (29,33) (30,31) (32,33) (32,34)\nIs there a path between node 21 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph588-4_31", + "image": "data/connectivity/graph_visual/hard/graph588.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,14) (0,7) (0,13) (0,3) (0,2) (0,11) (0,33) (1,29) (1,31) (1,27) (1,22) (1,28) (1,10) (1,4) (1,16) (1,5) (2,14) (2,7) (2,8) (2,13) (2,3) (2,24) (2,33) (3,14) (3,8) (3,11) (3,24) (3,33) (4,29) (4,31) (4,27) (4,22) (4,28) (4,10) (4,21) (4,5) (5,29) (5,31) (5,27) (5,22) (5,28) (5,10) (5,12) (5,16) (5,21) (6,23) (6,30) (7,14) (7,8) (7,24) (7,33) (8,11) (8,24) (8,33) (9,17) (9,26) (9,25) (9,20) (9,18) (9,15) (9,32) (10,29) (10,31) (10,22) (10,28) (10,12) (10,16) (10,21) (11,14) (11,13) (11,33) (12,29) (12,31) (12,27) (12,28) (12,16) (13,14) (13,24) (13,33) (14,33) (15,26) (15,25) (15,20) (15,32) (16,31) (16,22) (16,28) (16,21) (17,26) (17,20) (17,18) (17,32) (18,26) (18,20) (19,23) (20,26) (20,25) (20,32) (21,29) (21,31) (21,22) (21,28) (22,27) (22,28) (23,30) (25,26) (25,32) (26,32) (27,29) (27,28) (29,31)\nIs there a path between node 4 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph82-17_15", + "image": "data/connectivity/graph_visual/hard/graph82.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,6) (0,11) (0,25) (0,15) (0,13) (0,16) (1,12) (1,7) (1,3) (1,9) (1,4) (1,22) (1,23) (1,2) (1,19) (1,18) (1,8) (1,14) (1,20) (2,12) (2,26) (2,7) (2,9) (2,21) (2,22) (2,23) (2,19) (2,18) (2,5) (2,10) (2,8) (2,14) (2,20) (3,9) (3,4) (3,21) (3,23) (3,18) (3,5) (3,10) (3,8) (3,14) (3,20) (4,12) (4,7) (4,21) (4,22) (4,19) (4,18) (4,17) (4,10) (4,8) (4,14) (4,20) (5,12) (5,7) (5,9) (5,21) (5,22) (5,23) (5,10) (5,14) (5,20) (6,11) (6,13) (7,9) (7,21) (7,22) (7,23) (7,19) (7,18) (7,17) (7,14) (7,20) (8,12) (8,26) (8,9) (8,22) (8,23) (8,19) (8,18) (8,17) (8,10) (8,20) (9,12) (9,22) (9,23) (9,19) (9,18) (9,17) (9,10) (9,14) (9,20) (10,12) (10,21) (10,22) (10,23) (10,19) (10,18) (10,17) (10,20) (11,25) (11,15) (11,16) (12,26) (12,21) (12,22) (12,23) (12,19) (12,17) (12,14) (13,25) (13,15) (13,16) (14,26) (14,21) (14,22) (14,23) (14,19) (14,20) (15,16) (17,26) (17,19) (17,20) (18,26) (18,21) (18,22) (18,23) (18,19) (19,26) (19,21) (19,22) (19,20) (20,23) (21,26) (21,23) (22,23) (23,26)\nIs there a path between node 17 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph398-9_31", + "image": "data/connectivity/graph_visual/hard/graph398.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,27) (0,2) (0,28) (0,32) (0,14) (0,1) (0,10) (1,30) (1,20) (1,2) (1,28) (1,32) (1,12) (1,16) (2,30) (2,8) (2,26) (2,16) (2,17) (2,3) (3,20) (3,4) (3,5) (3,28) (3,16) (3,10) (4,8) (4,27) (4,20) (4,28) (4,26) (4,25) (4,17) (5,30) (5,21) (5,31) (5,26) (5,25) (5,18) (6,29) (6,13) (7,22) (8,24) (8,32) (8,12) (8,26) (8,23) (8,18) (9,13) (10,30) (10,24) (10,27) (10,15) (10,12) (10,19) (11,22) (12,15) (12,26) (12,17) (14,30) (14,26) (14,16) (14,19) (15,30) (15,31) (15,32) (15,23) (15,19) (16,27) (16,28) (16,31) (16,32) (16,25) (16,23) (17,24) (17,27) (18,24) (18,28) (18,32) (18,23) (18,19) (19,20) (19,28) (20,24) (20,21) (20,26) (20,25) (21,28) (21,32) (21,26) (21,23) (22,29) (23,24) (23,28) (23,31) (24,30) (24,28) (24,26) (26,32) (30,31)\nIs there a path between node 9 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph22-2_18", + "image": "data/connectivity/graph_visual/hard/graph22.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,19) (0,16) (1,3) (1,4) (1,19) (1,16) (1,10) (2,17) (2,7) (2,9) (2,23) (2,5) (2,18) (3,19) (3,6) (4,14) (5,24) (5,15) (8,13) (8,20) (8,25) (8,23) (8,15) (8,12) (9,17) (9,22) (9,23) (9,21) (11,13) (11,24) (11,22) (11,25) (11,15) (12,13) (12,17) (12,22) (12,18) (13,24) (15,24) (15,17) (15,22) (15,20) (15,18) (15,21) (17,22) (18,22) (20,22) (21,23) (22,24) (24,25)\nIs there a path between node 2 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph11-12_18", + "image": "data/connectivity/graph_visual/hard/graph11.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,15) (0,2) (0,1) (0,23) (0,8) (0,24) (0,6) (0,22) (0,4) (0,11) (1,15) (1,14) (1,2) (1,8) (1,12) (1,17) (1,19) (2,15) (2,14) (2,23) (2,8) (2,20) (2,6) (2,22) (2,4) (2,17) (2,11) (2,19) (2,7) (3,18) (3,9) (3,10) (3,21) (3,13) (3,16) (4,15) (4,14) (4,5) (4,23) (4,24) (4,12) (4,17) (4,11) (4,19) (4,7) (5,15) (5,14) (5,8) (5,20) (5,6) (5,22) (5,12) (5,17) (5,11) (5,19) (5,7) (6,15) (6,14) (6,23) (6,8) (6,20) (6,22) (6,12) (6,11) (6,19) (7,15) (7,23) (7,22) (7,12) (7,17) (7,19) (8,15) (8,14) (8,23) (8,24) (8,12) (8,17) (9,18) (9,21) (9,13) (9,16) (10,25) (10,16) (11,15) (11,14) (11,23) (11,24) (11,17) (11,19) (12,14) (12,22) (12,19) (13,25) (13,18) (13,21) (13,16) (14,15) (14,23) (14,22) (14,17) (14,19) (15,23) (15,24) (15,20) (15,22) (15,17) (15,19) (16,18) (17,23) (17,24) (17,19) (18,25) (18,21) (19,23) (19,24) (19,20) (20,23) (20,22) (21,25) (23,24)\nIs there a path between node 12 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph417-18_22", + "image": "data/connectivity/graph_visual/hard/graph417.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,27) (1,2) (1,17) (2,10) (2,29) (2,31) (2,17) (2,24) (2,32) (3,27) (3,29) (3,32) (4,22) (4,23) (4,18) (4,12) (4,13) (4,6) (4,26) (5,15) (5,9) (5,13) (6,23) (6,20) (6,18) (6,9) (6,26) (7,10) (7,25) (7,21) (7,31) (8,27) (8,31) (8,30) (8,24) (8,11) (9,22) (9,20) (9,18) (9,15) (9,12) (9,26) (10,29) (11,31) (11,30) (11,32) (12,23) (12,20) (12,19) (13,28) (13,22) (13,20) (13,15) (13,26) (14,20) (14,18) (15,22) (15,19) (15,26) (16,24) (17,29) (17,21) (17,30) (17,32) (18,22) (18,19) (19,26) (20,28) (20,22) (21,25) (21,31) (21,24) (22,23) (24,27) (24,32) (26,28)\nIs there a path between node 18 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph193-12_17", + "image": "data/connectivity/graph_visual/hard/graph193.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,27) (0,4) (0,20) (0,21) (0,19) (1,29) (1,24) (1,14) (1,28) (1,23) (2,29) (2,12) (2,24) (2,3) (2,28) (2,8) (2,25) (3,29) (3,12) (3,24) (3,17) (3,8) (4,9) (4,21) (4,6) (5,13) (5,26) (5,29) (5,14) (5,7) (5,28) (6,18) (6,19) (7,26) (7,12) (7,14) (7,25) (8,26) (8,24) (8,11) (8,23) (9,27) (9,20) (9,19) (10,18) (10,19) (11,13) (11,26) (11,29) (11,12) (11,24) (11,28) (12,24) (12,14) (13,26) (13,25) (15,22) (15,21) (15,16) (16,21) (16,18) (17,26) (17,29) (17,23) (17,25) (18,20) (18,19) (19,22) (20,21) (21,27) (21,22) (22,27) (23,26) (23,28) (23,25) (26,28)\nIs there a path between node 12 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph267-14_0", + "image": "data/connectivity/graph_visual/hard/graph267.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,3) (0,16) (0,21) (0,15) (1,18) (1,11) (1,22) (1,30) (1,12) (2,3) (2,25) (2,7) (3,17) (3,25) (3,19) (4,22) (4,30) (5,28) (7,16) (7,25) (7,14) (7,21) (7,19) (7,27) (8,9) (10,13) (10,30) (10,12) (10,26) (11,18) (11,30) (11,26) (12,29) (12,18) (12,30) (15,17) (15,25) (15,19) (17,25) (18,22) (18,26) (19,27) (20,28) (22,29) (24,26) (26,29)\nIs there a path between node 14 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph148-14_0", + "image": "data/connectivity/graph_visual/hard/graph148.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,10) (0,6) (1,10) (2,21) (2,9) (2,13) (2,25) (2,22) (2,27) (2,11) (2,7) (2,15) (2,8) (2,12) (2,23) (2,3) (2,28) (2,14) (2,19) (3,21) (3,9) (3,13) (3,5) (3,22) (3,27) (3,11) (3,17) (3,7) (3,20) (3,15) (3,8) (3,12) (3,18) (3,24) (4,21) (4,9) (4,26) (4,13) (4,25) (4,5) (4,22) (4,27) (4,17) (4,7) (4,15) (4,16) (4,8) (4,12) (4,18) (4,24) (4,23) (4,28) (4,14) (4,19) (5,21) (5,9) (5,26) (5,13) (5,22) (5,27) (5,11) (5,17) (5,20) (5,15) (5,16) (5,8) (5,18) (5,23) (5,28) (6,10) (7,9) (7,13) (7,25) (7,22) (7,27) (7,11) (7,17) (7,20) (7,15) (7,16) (7,12) (7,18) (7,24) (7,23) (7,14) (8,21) (8,13) (8,25) (8,27) (8,11) (8,17) (8,20) (8,15) (8,16) (8,23) (8,14) (8,19) (9,25) (9,27) (9,11) (9,17) (9,20) (9,16) (9,12) (9,24) (9,28) (11,26) (11,13) (11,25) (11,22) (11,27) (11,17) (11,20) (11,15) (11,16) (11,12) (11,24) (11,28) (11,14) (12,21) (12,26) (12,13) (12,25) (12,27) (12,17) (12,20) (12,15) (12,18) (12,24) (12,23) (12,28) (12,19) (13,21) (13,26) (13,25) (13,22) (13,27) (13,17) (13,20) (13,15) (13,16) (13,18) (13,24) (13,23) (13,28) (13,14) (13,19) (14,25) (14,22) (14,27) (14,17) (14,20) (14,15) (14,16) (14,18) (14,24) (14,28) (15,26) (15,27) (15,20) (15,18) (15,24) (15,28) (16,21) (16,26) (16,25) (16,27) (16,20) (16,18) (16,24) (16,23) (16,28) (16,19) (17,21) (17,25) (17,22) (17,27) (17,20) (17,23) (17,28) (17,19) (18,26) (18,25) (18,27) (18,20) (18,24) (18,28) (19,26) (19,25) (19,22) (19,27) (19,20) (19,24) (19,23) (19,28) (20,26) (20,25) (20,27) (20,24) (20,23) (20,28) (21,26) (21,22) (21,28) (22,25) (22,27) (22,28) (23,27) (23,24) (23,28) (24,25) (24,27) (24,28) (25,26) (25,28) (26,28) (27,28)\nIs there a path between node 14 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph38-2_4", + "image": "data/connectivity/graph_visual/hard/graph38.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,7) (0,4) (0,24) (0,15) (1,2) (1,19) (1,6) (1,23) (1,13) (1,5) (1,20) (1,16) (1,25) (1,9) (1,21) (2,3) (2,6) (2,12) (2,23) (2,13) (2,5) (2,20) (2,16) (2,25) (2,9) (2,21) (2,8) (3,10) (3,22) (3,19) (3,6) (3,12) (3,14) (3,23) (3,13) (3,5) (3,20) (3,25) (3,9) (3,8) (4,11) (4,15) (5,6) (5,12) (5,23) (5,20) (5,17) (5,8) (6,22) (6,19) (6,14) (6,23) (6,13) (6,25) (6,17) (6,9) (7,15) (8,10) (8,22) (8,12) (8,13) (8,20) (8,16) (8,25) (8,9) (8,21) (9,22) (9,19) (9,12) (9,14) (9,23) (9,16) (9,25) (9,21) (10,12) (10,14) (10,20) (10,16) (10,25) (11,24) (11,15) (12,22) (12,16) (12,25) (12,17) (12,21) (13,22) (13,19) (13,14) (13,23) (13,20) (13,16) (13,17) (14,22) (14,19) (14,23) (14,25) (14,21) (15,18) (16,22) (16,23) (16,20) (16,25) (17,22) (17,19) (17,23) (17,20) (18,24) (19,22) (19,21) (20,23) (20,25) (21,22) (21,25) (22,25) (23,25)\nIs there a path between node 2 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph690-34_20", + "image": "data/connectivity/graph_visual/hard/graph690.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,10) (0,7) (0,14) (0,32) (0,24) (0,29) (1,27) (1,31) (1,25) (1,3) (1,18) (1,9) (1,16) (1,33) (1,15) (1,13) (1,19) (1,22) (1,21) (1,30) (2,11) (3,31) (3,25) (3,18) (3,34) (3,20) (3,9) (3,16) (3,33) (3,13) (3,22) (3,21) (3,30) (4,27) (4,31) (4,34) (4,20) (4,9) (4,16) (4,15) (4,13) (4,19) (4,30) (5,17) (5,8) (6,12) (6,10) (6,28) (6,7) (6,14) (6,32) (6,29) (7,26) (7,12) (7,14) (7,32) (7,23) (7,24) (7,29) (8,17) (9,31) (9,18) (9,34) (9,20) (9,16) (9,22) (10,26) (10,12) (10,28) (10,32) (10,24) (12,26) (12,14) (12,24) (12,29) (13,27) (13,31) (13,25) (13,18) (13,34) (13,16) (13,33) (13,19) (13,22) (13,21) (13,30) (14,26) (14,28) (14,32) (15,25) (15,18) (15,34) (15,20) (15,33) (15,19) (15,22) (15,30) (16,27) (16,18) (16,34) (16,20) (16,33) (16,19) (16,22) (16,21) (18,25) (18,34) (18,22) (18,21) (18,30) (19,27) (19,31) (19,25) (19,20) (19,33) (19,22) (19,21) (19,30) (20,27) (20,31) (20,34) (20,33) (20,22) (20,21) (21,31) (21,22) (21,30) (22,27) (22,31) (22,25) (22,34) (22,30) (23,26) (23,28) (23,32) (23,29) (24,28) (24,32) (24,29) (25,27) (25,31) (25,33) (25,30) (26,28) (27,31) (27,34) (27,30) (28,29) (29,32) (30,34) (30,33) (31,34) (31,33)\nIs there a path between node 34 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph54-2_6", + "image": "data/connectivity/graph_visual/hard/graph54.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,14) (0,25) (0,10) (0,26) (0,16) (0,1) (0,5) (0,22) (0,21) (0,15) (0,2) (0,24) (0,13) (0,7) (1,14) (1,25) (1,10) (1,16) (1,5) (1,22) (1,17) (1,2) (1,24) (1,19) (1,12) (2,25) (2,16) (2,23) (2,22) (2,17) (2,21) (2,8) (2,24) (2,13) (2,7) (2,12) (3,18) (3,9) (4,25) (4,10) (4,26) (4,16) (4,5) (4,22) (4,21) (4,15) (4,8) (4,24) (4,12) (5,14) (5,25) (5,26) (5,16) (5,23) (5,22) (5,17) (5,21) (5,15) (5,13) (5,19) (5,7) (5,12) (7,14) (7,25) (7,10) (7,16) (7,22) (7,21) (7,8) (7,13) (7,19) (7,12) (8,14) (8,25) (8,26) (8,16) (8,23) (8,22) (8,17) (8,15) (8,19) (8,12) (9,11) (9,18) (9,20) (10,25) (10,26) (10,16) (10,23) (10,22) (10,17) (10,21) (10,24) (10,13) (10,19) (10,12) (11,18) (11,20) (12,14) (12,25) (12,26) (12,16) (12,23) (12,22) (12,24) (12,13) (13,14) (13,26) (13,23) (13,17) (13,21) (13,15) (14,26) (14,16) (14,23) (14,22) (14,17) (14,21) (14,15) (14,24) (14,19) (15,25) (15,26) (15,23) (15,17) (15,21) (15,24) (15,19) (16,25) (16,26) (16,23) (16,21) (16,19) (17,25) (17,23) (17,22) (17,21) (17,24) (17,19) (19,25) (19,26) (19,23) (19,22) (19,21) (19,24) (21,25) (21,26) (22,25) (22,26) (22,23) (22,24) (23,25) (23,26) (23,24) (24,25) (25,26)\nIs there a path between node 2 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph579-22_29", + "image": "data/connectivity/graph_visual/hard/graph579.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,29) (0,12) (0,5) (0,30) (0,19) (0,21) (0,28) (1,17) (1,31) (1,6) (1,16) (1,2) (1,32) (1,4) (1,3) (1,18) (2,23) (2,17) (2,8) (2,6) (2,24) (2,16) (2,33) (2,13) (2,22) (2,3) (3,23) (3,17) (3,31) (3,8) (3,6) (3,24) (3,16) (3,33) (3,4) (3,18) (4,23) (4,17) (4,31) (4,6) (4,24) (4,33) (4,32) (5,29) (5,12) (5,21) (5,28) (5,11) (6,23) (6,17) (6,31) (6,8) (6,24) (6,16) (6,33) (6,13) (6,22) (6,32) (7,20) (7,26) (7,15) (7,14) (7,27) (7,25) (8,17) (8,31) (8,24) (8,33) (8,13) (8,22) (8,32) (8,18) (9,26) (9,15) (9,10) (9,14) (9,27) (9,25) (10,20) (10,26) (10,27) (10,25) (11,29) (11,12) (11,19) (11,28) (12,29) (12,30) (12,19) (12,21) (12,28) (13,23) (13,17) (13,31) (13,24) (13,16) (13,33) (13,22) (14,20) (14,15) (14,27) (14,25) (15,20) (15,26) (15,27) (15,25) (16,31) (16,33) (16,32) (16,18) (17,33) (18,23) (18,33) (18,22) (18,32) (19,29) (19,30) (19,21) (21,30) (22,31) (22,24) (22,33) (22,32) (23,31) (23,24) (23,33) (24,31) (24,33) (24,32) (25,26) (25,27) (26,27) (28,29) (29,30) (31,33) (31,32)\nIs there a path between node 22 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph426-13_28", + "image": "data/connectivity/graph_visual/hard/graph426.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,13) (1,19) (1,11) (1,30) (1,32) (1,15) (1,25) (1,22) (1,14) (1,12) (1,10) (1,4) (1,26) (1,24) (1,9) (1,18) (1,16) (1,28) (1,21) (1,31) (1,27) (1,17) (1,8) (1,3) (1,7) (1,5) (1,6) (2,19) (2,11) (2,30) (2,32) (2,15) (2,25) (2,22) (2,12) (2,10) (2,4) (2,26) (2,9) (2,16) (2,28) (2,21) (2,31) (2,27) (2,3) (2,7) (2,6) (3,19) (3,11) (3,32) (3,25) (3,22) (3,10) (3,4) (3,29) (3,26) (3,9) (3,16) (3,28) (3,21) (3,31) (3,27) (3,8) (3,7) (3,5) (3,6) (4,19) (4,11) (4,32) (4,14) (4,12) (4,10) (4,29) (4,26) (4,24) (4,9) (4,18) (4,28) (4,21) (4,31) (4,27) (4,20) (4,8) (4,7) (4,5) (5,19) (5,30) (5,15) (5,22) (5,14) (5,29) (5,26) (5,24) (5,9) (5,18) (5,16) (5,28) (5,27) (5,20) (5,6) (6,19) (6,11) (6,30) (6,32) (6,25) (6,22) (6,14) (6,12) (6,10) (6,29) (6,24) (6,9) (6,18) (6,16) (6,28) (6,21) (6,27) (6,7) (7,19) (7,11) (7,30) (7,32) (7,25) (7,22) (7,12) (7,29) (7,26) (7,24) (7,9) (7,18) (7,16) (7,28) (7,31) (7,20) (7,17) (7,8) (8,19) (8,11) (8,30) (8,25) (8,14) (8,12) (8,10) (8,29) (8,24) (8,18) (8,16) (8,28) (8,21) (8,27) (9,19) (9,30) (9,15) (9,25) (9,22) (9,14) (9,12) (9,10) (9,29) (9,24) (9,18) (9,16) (9,28) (9,21) (9,31) (9,20) (9,17) (10,19) (10,11) (10,25) (10,14) (10,12) (10,29) (10,24) (10,18) (10,16) (10,28) (10,27) (10,20) (11,19) (11,30) (11,22) (11,14) (11,12) (11,29) (11,24) (11,18) (11,16) (11,28) (11,21) (11,31) (12,19) (12,32) (12,15) (12,25) (12,22) (12,14) (12,26) (12,24) (12,18) (12,21) (12,31) (12,27) (12,17) (14,19) (14,30) (14,15) (14,25) (14,22) (14,26) (14,24) (14,28) (14,21) (14,31) (14,27) (14,20) (14,17) (15,19) (15,32) (15,25) (15,22) (15,29) (15,24) (15,18) (15,16) (15,28) (15,21) (15,31) (15,27) (15,20) (15,17) (16,19) (16,25) (16,22) (16,26) (16,21) (16,31) (16,27) (16,20) (17,19) (17,32) (17,25) (17,29) (17,26) (17,18) (17,28) (17,31) (17,27) (17,20) (18,19) (18,30) (18,25) (18,22) (18,26) (18,24) (18,21) (18,27) (18,20) (19,30) (19,32) (19,25) (19,26) (19,28) (19,21) (19,31) (20,32) (20,25) (20,22) (20,29) (20,26) (20,24) (20,28) (20,21) (20,27) (21,30) (21,32) (21,25) (21,29) (21,26) (21,24) (21,28) (22,32) (22,25) (22,29) (22,26) (22,24) (22,31) (24,30) (24,32) (24,25) (24,29) (24,26) (24,28) (24,31) (26,30) (26,32) (26,29) (26,28) (26,31) (27,30) (27,31) (28,30) (28,32) (28,29) (28,31) (29,30) (29,32) (29,31) (31,32)\nIs there a path between node 13 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph453-25_3", + "image": "data/connectivity/graph_visual/hard/graph453.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,18) (0,26) (0,7) (0,3) (0,13) (0,11) (0,19) (1,8) (1,12) (1,23) (1,24) (1,15) (1,6) (2,4) (2,15) (2,6) (3,28) (3,11) (3,19) (4,8) (4,5) (4,15) (4,6) (5,32) (5,8) (5,30) (5,27) (5,12) (5,23) (6,32) (6,23) (7,31) (7,19) (8,23) (8,15) (9,22) (10,25) (10,13) (10,11) (11,14) (11,26) (12,29) (13,28) (13,31) (13,19) (14,18) (15,29) (15,27) (15,24) (16,18) (18,28) (19,26) (23,30) (24,27) (25,28) (26,28)\nIs there a path between node 25 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph200-8_23", + "image": "data/connectivity/graph_visual/hard/graph200.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,26) (0,1) (0,17) (0,6) (0,27) (0,11) (0,2) (1,16) (1,26) (1,17) (1,6) (1,27) (1,11) (1,2) (2,17) (2,27) (2,11) (3,5) (3,23) (3,22) (3,4) (4,23) (4,14) (5,23) (5,14) (5,18) (6,16) (6,17) (6,27) (7,8) (7,24) (7,19) (7,10) (7,9) (7,12) (7,21) (7,25) (7,28) (7,15) (8,24) (8,19) (8,10) (8,9) (8,21) (8,13) (8,28) (8,15) (9,24) (9,19) (9,10) (9,20) (9,12) (9,13) (9,29) (9,15) (10,24) (10,19) (10,20) (10,21) (10,25) (10,29) (10,28) (10,15) (11,16) (11,26) (11,27) (12,24) (12,19) (12,20) (12,21) (12,25) (12,29) (12,28) (13,19) (13,20) (13,21) (13,25) (13,28) (13,15) (14,23) (14,18) (15,24) (15,19) (15,25) (15,28) (16,26) (16,17) (16,27) (17,27) (18,22) (19,24) (19,20) (19,29) (19,28) (20,24) (20,29) (20,28) (21,24) (21,25) (21,29) (21,28) (22,23) (24,25) (24,29) (24,28) (25,28) (26,27) (28,29)\nIs there a path between node 8 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph202-17_14", + "image": "data/connectivity/graph_visual/hard/graph202.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,29) (1,27) (1,24) (1,21) (1,3) (2,10) (2,22) (2,6) (2,18) (2,25) (2,12) (3,19) (3,27) (3,24) (4,10) (4,6) (4,18) (4,25) (5,28) (5,16) (6,10) (6,13) (6,25) (6,12) (6,9) (7,28) (8,10) (8,14) (8,18) (8,29) (8,25) (8,23) (9,13) (9,14) (10,29) (10,25) (12,22) (12,18) (12,17) (13,29) (13,26) (14,20) (14,17) (15,19) (17,25) (18,20) (18,25) (20,29) (20,26) (20,23) (21,27) (21,24) (23,26) (23,25) (24,27) (26,29)\nIs there a path between node 17 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph542-4_19", + "image": "data/connectivity/graph_visual/hard/graph542.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,19) (0,10) (0,11) (0,4) (0,22) (0,30) (0,5) (0,31) (0,14) (0,12) (1,8) (1,11) (1,4) (1,22) (1,33) (1,5) (1,9) (1,14) (1,12) (2,13) (2,26) (2,27) (2,28) (2,18) (2,29) (2,24) (2,3) (2,17) (2,25) (3,20) (3,15) (3,23) (3,28) (3,18) (3,29) (3,32) (3,24) (3,7) (3,21) (3,17) (3,25) (4,8) (4,10) (4,22) (4,33) (4,9) (4,31) (5,8) (5,19) (5,11) (5,33) (5,9) (5,31) (5,14) (5,12) (6,23) (6,27) (6,28) (6,18) (6,29) (6,32) (6,24) (6,7) (6,21) (6,25) (7,20) (7,13) (7,26) (7,23) (7,28) (7,18) (7,21) (7,17) (7,25) (8,19) (8,22) (8,33) (8,30) (8,31) (8,14) (8,12) (9,19) (9,10) (9,11) (9,22) (9,30) (9,31) (10,19) (10,11) (10,22) (10,30) (10,31) (10,14) (11,22) (11,31) (11,12) (12,19) (12,30) (12,14) (13,20) (13,26) (13,15) (13,23) (13,27) (13,28) (13,29) (13,32) (13,24) (14,19) (14,22) (14,33) (15,20) (15,23) (15,27) (15,18) (15,29) (15,32) (15,24) (15,17) (17,26) (17,23) (17,28) (17,18) (17,29) (17,32) (17,24) (17,21) (17,25) (18,20) (18,29) (19,33) (19,30) (19,31) (20,26) (20,23) (20,27) (20,28) (20,25) (21,23) (21,27) (21,28) (21,29) (21,32) (21,24) (21,25) (22,33) (22,30) (23,27) (23,28) (23,29) (23,32) (23,25) (24,26) (24,27) (24,32) (25,27) (25,28) (25,29) (26,27) (26,28) (26,32) (27,28) (27,29) (27,32) (29,32) (30,33) (30,31) (31,33)\nIs there a path between node 4 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph631-5_17", + "image": "data/connectivity/graph_visual/hard/graph631.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,16) (1,33) (1,17) (1,12) (1,25) (1,7) (1,18) (1,32) (1,11) (1,10) (1,15) (1,9) (1,5) (1,26) (1,4) (2,19) (2,33) (2,18) (2,30) (3,34) (3,31) (3,14) (3,6) (3,17) (3,11) (3,22) (3,29) (3,15) (3,24) (3,30) (4,16) (4,6) (4,12) (4,32) (4,24) (5,31) (5,16) (5,8) (5,23) (5,24) (5,21) (6,19) (6,33) (6,25) (6,11) (6,10) (6,24) (6,30) (7,12) (7,15) (7,9) (7,30) (8,17) (8,12) (8,32) (8,22) (8,29) (8,24) (8,30) (9,16) (9,14) (9,12) (9,25) (9,18) (9,23) (9,26) (10,31) (10,14) (10,19) (10,25) (10,32) (10,22) (10,23) (10,21) (11,34) (11,14) (11,17) (11,27) (11,25) (11,18) (11,26) (14,19) (14,33) (14,25) (14,18) (14,30) (14,26) (14,21) (15,34) (15,31) (15,33) (15,32) (15,24) (15,26) (15,21) (16,34) (16,22) (16,29) (16,24) (16,26) (17,31) (17,18) (17,23) (17,26) (18,22) (18,26) (19,33) (19,27) (19,25) (19,29) (19,26) (21,34) (21,31) (21,33) (21,25) (21,22) (21,24) (21,30) (22,34) (22,29) (22,24) (23,33) (23,27) (23,32) (24,33) (24,27) (24,32) (25,34) (25,31) (26,29) (27,34) (27,33) (29,31) (29,33) (29,30) (30,31) (31,34)\nIs there a path between node 5 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph402-16_2", + "image": "data/connectivity/graph_visual/hard/graph402.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,32) (0,31) (0,24) (0,30) (0,3) (0,16) (0,5) (0,1) (0,23) (1,14) (1,32) (1,17) (1,20) (1,31) (1,27) (1,24) (1,3) (1,16) (1,7) (1,5) (1,23) (2,8) (2,11) (2,28) (2,19) (2,22) (2,29) (2,26) (2,18) (3,14) (3,32) (3,31) (3,27) (3,24) (3,30) (3,10) (3,16) (3,7) (3,5) (3,23) (4,25) (4,11) (4,28) (4,21) (4,29) (4,18) (4,15) (5,14) (5,17) (5,31) (5,27) (5,30) (5,10) (5,7) (5,23) (6,25) (6,8) (6,11) (6,28) (6,19) (6,21) (6,29) (6,26) (6,15) (7,32) (7,17) (7,30) (7,10) (8,11) (8,28) (8,19) (8,22) (8,21) (8,29) (8,18) (8,15) (9,12) (10,14) (10,32) (10,20) (10,27) (10,24) (10,30) (10,16) (11,25) (11,28) (11,21) (11,26) (11,18) (12,13) (14,32) (14,17) (14,20) (14,31) (14,24) (14,16) (14,23) (15,28) (15,19) (15,22) (15,29) (15,18) (16,20) (16,31) (16,27) (16,24) (16,30) (16,23) (17,32) (17,20) (17,27) (17,24) (17,30) (17,23) (18,25) (18,22) (19,25) (19,28) (19,22) (19,26) (20,27) (20,24) (20,23) (21,28) (21,22) (22,25) (22,28) (22,29) (23,32) (23,27) (23,24) (24,32) (24,31) (24,27) (24,30) (25,28) (25,29) (25,26) (26,28) (27,32) (27,31) (28,29) (30,32) (30,31)\nIs there a path between node 16 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph92-24_26", + "image": "data/connectivity/graph_visual/hard/graph92.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,11) (0,1) (0,5) (0,24) (0,22) (0,12) (0,19) (0,25) (0,26) (1,3) (1,24) (1,22) (1,20) (1,26) (2,3) (2,14) (2,9) (2,25) (3,15) (3,12) (3,19) (3,20) (3,16) (4,21) (4,8) (5,27) (5,19) (5,16) (6,24) (6,9) (6,20) (6,16) (7,8) (7,23) (8,13) (8,18) (9,27) (9,11) (9,15) (9,22) (10,24) (10,12) (10,16) (11,12) (11,25) (11,16) (12,25) (12,16) (12,26) (13,21) (14,27) (14,24) (14,22) (14,25) (14,16) (14,26) (15,16) (16,27) (16,25) (16,26) (17,18) (18,21) (18,23) (19,27) (19,26) (20,27) (20,22) (24,27) (24,25) (25,27) (25,26)\nIs there a path between node 24 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph41-6_1", + "image": "data/connectivity/graph_visual/hard/graph41.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,17) (0,2) (0,25) (0,14) (0,9) (0,15) (0,12) (0,1) (0,7) (0,16) (0,18) (0,11) (0,10) (0,5) (1,17) (1,2) (1,21) (1,14) (1,9) (1,15) (1,12) (1,19) (1,8) (1,7) (1,18) (1,11) (1,10) (1,5) (2,17) (2,21) (2,14) (2,9) (2,13) (2,3) (2,12) (2,6) (2,19) (2,7) (2,18) (2,11) (2,5) (3,17) (3,22) (3,21) (3,9) (3,15) (3,13) (3,6) (3,19) (3,8) (3,7) (3,16) (3,18) (3,11) (4,20) (4,23) (4,24) (5,17) (5,22) (5,21) (5,9) (5,15) (5,12) (5,19) (5,8) (5,16) (5,11) (5,10) (6,22) (6,25) (6,9) (6,15) (6,13) (6,12) (6,19) (6,8) (6,7) (6,16) (7,17) (7,22) (7,25) (7,9) (7,15) (7,13) (7,12) (7,19) (7,8) (7,16) (7,11) (7,10) (8,17) (8,22) (8,14) (8,12) (8,16) (8,18) (8,11) (9,17) (9,22) (9,25) (9,15) (9,13) (9,12) (9,19) (9,16) (9,18) (9,11) (10,17) (10,22) (10,25) (10,13) (10,19) (10,11) (11,17) (11,25) (11,14) (11,15) (11,13) (11,12) (11,19) (12,22) (12,21) (12,14) (12,19) (12,16) (13,22) (13,25) (13,21) (13,14) (13,16) (14,17) (14,21) (14,15) (14,19) (14,16) (14,18) (15,17) (15,25) (15,21) (15,16) (16,22) (16,25) (16,21) (16,19) (16,18) (17,22) (17,25) (17,21) (17,19) (17,18) (18,22) (18,21) (18,19) (19,22) (19,25) (19,21) (20,23) (20,24) (21,22) (21,25) (23,24)\nIs there a path between node 6 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph644-4_21", + "image": "data/connectivity/graph_visual/hard/graph644.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,34) (0,17) (0,18) (0,1) (0,4) (0,28) (0,14) (0,22) (0,12) (1,20) (1,5) (1,26) (1,8) (1,34) (1,17) (1,28) (1,22) (2,9) (2,30) (2,6) (2,21) (2,23) (2,19) (2,25) (2,29) (2,13) (2,15) (2,16) (2,10) (2,27) (3,9) (3,31) (3,6) (3,21) (3,23) (3,19) (3,33) (3,25) (3,13) (3,15) (3,7) (3,16) (3,10) (3,24) (3,32) (3,11) (3,27) (4,5) (4,26) (4,8) (4,34) (4,17) (4,18) (4,28) (4,14) (5,20) (5,26) (5,8) (5,34) (5,17) (5,18) (5,14) (6,30) (6,31) (6,23) (6,33) (6,29) (6,7) (6,16) (6,10) (6,11) (7,9) (7,30) (7,31) (7,21) (7,23) (7,19) (7,29) (7,13) (7,16) (7,10) (7,24) (7,32) (7,11) (7,27) (8,20) (8,17) (8,18) (8,28) (8,14) (8,22) (9,30) (9,31) (9,21) (9,19) (9,33) (9,25) (9,10) (9,32) (9,11) (10,23) (10,19) (10,33) (10,25) (10,13) (10,15) (10,16) (10,24) (10,32) (10,27) (11,30) (11,31) (11,21) (11,23) (11,33) (11,25) (11,29) (11,13) (11,15) (11,16) (11,24) (11,27) (12,20) (12,26) (12,34) (12,18) (12,22) (13,31) (13,21) (13,33) (13,25) (13,15) (13,16) (13,27) (14,20) (14,26) (14,34) (14,17) (14,28) (14,22) (15,30) (15,23) (15,19) (15,25) (15,24) (15,32) (15,27) (16,30) (16,31) (16,21) (16,23) (16,24) (16,32) (17,20) (17,26) (17,34) (17,28) (17,22) (18,20) (18,26) (18,34) (18,22) (19,30) (19,31) (19,23) (19,25) (19,27) (20,34) (21,23) (21,33) (21,25) (21,29) (21,24) (21,27) (22,34) (22,28) (23,31) (23,29) (23,24) (23,32) (24,30) (24,31) (24,33) (24,29) (24,32) (24,27) (25,30) (25,31) (25,33) (25,32) (25,27) (26,34) (27,30) (27,33) (29,30) (29,31) (30,33) (30,32) (31,33) (31,32)\nIs there a path between node 4 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph362-17_23", + "image": "data/connectivity/graph_visual/hard/graph362.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,30) (0,28) (0,21) (0,5) (0,20) (0,13) (1,26) (1,17) (2,27) (2,15) (3,19) (3,24) (3,21) (3,14) (3,4) (3,22) (3,12) (3,13) (4,16) (4,31) (4,11) (5,7) (5,23) (5,14) (5,6) (5,12) (6,7) (6,24) (6,16) (6,28) (6,14) (7,25) (7,28) (7,14) (7,20) (7,22) (7,11) (7,12) (8,10) (8,18) (9,27) (9,15) (10,27) (10,15) (10,18) (11,24) (11,21) (12,25) (12,24) (12,20) (12,22) (12,13) (13,29) (13,25) (13,24) (13,31) (14,16) (14,22) (15,26) (15,17) (16,29) (16,21) (16,31) (16,20) (17,26) (18,26) (19,29) (19,23) (19,20) (20,22) (21,25) (21,24) (21,30) (21,22) (22,30) (23,30) (23,31) (24,25) (24,30) (24,31) (26,27) (29,30)\nIs there a path between node 17 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph472-26_15", + "image": "data/connectivity/graph_visual/hard/graph472.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,23) (0,29) (0,31) (0,6) (0,24) (0,27) (0,20) (0,16) (0,10) (0,25) (0,26) (0,8) (0,9) (0,7) (0,18) (0,1) (1,30) (1,23) (1,15) (1,29) (1,6) (1,24) (1,27) (1,20) (1,5) (1,25) (1,8) (1,12) (1,9) (1,7) (1,21) (2,23) (2,15) (2,29) (2,6) (2,24) (2,27) (2,20) (2,16) (2,5) (2,25) (2,8) (2,12) (2,9) (2,11) (2,7) (2,21) (2,18) (3,30) (3,23) (3,15) (3,29) (3,31) (3,6) (3,24) (3,27) (3,20) (3,16) (3,10) (3,25) (3,26) (3,8) (3,12) (3,11) (3,7) (3,21) (4,28) (4,22) (4,32) (4,13) (4,14) (5,30) (5,29) (5,31) (5,6) (5,20) (5,16) (5,10) (5,8) (5,12) (5,9) (5,7) (5,21) (5,18) (6,23) (6,15) (6,29) (6,31) (6,27) (6,20) (6,10) (6,25) (6,26) (6,12) (6,9) (6,7) (6,21) (6,18) (7,30) (7,23) (7,29) (7,27) (7,20) (7,16) (7,26) (7,9) (7,11) (7,21) (7,18) (8,23) (8,15) (8,29) (8,24) (8,16) (8,10) (8,25) (8,12) (8,9) (8,11) (8,21) (8,18) (9,30) (9,23) (9,15) (9,31) (9,24) (9,27) (9,20) (9,16) (9,10) (9,26) (9,12) (9,11) (9,21) (10,30) (10,15) (10,31) (10,24) (10,27) (10,16) (10,25) (10,26) (10,12) (10,11) (10,21) (10,18) (11,30) (11,15) (11,31) (11,24) (11,26) (11,12) (11,21) (12,15) (12,29) (12,31) (12,24) (12,27) (12,25) (12,21) (12,18) (13,28) (13,22) (13,32) (13,14) (14,28) (14,32) (14,19) (15,30) (15,23) (15,31) (15,24) (15,27) (15,20) (15,16) (15,25) (15,26) (15,21) (16,30) (16,29) (16,24) (16,21) (18,30) (18,23) (18,29) (18,24) (18,27) (18,20) (18,25) (19,28) (19,22) (20,23) (20,29) (20,31) (20,24) (20,25) (20,26) (20,21) (21,30) (21,23) (21,31) (21,24) (21,27) (21,25) (22,28) (22,32) (23,30) (23,29) (23,31) (23,24) (23,25) (23,26) (24,29) (24,31) (24,27) (24,25) (24,26) (25,30) (25,29) (25,31) (25,27) (26,30) (26,29) (26,31) (26,27) (27,30) (27,29) (28,32) (29,31) (30,31)\nIs there a path between node 26 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph127-11_2", + "image": "data/connectivity/graph_visual/hard/graph127.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,14) (0,20) (0,10) (0,6) (0,18) (1,24) (1,16) (1,27) (1,19) (1,12) (1,11) (1,17) (1,23) (1,26) (1,15) (1,4) (2,14) (2,25) (2,20) (2,6) (3,7) (4,24) (4,16) (4,12) (4,11) (4,8) (4,23) (4,26) (4,5) (5,27) (5,19) (5,17) (5,23) (5,13) (5,26) (5,15) (5,22) (6,14) (6,20) (6,10) (6,21) (6,18) (8,24) (8,16) (8,27) (8,12) (8,11) (8,17) (8,23) (8,26) (8,22) (10,14) (10,20) (10,21) (10,18) (11,24) (11,16) (11,19) (11,17) (11,23) (11,26) (11,15) (11,22) (12,27) (12,19) (12,17) (12,13) (12,26) (12,15) (12,22) (13,24) (13,19) (13,17) (13,23) (13,15) (13,22) (14,25) (14,20) (15,24) (15,16) (15,17) (15,23) (15,26) (15,22) (16,24) (16,17) (16,23) (16,22) (17,24) (17,19) (17,23) (17,22) (18,25) (18,20) (18,21) (19,23) (19,26) (20,25) (22,24) (22,23) (22,26) (24,27) (24,26)\nIs there a path between node 11 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph562-24_6", + "image": "data/connectivity/graph_visual/hard/graph562.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,27) (0,10) (0,8) (0,23) (1,2) (1,21) (1,17) (1,31) (2,6) (2,33) (2,9) (2,3) (2,21) (2,7) (2,16) (3,17) (3,24) (3,5) (4,32) (4,22) (4,12) (5,33) (5,28) (6,24) (6,26) (6,19) (6,16) (6,28) (7,33) (7,24) (7,13) (8,27) (9,31) (9,16) (9,13) (10,27) (10,29) (10,20) (10,12) (11,32) (12,29) (12,22) (13,15) (13,21) (13,26) (13,19) (13,18) (15,21) (16,24) (16,26) (16,18) (17,21) (17,28) (18,33) (18,21) (18,26) (19,21) (19,28) (20,25) (20,22) (21,26) (21,28) (22,30) (22,29) (22,23) (23,29) (23,25) (24,33) (25,29) (26,28) (28,33) (28,31) (29,32) (30,32)\nIs there a path between node 24 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph638-19_32", + "image": "data/connectivity/graph_visual/hard/graph638.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,1) (0,19) (0,15) (0,20) (0,9) (0,21) (0,3) (0,22) (0,32) (0,24) (0,14) (0,11) (0,17) (0,5) (0,34) (0,4) (0,26) (0,10) (0,8) (1,27) (1,23) (1,30) (1,6) (1,19) (1,20) (1,2) (1,9) (1,21) (1,3) (1,22) (1,24) (1,14) (1,11) (1,17) (1,5) (1,4) (1,26) (1,8) (2,27) (2,30) (2,6) (2,19) (2,20) (2,9) (2,21) (2,3) (2,22) (2,32) (2,7) (2,11) (2,17) (2,5) (2,34) (2,4) (2,26) (2,12) (2,10) (3,27) (3,23) (3,30) (3,6) (3,19) (3,15) (3,20) (3,9) (3,22) (3,24) (3,14) (3,34) (3,4) (3,12) (3,10) (3,8) (3,28) (4,27) (4,23) (4,30) (4,19) (4,15) (4,20) (4,9) (4,21) (4,32) (4,24) (4,14) (4,7) (4,11) (4,17) (4,5) (4,26) (4,12) (4,8) (4,28) (5,30) (5,19) (5,9) (5,21) (5,24) (5,7) (5,11) (5,17) (5,34) (5,12) (6,27) (6,23) (6,30) (6,19) (6,20) (6,9) (6,21) (6,22) (6,32) (6,24) (6,14) (6,7) (6,11) (6,17) (6,34) (6,26) (6,8) (6,28) (7,23) (7,30) (7,19) (7,15) (7,20) (7,21) (7,32) (7,24) (7,11) (7,17) (7,34) (7,12) (7,10) (7,8) (7,28) (8,23) (8,15) (8,20) (8,24) (8,14) (8,11) (8,17) (8,34) (8,26) (8,12) (8,10) (8,28) (9,30) (9,19) (9,15) (9,20) (9,22) (9,32) (9,24) (9,11) (9,34) (9,12) (9,10) (9,28) (10,27) (10,23) (10,30) (10,19) (10,21) (10,32) (10,24) (10,26) (10,12) (11,27) (11,30) (11,19) (11,20) (11,21) (11,22) (11,32) (11,24) (11,14) (11,17) (11,34) (11,12) (12,27) (12,30) (12,19) (12,20) (12,22) (12,32) (12,24) (12,14) (12,17) (12,34) (12,28) (14,27) (14,23) (14,30) (14,19) (14,15) (14,21) (14,22) (14,32) (14,17) (14,34) (14,28) (15,19) (15,20) (15,21) (15,22) (15,32) (15,24) (15,34) (15,26) (15,28) (16,33) (16,29) (16,18) (16,31) (17,27) (17,23) (17,30) (17,19) (17,20) (17,21) (17,22) (17,32) (17,24) (17,34) (17,28) (18,33) (18,31) (18,25) (19,27) (19,23) (19,30) (19,20) (19,22) (19,32) (19,34) (19,26) (19,28) (20,23) (20,30) (20,21) (20,22) (20,32) (20,24) (20,34) (20,26) (21,27) (21,23) (21,30) (21,22) (21,32) (21,24) (21,34) (21,26) (21,28) (22,27) (22,23) (22,24) (22,34) (22,26) (22,28) (23,32) (23,26) (23,28) (24,27) (24,32) (24,34) (24,26) (25,33) (26,30) (26,32) (26,34) (27,30) (27,32) (27,28) (28,30) (28,32) (28,34) (29,33) (29,31) (31,33) (32,34)\nIs there a path between node 19 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph306-4_22", + "image": "data/connectivity/graph_visual/hard/graph306.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,8) (0,24) (0,6) (0,14) (0,26) (0,29) (0,10) (0,27) (0,5) (1,15) (2,18) (2,3) (2,6) (2,7) (2,13) (2,17) (2,20) (3,24) (3,22) (3,21) (3,12) (3,7) (3,19) (3,13) (3,25) (5,31) (5,16) (5,22) (5,7) (5,9) (5,14) (5,26) (5,25) (5,29) (5,30) (6,12) (6,14) (6,17) (6,20) (6,29) (6,27) (7,8) (7,18) (7,22) (7,28) (7,14) (7,26) (7,25) (7,30) (8,16) (8,9) (8,14) (8,19) (8,10) (9,31) (9,16) (9,21) (9,12) (9,13) (9,27) (10,31) (10,26) (10,17) (10,25) (10,29) (12,18) (12,26) (12,20) (13,28) (13,26) (13,29) (14,24) (14,21) (14,26) (14,17) (14,29) (15,23) (16,24) (16,31) (16,21) (16,26) (16,20) (16,29) (16,30) (17,31) (17,22) (17,19) (17,20) (17,29) (18,22) (18,21) (18,25) (18,29) (19,31) (19,22) (19,26) (19,20) (19,30) (20,25) (21,25) (22,26) (24,28) (25,28) (25,29) (25,27) (25,30) (27,31) (28,31)\nIs there a path between node 4 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph281-18_12", + "image": "data/connectivity/graph_visual/hard/graph281.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,2) (0,5) (0,10) (0,18) (0,14) (0,28) (0,25) (0,7) (0,17) (0,13) (0,22) (0,20) (0,11) (1,9) (1,3) (1,6) (1,24) (1,4) (1,21) (1,27) (1,16) (2,5) (2,14) (2,26) (2,25) (2,7) (2,20) (2,11) (3,9) (3,6) (3,24) (3,4) (3,21) (3,30) (3,15) (3,16) (3,8) (4,12) (4,6) (4,24) (4,23) (4,21) (4,27) (4,15) (4,16) (4,8) (5,10) (5,29) (5,26) (5,19) (5,17) (5,13) (5,20) (6,9) (6,24) (6,23) (6,16) (7,18) (7,14) (7,29) (7,28) (7,25) (7,19) (7,17) (7,20) (8,9) (8,24) (8,27) (8,30) (9,12) (9,23) (9,21) (9,27) (9,30) (9,16) (10,18) (10,14) (10,26) (10,28) (10,13) (10,22) (10,20) (10,11) (11,18) (11,29) (11,26) (11,28) (11,25) (11,19) (11,17) (11,13) (12,24) (12,21) (12,30) (12,15) (13,18) (13,14) (13,29) (13,26) (13,19) (13,17) (13,22) (13,20) (14,18) (14,29) (14,26) (14,28) (14,25) (14,19) (14,22) (14,20) (15,24) (15,30) (15,16) (16,24) (16,23) (16,21) (16,27) (17,18) (17,26) (17,25) (17,20) (18,29) (18,28) (18,25) (18,19) (18,22) (19,26) (19,28) (19,25) (20,29) (20,28) (20,25) (20,22) (21,24) (21,23) (21,27) (22,26) (22,25) (23,24) (23,27) (23,30) (24,30) (25,29) (25,28) (26,28) (27,30) (28,29)\nIs there a path between node 18 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph401-2_10", + "image": "data/connectivity/graph_visual/hard/graph401.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,11) (0,15) (0,31) (0,7) (0,4) (0,28) (0,32) (0,19) (0,16) (0,25) (0,17) (0,12) (0,27) (0,9) (0,23) (0,3) (0,14) (0,1) (0,2) (0,29) (1,30) (1,31) (1,13) (1,7) (1,4) (1,6) (1,32) (1,19) (1,22) (1,26) (1,16) (1,25) (1,17) (1,27) (1,9) (1,24) (1,14) (1,2) (2,15) (2,30) (2,31) (2,13) (2,7) (2,4) (2,6) (2,32) (2,8) (2,19) (2,26) (2,17) (2,12) (2,18) (2,27) (2,9) (2,24) (2,23) (2,5) (2,3) (2,14) (2,29) (3,11) (3,30) (3,31) (3,13) (3,7) (3,4) (3,28) (3,6) (3,32) (3,8) (3,22) (3,26) (3,16) (3,25) (3,17) (3,18) (3,27) (3,23) (3,5) (3,14) (3,29) (4,11) (4,30) (4,31) (4,6) (4,32) (4,19) (4,16) (4,25) (4,17) (4,12) (4,18) (4,27) (4,9) (4,24) (4,5) (4,14) (5,11) (5,31) (5,13) (5,7) (5,28) (5,19) (5,26) (5,25) (5,12) (5,18) (5,24) (5,23) (5,14) (6,11) (6,15) (6,30) (6,31) (6,13) (6,7) (6,28) (6,8) (6,22) (6,26) (6,16) (6,25) (6,17) (6,12) (6,14) (6,29) (7,11) (7,15) (7,30) (7,31) (7,28) (7,32) (7,19) (7,22) (7,17) (7,12) (7,18) (7,27) (7,24) (7,23) (7,29) (8,11) (8,15) (8,30) (8,31) (8,13) (8,28) (8,32) (8,19) (8,26) (8,16) (8,17) (8,12) (8,9) (8,24) (8,23) (8,14) (8,29) (9,11) (9,30) (9,13) (9,32) (9,19) (9,26) (9,16) (9,25) (9,12) (9,18) (9,27) (9,24) (9,29) (10,20) (11,31) (11,13) (11,28) (11,32) (11,19) (11,22) (11,16) (11,25) (11,17) (11,27) (11,24) (11,23) (11,29) (12,15) (12,13) (12,28) (12,32) (12,19) (12,26) (12,25) (12,27) (12,23) (12,29) (13,15) (13,31) (13,28) (13,32) (13,22) (13,26) (13,16) (13,25) (13,18) (13,27) (13,24) (13,23) (13,29) (14,15) (14,30) (14,31) (14,28) (14,32) (14,19) (14,22) (14,26) (14,16) (14,25) (14,17) (14,18) (14,27) (14,24) (14,23) (14,29) (15,31) (15,19) (15,22) (15,17) (15,18) (15,27) (15,24) (15,23) (15,29) (16,30) (16,31) (16,32) (16,19) (16,22) (16,26) (16,27) (16,24) (17,28) (17,32) (17,19) (17,18) (17,27) (18,30) (18,31) (18,28) (18,32) (18,19) (18,22) (18,27) (18,24) (18,23) (19,30) (19,31) (19,28) (19,32) (19,22) (19,25) (19,27) (19,23) (19,29) (20,21) (22,30) (22,26) (22,25) (22,27) (22,29) (23,30) (23,28) (23,32) (23,26) (23,25) (23,27) (23,24) (23,29) (24,30) (24,31) (24,28) (24,32) (24,25) (24,27) (24,29) (25,30) (25,28) (25,32) (25,27) (25,29) (26,30) (26,32) (26,27) (26,29) (27,28) (27,29) (28,29) (29,31) (29,32) (30,32) (31,32)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph208-6_22", + "image": "data/connectivity/graph_visual/hard/graph208.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,25) (0,2) (1,25) (1,8) (1,18) (1,2) (2,25) (3,28) (3,19) (3,26) (4,23) (4,10) (5,14) (6,23) (6,10) (6,9) (7,21) (7,26) (7,15) (8,14) (9,20) (9,23) (9,29) (9,11) (10,29) (10,11) (11,23) (11,29) (11,17) (12,16) (15,27) (15,19) (15,26) (16,19) (16,21) (16,26) (17,29) (19,28) (20,29) (20,22) (21,24) (22,29) (23,29) (24,28) (27,28)\nIs there a path between node 6 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph645-9_30", + "image": "data/connectivity/graph_visual/hard/graph645.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,16) (0,18) (0,5) (0,29) (0,21) (0,22) (0,7) (0,2) (0,13) (0,27) (0,26) (0,14) (0,33) (0,8) (0,10) (1,32) (1,16) (1,18) (1,29) (1,17) (1,2) (1,13) (1,26) (1,14) (1,31) (1,33) (1,10) (2,23) (2,32) (2,16) (2,18) (2,5) (2,29) (2,17) (2,21) (2,7) (2,13) (2,27) (2,9) (2,31) (2,33) (2,8) (3,12) (3,15) (3,19) (3,20) (3,34) (3,4) (3,11) (4,12) (4,28) (4,6) (4,15) (4,19) (4,34) (4,30) (4,11) (5,16) (5,18) (5,17) (5,21) (5,22) (5,13) (5,24) (5,9) (5,26) (5,31) (5,33) (5,10) (6,12) (6,28) (6,15) (6,19) (6,20) (6,30) (6,11) (6,25) (7,32) (7,16) (7,18) (7,22) (7,13) (7,24) (7,27) (7,9) (7,26) (7,14) (7,31) (7,33) (7,8) (7,10) (8,23) (8,16) (8,18) (8,29) (8,17) (8,21) (8,22) (8,13) (8,24) (8,26) (8,14) (8,31) (8,33) (8,10) (9,23) (9,32) (9,16) (9,18) (9,17) (9,21) (9,22) (9,13) (9,24) (9,27) (9,26) (9,14) (9,31) (9,33) (9,10) (10,23) (10,32) (10,16) (10,18) (10,17) (10,21) (10,13) (10,24) (10,27) (10,26) (10,14) (11,28) (11,15) (11,34) (11,30) (11,25) (12,28) (12,15) (12,20) (12,30) (12,25) (13,23) (13,32) (13,16) (13,18) (13,29) (13,17) (13,22) (13,24) (13,27) (13,26) (13,14) (13,33) (14,23) (14,29) (14,17) (14,21) (14,22) (14,27) (14,26) (15,20) (15,30) (16,23) (16,29) (16,17) (16,21) (16,22) (16,24) (16,27) (16,26) (16,31) (17,23) (17,32) (17,18) (17,21) (17,24) (17,27) (17,31) (18,23) (18,29) (18,21) (18,27) (18,26) (18,31) (18,33) (19,20) (19,34) (19,30) (19,25) (20,28) (20,34) (20,30) (20,25) (21,32) (21,22) (21,24) (21,27) (21,26) (21,31) (22,23) (22,32) (22,29) (22,24) (22,26) (22,31) (22,33) (23,32) (23,29) (23,24) (23,26) (23,31) (24,29) (24,27) (24,26) (24,33) (25,28) (25,34) (25,30) (26,32) (26,29) (27,29) (27,33) (28,30) (29,32) (30,34) (31,32) (32,33)\nIs there a path between node 9 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph380-19_29", + "image": "data/connectivity/graph_visual/hard/graph380.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,23) (0,8) (0,15) (0,6) (0,5) (0,13) (0,21) (0,18) (1,4) (1,7) (1,23) (1,15) (1,6) (1,21) (2,10) (2,16) (2,26) (2,12) (2,22) (2,27) (2,30) (2,17) (2,31) (3,9) (3,25) (3,20) (3,28) (3,11) (3,19) (4,8) (4,15) (4,5) (4,13) (4,21) (4,18) (5,7) (5,8) (5,15) (5,6) (5,13) (5,21) (5,18) (6,23) (6,8) (6,15) (6,21) (6,18) (7,23) (7,8) (7,21) (7,18) (8,23) (8,15) (8,13) (8,18) (9,25) (9,28) (9,11) (9,19) (10,26) (10,12) (10,24) (10,14) (10,30) (10,17) (10,31) (12,26) (12,27) (12,14) (12,30) (12,31) (13,23) (13,21) (14,16) (14,26) (14,22) (14,24) (14,30) (14,31) (15,23) (15,21) (15,18) (16,24) (16,27) (16,30) (16,17) (16,31) (17,26) (17,22) (17,27) (18,23) (19,25) (19,20) (19,28) (20,25) (20,28) (21,23) (22,26) (22,27) (22,30) (24,26) (24,27) (24,30) (24,31) (26,27) (26,30) (26,31) (27,30) (27,31) (30,31)\nIs there a path between node 19 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph564-11_19", + "image": "data/connectivity/graph_visual/hard/graph564.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,16) (1,3) (1,28) (1,21) (1,29) (1,27) (1,26) (3,28) (3,20) (3,26) (4,31) (4,8) (4,23) (4,17) (4,29) (4,33) (4,13) (4,26) (4,18) (4,9) (5,16) (6,11) (7,20) (7,29) (7,9) (7,12) (7,25) (8,30) (8,17) (8,14) (8,13) (8,18) (9,19) (9,21) (9,27) (9,26) (9,12) (12,30) (12,22) (12,19) (12,17) (12,14) (12,33) (13,20) (13,14) (13,27) (14,19) (14,21) (14,33) (14,25) (17,24) (17,21) (17,29) (17,27) (17,33) (17,26) (17,18) (18,31) (18,24) (18,27) (18,33) (18,25) (19,30) (19,23) (20,31) (20,24) (20,29) (20,27) (20,26) (21,31) (21,24) (21,28) (21,29) (22,30) (22,23) (22,28) (22,27) (23,30) (23,24) (23,25) (25,31) (25,27) (25,33) (26,29) (27,31) (27,28) (27,33) (28,31) (28,29) (29,31) (29,30)\nIs there a path between node 11 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph125-12_10", + "image": "data/connectivity/graph_visual/hard/graph125.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,4) (0,8) (0,14) (0,20) (0,23) (0,16) (0,3) (0,11) (0,12) (0,15) (0,13) (0,25) (1,22) (1,6) (1,10) (1,7) (2,26) (2,19) (2,9) (2,24) (3,4) (3,18) (3,8) (3,20) (3,11) (3,15) (3,25) (4,18) (4,8) (4,20) (4,23) (4,16) (4,11) (4,15) (4,25) (5,22) (6,22) (6,17) (6,7) (7,22) (7,10) (8,18) (8,14) (8,20) (8,23) (8,16) (8,12) (8,15) (8,13) (8,25) (9,21) (9,27) (9,26) (9,24) (11,20) (11,15) (11,25) (12,14) (12,20) (12,23) (12,15) (12,13) (12,25) (13,18) (13,14) (13,20) (13,23) (13,16) (13,25) (14,18) (14,20) (14,16) (14,15) (14,25) (15,18) (15,20) (15,23) (15,25) (16,20) (16,23) (17,22) (18,20) (18,25) (19,21) (19,27) (19,26) (19,24) (20,23) (20,25) (21,27) (21,24) (24,27) (24,26)\nIs there a path between node 12 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph550-23_7", + "image": "data/connectivity/graph_visual/hard/graph550.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,28) (0,23) (0,22) (0,32) (1,28) (1,15) (1,12) (1,13) (2,11) (2,19) (2,9) (4,16) (4,21) (4,24) (5,7) (5,8) (5,20) (6,19) (6,24) (6,27) (7,8) (7,20) (9,19) (9,24) (10,28) (10,12) (10,14) (10,32) (11,21) (12,18) (12,26) (12,22) (13,28) (13,15) (13,26) (14,18) (14,17) (14,22) (15,25) (15,26) (15,23) (16,30) (17,28) (17,32) (19,31) (19,21) (19,24) (19,33) (21,30) (21,24) (21,27) (23,28) (23,25) (25,26) (26,32) (30,31) (30,33)\nIs there a path between node 23 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph242-27_11", + "image": "data/connectivity/graph_visual/hard/graph242.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,17) (0,30) (0,27) (0,14) (1,30) (1,23) (1,29) (1,8) (1,12) (2,6) (2,25) (2,3) (3,9) (3,21) (3,7) (4,10) (4,8) (5,27) (5,15) (6,21) (7,9) (7,16) (8,23) (8,11) (8,14) (8,13) (9,28) (10,27) (10,24) (10,11) (11,30) (11,27) (11,13) (12,29) (13,18) (13,26) (14,26) (15,17) (15,24) (16,25) (17,30) (17,23) (17,26) (18,30) (18,27) (20,28) (21,28) (23,30) (24,27) (24,29) (26,27)\nIs there a path between node 27 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph199-9_13", + "image": "data/connectivity/graph_visual/hard/graph199.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,13) (0,15) (0,27) (0,28) (0,14) (0,17) (0,2) (0,19) (0,5) (0,26) (0,29) (0,4) (0,22) (0,6) (0,11) (0,25) (1,12) (1,28) (1,14) (1,17) (1,10) (1,19) (1,20) (1,18) (1,23) (1,26) (1,29) (1,8) (1,4) (1,22) (1,3) (1,11) (1,25) (2,12) (2,13) (2,15) (2,7) (2,27) (2,28) (2,14) (2,10) (2,19) (2,5) (2,20) (2,18) (2,23) (2,26) (2,29) (2,8) (2,4) (2,22) (2,6) (2,3) (2,11) (2,25) (3,12) (3,27) (3,19) (3,20) (3,18) (3,23) (3,26) (3,29) (3,8) (3,4) (3,22) (3,6) (3,25) (4,12) (4,13) (4,10) (4,5) (4,20) (4,18) (4,26) (4,22) (4,6) (4,11) (4,25) (5,12) (5,15) (5,7) (5,28) (5,17) (5,10) (5,19) (5,20) (5,18) (5,26) (5,29) (5,8) (5,22) (6,12) (6,13) (6,15) (6,27) (6,28) (6,17) (6,10) (6,19) (6,20) (6,18) (6,23) (6,26) (6,25) (7,12) (7,13) (7,15) (7,27) (7,10) (7,23) (7,29) (7,8) (7,22) (7,11) (8,13) (8,15) (8,28) (8,14) (8,17) (8,10) (8,19) (8,20) (8,18) (8,23) (8,26) (8,22) (8,11) (9,16) (9,21) (10,12) (10,13) (10,15) (10,28) (10,17) (10,19) (10,20) (10,18) (10,23) (10,29) (10,11) (11,28) (11,14) (11,17) (11,19) (11,20) (11,18) (11,23) (11,26) (11,29) (11,22) (11,25) (12,13) (12,15) (12,28) (12,14) (12,17) (12,19) (12,20) (12,23) (12,26) (12,29) (12,22) (12,25) (13,15) (13,28) (13,17) (13,20) (13,23) (13,26) (13,29) (13,22) (14,15) (14,27) (14,28) (14,17) (14,19) (14,20) (14,23) (14,26) (14,29) (14,25) (15,27) (15,28) (15,17) (15,19) (15,20) (15,18) (15,26) (15,22) (15,25) (16,21) (17,27) (17,19) (17,20) (17,18) (17,23) (17,26) (17,29) (17,22) (18,27) (18,28) (18,23) (18,26) (18,22) (19,27) (19,28) (19,22) (19,25) (20,26) (20,29) (20,25) (21,24) (22,27) (22,26) (22,29) (22,25) (23,27) (23,28) (23,29) (23,25) (25,28) (25,29) (26,27) (26,28) (27,28) (28,29)\nIs there a path between node 9 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph340-7_14", + "image": "data/connectivity/graph_visual/hard/graph340.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,14) (0,13) (0,27) (1,21) (1,24) (1,13) (1,5) (2,19) (3,30) (3,26) (3,10) (3,25) (5,15) (5,9) (5,27) (5,19) (6,22) (6,29) (6,16) (7,15) (7,24) (7,9) (7,19) (9,21) (9,15) (9,24) (10,31) (10,11) (10,23) (11,23) (11,26) (11,17) (12,22) (12,29) (12,16) (13,14) (13,24) (14,21) (14,24) (14,27) (15,21) (16,29) (17,23) (17,25) (18,20) (18,29) (20,22) (21,27) (24,27) (25,28)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph615-10_31", + "image": "data/connectivity/graph_visual/hard/graph615.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,29) (0,8) (0,16) (0,1) (0,28) (0,4) (0,33) (0,21) (0,3) (0,18) (0,17) (0,23) (0,14) (0,27) (0,25) (0,30) (0,11) (0,19) (0,7) (0,26) (0,5) (0,12) (1,8) (1,28) (1,33) (1,3) (1,18) (1,17) (1,23) (1,27) (1,25) (1,30) (1,15) (1,32) (1,19) (1,9) (1,5) (1,20) (1,2) (1,12) (1,34) (2,29) (2,24) (2,8) (2,16) (2,4) (2,33) (2,3) (2,18) (2,17) (2,23) (2,27) (2,25) (2,11) (2,15) (2,32) (2,19) (2,9) (2,26) (2,5) (2,12) (2,34) (3,29) (3,24) (3,8) (3,16) (3,28) (3,4) (3,33) (3,18) (3,17) (3,27) (3,30) (3,11) (3,6) (3,32) (3,9) (3,7) (3,12) (4,29) (4,24) (4,16) (4,33) (4,21) (4,18) (4,17) (4,14) (4,27) (4,25) (4,30) (4,11) (4,15) (4,32) (4,31) (4,19) (4,9) (4,7) (4,26) (4,5) (4,12) (5,29) (5,24) (5,8) (5,16) (5,28) (5,33) (5,18) (5,23) (5,14) (5,27) (5,25) (5,30) (5,15) (5,6) (5,31) (5,19) (5,9) (5,7) (5,26) (5,20) (5,12) (6,24) (6,8) (6,16) (6,28) (6,21) (6,17) (6,14) (6,27) (6,11) (6,15) (6,32) (6,19) (6,9) (6,7) (6,26) (6,20) (6,34) (7,24) (7,8) (7,33) (7,21) (7,18) (7,23) (7,14) (7,25) (7,30) (7,11) (7,15) (7,31) (7,9) (7,26) (7,20) (7,12) (7,34) (8,29) (8,24) (8,16) (8,17) (8,23) (8,14) (8,25) (8,30) (8,32) (8,31) (8,9) (8,20) (8,12) (9,29) (9,24) (9,16) (9,28) (9,21) (9,18) (9,17) (9,23) (9,27) (9,25) (9,15) (9,32) (9,31) (9,19) (9,26) (9,20) (9,12) (9,34) (10,13) (11,29) (11,24) (11,28) (11,33) (11,21) (11,18) (11,23) (11,14) (11,27) (11,25) (11,30) (11,32) (11,31) (11,26) (11,12) (11,34) (12,24) (12,16) (12,28) (12,33) (12,21) (12,18) (12,14) (12,27) (12,25) (12,15) (12,32) (12,26) (12,20) (12,34) (14,29) (14,24) (14,16) (14,28) (14,33) (14,21) (14,17) (14,23) (14,27) (14,25) (14,15) (14,31) (14,26) (14,20) (14,34) (15,29) (15,24) (15,28) (15,18) (15,17) (15,23) (15,27) (15,25) (15,30) (15,31) (15,19) (15,26) (15,34) (16,29) (16,24) (16,28) (16,33) (16,17) (16,27) (16,30) (16,31) (16,26) (16,20) (16,34) (17,24) (17,28) (17,33) (17,18) (17,23) (17,27) (17,30) (17,31) (17,19) (17,20) (17,34) (18,29) (18,28) (18,33) (18,21) (18,23) (18,27) (18,25) (18,30) (18,32) (18,31) (18,19) (18,34) (19,33) (19,21) (19,23) (19,27) (19,25) (19,31) (19,26) (19,20) (19,34) (20,21) (20,23) (20,27) (20,25) (20,30) (20,32) (20,26) (20,34) (21,29) (21,24) (21,33) (21,23) (21,31) (23,24) (23,28) (23,27) (23,25) (23,30) (23,32) (23,31) (23,26) (23,34) (24,29) (24,30) (24,32) (24,31) (24,26) (24,34) (25,29) (25,28) (25,33) (25,27) (25,31) (25,34) (26,28) (26,27) (26,32) (26,31) (26,34) (27,29) (27,33) (27,30) (27,32) (27,31) (28,29) (28,33) (28,30) (28,32) (28,31) (28,34) (29,33) (29,30) (29,32) (29,31) (29,34) (30,33) (30,32) (30,31) (30,34) (31,33) (31,34) (32,33) (32,34) (33,34)\nIs there a path between node 10 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph478-14_17", + "image": "data/connectivity/graph_visual/hard/graph478.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (0,6) (0,31) (0,20) (0,8) (0,4) (0,2) (0,28) (0,32) (0,3) (0,10) (0,5) (0,27) (0,16) (0,15) (0,14) (0,9) (0,26) (0,19) (1,17) (1,31) (1,20) (1,4) (1,29) (1,28) (1,32) (1,3) (1,10) (1,5) (1,16) (1,15) (1,9) (1,26) (1,19) (1,24) (2,17) (2,31) (2,20) (2,8) (2,4) (2,29) (2,3) (2,5) (2,27) (2,15) (2,14) (2,9) (3,6) (3,17) (3,31) (3,20) (3,8) (3,4) (3,28) (3,32) (3,10) (3,27) (3,15) (3,14) (3,9) (3,19) (4,6) (4,17) (4,31) (4,20) (4,8) (4,29) (4,28) (4,32) (4,10) (4,5) (4,27) (4,14) (4,26) (4,19) (4,24) (5,6) (5,17) (5,20) (5,8) (5,29) (5,32) (5,10) (5,27) (5,15) (5,14) (5,9) (5,26) (5,19) (5,24) (6,17) (6,8) (6,29) (6,32) (6,10) (6,16) (6,14) (6,9) (6,19) (6,24) (7,23) (7,25) (7,13) (7,21) (7,22) (7,30) (7,12) (8,17) (8,31) (8,20) (8,29) (8,28) (8,32) (8,10) (8,27) (8,16) (8,15) (8,14) (8,19) (8,24) (9,31) (9,28) (9,32) (9,10) (9,27) (9,16) (9,15) (9,14) (9,26) (9,19) (9,24) (10,17) (10,28) (10,32) (10,27) (10,16) (10,15) (10,26) (10,19) (10,24) (11,23) (11,18) (11,25) (11,13) (11,21) (11,22) (11,12) (12,18) (12,25) (12,13) (12,22) (12,30) (13,23) (13,18) (13,25) (13,21) (13,22) (14,17) (14,28) (14,27) (14,16) (14,15) (14,26) (14,19) (15,31) (15,20) (15,28) (15,32) (15,27) (15,26) (15,19) (15,24) (16,17) (16,31) (16,20) (16,29) (16,28) (16,26) (16,19) (16,24) (17,29) (17,28) (17,26) (17,19) (18,23) (18,25) (19,31) (19,20) (19,29) (19,32) (19,27) (20,31) (20,29) (20,28) (20,26) (21,25) (21,22) (21,30) (22,23) (22,25) (22,30) (23,30) (24,31) (24,29) (24,32) (24,26) (25,30) (26,31) (26,29) (26,28) (26,32) (27,31) (27,29) (27,28) (27,32) (28,31) (28,29) (28,32) (29,31) (29,32) (31,32)\nIs there a path between node 14 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph299-8_15", + "image": "data/connectivity/graph_visual/hard/graph299.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,31) (0,14) (0,18) (0,24) (0,23) (0,25) (0,30) (0,21) (0,26) (1,5) (1,19) (1,15) (1,28) (1,20) (1,2) (1,17) (1,27) (1,6) (2,5) (2,19) (2,15) (2,28) (2,20) (2,16) (2,17) (2,4) (2,8) (2,10) (2,6) (2,29) (2,12) (3,7) (3,31) (3,11) (3,14) (3,18) (3,24) (3,23) (3,25) (3,30) (4,5) (4,19) (4,15) (4,20) (4,16) (4,10) (4,6) (5,13) (5,22) (5,28) (5,20) (5,8) (5,6) (5,29) (5,12) (6,19) (6,13) (6,22) (6,20) (6,17) (6,8) (6,10) (6,27) (7,31) (7,11) (7,14) (7,23) (7,25) (7,30) (7,21) (7,26) (8,19) (8,20) (8,16) (8,27) (8,29) (8,12) (9,31) (9,11) (9,14) (9,24) (9,23) (9,30) (9,21) (9,26) (10,15) (10,13) (10,22) (10,28) (10,20) (10,16) (10,17) (10,12) (11,31) (11,18) (11,24) (11,30) (11,21) (11,26) (12,19) (12,15) (12,22) (12,28) (12,20) (12,16) (13,19) (13,15) (13,22) (13,28) (13,16) (13,27) (13,29) (14,31) (14,18) (14,23) (14,25) (14,30) (14,21) (15,22) (15,28) (15,20) (15,16) (15,17) (15,27) (15,29) (16,19) (16,22) (16,28) (16,17) (16,29) (17,19) (17,22) (17,20) (17,29) (18,31) (18,23) (18,25) (18,21) (19,20) (19,27) (20,22) (20,28) (20,27) (20,29) (21,24) (21,25) (21,30) (21,26) (22,28) (22,27) (23,25) (23,30) (23,26) (24,31) (24,25) (24,30) (24,26) (25,31) (25,30) (25,26) (26,31) (27,28) (27,29) (30,31)\nIs there a path between node 8 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph375-27_19", + "image": "data/connectivity/graph_visual/hard/graph375.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,20) (0,4) (0,29) (0,11) (0,3) (0,1) (0,22) (0,10) (0,13) (0,16) (0,19) (0,7) (0,15) (0,25) (0,2) (0,23) (0,5) (1,18) (1,12) (1,9) (1,27) (1,20) (1,14) (1,11) (1,3) (1,24) (1,28) (1,6) (1,22) (1,10) (1,13) (1,15) (1,25) (1,2) (1,23) (1,5) (1,17) (2,18) (2,12) (2,9) (2,27) (2,29) (2,14) (2,11) (2,28) (2,6) (2,22) (2,10) (2,16) (2,7) (2,15) (2,25) (2,23) (2,17) (3,9) (3,27) (3,4) (3,29) (3,11) (3,24) (3,6) (3,21) (3,22) (3,10) (3,13) (3,16) (3,19) (3,7) (3,15) (3,25) (3,23) (4,18) (4,9) (4,27) (4,29) (4,14) (4,21) (4,22) (4,16) (4,19) (4,25) (4,23) (5,9) (5,27) (5,20) (5,29) (5,14) (5,28) (5,6) (5,22) (5,13) (5,16) (5,15) (5,25) (5,23) (6,12) (6,9) (6,27) (6,20) (6,14) (6,11) (6,24) (6,21) (6,22) (6,10) (6,13) (6,16) (6,19) (6,15) (6,25) (6,23) (7,18) (7,12) (7,9) (7,27) (7,11) (7,24) (7,28) (7,21) (7,13) (7,19) (7,25) (9,18) (9,12) (9,27) (9,20) (9,14) (9,28) (9,21) (9,22) (9,10) (9,19) (9,25) (9,23) (9,17) (10,18) (10,12) (10,20) (10,29) (10,14) (10,11) (10,21) (10,22) (10,13) (10,16) (10,19) (10,15) (10,17) (11,18) (11,27) (11,20) (11,14) (11,28) (11,13) (11,19) (11,15) (11,25) (11,23) (12,27) (12,22) (12,13) (12,16) (12,19) (12,25) (12,23) (13,20) (13,14) (13,24) (13,28) (13,21) (13,22) (13,16) (13,15) (13,25) (13,23) (13,17) (14,18) (14,27) (14,20) (14,29) (14,24) (14,28) (14,21) (14,22) (14,16) (14,19) (14,25) (14,17) (15,27) (15,20) (15,29) (15,24) (15,28) (15,21) (15,22) (15,19) (15,25) (15,17) (16,18) (16,20) (16,29) (16,24) (16,22) (16,19) (16,25) (16,17) (17,18) (17,27) (17,29) (17,24) (17,28) (17,21) (17,22) (17,19) (17,25) (17,23) (18,20) (18,29) (18,24) (18,28) (18,21) (18,19) (18,23) (19,27) (19,20) (19,29) (19,24) (19,28) (19,23) (20,22) (20,25) (21,27) (21,29) (21,24) (21,28) (21,25) (21,23) (22,27) (22,24) (22,28) (22,23) (23,27) (23,29) (23,24) (23,28) (23,25) (24,27) (24,28) (25,29) (25,28) (26,31) (27,29) (27,28) (28,29) (30,31)\nIs there a path between node 27 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph230-2_14", + "image": "data/connectivity/graph_visual/hard/graph230.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,16) (0,8) (0,24) (0,3) (0,6) (0,21) (0,15) (0,29) (0,14) (0,1) (0,17) (0,12) (0,26) (1,16) (1,24) (1,3) (1,6) (1,21) (1,15) (1,20) (1,25) (1,29) (1,17) (1,12) (1,26) (2,22) (2,28) (2,4) (2,5) (2,19) (2,18) (2,9) (3,16) (3,24) (3,6) (3,21) (3,29) (3,11) (3,17) (3,12) (3,26) (4,22) (4,5) (4,19) (4,18) (4,23) (4,10) (4,13) (4,27) (5,22) (5,28) (5,18) (5,23) (5,9) (5,13) (5,27) (6,16) (6,8) (6,24) (6,21) (6,20) (6,11) (6,14) (6,17) (6,12) (6,26) (7,22) (7,28) (7,19) (7,18) (7,23) (7,9) (7,13) (7,27) (8,16) (8,24) (8,21) (8,20) (8,29) (8,11) (8,14) (8,12) (8,26) (9,23) (9,10) (9,13) (9,27) (10,22) (10,18) (10,23) (10,27) (11,16) (11,24) (11,21) (11,15) (11,20) (11,25) (11,14) (11,17) (11,12) (11,26) (12,16) (12,21) (12,15) (12,20) (12,25) (12,14) (12,17) (12,26) (13,19) (13,18) (14,16) (14,24) (14,21) (14,20) (14,25) (14,29) (14,17) (15,16) (15,24) (15,21) (15,20) (15,17) (15,26) (16,24) (16,20) (16,29) (16,17) (17,24) (17,21) (17,25) (17,29) (18,22) (18,28) (18,19) (18,23) (18,27) (19,22) (19,28) (19,23) (19,27) (20,21) (20,25) (20,29) (21,24) (21,25) (21,29) (21,26) (22,28) (22,23) (23,28) (23,27) (24,25) (24,29) (24,26) (25,29) (27,28)\nIs there a path between node 2 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph416-16_21", + "image": "data/connectivity/graph_visual/hard/graph416.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,25) (0,27) (1,14) (1,23) (1,5) (1,6) (1,20) (1,8) (2,10) (2,25) (2,22) (3,19) (3,26) (4,32) (4,7) (4,20) (4,8) (5,17) (6,17) (6,8) (8,14) (8,23) (8,32) (9,19) (9,26) (9,13) (10,25) (10,12) (10,11) (11,25) (11,22) (12,24) (12,16) (12,25) (12,21) (13,15) (15,29) (15,19) (16,25) (17,31) (17,23) (17,32) (18,29) (18,30) (21,24) (21,25) (24,27) (26,30)\nIs there a path between node 16 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph494-9_31", + "image": "data/connectivity/graph_visual/hard/graph494.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,12) (0,13) (0,2) (0,14) (0,23) (0,8) (0,1) (0,25) (0,27) (0,10) (1,29) (1,13) (1,19) (1,28) (1,23) (1,30) (1,25) (1,24) (2,12) (2,5) (2,14) (2,17) (2,23) (3,7) (3,12) (3,19) (3,23) (3,8) (3,30) (3,25) (3,24) (4,33) (5,20) (5,23) (5,30) (6,15) (6,11) (7,32) (7,17) (7,23) (7,8) (7,10) (8,29) (8,12) (8,32) (8,20) (8,19) (8,17) (8,30) (9,29) (9,28) (9,30) (9,24) (10,13) (10,20) (10,14) (10,22) (11,31) (12,13) (12,23) (12,27) (12,26) (13,29) (13,32) (13,14) (13,28) (13,30) (13,24) (14,17) (14,30) (14,22) (14,27) (15,16) (15,31) (15,33) (17,32) (17,20) (17,19) (17,27) (17,24) (17,26) (18,21) (20,28) (20,30) (20,25) (21,31) (22,32) (22,28) (22,30) (23,28) (23,25) (23,27) (24,29) (24,28) (24,26) (25,32) (26,29) (26,27) (27,32) (27,30) (28,32) (28,30)\nIs there a path between node 9 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph388-8_18", + "image": "data/connectivity/graph_visual/hard/graph388.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,17) (0,10) (0,28) (0,30) (0,29) (0,3) (1,14) (1,2) (2,25) (2,20) (2,7) (2,32) (2,22) (3,24) (3,19) (3,23) (3,4) (3,12) (3,29) (4,26) (4,24) (4,23) (4,8) (4,13) (5,26) (5,19) (5,23) (5,8) (5,15) (5,21) (6,14) (7,32) (8,16) (8,12) (8,29) (9,26) (9,13) (9,18) (9,29) (9,31) (10,17) (10,11) (10,30) (10,23) (10,13) (11,16) (11,17) (11,19) (11,28) (11,23) (12,26) (12,24) (12,21) (13,26) (13,17) (13,19) (13,30) (13,31) (14,25) (14,22) (15,16) (15,17) (15,23) (15,18) (15,29) (16,26) (16,24) (16,18) (16,21) (17,24) (17,19) (17,28) (17,30) (17,23) (18,24) (18,21) (19,26) (19,24) (19,28) (19,23) (20,32) (22,32) (22,27) (24,26) (24,30) (26,29) (28,29)\nIs there a path between node 8 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph168-16_8", + "image": "data/connectivity/graph_visual/hard/graph168.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,3) (1,12) (2,16) (2,13) (2,23) (4,5) (5,19) (5,20) (6,27) (6,13) (6,7) (7,28) (7,22) (7,23) (7,26) (8,9) (8,26) (9,27) (9,28) (9,23) (9,25) (9,24) (10,16) (10,27) (10,23) (10,25) (11,19) (11,17) (13,16) (13,27) (13,21) (13,22) (14,22) (15,16) (15,27) (15,28) (15,22) (15,24) (16,27) (16,28) (16,26) (17,18) (17,19) (18,20) (19,20) (22,23) (23,28) (23,26) (23,24) (24,25) (25,27) (25,26)\nIs there a path between node 16 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph159-19_15", + "image": "data/connectivity/graph_visual/hard/graph159.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,2) (0,26) (0,21) (0,9) (0,24) (0,17) (0,22) (1,16) (2,20) (2,11) (2,26) (2,27) (2,21) (2,12) (2,9) (2,23) (2,4) (2,19) (3,25) (4,8) (4,23) (4,17) (4,7) (4,13) (6,16) (7,10) (7,20) (7,12) (7,9) (7,23) (7,17) (7,22) (7,13) (7,19) (8,18) (8,11) (8,9) (8,17) (9,10) (9,11) (9,24) (9,23) (10,20) (10,11) (10,24) (10,13) (11,18) (11,12) (12,20) (12,24) (13,18) (13,20) (13,22) (13,14) (14,20) (14,24) (14,23) (14,19) (15,27) (15,23) (15,19) (17,28) (17,23) (18,21) (18,24) (18,19) (19,22) (20,28) (20,24) (21,28) (21,27) (22,28) (22,27) (23,26) (23,27) (23,24) (24,26) (26,28) (26,27) (27,28)\nIs there a path between node 19 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph309-10_31", + "image": "data/connectivity/graph_visual/hard/graph309.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,1) (0,12) (0,20) (0,31) (0,16) (0,24) (0,26) (1,31) (1,8) (1,18) (2,22) (3,10) (3,6) (3,19) (4,27) (5,14) (5,25) (5,11) (6,10) (6,7) (8,12) (8,29) (8,23) (8,15) (9,27) (10,22) (10,17) (11,25) (12,30) (12,23) (12,15) (13,22) (13,19) (14,25) (14,27) (15,16) (15,29) (15,23) (15,28) (16,31) (16,30) (16,24) (17,19) (18,20) (18,26) (18,28) (20,29) (20,26) (23,31) (23,30) (23,26) (23,28) (26,29) (26,28) (28,30)\nIs there a path between node 10 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph191-26_21", + "image": "data/connectivity/graph_visual/hard/graph191.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,13) (0,15) (0,29) (0,14) (0,4) (0,11) (1,21) (1,10) (1,9) (2,21) (2,8) (2,10) (2,23) (2,19) (2,9) (3,29) (3,11) (4,27) (4,15) (4,28) (4,11) (5,27) (6,16) (6,23) (7,16) (8,21) (8,19) (8,17) (8,9) (9,21) (9,19) (10,16) (10,23) (11,14) (12,22) (12,26) (14,27) (14,15) (16,21) (16,18) (22,24) (25,26) (28,29)\nIs there a path between node 26 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph149-28_25", + "image": "data/connectivity/graph_visual/hard/graph149.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,27) (0,6) (0,23) (0,8) (1,24) (1,12) (1,5) (1,22) (1,26) (1,18) (1,9) (1,7) (1,15) (1,19) (1,11) (1,16) (1,2) (1,3) (1,10) (2,24) (2,13) (2,5) (2,22) (2,21) (2,26) (2,18) (2,9) (2,14) (2,19) (2,20) (2,28) (2,10) (3,13) (3,12) (3,5) (3,22) (3,21) (3,26) (3,18) (3,7) (3,14) (3,15) (3,19) (3,11) (3,16) (3,17) (3,28) (3,10) (4,25) (4,27) (4,6) (4,23) (5,13) (5,22) (5,21) (5,26) (5,18) (5,7) (5,15) (5,19) (5,11) (5,20) (5,16) (5,10) (6,25) (6,27) (6,23) (7,13) (7,12) (7,21) (7,26) (7,18) (7,14) (7,15) (7,11) (7,17) (7,10) (8,25) (8,27) (8,23) (9,24) (9,12) (9,21) (9,14) (9,15) (9,19) (9,16) (10,24) (10,22) (10,26) (10,15) (10,20) (10,28) (11,24) (11,13) (11,12) (11,22) (11,21) (11,26) (11,15) (11,20) (11,17) (12,13) (12,22) (12,21) (12,18) (12,14) (12,15) (12,19) (12,20) (12,28) (13,24) (13,22) (13,21) (13,26) (13,18) (13,14) (13,15) (13,19) (13,16) (13,17) (13,28) (14,24) (14,21) (14,26) (14,18) (14,15) (14,19) (14,16) (14,28) (15,22) (15,21) (15,18) (15,20) (15,16) (15,17) (15,28) (16,22) (16,21) (16,26) (16,19) (16,28) (17,22) (17,21) (17,26) (17,19) (17,20) (18,22) (18,26) (18,20) (19,22) (19,21) (19,20) (19,28) (20,24) (20,22) (20,21) (20,28) (21,24) (21,22) (21,26) (21,28) (22,24) (22,26) (22,28) (23,25) (23,27) (24,26) (24,28) (25,27)\nIs there a path between node 28 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph129-17_19", + "image": "data/connectivity/graph_visual/hard/graph129.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,6) (0,7) (0,19) (0,18) (0,12) (0,17) (0,13) (0,24) (0,3) (0,1) (0,15) (0,11) (0,27) (0,16) (1,6) (1,8) (1,26) (1,7) (1,10) (1,19) (1,18) (1,24) (1,3) (1,9) (1,15) (1,11) (1,27) (2,20) (2,25) (2,14) (2,21) (3,6) (3,8) (3,26) (3,7) (3,10) (3,19) (3,18) (3,12) (3,17) (3,24) (3,9) (3,15) (3,11) (4,22) (5,23) (5,20) (5,25) (6,8) (6,26) (6,19) (6,18) (6,12) (6,17) (6,13) (6,24) (6,15) (6,11) (6,27) (6,16) (7,10) (7,19) (7,18) (7,17) (7,13) (7,24) (7,9) (7,16) (8,26) (8,19) (8,18) (8,12) (8,17) (8,13) (8,24) (8,9) (8,15) (8,27) (8,16) (9,26) (9,10) (9,18) (9,12) (9,17) (9,13) (9,15) (9,27) (9,16) (10,26) (10,19) (10,17) (10,13) (10,15) (10,16) (11,26) (11,19) (11,18) (11,12) (11,17) (11,15) (12,26) (12,19) (12,18) (12,13) (12,24) (13,18) (13,24) (13,27) (13,16) (14,23) (14,20) (14,21) (15,26) (15,19) (15,18) (15,17) (15,16) (16,26) (16,19) (16,24) (16,27) (17,26) (17,24) (17,27) (18,26) (18,19) (18,27) (19,26) (19,27) (20,25) (21,23) (21,25)\nIs there a path between node 17 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph156-27_16", + "image": "data/connectivity/graph_visual/hard/graph156.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,19) (0,17) (1,24) (1,25) (2,10) (2,3) (2,16) (3,20) (3,15) (4,5) (5,9) (5,23) (5,13) (6,21) (6,26) (7,25) (7,21) (8,24) (8,22) (9,23) (9,25) (10,20) (10,11) (10,27) (10,17) (11,15) (11,14) (12,27) (13,23) (13,22) (14,20) (14,15) (14,28) (14,16) (14,17) (15,28) (15,27) (20,28) (21,23) (21,22) (21,26) (22,25) (23,25) (24,26) (25,26)\nIs there a path between node 27 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph621-2_10", + "image": "data/connectivity/graph_visual/hard/graph621.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,9) (0,26) (0,24) (0,27) (0,11) (1,3) (1,2) (1,20) (1,6) (1,31) (2,3) (2,33) (2,30) (2,32) (2,19) (2,7) (3,31) (3,5) (4,33) (4,9) (4,30) (4,16) (4,25) (4,24) (5,30) (5,26) (5,27) (5,15) (6,33) (6,20) (6,24) (6,27) (6,11) (6,7) (7,33) (7,23) (7,30) (9,26) (9,29) (9,24) (9,31) (9,15) (10,28) (10,13) (10,22) (10,21) (11,16) (11,24) (12,15) (13,14) (13,17) (15,23) (15,20) (15,31) (16,20) (16,24) (16,19) (17,21) (19,33) (19,23) (19,25) (19,32) (20,33) (20,23) (20,32) (20,24) (20,27) (21,28) (23,33) (23,32) (24,30) (24,32) (24,29) (25,30) (25,32) (25,29) (25,27) (26,30) (26,32) (26,29) (27,33) (27,30) (29,30) (29,31) (30,32) (31,32)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph341-16_12", + "image": "data/connectivity/graph_visual/hard/graph341.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,30) (0,28) (0,1) (0,7) (0,13) (1,3) (1,10) (1,9) (1,14) (1,23) (1,13) (2,26) (2,10) (2,28) (2,7) (2,14) (2,13) (3,26) (3,10) (3,9) (3,11) (3,19) (3,4) (3,14) (3,13) (3,20) (4,26) (4,8) (4,9) (4,17) (4,12) (4,14) (4,23) (5,26) (5,8) (5,11) (5,27) (5,23) (6,21) (6,22) (6,18) (7,15) (7,26) (7,30) (7,10) (7,11) (7,23) (7,13) (7,31) (7,16) (8,15) (8,26) (8,10) (8,28) (8,17) (8,19) (8,23) (8,16) (9,15) (9,28) (9,11) (9,19) (9,27) (10,28) (10,11) (10,17) (10,13) (10,31) (10,16) (11,15) (11,30) (11,17) (11,14) (12,15) (12,23) (12,31) (12,16) (13,26) (13,19) (13,14) (13,27) (13,31) (14,30) (14,28) (14,19) (14,27) (14,20) (14,31) (15,26) (15,30) (15,19) (15,23) (15,20) (16,26) (16,30) (16,31) (17,27) (17,20) (18,22) (18,24) (19,26) (19,20) (20,28) (21,22) (21,25) (22,24) (22,25) (23,26) (24,25) (25,29) (26,30) (27,28) (28,31)\nIs there a path between node 16 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph610-10_7", + "image": "data/connectivity/graph_visual/hard/graph610.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,31) (0,11) (0,18) (0,1) (1,28) (1,31) (1,13) (1,8) (1,5) (1,32) (1,34) (2,17) (3,14) (3,15) (3,24) (4,32) (4,34) (5,8) (5,9) (6,25) (6,10) (6,15) (6,7) (6,19) (7,14) (7,10) (7,16) (7,12) (7,21) (8,18) (9,31) (9,11) (9,34) (10,23) (10,29) (10,33) (10,16) (10,30) (11,20) (11,18) (12,23) (12,14) (12,25) (12,19) (12,24) (13,34) (14,25) (15,23) (15,25) (15,24) (16,23) (16,25) (16,29) (16,33) (16,17) (17,30) (17,21) (17,24) (18,22) (18,20) (19,24) (20,28) (20,32) (20,34) (22,26) (22,34) (23,25) (23,30) (24,33) (24,30) (25,29) (25,33) (26,27) (27,32) (28,32) (28,34) (29,30) (30,33) (31,32)\nIs there a path between node 10 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph429-16_5", + "image": "data/connectivity/graph_visual/hard/graph429.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,30) (0,15) (0,16) (0,27) (0,1) (0,13) (1,14) (1,30) (1,27) (1,13) (2,9) (2,25) (2,22) (2,8) (2,5) (2,26) (2,20) (2,10) (2,6) (2,31) (2,32) (2,19) (2,17) (2,18) (2,23) (2,4) (2,11) (3,9) (3,25) (3,22) (3,8) (3,26) (3,20) (3,24) (3,10) (3,6) (3,31) (3,17) (3,18) (3,12) (3,23) (3,4) (4,25) (4,22) (4,8) (4,5) (4,20) (4,31) (4,32) (4,19) (4,17) (4,23) (4,11) (5,9) (5,25) (5,22) (5,8) (5,10) (5,6) (5,32) (5,19) (5,18) (5,12) (5,23) (5,11) (6,9) (6,25) (6,22) (6,26) (6,24) (6,31) (6,32) (6,19) (6,17) (6,18) (7,29) (7,28) (8,22) (8,26) (8,20) (8,10) (8,31) (8,19) (8,18) (8,11) (9,25) (9,22) (9,26) (9,20) (9,24) (9,31) (9,32) (9,19) (9,17) (9,12) (9,23) (10,25) (10,22) (10,20) (10,24) (10,31) (10,32) (10,19) (10,17) (10,18) (10,12) (10,23) (10,11) (11,26) (11,20) (11,24) (11,31) (11,19) (11,17) (12,25) (12,26) (12,20) (12,24) (12,31) (12,32) (12,19) (13,14) (13,30) (13,27) (14,30) (14,15) (14,16) (15,16) (17,25) (17,22) (17,26) (17,20) (17,24) (17,31) (17,32) (17,23) (18,25) (18,22) (18,26) (18,32) (19,25) (19,22) (19,26) (19,20) (19,32) (19,23) (20,25) (20,22) (20,26) (20,24) (20,31) (21,29) (22,25) (22,26) (22,24) (22,32) (23,25) (23,26) (23,24) (23,31) (24,26) (24,31) (24,32) (25,26) (25,31) (25,32) (27,30) (28,29)\nIs there a path between node 16 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph513-14_24", + "image": "data/connectivity/graph_visual/hard/graph513.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,17) (0,8) (0,6) (0,1) (0,22) (0,25) (0,11) (0,2) (1,10) (1,8) (1,22) (1,25) (1,11) (1,32) (1,29) (1,7) (1,3) (2,10) (2,18) (2,25) (2,30) (2,11) (2,15) (2,28) (2,7) (3,33) (3,8) (3,20) (3,30) (3,15) (3,19) (4,14) (4,12) (4,13) (5,33) (5,17) (5,21) (5,18) (5,22) (5,28) (5,7) (6,20) (6,30) (6,32) (6,27) (7,33) (7,21) (7,18) (7,22) (7,30) (7,15) (7,27) (7,28) (7,29) (8,21) (8,25) (8,20) (8,11) (8,27) (10,17) (10,20) (10,32) (10,27) (11,22) (11,25) (11,15) (11,27) (12,31) (12,16) (12,23) (13,16) (13,23) (14,31) (14,26) (15,25) (15,20) (15,27) (17,22) (17,20) (17,32) (17,29) (18,32) (19,25) (19,30) (19,32) (19,27) (20,33) (20,25) (20,30) (20,32) (20,27) (21,22) (21,29) (22,28) (23,31) (23,24) (24,31) (25,29) (26,31) (28,33) (29,30) (32,33)\nIs there a path between node 14 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph687-26_33", + "image": "data/connectivity/graph_visual/hard/graph687.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,11) (0,4) (0,9) (0,10) (0,14) (0,1) (0,34) (0,6) (0,20) (0,16) (0,32) (0,12) (0,19) (0,13) (1,11) (1,24) (1,26) (1,9) (1,10) (1,14) (1,34) (1,6) (1,5) (1,20) (1,27) (1,12) (1,19) (1,7) (1,28) (1,13) (1,15) (1,17) (2,11) (2,4) (2,24) (2,33) (2,26) (2,23) (2,9) (2,10) (2,34) (2,6) (2,5) (2,20) (2,16) (2,27) (2,32) (2,19) (2,7) (2,13) (2,15) (2,17) (3,30) (3,8) (4,11) (4,24) (4,33) (4,23) (4,31) (4,34) (4,6) (4,27) (4,32) (4,29) (4,12) (4,19) (4,13) (4,17) (5,11) (5,26) (5,23) (5,9) (5,31) (5,14) (5,34) (5,6) (5,16) (5,32) (5,19) (5,28) (5,13) (5,15) (5,17) (6,11) (6,23) (6,9) (6,10) (6,31) (6,14) (6,34) (6,20) (6,16) (6,27) (6,12) (6,19) (6,7) (6,28) (6,13) (6,15) (7,33) (7,26) (7,23) (7,10) (7,31) (7,14) (7,16) (7,27) (7,32) (7,12) (7,28) (7,13) (7,15) (8,22) (8,25) (8,18) (8,21) (9,11) (9,24) (9,26) (9,23) (9,10) (9,31) (9,34) (9,20) (9,16) (9,27) (9,32) (9,19) (9,28) (9,13) (9,15) (9,17) (10,24) (10,33) (10,26) (10,23) (10,31) (10,14) (10,34) (10,16) (10,27) (10,32) (10,29) (10,12) (10,28) (10,15) (11,33) (11,26) (11,23) (11,14) (11,34) (11,20) (11,16) (11,12) (11,19) (11,28) (11,15) (11,17) (12,24) (12,33) (12,23) (12,31) (12,14) (12,20) (12,27) (12,32) (12,19) (12,17) (13,24) (13,23) (13,31) (13,14) (13,34) (13,20) (13,16) (13,27) (13,32) (13,29) (13,19) (13,28) (14,24) (14,33) (14,26) (14,23) (14,31) (14,20) (14,16) (14,27) (14,32) (14,29) (14,28) (14,15) (14,17) (15,24) (15,33) (15,26) (15,23) (15,31) (15,34) (15,20) (15,16) (15,32) (16,24) (16,33) (16,26) (16,23) (16,34) (16,20) (16,27) (16,32) (16,29) (16,19) (16,28) (17,24) (17,33) (17,26) (17,23) (17,31) (17,34) (17,20) (17,27) (17,29) (17,19) (17,28) (18,22) (18,25) (18,21) (19,24) (19,33) (19,26) (19,31) (19,34) (19,20) (19,27) (19,32) (19,29) (19,28) (20,33) (20,26) (20,23) (20,31) (20,34) (20,27) (20,32) (20,29) (20,28) (21,22) (21,25) (21,30) (22,25) (23,26) (23,34) (23,27) (23,32) (23,29) (24,33) (24,31) (24,34) (24,27) (24,29) (24,28) (25,30) (26,33) (26,27) (26,32) (26,29) (26,28) (27,31) (27,34) (27,32) (27,29) (27,28) (28,33) (28,34) (28,32) (28,29) (29,33) (29,32) (31,33) (31,34) (31,32) (32,33) (32,34) (33,34)\nIs there a path between node 26 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph280-29_21", + "image": "data/connectivity/graph_visual/hard/graph280.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,12) (0,14) (0,16) (0,20) (0,8) (0,13) (0,18) (0,10) (0,29) (0,3) (0,7) (0,9) (1,26) (1,5) (1,11) (1,19) (1,28) (1,24) (1,6) (2,12) (2,14) (2,16) (2,20) (2,8) (2,13) (2,23) (2,18) (2,25) (2,3) (2,7) (2,9) (3,16) (3,8) (3,13) (3,18) (3,25) (3,10) (3,29) (3,7) (4,15) (4,27) (5,28) (5,24) (5,22) (6,26) (6,11) (6,19) (6,28) (6,24) (6,22) (7,14) (7,16) (7,20) (7,13) (7,23) (7,25) (7,10) (7,21) (7,9) (8,14) (8,20) (8,13) (8,23) (8,10) (9,14) (9,16) (9,20) (9,13) (9,18) (9,25) (9,21) (9,29) (10,14) (10,16) (10,20) (10,13) (10,23) (10,25) (10,21) (11,26) (11,17) (11,24) (11,22) (12,14) (12,16) (12,13) (12,23) (12,18) (12,25) (12,21) (12,29) (13,14) (13,16) (13,18) (13,21) (13,29) (14,16) (14,20) (14,23) (14,18) (14,21) (14,29) (15,30) (15,27) (16,20) (16,23) (16,25) (16,21) (16,29) (17,26) (17,19) (17,28) (17,22) (18,23) (18,25) (18,21) (18,29) (19,26) (20,23) (20,25) (20,29) (21,23) (21,25) (21,29) (22,26) (22,28) (22,24) (23,25) (23,29) (24,26) (24,28) (25,29) (26,28)\nIs there a path between node 29 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph186-15_2", + "image": "data/connectivity/graph_visual/hard/graph186.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,14) (0,10) (0,2) (2,15) (2,20) (2,23) (2,14) (2,17) (2,24) (2,18) (3,21) (4,27) (5,9) (5,22) (6,29) (6,8) (7,29) (7,25) (7,20) (7,17) (7,18) (7,8) (8,23) (8,24) (10,23) (10,18) (11,27) (12,13) (13,21) (14,25) (14,23) (14,17) (14,24) (15,29) (15,25) (15,23) (15,16) (16,29) (16,17) (17,25) (17,23) (17,24) (17,18) (18,29) (20,25) (22,26) (23,25) (24,29) (26,27)\nIs there a path between node 15 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph597-14_28", + "image": "data/connectivity/graph_visual/hard/graph597.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,16) (0,31) (0,29) (0,28) (0,7) (0,26) (0,22) (0,1) (0,33) (0,13) (0,12) (0,24) (0,17) (0,30) (0,20) (0,2) (0,4) (0,25) (1,16) (1,31) (1,28) (1,7) (1,26) (1,11) (1,12) (1,18) (1,6) (1,24) (1,17) (1,20) (1,3) (1,4) (1,25) (1,21) (2,16) (2,10) (2,31) (2,29) (2,7) (2,26) (2,33) (2,12) (2,18) (2,6) (2,24) (2,30) (2,20) (2,23) (2,3) (2,4) (2,25) (2,21) (3,10) (3,31) (3,29) (3,28) (3,7) (3,26) (3,33) (3,13) (3,12) (3,18) (3,30) (3,20) (3,23) (3,25) (3,21) (4,16) (4,29) (4,28) (4,26) (4,33) (4,11) (4,12) (4,18) (4,6) (4,24) (4,17) (4,30) (4,20) (4,25) (4,21) (5,27) (5,8) (5,15) (5,14) (5,9) (6,10) (6,31) (6,22) (6,33) (6,18) (6,24) (6,20) (6,21) (7,16) (7,10) (7,31) (7,29) (7,22) (7,13) (7,11) (7,12) (7,18) (7,24) (7,17) (7,30) (7,20) (7,23) (7,21) (8,15) (8,9) (9,14) (10,16) (10,31) (10,29) (10,28) (10,22) (10,33) (10,13) (10,11) (10,17) (10,30) (10,20) (10,25) (10,21) (11,16) (11,31) (11,29) (11,28) (11,26) (11,22) (11,33) (11,13) (11,12) (11,18) (11,30) (11,20) (11,23) (11,25) (11,21) (12,31) (12,29) (12,26) (12,22) (12,33) (12,13) (12,24) (12,17) (12,20) (12,23) (12,25) (12,21) (13,31) (13,29) (13,26) (13,24) (13,17) (13,30) (13,20) (13,23) (13,25) (14,27) (14,15) (15,27) (16,29) (16,26) (16,22) (16,33) (16,18) (16,17) (16,30) (16,20) (16,23) (16,25) (17,31) (17,24) (17,30) (17,23) (17,25) (18,31) (18,28) (18,22) (18,33) (18,24) (18,20) (18,23) (18,25) (19,32) (20,28) (20,22) (20,24) (20,30) (20,23) (20,25) (20,21) (21,31) (21,29) (21,22) (21,33) (21,24) (22,31) (22,29) (22,28) (22,26) (22,33) (22,24) (22,30) (22,23) (22,25) (23,31) (23,29) (23,28) (23,26) (23,33) (23,24) (23,30) (23,25) (24,31) (24,29) (24,28) (24,33) (24,30) (24,25) (25,29) (25,28) (26,31) (26,29) (26,28) (26,33) (28,31) (28,29) (28,33) (29,30) (30,31)\nIs there a path between node 14 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph691-20_27", + "image": "data/connectivity/graph_visual/hard/graph691.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,17) (0,8) (0,34) (0,14) (0,16) (0,5) (0,22) (0,9) (0,25) (0,3) (0,32) (1,10) (2,21) (2,33) (2,30) (2,20) (3,6) (3,17) (3,26) (3,8) (3,14) (3,23) (3,16) (3,5) (3,22) (3,25) (4,11) (4,28) (4,15) (4,13) (4,19) (4,12) (5,6) (5,26) (5,8) (5,14) (5,23) (5,16) (5,27) (5,25) (6,26) (6,34) (6,16) (6,27) (6,22) (6,9) (6,25) (6,32) (7,33) (7,18) (7,29) (7,30) (7,20) (8,26) (8,34) (8,23) (8,16) (8,27) (8,9) (8,25) (8,32) (9,17) (9,26) (9,34) (9,16) (9,25) (9,32) (11,28) (11,15) (11,13) (11,19) (11,12) (12,28) (12,24) (12,15) (12,19) (13,28) (13,24) (13,19) (14,17) (14,26) (14,34) (14,16) (14,27) (14,25) (14,32) (15,24) (15,19) (16,17) (16,34) (16,23) (16,27) (16,25) (16,32) (17,26) (17,23) (17,27) (17,22) (17,25) (18,21) (18,33) (18,30) (18,20) (19,28) (19,24) (20,21) (20,33) (21,33) (21,29) (21,30) (21,31) (22,26) (22,34) (22,27) (23,26) (23,34) (23,27) (23,32) (24,28) (25,26) (25,34) (25,32) (26,27) (26,32) (27,32) (29,33) (29,31) (30,33) (30,31) (32,34)\nIs there a path between node 20 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph392-18_21", + "image": "data/connectivity/graph_visual/hard/graph392.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,27) (0,32) (0,31) (0,24) (0,20) (0,23) (1,21) (1,15) (1,19) (1,30) (1,31) (1,26) (2,29) (2,3) (4,21) (4,15) (4,19) (4,30) (4,24) (4,23) (5,26) (5,20) (6,18) (7,32) (7,23) (7,9) (7,11) (8,17) (8,13) (9,30) (9,16) (10,30) (11,15) (11,19) (11,30) (11,31) (11,20) (11,23) (13,17) (14,18) (15,28) (15,25) (16,21) (16,19) (16,27) (16,26) (16,20) (16,23) (18,22) (19,21) (19,32) (19,23) (20,25) (21,27) (21,28) (21,30) (21,26) (21,24) (23,30) (24,28) (24,32) (24,26) (24,25) (25,27) (25,26) (26,30) (27,32) (27,30) (27,31) (28,30) (28,31) (31,32)\nIs there a path between node 18 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph202-18_17", + "image": "data/connectivity/graph_visual/hard/graph202.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,29) (1,27) (1,24) (1,21) (1,3) (2,10) (2,22) (2,6) (2,18) (2,25) (2,12) (3,19) (3,27) (3,24) (4,10) (4,6) (4,18) (4,25) (5,28) (5,16) (6,10) (6,13) (6,25) (6,12) (6,9) (7,28) (8,10) (8,14) (8,18) (8,29) (8,25) (8,23) (9,13) (9,14) (10,29) (10,25) (12,22) (12,18) (12,17) (13,29) (13,26) (14,20) (14,17) (15,19) (17,25) (18,20) (18,25) (20,29) (20,26) (20,23) (21,27) (21,24) (23,26) (23,25) (24,27) (26,29)\nIs there a path between node 18 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph505-1_32", + "image": "data/connectivity/graph_visual/hard/graph505.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,33) (0,8) (0,16) (0,5) (0,17) (0,23) (1,6) (1,7) (1,27) (1,14) (1,4) (1,13) (1,24) (1,21) (2,32) (2,19) (2,29) (2,12) (2,28) (2,15) (3,32) (3,19) (3,26) (3,12) (3,20) (3,30) (3,28) (3,15) (4,6) (4,9) (4,7) (4,14) (4,10) (4,24) (5,33) (5,8) (5,16) (5,31) (5,17) (5,23) (6,7) (6,27) (6,10) (6,25) (6,13) (7,27) (7,14) (7,10) (7,25) (7,24) (7,21) (8,16) (8,17) (9,27) (9,14) (9,10) (9,24) (9,21) (10,25) (10,21) (11,32) (11,19) (11,26) (11,12) (11,20) (11,30) (11,28) (11,22) (12,19) (12,29) (12,26) (12,20) (12,15) (12,22) (13,27) (13,14) (13,25) (13,24) (13,21) (14,25) (14,24) (14,21) (15,32) (15,19) (15,26) (15,20) (15,30) (15,28) (16,33) (16,18) (16,31) (16,23) (17,33) (17,18) (17,23) (18,33) (18,31) (19,32) (19,29) (19,26) (19,30) (19,28) (19,22) (20,32) (20,30) (20,28) (21,25) (22,32) (22,29) (22,26) (22,30) (22,28) (23,33) (24,27) (24,25) (25,27) (26,29) (26,30) (26,28) (28,30) (29,32) (29,30) (30,32) (31,33)\nIs there a path between node 1 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph705-17_20", + "image": "data/connectivity/graph_visual/hard/graph705.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,17) (0,1) (0,20) (0,5) (0,16) (0,34) (1,17) (1,9) (1,5) (1,16) (1,34) (2,30) (2,26) (2,25) (2,24) (3,18) (3,12) (3,4) (3,32) (3,7) (3,33) (3,22) (3,13) (3,15) (3,6) (3,10) (3,27) (4,12) (4,11) (4,7) (4,22) (4,19) (4,13) (4,15) (4,6) (4,21) (4,27) (5,17) (5,9) (5,20) (5,34) (6,18) (6,32) (6,11) (6,7) (6,33) (6,22) (6,19) (6,15) (6,21) (7,18) (7,11) (7,33) (7,22) (7,19) (7,13) (7,10) (7,27) (8,31) (8,29) (9,17) (9,20) (9,16) (9,34) (10,12) (10,32) (10,19) (10,13) (10,15) (10,27) (11,12) (11,32) (11,33) (11,22) (11,19) (11,13) (11,27) (12,22) (12,19) (12,13) (12,15) (12,27) (13,18) (13,32) (13,33) (13,19) (13,15) (13,21) (13,27) (14,28) (14,30) (14,25) (14,24) (15,18) (15,33) (15,22) (15,19) (15,21) (15,27) (16,20) (17,20) (18,33) (18,19) (18,27) (19,32) (19,33) (19,21) (19,27) (20,34) (21,32) (21,27) (22,32) (22,33) (22,27) (23,31) (23,29) (24,28) (24,25) (25,28) (25,26) (26,28) (26,30) (28,30) (29,31) (32,33)\nIs there a path between node 17 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph610-13_20", + "image": "data/connectivity/graph_visual/hard/graph610.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,31) (0,11) (0,18) (0,1) (1,28) (1,31) (1,13) (1,8) (1,5) (1,32) (1,34) (2,17) (3,14) (3,15) (3,24) (4,32) (4,34) (5,8) (5,9) (6,25) (6,10) (6,15) (6,7) (6,19) (7,14) (7,10) (7,16) (7,12) (7,21) (8,18) (9,31) (9,11) (9,34) (10,23) (10,29) (10,33) (10,16) (10,30) (11,20) (11,18) (12,23) (12,14) (12,25) (12,19) (12,24) (13,34) (14,25) (15,23) (15,25) (15,24) (16,23) (16,25) (16,29) (16,33) (16,17) (17,30) (17,21) (17,24) (18,22) (18,20) (19,24) (20,28) (20,32) (20,34) (22,26) (22,34) (23,25) (23,30) (24,33) (24,30) (25,29) (25,33) (26,27) (27,32) (28,32) (28,34) (29,30) (30,33) (31,32)\nIs there a path between node 13 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph287-24_18", + "image": "data/connectivity/graph_visual/hard/graph287.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,16) (0,19) (1,31) (1,27) (1,7) (2,26) (2,12) (2,4) (2,7) (2,23) (3,28) (3,10) (3,14) (3,19) (3,11) (3,25) (4,27) (4,24) (4,17) (5,20) (5,13) (5,10) (5,14) (5,19) (6,31) (6,15) (6,27) (6,21) (8,13) (9,13) (9,11) (9,18) (10,28) (10,14) (10,16) (10,19) (10,11) (10,18) (11,20) (11,22) (11,14) (11,16) (11,18) (12,31) (12,30) (12,27) (12,24) (12,23) (13,22) (13,14) (13,25) (14,22) (14,25) (14,18) (15,31) (15,26) (15,24) (16,18) (17,31) (17,26) (17,23) (18,19) (19,22) (20,25) (21,31) (21,24) (21,29) (21,23) (22,28) (22,25) (23,27) (23,29) (24,30) (26,27) (29,31)\nIs there a path between node 24 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph402-26_31", + "image": "data/connectivity/graph_visual/hard/graph402.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,32) (0,31) (0,24) (0,30) (0,3) (0,16) (0,5) (0,1) (0,23) (1,14) (1,32) (1,17) (1,20) (1,31) (1,27) (1,24) (1,3) (1,16) (1,7) (1,5) (1,23) (2,8) (2,11) (2,28) (2,19) (2,22) (2,29) (2,26) (2,18) (3,14) (3,32) (3,31) (3,27) (3,24) (3,30) (3,10) (3,16) (3,7) (3,5) (3,23) (4,25) (4,11) (4,28) (4,21) (4,29) (4,18) (4,15) (5,14) (5,17) (5,31) (5,27) (5,30) (5,10) (5,7) (5,23) (6,25) (6,8) (6,11) (6,28) (6,19) (6,21) (6,29) (6,26) (6,15) (7,32) (7,17) (7,30) (7,10) (8,11) (8,28) (8,19) (8,22) (8,21) (8,29) (8,18) (8,15) (9,12) (10,14) (10,32) (10,20) (10,27) (10,24) (10,30) (10,16) (11,25) (11,28) (11,21) (11,26) (11,18) (12,13) (14,32) (14,17) (14,20) (14,31) (14,24) (14,16) (14,23) (15,28) (15,19) (15,22) (15,29) (15,18) (16,20) (16,31) (16,27) (16,24) (16,30) (16,23) (17,32) (17,20) (17,27) (17,24) (17,30) (17,23) (18,25) (18,22) (19,25) (19,28) (19,22) (19,26) (20,27) (20,24) (20,23) (21,28) (21,22) (22,25) (22,28) (22,29) (23,32) (23,27) (23,24) (24,32) (24,31) (24,27) (24,30) (25,28) (25,29) (25,26) (26,28) (27,32) (27,31) (28,29) (30,32) (30,31)\nIs there a path between node 26 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph177-6_18", + "image": "data/connectivity/graph_visual/hard/graph177.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,7) (0,24) (0,22) (0,21) (0,20) (0,3) (1,13) (1,27) (1,23) (1,28) (1,2) (1,10) (1,11) (1,18) (1,14) (1,8) (1,16) (1,12) (2,13) (2,27) (2,23) (2,15) (2,26) (2,10) (2,9) (2,11) (2,14) (2,8) (2,5) (3,24) (3,22) (3,4) (3,21) (3,20) (4,7) (4,24) (4,21) (5,13) (5,23) (5,26) (5,28) (5,17) (5,11) (5,14) (5,8) (5,12) (6,13) (6,27) (6,23) (6,15) (6,26) (6,17) (6,10) (6,9) (6,19) (6,11) (6,14) (6,8) (6,16) (7,24) (7,22) (8,13) (8,27) (8,26) (8,28) (8,17) (8,10) (8,9) (8,19) (8,11) (8,18) (8,16) (9,13) (9,27) (9,15) (9,26) (9,28) (9,17) (9,10) (9,19) (9,11) (9,14) (9,16) (9,12) (10,13) (10,27) (10,23) (10,15) (10,28) (10,17) (10,19) (10,11) (10,18) (10,14) (11,13) (11,27) (11,23) (11,15) (11,28) (11,17) (11,19) (11,18) (11,14) (11,16) (12,23) (12,15) (12,17) (12,19) (12,18) (12,14) (13,27) (13,23) (13,15) (13,26) (13,17) (13,19) (13,18) (13,14) (13,16) (14,23) (14,15) (14,28) (14,17) (14,19) (15,26) (15,28) (15,17) (15,19) (15,16) (16,27) (16,26) (16,28) (16,19) (16,18) (17,27) (17,23) (17,19) (18,26) (18,28) (19,23) (19,26) (19,28) (20,24) (20,21) (21,24) (23,26) (26,28) (27,28)\nIs there a path between node 6 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph223-14_27", + "image": "data/connectivity/graph_visual/hard/graph223.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,3) (0,29) (0,1) (0,20) (0,7) (0,5) (0,9) (0,8) (0,26) (0,25) (1,21) (1,12) (1,3) (1,4) (1,29) (1,19) (1,11) (1,20) (1,7) (1,5) (1,9) (1,23) (1,8) (1,26) (1,25) (2,21) (2,3) (2,4) (2,29) (2,19) (2,7) (2,5) (2,9) (2,17) (2,25) (3,29) (3,10) (3,19) (3,11) (3,20) (3,7) (3,5) (3,9) (3,8) (3,17) (4,21) (4,29) (4,20) (4,7) (4,9) (4,23) (4,8) (4,17) (4,26) (4,25) (5,12) (5,10) (5,8) (5,17) (5,26) (5,25) (6,16) (6,18) (7,21) (7,29) (7,10) (7,19) (7,20) (7,9) (7,8) (7,17) (7,26) (7,25) (8,21) (8,29) (8,10) (8,19) (8,9) (8,23) (8,17) (8,26) (8,25) (9,21) (9,12) (9,10) (9,11) (9,20) (9,23) (9,17) (9,26) (10,29) (10,19) (10,11) (10,20) (10,25) (11,12) (11,29) (11,19) (11,20) (11,23) (11,17) (11,26) (11,25) (12,21) (12,29) (12,19) (12,23) (12,17) (12,26) (12,25) (13,22) (13,15) (14,18) (15,28) (15,27) (15,22) (15,24) (16,18) (17,21) (17,20) (17,23) (17,25) (19,29) (19,20) (19,26) (19,25) (20,21) (20,23) (20,26) (20,25) (21,25) (22,28) (22,24) (23,29) (23,26) (23,25) (24,27) (25,29) (25,26) (27,28)\nIs there a path between node 14 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph297-25_6", + "image": "data/connectivity/graph_visual/hard/graph297.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,11) (0,21) (0,15) (0,12) (0,7) (0,13) (0,10) (0,20) (0,19) (0,6) (0,26) (0,30) (0,1) (0,27) (0,16) (0,5) (0,3) (0,22) (0,14) (0,25) (1,9) (1,11) (1,21) (1,15) (1,12) (1,13) (1,20) (1,19) (1,26) (1,27) (1,16) (1,5) (1,29) (1,3) (1,24) (1,25) (2,18) (2,31) (2,23) (3,9) (3,4) (3,15) (3,7) (3,13) (3,6) (3,30) (3,16) (3,29) (3,28) (3,24) (3,14) (4,11) (4,21) (4,17) (4,12) (4,7) (4,19) (4,6) (4,26) (4,16) (4,5) (4,29) (4,28) (4,22) (4,14) (4,25) (5,9) (5,11) (5,17) (5,15) (5,12) (5,13) (5,10) (5,20) (5,26) (5,27) (5,16) (5,29) (5,22) (5,24) (5,14) (6,9) (6,11) (6,21) (6,17) (6,15) (6,12) (6,7) (6,10) (6,26) (6,16) (6,29) (6,28) (6,22) (6,24) (6,14) (6,25) (7,9) (7,21) (7,10) (7,20) (7,19) (7,26) (7,27) (7,16) (7,29) (7,22) (7,24) (7,25) (8,18) (8,31) (8,23) (9,11) (9,21) (9,17) (9,15) (9,12) (9,13) (9,19) (9,26) (9,30) (9,27) (9,16) (9,29) (9,28) (9,14) (10,11) (10,21) (10,17) (10,12) (10,20) (10,26) (10,27) (10,29) (10,22) (10,24) (10,14) (10,25) (11,21) (11,17) (11,13) (11,20) (11,19) (11,26) (11,27) (11,16) (11,29) (11,22) (11,24) (11,25) (12,17) (12,13) (12,20) (12,19) (12,30) (12,27) (12,16) (12,29) (12,24) (12,14) (13,21) (13,20) (13,19) (13,26) (13,30) (13,16) (13,28) (13,22) (13,25) (14,20) (14,19) (14,30) (14,27) (14,16) (14,29) (14,28) (14,22) (14,25) (15,21) (15,19) (15,30) (15,16) (15,29) (15,24) (15,25) (16,21) (16,17) (16,20) (16,19) (16,30) (16,27) (16,29) (16,28) (16,22) (16,24) (17,21) (17,19) (17,26) (17,30) (17,29) (17,28) (17,22) (17,25) (18,31) (18,23) (19,21) (19,20) (19,26) (19,30) (19,27) (19,29) (19,28) (19,24) (19,25) (20,26) (20,30) (20,27) (20,29) (20,28) (20,24) (20,25) (21,27) (21,29) (21,22) (21,25) (22,26) (22,30) (22,27) (22,28) (22,24) (22,25) (24,26) (24,30) (24,27) (24,28) (25,30) (25,29) (25,28) (26,30) (26,27) (26,29) (27,30) (28,30)\nIs there a path between node 25 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph560-31_8", + "image": "data/connectivity/graph_visual/hard/graph560.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,28) (0,2) (1,5) (1,7) (2,13) (2,31) (2,9) (2,18) (4,5) (4,7) (5,15) (5,14) (6,24) (6,19) (7,29) (7,15) (8,33) (9,28) (9,30) (9,27) (10,13) (10,21) (10,28) (10,22) (10,18) (12,28) (12,26) (13,25) (13,18) (13,27) (15,29) (17,30) (18,21) (18,23) (18,28) (18,26) (18,31) (21,30) (21,31) (22,27) (23,28) (23,25) (23,31) (25,28) (26,31) (28,31)\nIs there a path between node 31 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph624-14_19", + "image": "data/connectivity/graph_visual/hard/graph624.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,16) (0,7) (0,10) (0,15) (1,22) (1,11) (1,34) (1,29) (1,14) (2,27) (2,8) (2,32) (2,28) (2,9) (2,21) (2,4) (3,29) (3,20) (3,24) (4,27) (4,6) (4,28) (4,33) (4,15) (5,25) (5,26) (6,8) (6,7) (6,9) (6,18) (7,16) (7,32) (7,10) (7,33) (7,18) (7,15) (8,32) (8,10) (8,9) (8,18) (9,27) (9,16) (9,28) (9,33) (9,15) (10,15) (11,22) (11,30) (11,14) (11,12) (12,30) (12,29) (12,20) (12,31) (14,17) (14,29) (16,33) (17,30) (17,29) (18,27) (18,28) (18,33) (19,25) (20,22) (20,34) (20,24) (21,28) (22,30) (22,24) (23,24) (24,29)\nIs there a path between node 14 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph84-4_14", + "image": "data/connectivity/graph_visual/hard/graph84.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,13) (0,7) (1,14) (1,12) (1,2) (1,5) (1,3) (1,11) (1,9) (1,24) (1,19) (1,23) (2,14) (2,10) (2,16) (2,5) (2,3) (2,11) (2,24) (2,19) (2,23) (3,14) (3,10) (3,12) (3,16) (3,5) (3,11) (3,9) (3,24) (3,23) (4,25) (4,6) (4,15) (4,20) (4,8) (5,10) (5,16) (5,11) (5,9) (5,24) (5,19) (5,23) (6,25) (6,15) (6,18) (6,20) (6,8) (7,13) (7,26) (7,17) (8,25) (8,15) (8,20) (9,10) (9,12) (9,22) (9,24) (9,19) (9,23) (10,14) (10,12) (10,16) (10,11) (10,19) (11,12) (11,22) (11,16) (11,19) (11,23) (12,14) (12,22) (12,16) (12,19) (12,23) (13,21) (13,26) (13,17) (14,22) (14,16) (15,25) (15,18) (15,20) (16,22) (16,24) (16,19) (16,23) (17,26) (18,20) (19,22) (19,24) (19,23) (20,25) (22,24) (22,23) (23,24)\nIs there a path between node 4 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph3-20_21", + "image": "data/connectivity/graph_visual/hard/graph3.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,2) (0,10) (0,6) (0,8) (0,17) (0,25) (2,23) (2,21) (2,24) (2,15) (2,5) (2,22) (2,12) (2,19) (3,23) (3,8) (3,16) (4,14) (4,23) (4,10) (4,6) (4,8) (4,17) (4,16) (5,14) (5,18) (5,15) (5,10) (5,17) (6,22) (8,14) (8,23) (8,21) (8,24) (8,10) (9,18) (9,15) (9,22) (9,17) (10,20) (10,14) (10,23) (11,20) (11,14) (11,23) (11,22) (11,12) (11,17) (12,22) (12,17) (14,24) (15,23) (15,24) (15,25) (16,21) (16,24) (16,18) (17,20) (17,23) (17,21) (17,24) (18,20) (18,19) (19,20) (19,24) (19,22) (19,25) (20,23) (20,21) (22,25) (23,25)\nIs there a path between node 20 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph462-8_31", + "image": "data/connectivity/graph_visual/hard/graph462.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,8) (0,25) (0,23) (0,24) (1,19) (1,11) (1,3) (2,13) (2,18) (2,4) (2,29) (3,17) (3,6) (3,12) (3,31) (3,20) (3,15) (4,16) (4,13) (4,25) (4,29) (4,23) (4,24) (5,6) (5,31) (5,20) (5,30) (6,7) (6,14) (6,22) (6,9) (6,21) (6,15) (7,10) (7,28) (7,11) (7,22) (8,13) (8,26) (8,29) (9,19) (9,28) (9,11) (9,12) (9,22) (9,21) (9,15) (10,17) (10,11) (10,21) (11,19) (12,19) (13,25) (13,24) (14,28) (14,27) (15,19) (15,21) (15,27) (15,30) (16,25) (16,29) (16,24) (17,19) (17,31) (17,21) (17,30) (18,23) (18,24) (19,28) (19,20) (19,21) (20,28) (20,22) (21,22) (24,25) (25,26) (28,31)\nIs there a path between node 8 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph669-9_27", + "image": "data/connectivity/graph_visual/hard/graph669.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,17) (0,33) (0,14) (1,18) (1,14) (2,28) (2,24) (2,25) (2,20) (2,31) (2,22) (2,8) (3,30) (3,23) (3,17) (3,29) (3,21) (4,7) (4,11) (4,31) (4,22) (4,8) (5,28) (5,9) (5,34) (5,22) (6,20) (6,9) (6,15) (6,8) (7,11) (7,16) (8,25) (8,20) (8,9) (8,31) (8,15) (8,22) (8,19) (9,28) (9,32) (9,11) (9,31) (10,32) (10,20) (10,15) (10,22) (10,19) (11,28) (11,31) (11,15) (11,34) (12,18) (12,23) (12,13) (13,23) (13,29) (13,33) (14,26) (14,17) (14,29) (14,33) (16,24) (16,32) (16,22) (17,30) (17,23) (18,26) (18,23) (18,29) (18,21) (21,26) (21,23) (22,34) (23,26) (24,28) (24,32) (25,28) (25,34) (28,32) (29,30)\nIs there a path between node 9 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph695-33_0", + "image": "data/connectivity/graph_visual/hard/graph695.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,21) (0,22) (0,25) (0,23) (0,10) (0,16) (0,3) (0,4) (0,7) (0,34) (0,27) (0,28) (0,19) (0,1) (0,20) (1,14) (1,6) (1,12) (1,25) (1,8) (1,16) (1,4) (1,7) (1,34) (1,27) (1,28) (1,26) (2,5) (2,17) (2,18) (2,15) (2,11) (3,14) (3,13) (3,6) (3,21) (3,12) (3,25) (3,33) (3,8) (3,10) (3,4) (3,7) (3,34) (3,28) (3,19) (3,26) (4,13) (4,6) (4,21) (4,22) (4,12) (4,8) (4,23) (4,10) (4,16) (4,34) (4,29) (4,28) (4,20) (5,30) (5,24) (5,9) (5,31) (5,15) (5,11) (6,14) (6,13) (6,21) (6,25) (6,23) (6,16) (6,7) (6,34) (6,27) (6,29) (6,28) (6,19) (7,14) (7,22) (7,12) (7,33) (7,23) (7,10) (7,16) (7,28) (7,19) (7,26) (7,20) (8,14) (8,13) (8,22) (8,12) (8,25) (8,33) (8,23) (8,10) (8,16) (8,34) (8,27) (8,19) (8,26) (8,20) (9,30) (9,24) (9,18) (9,31) (9,32) (10,14) (10,21) (10,22) (10,12) (10,23) (10,34) (10,27) (10,28) (10,19) (10,26) (11,30) (11,24) (11,17) (11,18) (11,31) (11,15) (11,32) (12,14) (12,13) (12,22) (12,25) (12,33) (12,23) (12,34) (12,27) (12,29) (12,28) (12,19) (12,26) (13,21) (13,22) (13,25) (13,33) (13,23) (13,16) (13,34) (13,27) (13,26) (13,20) (14,21) (14,33) (14,16) (14,34) (14,27) (14,29) (14,26) (14,20) (15,30) (15,24) (15,31) (16,25) (16,33) (16,23) (16,27) (16,19) (16,26) (16,20) (18,30) (18,24) (18,31) (18,32) (19,25) (19,33) (19,23) (19,34) (19,27) (19,29) (19,26) (19,20) (20,22) (20,25) (20,33) (20,23) (20,34) (20,27) (20,28) (20,26) (21,33) (21,23) (21,34) (21,27) (21,29) (22,33) (22,23) (22,27) (22,28) (23,25) (23,33) (23,34) (23,29) (23,28) (23,26) (24,31) (25,33) (25,34) (25,27) (25,28) (25,26) (26,33) (26,34) (26,27) (26,28) (27,33) (27,34) (27,29) (27,28) (28,33) (28,34) (29,33) (29,34) (30,32)\nIs there a path between node 33 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph266-27_14", + "image": "data/connectivity/graph_visual/hard/graph266.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,20) (0,12) (0,25) (0,2) (0,23) (0,17) (0,28) (0,5) (0,10) (0,19) (1,30) (1,9) (1,15) (1,6) (1,10) (1,18) (2,20) (2,12) (2,8) (2,21) (2,28) (2,22) (2,10) (2,3) (2,4) (2,18) (3,25) (3,13) (3,21) (3,28) (3,29) (3,4) (3,18) (4,25) (4,30) (4,13) (4,23) (4,17) (4,28) (4,5) (4,15) (4,14) (4,7) (4,18) (5,20) (5,12) (5,30) (5,13) (5,9) (5,28) (5,16) (5,14) (5,11) (6,12) (6,25) (6,13) (6,21) (6,29) (6,19) (7,13) (7,8) (7,23) (7,28) (7,29) (8,27) (8,21) (8,23) (8,28) (8,22) (8,18) (9,20) (9,12) (9,18) (10,13) (10,22) (10,14) (10,29) (11,20) (11,13) (11,17) (11,15) (12,25) (12,23) (12,28) (12,18) (13,30) (13,27) (13,21) (13,16) (13,14) (14,30) (14,21) (14,16) (14,29) (14,19) (15,20) (15,30) (15,23) (16,20) (16,25) (16,21) (16,28) (17,20) (17,30) (17,28) (18,30) (18,27) (18,23) (18,22) (18,29) (19,23) (19,29) (20,30) (20,23) (20,29) (21,28) (22,29) (23,25) (23,30) (23,28) (25,29) (27,28) (28,30) (29,30)\nIs there a path between node 27 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph248-12_2", + "image": "data/connectivity/graph_visual/hard/graph248.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,9) (0,1) (0,25) (0,19) (0,16) (0,23) (0,6) (0,17) (0,13) (0,22) (0,21) (0,24) (0,8) (0,4) (1,29) (1,11) (1,25) (1,19) (1,16) (1,18) (1,23) (1,6) (1,17) (1,13) (1,5) (1,12) (1,22) (1,7) (1,24) (1,10) (1,28) (1,8) (1,4) (2,14) (2,26) (3,14) (3,26) (3,20) (4,29) (4,9) (4,11) (4,25) (4,19) (4,16) (4,15) (4,23) (4,6) (4,17) (4,13) (4,5) (4,12) (4,22) (4,21) (4,7) (4,24) (4,28) (4,8) (5,29) (5,27) (5,11) (5,25) (5,19) (5,16) (5,18) (5,23) (5,6) (5,17) (5,13) (5,12) (5,21) (5,7) (5,24) (5,28) (5,8) (6,29) (6,9) (6,11) (6,25) (6,15) (6,23) (6,17) (6,12) (6,21) (6,7) (6,24) (6,10) (6,28) (6,8) (7,9) (7,27) (7,11) (7,16) (7,18) (7,15) (7,17) (7,13) (7,22) (7,21) (7,24) (7,10) (7,28) (8,29) (8,27) (8,11) (8,25) (8,19) (8,16) (8,15) (8,13) (8,22) (8,21) (8,24) (8,10) (9,27) (9,11) (9,25) (9,19) (9,16) (9,18) (9,23) (9,17) (9,13) (9,12) (9,24) (9,10) (9,28) (10,29) (10,27) (10,11) (10,25) (10,19) (10,15) (10,23) (10,17) (10,13) (10,21) (10,24) (10,28) (11,27) (11,25) (11,19) (11,16) (11,18) (11,15) (11,23) (11,17) (11,13) (11,22) (11,21) (11,24) (11,28) (12,29) (12,27) (12,19) (12,16) (12,18) (12,23) (12,17) (12,13) (12,21) (12,24) (12,28) (13,29) (13,25) (13,16) (13,18) (13,23) (13,22) (13,24) (13,28) (14,26) (14,20) (15,29) (15,16) (15,23) (15,17) (15,22) (15,21) (15,28) (16,19) (16,18) (16,23) (16,22) (16,21) (16,24) (16,28) (17,29) (17,25) (17,19) (17,18) (17,23) (17,21) (17,28) (18,25) (18,19) (18,23) (18,22) (18,21) (19,27) (19,25) (19,23) (19,22) (19,21) (19,24) (19,28) (20,26) (21,29) (21,27) (21,22) (21,28) (22,29) (22,23) (22,24) (22,28) (23,25) (23,24) (24,29) (24,27) (24,25) (24,28) (25,28) (27,28) (28,29)\nIs there a path between node 12 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph429-21_14", + "image": "data/connectivity/graph_visual/hard/graph429.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,30) (0,15) (0,16) (0,27) (0,1) (0,13) (1,14) (1,30) (1,27) (1,13) (2,9) (2,25) (2,22) (2,8) (2,5) (2,26) (2,20) (2,10) (2,6) (2,31) (2,32) (2,19) (2,17) (2,18) (2,23) (2,4) (2,11) (3,9) (3,25) (3,22) (3,8) (3,26) (3,20) (3,24) (3,10) (3,6) (3,31) (3,17) (3,18) (3,12) (3,23) (3,4) (4,25) (4,22) (4,8) (4,5) (4,20) (4,31) (4,32) (4,19) (4,17) (4,23) (4,11) (5,9) (5,25) (5,22) (5,8) (5,10) (5,6) (5,32) (5,19) (5,18) (5,12) (5,23) (5,11) (6,9) (6,25) (6,22) (6,26) (6,24) (6,31) (6,32) (6,19) (6,17) (6,18) (7,29) (7,28) (8,22) (8,26) (8,20) (8,10) (8,31) (8,19) (8,18) (8,11) (9,25) (9,22) (9,26) (9,20) (9,24) (9,31) (9,32) (9,19) (9,17) (9,12) (9,23) (10,25) (10,22) (10,20) (10,24) (10,31) (10,32) (10,19) (10,17) (10,18) (10,12) (10,23) (10,11) (11,26) (11,20) (11,24) (11,31) (11,19) (11,17) (12,25) (12,26) (12,20) (12,24) (12,31) (12,32) (12,19) (13,14) (13,30) (13,27) (14,30) (14,15) (14,16) (15,16) (17,25) (17,22) (17,26) (17,20) (17,24) (17,31) (17,32) (17,23) (18,25) (18,22) (18,26) (18,32) (19,25) (19,22) (19,26) (19,20) (19,32) (19,23) (20,25) (20,22) (20,26) (20,24) (20,31) (21,29) (22,25) (22,26) (22,24) (22,32) (23,25) (23,26) (23,24) (23,31) (24,26) (24,31) (24,32) (25,26) (25,31) (25,32) (27,30) (28,29)\nIs there a path between node 21 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph145-18_14", + "image": "data/connectivity/graph_visual/hard/graph145.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,3) (0,24) (0,15) (0,16) (0,19) (0,7) (0,25) (0,26) (1,28) (1,23) (3,6) (3,18) (3,11) (3,24) (3,22) (3,4) (3,7) (3,25) (4,27) (4,24) (4,22) (4,12) (4,21) (4,16) (4,19) (5,6) (5,13) (5,22) (5,12) (5,16) (6,11) (6,21) (6,15) (6,25) (6,26) (7,14) (7,25) (8,23) (9,11) (9,13) (10,11) (10,15) (10,19) (11,27) (11,18) (11,22) (11,12) (11,21) (11,19) (11,25) (12,27) (12,14) (13,27) (13,18) (13,14) (13,21) (14,18) (14,24) (14,15) (15,22) (15,16) (15,26) (16,18) (16,22) (17,28) (17,23) (17,20) (18,27) (19,27) (19,24) (21,26) (22,25) (22,26) (23,28) (24,25) (24,26)\nIs there a path between node 18 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph364-19_24", + "image": "data/connectivity/graph_visual/hard/graph364.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,15) (0,25) (0,4) (0,27) (0,9) (0,10) (0,1) (0,7) (0,3) (0,31) (0,24) (0,20) (0,23) (1,15) (1,12) (1,25) (1,4) (1,27) (1,9) (1,30) (1,13) (1,8) (1,7) (1,3) (1,2) (1,20) (1,23) (2,15) (2,12) (2,25) (2,26) (2,9) (2,13) (2,8) (2,10) (2,22) (2,7) (2,3) (2,31) (2,19) (2,20) (2,23) (3,4) (3,27) (3,9) (3,13) (3,22) (3,7) (3,16) (3,24) (3,19) (3,20) (3,23) (4,12) (4,25) (4,27) (4,9) (4,13) (4,8) (4,10) (4,22) (4,31) (4,24) (4,23) (5,14) (5,17) (6,18) (6,21) (6,29) (6,28) (7,12) (7,25) (7,26) (7,9) (7,13) (7,8) (7,10) (7,22) (7,31) (7,16) (7,24) (7,19) (7,20) (7,23) (8,15) (8,25) (8,27) (8,30) (8,13) (8,10) (8,24) (8,19) (9,26) (9,27) (9,30) (9,22) (9,16) (9,20) (9,23) (10,12) (10,25) (10,30) (10,13) (10,22) (10,31) (10,24) (10,20) (10,23) (11,18) (11,21) (11,28) (12,25) (12,30) (12,13) (12,31) (12,16) (12,24) (12,20) (13,15) (13,25) (13,26) (13,27) (13,22) (13,24) (13,19) (13,20) (13,23) (14,17) (15,16) (15,19) (16,25) (16,27) (16,30) (16,22) (16,31) (16,19) (16,20) (16,23) (18,29) (19,25) (19,22) (19,31) (19,24) (19,20) (19,23) (20,26) (20,27) (20,30) (20,22) (20,31) (20,24) (20,23) (21,29) (21,28) (22,25) (22,26) (22,27) (22,30) (22,31) (22,24) (22,23) (23,25) (23,27) (23,30) (24,25) (24,26) (24,31) (25,26) (25,27) (25,30) (26,27) (26,30) (27,30) (27,31) (30,31)\nIs there a path between node 19 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph459-28_9", + "image": "data/connectivity/graph_visual/hard/graph459.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (0,9) (0,15) (0,6) (0,11) (1,5) (1,9) (1,18) (1,8) (1,12) (1,20) (1,6) (1,16) (1,17) (1,27) (1,2) (2,5) (2,9) (2,8) (2,12) (2,6) (2,11) (3,32) (3,13) (3,30) (3,10) (4,22) (5,8) (5,12) (5,31) (6,16) (6,11) (7,14) (7,32) (7,13) (7,22) (8,11) (9,11) (9,27) (10,13) (10,25) (10,26) (10,24) (11,12) (11,21) (11,31) (11,27) (12,20) (12,21) (12,17) (13,30) (13,22) (13,28) (15,20) (15,31) (15,17) (16,19) (17,19) (17,27) (18,29) (18,21) (18,27) (19,27) (20,21) (20,27) (21,29) (25,32) (25,26) (26,30) (26,28) (27,31) (30,32)\nIs there a path between node 28 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph239-24_0", + "image": "data/connectivity/graph_visual/hard/graph239.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,14) (0,11) (0,18) (0,3) (0,22) (1,21) (2,5) (2,15) (4,26) (4,9) (4,22) (5,17) (5,20) (6,23) (7,16) (7,8) (8,20) (8,13) (8,30) (9,11) (9,18) (9,26) (9,25) (9,22) (10,17) (10,30) (10,12) (10,15) (12,17) (12,16) (12,28) (13,17) (13,20) (14,18) (14,26) (14,25) (15,17) (15,24) (16,28) (17,29) (19,25) (19,22) (20,30) (22,25)\nIs there a path between node 24 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph343-16_3", + "image": "data/connectivity/graph_visual/hard/graph343.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,23) (0,28) (0,25) (0,17) (0,3) (0,10) (0,31) (0,7) (0,12) (0,14) (1,18) (1,28) (1,2) (1,3) (1,7) (1,30) (1,5) (2,24) (2,25) (2,29) (2,8) (2,30) (2,19) (2,5) (3,22) (3,25) (3,4) (3,29) (3,17) (3,21) (4,23) (4,21) (4,8) (4,19) (5,22) (5,9) (5,21) (5,10) (5,8) (5,30) (5,14) (6,18) (6,9) (6,10) (6,7) (6,14) (7,22) (7,18) (7,24) (7,9) (7,29) (7,8) (7,30) (7,13) (8,26) (8,23) (8,28) (8,9) (8,21) (9,26) (9,22) (9,25) (9,17) (9,31) (9,12) (9,14) (9,13) (10,22) (10,23) (10,28) (10,17) (10,21) (10,12) (10,13) (11,22) (11,24) (11,30) (12,23) (12,17) (12,30) (12,14) (13,23) (13,28) (13,30) (13,14) (14,22) (14,24) (14,25) (14,17) (14,21) (14,31) (14,30) (17,26) (17,22) (17,24) (18,26) (18,24) (18,30) (19,23) (19,29) (19,31) (21,23) (22,24) (22,29) (22,31) (23,26) (23,24) (23,28) (23,31) (24,28) (24,31) (25,28) (28,31) (29,31) (30,31)\nIs there a path between node 16 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph507-32_27", + "image": "data/connectivity/graph_visual/hard/graph507.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,29) (0,21) (0,6) (0,28) (0,24) (0,9) (0,2) (0,13) (0,15) (0,10) (1,30) (1,25) (1,33) (1,5) (1,27) (1,11) (1,22) (2,29) (2,6) (2,14) (2,8) (2,9) (2,13) (2,15) (2,26) (2,17) (2,32) (3,19) (3,20) (5,30) (5,27) (5,11) (5,31) (5,22) (6,29) (6,28) (6,14) (6,8) (6,9) (6,12) (6,18) (6,15) (6,26) (6,17) (6,32) (6,7) (6,10) (7,21) (7,28) (7,14) (7,8) (7,9) (7,16) (7,18) (7,15) (7,17) (7,32) (8,21) (8,28) (8,24) (8,9) (8,16) (8,12) (8,13) (8,23) (8,18) (8,15) (8,26) (8,17) (8,32) (8,10) (9,28) (9,14) (9,24) (9,12) (9,13) (9,23) (9,18) (9,15) (9,26) (9,17) (9,10) (10,29) (10,21) (10,28) (10,14) (10,24) (10,12) (10,13) (10,23) (10,18) (10,17) (11,30) (11,25) (11,33) (11,27) (11,31) (11,22) (12,29) (12,21) (12,28) (12,24) (12,16) (12,13) (12,23) (12,18) (12,15) (12,26) (12,32) (13,21) (13,28) (13,14) (13,24) (13,16) (13,23) (13,18) (13,26) (13,17) (14,29) (14,21) (14,28) (14,24) (14,16) (14,18) (14,32) (15,29) (15,21) (15,28) (15,24) (15,23) (15,32) (16,29) (16,21) (16,28) (16,24) (16,23) (16,18) (16,26) (16,32) (17,21) (17,23) (17,18) (17,26) (18,29) (18,21) (18,28) (18,24) (18,23) (18,26) (18,32) (19,20) (21,28) (21,23) (21,26) (21,32) (22,30) (22,25) (22,33) (22,27) (22,31) (23,29) (23,28) (23,24) (23,26) (23,32) (24,26) (24,32) (25,33) (25,31) (26,29) (26,28) (26,32) (27,30) (27,33) (28,29) (29,32) (30,33) (31,33)\nIs there a path between node 32 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph223-19_22", + "image": "data/connectivity/graph_visual/hard/graph223.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,3) (0,29) (0,1) (0,20) (0,7) (0,5) (0,9) (0,8) (0,26) (0,25) (1,21) (1,12) (1,3) (1,4) (1,29) (1,19) (1,11) (1,20) (1,7) (1,5) (1,9) (1,23) (1,8) (1,26) (1,25) (2,21) (2,3) (2,4) (2,29) (2,19) (2,7) (2,5) (2,9) (2,17) (2,25) (3,29) (3,10) (3,19) (3,11) (3,20) (3,7) (3,5) (3,9) (3,8) (3,17) (4,21) (4,29) (4,20) (4,7) (4,9) (4,23) (4,8) (4,17) (4,26) (4,25) (5,12) (5,10) (5,8) (5,17) (5,26) (5,25) (6,16) (6,18) (7,21) (7,29) (7,10) (7,19) (7,20) (7,9) (7,8) (7,17) (7,26) (7,25) (8,21) (8,29) (8,10) (8,19) (8,9) (8,23) (8,17) (8,26) (8,25) (9,21) (9,12) (9,10) (9,11) (9,20) (9,23) (9,17) (9,26) (10,29) (10,19) (10,11) (10,20) (10,25) (11,12) (11,29) (11,19) (11,20) (11,23) (11,17) (11,26) (11,25) (12,21) (12,29) (12,19) (12,23) (12,17) (12,26) (12,25) (13,22) (13,15) (14,18) (15,28) (15,27) (15,22) (15,24) (16,18) (17,21) (17,20) (17,23) (17,25) (19,29) (19,20) (19,26) (19,25) (20,21) (20,23) (20,26) (20,25) (21,25) (22,28) (22,24) (23,29) (23,26) (23,25) (24,27) (25,29) (25,26) (27,28)\nIs there a path between node 19 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph181-27_20", + "image": "data/connectivity/graph_visual/hard/graph181.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,18) (1,25) (1,22) (1,15) (1,20) (1,19) (1,11) (1,2) (1,23) (1,24) (2,25) (2,22) (2,15) (2,3) (2,11) (2,7) (2,6) (2,14) (2,24) (3,22) (3,16) (3,15) (3,19) (3,7) (3,23) (3,6) (3,14) (4,21) (4,9) (4,28) (4,8) (4,26) (4,17) (5,9) (5,12) (5,27) (5,26) (5,17) (6,25) (6,16) (6,15) (6,20) (6,19) (6,7) (6,14) (6,24) (7,25) (7,22) (7,16) (7,20) (7,19) (7,11) (7,23) (7,24) (8,21) (8,9) (8,12) (8,26) (8,17) (9,21) (9,10) (9,28) (9,12) (9,27) (9,26) (9,17) (10,21) (10,28) (10,12) (10,26) (10,17) (11,22) (11,16) (11,15) (11,20) (11,19) (11,23) (11,14) (11,24) (12,27) (12,26) (12,17) (13,18) (14,16) (14,15) (14,20) (14,24) (15,22) (15,16) (15,20) (15,23) (15,24) (16,25) (16,22) (16,20) (16,19) (16,23) (16,24) (17,21) (17,27) (17,26) (19,25) (19,22) (19,23) (19,24) (20,22) (20,23) (20,24) (21,28) (21,27) (21,26) (22,25) (23,25) (23,24) (24,25) (26,27)\nIs there a path between node 27 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph157-14_18", + "image": "data/connectivity/graph_visual/hard/graph157.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,24) (0,7) (1,14) (1,10) (1,28) (1,4) (2,11) (2,24) (2,7) (2,18) (2,27) (2,3) (2,19) (3,12) (3,27) (3,19) (4,16) (4,13) (5,14) (5,22) (5,10) (5,9) (7,11) (7,24) (7,18) (7,27) (7,19) (8,12) (8,19) (9,17) (9,10) (9,15) (10,21) (11,26) (12,24) (12,26) (13,14) (13,28) (14,17) (14,22) (14,21) (14,15) (15,17) (15,22) (16,22) (17,28) (18,25) (18,26) (19,23) (20,23) (21,28) (23,24) (23,27)\nIs there a path between node 14 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph148-19_10", + "image": "data/connectivity/graph_visual/hard/graph148.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,10) (0,6) (1,10) (2,21) (2,9) (2,13) (2,25) (2,22) (2,27) (2,11) (2,7) (2,15) (2,8) (2,12) (2,23) (2,3) (2,28) (2,14) (2,19) (3,21) (3,9) (3,13) (3,5) (3,22) (3,27) (3,11) (3,17) (3,7) (3,20) (3,15) (3,8) (3,12) (3,18) (3,24) (4,21) (4,9) (4,26) (4,13) (4,25) (4,5) (4,22) (4,27) (4,17) (4,7) (4,15) (4,16) (4,8) (4,12) (4,18) (4,24) (4,23) (4,28) (4,14) (4,19) (5,21) (5,9) (5,26) (5,13) (5,22) (5,27) (5,11) (5,17) (5,20) (5,15) (5,16) (5,8) (5,18) (5,23) (5,28) (6,10) (7,9) (7,13) (7,25) (7,22) (7,27) (7,11) (7,17) (7,20) (7,15) (7,16) (7,12) (7,18) (7,24) (7,23) (7,14) (8,21) (8,13) (8,25) (8,27) (8,11) (8,17) (8,20) (8,15) (8,16) (8,23) (8,14) (8,19) (9,25) (9,27) (9,11) (9,17) (9,20) (9,16) (9,12) (9,24) (9,28) (11,26) (11,13) (11,25) (11,22) (11,27) (11,17) (11,20) (11,15) (11,16) (11,12) (11,24) (11,28) (11,14) (12,21) (12,26) (12,13) (12,25) (12,27) (12,17) (12,20) (12,15) (12,18) (12,24) (12,23) (12,28) (12,19) (13,21) (13,26) (13,25) (13,22) (13,27) (13,17) (13,20) (13,15) (13,16) (13,18) (13,24) (13,23) (13,28) (13,14) (13,19) (14,25) (14,22) (14,27) (14,17) (14,20) (14,15) (14,16) (14,18) (14,24) (14,28) (15,26) (15,27) (15,20) (15,18) (15,24) (15,28) (16,21) (16,26) (16,25) (16,27) (16,20) (16,18) (16,24) (16,23) (16,28) (16,19) (17,21) (17,25) (17,22) (17,27) (17,20) (17,23) (17,28) (17,19) (18,26) (18,25) (18,27) (18,20) (18,24) (18,28) (19,26) (19,25) (19,22) (19,27) (19,20) (19,24) (19,23) (19,28) (20,26) (20,25) (20,27) (20,24) (20,23) (20,28) (21,26) (21,22) (21,28) (22,25) (22,27) (22,28) (23,27) (23,24) (23,28) (24,25) (24,27) (24,28) (25,26) (25,28) (26,28) (27,28)\nIs there a path between node 19 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph289-0_16", + "image": "data/connectivity/graph_visual/hard/graph289.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,21) (0,23) (0,2) (0,8) (1,18) (1,3) (1,16) (2,4) (2,5) (3,25) (3,13) (4,6) (4,27) (4,17) (4,8) (5,26) (5,19) (5,30) (5,28) (5,23) (5,15) (5,8) (6,26) (6,19) (6,30) (6,8) (8,26) (8,21) (8,23) (8,27) (9,14) (11,20) (11,16) (12,19) (12,30) (13,18) (13,29) (15,28) (16,24) (16,20) (16,29) (17,30) (17,21) (17,27) (19,30) (19,27) (20,25) (21,26) (21,28) (23,27) (25,29) (27,30) (27,28)\nIs there a path between node 0 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph425-21_14", + "image": "data/connectivity/graph_visual/hard/graph425.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,7) (0,12) (0,32) (0,22) (0,9) (0,20) (0,2) (0,5) (0,14) (0,4) (0,26) (0,21) (1,11) (1,8) (1,24) (1,3) (1,31) (1,28) (1,6) (2,16) (2,7) (2,32) (2,22) (2,9) (2,20) (2,14) (2,4) (2,21) (3,11) (3,8) (3,24) (3,31) (3,28) (4,16) (4,32) (4,22) (4,9) (4,20) (4,5) (4,14) (4,26) (5,16) (5,7) (5,12) (5,32) (5,22) (5,9) (5,20) (5,14) (5,26) (5,21) (6,8) (6,24) (6,31) (6,28) (7,12) (7,32) (7,22) (7,9) (7,14) (7,26) (7,21) (8,24) (8,31) (8,28) (9,16) (9,12) (9,32) (9,20) (9,26) (9,21) (10,23) (10,13) (10,29) (10,19) (10,25) (10,18) (12,32) (12,22) (12,20) (12,26) (12,21) (13,30) (13,27) (13,29) (13,19) (13,25) (13,18) (14,16) (14,32) (14,22) (14,20) (14,26) (15,30) (15,29) (15,25) (15,18) (16,32) (16,22) (16,20) (16,26) (16,21) (17,30) (17,27) (18,30) (18,29) (19,30) (19,23) (19,27) (19,25) (20,32) (20,22) (20,26) (21,32) (21,26) (22,32) (22,26) (23,30) (23,29) (23,25) (24,28) (26,32) (27,30) (27,29) (28,31) (29,30)\nIs there a path between node 21 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph314-9_21", + "image": "data/connectivity/graph_visual/hard/graph314.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,7) (1,5) (1,10) (1,23) (1,20) (2,30) (2,24) (2,18) (2,12) (2,16) (2,3) (2,11) (3,30) (3,4) (3,12) (3,10) (3,22) (3,19) (3,20) (4,30) (4,28) (4,18) (4,12) (4,10) (4,23) (4,22) (4,19) (5,28) (5,18) (5,12) (5,10) (5,19) (5,11) (6,8) (6,21) (6,13) (6,29) (7,8) (7,21) (7,13) (7,17) (7,29) (8,17) (8,15) (9,26) (9,23) (9,22) (9,19) (9,25) (9,20) (10,18) (10,16) (10,26) (10,22) (10,11) (11,30) (11,12) (11,22) (12,28) (12,16) (12,23) (13,17) (13,29) (14,31) (15,31) (15,29) (16,24) (16,28) (16,19) (16,20) (17,27) (17,21) (18,26) (18,19) (19,23) (20,24) (20,23) (22,28) (22,23) (22,25) (23,26) (24,28) (24,25) (25,30)\nIs there a path between node 9 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph613-20_29", + "image": "data/connectivity/graph_visual/hard/graph613.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,32) (0,13) (0,19) (0,6) (0,21) (0,10) (0,31) (0,16) (0,7) (0,20) (0,8) (0,17) (0,12) (0,3) (0,11) (0,23) (0,2) (0,22) (0,1) (0,18) (1,33) (1,32) (1,13) (1,19) (1,29) (1,26) (1,27) (1,6) (1,21) (1,10) (1,31) (1,16) (1,28) (1,7) (1,20) (1,8) (1,17) (1,12) (1,3) (1,2) (1,14) (1,22) (1,18) (1,5) (2,33) (2,13) (2,19) (2,29) (2,26) (2,27) (2,6) (2,10) (2,31) (2,16) (2,28) (2,7) (2,20) (2,24) (2,8) (2,17) (2,12) (2,22) (2,18) (3,32) (3,29) (3,27) (3,6) (3,21) (3,31) (3,16) (3,28) (3,7) (3,20) (3,8) (3,12) (3,23) (3,14) (3,22) (3,18) (3,5) (4,25) (4,34) (5,33) (5,32) (5,13) (5,19) (5,29) (5,26) (5,27) (5,6) (5,21) (5,10) (5,31) (5,16) (5,28) (5,20) (5,8) (5,12) (5,11) (5,23) (5,14) (5,22) (5,18) (6,32) (6,13) (6,19) (6,26) (6,27) (6,21) (6,10) (6,16) (6,28) (6,7) (6,20) (6,17) (6,12) (6,11) (6,23) (6,14) (6,22) (6,18) (7,32) (7,13) (7,29) (7,27) (7,21) (7,10) (7,16) (7,28) (7,20) (7,24) (7,17) (7,12) (7,11) (7,23) (7,14) (7,22) (7,18) (8,33) (8,32) (8,13) (8,19) (8,29) (8,26) (8,21) (8,10) (8,31) (8,16) (8,28) (8,20) (8,24) (8,17) (8,12) (8,11) (8,23) (8,14) (8,22) (8,18) (9,25) (9,34) (9,15) (9,30) (10,33) (10,32) (10,13) (10,19) (10,29) (10,26) (10,27) (10,16) (10,28) (10,12) (10,11) (10,14) (10,22) (11,33) (11,32) (11,13) (11,19) (11,29) (11,21) (11,28) (11,20) (11,24) (11,17) (11,12) (11,23) (11,14) (11,22) (11,18) (12,33) (12,32) (12,13) (12,19) (12,29) (12,26) (12,31) (12,16) (12,28) (12,20) (12,23) (12,18) (13,33) (13,32) (13,19) (13,29) (13,26) (13,27) (13,21) (13,31) (13,16) (13,28) (13,20) (13,17) (13,23) (13,14) (13,18) (14,33) (14,32) (14,19) (14,29) (14,26) (14,27) (14,21) (14,31) (14,16) (14,28) (14,20) (14,17) (14,22) (15,25) (15,30) (16,33) (16,32) (16,19) (16,29) (16,26) (16,27) (16,21) (16,31) (16,28) (16,20) (16,24) (16,17) (16,23) (16,22) (17,33) (17,32) (17,19) (17,29) (17,21) (17,28) (17,20) (17,24) (17,23) (17,22) (17,18) (18,32) (18,19) (18,29) (18,26) (18,27) (18,21) (18,31) (18,28) (18,24) (18,23) (18,22) (19,29) (19,27) (19,21) (19,31) (19,28) (19,20) (19,23) (20,33) (20,29) (20,26) (20,31) (20,28) (20,22) (21,33) (21,32) (21,29) (21,31) (21,24) (21,23) (22,29) (22,31) (22,24) (23,29) (23,26) (23,27) (23,31) (23,28) (23,24) (24,32) (24,26) (24,27) (24,31) (25,34) (26,32) (26,29) (26,27) (26,31) (26,28) (27,33) (27,29) (27,31) (28,33) (28,31) (29,33) (29,32) (30,34) (31,33) (31,32) (32,33)\nIs there a path between node 20 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph493-8_21", + "image": "data/connectivity/graph_visual/hard/graph493.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,4) (0,1) (0,5) (0,24) (0,3) (0,21) (0,19) (0,9) (0,15) (0,20) (0,27) (0,13) (1,24) (1,21) (1,31) (1,10) (1,7) (1,20) (1,27) (1,13) (2,6) (2,5) (2,24) (2,3) (2,21) (2,19) (2,9) (2,31) (2,15) (2,7) (2,27) (2,13) (3,6) (3,4) (3,5) (3,22) (3,24) (3,21) (3,19) (3,9) (3,31) (3,18) (3,7) (3,20) (4,5) (4,21) (4,19) (4,9) (4,31) (4,7) (4,20) (4,27) (4,13) (5,6) (5,22) (5,24) (5,21) (5,9) (5,31) (5,10) (5,15) (5,18) (5,20) (5,27) (5,13) (6,22) (6,21) (6,19) (6,9) (6,31) (6,10) (6,15) (6,18) (6,7) (6,27) (6,13) (7,22) (7,9) (7,10) (7,15) (7,18) (7,20) (7,27) (7,13) (8,16) (8,11) (8,28) (8,12) (8,25) (8,30) (8,14) (8,32) (8,29) (9,22) (9,24) (9,21) (9,19) (9,31) (9,10) (9,15) (9,18) (9,20) (10,22) (10,19) (10,31) (10,15) (10,20) (10,27) (10,13) (11,16) (11,28) (11,26) (11,23) (11,30) (11,14) (11,32) (11,17) (12,16) (12,28) (12,23) (12,30) (12,14) (12,33) (12,32) (12,17) (12,29) (13,22) (13,24) (13,21) (13,19) (13,15) (13,18) (13,20) (14,28) (14,26) (14,23) (14,25) (14,33) (14,32) (14,29) (15,22) (15,24) (15,21) (15,19) (15,20) (15,27) (16,26) (16,25) (16,30) (16,33) (16,32) (16,17) (16,29) (17,28) (17,26) (17,25) (17,30) (17,33) (17,32) (17,29) (18,24) (18,19) (18,31) (19,22) (19,24) (19,31) (19,20) (19,27) (20,21) (20,31) (20,27) (21,31) (23,28) (23,26) (23,25) (23,30) (24,31) (24,27) (25,26) (25,30) (25,33) (25,32) (25,29) (26,28) (26,33) (26,32) (28,30) (28,29) (29,30) (29,33) (29,32) (30,32)\nIs there a path between node 8 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph23-13_0", + "image": "data/connectivity/graph_visual/hard/graph23.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,21) (0,24) (0,3) (0,23) (0,2) (0,1) (0,22) (1,7) (1,2) (1,8) (1,11) (1,22) (2,23) (2,8) (2,10) (3,19) (3,20) (3,8) (4,9) (5,21) (5,24) (5,17) (5,15) (5,8) (6,14) (7,21) (7,24) (7,13) (7,15) (8,21) (8,16) (8,23) (8,22) (10,17) (10,18) (10,25) (10,22) (11,24) (11,23) (13,24) (13,20) (13,22) (15,20) (15,23) (15,25) (16,19) (16,20) (16,23) (17,21) (17,20) (17,23) (18,24) (18,23) (18,25) (21,22) (22,23) (23,24)\nIs there a path between node 13 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph295-18_30", + "image": "data/connectivity/graph_visual/hard/graph295.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,3) (0,10) (0,26) (0,13) (0,23) (0,14) (0,27) (0,30) (0,31) (0,28) (0,2) (0,8) (0,12) (0,9) (0,24) (0,5) (1,19) (1,15) (1,6) (1,11) (1,29) (1,17) (1,21) (1,4) (1,25) (1,7) (2,3) (2,14) (2,31) (2,28) (2,18) (2,8) (2,12) (2,9) (2,24) (2,5) (3,10) (3,13) (3,23) (3,27) (3,30) (3,31) (3,28) (3,18) (3,8) (3,12) (3,9) (3,24) (3,5) (4,20) (4,19) (4,15) (4,11) (4,29) (4,16) (4,22) (4,7) (5,10) (5,13) (5,23) (5,14) (5,27) (5,31) (5,18) (5,8) (5,12) (5,9) (6,20) (6,15) (6,11) (6,29) (6,17) (6,21) (6,16) (6,25) (6,7) (7,20) (7,15) (7,11) (7,29) (7,17) (7,21) (7,25) (8,10) (8,26) (8,13) (8,23) (8,14) (8,27) (8,30) (8,12) (8,24) (9,10) (9,26) (9,13) (9,14) (9,27) (9,30) (9,31) (9,18) (9,24) (10,26) (10,13) (10,23) (10,14) (10,27) (10,30) (10,31) (10,18) (11,20) (11,19) (11,15) (11,29) (11,17) (11,21) (11,16) (11,25) (11,22) (12,13) (12,23) (12,14) (12,27) (12,28) (13,26) (13,23) (13,14) (13,27) (13,31) (13,28) (14,23) (14,30) (14,28) (14,18) (14,24) (15,19) (15,29) (15,21) (15,16) (15,22) (16,20) (16,19) (16,29) (16,17) (16,21) (16,25) (17,20) (17,19) (17,29) (17,21) (17,25) (17,22) (18,26) (18,27) (18,30) (18,31) (18,28) (19,29) (19,21) (19,25) (19,22) (20,29) (20,22) (21,29) (21,25) (21,22) (22,25) (23,26) (23,27) (23,30) (23,31) (23,24) (24,27) (24,30) (24,31) (25,29) (26,27) (26,30) (26,28) (27,30) (27,31) (28,30) (28,31) (30,31)\nIs there a path between node 18 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph707-17_18", + "image": "data/connectivity/graph_visual/hard/graph707.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,20) (0,7) (0,13) (0,27) (0,34) (0,28) (0,19) (0,3) (0,17) (0,21) (0,6) (0,32) (0,31) (0,25) (0,24) (1,14) (1,29) (1,12) (1,23) (1,33) (1,11) (2,26) (2,18) (2,20) (2,7) (2,34) (2,28) (2,3) (2,15) (2,17) (2,21) (2,6) (2,32) (2,10) (2,31) (2,25) (2,22) (3,26) (3,18) (3,20) (3,7) (3,13) (3,27) (3,6) (3,32) (3,10) (3,9) (3,31) (3,25) (3,24) (4,29) (4,8) (4,5) (4,12) (4,30) (4,16) (5,14) (5,8) (5,12) (5,23) (5,30) (5,16) (5,33) (5,11) (6,7) (6,13) (6,34) (6,28) (6,19) (6,15) (6,17) (6,32) (6,31) (6,25) (6,24) (6,22) (7,18) (7,13) (7,27) (7,32) (7,9) (7,25) (7,24) (7,22) (8,29) (8,12) (8,23) (8,16) (8,33) (9,18) (9,13) (9,27) (9,34) (9,28) (9,19) (9,15) (9,17) (9,21) (9,32) (9,31) (9,25) (9,24) (9,22) (10,26) (10,20) (10,27) (10,34) (10,28) (10,19) (10,17) (10,32) (10,25) (11,29) (11,12) (11,30) (11,16) (12,23) (13,18) (13,20) (13,27) (13,28) (13,15) (13,17) (13,21) (13,32) (13,31) (13,25) (13,22) (14,29) (14,23) (14,16) (14,33) (15,18) (15,27) (15,34) (15,28) (15,19) (15,17) (15,32) (15,31) (15,24) (16,23) (16,30) (16,33) (17,26) (17,20) (17,27) (17,28) (17,19) (17,21) (17,32) (17,31) (17,25) (17,22) (18,20) (18,27) (18,28) (18,19) (18,32) (18,31) (18,25) (19,20) (19,27) (19,34) (19,21) (19,32) (19,31) (19,25) (19,24) (19,22) (20,26) (20,34) (20,21) (20,32) (20,31) (20,24) (21,26) (21,27) (21,32) (21,31) (21,25) (21,22) (22,28) (22,32) (22,31) (22,24) (23,29) (23,30) (23,33) (24,34) (24,28) (24,32) (24,25) (25,26) (25,27) (25,28) (25,32) (25,31) (26,27) (26,34) (26,28) (26,32) (26,31) (27,34) (27,28) (27,32) (27,31) (28,34) (28,32) (28,31) (29,30) (29,33) (30,33) (31,34) (32,34)\nIs there a path between node 17 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph464-11_23", + "image": "data/connectivity/graph_visual/hard/graph464.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,17) (0,8) (0,21) (0,6) (1,14) (1,13) (1,30) (1,12) (1,24) (2,15) (3,8) (3,5) (4,9) (5,7) (6,32) (6,19) (7,17) (7,25) (8,32) (9,26) (9,15) (10,14) (10,13) (10,24) (11,14) (11,13) (12,13) (12,30) (12,24) (13,29) (13,24) (13,27) (14,27) (15,16) (15,18) (16,31) (17,32) (17,25) (18,26) (19,23) (20,26) (21,32) (23,25)\nIs there a path between node 11 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph548-17_22", + "image": "data/connectivity/graph_visual/hard/graph548.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,2) (0,31) (1,4) (1,27) (1,25) (2,31) (2,24) (2,13) (2,10) (3,30) (3,32) (3,27) (3,15) (4,30) (4,6) (4,28) (4,8) (5,22) (6,27) (7,20) (7,11) (7,12) (8,15) (9,14) (10,17) (10,23) (10,13) (11,14) (12,18) (13,23) (14,22) (15,30) (15,27) (15,25) (15,16) (15,28) (17,23) (17,21) (18,22) (18,33) (20,22) (21,31) (23,24) (25,30) (25,27) (25,28) (26,31) (27,30) (27,32) (28,32)\nIs there a path between node 17 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph410-23_20", + "image": "data/connectivity/graph_visual/hard/graph410.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,2) (0,8) (1,11) (1,10) (1,31) (1,4) (2,7) (2,28) (2,29) (2,6) (3,28) (3,21) (4,13) (4,9) (4,18) (4,26) (4,24) (4,25) (4,15) (4,22) (4,23) (5,11) (5,18) (5,14) (5,17) (5,31) (5,23) (6,28) (6,20) (6,19) (7,19) (7,21) (7,27) (8,20) (8,19) (9,11) (9,18) (9,26) (9,12) (9,24) (9,17) (10,31) (11,13) (11,17) (11,25) (11,31) (11,15) (11,22) (12,31) (12,22) (12,23) (13,18) (13,26) (13,14) (13,16) (13,24) (13,17) (13,15) (13,22) (13,23) (14,32) (14,17) (14,23) (15,24) (15,31) (16,24) (16,17) (16,31) (17,32) (17,25) (18,24) (18,23) (19,28) (19,30) (19,21) (19,27) (20,30) (20,29) (21,28) (21,30) (21,29) (22,25) (23,32) (24,32) (25,32) (26,32) (26,31) (27,29) (28,29) (29,30)\nIs there a path between node 23 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph416-22_2", + "image": "data/connectivity/graph_visual/hard/graph416.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,25) (0,27) (1,14) (1,23) (1,5) (1,6) (1,20) (1,8) (2,10) (2,25) (2,22) (3,19) (3,26) (4,32) (4,7) (4,20) (4,8) (5,17) (6,17) (6,8) (8,14) (8,23) (8,32) (9,19) (9,26) (9,13) (10,25) (10,12) (10,11) (11,25) (11,22) (12,24) (12,16) (12,25) (12,21) (13,15) (15,29) (15,19) (16,25) (17,31) (17,23) (17,32) (18,29) (18,30) (21,24) (21,25) (24,27) (26,30)\nIs there a path between node 22 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph207-21_2", + "image": "data/connectivity/graph_visual/hard/graph207.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,1) (0,18) (0,29) (1,18) (1,25) (2,28) (2,4) (2,14) (2,19) (2,12) (3,17) (4,5) (4,21) (5,22) (5,24) (5,11) (5,28) (5,7) (5,12) (6,22) (6,24) (6,28) (6,19) (7,11) (7,19) (7,21) (7,17) (8,16) (9,16) (9,20) (9,13) (9,15) (10,22) (10,14) (11,27) (11,14) (11,12) (12,24) (12,14) (12,19) (13,18) (13,26) (14,22) (15,16) (15,25) (17,22) (17,24) (17,27) (17,19) (17,21) (18,23) (19,22) (19,24) (20,29) (20,23) (20,25) (22,24) (22,27) (24,27) (24,28) (25,29)\nIs there a path between node 21 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph59-4_3", + "image": "data/connectivity/graph_visual/hard/graph59.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,4) (0,22) (0,15) (0,18) (0,14) (0,5) (0,2) (0,13) (1,16) (1,20) (1,6) (1,24) (1,8) (1,21) (1,23) (2,4) (2,22) (2,15) (2,25) (2,14) (2,19) (2,5) (2,3) (3,4) (3,22) (3,15) (3,18) (3,25) (3,19) (3,5) (3,13) (4,22) (4,15) (4,26) (4,25) (4,14) (4,13) (5,22) (5,15) (5,26) (5,18) (5,25) (5,14) (5,19) (5,13) (6,16) (6,17) (6,20) (6,9) (6,7) (6,24) (6,12) (6,11) (7,16) (7,17) (7,20) (7,9) (7,24) (7,8) (7,10) (7,23) (8,16) (8,17) (8,20) (8,9) (8,24) (8,12) (8,21) (8,10) (9,16) (9,17) (9,20) (9,24) (9,11) (9,21) (9,23) (10,16) (10,17) (10,20) (10,24) (10,12) (10,21) (11,16) (11,12) (11,21) (11,23) (12,16) (12,17) (12,20) (12,21) (13,22) (13,15) (13,26) (13,25) (13,14) (13,19) (14,22) (14,15) (14,26) (14,18) (14,25) (14,19) (15,26) (15,19) (16,17) (16,20) (16,21) (16,23) (17,20) (17,21) (18,22) (18,26) (18,25) (18,19) (19,22) (19,26) (19,25) (20,24) (21,24) (21,23) (22,26) (22,25) (23,24) (25,26)\nIs there a path between node 4 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph554-26_7", + "image": "data/connectivity/graph_visual/hard/graph554.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,3) (0,14) (0,1) (0,17) (1,23) (1,3) (1,13) (1,14) (2,30) (2,20) (2,31) (3,25) (3,14) (3,6) (3,7) (3,10) (3,33) (4,27) (4,8) (4,5) (4,20) (5,27) (5,22) (5,15) (5,8) (5,29) (6,11) (6,19) (6,18) (6,13) (6,7) (6,17) (7,13) (7,33) (8,26) (8,12) (8,29) (8,24) (9,19) (9,33) (10,11) (10,23) (10,19) (11,23) (11,19) (11,13) (11,21) (12,30) (12,22) (12,31) (13,23) (13,19) (13,14) (14,28) (15,30) (15,16) (15,32) (15,31) (15,24) (16,32) (16,20) (17,18) (17,33) (18,25) (18,21) (19,25) (19,21) (20,30) (20,31) (20,24) (22,24) (23,25) (23,28) (24,27) (24,30) (24,31) (25,33) (26,29) (29,32) (31,32)\nIs there a path between node 26 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph411-31_14", + "image": "data/connectivity/graph_visual/hard/graph411.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,32) (0,6) (0,21) (0,30) (0,12) (0,19) (0,8) (0,31) (1,15) (2,20) (2,11) (2,5) (2,29) (2,26) (2,24) (2,12) (2,9) (2,22) (4,23) (4,5) (4,25) (4,16) (4,21) (4,12) (4,9) (4,17) (4,8) (4,22) (5,20) (5,25) (5,9) (5,22) (6,23) (6,11) (6,29) (6,21) (6,19) (6,9) (6,8) (8,16) (8,29) (8,14) (8,13) (8,26) (8,24) (8,22) (8,31) (9,23) (9,29) (9,14) (9,19) (11,23) (11,14) (11,26) (11,28) (11,31) (12,20) (12,23) (12,29) (12,21) (12,26) (12,30) (12,19) (13,29) (13,26) (13,30) (13,28) (13,22) (13,31) (14,16) (14,31) (16,29) (16,21) (17,20) (17,32) (17,24) (17,31) (19,20) (19,24) (19,30) (19,28) (19,22) (20,23) (20,32) (20,26) (20,24) (20,30) (20,22) (20,31) (21,32) (21,29) (21,26) (21,24) (21,30) (21,22) (21,31) (22,23) (22,32) (22,26) (22,24) (22,30) (23,32) (23,29) (23,26) (23,30) (24,32) (24,25) (24,31) (25,26) (26,29) (26,30) (30,31) (31,32)\nIs there a path between node 31 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph298-29_9", + "image": "data/connectivity/graph_visual/hard/graph298.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,31) (0,27) (0,3) (0,21) (0,19) (0,23) (0,18) (0,29) (0,16) (0,24) (1,25) (1,5) (1,6) (2,12) (2,10) (2,17) (2,13) (3,4) (3,31) (3,27) (3,21) (3,15) (3,23) (3,18) (3,16) (3,24) (4,27) (4,15) (4,23) (4,18) (4,29) (4,22) (4,16) (4,24) (5,25) (5,6) (6,25) (7,20) (7,11) (8,25) (9,12) (9,14) (9,10) (9,17) (9,13) (10,12) (10,14) (10,17) (10,13) (11,26) (11,20) (11,28) (12,17) (13,14) (13,17) (14,17) (15,31) (15,27) (15,21) (15,30) (15,23) (15,29) (15,22) (15,24) (16,27) (16,30) (16,19) (16,23) (16,22) (16,24) (18,31) (18,27) (18,21) (18,30) (18,19) (18,23) (18,22) (19,31) (19,27) (19,21) (19,24) (20,26) (21,27) (21,30) (21,23) (21,29) (21,22) (22,31) (22,27) (22,30) (22,29) (23,31) (23,29) (24,27) (24,29) (26,28) (29,31) (29,30) (30,31)\nIs there a path between node 29 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph387-14_25", + "image": "data/connectivity/graph_visual/hard/graph387.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,27) (0,28) (0,29) (0,22) (0,23) (0,8) (0,19) (0,6) (0,16) (0,7) (0,15) (0,26) (0,1) (1,3) (1,27) (1,20) (1,22) (1,23) (1,8) (1,19) (1,18) (1,6) (1,5) (1,16) (1,10) (1,7) (1,26) (2,31) (2,21) (2,11) (2,17) (2,12) (3,22) (3,8) (3,19) (3,6) (3,16) (3,10) (3,7) (3,15) (4,31) (4,14) (4,11) (4,17) (4,25) (4,24) (4,13) (4,12) (4,30) (5,28) (5,29) (5,23) (5,19) (5,18) (5,10) (5,15) (5,26) (6,27) (6,29) (6,20) (6,23) (6,8) (6,18) (6,16) (6,10) (6,15) (6,26) (7,27) (7,28) (7,20) (7,22) (7,23) (7,8) (7,19) (7,18) (7,16) (7,15) (7,26) (8,27) (8,28) (8,29) (8,20) (8,22) (8,23) (8,18) (8,16) (9,31) (9,21) (9,11) (9,17) (9,25) (9,24) (9,12) (10,27) (10,28) (10,29) (10,20) (10,22) (10,23) (10,19) (10,16) (10,15) (10,26) (11,31) (11,21) (11,25) (11,24) (11,12) (12,31) (12,21) (12,14) (12,17) (12,25) (12,24) (12,30) (13,21) (13,25) (13,24) (13,30) (14,31) (14,17) (14,25) (14,24) (14,30) (15,29) (15,20) (15,22) (15,23) (15,19) (15,18) (15,26) (16,27) (16,28) (16,29) (16,20) (16,22) (16,18) (16,26) (17,31) (17,21) (17,25) (17,24) (17,30) (18,28) (18,29) (18,20) (18,22) (18,19) (19,27) (19,28) (19,29) (19,20) (19,22) (19,23) (19,26) (20,27) (20,28) (20,29) (20,22) (20,23) (21,25) (22,27) (22,28) (22,29) (23,28) (24,25) (24,30) (25,31) (25,30) (26,27) (26,28) (26,29) (27,28) (27,29) (28,29) (30,31)\nIs there a path between node 14 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph659-31_0", + "image": "data/connectivity/graph_visual/hard/graph659.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,14) (0,7) (0,19) (0,24) (0,30) (0,33) (0,5) (0,3) (0,6) (0,25) (0,13) (0,22) (0,29) (1,27) (1,9) (2,26) (2,13) (3,30) (3,33) (3,17) (3,6) (3,26) (3,21) (3,13) (3,4) (3,18) (3,12) (4,30) (4,34) (4,17) (4,5) (4,6) (4,21) (4,13) (5,7) (5,24) (5,30) (5,17) (5,25) (5,32) (5,18) (6,19) (6,30) (6,26) (6,28) (6,21) (6,25) (6,23) (6,13) (6,12) (7,19) (7,24) (7,10) (7,33) (7,17) (7,21) (7,13) (8,16) (8,20) (8,9) (9,27) (9,31) (10,30) (10,34) (10,18) (10,12) (11,20) (12,24) (12,30) (12,17) (12,15) (12,23) (12,22) (12,29) (12,18) (13,30) (13,28) (13,22) (13,18) (14,17) (14,15) (14,29) (14,18) (15,30) (15,33) (15,28) (15,25) (15,29) (16,20) (17,24) (17,33) (17,25) (17,23) (17,22) (17,18) (18,19) (18,21) (18,23) (18,32) (18,29) (19,24) (19,30) (19,34) (19,33) (19,28) (19,21) (19,25) (19,32) (20,27) (21,30) (21,33) (21,26) (21,28) (21,25) (21,32) (22,24) (22,30) (22,34) (23,30) (23,33) (23,32) (24,30) (24,33) (24,29) (25,30) (25,34) (25,26) (25,28) (25,29) (26,30) (26,33) (26,28) (28,33) (29,34) (33,34)\nIs there a path between node 31 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph708-28_21", + "image": "data/connectivity/graph_visual/hard/graph708.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,33) (0,7) (0,24) (0,22) (0,27) (0,17) (0,20) (1,21) (1,9) (1,15) (1,33) (1,7) (1,25) (1,24) (1,22) (1,8) (1,27) (1,20) (2,23) (2,14) (2,31) (2,10) (2,4) (2,30) (2,26) (2,6) (2,16) (2,11) (3,29) (4,23) (4,14) (4,31) (4,10) (4,12) (4,30) (4,26) (4,32) (4,16) (4,18) (4,19) (4,11) (4,34) (5,21) (5,9) (5,15) (5,33) (5,7) (5,25) (5,24) (5,22) (5,8) (5,27) (5,17) (5,20) (6,23) (6,13) (6,14) (6,31) (6,12) (6,30) (6,26) (6,16) (6,19) (6,11) (6,34) (7,21) (7,9) (7,15) (7,33) (7,25) (7,24) (7,22) (7,27) (7,17) (8,21) (8,9) (8,33) (8,25) (8,24) (8,22) (8,27) (8,17) (9,21) (9,15) (9,33) (9,24) (9,22) (9,27) (9,17) (9,20) (10,14) (10,31) (10,12) (10,30) (10,26) (10,32) (10,18) (10,19) (11,23) (11,13) (11,14) (11,31) (11,30) (11,32) (11,16) (11,18) (11,19) (12,13) (12,14) (12,31) (12,30) (12,26) (12,16) (12,19) (12,34) (13,23) (13,14) (13,31) (13,30) (13,32) (13,16) (13,19) (13,34) (14,23) (14,31) (14,30) (14,26) (14,32) (14,16) (14,19) (15,21) (15,33) (15,25) (15,24) (15,22) (15,27) (15,20) (16,23) (16,31) (16,26) (16,32) (16,18) (16,19) (16,34) (17,25) (17,24) (18,23) (18,31) (18,26) (18,32) (18,19) (19,31) (19,30) (19,32) (20,21) (20,22) (21,33) (21,25) (21,22) (21,27) (22,33) (22,25) (22,24) (22,27) (23,31) (23,26) (23,32) (23,34) (24,33) (24,25) (24,27) (25,33) (26,31) (26,30) (26,34) (27,33) (28,29) (30,31) (32,34)\nIs there a path between node 28 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph440-31_30", + "image": "data/connectivity/graph_visual/hard/graph440.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,27) (0,8) (0,29) (1,18) (1,24) (1,2) (1,28) (1,12) (1,17) (1,25) (1,16) (2,24) (2,3) (2,10) (2,31) (2,12) (2,30) (2,17) (2,16) (2,21) (3,10) (3,28) (3,30) (3,17) (3,25) (3,16) (3,21) (4,19) (4,20) (4,9) (4,13) (4,32) (4,26) (5,23) (5,29) (6,11) (6,27) (6,8) (6,29) (7,19) (7,15) (7,22) (7,20) (7,9) (7,13) (7,26) (8,23) (8,14) (8,27) (9,19) (9,15) (9,22) (9,13) (9,26) (10,18) (10,28) (10,12) (10,17) (10,16) (10,21) (11,23) (11,14) (11,29) (12,18) (12,24) (12,31) (12,28) (12,30) (12,17) (13,19) (13,15) (13,22) (13,20) (13,26) (14,23) (14,27) (15,22) (15,32) (15,26) (16,18) (16,24) (16,31) (16,28) (16,30) (16,17) (16,25) (16,21) (17,18) (17,24) (17,31) (17,28) (17,30) (18,24) (18,31) (18,28) (18,30) (18,21) (19,22) (20,32) (20,26) (21,24) (21,28) (23,29) (24,28) (24,30) (24,25) (25,31) (25,28) (25,30) (26,32) (27,29) (28,30) (30,31)\nIs there a path between node 31 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph155-16_12", + "image": "data/connectivity/graph_visual/hard/graph155.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,9) (0,15) (1,5) (1,22) (1,4) (1,20) (1,12) (1,25) (2,5) (2,22) (2,13) (2,12) (2,10) (3,23) (4,19) (4,14) (4,18) (4,28) (4,11) (5,12) (5,24) (5,28) (6,16) (6,17) (7,15) (8,15) (10,19) (10,14) (10,24) (10,28) (11,22) (11,19) (12,13) (12,27) (12,20) (13,19) (13,20) (13,25) (14,26) (14,18) (14,24) (14,25) (17,21) (18,26) (18,27) (18,20) (18,28) (18,25) (19,26) (19,27) (19,24) (19,28) (20,27) (20,24) (24,28) (26,28)\nIs there a path between node 16 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph21-4_18", + "image": "data/connectivity/graph_visual/hard/graph21.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,19) (1,15) (1,18) (1,9) (1,21) (2,5) (2,10) (2,23) (3,6) (3,18) (4,22) (4,13) (4,9) (4,11) (6,17) (6,22) (6,18) (6,9) (6,7) (6,12) (6,21) (7,15) (7,17) (8,15) (8,18) (8,9) (8,11) (8,21) (9,15) (9,22) (10,25) (11,15) (11,17) (11,22) (11,13) (11,12) (11,21) (12,13) (13,15) (13,17) (14,15) (14,18) (14,21) (15,17) (15,21) (16,25) (17,22) (17,18) (18,22)\nIs there a path between node 4 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph218-13_19", + "image": "data/connectivity/graph_visual/hard/graph218.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,7) (0,15) (0,18) (0,27) (0,9) (0,13) (0,25) (0,3) (1,8) (1,5) (1,26) (1,12) (1,2) (1,16) (1,14) (2,8) (2,26) (2,12) (2,16) (2,14) (3,7) (3,4) (3,15) (3,18) (3,27) (3,13) (4,7) (4,15) (4,18) (4,27) (4,13) (5,8) (5,12) (5,11) (5,16) (5,14) (5,20) (6,17) (6,21) (6,29) (6,28) (7,15) (7,18) (7,27) (7,9) (7,13) (8,26) (8,23) (8,16) (8,14) (9,15) (10,29) (10,24) (11,12) (11,16) (11,14) (11,20) (12,22) (12,23) (12,14) (12,20) (13,18) (13,27) (14,26) (14,22) (14,23) (14,20) (15,18) (15,27) (15,25) (16,26) (16,22) (16,23) (16,20) (17,21) (17,19) (17,24) (17,28) (19,21) (19,29) (19,24) (19,28) (20,26) (20,22) (20,23) (21,29) (21,24) (22,26) (22,23) (24,29) (24,28) (25,27)\nIs there a path between node 13 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph458-15_25", + "image": "data/connectivity/graph_visual/hard/graph458.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,32) (0,6) (0,21) (1,7) (2,18) (3,17) (3,23) (4,27) (4,7) (4,18) (5,27) (6,12) (7,27) (8,28) (8,26) (9,29) (9,31) (10,30) (10,16) (10,25) (10,12) (13,18) (14,30) (14,32) (14,15) (15,19) (15,32) (15,25) (16,19) (16,30) (16,25) (16,21) (17,28) (17,29) (21,30) (21,25) (23,28) (23,29) (26,29) (26,31) (30,32)\nIs there a path between node 15 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph618-8_29", + "image": "data/connectivity/graph_visual/hard/graph618.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,34) (0,19) (0,17) (0,16) (0,31) (0,2) (0,7) (0,25) (0,22) (0,14) (1,28) (1,19) (1,16) (1,31) (1,8) (1,2) (1,7) (1,25) (1,14) (1,15) (2,28) (2,19) (2,17) (2,3) (2,31) (2,8) (2,7) (2,25) (2,20) (2,22) (2,14) (3,34) (3,19) (3,17) (3,16) (3,31) (3,7) (3,25) (3,22) (3,14) (4,18) (4,10) (4,24) (4,11) (4,6) (4,12) (4,26) (4,27) (4,13) (4,30) (4,21) (4,29) (5,18) (5,9) (5,11) (5,6) (5,26) (5,27) (5,30) (5,29) (6,18) (6,9) (6,24) (6,33) (6,12) (6,23) (6,27) (6,30) (7,34) (7,19) (7,16) (7,31) (7,8) (7,20) (7,14) (7,15) (8,28) (8,17) (8,16) (8,31) (8,25) (8,15) (9,18) (9,10) (9,24) (9,11) (9,33) (9,12) (9,32) (9,23) (9,13) (9,30) (9,29) (10,18) (10,24) (10,11) (10,33) (10,12) (10,32) (10,13) (10,30) (10,21) (10,29) (11,18) (11,12) (11,32) (11,23) (11,26) (11,27) (11,13) (11,30) (11,21) (12,18) (12,24) (12,33) (12,32) (12,23) (12,26) (12,27) (12,13) (12,21) (12,29) (13,18) (13,24) (13,33) (13,32) (13,23) (13,26) (13,27) (13,29) (14,34) (14,28) (14,19) (14,25) (14,22) (14,15) (15,34) (15,28) (15,19) (15,17) (15,16) (15,25) (15,20) (16,28) (16,31) (16,25) (16,22) (17,28) (17,19) (17,31) (17,25) (17,20) (17,22) (18,33) (18,32) (18,23) (18,26) (18,27) (19,34) (19,31) (19,22) (20,34) (20,31) (20,25) (20,22) (21,24) (21,33) (21,32) (21,27) (21,30) (21,29) (22,28) (22,31) (22,25) (23,24) (23,33) (23,32) (23,26) (23,27) (23,30) (24,32) (24,27) (24,30) (24,29) (25,28) (26,32) (26,27) (26,29) (28,34) (28,31) (29,32) (29,30) (30,33) (30,32) (31,34) (32,33)\nIs there a path between node 8 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph238-14_16", + "image": "data/connectivity/graph_visual/hard/graph238.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,13) (0,4) (0,26) (1,6) (1,15) (1,30) (1,24) (2,3) (2,20) (2,25) (2,26) (3,12) (3,10) (3,25) (4,12) (4,13) (4,10) (4,7) (4,25) (4,26) (5,29) (5,20) (5,11) (5,25) (5,26) (6,14) (6,30) (6,28) (6,17) (7,29) (7,12) (7,13) (7,10) (7,20) (7,25) (7,26) (8,19) (8,27) (8,24) (9,22) (9,11) (9,25) (10,22) (10,29) (10,12) (10,13) (10,25) (10,26) (11,22) (11,23) (11,20) (12,29) (12,23) (14,27) (14,28) (14,24) (15,21) (15,19) (16,30) (16,24) (17,19) (17,28) (17,24) (18,20) (18,25) (20,22) (20,29) (20,25) (21,30) (21,24) (22,23) (22,25) (22,26) (23,29) (25,29) (25,26) (26,29) (28,30)\nIs there a path between node 14 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph147-4_14", + "image": "data/connectivity/graph_visual/hard/graph147.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,8) (0,19) (0,26) (0,7) (0,14) (0,5) (0,21) (0,13) (0,24) (0,17) (0,1) (0,9) (0,3) (0,16) (0,25) (1,8) (1,19) (1,26) (1,2) (1,7) (1,14) (1,5) (1,27) (1,4) (1,28) (1,15) (1,24) (1,17) (1,9) (1,23) (1,11) (1,3) (1,16) (2,12) (2,8) (2,22) (2,19) (2,26) (2,7) (2,18) (2,21) (2,27) (2,13) (2,15) (2,17) (2,9) (2,10) (2,23) (2,3) (2,16) (2,25) (3,12) (3,22) (3,19) (3,26) (3,7) (3,14) (3,18) (3,5) (3,21) (3,27) (3,4) (3,28) (3,13) (3,15) (3,24) (3,17) (3,9) (3,23) (3,11) (3,16) (4,12) (4,8) (4,26) (4,14) (4,18) (4,21) (4,13) (4,15) (4,24) (4,17) (4,23) (4,16) (5,12) (5,8) (5,22) (5,26) (5,14) (5,18) (5,21) (5,27) (5,28) (5,13) (5,15) (5,17) (5,10) (5,11) (5,25) (7,12) (7,8) (7,26) (7,14) (7,18) (7,21) (7,27) (7,13) (7,15) (7,17) (7,9) (7,10) (7,11) (7,16) (7,25) (8,12) (8,19) (8,14) (8,18) (8,21) (8,27) (8,13) (8,24) (8,17) (8,9) (8,10) (8,23) (8,16) (8,25) (9,12) (9,19) (9,14) (9,18) (9,27) (9,28) (9,13) (9,15) (9,17) (9,10) (9,23) (9,11) (9,16) (9,25) (10,12) (10,22) (10,19) (10,14) (10,18) (10,21) (10,27) (10,28) (10,13) (10,24) (10,23) (10,11) (10,25) (11,22) (11,19) (11,27) (11,13) (11,15) (11,23) (11,25) (12,19) (12,14) (12,18) (12,21) (12,27) (12,15) (12,24) (12,17) (12,25) (13,22) (13,19) (13,26) (13,14) (13,18) (13,21) (13,28) (13,15) (13,17) (13,23) (13,16) (13,25) (14,18) (14,21) (14,27) (14,28) (14,17) (14,23) (14,16) (14,25) (15,22) (15,19) (15,18) (15,24) (15,17) (15,23) (15,25) (16,22) (16,19) (16,26) (16,18) (16,21) (16,27) (16,28) (16,24) (16,17) (16,23) (16,25) (17,22) (17,19) (17,18) (17,21) (17,27) (17,24) (17,23) (17,25) (18,22) (18,19) (18,26) (18,21) (18,27) (18,28) (18,24) (18,23) (19,22) (19,26) (19,28) (19,24) (19,23) (19,25) (21,22) (21,26) (21,27) (21,28) (21,25) (22,26) (22,27) (22,24) (22,23) (22,25) (23,26) (23,27) (23,28) (23,24) (23,25) (24,26) (24,28) (24,25) (25,26) (25,27) (25,28) (27,28)\nIs there a path between node 4 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph380-30_12", + "image": "data/connectivity/graph_visual/hard/graph380.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,23) (0,8) (0,15) (0,6) (0,5) (0,13) (0,21) (0,18) (1,4) (1,7) (1,23) (1,15) (1,6) (1,21) (2,10) (2,16) (2,26) (2,12) (2,22) (2,27) (2,30) (2,17) (2,31) (3,9) (3,25) (3,20) (3,28) (3,11) (3,19) (4,8) (4,15) (4,5) (4,13) (4,21) (4,18) (5,7) (5,8) (5,15) (5,6) (5,13) (5,21) (5,18) (6,23) (6,8) (6,15) (6,21) (6,18) (7,23) (7,8) (7,21) (7,18) (8,23) (8,15) (8,13) (8,18) (9,25) (9,28) (9,11) (9,19) (10,26) (10,12) (10,24) (10,14) (10,30) (10,17) (10,31) (12,26) (12,27) (12,14) (12,30) (12,31) (13,23) (13,21) (14,16) (14,26) (14,22) (14,24) (14,30) (14,31) (15,23) (15,21) (15,18) (16,24) (16,27) (16,30) (16,17) (16,31) (17,26) (17,22) (17,27) (18,23) (19,25) (19,20) (19,28) (20,25) (20,28) (21,23) (22,26) (22,27) (22,30) (24,26) (24,27) (24,30) (24,31) (26,27) (26,30) (26,31) (27,30) (27,31) (30,31)\nIs there a path between node 30 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph499-21_27", + "image": "data/connectivity/graph_visual/hard/graph499.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,17) (0,31) (0,6) (0,29) (0,16) (2,21) (2,22) (2,5) (2,24) (2,31) (2,18) (3,17) (3,24) (3,27) (3,32) (3,30) (3,31) (3,7) (3,6) (4,13) (4,11) (4,27) (4,32) (4,26) (4,7) (4,18) (4,10) (5,13) (5,11) (5,27) (5,18) (5,6) (6,23) (6,32) (6,7) (6,12) (7,22) (7,27) (7,26) (7,30) (7,9) (8,33) (9,21) (9,22) (9,17) (9,23) (9,12) (9,25) (10,11) (10,17) (10,23) (10,31) (10,20) (10,12) (10,25) (10,29) (11,24) (11,31) (11,20) (11,25) (11,16) (12,24) (12,20) (12,18) (12,29) (13,22) (13,17) (13,24) (15,33) (15,19) (16,22) (16,24) (17,25) (18,21) (18,24) (18,27) (18,30) (19,33) (19,28) (20,22) (20,27) (20,29) (21,31) (22,27) (22,23) (22,32) (22,26) (23,25) (23,29) (24,25) (24,29) (25,29) (26,27) (26,31) (27,32) (28,33)\nIs there a path between node 21 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph470-2_3", + "image": "data/connectivity/graph_visual/hard/graph470.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,29) (0,16) (0,15) (0,25) (0,23) (0,24) (1,5) (1,2) (1,21) (1,19) (1,30) (1,27) (1,9) (1,18) (1,31) (1,13) (1,32) (1,12) (1,22) (1,8) (2,4) (2,5) (2,21) (2,11) (2,6) (2,30) (2,3) (2,9) (2,7) (2,18) (2,31) (2,13) (2,32) (2,12) (2,22) (2,8) (3,4) (3,5) (3,21) (3,11) (3,19) (3,30) (3,9) (3,7) (3,31) (3,13) (3,32) (3,12) (3,26) (3,8) (4,21) (4,11) (4,30) (4,27) (4,9) (4,18) (4,13) (4,17) (4,32) (4,12) (4,26) (4,22) (5,21) (5,11) (5,6) (5,19) (5,30) (5,27) (5,18) (5,31) (5,13) (5,17) (5,32) (5,12) (5,26) (5,8) (6,21) (6,11) (6,19) (6,30) (6,27) (6,7) (6,31) (6,13) (6,17) (6,12) (6,26) (7,21) (7,19) (7,30) (7,9) (7,18) (7,31) (7,13) (7,17) (7,32) (7,12) (8,21) (8,11) (8,27) (8,9) (8,18) (8,31) (8,13) (8,17) (8,32) (8,12) (8,22) (9,19) (9,27) (9,31) (9,13) (9,32) (9,12) (9,26) (9,22) (10,14) (10,28) (11,19) (11,30) (11,31) (11,17) (11,12) (11,26) (12,21) (12,19) (12,30) (12,31) (12,13) (12,17) (12,32) (13,21) (13,27) (13,18) (13,31) (13,22) (14,28) (15,29) (15,16) (15,25) (15,20) (15,23) (15,24) (16,25) (16,20) (16,24) (17,21) (17,30) (17,31) (17,32) (17,26) (17,22) (18,21) (18,19) (18,31) (18,32) (18,26) (18,22) (19,21) (19,30) (19,27) (19,32) (19,26) (19,22) (20,29) (20,25) (20,23) (20,24) (21,30) (21,27) (21,31) (21,32) (21,26) (21,22) (22,30) (22,27) (22,26) (23,29) (23,25) (23,24) (24,29) (24,25) (25,29) (26,30) (26,27) (26,32) (27,31) (27,32) (30,32) (31,32)\nIs there a path between node 2 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph335-21_20", + "image": "data/connectivity/graph_visual/hard/graph335.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,12) (0,9) (0,4) (0,16) (0,26) (1,19) (1,31) (1,9) (1,4) (1,21) (1,26) (2,13) (2,19) (2,12) (2,31) (2,4) (2,21) (2,26) (3,22) (3,11) (3,6) (3,7) (3,5) (3,8) (3,17) (3,29) (3,28) (3,23) (3,10) (3,25) (3,24) (4,13) (4,16) (4,21) (5,22) (5,7) (5,15) (5,30) (5,8) (5,17) (5,29) (5,27) (5,28) (5,23) (5,10) (6,7) (6,8) (6,17) (6,27) (6,18) (6,28) (6,10) (6,25) (6,24) (6,20) (7,22) (7,11) (7,15) (7,30) (7,29) (7,18) (7,28) (7,23) (7,10) (7,25) (7,20) (8,11) (8,30) (8,17) (8,29) (8,27) (8,23) (8,10) (8,25) (8,20) (9,13) (9,12) (9,31) (9,14) (9,16) (9,26) (10,22) (10,15) (10,30) (10,17) (10,29) (10,27) (10,18) (10,28) (10,23) (10,24) (11,15) (11,17) (11,29) (11,18) (11,28) (11,23) (11,25) (11,24) (12,13) (12,19) (12,31) (12,14) (12,16) (13,31) (13,14) (13,21) (13,26) (14,19) (14,31) (14,16) (14,21) (14,26) (15,22) (15,30) (15,27) (15,28) (15,23) (15,25) (15,20) (16,19) (16,21) (17,22) (17,30) (17,29) (17,27) (17,18) (17,28) (17,23) (17,25) (17,20) (18,22) (18,29) (18,28) (18,25) (18,24) (19,31) (19,21) (19,26) (20,27) (20,28) (20,23) (20,25) (20,24) (21,31) (21,26) (22,27) (22,28) (22,23) (22,25) (22,24) (23,30) (23,29) (23,27) (23,28) (23,25) (23,24) (24,30) (24,29) (24,27) (24,25) (25,29) (25,28) (26,31) (27,30) (27,29) (27,28) (28,30) (28,29) (29,30)\nIs there a path between node 21 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph552-33_15", + "image": "data/connectivity/graph_visual/hard/graph552.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,27) (0,26) (0,3) (0,13) (0,22) (0,12) (0,31) (0,17) (1,2) (1,20) (1,23) (1,13) (1,4) (1,29) (2,20) (2,5) (2,6) (2,22) (2,16) (2,31) (2,17) (2,29) (3,27) (3,5) (3,23) (3,24) (3,15) (3,13) (3,4) (3,17) (4,7) (4,5) (4,15) (4,13) (4,10) (4,22) (4,16) (4,18) (4,12) (4,21) (5,27) (5,20) (5,14) (5,23) (5,6) (5,15) (5,13) (5,28) (5,12) (5,21) (5,8) (5,25) (6,26) (6,20) (6,23) (6,24) (6,15) (6,9) (6,28) (6,22) (6,16) (6,8) (7,9) (7,19) (7,12) (7,21) (7,25) (8,24) (8,15) (8,32) (8,31) (8,25) (9,23) (9,22) (9,19) (9,12) (9,17) (10,26) (10,14) (10,23) (10,28) (10,29) (11,33) (12,15) (12,28) (12,16) (12,29) (13,14) (13,24) (13,32) (13,18) (13,17) (14,27) (14,26) (14,15) (14,31) (14,17) (14,25) (15,27) (15,26) (15,28) (15,19) (15,25) (16,20) (16,19) (16,18) (16,25) (17,20) (17,24) (17,32) (17,18) (17,25) (18,27) (18,24) (18,22) (18,31) (18,29) (19,26) (19,29) (19,25) (20,27) (20,23) (20,24) (20,22) (20,31) (21,22) (22,32) (22,28) (22,29) (22,25) (23,32) (23,25) (24,31) (26,27) (26,32) (27,29) (28,32) (28,31) (29,31)\nIs there a path between node 33 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph40-15_19", + "image": "data/connectivity/graph_visual/hard/graph40.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,11) (0,13) (0,8) (0,3) (0,23) (0,4) (0,12) (0,7) (1,25) (1,14) (1,9) (2,20) (2,22) (2,21) (2,6) (2,15) (2,17) (2,19) (3,11) (3,13) (3,23) (3,18) (3,5) (3,16) (3,7) (4,11) (4,13) (4,8) (4,23) (4,18) (4,5) (4,16) (4,7) (5,11) (5,13) (5,23) (5,18) (5,16) (5,12) (5,7) (6,20) (6,22) (6,10) (6,21) (6,15) (6,17) (6,19) (7,11) (7,13) (7,8) (7,18) (7,12) (8,11) (8,13) (8,23) (8,18) (8,16) (8,12) (9,14) (10,20) (10,22) (10,17) (10,19) (11,23) (11,18) (11,16) (11,12) (12,13) (12,16) (13,16) (15,22) (15,21) (15,17) (15,19) (16,23) (16,18) (17,20) (17,22) (17,19) (18,23) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22) (24,25)\nIs there a path between node 15 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph542-18_3", + "image": "data/connectivity/graph_visual/hard/graph542.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,19) (0,10) (0,11) (0,4) (0,22) (0,30) (0,5) (0,31) (0,14) (0,12) (1,8) (1,11) (1,4) (1,22) (1,33) (1,5) (1,9) (1,14) (1,12) (2,13) (2,26) (2,27) (2,28) (2,18) (2,29) (2,24) (2,3) (2,17) (2,25) (3,20) (3,15) (3,23) (3,28) (3,18) (3,29) (3,32) (3,24) (3,7) (3,21) (3,17) (3,25) (4,8) (4,10) (4,22) (4,33) (4,9) (4,31) (5,8) (5,19) (5,11) (5,33) (5,9) (5,31) (5,14) (5,12) (6,23) (6,27) (6,28) (6,18) (6,29) (6,32) (6,24) (6,7) (6,21) (6,25) (7,20) (7,13) (7,26) (7,23) (7,28) (7,18) (7,21) (7,17) (7,25) (8,19) (8,22) (8,33) (8,30) (8,31) (8,14) (8,12) (9,19) (9,10) (9,11) (9,22) (9,30) (9,31) (10,19) (10,11) (10,22) (10,30) (10,31) (10,14) (11,22) (11,31) (11,12) (12,19) (12,30) (12,14) (13,20) (13,26) (13,15) (13,23) (13,27) (13,28) (13,29) (13,32) (13,24) (14,19) (14,22) (14,33) (15,20) (15,23) (15,27) (15,18) (15,29) (15,32) (15,24) (15,17) (17,26) (17,23) (17,28) (17,18) (17,29) (17,32) (17,24) (17,21) (17,25) (18,20) (18,29) (19,33) (19,30) (19,31) (20,26) (20,23) (20,27) (20,28) (20,25) (21,23) (21,27) (21,28) (21,29) (21,32) (21,24) (21,25) (22,33) (22,30) (23,27) (23,28) (23,29) (23,32) (23,25) (24,26) (24,27) (24,32) (25,27) (25,28) (25,29) (26,27) (26,28) (26,32) (27,28) (27,29) (27,32) (29,32) (30,33) (30,31) (31,33)\nIs there a path between node 18 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph300-18_12", + "image": "data/connectivity/graph_visual/hard/graph300.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,22) (0,19) (0,24) (0,1) (0,2) (0,5) (0,28) (0,29) (0,31) (0,12) (0,23) (0,15) (0,11) (0,10) (1,6) (1,22) (1,19) (1,24) (1,2) (1,5) (1,28) (1,29) (1,31) (1,14) (1,23) (1,15) (1,11) (2,6) (2,22) (2,19) (2,5) (2,28) (2,18) (2,31) (2,14) (2,12) (2,15) (2,11) (2,10) (3,6) (3,19) (3,28) (3,29) (3,18) (3,23) (3,15) (3,10) (4,25) (4,20) (4,17) (4,30) (4,27) (4,9) (4,21) (4,26) (4,13) (4,7) (4,16) (5,6) (5,19) (5,24) (5,28) (5,18) (5,31) (5,14) (5,12) (5,23) (5,15) (5,11) (6,19) (6,24) (6,29) (6,18) (6,31) (6,12) (6,15) (6,10) (7,25) (7,20) (7,17) (7,30) (7,27) (7,9) (7,21) (7,26) (7,13) (7,16) (8,25) (8,9) (9,25) (9,20) (9,17) (9,30) (9,21) (9,26) (9,13) (9,16) (10,22) (10,24) (10,28) (10,29) (10,18) (10,31) (10,14) (10,15) (11,24) (11,28) (11,29) (11,18) (11,14) (11,12) (11,15) (12,29) (12,18) (12,31) (12,15) (13,20) (13,17) (13,30) (13,27) (13,21) (13,26) (13,16) (14,22) (14,19) (14,24) (14,18) (14,31) (14,23) (14,15) (15,22) (15,19) (15,24) (15,28) (15,29) (15,18) (16,20) (16,17) (16,30) (16,21) (16,26) (17,25) (17,20) (17,27) (18,22) (18,19) (18,24) (18,28) (18,29) (18,31) (19,22) (19,24) (19,28) (19,29) (19,23) (20,30) (20,27) (20,21) (20,26) (21,25) (21,30) (21,27) (21,26) (22,24) (22,28) (22,31) (22,23) (23,28) (23,29) (23,31) (24,28) (24,31) (25,30) (26,30) (26,27) (28,29) (28,31) (29,31)\nIs there a path between node 18 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph351-7_11", + "image": "data/connectivity/graph_visual/hard/graph351.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,31) (0,26) (0,30) (0,17) (0,9) (0,11) (0,2) (0,12) (1,10) (1,31) (1,26) (1,17) (1,28) (1,3) (1,21) (2,20) (2,17) (2,3) (2,18) (2,21) (3,20) (3,19) (3,31) (3,26) (3,28) (4,29) (4,19) (4,26) (4,11) (4,28) (4,18) (4,12) (4,27) (5,19) (5,11) (5,28) (5,21) (5,27) (6,20) (6,19) (6,14) (6,16) (6,25) (6,26) (6,30) (7,10) (7,20) (7,14) (7,31) (7,30) (7,17) (7,28) (7,21) (7,27) (9,10) (9,16) (9,25) (9,17) (9,12) (10,20) (10,16) (10,30) (10,22) (10,11) (10,27) (11,29) (11,30) (12,29) (12,16) (12,22) (13,20) (13,14) (13,31) (13,27) (14,30) (14,17) (16,20) (16,19) (16,31) (17,29) (17,20) (17,26) (18,19) (18,31) (18,30) (18,28) (19,29) (19,22) (20,30) (20,22) (21,30) (21,27) (22,28) (25,28) (26,29) (27,28) (28,31) (28,30) (29,30) (30,31)\nIs there a path between node 7 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph701-3_5", + "image": "data/connectivity/graph_visual/hard/graph701.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,12) (0,6) (0,25) (0,9) (0,33) (0,3) (0,2) (0,24) (0,10) (0,28) (0,4) (0,29) (0,31) (0,21) (0,26) (0,13) (0,8) (0,5) (1,20) (1,34) (1,32) (1,19) (1,16) (2,15) (2,12) (2,25) (2,9) (2,33) (2,3) (2,28) (2,4) (2,29) (2,31) (2,26) (2,8) (2,5) (3,15) (3,12) (3,33) (3,28) (3,4) (3,29) (3,31) (3,21) (3,26) (3,8) (4,25) (4,9) (4,28) (4,31) (4,13) (4,8) (5,15) (5,12) (5,25) (5,33) (5,24) (5,10) (5,26) (5,13) (5,8) (6,12) (6,25) (6,9) (6,33) (6,24) (6,10) (6,28) (6,29) (6,31) (6,21) (6,13) (6,8) (7,20) (7,34) (7,32) (7,19) (7,16) (8,12) (8,25) (8,33) (8,10) (8,28) (8,29) (8,21) (8,26) (9,12) (9,33) (9,24) (9,10) (9,28) (9,26) (10,15) (10,12) (10,33) (10,24) (10,29) (10,31) (10,21) (10,26) (10,13) (11,22) (11,23) (11,14) (11,17) (12,28) (12,29) (12,21) (12,26) (12,13) (13,25) (13,33) (13,24) (13,28) (13,29) (13,31) (13,21) (13,26) (14,18) (14,22) (14,23) (14,27) (14,17) (14,30) (15,33) (15,24) (15,28) (15,29) (15,31) (15,21) (15,26) (16,20) (16,34) (16,32) (17,22) (17,23) (17,30) (18,27) (18,30) (19,20) (19,32) (20,34) (20,32) (21,25) (21,24) (21,28) (21,29) (21,26) (22,23) (22,27) (22,30) (23,30) (24,25) (24,28) (24,29) (24,26) (25,33) (25,28) (25,29) (25,31) (26,33) (26,29) (27,30) (28,33) (28,29) (29,33) (29,31) (31,33) (32,34)\nIs there a path between node 3 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph114-1_23", + "image": "data/connectivity/graph_visual/hard/graph114.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,11) (0,16) (1,13) (2,27) (2,10) (2,5) (2,25) (2,16) (2,4) (3,10) (3,21) (3,7) (4,5) (4,22) (4,25) (4,21) (4,16) (4,6) (4,14) (5,10) (5,22) (5,25) (5,21) (5,11) (5,16) (5,19) (6,21) (6,19) (7,10) (7,21) (7,14) (7,19) (8,15) (9,13) (9,20) (9,23) (10,22) (10,11) (10,16) (10,19) (11,25) (12,15) (13,20) (14,16) (14,19) (15,24) (15,20) (16,27) (16,22) (16,25) (17,27) (17,22) (17,25) (19,27) (19,26) (20,23) (21,25) (21,26) (25,27) (26,27)\nIs there a path between node 1 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph272-3_0", + "image": "data/connectivity/graph_visual/hard/graph272.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,12) (0,19) (0,23) (0,5) (0,25) (0,29) (0,11) (0,28) (0,21) (0,30) (0,16) (0,6) (0,13) (0,14) (1,12) (1,19) (1,23) (1,3) (1,15) (1,10) (1,18) (1,29) (1,11) (1,28) (1,21) (1,26) (1,16) (1,8) (1,6) (1,13) (1,14) (2,12) (2,19) (2,23) (2,3) (2,10) (2,5) (2,9) (2,25) (2,29) (2,11) (2,28) (2,21) (2,26) (2,16) (2,8) (2,13) (2,14) (3,19) (3,15) (3,10) (3,18) (3,9) (3,25) (3,29) (3,21) (3,30) (3,26) (3,16) (3,13) (3,14) (4,24) (4,7) (5,12) (5,19) (5,23) (5,15) (5,18) (5,25) (5,29) (5,28) (5,30) (5,26) (5,16) (5,8) (5,6) (5,14) (6,12) (6,19) (6,23) (6,15) (6,10) (6,18) (6,9) (6,25) (6,29) (6,21) (6,30) (6,26) (6,16) (6,8) (6,13) (6,14) (7,24) (8,12) (8,23) (8,15) (8,10) (8,18) (8,9) (8,25) (8,29) (8,11) (8,28) (8,16) (8,14) (9,19) (9,18) (9,25) (9,29) (9,11) (9,21) (9,30) (9,16) (9,13) (9,14) (10,12) (10,19) (10,23) (10,25) (10,29) (10,11) (10,28) (10,21) (10,30) (11,12) (11,19) (11,23) (11,15) (11,18) (11,29) (11,21) (11,16) (11,13) (12,19) (12,23) (12,15) (12,21) (12,30) (12,16) (12,13) (12,14) (13,19) (13,15) (13,28) (13,30) (13,26) (13,16) (13,14) (14,23) (14,15) (14,18) (14,25) (14,28) (14,21) (14,26) (14,16) (15,23) (15,25) (15,29) (15,21) (15,26) (15,16) (16,25) (16,29) (16,28) (16,30) (16,26) (18,19) (18,23) (18,25) (18,28) (18,26) (19,23) (19,25) (19,28) (19,30) (19,26) (20,27) (20,22) (21,23) (21,25) (21,29) (21,30) (21,26) (22,27) (23,25) (23,29) (23,28) (23,30) (23,26) (25,29) (25,28) (25,30) (25,26) (26,29) (26,28) (26,30) (28,30)\nIs there a path between node 3 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph440-2_10", + "image": "data/connectivity/graph_visual/hard/graph440.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,27) (0,8) (0,29) (1,18) (1,24) (1,2) (1,28) (1,12) (1,17) (1,25) (1,16) (2,24) (2,3) (2,10) (2,31) (2,12) (2,30) (2,17) (2,16) (2,21) (3,10) (3,28) (3,30) (3,17) (3,25) (3,16) (3,21) (4,19) (4,20) (4,9) (4,13) (4,32) (4,26) (5,23) (5,29) (6,11) (6,27) (6,8) (6,29) (7,19) (7,15) (7,22) (7,20) (7,9) (7,13) (7,26) (8,23) (8,14) (8,27) (9,19) (9,15) (9,22) (9,13) (9,26) (10,18) (10,28) (10,12) (10,17) (10,16) (10,21) (11,23) (11,14) (11,29) (12,18) (12,24) (12,31) (12,28) (12,30) (12,17) (13,19) (13,15) (13,22) (13,20) (13,26) (14,23) (14,27) (15,22) (15,32) (15,26) (16,18) (16,24) (16,31) (16,28) (16,30) (16,17) (16,25) (16,21) (17,18) (17,24) (17,31) (17,28) (17,30) (18,24) (18,31) (18,28) (18,30) (18,21) (19,22) (20,32) (20,26) (21,24) (21,28) (23,29) (24,28) (24,30) (24,25) (25,31) (25,28) (25,30) (26,32) (27,29) (28,30) (30,31)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph44-12_25", + "image": "data/connectivity/graph_visual/hard/graph44.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,26) (0,15) (0,25) (0,14) (0,7) (0,2) (0,9) (0,5) (1,26) (1,15) (1,25) (1,7) (1,6) (1,2) (1,20) (1,22) (2,25) (2,19) (2,14) (2,4) (3,12) (3,16) (4,15) (4,7) (4,6) (4,8) (5,26) (5,20) (5,8) (5,9) (5,22) (5,13) (6,19) (6,17) (6,7) (6,20) (6,22) (7,19) (7,17) (7,9) (8,19) (9,26) (9,14) (9,24) (11,12) (12,21) (12,18) (12,16) (13,17) (13,22) (14,26) (14,22) (15,19) (15,20) (16,21) (18,23) (19,20) (19,22) (25,26)\nIs there a path between node 12 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph68-17_12", + "image": "data/connectivity/graph_visual/hard/graph68.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,24) (0,11) (0,6) (1,22) (1,26) (1,12) (2,14) (2,11) (2,4) (3,21) (3,11) (3,18) (3,9) (4,17) (4,21) (4,14) (5,7) (5,25) (5,10) (5,20) (6,16) (7,15) (7,26) (8,20) (9,17) (9,23) (9,24) (9,13) (9,11) (9,18) (10,25) (11,14) (12,20) (13,17) (13,21) (13,24) (13,19) (14,18) (15,25) (16,23) (16,21) (18,23) (19,23) (19,24) (20,26) (21,24) (22,25)\nIs there a path between node 17 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph194-17_27", + "image": "data/connectivity/graph_visual/hard/graph194.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,28) (0,1) (0,22) (0,20) (0,15) (0,18) (0,2) (0,5) (0,10) (0,8) (0,14) (0,6) (1,27) (1,12) (1,19) (1,28) (1,25) (1,29) (1,22) (1,4) (1,7) (1,15) (1,18) (1,3) (1,2) (1,24) (1,5) (1,11) (1,14) (1,13) (1,6) (2,12) (2,19) (2,28) (2,29) (2,4) (2,15) (2,16) (2,18) (2,3) (2,10) (2,13) (2,21) (2,6) (3,27) (3,19) (3,28) (3,20) (3,4) (3,7) (3,16) (3,18) (3,9) (3,24) (3,5) (3,11) (3,10) (3,8) (3,14) (3,23) (3,21) (3,6) (4,27) (4,12) (4,19) (4,28) (4,25) (4,20) (4,7) (4,15) (4,16) (4,5) (4,8) (4,14) (4,13) (4,21) (4,6) (5,27) (5,12) (5,19) (5,28) (5,25) (5,29) (5,22) (5,20) (5,7) (5,15) (5,16) (5,24) (5,11) (5,10) (5,8) (5,14) (5,23) (5,13) (5,21) (5,6) (6,27) (6,12) (6,28) (6,25) (6,29) (6,22) (6,20) (6,7) (6,16) (6,18) (6,9) (6,24) (6,8) (6,14) (6,21) (7,19) (7,25) (7,29) (7,22) (7,20) (7,15) (7,16) (7,24) (7,11) (7,10) (7,14) (7,23) (7,21) (8,27) (8,12) (8,19) (8,29) (8,22) (8,20) (8,15) (8,16) (8,9) (8,24) (8,11) (8,10) (8,14) (8,13) (9,12) (9,19) (9,25) (9,22) (9,20) (9,18) (9,24) (9,11) (9,10) (9,14) (9,23) (9,13) (9,21) (10,27) (10,12) (10,19) (10,28) (10,25) (10,29) (10,16) (10,18) (10,24) (10,14) (10,23) (10,13) (10,21) (11,27) (11,12) (11,25) (11,22) (11,20) (11,18) (11,24) (12,19) (12,28) (12,29) (12,22) (12,15) (12,16) (12,18) (12,14) (12,23) (12,13) (12,21) (13,27) (13,28) (13,25) (13,29) (13,22) (13,20) (13,15) (13,18) (13,24) (14,19) (14,28) (14,25) (14,29) (14,15) (14,16) (14,18) (14,24) (14,23) (15,27) (15,28) (15,25) (15,29) (15,20) (15,18) (15,23) (15,21) (16,27) (16,19) (16,28) (16,25) (16,29) (16,22) (16,20) (16,18) (16,24) (16,21) (18,19) (18,28) (18,29) (18,22) (18,20) (18,24) (18,23) (18,21) (19,27) (19,28) (19,25) (19,29) (19,22) (19,20) (19,24) (19,23) (19,21) (20,27) (20,28) (20,29) (20,22) (20,23) (20,21) (21,27) (21,28) (21,24) (21,23) (22,27) (22,28) (22,29) (22,23) (23,27) (23,28) (23,25) (23,29) (24,27) (24,28) (24,25) (24,29) (25,27) (25,29) (27,28) (27,29)\nIs there a path between node 17 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph694-14_13", + "image": "data/connectivity/graph_visual/hard/graph694.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,29) (0,33) (0,25) (0,14) (0,16) (0,4) (0,26) (0,5) (0,27) (0,20) (0,1) (0,7) (0,30) (0,2) (0,9) (0,13) (0,23) (1,29) (1,33) (1,25) (1,14) (1,26) (1,5) (1,20) (1,7) (1,31) (1,30) (1,9) (1,13) (1,23) (2,29) (2,33) (2,25) (2,14) (2,16) (2,4) (2,26) (2,5) (2,27) (2,20) (2,7) (2,31) (2,12) (2,9) (2,23) (3,32) (3,10) (3,6) (3,19) (3,8) (3,15) (3,17) (3,22) (3,21) (3,28) (4,29) (4,33) (4,25) (4,16) (4,26) (4,5) (4,27) (4,31) (4,30) (4,12) (4,13) (4,34) (4,23) (5,29) (5,25) (5,26) (5,27) (5,20) (5,7) (5,31) (5,30) (5,12) (5,9) (5,13) (5,34) (5,23) (6,11) (6,32) (6,19) (6,8) (6,24) (6,18) (6,17) (6,22) (6,21) (6,28) (7,29) (7,33) (7,25) (7,14) (7,16) (7,26) (7,31) (7,30) (7,12) (7,9) (7,13) (7,34) (7,23) (8,11) (8,10) (8,19) (8,15) (8,24) (8,17) (8,22) (8,21) (9,33) (9,25) (9,14) (9,16) (9,26) (9,20) (9,31) (9,12) (9,34) (9,23) (10,11) (10,32) (10,24) (10,18) (10,28) (11,32) (11,19) (11,15) (11,24) (11,18) (11,17) (11,21) (12,29) (12,33) (12,25) (12,16) (12,26) (12,27) (12,31) (12,30) (12,13) (12,34) (13,33) (13,25) (13,27) (13,20) (13,31) (13,30) (13,34) (14,29) (14,33) (14,25) (14,16) (14,27) (14,31) (14,34) (14,23) (15,32) (15,19) (15,22) (15,21) (15,28) (16,33) (16,25) (16,26) (16,27) (16,30) (17,32) (17,24) (17,18) (17,22) (17,28) (18,32) (18,19) (18,24) (18,22) (18,21) (18,28) (19,32) (19,24) (19,22) (19,21) (20,25) (20,26) (20,27) (20,31) (20,30) (20,23) (21,24) (21,22) (21,28) (22,24) (22,28) (23,29) (23,33) (23,26) (23,31) (23,34) (24,32) (24,28) (25,29) (25,33) (25,27) (25,31) (25,30) (25,34) (26,33) (26,27) (26,30) (26,34) (27,29) (27,31) (27,30) (27,34) (28,32) (29,33) (29,30) (29,34) (30,33) (30,31) (30,34) (31,33) (31,34) (33,34)\nIs there a path between node 14 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph416-17_14", + "image": "data/connectivity/graph_visual/hard/graph416.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,25) (0,27) (1,14) (1,23) (1,5) (1,6) (1,20) (1,8) (2,10) (2,25) (2,22) (3,19) (3,26) (4,32) (4,7) (4,20) (4,8) (5,17) (6,17) (6,8) (8,14) (8,23) (8,32) (9,19) (9,26) (9,13) (10,25) (10,12) (10,11) (11,25) (11,22) (12,24) (12,16) (12,25) (12,21) (13,15) (15,29) (15,19) (16,25) (17,31) (17,23) (17,32) (18,29) (18,30) (21,24) (21,25) (24,27) (26,30)\nIs there a path between node 17 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph520-26_13", + "image": "data/connectivity/graph_visual/hard/graph520.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,20) (0,15) (0,25) (0,6) (0,17) (0,30) (0,27) (1,29) (1,31) (2,10) (2,23) (2,31) (2,21) (2,14) (2,7) (3,33) (3,18) (3,31) (3,13) (3,32) (4,10) (4,31) (4,21) (4,14) (5,16) (5,24) (5,17) (5,19) (5,26) (6,28) (6,24) (6,22) (6,27) (6,11) (7,31) (7,9) (8,24) (8,17) (8,26) (9,23) (9,29) (9,18) (9,13) (9,32) (10,18) (10,13) (10,21) (11,15) (11,30) (12,15) (12,17) (12,27) (13,33) (13,18) (14,29) (15,20) (15,28) (15,24) (15,22) (15,17) (15,27) (16,30) (17,24) (17,30) (17,27) (19,24) (19,26) (20,25) (21,23) (21,31) (23,32) (24,25) (24,30) (24,27) (25,30) (26,30) (31,33)\nIs there a path between node 26 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph384-4_31", + "image": "data/connectivity/graph_visual/hard/graph384.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (0,5) (0,30) (0,29) (0,17) (0,3) (0,22) (0,12) (0,15) (0,27) (1,2) (1,9) (1,31) (1,13) (1,16) (1,20) (1,18) (1,25) (2,9) (2,31) (2,13) (2,21) (2,16) (2,10) (2,20) (3,23) (3,4) (3,5) (3,24) (3,17) (3,7) (3,22) (3,19) (3,15) (3,27) (3,14) (4,23) (4,24) (4,30) (4,29) (4,7) (4,22) (4,26) (4,19) (4,28) (4,15) (4,27) (4,14) (5,23) (5,24) (5,29) (5,7) (5,26) (5,19) (5,12) (5,28) (5,15) (5,27) (6,9) (6,31) (6,13) (6,21) (6,16) (6,10) (6,18) (6,25) (7,23) (7,24) (7,30) (7,29) (7,17) (7,22) (7,28) (7,15) (7,27) (8,11) (9,13) (9,21) (9,16) (9,10) (9,18) (9,25) (10,31) (10,13) (10,21) (10,16) (12,23) (12,30) (12,17) (12,22) (12,26) (12,19) (12,28) (12,27) (13,31) (13,21) (13,25) (14,24) (14,30) (14,29) (14,17) (14,22) (14,19) (14,28) (14,15) (14,27) (15,23) (15,24) (15,17) (15,22) (15,26) (15,28) (15,27) (16,31) (16,18) (16,25) (17,23) (17,24) (17,30) (17,22) (17,28) (18,31) (18,20) (18,25) (19,23) (19,24) (19,29) (19,22) (19,27) (20,31) (21,25) (22,23) (22,30) (22,29) (22,26) (22,28) (22,27) (23,30) (23,29) (23,26) (23,28) (24,30) (24,29) (24,28) (24,27) (25,31) (26,30) (26,29) (26,28) (26,27) (27,28) (28,30) (28,29)\nIs there a path between node 4 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph486-28_26", + "image": "data/connectivity/graph_visual/hard/graph486.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,26) (0,9) (0,24) (0,21) (0,11) (0,22) (1,7) (1,27) (1,29) (1,8) (1,3) (1,15) (1,17) (1,10) (2,7) (2,5) (2,18) (2,29) (2,6) (2,3) (2,15) (2,17) (2,10) (3,7) (3,5) (3,27) (3,18) (3,29) (3,28) (3,8) (4,20) (4,13) (4,23) (4,25) (4,16) (4,12) (4,32) (4,30) (5,7) (5,18) (5,29) (5,28) (5,8) (5,15) (5,17) (5,10) (6,7) (6,27) (6,29) (6,28) (6,8) (6,15) (6,17) (6,10) (7,18) (7,29) (7,28) (7,8) (7,15) (7,17) (7,10) (8,27) (8,18) (8,28) (8,15) (8,17) (9,14) (9,31) (9,26) (9,24) (9,21) (9,22) (10,18) (10,28) (10,17) (11,14) (11,19) (11,31) (11,26) (11,21) (12,20) (12,13) (12,23) (12,25) (12,16) (12,32) (12,30) (13,20) (13,23) (13,16) (13,32) (13,30) (14,19) (14,31) (14,24) (14,21) (15,27) (15,29) (15,28) (16,20) (16,23) (16,25) (16,32) (16,30) (17,27) (17,18) (17,29) (17,28) (18,29) (18,28) (19,31) (19,26) (19,24) (19,21) (19,22) (20,23) (20,25) (20,32) (21,26) (21,24) (21,22) (22,26) (22,24) (23,25) (23,32) (23,30) (24,26) (26,31) (27,29) (27,28) (28,29) (30,32)\nIs there a path between node 28 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph270-12_0", + "image": "data/connectivity/graph_visual/hard/graph270.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,20) (0,14) (0,18) (0,16) (1,27) (1,28) (1,9) (1,22) (1,21) (1,19) (1,10) (1,23) (1,7) (1,2) (2,26) (2,25) (2,6) (2,9) (2,22) (2,21) (2,10) (2,23) (2,7) (2,30) (2,12) (3,5) (3,15) (3,11) (3,29) (3,4) (4,5) (4,15) (4,11) (5,15) (5,24) (5,29) (5,8) (6,25) (6,22) (6,17) (6,21) (6,19) (6,10) (6,23) (6,7) (6,30) (7,26) (7,25) (7,9) (7,22) (7,17) (7,21) (7,19) (7,10) (7,23) (7,12) (8,24) (9,27) (9,26) (9,22) (9,21) (9,19) (9,23) (9,30) (9,12) (10,28) (10,26) (10,22) (10,17) (10,21) (10,23) (10,30) (10,12) (11,15) (11,24) (11,29) (12,27) (12,28) (12,26) (12,25) (12,17) (12,21) (12,19) (12,23) (12,30) (13,14) (13,16) (14,18) (14,16) (15,24) (15,29) (16,20) (16,18) (17,27) (17,26) (17,22) (17,19) (17,30) (18,20) (19,27) (19,26) (19,22) (19,23) (19,30) (21,28) (21,26) (21,25) (21,22) (21,23) (21,30) (22,27) (22,28) (22,25) (22,23) (22,30) (23,27) (23,28) (23,26) (23,25) (23,30) (24,29) (25,26) (26,27) (26,28) (26,30) (27,28) (27,30) (28,30)\nIs there a path between node 12 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph608-13_16", + "image": "data/connectivity/graph_visual/hard/graph608.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,16) (0,32) (0,6) (0,11) (0,34) (1,26) (1,18) (2,13) (2,8) (2,34) (2,20) (3,30) (3,8) (3,11) (4,10) (5,7) (5,29) (6,32) (6,13) (6,28) (6,20) (7,22) (7,12) (7,23) (7,33) (8,16) (8,32) (8,13) (8,28) (8,20) (9,31) (10,19) (11,34) (13,34) (13,28) (13,20) (14,21) (16,32) (16,30) (16,28) (17,34) (17,28) (19,21) (20,32) (21,25) (22,26) (25,27) (28,30) (30,32)\nIs there a path between node 13 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph707-21_14", + "image": "data/connectivity/graph_visual/hard/graph707.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,20) (0,7) (0,13) (0,27) (0,34) (0,28) (0,19) (0,3) (0,17) (0,21) (0,6) (0,32) (0,31) (0,25) (0,24) (1,14) (1,29) (1,12) (1,23) (1,33) (1,11) (2,26) (2,18) (2,20) (2,7) (2,34) (2,28) (2,3) (2,15) (2,17) (2,21) (2,6) (2,32) (2,10) (2,31) (2,25) (2,22) (3,26) (3,18) (3,20) (3,7) (3,13) (3,27) (3,6) (3,32) (3,10) (3,9) (3,31) (3,25) (3,24) (4,29) (4,8) (4,5) (4,12) (4,30) (4,16) (5,14) (5,8) (5,12) (5,23) (5,30) (5,16) (5,33) (5,11) (6,7) (6,13) (6,34) (6,28) (6,19) (6,15) (6,17) (6,32) (6,31) (6,25) (6,24) (6,22) (7,18) (7,13) (7,27) (7,32) (7,9) (7,25) (7,24) (7,22) (8,29) (8,12) (8,23) (8,16) (8,33) (9,18) (9,13) (9,27) (9,34) (9,28) (9,19) (9,15) (9,17) (9,21) (9,32) (9,31) (9,25) (9,24) (9,22) (10,26) (10,20) (10,27) (10,34) (10,28) (10,19) (10,17) (10,32) (10,25) (11,29) (11,12) (11,30) (11,16) (12,23) (13,18) (13,20) (13,27) (13,28) (13,15) (13,17) (13,21) (13,32) (13,31) (13,25) (13,22) (14,29) (14,23) (14,16) (14,33) (15,18) (15,27) (15,34) (15,28) (15,19) (15,17) (15,32) (15,31) (15,24) (16,23) (16,30) (16,33) (17,26) (17,20) (17,27) (17,28) (17,19) (17,21) (17,32) (17,31) (17,25) (17,22) (18,20) (18,27) (18,28) (18,19) (18,32) (18,31) (18,25) (19,20) (19,27) (19,34) (19,21) (19,32) (19,31) (19,25) (19,24) (19,22) (20,26) (20,34) (20,21) (20,32) (20,31) (20,24) (21,26) (21,27) (21,32) (21,31) (21,25) (21,22) (22,28) (22,32) (22,31) (22,24) (23,29) (23,30) (23,33) (24,34) (24,28) (24,32) (24,25) (25,26) (25,27) (25,28) (25,32) (25,31) (26,27) (26,34) (26,28) (26,32) (26,31) (27,34) (27,28) (27,32) (27,31) (28,34) (28,32) (28,31) (29,30) (29,33) (30,33) (31,34) (32,34)\nIs there a path between node 21 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph390-15_12", + "image": "data/connectivity/graph_visual/hard/graph390.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,2) (0,17) (1,4) (2,10) (3,19) (3,30) (3,13) (3,25) (3,8) (4,31) (5,16) (6,29) (6,11) (6,32) (7,14) (7,17) (8,21) (8,30) (8,13) (8,28) (9,20) (9,25) (11,29) (11,26) (11,22) (13,21) (13,15) (13,28) (13,23) (15,31) (15,16) (15,28) (15,23) (16,21) (16,25) (16,23) (18,29) (18,24) (20,31) (20,30) (20,25) (21,25) (22,24) (23,25) (23,28) (24,29) (24,32) (25,30) (26,32) (28,30)\nIs there a path between node 15 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph621-13_0", + "image": "data/connectivity/graph_visual/hard/graph621.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,9) (0,26) (0,24) (0,27) (0,11) (1,3) (1,2) (1,20) (1,6) (1,31) (2,3) (2,33) (2,30) (2,32) (2,19) (2,7) (3,31) (3,5) (4,33) (4,9) (4,30) (4,16) (4,25) (4,24) (5,30) (5,26) (5,27) (5,15) (6,33) (6,20) (6,24) (6,27) (6,11) (6,7) (7,33) (7,23) (7,30) (9,26) (9,29) (9,24) (9,31) (9,15) (10,28) (10,13) (10,22) (10,21) (11,16) (11,24) (12,15) (13,14) (13,17) (15,23) (15,20) (15,31) (16,20) (16,24) (16,19) (17,21) (19,33) (19,23) (19,25) (19,32) (20,33) (20,23) (20,32) (20,24) (20,27) (21,28) (23,33) (23,32) (24,30) (24,32) (24,29) (25,30) (25,32) (25,29) (25,27) (26,30) (26,32) (26,29) (27,33) (27,30) (29,30) (29,31) (30,32) (31,32)\nIs there a path between node 13 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph77-7_14", + "image": "data/connectivity/graph_visual/hard/graph77.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,14) (0,7) (0,20) (0,17) (0,19) (0,8) (0,11) (0,18) (0,10) (0,23) (0,15) (0,25) (0,24) (1,14) (1,7) (1,9) (1,17) (1,19) (1,5) (1,8) (1,11) (1,18) (1,10) (1,3) (1,23) (1,25) (1,24) (2,4) (2,26) (2,13) (2,12) (2,21) (2,22) (3,14) (3,7) (3,9) (3,17) (3,19) (3,5) (3,8) (3,6) (3,10) (3,23) (3,25) (3,24) (4,21) (4,16) (5,14) (5,20) (5,9) (5,17) (5,8) (5,6) (5,18) (5,10) (5,15) (5,25) (5,24) (6,7) (6,20) (6,8) (6,18) (6,10) (6,23) (6,15) (6,25) (6,24) (7,14) (7,20) (7,9) (7,19) (7,11) (7,10) (7,15) (8,20) (8,17) (8,19) (8,11) (8,18) (8,10) (8,23) (8,24) (9,20) (9,19) (9,11) (9,18) (9,10) (9,23) (9,25) (10,14) (10,17) (10,19) (10,11) (10,18) (10,23) (10,15) (10,24) (11,14) (11,20) (11,18) (11,23) (11,15) (11,25) (12,26) (12,16) (12,22) (13,26) (13,16) (13,22) (14,20) (14,17) (14,19) (14,18) (14,23) (14,25) (15,20) (15,19) (15,18) (15,25) (16,21) (16,22) (17,20) (17,19) (17,23) (18,20) (18,19) (18,23) (18,24) (19,20) (19,23) (19,25) (20,23) (20,25) (20,24) (21,22) (22,26)\nIs there a path between node 7 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph90-15_24", + "image": "data/connectivity/graph_visual/hard/graph90.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,7) (0,13) (0,8) (0,18) (0,25) (0,14) (0,17) (0,21) (1,13) (1,26) (1,14) (1,20) (1,17) (1,24) (1,6) (2,8) (2,18) (2,9) (2,26) (2,14) (2,10) (2,15) (3,16) (3,12) (4,13) (4,8) (4,18) (4,25) (4,6) (5,19) (5,13) (5,10) (5,20) (5,22) (5,17) (5,6) (6,8) (6,18) (6,9) (6,26) (6,14) (6,17) (6,21) (6,15) (6,23) (7,25) (7,14) (7,22) (7,24) (7,15) (7,23) (8,13) (8,25) (8,24) (8,23) (9,25) (9,27) (9,26) (9,14) (9,17) (9,24) (9,23) (10,19) (10,13) (10,25) (10,22) (11,12) (12,16) (13,19) (13,18) (13,21) (14,19) (14,18) (14,22) (15,19) (15,25) (15,23) (17,25) (17,22) (17,21) (17,24) (18,21) (18,24) (19,26) (19,22) (19,24) (19,23) (20,25) (20,26) (20,24) (20,23) (21,27) (21,23) (22,25) (22,26) (22,23) (25,27) (25,26)\nIs there a path between node 15 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph665-11_8", + "image": "data/connectivity/graph_visual/hard/graph665.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,3) (0,29) (0,7) (0,32) (0,4) (0,17) (0,9) (1,12) (1,14) (1,7) (1,28) (1,23) (1,9) (1,33) (1,30) (1,6) (1,8) (2,14) (2,29) (2,32) (2,15) (2,30) (2,6) (2,10) (3,12) (3,14) (3,4) (3,23) (3,9) (3,31) (3,30) (3,20) (4,27) (4,19) (4,17) (4,15) (4,31) (4,30) (5,34) (5,18) (5,13) (6,7) (6,16) (6,23) (6,22) (6,30) (7,12) (7,15) (7,11) (7,31) (7,30) (7,24) (7,10) (8,29) (8,32) (8,16) (8,27) (8,23) (8,20) (9,28) (9,15) (9,33) (9,31) (9,30) (9,24) (9,10) (10,12) (10,19) (10,17) (10,33) (10,22) (10,20) (11,32) (11,16) (11,19) (11,17) (11,22) (12,32) (12,28) (12,23) (12,33) (14,32) (14,30) (14,20) (15,17) (15,30) (16,19) (16,17) (16,23) (16,33) (16,30) (17,29) (17,27) (17,30) (17,24) (17,20) (18,25) (19,32) (19,28) (19,30) (19,20) (20,28) (20,23) (20,30) (22,28) (22,33) (23,29) (23,31) (24,31) (26,34) (28,29) (28,33) (29,31) (30,33)\nIs there a path between node 11 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph532-18_25", + "image": "data/connectivity/graph_visual/hard/graph532.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,16) (0,2) (1,20) (1,25) (1,8) (1,29) (1,19) (1,12) (1,33) (1,9) (1,30) (1,11) (1,7) (1,13) (1,4) (1,26) (1,10) (1,24) (1,5) (3,6) (3,22) (3,27) (3,15) (3,32) (4,20) (4,25) (4,8) (4,29) (4,19) (4,23) (4,21) (4,12) (4,28) (4,33) (4,31) (4,9) (4,13) (4,18) (4,14) (4,26) (5,20) (5,25) (5,8) (5,19) (5,21) (5,17) (5,33) (5,31) (5,9) (5,30) (5,11) (5,7) (5,13) (5,10) (5,24) (6,27) (6,15) (6,32) (7,8) (7,29) (7,19) (7,23) (7,12) (7,17) (7,28) (7,33) (7,9) (7,11) (7,18) (7,24) (8,20) (8,29) (8,23) (8,21) (8,17) (8,28) (8,9) (8,13) (8,18) (8,14) (8,10) (9,25) (9,29) (9,19) (9,23) (9,17) (9,33) (9,31) (9,30) (9,11) (9,14) (9,26) (9,10) (9,24) (10,20) (10,25) (10,29) (10,19) (10,23) (10,21) (10,12) (10,17) (10,31) (10,30) (10,11) (10,13) (10,18) (10,14) (10,26) (10,24) (11,20) (11,25) (11,29) (11,19) (11,12) (11,17) (11,33) (11,31) (11,30) (11,13) (11,18) (11,14) (11,26) (12,20) (12,29) (12,23) (12,17) (12,28) (12,33) (12,31) (12,30) (12,13) (12,18) (12,14) (12,26) (12,24) (13,20) (13,25) (13,29) (13,23) (13,21) (13,28) (13,33) (13,30) (13,18) (13,26) (13,24) (14,20) (14,29) (14,21) (14,28) (14,33) (14,31) (14,30) (14,24) (15,22) (17,25) (17,19) (17,21) (17,28) (17,33) (17,31) (17,30) (17,18) (17,26) (17,24) (18,20) (18,25) (18,19) (18,33) (18,31) (18,30) (18,26) (18,24) (19,25) (19,29) (19,23) (19,33) (19,30) (19,26) (20,29) (20,28) (20,31) (20,30) (20,26) (21,25) (21,29) (21,23) (21,33) (21,31) (23,25) (23,33) (23,31) (23,30) (23,26) (24,28) (24,33) (24,31) (24,30) (24,26) (25,29) (25,28) (25,31) (26,29) (26,28) (26,33) (26,31) (28,29) (28,33) (28,31) (29,33) (29,30) (30,33) (31,33)\nIs there a path between node 18 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph391-11_12", + "image": "data/connectivity/graph_visual/hard/graph391.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,9) (0,18) (0,31) (0,7) (0,30) (0,1) (0,21) (0,2) (1,13) (1,18) (1,12) (1,26) (1,24) (1,2) (2,14) (2,16) (2,22) (3,27) (4,27) (5,27) (6,7) (6,30) (6,24) (6,23) (7,13) (7,32) (7,23) (8,19) (8,12) (8,26) (8,21) (8,23) (8,16) (8,22) (9,18) (9,24) (9,23) (11,18) (11,12) (11,23) (11,16) (12,13) (12,14) (12,26) (12,24) (12,21) (12,16) (13,19) (13,18) (13,14) (13,24) (13,16) (14,19) (14,18) (14,30) (14,21) (14,16) (14,22) (16,31) (16,24) (16,23) (16,22) (18,26) (18,32) (21,26) (21,23) (21,22) (22,26) (22,24) (25,28) (31,32)\nIs there a path between node 11 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph588-0_7", + "image": "data/connectivity/graph_visual/hard/graph588.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,14) (0,7) (0,13) (0,3) (0,2) (0,11) (0,33) (1,29) (1,31) (1,27) (1,22) (1,28) (1,10) (1,4) (1,16) (1,5) (2,14) (2,7) (2,8) (2,13) (2,3) (2,24) (2,33) (3,14) (3,8) (3,11) (3,24) (3,33) (4,29) (4,31) (4,27) (4,22) (4,28) (4,10) (4,21) (4,5) (5,29) (5,31) (5,27) (5,22) (5,28) (5,10) (5,12) (5,16) (5,21) (6,23) (6,30) (7,14) (7,8) (7,24) (7,33) (8,11) (8,24) (8,33) (9,17) (9,26) (9,25) (9,20) (9,18) (9,15) (9,32) (10,29) (10,31) (10,22) (10,28) (10,12) (10,16) (10,21) (11,14) (11,13) (11,33) (12,29) (12,31) (12,27) (12,28) (12,16) (13,14) (13,24) (13,33) (14,33) (15,26) (15,25) (15,20) (15,32) (16,31) (16,22) (16,28) (16,21) (17,26) (17,20) (17,18) (17,32) (18,26) (18,20) (19,23) (20,26) (20,25) (20,32) (21,29) (21,31) (21,22) (21,28) (22,27) (22,28) (23,30) (25,26) (25,32) (26,32) (27,29) (27,28) (29,31)\nIs there a path between node 0 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph90-12_0", + "image": "data/connectivity/graph_visual/hard/graph90.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,7) (0,13) (0,8) (0,18) (0,25) (0,14) (0,17) (0,21) (1,13) (1,26) (1,14) (1,20) (1,17) (1,24) (1,6) (2,8) (2,18) (2,9) (2,26) (2,14) (2,10) (2,15) (3,16) (3,12) (4,13) (4,8) (4,18) (4,25) (4,6) (5,19) (5,13) (5,10) (5,20) (5,22) (5,17) (5,6) (6,8) (6,18) (6,9) (6,26) (6,14) (6,17) (6,21) (6,15) (6,23) (7,25) (7,14) (7,22) (7,24) (7,15) (7,23) (8,13) (8,25) (8,24) (8,23) (9,25) (9,27) (9,26) (9,14) (9,17) (9,24) (9,23) (10,19) (10,13) (10,25) (10,22) (11,12) (12,16) (13,19) (13,18) (13,21) (14,19) (14,18) (14,22) (15,19) (15,25) (15,23) (17,25) (17,22) (17,21) (17,24) (18,21) (18,24) (19,26) (19,22) (19,24) (19,23) (20,25) (20,26) (20,24) (20,23) (21,27) (21,23) (22,25) (22,26) (22,23) (25,27) (25,26)\nIs there a path between node 12 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph571-32_23", + "image": "data/connectivity/graph_visual/hard/graph571.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,7) (0,31) (0,5) (0,13) (0,33) (0,4) (0,8) (0,16) (1,18) (1,29) (1,2) (2,29) (2,28) (3,20) (3,26) (3,25) (4,7) (4,11) (4,10) (4,31) (4,22) (4,24) (4,16) (5,11) (5,13) (5,17) (6,26) (6,29) (7,10) (7,32) (7,33) (7,8) (7,24) (8,14) (8,10) (8,13) (8,33) (9,12) (9,21) (10,11) (10,24) (10,17) (11,31) (11,13) (11,16) (11,17) (12,30) (13,14) (13,32) (14,31) (14,15) (15,32) (15,24) (18,26) (18,29) (18,28) (20,27) (20,28) (21,23) (22,31) (22,33) (25,29) (26,27) (27,29) (27,28) (28,29) (31,32) (31,33) (32,33)\nIs there a path between node 32 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph552-27_2", + "image": "data/connectivity/graph_visual/hard/graph552.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,27) (0,26) (0,3) (0,13) (0,22) (0,12) (0,31) (0,17) (1,2) (1,20) (1,23) (1,13) (1,4) (1,29) (2,20) (2,5) (2,6) (2,22) (2,16) (2,31) (2,17) (2,29) (3,27) (3,5) (3,23) (3,24) (3,15) (3,13) (3,4) (3,17) (4,7) (4,5) (4,15) (4,13) (4,10) (4,22) (4,16) (4,18) (4,12) (4,21) (5,27) (5,20) (5,14) (5,23) (5,6) (5,15) (5,13) (5,28) (5,12) (5,21) (5,8) (5,25) (6,26) (6,20) (6,23) (6,24) (6,15) (6,9) (6,28) (6,22) (6,16) (6,8) (7,9) (7,19) (7,12) (7,21) (7,25) (8,24) (8,15) (8,32) (8,31) (8,25) (9,23) (9,22) (9,19) (9,12) (9,17) (10,26) (10,14) (10,23) (10,28) (10,29) (11,33) (12,15) (12,28) (12,16) (12,29) (13,14) (13,24) (13,32) (13,18) (13,17) (14,27) (14,26) (14,15) (14,31) (14,17) (14,25) (15,27) (15,26) (15,28) (15,19) (15,25) (16,20) (16,19) (16,18) (16,25) (17,20) (17,24) (17,32) (17,18) (17,25) (18,27) (18,24) (18,22) (18,31) (18,29) (19,26) (19,29) (19,25) (20,27) (20,23) (20,24) (20,22) (20,31) (21,22) (22,32) (22,28) (22,29) (22,25) (23,32) (23,25) (24,31) (26,27) (26,32) (27,29) (28,32) (28,31) (29,31)\nIs there a path between node 27 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph447-26_22", + "image": "data/connectivity/graph_visual/hard/graph447.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (1,11) (1,25) (1,27) (1,20) (1,24) (2,14) (3,19) (3,17) (5,18) (5,27) (5,28) (6,7) (6,13) (6,29) (7,8) (7,10) (7,17) (8,31) (8,13) (9,10) (9,13) (10,19) (10,12) (11,25) (11,28) (12,13) (12,29) (13,29) (15,22) (15,25) (15,23) (15,27) (18,22) (18,23) (18,24) (19,31) (19,29) (20,23) (20,28) (20,24) (21,26) (22,25) (22,23) (22,27) (25,28) (27,28)\nIs there a path between node 26 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph677-16_8", + "image": "data/connectivity/graph_visual/hard/graph677.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,7) (0,9) (0,11) (0,27) (0,24) (0,29) (0,22) (0,20) (1,4) (1,17) (1,28) (1,12) (1,14) (1,31) (1,24) (1,13) (1,3) (1,22) (1,20) (2,18) (2,4) (2,6) (2,28) (2,12) (2,31) (2,29) (2,22) (2,23) (2,5) (2,19) (3,14) (3,24) (3,20) (3,5) (3,30) (3,19) (4,17) (4,9) (4,27) (4,13) (4,5) (4,30) (4,19) (5,8) (5,18) (5,28) (5,31) (5,9) (5,11) (5,13) (5,22) (5,23) (6,18) (6,28) (6,31) (6,9) (6,20) (7,8) (7,18) (7,9) (8,17) (8,14) (8,31) (8,27) (8,22) (8,20) (8,30) (8,33) (8,19) (9,28) (9,14) (9,31) (10,13) (10,19) (11,18) (11,28) (11,14) (11,31) (11,27) (11,29) (11,22) (11,30) (11,33) (12,18) (12,17) (12,24) (12,23) (13,18) (13,17) (13,28) (13,31) (13,22) (14,18) (14,29) (14,22) (14,30) (14,33) (15,16) (17,27) (17,25) (17,29) (17,22) (17,20) (17,30) (17,33) (18,28) (18,24) (18,22) (18,20) (18,19) (19,27) (19,24) (19,23) (20,29) (20,33) (21,32) (21,34) (22,23) (22,33) (23,24) (23,25) (25,29) (27,30) (27,33) (29,33) (30,31) (31,33) (32,34)\nIs there a path between node 16 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph542-7_20", + "image": "data/connectivity/graph_visual/hard/graph542.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,19) (0,10) (0,11) (0,4) (0,22) (0,30) (0,5) (0,31) (0,14) (0,12) (1,8) (1,11) (1,4) (1,22) (1,33) (1,5) (1,9) (1,14) (1,12) (2,13) (2,26) (2,27) (2,28) (2,18) (2,29) (2,24) (2,3) (2,17) (2,25) (3,20) (3,15) (3,23) (3,28) (3,18) (3,29) (3,32) (3,24) (3,7) (3,21) (3,17) (3,25) (4,8) (4,10) (4,22) (4,33) (4,9) (4,31) (5,8) (5,19) (5,11) (5,33) (5,9) (5,31) (5,14) (5,12) (6,23) (6,27) (6,28) (6,18) (6,29) (6,32) (6,24) (6,7) (6,21) (6,25) (7,20) (7,13) (7,26) (7,23) (7,28) (7,18) (7,21) (7,17) (7,25) (8,19) (8,22) (8,33) (8,30) (8,31) (8,14) (8,12) (9,19) (9,10) (9,11) (9,22) (9,30) (9,31) (10,19) (10,11) (10,22) (10,30) (10,31) (10,14) (11,22) (11,31) (11,12) (12,19) (12,30) (12,14) (13,20) (13,26) (13,15) (13,23) (13,27) (13,28) (13,29) (13,32) (13,24) (14,19) (14,22) (14,33) (15,20) (15,23) (15,27) (15,18) (15,29) (15,32) (15,24) (15,17) (17,26) (17,23) (17,28) (17,18) (17,29) (17,32) (17,24) (17,21) (17,25) (18,20) (18,29) (19,33) (19,30) (19,31) (20,26) (20,23) (20,27) (20,28) (20,25) (21,23) (21,27) (21,28) (21,29) (21,32) (21,24) (21,25) (22,33) (22,30) (23,27) (23,28) (23,29) (23,32) (23,25) (24,26) (24,27) (24,32) (25,27) (25,28) (25,29) (26,27) (26,28) (26,32) (27,28) (27,29) (27,32) (29,32) (30,33) (30,31) (31,33)\nIs there a path between node 7 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph143-18_21", + "image": "data/connectivity/graph_visual/hard/graph143.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,8) (0,13) (0,3) (0,11) (1,26) (1,15) (1,11) (2,5) (2,10) (2,14) (2,4) (2,27) (3,15) (3,11) (4,24) (4,27) (5,18) (5,27) (6,8) (6,13) (6,22) (6,11) (7,9) (7,10) (7,21) (7,14) (7,20) (8,26) (9,27) (10,14) (10,27) (11,28) (12,26) (12,19) (12,15) (12,13) (15,17) (15,28) (15,22) (16,26) (16,22) (16,25) (17,28) (17,22) (17,25) (19,26) (21,24) (22,28) (22,25) (26,28)\nIs there a path between node 18 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph446-6_20", + "image": "data/connectivity/graph_visual/hard/graph446.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (0,27) (0,21) (0,12) (0,24) (0,16) (0,13) (0,20) (0,23) (0,22) (0,31) (0,29) (1,32) (2,25) (3,5) (3,24) (3,19) (3,13) (3,18) (3,15) (3,10) (3,22) (3,7) (3,17) (4,5) (4,13) (4,18) (4,15) (4,31) (4,17) (4,26) (5,21) (5,14) (5,19) (5,15) (5,22) (5,26) (6,28) (7,19) (7,13) (7,18) (7,10) (7,29) (7,17) (8,12) (8,24) (8,20) (8,18) (8,15) (8,26) (9,27) (9,24) (9,16) (9,13) (9,20) (9,18) (9,10) (9,26) (10,27) (10,12) (10,19) (10,18) (10,15) (10,23) (10,22) (10,11) (10,31) (10,29) (10,30) (11,27) (11,12) (11,24) (11,16) (11,20) (11,18) (11,22) (11,30) (12,18) (12,15) (12,31) (12,29) (12,17) (13,19) (13,16) (13,20) (13,23) (14,21) (14,16) (14,15) (14,30) (15,18) (15,22) (15,30) (15,26) (16,19) (16,29) (16,30) (17,18) (18,24) (18,23) (18,22) (19,20) (19,23) (20,24) (20,22) (21,27) (21,23) (21,30) (22,23) (23,31) (23,26) (24,27) (24,26) (25,28) (29,31)\nIs there a path between node 6 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph296-23_1", + "image": "data/connectivity/graph_visual/hard/graph296.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,1) (0,24) (0,3) (0,16) (0,17) (0,30) (0,27) (0,19) (0,11) (0,23) (0,31) (1,10) (1,24) (1,2) (1,17) (1,30) (1,29) (1,4) (1,27) (1,21) (1,11) (2,10) (2,18) (2,3) (2,15) (2,17) (2,29) (2,27) (2,19) (2,21) (2,26) (2,31) (3,10) (3,18) (3,24) (3,16) (3,17) (3,29) (3,4) (3,19) (3,21) (3,26) (3,31) (4,18) (4,15) (4,16) (4,17) (4,30) (4,27) (4,19) (4,21) (4,31) (6,22) (7,12) (7,8) (7,28) (7,20) (7,9) (8,13) (8,12) (8,20) (8,9) (9,13) (9,12) (9,25) (9,28) (10,18) (10,24) (10,15) (10,17) (10,30) (10,27) (10,19) (10,21) (10,11) (10,23) (10,31) (11,18) (11,24) (11,15) (11,16) (11,30) (11,27) (11,19) (11,21) (11,23) (11,26) (11,31) (12,13) (12,25) (12,28) (13,25) (13,28) (13,20) (15,17) (15,29) (15,27) (15,19) (15,23) (15,31) (16,24) (16,17) (16,29) (16,19) (16,21) (16,23) (16,26) (17,18) (17,24) (17,30) (17,29) (17,27) (17,19) (17,23) (17,26) (17,31) (18,24) (18,30) (18,27) (18,19) (18,23) (19,30) (19,29) (19,27) (19,21) (19,23) (19,26) (20,28) (21,29) (21,27) (21,26) (21,31) (23,24) (23,26) (23,31) (24,30) (24,27) (24,26) (25,28) (26,30) (26,29) (26,27) (26,31) (27,30) (27,31) (29,30) (29,31) (30,31)\nIs there a path between node 23 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph151-22_6", + "image": "data/connectivity/graph_visual/hard/graph151.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,6) (0,27) (0,11) (0,4) (0,9) (0,25) (0,16) (0,2) (0,23) (0,3) (0,28) (0,10) (0,5) (1,6) (1,27) (1,20) (1,11) (1,24) (1,4) (1,14) (1,13) (1,9) (1,25) (1,2) (1,17) (1,23) (1,3) (1,28) (1,10) (1,22) (2,6) (2,24) (2,4) (2,14) (2,17) (2,23) (2,28) (2,22) (2,5) (3,6) (3,27) (3,20) (3,11) (3,4) (3,16) (3,17) (3,23) (3,28) (3,22) (3,5) (4,27) (4,20) (4,14) (4,9) (4,25) (4,16) (4,17) (4,23) (4,28) (4,10) (4,22) (5,27) (5,20) (5,11) (5,24) (5,13) (5,9) (5,16) (5,17) (5,28) (5,10) (6,20) (6,11) (6,24) (6,13) (6,9) (6,25) (6,16) (6,17) (6,28) (6,10) (6,22) (7,12) (7,26) (7,21) (8,15) (8,18) (9,27) (9,20) (9,11) (9,24) (9,14) (9,13) (9,25) (9,16) (9,10) (9,22) (10,27) (10,20) (10,24) (10,13) (10,25) (10,16) (10,17) (10,23) (10,28) (11,20) (11,24) (11,14) (11,16) (11,17) (11,28) (12,26) (12,21) (13,27) (13,24) (13,25) (13,17) (13,23) (14,20) (14,25) (14,16) (14,23) (14,28) (15,19) (15,18) (16,27) (16,20) (16,24) (16,25) (16,17) (16,23) (16,28) (16,22) (17,27) (17,24) (17,25) (18,19) (20,24) (20,25) (20,22) (21,26) (22,27) (22,24) (22,25) (23,24) (23,25) (24,27) (24,25) (24,28) (25,28) (27,28)\nIs there a path between node 22 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph33-20_18", + "image": "data/connectivity/graph_visual/hard/graph33.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,22) (0,7) (0,18) (0,14) (0,20) (0,13) (0,24) (0,17) (1,25) (1,9) (1,21) (1,15) (1,23) (1,19) (1,16) (1,8) (2,9) (2,21) (2,23) (2,19) (2,6) (2,3) (2,8) (2,5) (3,25) (3,21) (3,15) (3,23) (3,4) (3,19) (4,25) (4,10) (4,9) (4,21) (4,23) (4,19) (4,6) (4,5) (5,25) (5,10) (5,9) (5,23) (5,16) (5,8) (6,9) (6,21) (6,15) (6,19) (6,16) (7,22) (7,14) (7,13) (7,24) (7,17) (8,25) (8,10) (8,9) (8,21) (8,15) (8,23) (8,19) (8,16) (9,10) (9,15) (9,19) (9,16) (10,23) (10,16) (11,22) (11,18) (11,14) (11,20) (11,12) (11,13) (11,24) (11,17) (12,22) (12,18) (12,20) (12,24) (12,17) (13,18) (13,14) (13,20) (13,24) (13,17) (14,22) (14,18) (14,20) (14,24) (14,17) (15,25) (15,21) (15,19) (15,16) (16,25) (16,21) (16,23) (17,18) (17,20) (17,24) (18,22) (18,20) (18,24) (19,25) (19,21) (20,22) (20,24) (21,25) (21,23) (23,25)\nIs there a path between node 20 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph209-15_11", + "image": "data/connectivity/graph_visual/hard/graph209.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,22) (1,18) (1,25) (1,8) (1,16) (1,11) (1,6) (1,24) (2,22) (2,18) (2,17) (2,20) (2,11) (2,6) (3,13) (4,22) (4,25) (4,21) (4,17) (4,11) (4,6) (5,27) (5,13) (6,29) (6,24) (7,22) (7,21) (7,17) (7,16) (7,11) (7,24) (7,15) (7,19) (8,18) (8,12) (8,11) (8,24) (9,28) (10,26) (10,23) (11,17) (12,17) (12,20) (12,16) (13,27) (16,22) (16,25) (16,21) (16,29) (16,19) (17,29) (17,20) (19,21) (19,29) (19,20) (20,22) (21,22) (21,25) (21,29) (27,28)\nIs there a path between node 15 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph358-31_0", + "image": "data/connectivity/graph_visual/hard/graph358.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,18) (0,7) (0,1) (0,10) (0,13) (0,26) (0,12) (1,11) (1,4) (1,10) (1,13) (1,24) (1,22) (1,17) (2,8) (2,29) (2,7) (2,4) (2,10) (2,19) (2,30) (3,6) (3,11) (3,29) (3,7) (3,26) (3,22) (4,14) (4,29) (4,7) (4,13) (4,12) (4,22) (5,6) (5,8) (5,11) (5,7) (5,15) (5,12) (5,22) (5,17) (6,8) (6,29) (6,15) (6,10) (6,13) (6,19) (6,22) (6,17) (7,14) (7,28) (7,11) (7,13) (7,26) (7,24) (7,19) (7,21) (7,30) (8,28) (8,20) (8,11) (8,25) (8,27) (8,15) (8,10) (8,26) (8,12) (8,24) (8,22) (8,21) (10,18) (10,27) (10,15) (10,24) (11,14) (11,18) (11,19) (11,22) (11,21) (11,17) (11,30) (12,14) (12,20) (12,29) (12,27) (12,13) (12,26) (12,19) (13,14) (13,20) (13,18) (13,25) (14,28) (14,25) (14,27) (14,24) (14,22) (15,28) (15,20) (15,26) (15,30) (16,23) (17,28) (17,20) (17,27) (17,19) (17,22) (18,24) (18,22) (18,30) (19,20) (19,29) (19,25) (19,27) (19,30) (20,30) (21,29) (21,27) (21,26) (21,24) (21,22) (21,30) (22,28) (22,29) (22,26) (22,30) (24,25) (25,29) (27,28) (27,29) (27,30)\nIs there a path between node 31 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph661-27_19", + "image": "data/connectivity/graph_visual/hard/graph661.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,27) (0,32) (0,11) (0,33) (0,5) (0,31) (0,30) (0,2) (0,9) (1,26) (1,25) (1,4) (2,24) (2,17) (2,3) (2,34) (2,10) (2,9) (2,29) (3,24) (3,14) (3,34) (3,5) (3,30) (3,9) (5,33) (5,10) (5,9) (6,17) (6,20) (6,15) (6,30) (7,24) (7,16) (7,20) (7,33) (8,21) (8,13) (8,19) (8,18) (9,27) (9,30) (10,24) (10,16) (10,15) (10,11) (10,28) (10,30) (11,27) (11,33) (11,28) (11,34) (11,30) (12,13) (12,19) (12,18) (13,19) (13,18) (13,22) (14,24) (14,27) (14,32) (15,17) (15,20) (15,33) (15,29) (16,24) (17,24) (17,27) (17,32) (17,33) (17,28) (17,30) (18,22) (19,26) (19,25) (19,23) (19,22) (21,25) (24,33) (25,26) (27,34) (28,32) (28,33) (28,31) (30,34) (31,33) (31,34) (33,34)\nIs there a path between node 27 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph511-31_19", + "image": "data/connectivity/graph_visual/hard/graph511.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,9) (0,33) (0,13) (0,21) (0,24) (0,14) (0,17) (0,25) (1,11) (1,4) (1,18) (1,19) (1,31) (1,27) (1,15) (2,23) (3,33) (3,13) (3,21) (3,26) (3,14) (3,17) (4,11) (4,18) (4,6) (4,27) (4,7) (4,5) (5,11) (5,18) (5,19) (5,6) (5,31) (5,27) (5,30) (5,7) (6,11) (6,18) (6,31) (6,27) (6,30) (6,7) (7,31) (7,27) (7,15) (7,30) (8,29) (8,32) (8,12) (8,16) (8,22) (8,20) (8,10) (9,33) (9,13) (9,26) (9,24) (9,14) (9,17) (9,25) (10,29) (10,32) (10,12) (10,22) (10,20) (11,18) (11,27) (12,29) (12,32) (12,16) (12,22) (12,20) (13,33) (13,21) (13,26) (13,24) (13,14) (13,17) (13,25) (14,33) (14,21) (14,24) (14,25) (15,31) (15,27) (16,29) (16,32) (16,28) (16,22) (16,20) (17,33) (17,26) (17,24) (17,25) (18,19) (18,31) (18,27) (18,30) (19,31) (19,30) (20,29) (20,32) (20,28) (21,33) (21,24) (22,29) (22,32) (24,26) (24,25) (26,33) (28,29) (28,32) (29,32)\nIs there a path between node 31 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph696-7_32", + "image": "data/connectivity/graph_visual/hard/graph696.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,18) (0,15) (0,33) (0,8) (0,1) (0,24) (0,17) (0,4) (0,31) (0,12) (0,26) (0,14) (0,30) (0,32) (0,29) (0,2) (1,25) (1,19) (1,33) (1,8) (1,21) (1,24) (1,17) (1,4) (1,31) (1,12) (1,27) (1,10) (1,26) (1,14) (1,30) (1,29) (1,5) (1,3) (1,22) (2,18) (2,15) (2,19) (2,33) (2,8) (2,24) (2,17) (2,4) (2,27) (2,7) (2,10) (2,26) (2,14) (2,34) (2,30) (2,16) (2,29) (2,3) (2,22) (3,18) (3,33) (3,8) (3,21) (3,17) (3,4) (3,31) (3,12) (3,27) (3,7) (3,10) (3,26) (3,14) (3,34) (3,30) (3,29) (4,18) (4,25) (4,19) (4,33) (4,8) (4,21) (4,17) (4,27) (4,7) (4,10) (4,14) (4,30) (4,32) (4,16) (4,29) (4,5) (4,22) (5,15) (5,25) (5,8) (5,21) (5,17) (5,31) (5,26) (5,34) (5,30) (5,32) (5,16) (5,29) (6,23) (6,28) (6,9) (6,13) (7,18) (7,15) (7,25) (7,8) (7,21) (7,24) (7,17) (7,27) (7,10) (7,34) (7,30) (7,32) (7,16) (7,29) (7,22) (8,18) (8,15) (8,19) (8,21) (8,24) (8,17) (8,31) (8,27) (8,10) (8,26) (8,34) (8,30) (8,32) (8,16) (8,29) (8,22) (9,28) (9,20) (9,13) (9,11) (10,18) (10,15) (10,19) (10,21) (10,31) (10,12) (10,27) (10,26) (10,14) (10,30) (10,16) (10,29) (11,23) (11,28) (12,18) (12,15) (12,25) (12,19) (12,33) (12,24) (12,31) (12,27) (12,14) (12,34) (12,30) (12,32) (12,29) (12,22) (13,23) (13,28) (13,20) (14,18) (14,15) (14,25) (14,19) (14,21) (14,24) (14,17) (14,31) (14,27) (14,26) (14,30) (14,32) (14,16) (14,29) (14,22) (15,18) (15,25) (15,24) (15,17) (15,31) (15,27) (15,26) (15,30) (15,32) (15,16) (15,29) (16,18) (16,25) (16,19) (16,33) (16,21) (16,17) (16,27) (16,26) (16,30) (16,32) (16,29) (16,22) (17,18) (17,25) (17,19) (17,33) (17,24) (17,31) (17,27) (17,26) (17,30) (17,32) (17,29) (18,25) (18,19) (18,33) (18,21) (18,31) (18,27) (18,26) (18,34) (18,30) (18,32) (18,29) (19,33) (19,21) (19,31) (19,27) (19,26) (19,34) (19,30) (19,32) (19,22) (20,23) (20,28) (21,25) (21,24) (21,31) (21,27) (21,26) (21,34) (21,32) (21,29) (22,33) (22,31) (22,26) (22,34) (22,32) (22,29) (24,25) (24,31) (24,26) (24,34) (24,30) (24,29) (25,33) (25,31) (25,27) (25,34) (25,30) (25,32) (25,29) (26,31) (26,34) (26,30) (27,33) (27,34) (29,33) (29,31) (29,34) (29,30) (30,33) (30,31) (30,34) (30,32) (31,34) (31,32) (32,33) (33,34)\nIs there a path between node 7 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph135-24_19", + "image": "data/connectivity/graph_visual/hard/graph135.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,10) (0,7) (0,5) (0,3) (0,6) (0,27) (0,16) (0,8) (0,19) (0,24) (0,22) (0,21) (0,17) (0,20) (0,1) (0,25) (1,23) (1,3) (1,6) (1,26) (1,27) (1,16) (1,8) (1,19) (1,4) (1,22) (1,21) (1,17) (1,25) (2,13) (2,11) (3,10) (3,7) (3,5) (3,26) (3,16) (3,8) (3,19) (3,24) (3,18) (3,20) (3,15) (3,25) (4,5) (4,6) (4,26) (4,16) (4,8) (4,19) (4,24) (4,22) (4,21) (4,9) (4,17) (4,15) (5,10) (5,7) (5,6) (5,26) (5,27) (5,16) (5,8) (5,19) (5,22) (5,18) (5,21) (5,17) (5,20) (5,25) (6,10) (6,7) (6,23) (6,26) (6,27) (6,16) (6,19) (6,24) (6,22) (6,18) (6,21) (6,9) (6,17) (6,15) (6,25) (7,10) (7,23) (7,26) (7,8) (7,19) (7,24) (7,21) (7,9) (7,17) (7,20) (7,25) (8,10) (8,23) (8,26) (8,27) (8,16) (8,19) (8,24) (8,22) (8,9) (8,15) (9,10) (9,23) (9,27) (9,16) (9,24) (9,22) (9,18) (9,21) (9,17) (9,20) (9,15) (10,23) (10,27) (10,16) (10,24) (10,22) (10,17) (10,25) (11,13) (11,14) (12,13) (12,14) (15,23) (15,27) (15,19) (15,24) (15,22) (15,18) (15,21) (15,20) (15,25) (16,23) (16,27) (16,24) (16,22) (16,18) (16,17) (16,25) (17,23) (17,26) (17,27) (17,19) (17,22) (17,21) (17,20) (17,25) (18,26) (18,27) (18,19) (18,24) (18,22) (19,23) (19,24) (19,21) (19,25) (20,27) (20,24) (20,22) (20,25) (21,23) (21,26) (21,27) (21,24) (21,22) (21,25) (22,23) (22,26) (22,24) (23,26) (23,27) (23,24) (23,25) (24,27) (24,25) (25,27)\nIs there a path between node 24 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph383-13_0", + "image": "data/connectivity/graph_visual/hard/graph383.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,29) (0,28) (0,8) (0,23) (0,6) (0,10) (0,11) (0,31) (0,2) (0,9) (0,21) (0,12) (0,22) (0,14) (0,30) (1,15) (1,26) (1,19) (1,13) (1,20) (2,29) (2,28) (2,8) (2,6) (2,10) (2,11) (2,31) (2,21) (2,12) (2,14) (3,24) (3,26) (3,19) (3,13) (3,4) (4,15) (4,26) (4,19) (5,16) (5,7) (5,17) (6,28) (6,23) (6,10) (6,11) (6,31) (6,9) (6,22) (6,14) (6,30) (7,27) (8,29) (8,28) (8,23) (8,10) (8,11) (8,31) (8,9) (8,25) (8,21) (8,12) (8,14) (9,18) (9,29) (9,23) (9,10) (9,11) (9,31) (9,25) (9,14) (10,18) (10,28) (10,23) (10,11) (10,21) (10,12) (10,14) (10,30) (11,18) (11,28) (11,23) (11,31) (11,25) (11,21) (11,12) (11,22) (11,14) (11,30) (12,18) (12,29) (12,28) (12,31) (12,25) (12,22) (12,14) (13,24) (13,15) (13,26) (13,19) (14,18) (14,23) (14,31) (14,25) (14,21) (14,22) (14,30) (15,19) (15,20) (16,27) (16,17) (17,27) (18,29) (18,23) (18,31) (18,25) (19,24) (19,26) (19,20) (20,26) (21,29) (21,28) (21,23) (21,25) (21,22) (22,29) (22,28) (22,23) (22,31) (22,25) (22,30) (23,29) (23,28) (23,31) (23,25) (25,29) (25,28) (25,31) (25,30) (28,29) (28,31) (28,30) (29,30) (30,31)\nIs there a path between node 13 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph202-10_3", + "image": "data/connectivity/graph_visual/hard/graph202.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,29) (1,27) (1,24) (1,21) (1,3) (2,10) (2,22) (2,6) (2,18) (2,25) (2,12) (3,19) (3,27) (3,24) (4,10) (4,6) (4,18) (4,25) (5,28) (5,16) (6,10) (6,13) (6,25) (6,12) (6,9) (7,28) (8,10) (8,14) (8,18) (8,29) (8,25) (8,23) (9,13) (9,14) (10,29) (10,25) (12,22) (12,18) (12,17) (13,29) (13,26) (14,20) (14,17) (15,19) (17,25) (18,20) (18,25) (20,29) (20,26) (20,23) (21,27) (21,24) (23,26) (23,25) (24,27) (26,29)\nIs there a path between node 10 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph344-21_18", + "image": "data/connectivity/graph_visual/hard/graph344.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,19) (0,22) (0,8) (0,14) (1,9) (1,11) (1,21) (1,16) (1,28) (1,25) (1,6) (1,10) (2,12) (2,18) (2,25) (2,20) (2,10) (3,18) (3,23) (3,5) (4,24) (5,26) (5,21) (5,29) (5,25) (5,20) (5,31) (6,12) (6,18) (6,17) (7,15) (7,14) (8,30) (8,19) (8,13) (9,21) (9,28) (9,25) (9,17) (10,26) (10,11) (10,25) (10,17) (11,18) (11,23) (11,25) (11,20) (12,21) (12,18) (12,23) (13,24) (13,19) (13,15) (13,14) (14,27) (14,22) (15,24) (15,22) (16,23) (16,17) (18,26) (18,28) (18,23) (18,20) (19,24) (19,30) (20,21) (20,28) (21,26) (21,25) (23,26) (24,30) (25,31) (26,28) (26,31) (28,31)\nIs there a path between node 21 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph229-25_27", + "image": "data/connectivity/graph_visual/hard/graph229.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,26) (0,13) (1,23) (1,10) (1,16) (1,11) (1,19) (1,8) (1,2) (1,14) (1,29) (1,25) (1,9) (1,17) (1,28) (2,24) (2,23) (2,10) (2,16) (2,11) (2,19) (2,20) (2,21) (2,14) (2,25) (2,9) (2,4) (2,17) (2,28) (3,5) (3,15) (3,6) (3,7) (4,24) (4,16) (4,11) (4,19) (4,8) (4,18) (4,14) (4,29) (4,25) (4,22) (4,17) (4,28) (5,27) (5,15) (5,6) (6,27) (7,27) (7,15) (8,24) (8,23) (8,10) (8,19) (8,20) (8,18) (8,29) (8,25) (8,17) (8,28) (9,24) (9,23) (9,10) (9,19) (9,18) (9,29) (9,25) (9,22) (9,17) (10,24) (10,23) (10,16) (10,11) (10,19) (10,20) (10,21) (10,18) (10,29) (10,25) (10,22) (10,17) (10,28) (11,24) (11,23) (11,16) (11,19) (11,21) (11,18) (11,14) (11,29) (11,22) (11,28) (12,26) (13,26) (14,24) (14,16) (14,20) (14,21) (14,18) (14,29) (14,25) (14,22) (15,27) (16,23) (16,20) (16,18) (16,29) (16,25) (17,23) (17,20) (17,29) (17,22) (17,28) (18,23) (18,19) (18,20) (18,21) (18,29) (18,25) (18,28) (19,24) (19,21) (19,29) (19,25) (19,22) (19,28) (20,24) (20,21) (20,25) (20,22) (20,28) (21,23) (21,29) (21,22) (22,23) (22,29) (23,29) (23,25) (23,28) (24,25) (25,28) (28,29)\nIs there a path between node 25 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph606-4_16", + "image": "data/connectivity/graph_visual/hard/graph606.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,31) (0,3) (0,23) (0,7) (0,4) (1,10) (1,28) (1,8) (1,24) (2,5) (2,21) (2,6) (2,29) (3,32) (3,31) (3,30) (3,29) (4,5) (4,31) (4,11) (4,30) (5,14) (5,30) (5,7) (5,20) (6,14) (6,21) (6,29) (6,20) (7,16) (7,14) (7,31) (7,30) (8,15) (8,10) (8,28) (8,19) (9,22) (9,26) (9,28) (9,25) (10,34) (10,33) (10,18) (10,24) (10,19) (11,16) (11,14) (11,13) (11,23) (12,17) (13,14) (13,27) (13,29) (14,16) (14,32) (15,25) (15,18) (15,24) (16,32) (16,21) (16,30) (16,29) (16,20) (19,34) (19,26) (19,25) (19,24) (20,31) (20,30) (20,29) (21,30) (21,27) (22,34) (22,33) (23,30) (23,29) (24,26) (25,33) (26,28) (27,32) (28,34) (29,31)\nIs there a path between node 4 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph454-18_24", + "image": "data/connectivity/graph_visual/hard/graph454.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,19) (0,7) (0,4) (0,23) (0,21) (0,18) (1,10) (1,19) (1,24) (1,18) (1,5) (2,11) (2,14) (2,22) (2,23) (2,13) (2,15) (2,31) (2,20) (3,11) (3,22) (3,16) (3,30) (3,13) (3,20) (3,18) (4,11) (4,14) (4,6) (4,23) (4,24) (4,31) (4,32) (4,18) (4,5) (5,19) (5,11) (5,7) (5,23) (5,15) (5,31) (6,19) (6,7) (6,13) (6,8) (7,11) (7,22) (7,28) (7,30) (7,21) (7,31) (8,10) (8,12) (8,14) (8,16) (8,30) (8,21) (9,17) (10,12) (10,24) (10,21) (10,32) (10,20) (11,22) (11,23) (11,13) (11,15) (11,18) (12,22) (12,31) (12,18) (13,16) (13,30) (13,23) (13,21) (13,15) (13,32) (14,19) (14,30) (14,23) (14,31) (15,30) (15,31) (15,32) (15,20) (16,30) (16,24) (16,21) (16,32) (17,25) (18,19) (18,28) (18,24) (19,21) (20,22) (20,21) (22,30) (22,23) (22,32) (24,28) (24,31) (24,32) (25,26) (25,27)\nIs there a path between node 18 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph238-5_14", + "image": "data/connectivity/graph_visual/hard/graph238.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,13) (0,4) (0,26) (1,6) (1,15) (1,30) (1,24) (2,3) (2,20) (2,25) (2,26) (3,12) (3,10) (3,25) (4,12) (4,13) (4,10) (4,7) (4,25) (4,26) (5,29) (5,20) (5,11) (5,25) (5,26) (6,14) (6,30) (6,28) (6,17) (7,29) (7,12) (7,13) (7,10) (7,20) (7,25) (7,26) (8,19) (8,27) (8,24) (9,22) (9,11) (9,25) (10,22) (10,29) (10,12) (10,13) (10,25) (10,26) (11,22) (11,23) (11,20) (12,29) (12,23) (14,27) (14,28) (14,24) (15,21) (15,19) (16,30) (16,24) (17,19) (17,28) (17,24) (18,20) (18,25) (20,22) (20,29) (20,25) (21,30) (21,24) (22,23) (22,25) (22,26) (23,29) (25,29) (25,26) (26,29) (28,30)\nIs there a path between node 5 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph13-6_7", + "image": "data/connectivity/graph_visual/hard/graph13.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (0,8) (0,5) (0,19) (1,8) (1,5) (1,19) (2,12) (2,15) (2,16) (2,24) (2,17) (2,3) (2,20) (2,9) (2,21) (2,23) (2,25) (2,11) (2,14) (2,22) (3,10) (3,15) (3,16) (3,24) (3,20) (3,4) (3,21) (3,23) (3,25) (3,14) (3,6) (3,22) (4,10) (4,13) (4,15) (4,16) (4,24) (4,20) (4,21) (4,23) (4,25) (4,14) (4,6) (4,22) (5,18) (5,7) (5,19) (6,12) (6,13) (6,24) (6,17) (6,20) (6,9) (6,23) (6,14) (6,22) (7,8) (8,18) (9,10) (9,12) (9,15) (9,16) (9,24) (9,17) (9,23) (9,25) (9,11) (9,14) (9,22) (10,12) (10,13) (10,16) (10,24) (10,17) (10,21) (10,23) (10,25) (10,11) (10,14) (10,22) (11,13) (11,16) (11,20) (11,21) (11,23) (11,25) (11,22) (12,24) (12,17) (12,20) (12,23) (12,22) (13,15) (13,24) (13,17) (13,20) (13,21) (13,25) (13,22) (14,15) (14,16) (14,24) (14,17) (14,20) (14,21) (14,23) (14,25) (15,24) (15,17) (15,20) (15,23) (15,25) (16,24) (16,17) (16,20) (16,21) (16,23) (16,25) (16,22) (17,24) (17,20) (17,23) (17,22) (18,19) (20,24) (20,21) (20,22) (21,24) (21,25) (21,22) (22,23) (22,25) (23,24) (23,25) (24,25)\nIs there a path between node 6 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph386-13_31", + "image": "data/connectivity/graph_visual/hard/graph386.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,16) (0,20) (0,21) (0,24) (0,6) (0,31) (0,26) (0,2) (0,7) (0,14) (0,27) (0,11) (0,1) (1,16) (1,21) (1,24) (1,31) (1,18) (1,25) (1,26) (1,2) (1,7) (1,14) (1,27) (1,11) (1,10) (2,16) (2,20) (2,21) (2,24) (2,6) (2,31) (2,14) (2,27) (2,10) (3,15) (3,29) (3,4) (3,13) (3,8) (3,19) (3,5) (3,22) (4,30) (4,12) (4,17) (4,29) (4,13) (4,5) (4,22) (5,30) (5,12) (5,15) (5,28) (5,29) (5,19) (5,22) (5,23) (6,9) (6,16) (6,24) (6,31) (6,25) (6,7) (6,27) (6,11) (7,16) (7,21) (7,24) (7,18) (7,14) (7,11) (7,10) (8,12) (8,17) (8,15) (8,13) (8,19) (8,22) (8,23) (9,20) (9,21) (9,24) (9,31) (9,18) (9,26) (9,14) (10,21) (10,31) (10,18) (10,25) (10,26) (10,14) (10,27) (10,11) (11,16) (11,20) (11,21) (11,31) (11,18) (11,25) (11,26) (11,14) (12,28) (12,29) (12,13) (12,23) (13,30) (13,17) (13,15) (13,28) (13,19) (13,23) (14,20) (14,21) (14,31) (14,18) (14,25) (14,26) (14,27) (15,17) (15,28) (15,19) (15,23) (16,20) (16,21) (16,24) (16,18) (16,26) (17,30) (17,22) (17,23) (18,21) (18,31) (18,25) (18,27) (19,30) (19,28) (19,22) (19,23) (20,21) (20,31) (20,26) (20,27) (21,24) (21,31) (21,25) (21,26) (21,27) (22,30) (22,29) (23,30) (23,28) (23,29) (24,31) (24,25) (24,26) (25,31) (25,26) (25,27) (26,27) (27,31) (28,30) (28,29)\nIs there a path between node 13 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph250-20_5", + "image": "data/connectivity/graph_visual/hard/graph250.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,21) (0,16) (0,11) (0,5) (0,14) (0,8) (0,23) (0,15) (0,10) (0,7) (0,27) (0,6) (0,29) (0,19) (0,18) (0,22) (0,28) (0,2) (0,1) (0,9) (0,4) (1,26) (1,16) (1,11) (1,5) (1,14) (1,8) (1,10) (1,7) (1,6) (1,3) (1,29) (1,19) (1,17) (1,18) (1,28) (1,20) (1,9) (1,4) (2,26) (2,11) (2,5) (2,8) (2,15) (2,10) (2,7) (2,29) (2,19) (2,17) (2,18) (2,22) (2,28) (2,20) (2,4) (3,26) (3,21) (3,16) (3,11) (3,8) (3,15) (3,10) (3,27) (3,6) (3,29) (3,19) (3,17) (3,18) (3,22) (3,28) (3,30) (3,9) (3,4) (4,26) (4,16) (4,11) (4,5) (4,23) (4,15) (4,7) (4,27) (4,29) (4,20) (5,26) (5,16) (5,11) (5,8) (5,23) (5,10) (5,6) (5,29) (5,19) (5,17) (5,18) (5,22) (5,28) (5,30) (5,9) (6,16) (6,11) (6,8) (6,23) (6,15) (6,10) (6,27) (6,29) (6,19) (6,17) (6,18) (6,28) (6,20) (6,30) (6,9) (7,26) (7,21) (7,11) (7,8) (7,23) (7,15) (7,10) (7,27) (7,29) (7,19) (7,18) (7,22) (7,20) (7,30) (8,16) (8,23) (8,17) (8,18) (8,28) (8,20) (8,30) (8,9) (9,21) (9,16) (9,15) (9,10) (9,27) (9,29) (9,19) (9,17) (9,18) (9,22) (9,28) (9,20) (9,30) (10,26) (10,21) (10,16) (10,11) (10,15) (10,29) (10,19) (10,17) (10,18) (10,22) (10,28) (10,20) (10,30) (11,26) (11,21) (11,16) (11,14) (11,23) (11,29) (11,17) (11,18) (11,28) (11,20) (12,24) (13,24) (13,25) (14,26) (14,16) (14,23) (14,27) (14,19) (14,22) (14,28) (15,23) (15,29) (15,19) (15,17) (15,18) (15,22) (15,28) (15,20) (16,26) (16,21) (16,27) (16,19) (16,17) (16,18) (16,20) (17,26) (17,23) (17,19) (17,22) (17,28) (17,20) (18,26) (18,21) (18,23) (18,27) (18,19) (18,28) (18,30) (19,21) (19,23) (19,27) (19,29) (19,22) (19,20) (19,30) (20,26) (20,21) (20,23) (20,27) (20,22) (20,30) (21,26) (21,23) (21,27) (21,29) (21,28) (21,30) (22,26) (22,23) (22,29) (22,28) (22,30) (23,26) (23,27) (23,29) (23,30) (26,27) (26,30) (27,29) (27,28) (27,30) (28,29) (28,30) (29,30)\nIs there a path between node 20 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph664-3_22", + "image": "data/connectivity/graph_visual/hard/graph664.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (0,14) (0,16) (0,33) (0,10) (0,7) (0,25) (1,28) (1,2) (1,12) (1,17) (1,13) (1,18) (1,32) (1,20) (1,16) (1,30) (1,7) (1,25) (1,31) (2,17) (2,18) (2,21) (2,33) (2,8) (2,11) (3,24) (3,6) (3,19) (4,6) (4,23) (4,34) (4,26) (5,24) (5,23) (5,26) (6,23) (6,19) (7,28) (7,13) (7,20) (7,22) (8,17) (8,20) (8,16) (8,22) (9,28) (9,18) (9,32) (9,16) (9,30) (9,11) (10,28) (10,14) (10,22) (10,25) (11,28) (11,12) (11,17) (11,18) (11,22) (11,33) (12,28) (12,15) (12,14) (12,16) (12,29) (12,33) (12,25) (13,30) (14,17) (14,18) (14,16) (14,22) (14,31) (15,18) (15,21) (15,16) (15,30) (16,28) (16,21) (16,20) (16,22) (16,31) (17,28) (17,18) (17,32) (17,20) (18,32) (18,21) (18,22) (18,30) (19,23) (19,34) (20,27) (20,25) (20,31) (21,32) (21,29) (21,33) (21,31) (22,31) (25,28) (25,32) (25,27) (26,34) (27,29) (30,31) (31,32) (31,33) (32,33)\nIs there a path between node 3 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph235-15_20", + "image": "data/connectivity/graph_visual/hard/graph235.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,29) (0,27) (0,23) (0,4) (0,20) (0,17) (0,6) (1,5) (1,22) (1,11) (1,19) (1,24) (1,2) (1,15) (1,8) (1,30) (1,9) (1,28) (1,18) (2,5) (2,22) (2,24) (2,15) (2,8) (2,30) (2,9) (2,28) (2,18) (3,26) (3,13) (4,21) (4,29) (4,23) (4,20) (4,17) (4,6) (5,22) (5,19) (5,24) (5,14) (5,30) (5,28) (5,18) (6,21) (6,29) (6,27) (6,23) (6,20) (6,17) (7,26) (7,10) (7,13) (7,16) (7,12) (8,11) (8,24) (8,14) (8,30) (8,9) (8,28) (8,18) (9,22) (9,11) (9,19) (9,15) (9,28) (10,16) (10,12) (11,15) (11,30) (11,28) (11,18) (12,13) (12,16) (13,26) (13,16) (13,25) (14,22) (14,19) (14,15) (14,30) (15,19) (15,30) (15,28) (15,18) (16,26) (16,25) (17,29) (17,23) (18,19) (18,24) (18,28) (19,30) (19,28) (20,21) (20,27) (21,29) (21,27) (21,23) (22,24) (22,28) (23,27) (24,30) (24,28) (25,26) (28,30)\nIs there a path between node 15 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph3-9_14", + "image": "data/connectivity/graph_visual/hard/graph3.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,2) (0,10) (0,6) (0,8) (0,17) (0,25) (2,23) (2,21) (2,24) (2,15) (2,5) (2,22) (2,12) (2,19) (3,23) (3,8) (3,16) (4,14) (4,23) (4,10) (4,6) (4,8) (4,17) (4,16) (5,14) (5,18) (5,15) (5,10) (5,17) (6,22) (8,14) (8,23) (8,21) (8,24) (8,10) (9,18) (9,15) (9,22) (9,17) (10,20) (10,14) (10,23) (11,20) (11,14) (11,23) (11,22) (11,12) (11,17) (12,22) (12,17) (14,24) (15,23) (15,24) (15,25) (16,21) (16,24) (16,18) (17,20) (17,23) (17,21) (17,24) (18,20) (18,19) (19,20) (19,24) (19,22) (19,25) (20,23) (20,21) (22,25) (23,25)\nIs there a path between node 9 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph205-28_16", + "image": "data/connectivity/graph_visual/hard/graph205.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,21) (0,12) (0,22) (0,29) (0,26) (0,4) (0,28) (1,22) (1,16) (1,19) (1,23) (1,25) (2,12) (2,22) (2,29) (2,5) (2,8) (3,15) (3,10) (3,18) (3,21) (3,12) (3,22) (3,26) (3,14) (3,27) (3,28) (3,8) (4,10) (4,20) (4,16) (4,26) (4,27) (4,28) (4,5) (5,15) (5,10) (5,12) (5,20) (5,16) (5,7) (5,14) (5,27) (5,17) (7,29) (7,16) (7,23) (7,28) (8,15) (8,23) (8,26) (8,11) (8,17) (10,18) (10,13) (10,22) (10,16) (11,21) (11,12) (11,29) (11,16) (11,14) (12,21) (12,20) (12,23) (12,17) (13,29) (13,20) (14,18) (14,21) (14,23) (14,26) (14,27) (14,17) (15,29) (15,19) (15,23) (15,26) (15,25) (16,18) (16,21) (16,29) (16,27) (16,25) (16,28) (16,17) (17,26) (18,21) (18,20) (18,19) (18,23) (19,26) (20,23) (20,25) (21,22) (22,23) (22,27) (22,28) (23,29) (23,26) (23,27) (23,28) (25,29) (25,27)\nIs there a path between node 28 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph648-7_29", + "image": "data/connectivity/graph_visual/hard/graph648.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,1) (0,27) (0,3) (0,2) (1,3) (1,2) (2,27) (3,27) (4,9) (4,7) (4,29) (4,34) (4,31) (4,21) (4,16) (4,17) (4,15) (4,25) (4,18) (4,5) (4,6) (4,20) (4,11) (5,9) (5,7) (5,24) (5,32) (5,23) (5,30) (5,31) (5,16) (5,17) (5,25) (5,26) (5,18) (5,6) (5,13) (5,11) (6,7) (6,29) (6,34) (6,24) (6,32) (6,23) (6,31) (6,21) (6,26) (6,18) (6,20) (6,11) (7,24) (7,32) (7,31) (7,16) (7,17) (7,15) (7,25) (7,12) (7,26) (7,20) (7,13) (7,11) (8,10) (8,14) (8,22) (8,19) (9,29) (9,24) (9,32) (9,23) (9,31) (9,21) (9,16) (9,17) (9,25) (9,12) (9,26) (9,18) (9,20) (9,13) (9,11) (10,33) (10,28) (10,22) (10,19) (11,29) (11,34) (11,24) (11,32) (11,30) (11,31) (11,21) (11,25) (11,12) (11,26) (11,18) (11,13) (12,29) (12,34) (12,24) (12,32) (12,23) (12,15) (12,25) (12,18) (12,20) (12,13) (13,29) (13,34) (13,24) (13,30) (13,17) (13,15) (13,18) (13,20) (14,28) (14,22) (14,19) (15,29) (15,34) (15,24) (15,32) (15,23) (15,21) (15,16) (15,17) (15,25) (15,26) (15,18) (15,20) (16,29) (16,34) (16,24) (16,32) (16,23) (16,30) (16,31) (16,21) (16,25) (16,26) (17,29) (17,34) (17,32) (17,23) (17,30) (17,31) (17,21) (17,26) (17,18) (17,20) (18,24) (18,32) (18,30) (18,31) (18,21) (18,25) (18,20) (19,33) (19,28) (19,22) (20,29) (20,34) (20,30) (20,31) (20,21) (20,25) (20,26) (21,29) (21,34) (21,24) (21,31) (21,25) (21,26) (22,33) (22,28) (23,29) (23,24) (23,32) (23,30) (23,25) (23,26) (24,29) (24,32) (24,31) (24,25) (24,26) (25,34) (25,32) (25,30) (25,26) (26,34) (26,30) (29,32) (29,30) (29,31) (30,32) (31,34) (31,32) (32,34)\nIs there a path between node 7 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph133-13_0", + "image": "data/connectivity/graph_visual/hard/graph133.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,6) (0,2) (0,5) (0,27) (0,8) (0,1) (0,21) (0,24) (0,10) (0,4) (0,11) (0,19) (0,25) (0,7) (0,9) (0,13) (0,18) (1,6) (1,12) (1,27) (1,8) (1,21) (1,10) (1,4) (1,11) (1,19) (1,25) (1,7) (1,26) (1,18) (2,6) (2,12) (2,27) (2,8) (2,21) (2,24) (2,22) (2,10) (2,4) (2,3) (2,19) (2,7) (2,9) (2,13) (2,18) (3,6) (3,5) (3,12) (3,27) (3,8) (3,21) (3,24) (3,22) (3,10) (3,4) (3,11) (3,25) (3,9) (3,13) (3,18) (4,6) (4,5) (4,12) (4,27) (4,21) (4,24) (4,22) (4,10) (4,19) (4,25) (4,7) (4,13) (5,6) (5,27) (5,22) (5,10) (5,11) (5,19) (5,25) (5,7) (5,13) (5,26) (5,18) (6,12) (6,27) (6,8) (6,24) (6,22) (6,10) (6,11) (6,19) (6,25) (6,7) (6,13) (6,26) (7,12) (7,27) (7,8) (7,21) (7,24) (7,22) (7,25) (7,9) (7,13) (7,26) (7,18) (8,12) (8,27) (8,21) (8,24) (8,22) (8,11) (8,19) (8,25) (8,9) (8,13) (8,26) (9,12) (9,21) (9,24) (9,22) (9,11) (9,19) (9,25) (9,13) (9,26) (10,27) (10,21) (10,24) (10,22) (10,19) (10,25) (10,13) (11,12) (11,27) (11,24) (11,22) (11,19) (11,25) (11,13) (11,26) (11,18) (12,21) (12,25) (12,13) (12,26) (12,18) (13,27) (13,24) (13,22) (13,19) (13,25) (13,26) (13,18) (14,15) (14,17) (14,23) (14,16) (14,20) (15,17) (15,23) (15,20) (16,17) (16,20) (18,22) (18,19) (18,26) (19,27) (19,21) (19,26) (20,23) (21,27) (21,24) (21,22) (21,26) (22,27) (22,26) (24,25) (25,26) (26,27)\nIs there a path between node 13 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph473-14_6", + "image": "data/connectivity/graph_visual/hard/graph473.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,17) (1,2) (1,14) (1,9) (1,18) (1,5) (1,25) (1,28) (1,13) (1,10) (2,31) (2,14) (2,4) (2,18) (2,5) (2,28) (2,13) (2,19) (2,22) (2,10) (2,15) (3,27) (4,21) (4,9) (4,18) (4,25) (4,28) (4,13) (4,22) (4,7) (4,16) (5,21) (5,31) (5,9) (5,18) (5,25) (5,28) (5,13) (5,19) (5,22) (5,16) (5,10) (5,15) (6,17) (6,32) (7,31) (7,14) (7,9) (7,18) (7,25) (7,28) (7,13) (7,19) (7,16) (7,10) (8,11) (8,23) (8,30) (8,12) (8,29) (9,21) (9,31) (9,18) (9,25) (9,13) (9,10) (10,31) (10,18) (10,28) (10,19) (10,22) (10,16) (10,15) (11,24) (11,30) (11,26) (12,24) (12,23) (12,20) (12,26) (12,29) (13,14) (13,18) (13,28) (13,19) (13,22) (13,16) (14,31) (14,18) (14,16) (14,15) (15,31) (15,18) (15,19) (15,22) (15,16) (16,21) (16,31) (16,18) (16,28) (16,19) (18,21) (18,31) (18,25) (18,28) (18,22) (19,31) (19,25) (19,28) (19,22) (20,24) (20,23) (20,30) (20,29) (21,31) (21,28) (21,22) (22,25) (22,28) (23,30) (23,26) (23,29) (24,30) (25,31) (25,28) (26,30) (28,31) (29,30)\nIs there a path between node 14 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph612-1_7", + "image": "data/connectivity/graph_visual/hard/graph612.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,21) (0,26) (0,9) (0,3) (0,4) (0,30) (0,16) (0,22) (0,12) (0,5) (0,28) (0,29) (0,19) (0,31) (0,27) (0,8) (0,32) (0,15) (0,23) (0,25) (1,34) (2,21) (2,26) (2,20) (2,3) (2,6) (2,30) (2,16) (2,22) (2,12) (2,13) (2,5) (2,33) (2,28) (2,24) (2,29) (2,19) (2,31) (2,17) (2,27) (2,8) (2,32) (2,15) (2,23) (3,21) (3,26) (3,9) (3,20) (3,6) (3,30) (3,7) (3,22) (3,12) (3,13) (3,5) (3,33) (3,28) (3,24) (3,29) (3,19) (3,31) (3,27) (3,8) (3,32) (3,15) (3,18) (3,23) (3,25) (4,21) (4,26) (4,9) (4,20) (4,6) (4,30) (4,7) (4,12) (4,13) (4,5) (4,33) (4,28) (4,29) (4,19) (4,27) (4,8) (4,32) (4,18) (5,21) (5,6) (5,7) (5,13) (5,33) (5,24) (5,31) (5,17) (5,27) (5,32) (5,15) (5,18) (5,25) (6,26) (6,9) (6,20) (6,30) (6,7) (6,22) (6,13) (6,28) (6,24) (6,29) (6,19) (6,31) (6,27) (6,8) (6,32) (6,18) (6,23) (6,25) (7,21) (7,26) (7,9) (7,20) (7,30) (7,22) (7,12) (7,13) (7,28) (7,29) (7,19) (7,31) (7,17) (7,27) (7,32) (7,15) (7,18) (7,23) (7,25) (8,21) (8,9) (8,20) (8,30) (8,16) (8,22) (8,12) (8,13) (8,33) (8,28) (8,31) (8,17) (8,15) (8,18) (8,23) (8,25) (9,21) (9,26) (9,20) (9,30) (9,22) (9,33) (9,28) (9,24) (9,29) (9,19) (9,31) (9,27) (9,32) (9,15) (9,23) (9,25) (10,34) (10,14) (11,34) (11,14) (12,21) (12,26) (12,20) (12,30) (12,22) (12,13) (12,28) (12,24) (12,32) (12,18) (12,25) (13,21) (13,26) (13,20) (13,30) (13,16) (13,22) (13,33) (13,24) (13,29) (13,19) (13,17) (13,27) (13,32) (13,15) (13,18) (13,25) (14,34) (15,21) (15,20) (15,22) (15,33) (15,28) (15,24) (15,29) (15,19) (15,31) (15,17) (15,27) (15,18) (15,23) (16,21) (16,26) (16,30) (16,22) (16,33) (16,28) (16,24) (16,29) (16,27) (16,32) (16,23) (17,21) (17,30) (17,22) (17,33) (17,28) (17,24) (17,29) (17,19) (17,31) (17,27) (17,32) (17,23) (17,25) (18,20) (18,30) (18,33) (18,29) (18,19) (18,31) (18,27) (18,32) (18,23) (18,25) (19,26) (19,20) (19,30) (19,22) (19,33) (19,28) (19,29) (19,32) (19,23) (19,25) (20,30) (20,22) (20,33) (20,28) (20,31) (20,27) (20,32) (20,23) (20,25) (21,22) (21,33) (21,24) (21,29) (21,31) (21,32) (22,26) (22,30) (22,33) (22,28) (22,29) (22,31) (22,27) (22,32) (22,25) (23,26) (23,30) (23,33) (23,28) (23,24) (23,29) (23,31) (23,27) (24,26) (24,30) (24,31) (24,32) (25,26) (25,28) (25,29) (25,32) (26,33) (26,28) (26,27) (27,28) (27,29) (27,31) (27,32) (28,33) (28,29) (28,31) (28,32) (29,30) (29,33) (29,31) (29,32) (30,33) (30,31) (30,32) (31,32) (32,33)\nIs there a path between node 1 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph327-13_4", + "image": "data/connectivity/graph_visual/hard/graph327.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,3) (0,10) (0,27) (0,1) (0,29) (0,7) (0,14) (0,13) (0,20) (0,6) (1,3) (1,4) (1,10) (1,27) (1,7) (1,16) (1,14) (1,13) (1,20) (1,15) (1,6) (2,30) (2,12) (2,5) (2,11) (2,21) (2,28) (2,22) (2,25) (2,31) (2,19) (3,4) (3,29) (3,16) (3,14) (3,13) (3,20) (3,15) (4,10) (4,7) (4,16) (4,13) (4,15) (4,6) (5,12) (5,23) (5,24) (5,21) (5,28) (5,25) (5,31) (5,19) (6,27) (6,29) (6,7) (6,14) (6,13) (6,20) (6,15) (7,10) (7,27) (7,20) (8,18) (9,26) (9,18) (10,27) (10,29) (10,16) (10,13) (10,15) (11,30) (11,24) (11,21) (11,17) (11,28) (11,25) (12,23) (12,24) (12,21) (12,17) (12,28) (12,22) (12,25) (12,19) (13,27) (13,16) (13,20) (13,15) (14,27) (14,29) (14,16) (14,15) (15,27) (15,29) (15,16) (15,20) (16,27) (16,29) (16,20) (17,30) (17,23) (17,24) (17,21) (17,28) (17,22) (17,25) (17,31) (17,19) (18,26) (19,30) (19,23) (19,24) (19,21) (19,28) (19,25) (19,31) (20,27) (21,30) (21,24) (21,28) (21,22) (21,25) (21,31) (22,30) (22,23) (22,24) (22,28) (22,25) (22,31) (23,30) (23,24) (23,25) (23,31) (24,28) (24,25) (24,31) (25,30) (25,28) (25,31) (27,29) (28,30) (30,31)\nIs there a path between node 13 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph204-25_0", + "image": "data/connectivity/graph_visual/hard/graph204.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,15) (0,26) (0,23) (0,4) (0,6) (0,3) (0,24) (2,17) (2,6) (2,3) (2,9) (2,11) (3,18) (3,14) (3,9) (3,11) (4,17) (4,15) (4,21) (4,29) (4,23) (4,13) (4,27) (4,9) (4,8) (5,22) (5,10) (5,15) (5,23) (5,9) (5,8) (6,22) (6,10) (6,26) (6,27) (6,24) (6,8) (6,11) (8,10) (8,21) (9,19) (9,17) (9,15) (9,29) (9,25) (9,23) (9,14) (9,27) (10,22) (10,29) (10,25) (10,23) (10,18) (10,13) (10,24) (10,11) (11,22) (11,19) (11,15) (11,29) (11,14) (13,19) (13,17) (13,29) (13,26) (13,23) (13,27) (13,24) (14,17) (14,21) (14,29) (14,23) (14,18) (14,27) (14,28) (15,19) (15,29) (15,25) (17,22) (17,21) (17,26) (17,23) (18,22) (18,29) (18,26) (18,28) (19,22) (19,26) (21,25) (21,28) (22,25) (22,26) (22,23) (22,24) (24,28) (25,28) (26,27) (27,28)\nIs there a path between node 25 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph458-15_21", + "image": "data/connectivity/graph_visual/hard/graph458.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,32) (0,6) (0,21) (1,7) (2,18) (3,17) (3,23) (4,27) (4,7) (4,18) (5,27) (6,12) (7,27) (8,28) (8,26) (9,29) (9,31) (10,30) (10,16) (10,25) (10,12) (13,18) (14,30) (14,32) (14,15) (15,19) (15,32) (15,25) (16,19) (16,30) (16,25) (16,21) (17,28) (17,29) (21,30) (21,25) (23,28) (23,29) (26,29) (26,31) (30,32)\nIs there a path between node 15 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph87-6_13", + "image": "data/connectivity/graph_visual/hard/graph87.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,14) (0,20) (0,2) (0,6) (0,11) (0,8) (0,12) (0,9) (0,5) (0,26) (0,24) (0,17) (1,14) (1,20) (1,6) (1,11) (1,8) (1,12) (1,9) (1,7) (1,13) (1,5) (1,19) (1,16) (1,24) (1,17) (1,25) (2,12) (2,9) (2,7) (2,5) (2,19) (2,16) (2,26) (2,24) (2,17) (2,25) (3,21) (3,4) (3,15) (3,18) (3,22) (3,23) (4,21) (4,15) (4,18) (4,23) (4,10) (5,14) (5,11) (5,8) (5,7) (5,19) (5,16) (5,24) (5,17) (6,20) (6,11) (6,8) (6,12) (6,7) (6,13) (6,19) (6,16) (6,26) (6,17) (7,14) (7,20) (7,11) (7,8) (7,12) (7,9) (7,13) (7,19) (7,16) (7,26) (7,24) (7,17) (7,25) (8,14) (8,20) (8,11) (8,9) (8,19) (8,16) (8,26) (8,24) (9,20) (9,13) (9,19) (9,16) (9,24) (9,17) (10,15) (10,22) (10,23) (11,20) (11,13) (11,19) (12,14) (12,20) (12,13) (12,19) (12,16) (12,24) (12,17) (12,25) (13,20) (13,19) (13,26) (13,24) (13,25) (14,19) (14,16) (14,26) (14,24) (14,17) (15,21) (15,18) (15,23) (16,20) (16,19) (16,26) (16,24) (16,17) (17,20) (17,19) (17,26) (17,24) (17,25) (18,21) (18,22) (19,20) (19,26) (19,24) (19,25) (20,26) (20,24) (21,22) (21,23) (22,23)\nIs there a path between node 6 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph546-11_29", + "image": "data/connectivity/graph_visual/hard/graph546.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,8) (2,3) (2,28) (2,27) (2,22) (2,11) (2,21) (2,9) (2,26) (2,6) (2,14) (2,7) (2,5) (2,13) (2,10) (3,30) (3,28) (3,27) (3,22) (3,11) (3,4) (3,9) (3,7) (3,12) (3,16) (3,13) (3,10) (4,30) (4,28) (4,27) (4,22) (4,11) (4,21) (4,9) (4,26) (4,6) (4,14) (4,12) (4,5) (4,13) (5,30) (5,27) (5,21) (5,9) (5,26) (5,6) (5,14) (5,16) (5,13) (5,10) (6,30) (6,28) (6,27) (6,22) (6,21) (6,9) (6,12) (6,16) (6,13) (6,10) (7,27) (7,11) (7,9) (7,26) (7,14) (7,16) (7,10) (9,30) (9,28) (9,27) (9,22) (9,21) (9,26) (9,14) (9,13) (10,30) (10,28) (10,27) (10,22) (10,11) (10,21) (10,26) (10,12) (10,16) (10,13) (11,30) (11,28) (11,22) (11,21) (11,14) (11,16) (11,13) (12,30) (12,28) (12,27) (12,21) (12,26) (12,16) (12,13) (13,28) (13,27) (13,22) (13,26) (14,30) (14,28) (14,21) (14,16) (15,18) (15,20) (15,25) (15,31) (15,32) (15,19) (15,33) (16,30) (16,28) (16,27) (16,21) (17,18) (17,24) (17,20) (17,25) (17,31) (17,32) (17,23) (17,19) (17,33) (18,24) (18,20) (18,31) (18,32) (18,23) (18,19) (19,29) (19,20) (19,25) (19,31) (19,32) (19,33) (20,29) (20,24) (20,25) (20,31) (20,32) (20,33) (21,22) (21,26) (22,30) (22,27) (22,26) (23,24) (23,25) (23,31) (23,33) (24,29) (24,25) (24,33) (25,29) (25,32) (26,30) (26,28) (26,27) (27,30) (27,28) (28,30) (29,31) (29,32) (29,33) (31,32) (31,33)\nIs there a path between node 11 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph636-27_33", + "image": "data/connectivity/graph_visual/hard/graph636.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,23) (0,32) (0,18) (0,25) (1,13) (1,17) (1,28) (1,2) (1,33) (2,17) (2,28) (2,15) (2,26) (2,16) (3,30) (3,26) (5,17) (5,28) (5,27) (6,22) (6,21) (7,34) (7,22) (7,24) (8,19) (10,29) (10,22) (10,31) (10,24) (10,21) (10,11) (11,34) (13,30) (13,15) (13,27) (13,33) (13,26) (13,16) (14,32) (15,28) (15,26) (16,28) (16,26) (17,30) (18,25) (20,28) (20,26) (21,31) (21,24) (22,34) (22,31) (22,24) (23,32) (24,29) (26,33) (28,33) (31,34)\nIs there a path between node 27 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph377-19_25", + "image": "data/connectivity/graph_visual/hard/graph377.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,27) (0,28) (0,4) (1,18) (1,27) (1,28) (1,25) (1,4) (2,30) (2,20) (2,5) (2,21) (2,31) (2,11) (2,9) (2,6) (2,17) (2,29) (2,22) (2,23) (2,15) (2,24) (2,19) (2,3) (2,16) (2,12) (2,14) (3,30) (3,21) (3,7) (3,31) (3,9) (3,8) (3,6) (3,17) (3,13) (3,22) (3,23) (3,15) (3,24) (3,16) (3,12) (3,14) (4,18) (4,27) (4,28) (5,30) (5,21) (5,7) (5,31) (5,11) (5,9) (5,8) (5,6) (5,13) (5,26) (5,15) (5,19) (5,10) (5,12) (5,14) (6,30) (6,20) (6,21) (6,7) (6,31) (6,11) (6,9) (6,29) (6,23) (6,15) (6,19) (6,10) (6,16) (6,12) (6,14) (7,30) (7,20) (7,11) (7,9) (7,8) (7,17) (7,29) (7,13) (7,22) (7,23) (7,15) (7,19) (7,10) (7,12) (8,30) (8,21) (8,31) (8,11) (8,9) (8,29) (8,26) (8,22) (8,23) (8,24) (8,19) (8,10) (8,16) (9,30) (9,20) (9,21) (9,31) (9,11) (9,29) (9,13) (9,26) (9,22) (9,23) (9,24) (9,19) (9,12) (9,14) (10,30) (10,20) (10,21) (10,11) (10,23) (10,15) (10,24) (10,19) (10,16) (11,31) (11,29) (11,13) (11,26) (11,22) (11,23) (11,16) (11,12) (11,14) (12,30) (12,20) (12,21) (12,17) (12,29) (12,13) (12,26) (12,22) (12,23) (12,24) (12,19) (12,16) (12,14) (13,30) (13,21) (13,31) (13,17) (13,29) (13,26) (13,23) (13,15) (13,24) (13,19) (13,16) (13,14) (14,30) (14,21) (14,31) (14,22) (14,19) (14,16) (15,20) (15,29) (15,26) (15,23) (15,24) (16,30) (16,20) (16,31) (16,17) (16,29) (16,19) (17,21) (17,31) (17,26) (17,23) (17,19) (18,27) (19,30) (19,21) (19,29) (19,26) (19,22) (19,23) (20,21) (20,31) (20,29) (20,23) (21,30) (21,31) (21,29) (21,26) (21,23) (21,24) (22,30) (22,31) (22,29) (22,26) (22,23) (22,24) (23,31) (23,29) (23,26) (24,30) (24,29) (24,26) (25,28) (26,29) (29,31) (30,31)\nIs there a path between node 19 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph297-29_8", + "image": "data/connectivity/graph_visual/hard/graph297.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,11) (0,21) (0,15) (0,12) (0,7) (0,13) (0,10) (0,20) (0,19) (0,6) (0,26) (0,30) (0,1) (0,27) (0,16) (0,5) (0,3) (0,22) (0,14) (0,25) (1,9) (1,11) (1,21) (1,15) (1,12) (1,13) (1,20) (1,19) (1,26) (1,27) (1,16) (1,5) (1,29) (1,3) (1,24) (1,25) (2,18) (2,31) (2,23) (3,9) (3,4) (3,15) (3,7) (3,13) (3,6) (3,30) (3,16) (3,29) (3,28) (3,24) (3,14) (4,11) (4,21) (4,17) (4,12) (4,7) (4,19) (4,6) (4,26) (4,16) (4,5) (4,29) (4,28) (4,22) (4,14) (4,25) (5,9) (5,11) (5,17) (5,15) (5,12) (5,13) (5,10) (5,20) (5,26) (5,27) (5,16) (5,29) (5,22) (5,24) (5,14) (6,9) (6,11) (6,21) (6,17) (6,15) (6,12) (6,7) (6,10) (6,26) (6,16) (6,29) (6,28) (6,22) (6,24) (6,14) (6,25) (7,9) (7,21) (7,10) (7,20) (7,19) (7,26) (7,27) (7,16) (7,29) (7,22) (7,24) (7,25) (8,18) (8,31) (8,23) (9,11) (9,21) (9,17) (9,15) (9,12) (9,13) (9,19) (9,26) (9,30) (9,27) (9,16) (9,29) (9,28) (9,14) (10,11) (10,21) (10,17) (10,12) (10,20) (10,26) (10,27) (10,29) (10,22) (10,24) (10,14) (10,25) (11,21) (11,17) (11,13) (11,20) (11,19) (11,26) (11,27) (11,16) (11,29) (11,22) (11,24) (11,25) (12,17) (12,13) (12,20) (12,19) (12,30) (12,27) (12,16) (12,29) (12,24) (12,14) (13,21) (13,20) (13,19) (13,26) (13,30) (13,16) (13,28) (13,22) (13,25) (14,20) (14,19) (14,30) (14,27) (14,16) (14,29) (14,28) (14,22) (14,25) (15,21) (15,19) (15,30) (15,16) (15,29) (15,24) (15,25) (16,21) (16,17) (16,20) (16,19) (16,30) (16,27) (16,29) (16,28) (16,22) (16,24) (17,21) (17,19) (17,26) (17,30) (17,29) (17,28) (17,22) (17,25) (18,31) (18,23) (19,21) (19,20) (19,26) (19,30) (19,27) (19,29) (19,28) (19,24) (19,25) (20,26) (20,30) (20,27) (20,29) (20,28) (20,24) (20,25) (21,27) (21,29) (21,22) (21,25) (22,26) (22,30) (22,27) (22,28) (22,24) (22,25) (24,26) (24,30) (24,27) (24,28) (25,30) (25,29) (25,28) (26,30) (26,27) (26,29) (27,30) (28,30)\nIs there a path between node 29 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph51-23_21", + "image": "data/connectivity/graph_visual/hard/graph51.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,4) (0,11) (0,16) (2,19) (2,4) (2,11) (3,4) (3,11) (5,8) (5,20) (5,25) (6,8) (6,22) (6,7) (6,18) (6,25) (7,22) (8,18) (8,24) (8,20) (8,21) (10,20) (10,26) (10,13) (11,19) (11,23) (13,22) (13,25) (15,24) (15,20) (15,25) (15,21) (16,23) (18,26) (19,23) (21,24) (21,25) (22,25) (22,26) (24,26)\nIs there a path between node 23 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph25-15_8", + "image": "data/connectivity/graph_visual/hard/graph25.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,7) (0,25) (0,15) (0,16) (0,20) (0,4) (1,7) (1,11) (1,20) (2,23) (2,6) (2,5) (3,25) (3,15) (3,14) (3,19) (3,12) (3,4) (4,17) (4,15) (4,11) (4,22) (4,12) (5,6) (6,13) (7,24) (7,14) (7,19) (7,22) (8,18) (8,13) (8,9) (9,23) (9,10) (11,25) (11,15) (11,16) (11,12) (12,24) (12,25) (12,14) (12,20) (12,22) (13,23) (13,18) (14,22) (15,17) (16,24) (16,25) (16,17) (16,20) (17,24) (20,25) (22,25) (24,25)\nIs there a path between node 15 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph375-22_27", + "image": "data/connectivity/graph_visual/hard/graph375.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,20) (0,4) (0,29) (0,11) (0,3) (0,1) (0,22) (0,10) (0,13) (0,16) (0,19) (0,7) (0,15) (0,25) (0,2) (0,23) (0,5) (1,18) (1,12) (1,9) (1,27) (1,20) (1,14) (1,11) (1,3) (1,24) (1,28) (1,6) (1,22) (1,10) (1,13) (1,15) (1,25) (1,2) (1,23) (1,5) (1,17) (2,18) (2,12) (2,9) (2,27) (2,29) (2,14) (2,11) (2,28) (2,6) (2,22) (2,10) (2,16) (2,7) (2,15) (2,25) (2,23) (2,17) (3,9) (3,27) (3,4) (3,29) (3,11) (3,24) (3,6) (3,21) (3,22) (3,10) (3,13) (3,16) (3,19) (3,7) (3,15) (3,25) (3,23) (4,18) (4,9) (4,27) (4,29) (4,14) (4,21) (4,22) (4,16) (4,19) (4,25) (4,23) (5,9) (5,27) (5,20) (5,29) (5,14) (5,28) (5,6) (5,22) (5,13) (5,16) (5,15) (5,25) (5,23) (6,12) (6,9) (6,27) (6,20) (6,14) (6,11) (6,24) (6,21) (6,22) (6,10) (6,13) (6,16) (6,19) (6,15) (6,25) (6,23) (7,18) (7,12) (7,9) (7,27) (7,11) (7,24) (7,28) (7,21) (7,13) (7,19) (7,25) (9,18) (9,12) (9,27) (9,20) (9,14) (9,28) (9,21) (9,22) (9,10) (9,19) (9,25) (9,23) (9,17) (10,18) (10,12) (10,20) (10,29) (10,14) (10,11) (10,21) (10,22) (10,13) (10,16) (10,19) (10,15) (10,17) (11,18) (11,27) (11,20) (11,14) (11,28) (11,13) (11,19) (11,15) (11,25) (11,23) (12,27) (12,22) (12,13) (12,16) (12,19) (12,25) (12,23) (13,20) (13,14) (13,24) (13,28) (13,21) (13,22) (13,16) (13,15) (13,25) (13,23) (13,17) (14,18) (14,27) (14,20) (14,29) (14,24) (14,28) (14,21) (14,22) (14,16) (14,19) (14,25) (14,17) (15,27) (15,20) (15,29) (15,24) (15,28) (15,21) (15,22) (15,19) (15,25) (15,17) (16,18) (16,20) (16,29) (16,24) (16,22) (16,19) (16,25) (16,17) (17,18) (17,27) (17,29) (17,24) (17,28) (17,21) (17,22) (17,19) (17,25) (17,23) (18,20) (18,29) (18,24) (18,28) (18,21) (18,19) (18,23) (19,27) (19,20) (19,29) (19,24) (19,28) (19,23) (20,22) (20,25) (21,27) (21,29) (21,24) (21,28) (21,25) (21,23) (22,27) (22,24) (22,28) (22,23) (23,27) (23,29) (23,24) (23,28) (23,25) (24,27) (24,28) (25,29) (25,28) (26,31) (27,29) (27,28) (28,29) (30,31)\nIs there a path between node 22 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph274-17_9", + "image": "data/connectivity/graph_visual/hard/graph274.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,27) (0,3) (0,14) (0,23) (0,10) (0,25) (1,22) (1,28) (1,8) (1,30) (1,2) (1,4) (1,21) (1,29) (1,9) (2,22) (2,28) (2,8) (2,30) (2,4) (2,9) (3,27) (3,6) (3,14) (3,15) (3,7) (3,5) (3,20) (3,10) (3,25) (4,28) (4,30) (4,21) (4,29) (4,9) (4,13) (5,27) (5,6) (5,15) (5,7) (5,23) (5,20) (5,10) (6,27) (6,14) (6,15) (6,23) (6,20) (6,10) (7,27) (7,14) (7,15) (7,10) (7,25) (8,22) (8,30) (8,21) (8,9) (9,22) (9,28) (9,30) (9,29) (9,13) (10,27) (10,23) (10,20) (10,25) (11,24) (11,19) (11,26) (11,18) (11,12) (11,17) (11,16) (12,19) (12,26) (12,18) (12,17) (12,16) (13,22) (13,28) (13,30) (13,21) (13,29) (14,27) (14,15) (14,23) (14,25) (15,27) (15,23) (15,20) (16,24) (16,26) (16,17) (17,24) (17,19) (17,26) (17,18) (18,26) (19,24) (20,27) (20,23) (20,25) (21,22) (21,28) (22,28) (22,30) (22,29) (23,27) (24,26) (25,27) (28,30) (28,29)\nIs there a path between node 17 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph245-9_27", + "image": "data/connectivity/graph_visual/hard/graph245.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,3) (0,14) (0,17) (0,2) (0,25) (0,8) (0,21) (0,10) (0,18) (0,19) (0,26) (0,4) (0,29) (0,20) (0,13) (0,12) (1,3) (1,14) (1,17) (1,25) (1,8) (1,21) (1,16) (1,15) (1,10) (1,19) (1,9) (1,4) (1,5) (1,29) (1,30) (1,27) (1,13) (1,12) (2,3) (2,17) (2,24) (2,8) (2,16) (2,15) (2,26) (2,4) (2,29) (2,30) (2,27) (2,13) (3,14) (3,17) (3,24) (3,25) (3,8) (3,21) (3,16) (3,10) (3,9) (3,26) (3,29) (3,30) (3,27) (3,20) (3,13) (3,12) (4,25) (4,8) (4,21) (4,16) (4,10) (4,18) (4,19) (4,9) (4,5) (4,30) (4,27) (4,20) (5,14) (5,17) (5,24) (5,8) (5,21) (5,16) (5,15) (5,10) (5,18) (5,19) (5,9) (5,26) (5,30) (5,27) (5,20) (6,22) (6,7) (6,23) (8,14) (8,17) (8,25) (8,16) (8,15) (8,18) (8,19) (8,9) (8,26) (8,29) (8,30) (8,27) (8,13) (9,14) (9,17) (9,24) (9,25) (9,16) (9,15) (9,10) (9,26) (9,30) (9,20) (9,13) (10,14) (10,17) (10,24) (10,25) (10,21) (10,18) (10,29) (10,30) (10,27) (10,20) (10,13) (10,12) (11,28) (12,14) (12,25) (12,21) (12,16) (12,18) (12,19) (12,29) (12,27) (13,14) (13,17) (13,24) (13,16) (13,15) (13,19) (13,29) (13,30) (13,27) (14,17) (14,25) (14,21) (14,18) (14,19) (14,26) (14,29) (14,27) (14,20) (15,17) (15,24) (15,25) (15,16) (15,18) (15,19) (15,26) (15,29) (15,30) (15,20) (16,17) (16,24) (16,19) (16,26) (16,29) (16,30) (16,27) (16,20) (17,24) (17,21) (17,19) (17,30) (17,27) (18,24) (18,25) (18,21) (18,19) (18,26) (18,29) (18,30) (18,27) (19,25) (19,26) (19,29) (19,27) (19,20) (20,24) (20,25) (20,26) (20,29) (20,30) (20,27) (21,25) (21,26) (21,29) (21,30) (21,27) (24,25) (24,26) (24,29) (24,27) (25,26) (25,30) (25,27) (26,30) (26,27) (27,29) (29,30)\nIs there a path between node 9 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph575-15_27", + "image": "data/connectivity/graph_visual/hard/graph575.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,30) (0,10) (0,23) (0,11) (0,31) (1,28) (1,26) (1,5) (1,20) (1,18) (1,29) (1,8) (1,9) (1,13) (2,3) (2,28) (2,26) (2,15) (2,20) (2,21) (2,12) (2,18) (2,29) (2,8) (2,9) (2,13) (2,16) (3,22) (3,28) (3,15) (3,20) (3,21) (3,12) (3,18) (3,29) (3,8) (3,9) (3,13) (3,16) (4,24) (4,30) (4,10) (4,23) (4,7) (4,17) (4,6) (5,28) (5,26) (5,27) (5,21) (5,12) (5,18) (5,29) (5,8) (5,9) (5,13) (5,16) (6,30) (6,10) (6,23) (6,11) (6,31) (6,7) (6,17) (7,30) (7,10) (7,23) (7,11) (7,31) (8,28) (8,32) (8,26) (8,27) (8,15) (8,18) (8,29) (8,9) (8,16) (9,27) (9,15) (9,21) (9,29) (9,16) (10,24) (10,30) (10,23) (10,11) (10,31) (10,17) (11,30) (11,31) (12,22) (12,32) (12,27) (12,15) (12,20) (12,21) (12,13) (12,16) (13,32) (13,26) (13,15) (13,20) (13,21) (13,29) (13,16) (14,33) (14,19) (15,28) (15,26) (15,27) (15,21) (15,16) (16,22) (16,28) (16,32) (16,26) (16,27) (16,18) (16,29) (17,23) (17,31) (18,22) (18,28) (18,32) (18,26) (18,27) (18,20) (18,21) (19,33) (20,22) (20,28) (20,26) (20,21) (20,29) (21,22) (21,32) (21,26) (21,27) (22,26) (22,27) (23,30) (23,31) (26,27) (26,29) (27,28) (27,32) (27,29)\nIs there a path between node 15 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph104-19_1", + "image": "data/connectivity/graph_visual/hard/graph104.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,27) (0,14) (0,21) (0,10) (0,18) (0,12) (1,20) (1,17) (1,9) (1,4) (1,5) (1,24) (1,3) (1,2) (1,16) (1,13) (2,20) (2,19) (2,6) (2,9) (2,4) (2,5) (2,8) (2,22) (2,24) (2,11) (2,3) (2,16) (2,13) (2,7) (3,20) (3,19) (3,9) (3,4) (3,5) (3,8) (3,24) (3,16) (3,13) (3,7) (4,19) (4,17) (4,6) (4,9) (4,5) (4,8) (4,22) (4,11) (4,16) (4,13) (4,7) (5,20) (5,19) (5,17) (5,6) (5,9) (5,8) (5,22) (5,24) (5,11) (5,13) (6,20) (6,19) (6,17) (6,9) (6,22) (6,24) (6,16) (6,7) (7,19) (7,17) (7,9) (7,8) (7,22) (7,24) (7,11) (7,13) (8,20) (8,17) (8,9) (8,24) (8,11) (8,16) (8,13) (9,20) (9,19) (9,24) (9,11) (9,13) (10,25) (10,15) (10,26) (10,27) (10,14) (10,21) (10,23) (10,12) (11,20) (11,17) (11,22) (11,24) (11,13) (12,15) (12,14) (12,18) (13,20) (13,17) (13,22) (13,24) (13,16) (14,25) (14,15) (14,26) (14,27) (14,23) (15,25) (15,26) (15,21) (15,18) (16,20) (16,22) (16,24) (17,20) (17,19) (18,25) (18,26) (18,27) (18,21) (18,23) (19,24) (20,22) (21,25) (21,27) (23,25) (23,26) (25,26) (25,27) (26,27)\nIs there a path between node 19 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph125-15_27", + "image": "data/connectivity/graph_visual/hard/graph125.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,4) (0,8) (0,14) (0,20) (0,23) (0,16) (0,3) (0,11) (0,12) (0,15) (0,13) (0,25) (1,22) (1,6) (1,10) (1,7) (2,26) (2,19) (2,9) (2,24) (3,4) (3,18) (3,8) (3,20) (3,11) (3,15) (3,25) (4,18) (4,8) (4,20) (4,23) (4,16) (4,11) (4,15) (4,25) (5,22) (6,22) (6,17) (6,7) (7,22) (7,10) (8,18) (8,14) (8,20) (8,23) (8,16) (8,12) (8,15) (8,13) (8,25) (9,21) (9,27) (9,26) (9,24) (11,20) (11,15) (11,25) (12,14) (12,20) (12,23) (12,15) (12,13) (12,25) (13,18) (13,14) (13,20) (13,23) (13,16) (13,25) (14,18) (14,20) (14,16) (14,15) (14,25) (15,18) (15,20) (15,23) (15,25) (16,20) (16,23) (17,22) (18,20) (18,25) (19,21) (19,27) (19,26) (19,24) (20,23) (20,25) (21,27) (21,24) (24,27) (24,26)\nIs there a path between node 15 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph453-13_25", + "image": "data/connectivity/graph_visual/hard/graph453.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,18) (0,26) (0,7) (0,3) (0,13) (0,11) (0,19) (1,8) (1,12) (1,23) (1,24) (1,15) (1,6) (2,4) (2,15) (2,6) (3,28) (3,11) (3,19) (4,8) (4,5) (4,15) (4,6) (5,32) (5,8) (5,30) (5,27) (5,12) (5,23) (6,32) (6,23) (7,31) (7,19) (8,23) (8,15) (9,22) (10,25) (10,13) (10,11) (11,14) (11,26) (12,29) (13,28) (13,31) (13,19) (14,18) (15,29) (15,27) (15,24) (16,18) (18,28) (19,26) (23,30) (24,27) (25,28) (26,28)\nIs there a path between node 13 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph600-8_0", + "image": "data/connectivity/graph_visual/hard/graph600.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,29) (0,1) (0,9) (0,20) (0,34) (0,7) (0,19) (0,22) (0,31) (1,11) (1,30) (1,6) (1,21) (1,14) (1,28) (1,19) (1,31) (1,4) (2,3) (2,11) (2,18) (2,21) (2,20) (2,14) (2,7) (2,17) (3,11) (3,33) (3,15) (3,30) (3,18) (3,21) (3,14) (3,5) (4,10) (4,26) (4,27) (4,21) (4,34) (5,9) (5,27) (5,30) (5,6) (5,24) (5,14) (5,34) (5,28) (5,17) (6,11) (6,25) (6,10) (6,26) (6,29) (6,15) (6,16) (6,14) (6,7) (6,12) (6,22) (7,10) (7,26) (7,27) (7,18) (7,24) (7,8) (7,31) (8,11) (8,33) (8,9) (8,30) (8,24) (8,20) (8,16) (8,22) (8,17) (9,10) (9,20) (9,16) (9,14) (10,25) (10,33) (10,30) (10,18) (10,24) (10,20) (10,31) (11,15) (11,12) (11,19) (11,17) (12,25) (12,29) (12,27) (12,30) (12,34) (12,28) (12,17) (14,25) (14,33) (14,26) (14,29) (14,30) (14,21) (14,17) (15,20) (15,17) (16,21) (16,28) (16,19) (16,22) (17,27) (17,30) (17,24) (17,19) (18,26) (18,21) (18,28) (19,33) (19,27) (19,34) (19,22) (20,25) (20,26) (20,27) (20,21) (20,28) (20,31) (21,22) (22,24) (22,31) (24,34) (24,28) (25,26) (25,29) (25,27) (26,33) (26,27) (26,30) (27,30) (27,28) (28,31) (29,30) (29,34) (29,31) (30,33) (30,34) (31,33) (31,34)\nIs there a path between node 8 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph233-2_15", + "image": "data/connectivity/graph_visual/hard/graph233.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,8) (0,16) (0,2) (0,21) (0,12) (0,22) (0,14) (0,1) (0,5) (0,27) (0,10) (0,23) (0,20) (1,8) (1,18) (1,26) (1,21) (1,22) (1,14) (1,6) (1,27) (1,3) (1,15) (1,10) (1,7) (1,23) (1,20) (2,18) (2,26) (2,21) (2,22) (2,14) (2,6) (2,3) (2,15) (2,10) (2,13) (2,7) (2,23) (2,20) (3,21) (3,14) (3,6) (3,15) (3,13) (3,7) (3,23) (4,11) (4,17) (4,9) (4,19) (5,8) (5,16) (5,21) (5,12) (5,14) (5,6) (5,15) (5,10) (5,13) (5,7) (6,16) (6,26) (6,21) (6,12) (6,27) (6,13) (6,7) (6,23) (7,8) (7,16) (7,18) (7,12) (7,22) (7,14) (7,27) (7,15) (7,10) (7,13) (7,23) (7,20) (8,16) (8,18) (8,26) (8,21) (8,22) (8,14) (8,27) (8,15) (8,13) (8,23) (8,20) (9,17) (10,16) (10,18) (10,26) (10,21) (10,12) (10,22) (10,14) (10,23) (10,20) (11,17) (11,28) (11,25) (11,19) (11,29) (12,16) (12,21) (12,22) (12,14) (12,27) (12,15) (12,13) (12,20) (13,16) (13,26) (13,21) (13,22) (13,14) (13,15) (13,23) (13,20) (14,16) (14,26) (14,21) (14,27) (14,15) (15,16) (15,18) (15,26) (15,21) (15,27) (15,23) (16,18) (16,26) (16,21) (16,22) (16,27) (16,20) (17,28) (17,25) (17,19) (17,29) (18,23) (19,28) (19,25) (20,26) (20,21) (20,27) (20,23) (21,26) (21,23) (22,26) (22,27) (23,26) (25,28) (25,29) (26,27) (28,29)\nIs there a path between node 2 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph180-24_7", + "image": "data/connectivity/graph_visual/hard/graph180.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,6) (0,15) (0,9) (0,19) (0,26) (0,21) (0,13) (0,24) (0,11) (0,2) (0,25) (0,3) (0,12) (0,23) (0,27) (0,4) (1,28) (1,16) (1,7) (1,10) (2,8) (2,6) (2,15) (2,26) (2,17) (2,21) (2,13) (2,11) (2,14) (2,18) (2,5) (2,12) (2,4) (3,8) (3,22) (3,6) (3,15) (3,9) (3,19) (3,17) (3,21) (3,24) (3,11) (3,25) (3,14) (3,23) (3,4) (4,22) (4,15) (4,9) (4,19) (4,17) (4,13) (4,24) (4,25) (4,14) (4,18) (4,5) (4,23) (4,27) (5,8) (5,15) (5,9) (5,26) (5,17) (5,13) (5,24) (5,25) (5,12) (5,23) (5,27) (6,15) (6,19) (6,26) (6,17) (6,21) (6,13) (6,14) (6,12) (6,23) (6,27) (7,16) (7,20) (8,22) (8,9) (8,19) (8,17) (8,13) (8,24) (8,14) (8,18) (8,23) (8,27) (9,22) (9,19) (9,17) (9,21) (9,24) (9,11) (9,25) (9,14) (9,18) (9,12) (9,23) (9,27) (10,28) (10,16) (10,20) (11,22) (11,19) (11,26) (11,21) (11,24) (11,14) (11,18) (11,12) (11,23) (11,27) (12,22) (12,19) (12,26) (12,21) (12,13) (12,24) (12,14) (12,18) (12,27) (13,22) (13,15) (13,26) (13,21) (13,25) (13,14) (13,18) (13,27) (14,22) (14,15) (14,19) (14,26) (14,17) (14,21) (14,24) (14,18) (14,23) (14,27) (15,22) (15,19) (15,17) (15,21) (15,24) (15,25) (15,18) (15,27) (16,28) (17,22) (17,26) (17,21) (17,24) (17,25) (17,23) (17,27) (18,19) (18,26) (18,21) (18,23) (18,27) (19,22) (19,24) (20,28) (21,22) (21,26) (21,23) (21,27) (22,26) (22,24) (22,27) (23,26) (23,24) (23,25) (23,27) (24,25) (24,27) (25,26) (26,27)\nIs there a path between node 24 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph702-21_26", + "image": "data/connectivity/graph_visual/hard/graph702.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,12) (0,4) (0,34) (0,32) (0,13) (0,20) (0,11) (0,14) (0,6) (0,3) (1,12) (1,17) (1,33) (1,20) (1,23) (1,11) (1,6) (1,3) (2,31) (2,30) (2,21) (2,27) (2,7) (2,29) (2,15) (2,19) (2,5) (2,9) (2,16) (2,18) (2,24) (2,26) (3,12) (3,33) (3,4) (3,34) (3,32) (3,20) (3,11) (3,6) (4,33) (4,13) (4,14) (5,25) (5,10) (5,21) (5,27) (5,7) (5,29) (5,8) (5,16) (5,18) (5,22) (5,24) (6,34) (6,13) (6,23) (6,11) (6,14) (7,31) (7,25) (7,30) (7,27) (7,29) (7,9) (7,8) (7,18) (7,22) (7,24) (7,26) (8,25) (8,30) (8,21) (8,27) (8,19) (8,9) (8,16) (8,22) (8,28) (8,24) (9,31) (9,25) (9,30) (9,21) (9,27) (9,29) (9,16) (9,22) (9,28) (9,24) (10,31) (10,25) (10,30) (10,21) (10,29) (10,15) (10,19) (10,16) (10,18) (10,22) (10,26) (11,33) (11,34) (11,32) (11,23) (11,14) (12,17) (12,32) (12,23) (12,14) (13,17) (13,33) (13,34) (13,32) (13,20) (13,23) (13,14) (14,17) (14,34) (14,32) (14,20) (15,25) (15,21) (15,29) (15,19) (15,16) (15,18) (15,28) (15,24) (16,31) (16,25) (16,21) (16,27) (16,29) (16,19) (16,22) (16,28) (16,24) (16,26) (17,33) (17,34) (17,32) (17,20) (18,31) (18,25) (18,30) (18,21) (18,27) (18,29) (18,19) (18,22) (18,28) (18,24) (18,26) (19,31) (19,25) (19,21) (19,28) (19,26) (20,33) (20,34) (20,32) (20,23) (21,31) (21,25) (21,30) (21,27) (21,24) (22,31) (22,25) (22,30) (22,27) (22,29) (22,28) (22,24) (22,26) (23,34) (23,32) (24,31) (24,25) (24,30) (24,29) (24,28) (25,31) (25,30) (25,29) (25,28) (25,26) (26,27) (26,29) (26,28) (27,31) (27,29) (27,28) (28,30) (29,31) (29,30) (30,31) (33,34)\nIs there a path between node 21 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph270-10_29", + "image": "data/connectivity/graph_visual/hard/graph270.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,20) (0,14) (0,18) (0,16) (1,27) (1,28) (1,9) (1,22) (1,21) (1,19) (1,10) (1,23) (1,7) (1,2) (2,26) (2,25) (2,6) (2,9) (2,22) (2,21) (2,10) (2,23) (2,7) (2,30) (2,12) (3,5) (3,15) (3,11) (3,29) (3,4) (4,5) (4,15) (4,11) (5,15) (5,24) (5,29) (5,8) (6,25) (6,22) (6,17) (6,21) (6,19) (6,10) (6,23) (6,7) (6,30) (7,26) (7,25) (7,9) (7,22) (7,17) (7,21) (7,19) (7,10) (7,23) (7,12) (8,24) (9,27) (9,26) (9,22) (9,21) (9,19) (9,23) (9,30) (9,12) (10,28) (10,26) (10,22) (10,17) (10,21) (10,23) (10,30) (10,12) (11,15) (11,24) (11,29) (12,27) (12,28) (12,26) (12,25) (12,17) (12,21) (12,19) (12,23) (12,30) (13,14) (13,16) (14,18) (14,16) (15,24) (15,29) (16,20) (16,18) (17,27) (17,26) (17,22) (17,19) (17,30) (18,20) (19,27) (19,26) (19,22) (19,23) (19,30) (21,28) (21,26) (21,25) (21,22) (21,23) (21,30) (22,27) (22,28) (22,25) (22,23) (22,30) (23,27) (23,28) (23,26) (23,25) (23,30) (24,29) (25,26) (26,27) (26,28) (26,30) (27,28) (27,30) (28,30)\nIs there a path between node 10 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph1-12_21", + "image": "data/connectivity/graph_visual/hard/graph1.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,4) (0,8) (0,2) (0,20) (0,16) (0,14) (0,15) (0,7) (1,18) (1,24) (1,22) (1,5) (1,19) (1,11) (1,17) (2,6) (2,4) (2,23) (2,8) (2,20) (2,16) (2,21) (2,14) (2,15) (2,10) (3,6) (3,4) (3,23) (3,8) (3,16) (3,14) (3,25) (3,15) (3,7) (4,6) (4,23) (4,8) (4,20) (4,16) (4,21) (4,14) (4,15) (4,10) (4,7) (5,18) (5,24) (5,22) (5,13) (5,9) (5,11) (5,12) (6,23) (6,8) (6,20) (6,16) (6,14) (6,25) (6,15) (7,23) (7,20) (7,16) (7,21) (7,14) (7,25) (7,15) (7,10) (8,20) (8,16) (8,14) (8,25) (8,15) (9,18) (9,24) (9,22) (9,19) (9,11) (9,17) (9,12) (10,23) (10,20) (10,16) (10,21) (10,14) (10,25) (11,22) (11,19) (11,17) (11,12) (12,18) (12,13) (12,19) (13,18) (13,24) (13,22) (13,17) (14,23) (14,20) (14,16) (14,25) (15,20) (15,16) (15,21) (15,25) (16,23) (16,20) (16,25) (17,18) (17,22) (17,19) (18,24) (18,22) (18,19) (19,24) (19,22) (20,21) (20,25) (21,23) (21,25) (22,24) (23,25)\nIs there a path between node 12 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph593-25_18", + "image": "data/connectivity/graph_visual/hard/graph593.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,3) (0,18) (0,13) (0,17) (0,4) (0,15) (0,28) (0,19) (0,14) (0,31) (0,25) (0,29) (0,30) (0,26) (0,2) (0,23) (0,5) (0,8) (1,3) (1,18) (1,13) (1,17) (1,15) (1,28) (1,19) (1,14) (1,25) (1,2) (1,23) (1,5) (1,8) (2,18) (2,13) (2,17) (2,28) (2,14) (2,29) (2,30) (2,23) (2,5) (2,32) (2,8) (3,13) (3,4) (3,15) (3,28) (3,19) (3,14) (3,31) (3,29) (3,10) (3,30) (3,5) (3,32) (4,18) (4,13) (4,17) (4,15) (4,28) (4,31) (4,25) (4,29) (4,10) (4,30) (4,26) (4,5) (4,22) (4,32) (4,8) (5,13) (5,28) (5,19) (5,14) (5,25) (5,29) (5,10) (5,30) (5,26) (5,23) (5,22) (5,8) (6,16) (6,27) (6,9) (6,21) (6,12) (6,11) (6,20) (7,16) (7,27) (7,33) (7,9) (7,21) (7,12) (7,11) (8,13) (8,17) (8,15) (8,14) (8,25) (8,29) (8,10) (8,30) (8,23) (9,16) (9,27) (9,33) (9,21) (9,12) (9,20) (10,13) (10,17) (10,15) (10,28) (10,14) (10,25) (10,23) (10,22) (10,32) (11,16) (11,27) (11,33) (11,20) (12,16) (12,33) (12,24) (13,18) (13,28) (13,31) (13,25) (13,29) (13,30) (13,26) (13,23) (13,22) (14,18) (14,15) (14,19) (14,31) (14,25) (14,29) (14,23) (14,22) (14,32) (15,18) (15,17) (15,28) (15,31) (15,29) (15,30) (15,26) (15,23) (15,22) (15,32) (16,27) (16,33) (17,18) (17,28) (17,19) (17,31) (17,25) (17,29) (17,26) (17,23) (17,22) (17,32) (18,19) (18,29) (18,22) (19,28) (19,31) (19,25) (19,29) (19,30) (19,26) (19,23) (19,22) (19,32) (20,27) (20,21) (20,24) (21,27) (21,24) (22,28) (22,25) (22,29) (22,30) (22,26) (22,23) (22,32) (23,28) (23,29) (23,30) (23,26) (25,31) (25,26) (26,28) (26,29) (26,30) (27,33) (28,30) (28,32) (29,30) (29,32) (30,31) (30,32) (31,32)\nIs there a path between node 25 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph201-3_27", + "image": "data/connectivity/graph_visual/hard/graph201.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,28) (0,3) (0,20) (0,27) (0,24) (0,12) (0,5) (0,17) (0,26) (0,10) (0,11) (0,7) (0,1) (0,19) (0,9) (0,14) (1,28) (1,16) (1,3) (1,15) (1,20) (1,21) (1,27) (1,24) (1,12) (1,25) (1,5) (1,17) (1,6) (1,26) (1,11) (1,2) (1,19) (1,14) (1,23) (2,28) (2,16) (2,15) (2,20) (2,21) (2,27) (2,24) (2,12) (2,25) (2,5) (2,17) (2,26) (2,10) (2,9) (2,23) (3,28) (3,16) (3,20) (3,27) (3,25) (3,5) (3,6) (3,11) (3,7) (3,9) (3,14) (4,18) (4,29) (4,22) (4,8) (5,16) (5,20) (5,21) (5,27) (5,24) (5,12) (5,25) (5,17) (5,6) (5,26) (5,10) (5,11) (5,19) (5,9) (5,14) (5,23) (6,28) (6,16) (6,15) (6,20) (6,21) (6,27) (6,12) (6,17) (6,26) (6,10) (6,11) (6,7) (6,19) (6,9) (6,23) (7,28) (7,16) (7,20) (7,24) (7,25) (7,17) (7,10) (7,11) (7,19) (7,9) (7,23) (8,18) (8,29) (8,22) (9,15) (9,20) (9,27) (9,24) (9,17) (9,19) (9,14) (9,23) (10,16) (10,15) (10,27) (10,24) (10,12) (10,17) (10,26) (10,11) (10,19) (10,23) (11,28) (11,16) (11,15) (11,20) (11,21) (11,24) (11,25) (11,17) (11,26) (11,14) (11,23) (12,16) (12,15) (12,20) (12,21) (12,27) (12,25) (12,26) (12,19) (12,14) (12,23) (13,18) (14,16) (14,15) (14,20) (14,21) (14,27) (14,25) (14,26) (14,19) (14,23) (15,21) (15,27) (15,24) (15,25) (15,17) (15,26) (15,23) (16,20) (16,27) (16,24) (16,17) (16,19) (16,23) (17,28) (17,20) (17,21) (17,27) (17,24) (17,25) (17,19) (18,29) (18,22) (19,28) (19,20) (19,21) (19,27) (19,24) (19,23) (20,21) (20,27) (20,25) (20,26) (20,23) (21,28) (21,24) (21,25) (21,26) (21,23) (22,29) (23,28) (23,25) (23,26) (24,27) (24,25) (24,26) (25,27) (25,26) (26,28) (26,27) (27,28)\nIs there a path between node 3 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph591-15_17", + "image": "data/connectivity/graph_visual/hard/graph591.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,13) (0,31) (0,32) (0,33) (0,15) (1,5) (1,19) (1,16) (1,18) (1,11) (1,10) (1,9) (1,28) (1,14) (1,3) (1,8) (2,7) (2,5) (2,19) (2,16) (2,29) (2,18) (2,11) (2,25) (2,9) (2,28) (2,14) (2,3) (2,30) (2,8) (2,27) (3,7) (3,5) (3,19) (3,29) (3,18) (3,11) (3,6) (3,10) (3,25) (3,9) (3,28) (3,14) (3,30) (3,8) (4,26) (4,32) (4,17) (4,33) (4,15) (5,7) (5,19) (5,16) (5,18) (5,11) (5,10) (5,14) (5,30) (5,8) (5,27) (6,7) (6,19) (6,16) (6,11) (6,10) (6,25) (6,9) (6,28) (6,14) (6,30) (6,27) (7,16) (7,18) (7,11) (7,10) (7,25) (7,28) (7,14) (7,8) (7,27) (8,19) (8,16) (8,11) (8,10) (8,9) (8,27) (9,19) (9,16) (9,29) (9,11) (9,10) (9,27) (10,29) (10,11) (10,14) (10,30) (10,27) (11,19) (11,18) (11,30) (11,27) (12,24) (12,20) (13,26) (13,32) (13,17) (13,33) (13,15) (14,19) (14,16) (14,29) (14,25) (14,28) (14,30) (14,27) (15,31) (15,26) (15,32) (15,17) (16,19) (16,18) (16,25) (16,27) (17,31) (17,23) (17,26) (17,32) (17,33) (18,19) (18,29) (18,28) (18,30) (18,27) (19,29) (19,25) (19,28) (19,30) (19,27) (20,22) (20,24) (20,21) (21,24) (22,24) (23,31) (23,26) (23,33) (25,29) (25,28) (25,30) (25,27) (26,31) (26,32) (26,33) (27,29) (27,30) (28,29) (28,30) (29,30) (31,32) (32,33)\nIs there a path between node 15 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph25-16_3", + "image": "data/connectivity/graph_visual/hard/graph25.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,7) (0,25) (0,15) (0,16) (0,20) (0,4) (1,7) (1,11) (1,20) (2,23) (2,6) (2,5) (3,25) (3,15) (3,14) (3,19) (3,12) (3,4) (4,17) (4,15) (4,11) (4,22) (4,12) (5,6) (6,13) (7,24) (7,14) (7,19) (7,22) (8,18) (8,13) (8,9) (9,23) (9,10) (11,25) (11,15) (11,16) (11,12) (12,24) (12,25) (12,14) (12,20) (12,22) (13,23) (13,18) (14,22) (15,17) (16,24) (16,25) (16,17) (16,20) (17,24) (20,25) (22,25) (24,25)\nIs there a path between node 16 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph667-0_24", + "image": "data/connectivity/graph_visual/hard/graph667.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,15) (0,11) (1,29) (2,9) (2,22) (2,23) (2,18) (2,33) (2,8) (2,5) (2,17) (3,4) (3,29) (4,24) (4,21) (4,12) (5,13) (5,23) (5,18) (5,16) (5,8) (5,27) (5,17) (6,14) (6,22) (6,7) (6,10) (6,27) (6,28) (6,11) (7,9) (7,34) (7,23) (7,18) (7,33) (7,17) (8,14) (8,22) (8,15) (8,34) (8,32) (8,19) (8,33) (8,30) (8,27) (9,16) (10,22) (10,34) (10,23) (10,32) (10,33) (10,30) (10,11) (11,15) (11,18) (11,16) (11,19) (11,30) (12,24) (12,31) (13,22) (13,32) (13,19) (14,18) (14,32) (14,17) (15,33) (16,26) (17,26) (17,33) (17,27) (18,23) (18,19) (18,30) (18,27) (18,28) (19,27) (20,31) (22,34) (22,32) (22,30) (23,30) (23,27) (23,28) (24,25) (26,27) (27,32) (27,33) (28,34) (29,31) (30,33)\nIs there a path between node 0 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph452-31_24", + "image": "data/connectivity/graph_visual/hard/graph452.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,20) (0,27) (0,5) (0,16) (0,8) (0,30) (0,3) (0,31) (1,7) (1,4) (1,18) (2,17) (2,21) (2,23) (2,26) (2,30) (2,14) (2,11) (2,29) (2,31) (3,19) (3,20) (3,28) (3,16) (3,23) (3,10) (3,26) (3,32) (3,14) (3,6) (3,9) (5,19) (5,20) (5,23) (5,32) (5,29) (6,15) (6,13) (6,26) (6,22) (7,18) (8,15) (8,17) (8,10) (8,26) (8,30) (8,29) (8,31) (9,20) (9,13) (9,23) (9,14) (9,22) (10,15) (10,13) (10,21) (10,25) (10,26) (10,31) (11,15) (11,28) (11,16) (11,17) (11,25) (11,22) (12,24) (13,19) (13,15) (13,27) (13,28) (13,25) (13,26) (14,19) (14,27) (14,32) (14,29) (14,22) (15,27) (15,23) (15,26) (15,32) (16,23) (16,29) (16,22) (16,31) (17,27) (17,21) (19,27) (19,32) (19,31) (21,25) (21,32) (21,29) (21,22) (21,31) (22,23) (22,30) (23,27) (23,28) (25,32) (26,28) (26,29) (28,30) (28,29) (31,32)\nIs there a path between node 31 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph626-7_27", + "image": "data/connectivity/graph_visual/hard/graph626.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,16) (0,33) (0,10) (1,27) (2,15) (2,34) (2,3) (2,23) (3,14) (3,8) (3,34) (3,23) (4,13) (4,9) (4,20) (4,30) (4,29) (4,5) (5,27) (5,30) (5,24) (5,29) (5,7) (6,13) (6,28) (6,24) (6,29) (6,18) (7,28) (7,24) (8,32) (8,31) (9,28) (9,27) (9,24) (9,29) (10,26) (12,15) (12,21) (12,32) (12,23) (13,20) (13,30) (13,29) (13,18) (14,15) (14,23) (14,17) (15,31) (17,32) (18,29) (20,24) (21,32) (21,25) (24,28) (27,28) (28,29)\nIs there a path between node 7 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph689-26_25", + "image": "data/connectivity/graph_visual/hard/graph689.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,17) (0,16) (0,10) (0,7) (1,2) (1,13) (1,7) (2,22) (2,13) (2,17) (2,9) (3,8) (3,31) (3,25) (3,20) (3,21) (3,34) (3,18) (3,23) (3,27) (3,12) (3,28) (3,29) (3,24) (3,5) (3,6) (4,15) (5,8) (5,31) (5,25) (5,21) (5,34) (5,11) (5,18) (5,27) (5,28) (5,29) (5,6) (6,8) (6,31) (6,25) (6,21) (6,26) (6,30) (6,18) (6,23) (6,14) (6,12) (6,33) (6,24) (6,19) (7,22) (7,13) (7,17) (7,16) (7,9) (7,10) (8,21) (8,26) (8,11) (8,18) (8,23) (8,14) (8,27) (8,28) (8,29) (8,19) (9,13) (9,17) (9,10) (10,22) (10,13) (10,17) (10,16) (11,31) (11,25) (11,20) (11,21) (11,26) (11,34) (11,18) (11,23) (11,14) (11,27) (11,12) (11,33) (11,28) (11,29) (11,24) (11,19) (12,31) (12,25) (12,20) (12,21) (12,26) (12,34) (12,30) (12,14) (12,27) (12,28) (13,22) (13,17) (14,31) (14,25) (14,20) (14,21) (14,26) (14,30) (14,18) (14,23) (14,27) (14,28) (14,29) (14,19) (15,32) (16,17) (18,34) (18,30) (18,23) (18,27) (18,33) (18,28) (18,29) (18,24) (18,19) (19,31) (19,20) (19,21) (19,34) (19,30) (19,23) (19,27) (19,33) (19,28) (19,29) (19,24) (20,31) (20,25) (20,21) (20,26) (20,34) (20,23) (20,33) (20,28) (20,24) (21,31) (21,25) (21,34) (21,27) (21,33) (21,29) (21,24) (23,34) (23,27) (23,33) (23,28) (24,31) (24,26) (24,34) (24,30) (24,27) (24,28) (24,29) (25,31) (25,26) (25,34) (25,30) (25,27) (25,33) (25,29) (26,30) (26,27) (26,33) (26,28) (26,29) (27,34) (27,30) (27,33) (27,28) (27,29) (28,31) (28,30) (28,33) (28,29) (29,31) (29,34) (29,33) (30,31) (30,34) (31,33) (33,34)\nIs there a path between node 26 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph518-30_6", + "image": "data/connectivity/graph_visual/hard/graph518.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,7) (0,25) (0,10) (0,9) (0,17) (0,16) (0,1) (0,15) (1,28) (1,8) (1,16) (1,3) (1,29) (1,31) (2,5) (2,4) (3,28) (3,32) (3,15) (3,20) (4,21) (4,14) (5,21) (5,14) (6,7) (6,28) (6,24) (6,19) (6,33) (6,23) (6,8) (6,29) (6,31) (7,25) (7,22) (7,15) (8,28) (8,25) (8,33) (8,10) (8,22) (8,17) (8,23) (8,26) (8,15) (9,28) (9,33) (9,10) (9,32) (9,17) (9,12) (9,29) (10,11) (10,25) (10,18) (10,19) (10,17) (10,26) (10,12) (10,20) (10,29) (10,31) (11,30) (11,20) (12,22) (12,32) (12,15) (12,20) (12,31) (13,14) (15,32) (15,17) (15,29) (16,19) (16,33) (16,17) (16,20) (16,29) (17,25) (17,18) (17,32) (18,33) (18,32) (18,29) (19,28) (19,30) (19,23) (19,29) (19,31) (20,30) (22,28) (22,30) (23,28) (23,25) (23,31) (24,28) (24,30) (25,28) (25,33) (25,29) (28,32) (29,33) (29,31) (31,33)\nIs there a path between node 30 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph397-15_24", + "image": "data/connectivity/graph_visual/hard/graph397.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,27) (0,1) (0,32) (0,9) (1,25) (1,20) (1,23) (1,24) (1,8) (2,25) (2,20) (2,23) (2,16) (2,19) (3,24) (3,32) (3,19) (4,13) (5,13) (5,7) (5,26) (5,29) (5,6) (5,22) (6,28) (7,13) (7,21) (7,22) (7,18) (7,28) (8,24) (8,31) (8,10) (8,9) (9,11) (9,10) (9,32) (9,19) (9,14) (10,24) (10,15) (11,25) (11,20) (11,19) (12,30) (12,20) (12,24) (13,21) (13,29) (13,18) (13,28) (14,20) (14,23) (14,24) (14,27) (14,15) (15,16) (16,27) (16,31) (17,28) (18,21) (18,26) (19,24) (20,30) (20,27) (20,32) (21,28) (24,25) (24,27) (24,31) (24,32) (25,27) (25,31) (27,32)\nIs there a path between node 15 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph472-1_13", + "image": "data/connectivity/graph_visual/hard/graph472.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,23) (0,29) (0,31) (0,6) (0,24) (0,27) (0,20) (0,16) (0,10) (0,25) (0,26) (0,8) (0,9) (0,7) (0,18) (0,1) (1,30) (1,23) (1,15) (1,29) (1,6) (1,24) (1,27) (1,20) (1,5) (1,25) (1,8) (1,12) (1,9) (1,7) (1,21) (2,23) (2,15) (2,29) (2,6) (2,24) (2,27) (2,20) (2,16) (2,5) (2,25) (2,8) (2,12) (2,9) (2,11) (2,7) (2,21) (2,18) (3,30) (3,23) (3,15) (3,29) (3,31) (3,6) (3,24) (3,27) (3,20) (3,16) (3,10) (3,25) (3,26) (3,8) (3,12) (3,11) (3,7) (3,21) (4,28) (4,22) (4,32) (4,13) (4,14) (5,30) (5,29) (5,31) (5,6) (5,20) (5,16) (5,10) (5,8) (5,12) (5,9) (5,7) (5,21) (5,18) (6,23) (6,15) (6,29) (6,31) (6,27) (6,20) (6,10) (6,25) (6,26) (6,12) (6,9) (6,7) (6,21) (6,18) (7,30) (7,23) (7,29) (7,27) (7,20) (7,16) (7,26) (7,9) (7,11) (7,21) (7,18) (8,23) (8,15) (8,29) (8,24) (8,16) (8,10) (8,25) (8,12) (8,9) (8,11) (8,21) (8,18) (9,30) (9,23) (9,15) (9,31) (9,24) (9,27) (9,20) (9,16) (9,10) (9,26) (9,12) (9,11) (9,21) (10,30) (10,15) (10,31) (10,24) (10,27) (10,16) (10,25) (10,26) (10,12) (10,11) (10,21) (10,18) (11,30) (11,15) (11,31) (11,24) (11,26) (11,12) (11,21) (12,15) (12,29) (12,31) (12,24) (12,27) (12,25) (12,21) (12,18) (13,28) (13,22) (13,32) (13,14) (14,28) (14,32) (14,19) (15,30) (15,23) (15,31) (15,24) (15,27) (15,20) (15,16) (15,25) (15,26) (15,21) (16,30) (16,29) (16,24) (16,21) (18,30) (18,23) (18,29) (18,24) (18,27) (18,20) (18,25) (19,28) (19,22) (20,23) (20,29) (20,31) (20,24) (20,25) (20,26) (20,21) (21,30) (21,23) (21,31) (21,24) (21,27) (21,25) (22,28) (22,32) (23,30) (23,29) (23,31) (23,24) (23,25) (23,26) (24,29) (24,31) (24,27) (24,25) (24,26) (25,30) (25,29) (25,31) (25,27) (26,30) (26,29) (26,31) (26,27) (27,30) (27,29) (28,32) (29,31) (30,31)\nIs there a path between node 1 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph594-33_9", + "image": "data/connectivity/graph_visual/hard/graph594.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,6) (0,3) (0,26) (0,7) (0,22) (0,17) (0,18) (0,8) (1,20) (1,33) (1,14) (1,30) (1,25) (1,12) (1,24) (1,19) (1,28) (1,9) (1,32) (1,21) (1,13) (1,2) (1,16) (2,33) (2,14) (2,23) (2,25) (2,27) (2,4) (2,19) (2,28) (2,9) (2,32) (2,21) (2,16) (3,6) (3,5) (3,26) (3,7) (3,11) (3,22) (3,17) (3,31) (3,15) (3,18) (3,29) (3,8) (3,10) (4,33) (4,14) (4,23) (4,30) (4,27) (4,24) (4,28) (4,9) (4,32) (4,21) (4,13) (4,16) (5,6) (5,11) (5,22) (5,17) (5,31) (5,15) (5,18) (5,29) (5,10) (6,26) (6,11) (6,22) (6,17) (6,31) (6,15) (6,8) (6,10) (7,26) (7,11) (7,22) (7,31) (7,15) (7,18) (7,29) (7,8) (8,26) (8,11) (8,22) (8,31) (8,15) (8,10) (9,20) (9,33) (9,14) (9,23) (9,12) (9,27) (9,24) (9,19) (9,21) (9,13) (9,16) (10,11) (10,17) (10,31) (10,15) (10,18) (11,17) (11,31) (11,18) (11,29) (12,20) (12,23) (12,25) (12,27) (12,19) (12,28) (12,32) (12,21) (12,13) (13,33) (13,14) (13,23) (13,30) (13,27) (13,24) (13,19) (13,32) (13,21) (13,16) (14,23) (14,30) (14,27) (14,19) (14,32) (14,16) (15,22) (15,31) (15,18) (15,29) (16,20) (16,23) (16,25) (16,19) (16,28) (16,32) (16,21) (17,26) (17,22) (17,31) (17,18) (17,29) (18,31) (18,29) (19,33) (19,25) (19,27) (19,28) (19,21) (20,33) (20,30) (20,25) (20,28) (20,32) (21,23) (21,30) (21,25) (21,27) (21,24) (22,31) (22,29) (23,30) (23,25) (23,27) (23,24) (23,28) (24,33) (24,27) (24,28) (24,32) (25,30) (25,27) (25,28) (25,32) (26,31) (26,29) (27,32) (28,33) (29,31) (30,32) (32,33)\nIs there a path between node 33 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph292-21_8", + "image": "data/connectivity/graph_visual/hard/graph292.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,29) (0,7) (0,26) (1,20) (1,21) (1,24) (2,13) (3,17) (3,25) (3,26) (4,20) (4,27) (4,24) (5,9) (5,12) (5,8) (6,9) (6,7) (6,26) (6,22) (7,10) (7,9) (7,12) (7,25) (7,22) (8,9) (8,29) (8,22) (9,17) (9,10) (9,25) (10,17) (10,16) (10,29) (10,18) (10,25) (10,22) (11,13) (12,29) (12,26) (13,23) (13,30) (13,28) (13,27) (14,15) (14,19) (15,31) (16,25) (18,26) (18,22) (19,31) (20,27) (20,21) (21,23) (21,30) (21,27) (23,28) (23,27)\nIs there a path between node 21 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph626-24_17", + "image": "data/connectivity/graph_visual/hard/graph626.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,16) (0,33) (0,10) (1,27) (2,15) (2,34) (2,3) (2,23) (3,14) (3,8) (3,34) (3,23) (4,13) (4,9) (4,20) (4,30) (4,29) (4,5) (5,27) (5,30) (5,24) (5,29) (5,7) (6,13) (6,28) (6,24) (6,29) (6,18) (7,28) (7,24) (8,32) (8,31) (9,28) (9,27) (9,24) (9,29) (10,26) (12,15) (12,21) (12,32) (12,23) (13,20) (13,30) (13,29) (13,18) (14,15) (14,23) (14,17) (15,31) (17,32) (18,29) (20,24) (21,32) (21,25) (24,28) (27,28) (28,29)\nIs there a path between node 24 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph139-14_7", + "image": "data/connectivity/graph_visual/hard/graph139.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,9) (2,8) (2,6) (3,10) (3,16) (3,23) (4,28) (4,8) (5,7) (5,13) (5,18) (5,8) (5,6) (6,7) (6,13) (6,24) (6,18) (6,28) (7,13) (7,11) (8,24) (8,28) (8,22) (9,10) (9,16) (9,15) (10,23) (11,24) (11,18) (12,21) (13,28) (13,22) (14,27) (14,20) (15,27) (15,16) (16,19) (17,19) (19,27) (20,27) (22,28) (23,27) (25,26)\nIs there a path between node 14 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph85-13_25", + "image": "data/connectivity/graph_visual/hard/graph85.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,20) (0,15) (0,19) (0,3) (0,5) (1,12) (1,17) (1,6) (1,16) (1,24) (1,13) (1,23) (1,4) (1,11) (1,26) (1,8) (2,17) (2,25) (2,16) (2,10) (2,13) (2,23) (2,21) (2,14) (2,22) (2,26) (2,8) (3,20) (3,19) (4,12) (4,6) (4,25) (4,9) (4,16) (4,24) (4,10) (4,13) (4,21) (4,22) (4,26) (4,8) (5,20) (5,15) (5,19) (5,18) (6,9) (6,10) (6,13) (6,23) (6,14) (6,22) (6,8) (7,12) (7,17) (7,25) (7,9) (7,24) (7,13) (7,21) (7,14) (7,26) (7,8) (8,12) (8,17) (8,25) (8,9) (8,16) (8,24) (8,10) (8,13) (8,23) (8,21) (8,11) (8,22) (8,26) (9,12) (9,17) (9,25) (9,16) (9,24) (9,10) (9,13) (9,23) (9,21) (9,14) (9,22) (9,26) (10,12) (10,17) (10,25) (10,16) (10,24) (10,23) (10,21) (10,22) (10,26) (11,12) (11,17) (11,25) (11,16) (11,23) (11,21) (11,14) (11,22) (12,17) (12,13) (12,23) (12,21) (12,14) (12,22) (13,17) (13,16) (13,21) (13,14) (13,22) (13,26) (14,25) (14,16) (14,23) (14,21) (14,22) (14,26) (15,19) (15,18) (16,17) (16,25) (16,24) (16,23) (16,21) (17,25) (17,23) (17,21) (18,20) (21,25) (21,24) (21,22) (21,26) (22,24) (22,26) (23,26) (24,26)\nIs there a path between node 13 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph110-16_7", + "image": "data/connectivity/graph_visual/hard/graph110.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,1) (0,14) (0,9) (0,27) (1,26) (1,14) (1,4) (1,15) (1,7) (3,22) (4,21) (4,10) (4,11) (4,5) (4,20) (4,24) (4,15) (4,8) (5,18) (5,14) (5,13) (5,12) (5,24) (6,17) (6,27) (6,24) (6,15) (7,21) (7,18) (7,13) (7,23) (7,12) (8,18) (8,13) (8,23) (8,15) (8,25) (9,21) (9,14) (9,20) (10,18) (10,17) (10,20) (11,26) (11,23) (11,19) (11,27) (11,24) (12,18) (12,13) (12,23) (12,19) (12,17) (12,20) (12,25) (13,18) (13,23) (13,27) (14,21) (14,23) (14,19) (14,25) (15,21) (15,23) (15,20) (16,22) (17,21) (18,19) (18,20) (18,27) (18,24) (19,21) (19,20) (19,27) (20,26) (20,21) (20,24) (21,25) (23,25) (24,25) (25,26) (25,27)\nIs there a path between node 16 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph195-18_21", + "image": "data/connectivity/graph_visual/hard/graph195.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,28) (0,13) (0,26) (0,17) (0,6) (0,29) (0,18) (0,27) (1,12) (1,9) (1,20) (1,4) (1,7) (1,22) (1,11) (1,15) (2,12) (2,9) (2,23) (2,20) (2,24) (2,22) (2,11) (2,15) (3,8) (3,28) (3,26) (3,17) (3,6) (3,29) (3,25) (3,18) (3,27) (4,12) (4,9) (4,20) (4,24) (4,22) (4,11) (5,10) (5,21) (6,8) (6,28) (6,13) (6,26) (6,17) (6,25) (6,18) (7,24) (7,22) (7,11) (7,15) (8,13) (8,19) (8,29) (8,25) (8,27) (9,23) (9,20) (9,24) (9,22) (10,16) (10,14) (10,21) (11,12) (11,23) (11,20) (11,24) (12,23) (12,20) (12,24) (13,28) (13,26) (13,17) (13,19) (13,29) (13,25) (13,18) (13,27) (14,16) (15,23) (15,20) (15,24) (15,22) (17,28) (17,26) (17,19) (17,29) (17,25) (17,18) (17,27) (18,28) (18,26) (18,19) (18,25) (18,27) (19,28) (19,26) (19,29) (19,25) (20,23) (20,22) (22,23) (22,24) (23,24) (25,26) (25,29) (25,27) (26,28) (26,29) (27,28)\nIs there a path between node 18 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph345-22_26", + "image": "data/connectivity/graph_visual/hard/graph345.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,30) (0,19) (0,26) (0,8) (0,7) (2,6) (3,15) (3,9) (4,27) (4,17) (5,16) (5,26) (5,21) (7,30) (7,8) (7,21) (7,29) (7,25) (8,11) (8,31) (8,21) (8,29) (9,15) (9,27) (10,11) (10,19) (10,26) (10,21) (11,30) (11,23) (11,31) (11,21) (11,29) (12,15) (12,22) (12,17) (14,17) (15,27) (16,25) (17,22) (17,27) (19,23) (19,29) (21,23) (21,31) (21,25) (23,30) (25,26)\nIs there a path between node 22 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph684-1_23", + "image": "data/connectivity/graph_visual/hard/graph684.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,24) (0,29) (0,23) (0,13) (0,14) (0,33) (0,21) (0,20) (0,19) (0,28) (0,31) (0,27) (0,22) (0,34) (1,11) (1,32) (1,8) (1,7) (1,3) (1,2) (1,9) (2,11) (2,17) (2,32) (2,5) (2,8) (2,7) (2,16) (2,3) (2,9) (2,6) (3,11) (3,17) (3,32) (3,8) (3,16) (3,9) (4,24) (4,10) (4,29) (4,23) (4,13) (4,25) (4,14) (4,33) (4,20) (4,19) (4,31) (4,18) (4,27) (4,22) (4,15) (4,34) (4,26) (4,30) (4,12) (5,17) (5,32) (5,8) (5,7) (5,16) (5,9) (6,11) (6,17) (6,8) (6,7) (6,16) (7,11) (7,32) (7,8) (7,9) (8,11) (8,17) (8,32) (8,16) (8,9) (9,17) (9,32) (9,16) (10,24) (10,13) (10,25) (10,14) (10,33) (10,21) (10,20) (10,19) (10,28) (10,31) (10,27) (10,22) (10,34) (10,26) (11,17) (11,32) (11,16) (12,29) (12,13) (12,14) (12,33) (12,20) (12,28) (12,31) (12,18) (12,27) (12,22) (12,15) (12,34) (12,26) (13,24) (13,29) (13,14) (13,33) (13,21) (13,20) (13,19) (13,28) (13,18) (13,22) (13,26) (13,30) (14,24) (14,25) (14,33) (14,21) (14,20) (14,19) (14,28) (14,31) (14,27) (14,22) (14,15) (14,34) (14,26) (15,24) (15,29) (15,23) (15,21) (15,20) (15,19) (15,28) (15,31) (15,18) (15,27) (15,22) (15,26) (16,17) (17,32) (18,24) (18,29) (18,25) (18,33) (18,21) (18,19) (18,28) (18,31) (18,22) (18,34) (18,26) (18,30) (19,24) (19,23) (19,33) (19,20) (19,28) (19,31) (19,27) (19,34) (19,30) (20,29) (20,23) (20,25) (20,21) (20,28) (20,31) (20,27) (20,22) (20,34) (20,30) (21,29) (21,33) (21,28) (21,27) (21,22) (21,26) (21,30) (22,24) (22,29) (22,23) (22,25) (22,33) (22,28) (22,27) (22,34) (22,26) (23,29) (23,33) (23,27) (23,34) (23,26) (23,30) (24,29) (24,33) (24,28) (24,27) (24,34) (24,30) (25,29) (25,31) (25,27) (25,34) (25,26) (25,30) (26,29) (26,33) (26,31) (26,34) (26,30) (27,33) (27,28) (27,31) (27,34) (28,29) (28,33) (28,31) (28,30) (29,33) (29,31) (29,30) (30,31) (30,34) (31,34) (33,34)\nIs there a path between node 1 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph293-27_20", + "image": "data/connectivity/graph_visual/hard/graph293.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,20) (0,6) (0,21) (0,9) (0,19) (1,3) (1,7) (1,2) (1,5) (1,30) (2,15) (2,25) (2,26) (2,11) (2,31) (2,12) (2,30) (3,28) (3,11) (3,16) (3,5) (4,28) (4,25) (4,7) (4,11) (4,16) (4,31) (5,15) (5,25) (5,7) (6,20) (6,21) (7,25) (7,26) (7,16) (8,28) (8,26) (8,31) (10,15) (11,15) (11,16) (12,28) (12,16) (12,31) (13,20) (14,22) (15,25) (15,16) (16,31) (17,22) (19,20) (19,27) (20,21) (21,27) (21,24) (23,24) (25,29) (25,31) (25,30)\nIs there a path between node 27 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph249-21_27", + "image": "data/connectivity/graph_visual/hard/graph249.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,22) (0,29) (0,21) (0,1) (0,28) (0,15) (0,7) (0,12) (0,10) (0,19) (0,17) (0,8) (0,6) (1,22) (1,9) (1,21) (1,20) (1,18) (1,7) (1,14) (1,19) (1,17) (1,8) (1,2) (1,23) (2,22) (2,9) (2,29) (2,21) (2,18) (2,30) (2,12) (2,5) (2,19) (2,17) (2,25) (2,8) (2,6) (2,23) (3,4) (3,27) (3,11) (3,26) (4,27) (4,11) (4,26) (5,9) (5,21) (5,18) (5,13) (5,28) (5,30) (5,12) (5,10) (5,19) (5,6) (5,23) (6,29) (6,21) (6,20) (6,18) (6,13) (6,15) (6,7) (6,16) (6,30) (6,12) (6,10) (6,8) (6,23) (7,22) (7,9) (7,29) (7,21) (7,18) (7,28) (7,15) (7,30) (7,10) (7,14) (7,19) (7,17) (7,8) (7,23) (8,22) (8,9) (8,29) (8,21) (8,20) (8,18) (8,13) (8,15) (8,16) (8,30) (8,12) (8,10) (8,14) (8,19) (8,23) (9,22) (9,21) (9,20) (9,18) (9,13) (9,28) (9,30) (9,12) (9,10) (9,14) (9,19) (9,17) (9,25) (10,22) (10,21) (10,20) (10,18) (10,13) (10,28) (10,15) (10,25) (10,23) (11,27) (11,26) (12,22) (12,29) (12,21) (12,28) (12,15) (12,30) (12,19) (12,17) (12,25) (12,23) (13,29) (13,21) (13,20) (13,15) (13,16) (13,14) (13,19) (13,17) (13,25) (13,23) (14,21) (14,28) (14,15) (14,16) (14,30) (14,19) (14,25) (14,23) (15,22) (15,29) (15,20) (15,16) (15,30) (15,19) (15,17) (15,25) (15,23) (16,22) (16,20) (16,18) (16,28) (16,30) (16,19) (16,17) (16,25) (16,23) (17,29) (17,21) (17,18) (17,28) (17,25) (18,22) (18,29) (18,21) (18,20) (18,28) (18,30) (18,19) (18,25) (19,29) (19,20) (19,30) (19,25) (19,23) (20,29) (20,21) (20,28) (20,30) (20,23) (21,22) (21,28) (21,30) (21,25) (21,23) (22,29) (22,28) (22,25) (23,29) (23,28) (25,29) (25,28) (25,30) (26,27) (28,29) (28,30) (29,30)\nIs there a path between node 21 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph374-3_10", + "image": "data/connectivity/graph_visual/hard/graph374.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,25) (0,5) (0,14) (0,10) (0,3) (0,2) (0,18) (1,24) (1,15) (1,12) (2,14) (2,10) (2,3) (2,21) (2,16) (3,25) (3,5) (3,14) (3,10) (3,21) (3,18) (3,16) (4,31) (4,22) (4,20) (4,7) (4,28) (4,30) (4,9) (4,11) (4,17) (4,6) (4,23) (4,26) (5,25) (5,14) (5,10) (5,18) (5,16) (6,7) (6,28) (6,30) (6,9) (6,23) (7,31) (7,22) (7,20) (7,28) (7,19) (7,30) (7,9) (7,11) (7,17) (7,26) (8,29) (9,31) (9,22) (9,20) (9,19) (9,17) (9,23) (9,26) (10,25) (10,14) (10,18) (11,22) (11,20) (11,28) (11,19) (11,30) (11,17) (11,23) (12,27) (12,24) (12,15) (12,13) (13,15) (14,21) (14,18) (14,16) (15,27) (16,21) (16,18) (17,31) (17,20) (17,19) (17,30) (17,26) (18,25) (19,31) (19,22) (19,28) (19,30) (19,23) (20,31) (20,22) (20,28) (20,30) (20,23) (20,26) (22,31) (22,28) (22,23) (23,28) (23,30) (24,27) (26,31) (26,28) (28,31) (28,30) (30,31)\nIs there a path between node 3 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph543-5_6", + "image": "data/connectivity/graph_visual/hard/graph543.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,15) (0,7) (0,17) (0,2) (0,27) (1,3) (1,32) (1,26) (1,30) (1,19) (1,22) (1,4) (1,18) (1,20) (1,31) (1,25) (1,16) (1,13) (1,14) (1,23) (1,24) (2,15) (2,7) (2,17) (2,8) (2,27) (3,32) (3,26) (3,19) (3,6) (3,4) (3,18) (3,20) (3,31) (3,21) (3,16) (3,13) (3,23) (3,5) (3,29) (4,26) (4,30) (4,19) (4,6) (4,10) (4,18) (4,11) (4,20) (4,25) (4,21) (4,13) (4,14) (4,23) (4,12) (4,24) (4,29) (5,32) (5,9) (5,19) (5,6) (5,28) (5,10) (5,11) (5,20) (5,31) (5,25) (5,33) (5,16) (5,13) (5,14) (5,23) (5,24) (5,29) (6,32) (6,26) (6,30) (6,9) (6,19) (6,28) (6,10) (6,18) (6,11) (6,20) (6,31) (6,25) (6,33) (6,21) (6,16) (6,13) (6,14) (6,23) (6,24) (6,29) (7,15) (8,15) (8,27) (9,32) (9,30) (9,19) (9,28) (9,10) (9,18) (9,11) (9,20) (9,31) (9,25) (9,33) (9,16) (9,14) (9,12) (9,29) (10,32) (10,28) (10,18) (10,20) (10,33) (10,21) (10,16) (10,13) (10,23) (10,12) (10,24) (10,29) (11,32) (11,26) (11,30) (11,19) (11,22) (11,20) (11,31) (11,25) (11,33) (11,21) (11,14) (11,24) (11,29) (12,32) (12,26) (12,30) (12,19) (12,22) (12,18) (12,33) (12,21) (12,14) (12,23) (13,32) (13,26) (13,19) (13,22) (13,28) (13,18) (13,20) (13,31) (13,33) (13,23) (13,24) (13,29) (14,32) (14,26) (14,30) (14,19) (14,22) (14,28) (14,18) (14,20) (14,31) (14,25) (14,21) (14,16) (14,23) (15,17) (16,26) (16,19) (16,22) (16,28) (16,25) (16,33) (16,21) (16,29) (18,26) (18,30) (18,19) (18,22) (18,28) (18,31) (18,25) (18,21) (18,23) (18,29) (19,32) (19,26) (19,30) (19,22) (19,28) (19,25) (19,33) (19,23) (19,24) (19,29) (20,32) (20,26) (20,30) (20,22) (20,25) (20,33) (20,29) (21,26) (21,30) (21,22) (21,28) (21,31) (21,25) (21,33) (21,23) (21,29) (22,32) (22,26) (22,28) (22,31) (23,32) (23,31) (23,25) (23,33) (23,24) (23,29) (24,32) (24,26) (24,30) (24,28) (24,25) (24,33) (25,32) (25,26) (25,30) (25,33) (25,29) (26,33) (26,29) (28,30) (28,31) (28,33) (28,29) (29,32) (29,33) (30,33) (31,32) (32,33)\nIs there a path between node 5 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph111-1_13", + "image": "data/connectivity/graph_visual/hard/graph111.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,16) (0,20) (0,1) (0,19) (0,18) (0,7) (0,17) (0,11) (0,13) (0,5) (0,3) (1,16) (1,9) (1,27) (1,19) (1,18) (1,2) (2,20) (2,10) (2,24) (2,23) (3,10) (3,13) (3,12) (4,9) (4,8) (4,14) (4,19) (4,18) (4,7) (4,17) (4,13) (4,5) (4,12) (4,23) (5,16) (5,6) (5,8) (5,19) (5,24) (5,17) (5,26) (6,20) (6,10) (6,18) (6,7) (6,11) (6,25) (7,8) (7,18) (7,17) (8,19) (8,24) (8,11) (8,13) (9,19) (9,11) (9,25) (10,27) (10,19) (10,18) (10,17) (11,14) (11,18) (11,25) (12,16) (12,14) (13,24) (13,25) (14,25) (15,22) (16,19) (16,24) (16,25) (17,19) (17,25) (18,19) (19,20) (24,27)\nIs there a path between node 1 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph194-17_28", + "image": "data/connectivity/graph_visual/hard/graph194.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,12) (0,28) (0,1) (0,22) (0,20) (0,15) (0,18) (0,2) (0,5) (0,10) (0,8) (0,14) (0,6) (1,27) (1,12) (1,19) (1,28) (1,25) (1,29) (1,22) (1,4) (1,7) (1,15) (1,18) (1,3) (1,2) (1,24) (1,5) (1,11) (1,14) (1,13) (1,6) (2,12) (2,19) (2,28) (2,29) (2,4) (2,15) (2,16) (2,18) (2,3) (2,10) (2,13) (2,21) (2,6) (3,27) (3,19) (3,28) (3,20) (3,4) (3,7) (3,16) (3,18) (3,9) (3,24) (3,5) (3,11) (3,10) (3,8) (3,14) (3,23) (3,21) (3,6) (4,27) (4,12) (4,19) (4,28) (4,25) (4,20) (4,7) (4,15) (4,16) (4,5) (4,8) (4,14) (4,13) (4,21) (4,6) (5,27) (5,12) (5,19) (5,28) (5,25) (5,29) (5,22) (5,20) (5,7) (5,15) (5,16) (5,24) (5,11) (5,10) (5,8) (5,14) (5,23) (5,13) (5,21) (5,6) (6,27) (6,12) (6,28) (6,25) (6,29) (6,22) (6,20) (6,7) (6,16) (6,18) (6,9) (6,24) (6,8) (6,14) (6,21) (7,19) (7,25) (7,29) (7,22) (7,20) (7,15) (7,16) (7,24) (7,11) (7,10) (7,14) (7,23) (7,21) (8,27) (8,12) (8,19) (8,29) (8,22) (8,20) (8,15) (8,16) (8,9) (8,24) (8,11) (8,10) (8,14) (8,13) (9,12) (9,19) (9,25) (9,22) (9,20) (9,18) (9,24) (9,11) (9,10) (9,14) (9,23) (9,13) (9,21) (10,27) (10,12) (10,19) (10,28) (10,25) (10,29) (10,16) (10,18) (10,24) (10,14) (10,23) (10,13) (10,21) (11,27) (11,12) (11,25) (11,22) (11,20) (11,18) (11,24) (12,19) (12,28) (12,29) (12,22) (12,15) (12,16) (12,18) (12,14) (12,23) (12,13) (12,21) (13,27) (13,28) (13,25) (13,29) (13,22) (13,20) (13,15) (13,18) (13,24) (14,19) (14,28) (14,25) (14,29) (14,15) (14,16) (14,18) (14,24) (14,23) (15,27) (15,28) (15,25) (15,29) (15,20) (15,18) (15,23) (15,21) (16,27) (16,19) (16,28) (16,25) (16,29) (16,22) (16,20) (16,18) (16,24) (16,21) (18,19) (18,28) (18,29) (18,22) (18,20) (18,24) (18,23) (18,21) (19,27) (19,28) (19,25) (19,29) (19,22) (19,20) (19,24) (19,23) (19,21) (20,27) (20,28) (20,29) (20,22) (20,23) (20,21) (21,27) (21,28) (21,24) (21,23) (22,27) (22,28) (22,29) (22,23) (23,27) (23,28) (23,25) (23,29) (24,27) (24,28) (24,25) (24,29) (25,27) (25,29) (27,28) (27,29)\nIs there a path between node 17 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph637-21_12", + "image": "data/connectivity/graph_visual/hard/graph637.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,24) (0,28) (0,32) (0,1) (0,27) (0,13) (0,9) (1,31) (1,8) (1,15) (1,14) (1,21) (1,28) (1,4) (1,6) (2,3) (2,11) (2,24) (2,31) (2,14) (2,32) (2,4) (2,27) (2,9) (3,22) (3,14) (3,32) (3,20) (3,9) (4,11) (4,24) (4,34) (4,7) (4,19) (4,18) (4,29) (4,28) (4,32) (4,27) (4,13) (5,22) (5,7) (5,18) (5,6) (5,27) (5,13) (6,15) (6,29) (6,27) (6,13) (7,22) (7,33) (7,24) (7,8) (7,19) (7,25) (7,18) (7,30) (7,21) (7,28) (8,11) (8,33) (8,14) (8,25) (8,30) (8,32) (9,27) (9,20) (10,23) (11,22) (11,31) (11,15) (11,19) (11,30) (11,29) (12,17) (13,22) (13,33) (13,19) (13,16) (13,30) (13,21) (13,20) (14,34) (14,30) (15,22) (15,33) (15,24) (15,31) (15,18) (15,30) (15,21) (15,27) (16,24) (16,30) (18,22) (18,33) (18,31) (18,32) (19,22) (19,26) (19,25) (19,28) (19,32) (20,33) (20,24) (20,28) (21,25) (21,30) (21,29) (22,31) (22,28) (22,27) (24,34) (24,31) (24,26) (25,26) (25,29) (25,28) (26,34) (26,30) (26,28) (27,34) (27,28) (28,31) (30,31) (31,34) (32,33) (33,34)\nIs there a path between node 21 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph288-16_13", + "image": "data/connectivity/graph_visual/hard/graph288.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,23) (1,9) (1,11) (1,25) (1,30) (1,15) (1,21) (1,26) (2,16) (2,5) (2,19) (2,25) (2,24) (3,8) (4,27) (4,19) (4,30) (4,15) (4,20) (4,21) (5,27) (5,16) (5,18) (5,19) (5,15) (5,14) (5,31) (6,13) (7,10) (7,23) (8,12) (8,9) (8,28) (8,20) (9,11) (9,20) (9,21) (9,14) (10,29) (11,12) (11,30) (11,20) (11,21) (11,26) (12,19) (12,20) (12,14) (12,26) (13,17) (13,29) (14,28) (14,21) (14,26) (14,24) (15,27) (15,18) (15,21) (16,22) (16,25) (16,26) (16,24) (18,25) (18,31) (19,27) (19,28) (19,21) (20,28) (20,25) (20,30) (20,24) (21,28) (21,30) (21,26) (21,31) (22,27) (22,28) (22,31) (23,29) (24,28) (24,26) (24,31) (25,31) (26,27) (26,31) (27,31) (30,31)\nIs there a path between node 16 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph200-14_29", + "image": "data/connectivity/graph_visual/hard/graph200.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,26) (0,1) (0,17) (0,6) (0,27) (0,11) (0,2) (1,16) (1,26) (1,17) (1,6) (1,27) (1,11) (1,2) (2,17) (2,27) (2,11) (3,5) (3,23) (3,22) (3,4) (4,23) (4,14) (5,23) (5,14) (5,18) (6,16) (6,17) (6,27) (7,8) (7,24) (7,19) (7,10) (7,9) (7,12) (7,21) (7,25) (7,28) (7,15) (8,24) (8,19) (8,10) (8,9) (8,21) (8,13) (8,28) (8,15) (9,24) (9,19) (9,10) (9,20) (9,12) (9,13) (9,29) (9,15) (10,24) (10,19) (10,20) (10,21) (10,25) (10,29) (10,28) (10,15) (11,16) (11,26) (11,27) (12,24) (12,19) (12,20) (12,21) (12,25) (12,29) (12,28) (13,19) (13,20) (13,21) (13,25) (13,28) (13,15) (14,23) (14,18) (15,24) (15,19) (15,25) (15,28) (16,26) (16,17) (16,27) (17,27) (18,22) (19,24) (19,20) (19,29) (19,28) (20,24) (20,29) (20,28) (21,24) (21,25) (21,29) (21,28) (22,23) (24,25) (24,29) (24,28) (25,28) (26,27) (28,29)\nIs there a path between node 14 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph135-2_10", + "image": "data/connectivity/graph_visual/hard/graph135.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,10) (0,7) (0,5) (0,3) (0,6) (0,27) (0,16) (0,8) (0,19) (0,24) (0,22) (0,21) (0,17) (0,20) (0,1) (0,25) (1,23) (1,3) (1,6) (1,26) (1,27) (1,16) (1,8) (1,19) (1,4) (1,22) (1,21) (1,17) (1,25) (2,13) (2,11) (3,10) (3,7) (3,5) (3,26) (3,16) (3,8) (3,19) (3,24) (3,18) (3,20) (3,15) (3,25) (4,5) (4,6) (4,26) (4,16) (4,8) (4,19) (4,24) (4,22) (4,21) (4,9) (4,17) (4,15) (5,10) (5,7) (5,6) (5,26) (5,27) (5,16) (5,8) (5,19) (5,22) (5,18) (5,21) (5,17) (5,20) (5,25) (6,10) (6,7) (6,23) (6,26) (6,27) (6,16) (6,19) (6,24) (6,22) (6,18) (6,21) (6,9) (6,17) (6,15) (6,25) (7,10) (7,23) (7,26) (7,8) (7,19) (7,24) (7,21) (7,9) (7,17) (7,20) (7,25) (8,10) (8,23) (8,26) (8,27) (8,16) (8,19) (8,24) (8,22) (8,9) (8,15) (9,10) (9,23) (9,27) (9,16) (9,24) (9,22) (9,18) (9,21) (9,17) (9,20) (9,15) (10,23) (10,27) (10,16) (10,24) (10,22) (10,17) (10,25) (11,13) (11,14) (12,13) (12,14) (15,23) (15,27) (15,19) (15,24) (15,22) (15,18) (15,21) (15,20) (15,25) (16,23) (16,27) (16,24) (16,22) (16,18) (16,17) (16,25) (17,23) (17,26) (17,27) (17,19) (17,22) (17,21) (17,20) (17,25) (18,26) (18,27) (18,19) (18,24) (18,22) (19,23) (19,24) (19,21) (19,25) (20,27) (20,24) (20,22) (20,25) (21,23) (21,26) (21,27) (21,24) (21,22) (21,25) (22,23) (22,26) (22,24) (23,26) (23,27) (23,24) (23,25) (24,27) (24,25) (25,27)\nIs there a path between node 2 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph373-28_29", + "image": "data/connectivity/graph_visual/hard/graph373.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,12) (0,14) (0,23) (0,18) (0,24) (0,29) (0,15) (0,9) (0,22) (0,17) (0,4) (0,10) (0,3) (0,16) (0,19) (0,1) (1,18) (1,24) (1,29) (1,22) (1,31) (1,4) (1,10) (1,30) (1,3) (1,5) (1,6) (1,7) (1,19) (1,25) (2,13) (2,20) (2,28) (2,8) (2,27) (2,21) (3,24) (3,29) (3,15) (3,17) (3,4) (3,11) (3,30) (3,6) (3,7) (3,16) (3,19) (4,12) (4,23) (4,24) (4,29) (4,15) (4,22) (4,17) (4,31) (4,11) (4,5) (4,16) (4,25) (5,23) (5,18) (5,15) (5,9) (5,22) (5,17) (5,31) (5,10) (5,11) (5,6) (5,16) (5,19) (5,25) (5,26) (6,23) (6,18) (6,24) (6,29) (6,15) (6,22) (6,17) (6,31) (6,11) (6,30) (6,7) (6,19) (7,14) (7,18) (7,24) (7,29) (7,15) (7,9) (7,10) (7,11) (7,30) (7,16) (7,26) (8,13) (8,20) (8,28) (8,21) (9,12) (9,23) (9,18) (9,24) (9,29) (9,17) (9,31) (9,10) (9,11) (9,30) (9,16) (9,19) (10,12) (10,14) (10,23) (10,18) (10,24) (10,29) (10,15) (10,22) (10,17) (10,31) (10,30) (10,16) (10,19) (10,25) (10,26) (11,14) (11,18) (11,24) (11,15) (11,31) (11,30) (11,19) (11,25) (11,26) (12,14) (12,18) (12,24) (12,29) (12,15) (12,17) (12,31) (12,30) (12,16) (12,19) (12,25) (13,28) (13,27) (13,21) (14,23) (14,24) (14,29) (14,15) (14,22) (14,31) (14,30) (14,16) (14,26) (15,23) (15,18) (15,29) (15,22) (15,17) (15,31) (15,16) (15,26) (16,23) (16,18) (16,24) (16,29) (16,22) (16,17) (16,30) (17,18) (17,24) (17,22) (17,31) (17,30) (17,19) (17,25) (17,26) (18,23) (18,24) (18,22) (19,23) (19,29) (19,22) (19,31) (19,30) (19,25) (20,28) (20,21) (22,23) (22,29) (22,31) (22,30) (22,25) (22,26) (23,24) (23,31) (23,25) (24,31) (24,30) (24,25) (24,26) (25,29) (25,30) (25,26) (26,29) (26,30) (29,30) (30,31)\nIs there a path between node 28 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph247-8_28", + "image": "data/connectivity/graph_visual/hard/graph247.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,12) (0,22) (0,14) (0,30) (0,18) (0,17) (0,16) (0,10) (0,1) (0,11) (0,9) (0,7) (0,21) (0,2) (1,14) (1,30) (1,17) (1,6) (1,29) (1,16) (1,11) (1,9) (1,7) (1,8) (1,2) (2,12) (2,22) (2,14) (2,30) (2,18) (2,17) (2,6) (2,16) (2,10) (2,11) (2,7) (2,21) (3,24) (3,25) (3,5) (3,19) (4,24) (4,28) (4,25) (4,5) (4,19) (4,13) (4,20) (4,26) (5,28) (5,25) (5,19) (5,23) (5,20) (5,26) (6,22) (6,14) (6,17) (6,29) (6,10) (6,11) (6,9) (6,7) (6,8) (7,22) (7,14) (7,30) (7,17) (7,29) (7,9) (7,21) (8,12) (8,22) (8,14) (8,30) (8,18) (8,17) (8,29) (8,10) (9,22) (9,14) (9,18) (9,17) (9,29) (9,10) (9,21) (10,12) (10,22) (10,14) (10,18) (10,29) (10,16) (10,11) (10,21) (11,12) (11,22) (11,14) (11,30) (11,18) (11,16) (11,21) (12,22) (12,14) (12,30) (12,17) (12,29) (12,16) (12,21) (13,24) (13,28) (13,25) (13,19) (13,23) (13,20) (14,22) (14,17) (14,29) (15,27) (15,28) (15,19) (15,20) (15,26) (16,22) (16,30) (16,18) (16,17) (17,22) (17,21) (18,22) (18,30) (18,29) (18,21) (19,24) (19,28) (19,25) (19,23) (19,26) (20,24) (20,27) (20,28) (20,23) (20,26) (21,22) (21,30) (21,29) (22,30) (22,29) (23,24) (23,28) (23,25) (24,28) (24,25) (25,28) (26,27) (26,28)\nIs there a path between node 8 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph257-6_3", + "image": "data/connectivity/graph_visual/hard/graph257.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,10) (0,8) (0,15) (0,12) (0,27) (0,23) (0,29) (1,20) (1,7) (1,27) (1,4) (1,2) (1,3) (1,5) (1,29) (2,15) (2,7) (2,27) (2,17) (2,26) (2,30) (3,27) (3,25) (3,13) (3,26) (3,29) (3,30) (4,7) (4,27) (4,23) (4,5) (4,29) (5,20) (5,8) (5,14) (5,12) (5,26) (5,21) (5,30) (6,16) (6,28) (6,22) (7,8) (7,27) (7,9) (7,17) (7,29) (7,30) (8,20) (8,23) (8,25) (8,13) (8,26) (9,12) (9,27) (10,14) (10,23) (11,24) (11,16) (12,27) (12,13) (13,14) (13,21) (13,29) (14,20) (14,27) (14,23) (15,23) (15,26) (16,24) (16,18) (17,23) (17,26) (18,28) (18,22) (19,22) (21,23) (23,26) (25,27) (25,26) (26,27) (26,29) (27,30)\nIs there a path between node 6 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph601-3_25", + "image": "data/connectivity/graph_visual/hard/graph601.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,25) (0,3) (1,25) (1,29) (2,14) (2,13) (2,20) (2,18) (2,31) (2,9) (2,27) (2,21) (2,12) (2,7) (2,33) (2,11) (2,24) (2,26) (2,30) (3,25) (4,23) (4,22) (4,34) (4,5) (5,23) (5,22) (5,34) (6,14) (6,13) (6,20) (6,18) (6,27) (6,21) (6,12) (6,7) (6,28) (6,24) (6,26) (6,30) (7,14) (7,13) (7,20) (7,31) (7,17) (7,9) (7,27) (7,21) (7,12) (7,10) (7,33) (7,28) (7,30) (8,14) (8,13) (8,31) (8,17) (8,9) (8,27) (8,12) (8,33) (8,11) (8,28) (8,26) (8,30) (9,14) (9,13) (9,20) (9,18) (9,27) (9,21) (9,12) (9,10) (9,33) (9,24) (9,26) (9,19) (9,30) (10,13) (10,20) (10,18) (10,31) (10,17) (10,27) (10,12) (10,33) (10,11) (10,28) (10,24) (11,14) (11,13) (11,20) (11,18) (11,31) (11,12) (11,33) (11,28) (11,24) (11,26) (11,30) (12,14) (12,13) (12,20) (12,18) (12,17) (12,27) (12,21) (12,33) (12,19) (13,14) (13,20) (13,18) (13,31) (13,17) (13,21) (13,28) (13,24) (13,26) (14,18) (14,31) (14,17) (14,27) (14,21) (14,33) (14,26) (15,32) (17,18) (17,31) (17,27) (17,33) (17,28) (17,24) (17,26) (17,19) (17,30) (18,20) (18,31) (18,33) (18,24) (18,26) (18,19) (18,30) (19,31) (19,27) (19,21) (19,33) (19,28) (19,26) (20,31) (20,27) (20,21) (20,33) (20,24) (20,26) (20,30) (21,27) (21,33) (21,28) (21,24) (21,30) (22,23) (22,34) (23,34) (24,33) (24,26) (25,29) (26,31) (26,33) (26,30) (27,31) (27,33) (27,28) (27,30) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nIs there a path between node 3 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph353-26_18", + "image": "data/connectivity/graph_visual/hard/graph353.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,1) (0,17) (0,20) (0,10) (0,24) (1,11) (1,4) (1,30) (1,20) (2,18) (2,29) (2,17) (2,14) (2,31) (2,25) (2,13) (3,21) (3,16) (3,6) (4,11) (4,26) (4,29) (4,30) (4,20) (4,10) (5,6) (5,7) (5,23) (6,16) (6,23) (6,22) (7,21) (7,16) (7,23) (8,29) (8,13) (8,10) (9,29) (9,28) (9,31) (9,10) (9,27) (10,11) (10,18) (10,28) (10,31) (10,15) (11,26) (11,18) (11,25) (11,13) (11,27) (11,15) (12,21) (12,19) (13,18) (13,29) (13,17) (13,28) (13,31) (13,20) (13,24) (14,25) (14,20) (15,18) (15,29) (15,28) (17,28) (18,20) (20,26) (20,29) (20,31) (21,22) (24,26) (24,30) (24,28) (25,28) (26,31) (27,28) (27,31) (28,29) (29,30) (29,31) (30,31)\nIs there a path between node 26 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph196-24_15", + "image": "data/connectivity/graph_visual/hard/graph196.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,29) (0,15) (0,3) (0,14) (0,27) (0,1) (0,25) (0,12) (0,26) (1,22) (1,15) (1,3) (1,14) (1,27) (1,16) (1,5) (1,12) (2,10) (2,23) (3,29) (3,22) (3,15) (3,14) (3,25) (3,5) (3,12) (4,19) (4,11) (4,18) (4,28) (4,17) (5,7) (5,25) (5,16) (5,12) (6,9) (6,18) (6,20) (6,28) (6,13) (7,29) (7,22) (7,15) (7,25) (7,16) (7,26) (8,24) (8,10) (9,21) (9,20) (9,17) (10,23) (11,19) (11,20) (11,28) (12,29) (12,22) (12,14) (12,27) (12,25) (12,26) (13,21) (13,18) (13,17) (14,29) (14,22) (14,15) (14,27) (14,25) (14,16) (14,26) (15,29) (15,25) (15,16) (15,26) (16,29) (16,25) (17,18) (17,28) (18,19) (18,21) (18,20) (19,21) (20,21) (21,28) (22,25) (22,26) (23,24) (25,27) (25,26) (26,29) (26,27) (27,29)\nIs there a path between node 24 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph600-4_23", + "image": "data/connectivity/graph_visual/hard/graph600.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,26) (0,29) (0,1) (0,9) (0,20) (0,34) (0,7) (0,19) (0,22) (0,31) (1,11) (1,30) (1,6) (1,21) (1,14) (1,28) (1,19) (1,31) (1,4) (2,3) (2,11) (2,18) (2,21) (2,20) (2,14) (2,7) (2,17) (3,11) (3,33) (3,15) (3,30) (3,18) (3,21) (3,14) (3,5) (4,10) (4,26) (4,27) (4,21) (4,34) (5,9) (5,27) (5,30) (5,6) (5,24) (5,14) (5,34) (5,28) (5,17) (6,11) (6,25) (6,10) (6,26) (6,29) (6,15) (6,16) (6,14) (6,7) (6,12) (6,22) (7,10) (7,26) (7,27) (7,18) (7,24) (7,8) (7,31) (8,11) (8,33) (8,9) (8,30) (8,24) (8,20) (8,16) (8,22) (8,17) (9,10) (9,20) (9,16) (9,14) (10,25) (10,33) (10,30) (10,18) (10,24) (10,20) (10,31) (11,15) (11,12) (11,19) (11,17) (12,25) (12,29) (12,27) (12,30) (12,34) (12,28) (12,17) (14,25) (14,33) (14,26) (14,29) (14,30) (14,21) (14,17) (15,20) (15,17) (16,21) (16,28) (16,19) (16,22) (17,27) (17,30) (17,24) (17,19) (18,26) (18,21) (18,28) (19,33) (19,27) (19,34) (19,22) (20,25) (20,26) (20,27) (20,21) (20,28) (20,31) (21,22) (22,24) (22,31) (24,34) (24,28) (25,26) (25,29) (25,27) (26,33) (26,27) (26,30) (27,30) (27,28) (28,31) (29,30) (29,34) (29,31) (30,33) (30,34) (31,33) (31,34)\nIs there a path between node 4 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph617-27_23", + "image": "data/connectivity/graph_visual/hard/graph617.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,19) (0,23) (0,18) (0,2) (0,24) (0,14) (0,6) (0,7) (0,33) (0,30) (0,21) (0,11) (0,29) (0,10) (1,25) (1,31) (1,16) (1,34) (1,28) (2,22) (2,23) (2,18) (2,24) (2,32) (2,14) (2,6) (2,33) (2,8) (2,27) (2,21) (2,4) (2,29) (3,9) (3,13) (3,15) (3,5) (3,26) (4,19) (4,23) (4,18) (4,24) (4,12) (4,32) (4,6) (4,7) (4,33) (4,8) (4,27) (4,30) (4,17) (4,10) (5,9) (5,13) (5,15) (5,26) (6,19) (6,12) (6,32) (6,14) (6,33) (6,27) (6,10) (7,22) (7,19) (7,18) (7,24) (7,32) (7,14) (7,27) (7,30) (7,11) (7,10) (8,22) (8,19) (8,23) (8,12) (8,33) (8,30) (8,17) (8,11) (8,29) (8,10) (9,13) (9,15) (9,26) (10,19) (10,18) (10,12) (10,32) (10,33) (10,27) (10,17) (10,11) (10,29) (11,19) (11,23) (11,18) (11,24) (11,32) (11,33) (11,27) (11,21) (11,29) (12,19) (12,23) (12,18) (12,32) (12,14) (12,33) (12,27) (12,30) (12,21) (12,17) (13,26) (14,22) (14,19) (14,23) (14,18) (14,32) (14,30) (14,21) (14,29) (15,26) (16,25) (16,31) (16,34) (16,28) (17,19) (17,23) (17,18) (17,24) (17,33) (17,27) (17,29) (18,22) (18,19) (18,23) (18,33) (18,27) (18,21) (18,29) (19,22) (19,23) (19,33) (19,27) (19,29) (20,25) (20,31) (20,34) (21,22) (21,23) (21,32) (21,33) (21,27) (21,30) (21,29) (22,33) (22,27) (22,30) (23,24) (23,32) (23,33) (23,27) (23,29) (24,32) (24,33) (24,27) (24,30) (24,29) (25,31) (25,34) (27,32) (27,33) (27,29) (29,33) (30,32) (30,33) (31,34) (32,33)\nIs there a path between node 27 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph446-12_31", + "image": "data/connectivity/graph_visual/hard/graph446.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (0,27) (0,21) (0,12) (0,24) (0,16) (0,13) (0,20) (0,23) (0,22) (0,31) (0,29) (1,32) (2,25) (3,5) (3,24) (3,19) (3,13) (3,18) (3,15) (3,10) (3,22) (3,7) (3,17) (4,5) (4,13) (4,18) (4,15) (4,31) (4,17) (4,26) (5,21) (5,14) (5,19) (5,15) (5,22) (5,26) (6,28) (7,19) (7,13) (7,18) (7,10) (7,29) (7,17) (8,12) (8,24) (8,20) (8,18) (8,15) (8,26) (9,27) (9,24) (9,16) (9,13) (9,20) (9,18) (9,10) (9,26) (10,27) (10,12) (10,19) (10,18) (10,15) (10,23) (10,22) (10,11) (10,31) (10,29) (10,30) (11,27) (11,12) (11,24) (11,16) (11,20) (11,18) (11,22) (11,30) (12,18) (12,15) (12,31) (12,29) (12,17) (13,19) (13,16) (13,20) (13,23) (14,21) (14,16) (14,15) (14,30) (15,18) (15,22) (15,30) (15,26) (16,19) (16,29) (16,30) (17,18) (18,24) (18,23) (18,22) (19,20) (19,23) (20,24) (20,22) (21,27) (21,23) (21,30) (22,23) (23,31) (23,26) (24,27) (24,26) (25,28) (29,31)\nIs there a path between node 12 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph607-19_23", + "image": "data/connectivity/graph_visual/hard/graph607.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,8) (0,2) (0,29) (0,27) (0,13) (0,14) (0,6) (0,33) (0,24) (2,8) (2,20) (2,4) (2,16) (2,15) (2,11) (2,24) (2,25) (3,8) (3,22) (3,32) (3,28) (3,10) (3,27) (3,30) (3,13) (3,33) (3,24) (4,8) (4,17) (4,29) (4,10) (4,30) (4,16) (4,26) (4,15) (4,14) (4,33) (6,20) (6,22) (6,32) (6,19) (6,10) (6,13) (6,31) (6,24) (6,25) (8,22) (8,12) (8,27) (8,14) (8,11) (8,25) (9,32) (9,17) (9,30) (9,16) (9,33) (9,24) (9,25) (10,22) (10,26) (10,11) (10,25) (11,20) (11,27) (11,33) (11,25) (12,20) (12,22) (12,32) (12,29) (12,27) (12,14) (12,33) (12,24) (13,26) (13,31) (13,33) (13,24) (13,25) (14,32) (14,19) (14,27) (14,16) (14,15) (15,32) (15,19) (15,16) (15,25) (16,19) (16,17) (16,30) (16,31) (16,24) (16,25) (17,32) (17,28) (17,27) (17,33) (18,34) (19,20) (20,22) (20,30) (22,29) (22,30) (24,27) (24,30) (24,31) (24,33) (25,28) (25,26) (25,31) (26,27) (26,30) (27,28) (27,29) (27,30) (28,31) (28,33) (29,33) (31,32)\nIs there a path between node 19 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph4-6_11", + "image": "data/connectivity/graph_visual/hard/graph4.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,7) (0,23) (0,6) (1,15) (1,3) (2,14) (2,22) (3,14) (3,20) (3,22) (3,15) (4,25) (4,13) (5,20) (6,7) (6,25) (6,13) (7,23) (7,17) (8,25) (8,17) (9,12) (9,20) (9,24) (9,11) (10,16) (10,13) (11,15) (11,19) (12,21) (12,15) (12,24) (12,19) (14,21) (14,22) (14,15) (14,24) (15,21) (16,23) (18,24) (18,19) (19,24) (20,21) (21,22) (21,24)\nIs there a path between node 6 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph648-23_3", + "image": "data/connectivity/graph_visual/hard/graph648.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,1) (0,27) (0,3) (0,2) (1,3) (1,2) (2,27) (3,27) (4,9) (4,7) (4,29) (4,34) (4,31) (4,21) (4,16) (4,17) (4,15) (4,25) (4,18) (4,5) (4,6) (4,20) (4,11) (5,9) (5,7) (5,24) (5,32) (5,23) (5,30) (5,31) (5,16) (5,17) (5,25) (5,26) (5,18) (5,6) (5,13) (5,11) (6,7) (6,29) (6,34) (6,24) (6,32) (6,23) (6,31) (6,21) (6,26) (6,18) (6,20) (6,11) (7,24) (7,32) (7,31) (7,16) (7,17) (7,15) (7,25) (7,12) (7,26) (7,20) (7,13) (7,11) (8,10) (8,14) (8,22) (8,19) (9,29) (9,24) (9,32) (9,23) (9,31) (9,21) (9,16) (9,17) (9,25) (9,12) (9,26) (9,18) (9,20) (9,13) (9,11) (10,33) (10,28) (10,22) (10,19) (11,29) (11,34) (11,24) (11,32) (11,30) (11,31) (11,21) (11,25) (11,12) (11,26) (11,18) (11,13) (12,29) (12,34) (12,24) (12,32) (12,23) (12,15) (12,25) (12,18) (12,20) (12,13) (13,29) (13,34) (13,24) (13,30) (13,17) (13,15) (13,18) (13,20) (14,28) (14,22) (14,19) (15,29) (15,34) (15,24) (15,32) (15,23) (15,21) (15,16) (15,17) (15,25) (15,26) (15,18) (15,20) (16,29) (16,34) (16,24) (16,32) (16,23) (16,30) (16,31) (16,21) (16,25) (16,26) (17,29) (17,34) (17,32) (17,23) (17,30) (17,31) (17,21) (17,26) (17,18) (17,20) (18,24) (18,32) (18,30) (18,31) (18,21) (18,25) (18,20) (19,33) (19,28) (19,22) (20,29) (20,34) (20,30) (20,31) (20,21) (20,25) (20,26) (21,29) (21,34) (21,24) (21,31) (21,25) (21,26) (22,33) (22,28) (23,29) (23,24) (23,32) (23,30) (23,25) (23,26) (24,29) (24,32) (24,31) (24,25) (24,26) (25,34) (25,32) (25,30) (25,26) (26,34) (26,30) (29,32) (29,30) (29,31) (30,32) (31,34) (31,32) (32,34)\nIs there a path between node 23 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph312-7_15", + "image": "data/connectivity/graph_visual/hard/graph312.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,2) (0,19) (1,9) (1,26) (1,15) (1,27) (1,17) (1,4) (2,14) (3,29) (4,24) (4,28) (4,8) (4,27) (4,12) (5,23) (6,24) (6,10) (6,18) (6,17) (6,16) (7,26) (7,10) (7,18) (7,12) (8,15) (8,18) (8,17) (8,12) (8,16) (9,16) (10,20) (10,18) (12,13) (12,20) (12,17) (12,16) (13,24) (13,16) (15,24) (15,26) (15,18) (15,17) (16,28) (16,20) (17,20) (18,28) (18,20) (19,21) (20,24) (22,25) (22,29) (22,30) (27,28) (30,31)\nIs there a path between node 7 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph628-13_2", + "image": "data/connectivity/graph_visual/hard/graph628.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,33) (1,28) (1,34) (2,27) (2,4) (2,15) (2,23) (2,12) (3,33) (3,30) (3,26) (4,27) (4,15) (4,8) (5,26) (6,17) (6,22) (6,23) (6,11) (7,12) (7,32) (8,27) (8,10) (8,15) (8,9) (8,14) (8,20) (9,21) (9,11) (10,23) (10,32) (11,27) (11,15) (11,12) (11,32) (11,20) (12,17) (12,22) (12,32) (14,27) (14,19) (14,20) (15,27) (15,32) (15,21) (16,19) (16,32) (17,32) (18,28) (19,20) (20,22) (21,27) (22,27) (22,29) (22,23) (22,32) (23,27) (24,30) (24,26) (25,33) (27,29) (28,31) (29,32) (30,33)\nIs there a path between node 13 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph86-18_21", + "image": "data/connectivity/graph_visual/hard/graph86.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,25) (0,5) (0,14) (0,24) (1,7) (1,23) (1,18) (1,15) (1,26) (1,9) (1,22) (1,2) (1,3) (2,12) (2,16) (2,7) (2,15) (2,26) (2,9) (2,22) (2,3) (3,12) (3,16) (3,23) (3,8) (3,18) (3,26) (3,9) (3,22) (3,19) (4,10) (4,25) (4,20) (4,11) (4,14) (4,24) (4,13) (5,25) (5,14) (6,10) (6,21) (6,20) (6,13) (7,16) (7,23) (7,15) (7,26) (7,9) (7,22) (7,17) (7,19) (8,12) (8,16) (8,23) (8,18) (8,15) (8,26) (8,9) (8,22) (8,17) (8,19) (9,16) (9,18) (9,15) (9,26) (10,21) (10,20) (10,11) (10,14) (10,13) (11,21) (11,25) (11,20) (11,13) (12,16) (12,23) (12,15) (12,26) (12,22) (12,19) (13,21) (13,25) (13,20) (13,14) (13,24) (14,25) (15,16) (15,23) (15,18) (15,22) (15,17) (16,23) (16,26) (16,17) (16,19) (17,23) (17,18) (17,26) (17,22) (17,19) (18,23) (18,26) (18,22) (19,23) (19,26) (19,22) (20,21) (20,25) (20,24) (21,25) (21,24) (22,23) (22,26) (23,26) (24,25)\nIs there a path between node 18 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph545-0_11", + "image": "data/connectivity/graph_visual/hard/graph545.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,23) (1,15) (1,33) (1,7) (1,12) (1,25) (1,27) (1,17) (1,2) (1,6) (1,31) (1,5) (1,9) (1,13) (2,23) (2,33) (2,7) (2,26) (2,19) (2,8) (2,29) (2,25) (2,27) (2,6) (2,9) (2,13) (3,32) (3,11) (3,24) (3,30) (3,10) (3,16) (4,20) (4,21) (4,32) (4,11) (4,18) (4,24) (4,30) (4,10) (4,16) (5,15) (5,33) (5,7) (5,12) (5,26) (5,14) (5,19) (5,29) (5,17) (5,6) (5,31) (5,9) (5,13) (6,33) (6,7) (6,12) (6,26) (6,14) (6,8) (6,29) (6,27) (6,17) (6,28) (6,31) (6,9) (6,13) (7,23) (7,15) (7,12) (7,26) (7,19) (7,8) (7,25) (7,17) (7,28) (7,31) (7,9) (8,15) (8,33) (8,12) (8,14) (8,19) (8,27) (8,17) (8,13) (9,33) (9,12) (9,19) (9,27) (9,17) (9,28) (9,31) (9,13) (10,20) (10,32) (10,11) (10,18) (10,30) (10,16) (11,20) (11,21) (11,32) (11,22) (11,18) (11,24) (11,30) (12,19) (12,29) (12,13) (13,23) (13,33) (13,14) (13,19) (13,27) (13,17) (13,28) (13,31) (14,23) (14,33) (14,26) (14,19) (14,29) (14,25) (14,17) (14,28) (14,31) (15,23) (15,33) (15,26) (15,29) (15,25) (15,17) (15,28) (15,31) (16,20) (16,22) (16,18) (16,24) (16,30) (17,23) (17,26) (17,19) (17,29) (17,27) (17,28) (17,31) (18,20) (18,21) (18,32) (18,22) (18,30) (19,26) (19,29) (19,25) (19,27) (19,28) (19,31) (20,32) (20,22) (20,24) (21,22) (21,24) (22,24) (23,33) (23,29) (23,27) (23,28) (23,31) (24,32) (24,30) (25,33) (25,26) (25,29) (25,27) (25,28) (25,31) (26,33) (26,29) (26,27) (26,28) (27,33) (27,29) (27,28) (28,33) (28,29) (28,31) (31,33)\nIs there a path between node 0 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph332-25_18", + "image": "data/connectivity/graph_visual/hard/graph332.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,23) (0,2) (0,30) (0,21) (0,10) (0,18) (0,28) (0,12) (0,24) (0,19) (0,3) (0,14) (0,13) (1,26) (1,16) (1,11) (1,20) (1,8) (1,6) (1,25) (2,15) (2,29) (2,23) (2,7) (2,21) (2,10) (2,18) (2,12) (2,24) (2,27) (2,19) (2,14) (2,17) (2,13) (3,29) (3,23) (3,30) (3,7) (3,10) (3,24) (3,27) (3,19) (3,14) (3,31) (3,17) (3,4) (3,13) (4,23) (4,21) (4,10) (4,12) (4,27) (4,19) (4,14) (4,31) (4,17) (4,13) (5,26) (5,16) (5,20) (5,8) (5,6) (5,25) (6,9) (6,16) (6,11) (6,8) (7,29) (7,23) (7,30) (7,21) (7,10) (7,18) (7,28) (7,12) (7,24) (7,27) (7,19) (7,17) (7,22) (7,13) (8,9) (8,26) (8,16) (8,11) (8,20) (8,25) (9,26) (9,11) (9,20) (9,25) (10,15) (10,29) (10,28) (10,12) (10,24) (10,27) (10,31) (10,13) (11,16) (11,20) (11,25) (12,15) (12,29) (12,21) (12,24) (12,27) (12,19) (12,14) (12,31) (12,22) (13,15) (13,23) (13,30) (13,21) (13,18) (13,28) (13,24) (13,27) (13,19) (13,14) (13,22) (14,15) (14,29) (14,30) (14,21) (14,18) (14,24) (14,27) (14,19) (14,31) (14,22) (15,29) (15,23) (15,30) (15,21) (15,24) (15,19) (15,17) (16,26) (16,25) (17,21) (17,18) (17,28) (17,24) (17,27) (17,19) (17,31) (17,22) (18,23) (18,30) (18,21) (18,28) (18,27) (18,19) (18,31) (18,22) (19,23) (19,21) (19,28) (19,24) (19,27) (19,31) (19,22) (20,26) (20,25) (21,29) (21,23) (21,28) (21,24) (21,27) (21,22) (22,29) (22,23) (22,30) (22,24) (22,27) (22,31) (23,28) (23,31) (24,30) (24,27) (24,31) (25,26) (27,29) (27,28) (27,31) (28,29) (28,30) (28,31) (29,30) (29,31)\nIs there a path between node 25 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph364-18_1", + "image": "data/connectivity/graph_visual/hard/graph364.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,15) (0,25) (0,4) (0,27) (0,9) (0,10) (0,1) (0,7) (0,3) (0,31) (0,24) (0,20) (0,23) (1,15) (1,12) (1,25) (1,4) (1,27) (1,9) (1,30) (1,13) (1,8) (1,7) (1,3) (1,2) (1,20) (1,23) (2,15) (2,12) (2,25) (2,26) (2,9) (2,13) (2,8) (2,10) (2,22) (2,7) (2,3) (2,31) (2,19) (2,20) (2,23) (3,4) (3,27) (3,9) (3,13) (3,22) (3,7) (3,16) (3,24) (3,19) (3,20) (3,23) (4,12) (4,25) (4,27) (4,9) (4,13) (4,8) (4,10) (4,22) (4,31) (4,24) (4,23) (5,14) (5,17) (6,18) (6,21) (6,29) (6,28) (7,12) (7,25) (7,26) (7,9) (7,13) (7,8) (7,10) (7,22) (7,31) (7,16) (7,24) (7,19) (7,20) (7,23) (8,15) (8,25) (8,27) (8,30) (8,13) (8,10) (8,24) (8,19) (9,26) (9,27) (9,30) (9,22) (9,16) (9,20) (9,23) (10,12) (10,25) (10,30) (10,13) (10,22) (10,31) (10,24) (10,20) (10,23) (11,18) (11,21) (11,28) (12,25) (12,30) (12,13) (12,31) (12,16) (12,24) (12,20) (13,15) (13,25) (13,26) (13,27) (13,22) (13,24) (13,19) (13,20) (13,23) (14,17) (15,16) (15,19) (16,25) (16,27) (16,30) (16,22) (16,31) (16,19) (16,20) (16,23) (18,29) (19,25) (19,22) (19,31) (19,24) (19,20) (19,23) (20,26) (20,27) (20,30) (20,22) (20,31) (20,24) (20,23) (21,29) (21,28) (22,25) (22,26) (22,27) (22,30) (22,31) (22,24) (22,23) (23,25) (23,27) (23,30) (24,25) (24,26) (24,31) (25,26) (25,27) (25,30) (26,27) (26,30) (27,30) (27,31) (30,31)\nIs there a path between node 18 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph298-1_25", + "image": "data/connectivity/graph_visual/hard/graph298.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,31) (0,27) (0,3) (0,21) (0,19) (0,23) (0,18) (0,29) (0,16) (0,24) (1,25) (1,5) (1,6) (2,12) (2,10) (2,17) (2,13) (3,4) (3,31) (3,27) (3,21) (3,15) (3,23) (3,18) (3,16) (3,24) (4,27) (4,15) (4,23) (4,18) (4,29) (4,22) (4,16) (4,24) (5,25) (5,6) (6,25) (7,20) (7,11) (8,25) (9,12) (9,14) (9,10) (9,17) (9,13) (10,12) (10,14) (10,17) (10,13) (11,26) (11,20) (11,28) (12,17) (13,14) (13,17) (14,17) (15,31) (15,27) (15,21) (15,30) (15,23) (15,29) (15,22) (15,24) (16,27) (16,30) (16,19) (16,23) (16,22) (16,24) (18,31) (18,27) (18,21) (18,30) (18,19) (18,23) (18,22) (19,31) (19,27) (19,21) (19,24) (20,26) (21,27) (21,30) (21,23) (21,29) (21,22) (22,31) (22,27) (22,30) (22,29) (23,31) (23,29) (24,27) (24,29) (26,28) (29,31) (29,30) (30,31)\nIs there a path between node 1 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph655-27_30", + "image": "data/connectivity/graph_visual/hard/graph655.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,9) (0,3) (0,34) (0,12) (0,2) (0,13) (0,24) (0,31) (0,17) (0,6) (1,7) (1,10) (1,20) (1,22) (1,15) (1,16) (2,9) (2,27) (2,11) (2,34) (2,18) (2,31) (2,28) (2,17) (3,9) (3,27) (3,34) (3,21) (3,12) (3,13) (3,24) (3,31) (3,28) (3,17) (4,7) (4,10) (4,20) (4,22) (4,15) (5,7) (5,10) (5,30) (5,20) (5,16) (6,9) (6,34) (6,21) (6,12) (6,13) (6,31) (6,33) (6,17) (7,10) (7,30) (7,15) (7,16) (8,19) (8,29) (8,23) (9,27) (9,11) (9,34) (9,18) (9,13) (9,24) (9,31) (9,33) (9,28) (9,17) (10,30) (10,20) (10,15) (10,16) (11,27) (11,34) (11,21) (11,18) (11,12) (11,24) (11,31) (11,33) (11,28) (11,17) (12,34) (12,21) (12,18) (12,13) (12,24) (12,31) (12,33) (12,28) (12,17) (13,27) (13,34) (13,21) (13,18) (13,24) (13,33) (13,28) (13,17) (14,19) (14,29) (14,23) (14,25) (15,30) (15,20) (15,22) (16,30) (16,20) (16,22) (17,34) (17,21) (17,18) (17,31) (17,33) (17,28) (18,24) (18,33) (18,28) (19,29) (19,32) (19,25) (20,22) (21,27) (21,34) (21,24) (21,31) (21,28) (22,30) (23,26) (23,29) (24,27) (24,34) (24,31) (24,33) (24,28) (25,26) (25,32) (26,29) (26,32) (27,34) (27,31) (27,33) (28,34) (28,31) (29,32) (31,34) (33,34)\nIs there a path between node 27 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph44-12_14", + "image": "data/connectivity/graph_visual/hard/graph44.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,26) (0,15) (0,25) (0,14) (0,7) (0,2) (0,9) (0,5) (1,26) (1,15) (1,25) (1,7) (1,6) (1,2) (1,20) (1,22) (2,25) (2,19) (2,14) (2,4) (3,12) (3,16) (4,15) (4,7) (4,6) (4,8) (5,26) (5,20) (5,8) (5,9) (5,22) (5,13) (6,19) (6,17) (6,7) (6,20) (6,22) (7,19) (7,17) (7,9) (8,19) (9,26) (9,14) (9,24) (11,12) (12,21) (12,18) (12,16) (13,17) (13,22) (14,26) (14,22) (15,19) (15,20) (16,21) (18,23) (19,20) (19,22) (25,26)\nIs there a path between node 12 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph68-10_19", + "image": "data/connectivity/graph_visual/hard/graph68.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,24) (0,11) (0,6) (1,22) (1,26) (1,12) (2,14) (2,11) (2,4) (3,21) (3,11) (3,18) (3,9) (4,17) (4,21) (4,14) (5,7) (5,25) (5,10) (5,20) (6,16) (7,15) (7,26) (8,20) (9,17) (9,23) (9,24) (9,13) (9,11) (9,18) (10,25) (11,14) (12,20) (13,17) (13,21) (13,24) (13,19) (14,18) (15,25) (16,23) (16,21) (18,23) (19,23) (19,24) (20,26) (21,24) (22,25)\nIs there a path between node 10 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph331-1_19", + "image": "data/connectivity/graph_visual/hard/graph331.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,16) (0,12) (0,23) (0,10) (0,31) (0,3) (0,26) (0,22) (0,6) (0,25) (0,14) (0,24) (0,5) (1,29) (1,7) (1,16) (1,27) (1,12) (1,23) (1,31) (1,3) (1,19) (1,15) (1,9) (1,26) (1,6) (1,28) (1,13) (1,14) (1,24) (1,5) (2,20) (2,4) (2,17) (2,21) (2,30) (3,29) (3,7) (3,16) (3,27) (3,23) (3,31) (3,19) (3,15) (3,26) (3,6) (3,25) (3,28) (3,8) (3,13) (3,14) (3,24) (3,5) (4,20) (4,18) (4,30) (5,29) (5,7) (5,27) (5,12) (5,10) (5,9) (5,11) (5,26) (5,6) (5,28) (5,14) (5,24) (6,7) (6,16) (6,27) (6,23) (6,10) (6,15) (6,11) (6,26) (6,22) (6,25) (6,28) (6,13) (6,14) (7,29) (7,12) (7,23) (7,19) (7,15) (7,26) (7,22) (7,13) (7,14) (7,24) (8,29) (8,27) (8,23) (8,10) (8,19) (8,9) (8,11) (8,26) (8,22) (8,25) (8,14) (9,29) (9,12) (9,23) (9,10) (9,31) (9,19) (9,15) (9,22) (9,13) (9,24) (10,27) (10,12) (10,15) (10,11) (10,26) (10,25) (10,28) (10,13) (10,14) (11,29) (11,16) (11,27) (11,12) (11,23) (11,19) (11,15) (11,26) (11,28) (11,14) (11,24) (12,29) (12,23) (12,31) (12,19) (12,26) (12,22) (12,25) (12,28) (12,13) (12,24) (13,29) (13,16) (13,27) (13,31) (13,19) (13,22) (13,28) (13,14) (13,24) (14,29) (14,16) (14,27) (14,23) (14,31) (14,19) (14,26) (14,22) (14,25) (14,28) (14,24) (15,29) (15,16) (15,31) (15,19) (15,26) (15,22) (15,25) (15,28) (15,24) (16,29) (16,31) (16,26) (16,22) (16,25) (16,28) (16,24) (17,20) (17,18) (17,21) (17,30) (18,21) (18,30) (19,29) (19,27) (19,23) (19,22) (19,25) (20,21) (21,30) (22,29) (22,27) (22,23) (22,31) (22,25) (22,28) (22,24) (23,29) (23,27) (23,31) (23,24) (24,29) (24,27) (24,31) (24,26) (24,25) (24,28) (25,29) (25,27) (25,31) (25,28) (26,29) (26,27) (26,31) (27,29) (27,28) (28,29) (29,31)\nIs there a path between node 1 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph159-2_25", + "image": "data/connectivity/graph_visual/hard/graph159.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,2) (0,26) (0,21) (0,9) (0,24) (0,17) (0,22) (1,16) (2,20) (2,11) (2,26) (2,27) (2,21) (2,12) (2,9) (2,23) (2,4) (2,19) (3,25) (4,8) (4,23) (4,17) (4,7) (4,13) (6,16) (7,10) (7,20) (7,12) (7,9) (7,23) (7,17) (7,22) (7,13) (7,19) (8,18) (8,11) (8,9) (8,17) (9,10) (9,11) (9,24) (9,23) (10,20) (10,11) (10,24) (10,13) (11,18) (11,12) (12,20) (12,24) (13,18) (13,20) (13,22) (13,14) (14,20) (14,24) (14,23) (14,19) (15,27) (15,23) (15,19) (17,28) (17,23) (18,21) (18,24) (18,19) (19,22) (20,28) (20,24) (21,28) (21,27) (22,28) (22,27) (23,26) (23,27) (23,24) (24,26) (26,28) (26,27) (27,28)\nIs there a path between node 2 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph615-22_27", + "image": "data/connectivity/graph_visual/hard/graph615.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,29) (0,8) (0,16) (0,1) (0,28) (0,4) (0,33) (0,21) (0,3) (0,18) (0,17) (0,23) (0,14) (0,27) (0,25) (0,30) (0,11) (0,19) (0,7) (0,26) (0,5) (0,12) (1,8) (1,28) (1,33) (1,3) (1,18) (1,17) (1,23) (1,27) (1,25) (1,30) (1,15) (1,32) (1,19) (1,9) (1,5) (1,20) (1,2) (1,12) (1,34) (2,29) (2,24) (2,8) (2,16) (2,4) (2,33) (2,3) (2,18) (2,17) (2,23) (2,27) (2,25) (2,11) (2,15) (2,32) (2,19) (2,9) (2,26) (2,5) (2,12) (2,34) (3,29) (3,24) (3,8) (3,16) (3,28) (3,4) (3,33) (3,18) (3,17) (3,27) (3,30) (3,11) (3,6) (3,32) (3,9) (3,7) (3,12) (4,29) (4,24) (4,16) (4,33) (4,21) (4,18) (4,17) (4,14) (4,27) (4,25) (4,30) (4,11) (4,15) (4,32) (4,31) (4,19) (4,9) (4,7) (4,26) (4,5) (4,12) (5,29) (5,24) (5,8) (5,16) (5,28) (5,33) (5,18) (5,23) (5,14) (5,27) (5,25) (5,30) (5,15) (5,6) (5,31) (5,19) (5,9) (5,7) (5,26) (5,20) (5,12) (6,24) (6,8) (6,16) (6,28) (6,21) (6,17) (6,14) (6,27) (6,11) (6,15) (6,32) (6,19) (6,9) (6,7) (6,26) (6,20) (6,34) (7,24) (7,8) (7,33) (7,21) (7,18) (7,23) (7,14) (7,25) (7,30) (7,11) (7,15) (7,31) (7,9) (7,26) (7,20) (7,12) (7,34) (8,29) (8,24) (8,16) (8,17) (8,23) (8,14) (8,25) (8,30) (8,32) (8,31) (8,9) (8,20) (8,12) (9,29) (9,24) (9,16) (9,28) (9,21) (9,18) (9,17) (9,23) (9,27) (9,25) (9,15) (9,32) (9,31) (9,19) (9,26) (9,20) (9,12) (9,34) (10,13) (11,29) (11,24) (11,28) (11,33) (11,21) (11,18) (11,23) (11,14) (11,27) (11,25) (11,30) (11,32) (11,31) (11,26) (11,12) (11,34) (12,24) (12,16) (12,28) (12,33) (12,21) (12,18) (12,14) (12,27) (12,25) (12,15) (12,32) (12,26) (12,20) (12,34) (14,29) (14,24) (14,16) (14,28) (14,33) (14,21) (14,17) (14,23) (14,27) (14,25) (14,15) (14,31) (14,26) (14,20) (14,34) (15,29) (15,24) (15,28) (15,18) (15,17) (15,23) (15,27) (15,25) (15,30) (15,31) (15,19) (15,26) (15,34) (16,29) (16,24) (16,28) (16,33) (16,17) (16,27) (16,30) (16,31) (16,26) (16,20) (16,34) (17,24) (17,28) (17,33) (17,18) (17,23) (17,27) (17,30) (17,31) (17,19) (17,20) (17,34) (18,29) (18,28) (18,33) (18,21) (18,23) (18,27) (18,25) (18,30) (18,32) (18,31) (18,19) (18,34) (19,33) (19,21) (19,23) (19,27) (19,25) (19,31) (19,26) (19,20) (19,34) (20,21) (20,23) (20,27) (20,25) (20,30) (20,32) (20,26) (20,34) (21,29) (21,24) (21,33) (21,23) (21,31) (23,24) (23,28) (23,27) (23,25) (23,30) (23,32) (23,31) (23,26) (23,34) (24,29) (24,30) (24,32) (24,31) (24,26) (24,34) (25,29) (25,28) (25,33) (25,27) (25,31) (25,34) (26,28) (26,27) (26,32) (26,31) (26,34) (27,29) (27,33) (27,30) (27,32) (27,31) (28,29) (28,33) (28,30) (28,32) (28,31) (28,34) (29,33) (29,30) (29,32) (29,31) (29,34) (30,33) (30,32) (30,31) (30,34) (31,33) (31,34) (32,33) (32,34) (33,34)\nIs there a path between node 22 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph264-5_10", + "image": "data/connectivity/graph_visual/hard/graph264.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,14) (0,8) (0,20) (0,23) (0,29) (0,15) (0,25) (0,24) (0,18) (1,2) (2,21) (3,8) (3,17) (3,20) (3,12) (3,10) (3,5) (4,26) (4,14) (4,22) (4,8) (4,12) (4,7) (4,10) (4,5) (5,22) (5,13) (5,8) (5,19) (5,17) (5,12) (5,6) (5,7) (5,24) (6,26) (6,22) (6,29) (6,24) (7,26) (7,11) (7,17) (7,20) (7,23) (7,15) (7,10) (7,24) (8,11) (8,13) (8,19) (8,17) (8,29) (8,15) (8,10) (8,25) (9,21) (10,26) (10,28) (10,17) (10,15) (10,25) (10,18) (11,22) (11,28) (11,20) (11,12) (11,29) (11,18) (12,14) (12,13) (12,28) (12,15) (12,25) (13,19) (13,25) (13,18) (14,20) (14,15) (14,25) (15,25) (16,30) (16,21) (17,19) (17,23) (17,29) (17,24) (17,18) (18,22) (18,23) (18,29) (18,25) (18,24) (19,24) (20,22) (20,23) (20,25) (22,26) (22,28) (23,24) (24,26) (25,29) (26,29)\nIs there a path between node 5 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph499-24_28", + "image": "data/connectivity/graph_visual/hard/graph499.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,17) (0,31) (0,6) (0,29) (0,16) (2,21) (2,22) (2,5) (2,24) (2,31) (2,18) (3,17) (3,24) (3,27) (3,32) (3,30) (3,31) (3,7) (3,6) (4,13) (4,11) (4,27) (4,32) (4,26) (4,7) (4,18) (4,10) (5,13) (5,11) (5,27) (5,18) (5,6) (6,23) (6,32) (6,7) (6,12) (7,22) (7,27) (7,26) (7,30) (7,9) (8,33) (9,21) (9,22) (9,17) (9,23) (9,12) (9,25) (10,11) (10,17) (10,23) (10,31) (10,20) (10,12) (10,25) (10,29) (11,24) (11,31) (11,20) (11,25) (11,16) (12,24) (12,20) (12,18) (12,29) (13,22) (13,17) (13,24) (15,33) (15,19) (16,22) (16,24) (17,25) (18,21) (18,24) (18,27) (18,30) (19,33) (19,28) (20,22) (20,27) (20,29) (21,31) (22,27) (22,23) (22,32) (22,26) (23,25) (23,29) (24,25) (24,29) (25,29) (26,27) (26,31) (27,32) (28,33)\nIs there a path between node 24 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph43-11_24", + "image": "data/connectivity/graph_visual/hard/graph43.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,15) (0,20) (0,23) (0,5) (0,11) (0,9) (0,21) (0,13) (1,18) (1,22) (1,16) (1,25) (1,17) (1,24) (1,2) (1,14) (1,12) (2,18) (2,19) (2,22) (2,16) (2,25) (2,24) (2,14) (2,12) (2,6) (3,15) (3,20) (3,4) (3,7) (3,5) (3,11) (3,13) (4,15) (4,7) (4,23) (4,11) (4,9) (4,21) (4,13) (5,15) (5,7) (5,23) (5,9) (5,21) (5,13) (6,18) (6,19) (6,10) (6,25) (6,24) (6,8) (6,14) (7,15) (7,11) (7,21) (7,13) (8,18) (8,19) (8,22) (8,10) (8,17) (8,24) (8,14) (8,12) (9,15) (9,20) (9,11) (9,21) (10,18) (10,19) (10,16) (10,25) (10,17) (10,24) (10,12) (11,15) (11,23) (11,13) (12,18) (12,22) (12,16) (12,25) (12,24) (12,14) (13,23) (13,21) (14,18) (14,22) (14,16) (14,25) (14,17) (14,24) (15,20) (15,23) (15,21) (16,18) (16,19) (16,25) (16,17) (16,24) (17,19) (17,22) (18,19) (18,22) (18,24) (19,22) (19,25) (19,24) (20,23) (20,21) (21,23) (22,24) (24,25)\nIs there a path between node 11 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph313-14_11", + "image": "data/connectivity/graph_visual/hard/graph313.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,29) (0,15) (0,4) (1,14) (1,12) (1,13) (2,22) (3,27) (4,5) (4,29) (4,15) (5,9) (5,29) (5,18) (5,7) (5,30) (6,12) (6,10) (7,20) (7,25) (7,9) (7,15) (7,21) (9,20) (9,19) (9,29) (9,21) (11,16) (13,27) (14,28) (15,18) (15,21) (18,30) (19,29) (20,30) (22,26) (22,31) (25,29) (25,30)\nIs there a path between node 14 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph397-20_2", + "image": "data/connectivity/graph_visual/hard/graph397.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (0,27) (0,1) (0,32) (0,9) (1,25) (1,20) (1,23) (1,24) (1,8) (2,25) (2,20) (2,23) (2,16) (2,19) (3,24) (3,32) (3,19) (4,13) (5,13) (5,7) (5,26) (5,29) (5,6) (5,22) (6,28) (7,13) (7,21) (7,22) (7,18) (7,28) (8,24) (8,31) (8,10) (8,9) (9,11) (9,10) (9,32) (9,19) (9,14) (10,24) (10,15) (11,25) (11,20) (11,19) (12,30) (12,20) (12,24) (13,21) (13,29) (13,18) (13,28) (14,20) (14,23) (14,24) (14,27) (14,15) (15,16) (16,27) (16,31) (17,28) (18,21) (18,26) (19,24) (20,30) (20,27) (20,32) (21,28) (24,25) (24,27) (24,31) (24,32) (25,27) (25,31) (27,32)\nIs there a path between node 20 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph465-10_30", + "image": "data/connectivity/graph_visual/hard/graph465.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (1,5) (1,31) (1,4) (1,3) (1,30) (1,13) (2,22) (2,5) (2,31) (2,23) (2,3) (2,20) (2,30) (3,22) (3,31) (3,19) (4,22) (4,5) (4,23) (4,20) (5,7) (5,23) (5,19) (5,6) (6,28) (6,23) (6,19) (7,20) (7,13) (8,24) (8,21) (8,15) (8,25) (8,12) (10,26) (10,15) (10,14) (11,32) (11,27) (11,12) (12,29) (12,17) (13,20) (13,19) (14,21) (14,16) (14,17) (15,21) (15,17) (16,24) (16,32) (16,17) (17,24) (17,29) (19,28) (19,20) (19,30) (20,23) (22,30) (24,32) (24,29) (25,29) (27,29) (28,31) (28,30)\nIs there a path between node 10 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph582-14_11", + "image": "data/connectivity/graph_visual/hard/graph582.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,19) (0,10) (0,22) (0,8) (0,12) (0,9) (0,31) (0,16) (0,32) (0,24) (0,26) (0,15) (0,4) (0,21) (0,18) (0,2) (0,28) (0,1) (0,20) (0,27) (0,29) (0,14) (1,19) (1,23) (1,10) (1,22) (1,7) (1,30) (1,12) (1,9) (1,31) (1,16) (1,26) (1,13) (1,4) (1,21) (1,18) (1,2) (1,20) (1,27) (1,17) (1,29) (1,3) (1,11) (2,19) (2,23) (2,10) (2,22) (2,7) (2,8) (2,12) (2,9) (2,32) (2,24) (2,26) (2,15) (2,13) (2,4) (2,21) (2,18) (2,33) (2,28) (2,20) (2,14) (2,3) (2,11) (3,7) (3,8) (3,9) (3,31) (3,16) (3,24) (3,15) (3,4) (3,21) (3,18) (3,33) (3,28) (3,20) (3,27) (3,14) (3,11) (4,19) (4,23) (4,10) (4,22) (4,7) (4,8) (4,30) (4,12) (4,31) (4,16) (4,24) (4,15) (4,21) (4,18) (4,33) (4,28) (4,20) (4,27) (4,17) (4,14) (4,11) (5,25) (6,25) (7,23) (7,10) (7,22) (7,8) (7,31) (7,16) (7,24) (7,26) (7,13) (7,21) (7,18) (7,33) (7,28) (7,20) (7,17) (7,29) (7,14) (7,11) (8,19) (8,10) (8,22) (8,30) (8,31) (8,16) (8,24) (8,26) (8,15) (8,13) (8,21) (8,18) (8,33) (8,20) (8,17) (8,14) (8,11) (9,19) (9,23) (9,10) (9,30) (9,12) (9,16) (9,32) (9,26) (9,15) (9,21) (9,28) (9,20) (9,17) (9,29) (9,14) (9,11) (10,23) (10,12) (10,31) (10,16) (10,32) (10,24) (10,26) (10,21) (10,33) (10,27) (10,17) (10,14) (10,11) (11,19) (11,23) (11,22) (11,30) (11,12) (11,31) (11,16) (11,24) (11,26) (11,13) (11,21) (11,28) (11,20) (11,27) (12,19) (12,23) (12,22) (12,30) (12,16) (12,32) (12,15) (12,13) (12,21) (12,18) (12,33) (12,28) (12,29) (13,19) (13,30) (13,16) (13,32) (13,26) (13,33) (13,28) (13,29) (13,14) (14,19) (14,23) (14,22) (14,30) (14,24) (14,15) (14,33) (14,27) (14,17) (14,29) (15,19) (15,22) (15,30) (15,31) (15,21) (15,18) (15,27) (15,17) (15,29) (16,19) (16,22) (16,30) (16,32) (16,24) (16,33) (16,28) (16,20) (16,27) (16,17) (16,29) (17,19) (17,22) (17,30) (17,31) (17,32) (17,24) (17,26) (17,21) (17,33) (17,28) (17,20) (17,27) (17,29) (18,23) (18,22) (18,30) (18,32) (18,24) (18,21) (18,33) (18,28) (18,20) (18,27) (19,23) (19,22) (19,30) (19,31) (19,32) (19,24) (19,26) (19,21) (19,33) (19,28) (19,27) (19,29) (20,22) (20,30) (20,31) (20,26) (20,21) (20,33) (20,27) (20,29) (21,23) (21,22) (21,30) (21,31) (21,28) (21,27) (21,29) (22,30) (22,31) (22,24) (22,26) (22,33) (22,27) (23,32) (23,26) (23,28) (23,27) (23,29) (24,32) (24,33) (24,28) (24,27) (24,29) (26,30) (26,31) (26,28) (27,31) (27,32) (27,29) (28,30) (28,31) (28,33) (28,29) (29,30) (29,31) (29,32) (31,33)\nIs there a path between node 14 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph578-18_29", + "image": "data/connectivity/graph_visual/hard/graph578.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,8) (0,3) (0,27) (0,22) (0,26) (0,31) (0,21) (0,20) (0,4) (0,17) (0,11) (0,14) (0,28) (0,33) (1,15) (1,23) (1,9) (1,13) (1,29) (1,12) (1,5) (1,25) (1,18) (2,6) (2,24) (2,27) (2,22) (2,26) (2,21) (2,32) (2,4) (2,17) (2,16) (2,11) (2,14) (2,28) (2,33) (3,6) (3,24) (3,8) (3,19) (3,10) (3,27) (3,22) (3,26) (3,31) (3,20) (3,4) (3,17) (3,14) (3,28) (3,33) (4,6) (4,24) (4,19) (4,10) (4,22) (4,26) (4,20) (4,32) (4,17) (4,11) (4,28) (5,15) (5,23) (5,9) (5,13) (5,30) (5,29) (5,12) (5,18) (6,19) (6,27) (6,22) (6,31) (6,20) (6,32) (6,16) (6,14) (6,28) (6,33) (7,24) (7,8) (7,19) (7,27) (7,22) (7,31) (7,21) (7,20) (7,32) (7,16) (7,11) (7,28) (7,33) (8,24) (8,10) (8,27) (8,22) (8,26) (8,31) (8,21) (8,20) (8,17) (8,11) (8,14) (8,28) (9,15) (9,23) (9,30) (9,29) (9,12) (9,25) (9,18) (10,24) (10,19) (10,26) (10,31) (10,21) (10,20) (10,32) (10,16) (10,11) (10,14) (10,28) (10,33) (11,24) (11,19) (11,27) (11,22) (11,26) (11,21) (11,32) (11,17) (11,16) (11,28) (11,33) (12,15) (12,23) (12,13) (12,30) (12,29) (12,25) (12,18) (13,29) (13,25) (14,24) (14,19) (14,27) (14,22) (14,26) (14,31) (14,21) (14,20) (14,17) (14,16) (14,28) (15,29) (15,25) (15,18) (16,24) (16,19) (16,22) (16,26) (16,21) (16,20) (16,32) (16,33) (17,27) (17,22) (17,31) (17,21) (17,20) (17,32) (17,28) (17,33) (18,23) (18,30) (19,24) (19,27) (19,22) (19,26) (19,31) (19,21) (19,20) (19,32) (19,28) (20,24) (20,27) (20,26) (20,21) (20,32) (20,28) (20,33) (21,27) (21,26) (21,32) (21,28) (21,33) (22,24) (22,27) (22,31) (22,32) (22,28) (22,33) (23,30) (23,29) (23,25) (24,26) (24,31) (24,32) (26,27) (26,32) (26,28) (27,31) (27,32) (27,28) (28,33) (29,30) (32,33)\nIs there a path between node 18 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph260-21_0", + "image": "data/connectivity/graph_visual/hard/graph260.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,18) (0,28) (0,30) (0,24) (0,14) (1,13) (1,12) (2,10) (2,22) (2,12) (3,9) (4,20) (4,6) (4,7) (4,18) (4,30) (4,25) (4,14) (5,21) (5,26) (6,11) (6,15) (6,25) (6,14) (7,20) (7,18) (7,11) (7,28) (7,24) (7,17) (7,15) (7,14) (8,30) (8,24) (8,25) (8,14) (9,26) (11,28) (11,14) (13,16) (13,22) (14,20) (14,28) (14,17) (14,25) (15,25) (16,22) (16,23) (17,28) (17,24) (17,25) (18,19) (19,25) (20,28) (20,30) (20,25) (21,27) (21,26) (22,23) (27,29)\nIs there a path between node 21 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph511-18_3", + "image": "data/connectivity/graph_visual/hard/graph511.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,9) (0,33) (0,13) (0,21) (0,24) (0,14) (0,17) (0,25) (1,11) (1,4) (1,18) (1,19) (1,31) (1,27) (1,15) (2,23) (3,33) (3,13) (3,21) (3,26) (3,14) (3,17) (4,11) (4,18) (4,6) (4,27) (4,7) (4,5) (5,11) (5,18) (5,19) (5,6) (5,31) (5,27) (5,30) (5,7) (6,11) (6,18) (6,31) (6,27) (6,30) (6,7) (7,31) (7,27) (7,15) (7,30) (8,29) (8,32) (8,12) (8,16) (8,22) (8,20) (8,10) (9,33) (9,13) (9,26) (9,24) (9,14) (9,17) (9,25) (10,29) (10,32) (10,12) (10,22) (10,20) (11,18) (11,27) (12,29) (12,32) (12,16) (12,22) (12,20) (13,33) (13,21) (13,26) (13,24) (13,14) (13,17) (13,25) (14,33) (14,21) (14,24) (14,25) (15,31) (15,27) (16,29) (16,32) (16,28) (16,22) (16,20) (17,33) (17,26) (17,24) (17,25) (18,19) (18,31) (18,27) (18,30) (19,31) (19,30) (20,29) (20,32) (20,28) (21,33) (21,24) (22,29) (22,32) (24,26) (24,25) (26,33) (28,29) (28,32) (29,32)\nIs there a path between node 18 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph432-30_31", + "image": "data/connectivity/graph_visual/hard/graph432.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (0,28) (0,2) (0,26) (0,6) (0,8) (0,10) (0,16) (0,5) (0,21) (0,7) (0,24) (0,27) (1,9) (1,15) (1,17) (1,30) (1,3) (1,31) (1,25) (2,23) (2,28) (2,26) (2,6) (2,8) (2,18) (2,10) (2,16) (2,21) (2,7) (2,24) (3,13) (3,9) (3,15) (3,17) (3,12) (3,30) (3,31) (3,25) (4,20) (4,32) (4,29) (4,22) (4,14) (4,11) (5,28) (5,6) (5,18) (5,24) (5,27) (6,23) (6,28) (6,8) (6,18) (6,16) (6,7) (6,24) (6,27) (7,23) (7,28) (7,26) (7,8) (7,10) (7,21) (7,24) (7,27) (8,26) (8,18) (8,16) (8,21) (8,24) (8,27) (9,17) (9,12) (9,30) (9,31) (10,23) (10,26) (10,18) (10,16) (10,21) (11,29) (11,22) (11,14) (12,13) (12,17) (12,30) (12,31) (13,15) (13,17) (13,25) (14,20) (14,32) (14,29) (14,19) (14,22) (15,17) (15,31) (15,25) (16,23) (16,21) (16,24) (17,30) (17,31) (17,25) (18,23) (18,28) (18,26) (18,21) (18,24) (18,27) (19,20) (19,32) (19,29) (19,22) (20,29) (20,22) (21,26) (22,32) (22,29) (23,28) (23,26) (23,27) (24,28) (24,26) (24,27) (25,30) (25,31) (26,27) (27,28) (29,32)\nIs there a path between node 30 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph524-31_28", + "image": "data/connectivity/graph_visual/hard/graph524.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,25) (0,9) (0,32) (0,6) (0,20) (1,16) (1,29) (1,27) (1,18) (1,10) (1,12) (1,6) (2,19) (3,26) (5,16) (5,28) (5,10) (5,7) (6,16) (6,15) (6,18) (6,7) (6,12) (6,20) (7,32) (7,20) (8,11) (9,29) (9,10) (9,12) (9,32) (9,20) (9,23) (10,13) (10,23) (12,28) (12,25) (12,23) (13,18) (13,28) (13,23) (14,24) (14,30) (15,16) (15,23) (16,29) (16,27) (16,28) (16,20) (16,23) (17,19) (17,33) (17,24) (17,30) (17,21) (18,29) (19,22) (19,21) (20,27) (20,25) (21,24) (21,22) (22,24) (23,25) (25,29) (25,27) (25,28) (27,28) (27,32) (28,29)\nIs there a path between node 31 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph208-17_23", + "image": "data/connectivity/graph_visual/hard/graph208.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,25) (0,2) (1,25) (1,8) (1,18) (1,2) (2,25) (3,28) (3,19) (3,26) (4,23) (4,10) (5,14) (6,23) (6,10) (6,9) (7,21) (7,26) (7,15) (8,14) (9,20) (9,23) (9,29) (9,11) (10,29) (10,11) (11,23) (11,29) (11,17) (12,16) (15,27) (15,19) (15,26) (16,19) (16,21) (16,26) (17,29) (19,28) (20,29) (20,22) (21,24) (22,29) (23,29) (24,28) (27,28)\nIs there a path between node 17 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph76-22_20", + "image": "data/connectivity/graph_visual/hard/graph76.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,25) (0,17) (0,1) (0,22) (0,5) (0,26) (0,12) (0,6) (0,11) (0,2) (0,10) (0,9) (0,3) (0,14) (0,4) (0,23) (0,21) (1,17) (1,22) (1,5) (1,26) (1,24) (1,8) (1,16) (1,10) (1,9) (1,3) (1,14) (1,4) (1,23) (2,17) (2,18) (2,24) (2,12) (2,6) (2,11) (2,16) (2,10) (2,15) (2,9) (2,3) (2,14) (2,23) (3,25) (3,22) (3,5) (3,26) (3,24) (3,12) (3,6) (3,8) (3,11) (3,16) (3,10) (3,15) (3,14) (3,4) (3,23) (3,21) (4,25) (4,22) (4,18) (4,26) (4,8) (4,11) (4,16) (4,10) (4,15) (4,14) (4,21) (5,25) (5,22) (5,18) (5,24) (5,12) (5,6) (5,8) (5,11) (5,16) (5,10) (5,15) (5,9) (5,14) (5,23) (5,21) (6,25) (6,17) (6,18) (6,24) (6,8) (6,11) (6,16) (6,15) (6,9) (6,14) (7,13) (7,19) (7,20) (8,22) (8,26) (8,24) (8,12) (8,11) (8,15) (8,9) (9,25) (9,17) (9,22) (9,18) (9,26) (9,24) (9,10) (9,15) (9,14) (9,23) (9,21) (10,25) (10,18) (10,26) (10,11) (10,14) (10,23) (10,21) (11,25) (11,17) (11,22) (11,24) (11,16) (11,15) (11,14) (11,21) (12,18) (12,24) (12,23) (13,20) (14,25) (14,18) (14,26) (14,24) (14,15) (14,23) (14,21) (15,25) (15,17) (15,22) (15,18) (15,24) (15,16) (15,23) (16,17) (16,22) (16,18) (16,26) (17,22) (17,18) (17,24) (17,23) (18,25) (18,22) (18,24) (18,21) (19,20) (21,25) (21,26) (21,24) (21,23) (22,25) (22,23) (23,24) (24,25) (24,26)\nIs there a path between node 22 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph442-9_14", + "image": "data/connectivity/graph_visual/hard/graph442.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,11) (0,32) (0,29) (0,7) (0,15) (1,30) (1,10) (1,8) (2,27) (2,18) (2,20) (2,7) (2,26) (3,14) (3,9) (4,18) (4,11) (4,13) (4,15) (5,30) (5,21) (6,14) (6,21) (6,17) (7,18) (7,22) (7,31) (7,29) (7,26) (8,14) (8,10) (9,21) (10,12) (10,21) (10,17) (11,19) (11,22) (11,28) (11,32) (11,29) (11,15) (11,26) (12,30) (12,21) (13,27) (13,20) (13,28) (13,31) (14,17) (15,20) (15,31) (15,26) (16,27) (16,32) (17,30) (18,27) (18,28) (18,32) (18,26) (18,24) (18,23) (19,27) (19,20) (19,31) (19,29) (19,26) (19,24) (20,25) (20,28) (20,32) (20,26) (22,31) (22,23) (23,27) (23,28) (23,26) (25,26) (26,27) (26,28) (26,29) (28,32) (28,31) (29,31)\nIs there a path between node 9 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph91-12_4", + "image": "data/connectivity/graph_visual/hard/graph91.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,5) (0,3) (0,13) (1,26) (2,19) (3,22) (3,19) (4,9) (4,27) (4,6) (4,23) (5,7) (6,12) (6,27) (6,16) (6,8) (6,11) (7,19) (8,25) (8,24) (8,16) (8,11) (9,27) (9,21) (9,23) (11,25) (11,14) (11,24) (11,12) (11,23) (12,24) (12,27) (15,24) (15,20) (16,21) (16,23) (18,26) (20,25) (20,21) (21,27) (23,25)\nIs there a path between node 12 and node 4 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph590-29_10", + "image": "data/connectivity/graph_visual/hard/graph590.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,7) (0,19) (0,33) (0,32) (0,27) (0,10) (0,9) (0,16) (0,8) (0,25) (0,17) (0,3) (0,13) (0,18) (0,15) (0,2) (0,4) (1,22) (1,30) (1,7) (1,20) (1,6) (1,23) (1,33) (1,32) (1,27) (1,10) (1,9) (1,16) (1,17) (1,21) (1,5) (1,14) (1,2) (1,28) (1,12) (1,4) (2,22) (2,30) (2,7) (2,20) (2,6) (2,19) (2,23) (2,26) (2,27) (2,10) (2,8) (2,25) (2,17) (2,21) (2,13) (2,18) (2,5) (2,14) (2,12) (2,4) (3,7) (3,20) (3,19) (3,23) (3,26) (3,33) (3,24) (3,27) (3,10) (3,16) (3,25) (3,17) (3,21) (3,13) (3,18) (3,29) (3,5) (3,14) (3,15) (3,28) (3,12) (4,22) (4,30) (4,7) (4,20) (4,6) (4,19) (4,23) (4,33) (4,32) (4,24) (4,10) (4,9) (4,16) (4,25) (4,17) (4,21) (4,13) (4,18) (4,29) (4,5) (5,30) (5,7) (5,6) (5,19) (5,23) (5,33) (5,24) (5,9) (5,16) (5,8) (5,13) (5,18) (5,29) (5,14) (5,28) (6,22) (6,7) (6,20) (6,26) (6,32) (6,24) (6,10) (6,8) (6,25) (6,29) (6,14) (6,15) (7,22) (7,30) (7,19) (7,26) (7,32) (7,24) (7,27) (7,10) (7,16) (7,8) (7,25) (7,21) (7,13) (7,18) (7,29) (7,14) (7,12) (8,30) (8,20) (8,23) (8,26) (8,33) (8,32) (8,27) (8,10) (8,9) (8,16) (8,17) (8,21) (8,13) (8,18) (8,29) (8,14) (8,15) (8,28) (8,12) (9,30) (9,20) (9,19) (9,23) (9,26) (9,33) (9,32) (9,24) (9,27) (9,16) (9,25) (9,17) (9,13) (9,29) (9,14) (10,30) (10,20) (10,23) (10,26) (10,32) (10,24) (10,27) (10,16) (10,21) (10,13) (10,18) (10,14) (10,15) (10,12) (12,30) (12,19) (12,23) (12,33) (12,32) (12,16) (12,25) (12,17) (12,21) (12,29) (12,14) (12,15) (12,28) (13,22) (13,20) (13,19) (13,23) (13,26) (13,33) (13,32) (13,24) (13,27) (13,16) (13,17) (13,21) (13,29) (13,14) (13,15) (14,19) (14,23) (14,26) (14,33) (14,32) (14,24) (14,27) (14,16) (14,25) (14,17) (14,21) (14,18) (14,29) (14,15) (15,22) (15,30) (15,20) (15,23) (15,33) (15,24) (15,25) (15,17) (15,21) (16,30) (16,20) (16,19) (16,23) (16,33) (16,27) (16,21) (16,28) (17,22) (17,30) (17,20) (17,19) (17,23) (17,33) (17,32) (17,24) (17,25) (17,21) (17,29) (17,28) (18,22) (18,30) (18,23) (18,26) (18,32) (18,24) (18,27) (18,25) (18,21) (18,28) (19,20) (19,23) (19,33) (19,32) (19,25) (19,21) (19,29) (20,22) (20,30) (20,26) (20,33) (20,32) (20,24) (20,27) (20,25) (20,21) (20,29) (20,28) (21,22) (21,30) (21,26) (21,33) (21,32) (21,24) (21,27) (21,29) (21,28) (22,23) (22,26) (22,33) (22,32) (22,24) (22,27) (22,25) (22,29) (22,28) (23,26) (23,33) (23,27) (23,25) (23,29) (24,30) (24,26) (24,33) (24,32) (24,27) (24,25) (24,29) (25,30) (25,26) (25,33) (25,32) (25,27) (25,29) (25,28) (26,30) (26,33) (26,27) (26,28) (27,30) (27,32) (27,28) (28,30) (28,33) (28,32) (28,29) (29,30) (29,33) (30,33) (30,32)\nIs there a path between node 29 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph387-26_25", + "image": "data/connectivity/graph_visual/hard/graph387.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,27) (0,28) (0,29) (0,22) (0,23) (0,8) (0,19) (0,6) (0,16) (0,7) (0,15) (0,26) (0,1) (1,3) (1,27) (1,20) (1,22) (1,23) (1,8) (1,19) (1,18) (1,6) (1,5) (1,16) (1,10) (1,7) (1,26) (2,31) (2,21) (2,11) (2,17) (2,12) (3,22) (3,8) (3,19) (3,6) (3,16) (3,10) (3,7) (3,15) (4,31) (4,14) (4,11) (4,17) (4,25) (4,24) (4,13) (4,12) (4,30) (5,28) (5,29) (5,23) (5,19) (5,18) (5,10) (5,15) (5,26) (6,27) (6,29) (6,20) (6,23) (6,8) (6,18) (6,16) (6,10) (6,15) (6,26) (7,27) (7,28) (7,20) (7,22) (7,23) (7,8) (7,19) (7,18) (7,16) (7,15) (7,26) (8,27) (8,28) (8,29) (8,20) (8,22) (8,23) (8,18) (8,16) (9,31) (9,21) (9,11) (9,17) (9,25) (9,24) (9,12) (10,27) (10,28) (10,29) (10,20) (10,22) (10,23) (10,19) (10,16) (10,15) (10,26) (11,31) (11,21) (11,25) (11,24) (11,12) (12,31) (12,21) (12,14) (12,17) (12,25) (12,24) (12,30) (13,21) (13,25) (13,24) (13,30) (14,31) (14,17) (14,25) (14,24) (14,30) (15,29) (15,20) (15,22) (15,23) (15,19) (15,18) (15,26) (16,27) (16,28) (16,29) (16,20) (16,22) (16,18) (16,26) (17,31) (17,21) (17,25) (17,24) (17,30) (18,28) (18,29) (18,20) (18,22) (18,19) (19,27) (19,28) (19,29) (19,20) (19,22) (19,23) (19,26) (20,27) (20,28) (20,29) (20,22) (20,23) (21,25) (22,27) (22,28) (22,29) (23,28) (24,25) (24,30) (25,31) (25,30) (26,27) (26,28) (26,29) (27,28) (27,29) (28,29) (30,31)\nIs there a path between node 26 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph240-30_13", + "image": "data/connectivity/graph_visual/hard/graph240.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,13) (0,2) (0,9) (1,5) (1,13) (1,19) (1,16) (1,18) (1,9) (1,7) (1,3) (1,6) (2,30) (2,16) (2,18) (2,4) (2,9) (2,7) (2,14) (3,19) (3,24) (3,17) (3,7) (3,6) (3,23) (4,30) (4,16) (4,6) (5,26) (5,17) (5,14) (6,19) (6,29) (6,16) (6,7) (7,16) (7,24) (8,28) (9,26) (9,13) (9,19) (9,29) (9,25) (9,14) (10,22) (10,11) (10,20) (10,27) (11,27) (11,28) (12,20) (12,21) (13,26) (13,30) (13,29) (13,18) (13,14) (14,29) (14,16) (16,26) (16,17) (16,23) (17,18) (17,23) (18,30) (18,25) (19,29) (19,25) (20,27) (21,22) (21,28) (23,26) (23,30) (24,29) (24,25) (25,30) (26,29) (27,28)\nIs there a path between node 30 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph25-15_22", + "image": "data/connectivity/graph_visual/hard/graph25.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,7) (0,25) (0,15) (0,16) (0,20) (0,4) (1,7) (1,11) (1,20) (2,23) (2,6) (2,5) (3,25) (3,15) (3,14) (3,19) (3,12) (3,4) (4,17) (4,15) (4,11) (4,22) (4,12) (5,6) (6,13) (7,24) (7,14) (7,19) (7,22) (8,18) (8,13) (8,9) (9,23) (9,10) (11,25) (11,15) (11,16) (11,12) (12,24) (12,25) (12,14) (12,20) (12,22) (13,23) (13,18) (14,22) (15,17) (16,24) (16,25) (16,17) (16,20) (17,24) (20,25) (22,25) (24,25)\nIs there a path between node 15 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph395-4_30", + "image": "data/connectivity/graph_visual/hard/graph395.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,24) (0,18) (0,29) (0,9) (0,4) (0,14) (0,3) (0,13) (1,21) (1,24) (1,20) (1,9) (1,3) (2,10) (2,26) (2,28) (3,20) (3,6) (3,8) (3,5) (3,27) (4,21) (4,24) (4,29) (4,6) (4,9) (4,8) (4,17) (4,15) (4,27) (4,32) (4,13) (5,21) (5,16) (5,24) (5,9) (5,27) (6,24) (6,9) (6,17) (6,15) (6,32) (7,31) (8,16) (8,24) (8,11) (8,9) (8,27) (9,21) (9,16) (9,24) (9,11) (9,15) (9,14) (9,13) (11,16) (12,25) (13,16) (13,20) (13,30) (13,27) (14,16) (14,24) (14,18) (14,27) (15,24) (15,18) (15,20) (15,17) (16,21) (16,30) (16,27) (17,21) (17,20) (17,29) (18,20) (18,29) (18,30) (18,27) (19,25) (19,26) (19,22) (20,24) (21,24) (21,29) (22,26) (22,28) (23,25) (24,30) (26,28) (27,32) (29,32)\nIs there a path between node 4 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph232-0_23", + "image": "data/connectivity/graph_visual/hard/graph232.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,20) (0,9) (0,21) (0,1) (0,19) (0,7) (0,3) (0,27) (0,12) (0,23) (0,17) (1,9) (1,21) (1,10) (1,4) (1,19) (1,3) (1,12) (1,23) (1,17) (2,8) (2,28) (2,16) (2,24) (2,5) (2,11) (2,15) (3,20) (3,9) (3,21) (3,19) (3,27) (3,12) (3,23) (4,20) (4,9) (4,21) (4,19) (4,12) (4,23) (4,17) (5,18) (5,28) (5,16) (5,6) (5,14) (6,18) (6,28) (6,24) (7,20) (7,9) (7,12) (7,17) (8,16) (8,24) (8,15) (9,21) (9,10) (9,27) (9,12) (9,23) (9,17) (10,19) (10,27) (10,12) (10,23) (11,28) (11,16) (11,14) (11,24) (11,15) (12,20) (12,19) (12,27) (12,23) (12,17) (13,25) (13,26) (13,29) (14,28) (14,24) (14,15) (15,18) (15,28) (15,24) (16,18) (16,28) (17,20) (17,21) (17,23) (18,28) (18,24) (19,20) (19,21) (19,23) (20,27) (21,27) (22,25) (22,26) (22,29) (25,29) (26,29)\nIs there a path between node 0 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph221-23_17", + "image": "data/connectivity/graph_visual/hard/graph221.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,19) (0,14) (0,22) (0,24) (0,26) (0,8) (0,18) (0,10) (1,15) (1,9) (1,3) (1,20) (1,11) (1,5) (1,4) (1,7) (1,21) (1,12) (1,6) (1,27) (1,29) (1,25) (1,17) (2,19) (2,14) (2,16) (2,22) (2,24) (2,26) (2,8) (2,18) (2,28) (3,15) (3,20) (3,23) (3,11) (3,5) (3,7) (3,21) (3,6) (3,27) (3,29) (3,25) (3,17) (4,15) (4,23) (4,5) (4,7) (4,13) (4,21) (4,12) (4,29) (5,15) (5,23) (5,11) (5,21) (5,6) (5,27) (5,29) (5,25) (5,17) (6,15) (6,20) (6,23) (6,11) (6,13) (6,21) (6,12) (6,29) (6,25) (6,17) (7,15) (7,9) (7,20) (7,23) (7,11) (7,13) (7,21) (7,12) (7,27) (7,25) (7,17) (8,19) (8,14) (8,22) (8,26) (8,18) (8,28) (8,10) (9,20) (9,23) (9,11) (9,13) (9,21) (9,12) (9,27) (9,29) (9,25) (9,17) (10,16) (10,22) (10,24) (10,26) (10,18) (10,28) (11,15) (11,20) (11,23) (11,21) (11,27) (11,29) (12,15) (12,20) (12,13) (12,21) (12,27) (12,29) (12,25) (12,17) (13,15) (13,23) (13,21) (13,29) (13,25) (14,19) (14,16) (14,22) (14,24) (14,26) (14,18) (15,20) (15,23) (15,21) (15,29) (15,17) (16,19) (16,22) (17,20) (17,23) (17,21) (17,29) (17,25) (18,22) (18,24) (18,26) (18,28) (19,22) (19,24) (19,26) (19,28) (20,23) (20,27) (20,29) (21,23) (21,29) (21,25) (22,26) (22,28) (23,29) (24,26) (26,28) (27,29)\nIs there a path between node 23 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph475-4_31", + "image": "data/connectivity/graph_visual/hard/graph475.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,11) (0,23) (0,8) (0,30) (0,7) (0,14) (0,22) (0,1) (0,6) (0,17) (0,24) (0,4) (0,16) (0,13) (0,19) (0,26) (0,31) (0,2) (0,18) (0,5) (1,11) (1,12) (1,23) (1,8) (1,30) (1,7) (1,14) (1,27) (1,6) (1,17) (1,24) (1,4) (1,16) (1,29) (1,13) (1,19) (1,20) (1,26) (1,2) (1,18) (1,5) (2,12) (2,23) (2,8) (2,30) (2,7) (2,14) (2,22) (2,6) (2,17) (2,24) (2,4) (2,16) (2,29) (2,13) (2,19) (2,26) (2,18) (2,5) (3,28) (3,10) (3,15) (3,9) (4,11) (4,23) (4,8) (4,30) (4,7) (4,14) (4,27) (4,24) (4,16) (4,13) (4,19) (4,20) (4,31) (4,18) (4,5) (5,11) (5,12) (5,23) (5,8) (5,30) (5,7) (5,14) (5,27) (5,22) (5,17) (5,24) (5,29) (5,19) (5,20) (5,26) (5,31) (5,18) (6,11) (6,12) (6,23) (6,8) (6,30) (6,7) (6,14) (6,22) (6,17) (6,13) (6,19) (6,20) (6,26) (6,31) (6,18) (7,11) (7,23) (7,8) (7,30) (7,14) (7,27) (7,22) (7,24) (7,29) (7,13) (7,19) (7,20) (8,23) (8,30) (8,14) (8,22) (8,24) (8,16) (8,20) (8,26) (8,31) (8,18) (9,21) (9,25) (9,28) (10,21) (10,32) (10,25) (10,28) (10,15) (11,12) (11,30) (11,14) (11,27) (11,22) (11,17) (11,24) (11,16) (11,29) (11,13) (11,20) (11,26) (11,31) (11,18) (12,23) (12,30) (12,27) (12,22) (12,24) (12,29) (12,13) (12,20) (12,26) (12,31) (12,18) (13,23) (13,30) (13,14) (13,22) (13,17) (13,24) (13,19) (13,20) (13,26) (13,31) (13,18) (14,30) (14,27) (14,22) (14,24) (14,16) (14,29) (14,19) (14,20) (14,26) (14,31) (14,18) (15,21) (15,32) (15,25) (15,28) (16,23) (16,30) (16,22) (16,24) (16,29) (16,20) (16,26) (16,31) (16,18) (17,23) (17,30) (17,27) (17,22) (17,24) (17,29) (17,19) (17,26) (17,18) (18,23) (18,27) (18,24) (18,19) (18,20) (18,26) (19,30) (19,27) (19,29) (19,20) (19,26) (19,31) (20,30) (20,22) (20,24) (20,29) (20,26) (22,23) (22,27) (22,29) (22,31) (23,30) (23,26) (24,30) (24,27) (24,29) (24,26) (25,32) (25,28) (26,30) (26,27) (26,29) (27,30) (27,29) (28,32) (29,30) (29,31) (30,31)\nIs there a path between node 4 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph588-28_33", + "image": "data/connectivity/graph_visual/hard/graph588.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,14) (0,7) (0,13) (0,3) (0,2) (0,11) (0,33) (1,29) (1,31) (1,27) (1,22) (1,28) (1,10) (1,4) (1,16) (1,5) (2,14) (2,7) (2,8) (2,13) (2,3) (2,24) (2,33) (3,14) (3,8) (3,11) (3,24) (3,33) (4,29) (4,31) (4,27) (4,22) (4,28) (4,10) (4,21) (4,5) (5,29) (5,31) (5,27) (5,22) (5,28) (5,10) (5,12) (5,16) (5,21) (6,23) (6,30) (7,14) (7,8) (7,24) (7,33) (8,11) (8,24) (8,33) (9,17) (9,26) (9,25) (9,20) (9,18) (9,15) (9,32) (10,29) (10,31) (10,22) (10,28) (10,12) (10,16) (10,21) (11,14) (11,13) (11,33) (12,29) (12,31) (12,27) (12,28) (12,16) (13,14) (13,24) (13,33) (14,33) (15,26) (15,25) (15,20) (15,32) (16,31) (16,22) (16,28) (16,21) (17,26) (17,20) (17,18) (17,32) (18,26) (18,20) (19,23) (20,26) (20,25) (20,32) (21,29) (21,31) (21,22) (21,28) (22,27) (22,28) (23,30) (25,26) (25,32) (26,32) (27,29) (27,28) (29,31)\nIs there a path between node 28 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph162-22_6", + "image": "data/connectivity/graph_visual/hard/graph162.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,6) (0,22) (0,7) (0,3) (1,15) (1,16) (1,10) (2,15) (2,24) (2,16) (3,6) (3,7) (3,27) (3,5) (3,20) (4,11) (4,7) (4,27) (4,21) (5,26) (5,22) (5,19) (5,21) (5,20) (5,9) (6,7) (6,27) (6,21) (6,20) (7,21) (7,20) (8,13) (8,12) (8,16) (8,14) (9,11) (9,26) (9,19) (12,15) (12,16) (13,18) (16,18) (16,25) (17,24) (18,25) (19,22) (21,26)\nIs there a path between node 22 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph455-1_14", + "image": "data/connectivity/graph_visual/hard/graph455.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,30) (0,27) (0,29) (0,23) (0,28) (1,8) (1,9) (1,2) (1,20) (1,26) (1,23) (2,24) (2,8) (2,27) (2,20) (2,23) (3,11) (3,15) (3,16) (3,6) (3,12) (4,10) (4,9) (4,27) (4,20) (4,17) (4,32) (5,11) (5,22) (5,19) (5,6) (5,25) (5,18) (5,12) (6,22) (6,16) (6,25) (6,18) (7,24) (7,20) (7,29) (8,24) (8,17) (8,26) (8,32) (9,26) (9,21) (10,24) (10,30) (10,29) (11,25) (11,13) (13,15) (13,16) (13,14) (14,22) (14,19) (15,22) (15,25) (16,31) (16,19) (16,25) (17,24) (17,23) (17,28) (17,21) (18,22) (19,31) (20,26) (20,32) (21,30) (21,23) (22,25) (23,30) (24,30) (24,29) (26,27) (26,32) (28,32) (30,32)\nIs there a path between node 1 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph117-6_12", + "image": "data/connectivity/graph_visual/hard/graph117.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,19) (0,15) (0,14) (0,24) (0,5) (0,25) (0,2) (1,7) (1,11) (1,8) (1,17) (1,25) (1,16) (1,21) (1,2) (2,15) (2,12) (2,3) (2,16) (3,15) (3,11) (3,10) (3,20) (3,16) (3,21) (5,7) (5,14) (5,12) (5,11) (5,24) (5,10) (5,26) (5,6) (6,19) (6,9) (6,14) (6,11) (6,24) (6,10) (6,25) (6,21) (7,19) (7,15) (7,18) (7,11) (7,24) (8,19) (8,24) (8,10) (9,15) (9,18) (9,11) (9,27) (9,26) (9,20) (9,25) (9,21) (9,23) (10,17) (10,25) (11,27) (11,26) (11,17) (11,20) (11,16) (12,19) (12,14) (12,24) (12,17) (14,26) (15,18) (15,17) (16,24) (16,26) (16,17) (17,27) (17,25) (18,24) (18,25) (19,27) (19,23) (20,24) (20,27) (20,23) (21,24) (21,27)\nIs there a path between node 6 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph537-8_20", + "image": "data/connectivity/graph_visual/hard/graph537.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,16) (0,17) (0,4) (0,8) (0,12) (0,31) (1,19) (1,21) (1,2) (1,30) (1,26) (1,3) (1,9) (1,22) (1,6) (1,23) (1,18) (2,21) (2,28) (2,26) (2,3) (2,25) (2,20) (2,33) (2,9) (2,22) (2,6) (2,15) (2,7) (2,23) (2,18) (3,19) (3,30) (3,28) (3,26) (3,22) (3,32) (3,6) (3,15) (3,23) (3,18) (4,10) (4,16) (4,17) (4,5) (4,8) (4,12) (5,10) (5,13) (5,24) (5,16) (5,31) (6,19) (6,14) (6,30) (6,26) (6,25) (6,20) (6,11) (6,9) (6,22) (6,27) (6,32) (6,15) (6,29) (7,21) (7,30) (7,28) (7,26) (7,25) (7,33) (7,22) (7,27) (7,32) (7,15) (7,29) (7,23) (7,18) (8,13) (8,24) (8,16) (8,17) (8,31) (9,19) (9,21) (9,30) (9,20) (9,11) (9,22) (9,15) (9,23) (9,18) (10,13) (10,24) (10,16) (10,17) (10,12) (10,31) (11,19) (11,21) (11,14) (11,28) (11,26) (11,25) (11,20) (11,22) (11,32) (11,15) (11,29) (11,23) (11,18) (12,24) (12,17) (13,24) (13,16) (13,17) (14,19) (14,21) (14,30) (14,28) (14,25) (14,20) (14,33) (14,32) (14,15) (14,29) (14,23) (14,18) (15,30) (15,28) (15,26) (15,25) (15,20) (15,33) (15,22) (15,32) (15,29) (15,23) (15,18) (16,24) (16,17) (17,31) (18,19) (18,28) (18,26) (18,20) (18,33) (18,22) (18,27) (18,29) (18,23) (19,21) (19,28) (19,26) (19,20) (19,22) (19,29) (19,23) (20,21) (20,30) (20,26) (20,25) (20,22) (20,32) (20,29) (20,23) (21,28) (21,33) (21,22) (21,27) (21,32) (21,29) (22,30) (22,28) (22,26) (22,25) (22,27) (22,32) (22,23) (23,30) (23,28) (23,26) (23,33) (23,27) (23,32) (23,29) (24,31) (25,30) (25,26) (25,33) (25,27) (25,32) (25,29) (26,28) (26,27) (26,32) (26,29) (27,30) (27,28) (27,32) (27,29) (28,30) (28,33) (28,29) (29,32) (30,32) (32,33)\nIs there a path between node 8 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph598-30_7", + "image": "data/connectivity/graph_visual/hard/graph598.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,23) (0,14) (1,10) (1,13) (1,30) (1,17) (1,33) (1,21) (1,15) (1,29) (1,12) (1,11) (3,20) (3,22) (3,7) (3,5) (3,8) (3,25) (3,31) (3,27) (3,6) (3,9) (3,24) (3,26) (4,20) (4,22) (4,18) (4,7) (4,16) (4,5) (4,8) (4,25) (4,32) (4,31) (4,24) (5,20) (5,18) (5,8) (5,32) (5,31) (5,27) (5,6) (5,9) (5,24) (5,26) (6,22) (6,16) (6,8) (6,9) (6,26) (7,22) (7,18) (7,8) (7,25) (7,32) (7,27) (7,9) (7,24) (7,26) (8,20) (8,18) (8,16) (8,25) (8,32) (8,27) (8,9) (8,26) (9,20) (9,22) (9,18) (9,25) (9,32) (9,27) (9,24) (9,26) (10,30) (10,17) (10,33) (10,21) (10,15) (10,19) (10,12) (10,11) (11,28) (11,13) (11,17) (11,33) (11,21) (11,15) (11,19) (11,29) (11,12) (12,13) (12,15) (12,19) (12,29) (13,28) (13,30) (13,17) (13,33) (13,21) (13,15) (13,29) (14,23) (15,30) (15,33) (16,20) (16,25) (16,32) (16,31) (16,27) (16,24) (16,26) (17,30) (17,21) (17,19) (18,22) (18,25) (18,32) (18,31) (18,27) (18,24) (18,26) (19,28) (20,22) (20,31) (20,27) (20,24) (21,28) (21,30) (21,33) (21,29) (22,25) (22,27) (22,24) (22,26) (24,25) (24,32) (24,31) (24,27) (24,26) (25,31) (25,27) (26,32) (26,31) (27,32) (27,31) (28,30) (28,33) (28,29) (29,30) (29,33) (30,33) (31,32)\nIs there a path between node 30 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph141-19_27", + "image": "data/connectivity/graph_visual/hard/graph141.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,4) (0,12) (0,17) (0,3) (0,24) (0,10) (1,16) (1,24) (1,7) (1,2) (2,14) (2,11) (2,22) (2,15) (3,11) (3,24) (3,10) (4,17) (4,24) (4,10) (5,27) (5,23) (6,18) (7,22) (7,17) (7,15) (7,24) (9,27) (9,25) (10,14) (10,12) (10,15) (11,14) (11,12) (13,19) (14,16) (14,17) (15,22) (15,16) (16,17) (17,24) (19,26) (21,27) (23,27) (23,25) (25,28)\nIs there a path between node 19 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph217-24_1", + "image": "data/connectivity/graph_visual/hard/graph217.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,17) (0,13) (0,2) (0,27) (0,24) (0,6) (0,28) (0,10) (0,9) (1,25) (1,13) (1,24) (1,21) (1,16) (2,14) (2,16) (2,8) (2,23) (2,9) (3,18) (3,17) (3,25) (3,29) (3,27) (3,12) (3,28) (3,10) (3,8) (3,20) (4,17) (4,13) (4,5) (4,24) (4,21) (4,16) (5,14) (5,27) (5,28) (5,8) (5,20) (6,18) (6,13) (6,12) (7,26) (8,14) (8,17) (8,25) (8,27) (8,21) (8,11) (8,20) (9,14) (9,27) (9,11) (9,28) (9,10) (10,13) (10,29) (10,27) (10,24) (10,21) (10,16) (11,17) (12,21) (13,14) (13,18) (13,17) (13,25) (13,24) (14,18) (14,27) (14,16) (16,28) (16,20) (17,29) (17,21) (17,23) (17,20) (18,23) (20,23) (21,25) (21,28) (23,25) (23,27) (23,24) (23,28) (24,29) (24,27) (25,29) (25,28) (27,28)\nIs there a path between node 24 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph196-17_26", + "image": "data/connectivity/graph_visual/hard/graph196.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,29) (0,15) (0,3) (0,14) (0,27) (0,1) (0,25) (0,12) (0,26) (1,22) (1,15) (1,3) (1,14) (1,27) (1,16) (1,5) (1,12) (2,10) (2,23) (3,29) (3,22) (3,15) (3,14) (3,25) (3,5) (3,12) (4,19) (4,11) (4,18) (4,28) (4,17) (5,7) (5,25) (5,16) (5,12) (6,9) (6,18) (6,20) (6,28) (6,13) (7,29) (7,22) (7,15) (7,25) (7,16) (7,26) (8,24) (8,10) (9,21) (9,20) (9,17) (10,23) (11,19) (11,20) (11,28) (12,29) (12,22) (12,14) (12,27) (12,25) (12,26) (13,21) (13,18) (13,17) (14,29) (14,22) (14,15) (14,27) (14,25) (14,16) (14,26) (15,29) (15,25) (15,16) (15,26) (16,29) (16,25) (17,18) (17,28) (18,19) (18,21) (18,20) (19,21) (20,21) (21,28) (22,25) (22,26) (23,24) (25,27) (25,26) (26,29) (26,27) (27,29)\nIs there a path between node 17 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph42-9_25", + "image": "data/connectivity/graph_visual/hard/graph42.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,10) (0,8) (0,19) (0,7) (0,4) (0,21) (0,14) (0,25) (0,1) (0,17) (0,24) (0,9) (0,16) (0,20) (0,5) (0,13) (1,8) (1,19) (1,4) (1,18) (1,25) (1,17) (1,24) (1,9) (1,16) (1,13) (2,6) (2,11) (2,23) (2,3) (3,11) (4,10) (4,19) (4,7) (4,18) (4,25) (4,17) (4,24) (4,9) (4,20) (5,19) (5,21) (5,18) (5,14) (5,25) (5,17) (5,24) (5,16) (5,20) (6,11) (6,23) (7,10) (7,12) (7,8) (7,18) (7,14) (7,17) (7,24) (7,9) (7,16) (7,20) (7,13) (8,10) (8,12) (8,19) (8,18) (8,14) (8,25) (8,17) (8,16) (8,20) (9,10) (9,21) (9,18) (9,14) (9,25) (9,17) (9,24) (9,16) (9,13) (10,12) (10,19) (10,21) (10,14) (10,25) (10,17) (10,24) (10,16) (11,23) (12,19) (12,18) (12,14) (12,17) (12,24) (12,13) (13,19) (13,21) (13,14) (13,25) (13,17) (13,24) (13,20) (14,21) (14,18) (14,25) (14,24) (14,16) (14,20) (16,19) (16,25) (16,17) (16,24) (17,19) (17,21) (17,18) (17,25) (17,20) (18,21) (18,25) (18,24) (18,20) (19,25) (19,24) (19,20) (20,24) (21,25) (21,24)\nIs there a path between node 9 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph482-14_9", + "image": "data/connectivity/graph_visual/hard/graph482.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,10) (0,25) (0,7) (0,12) (0,23) (0,14) (0,17) (0,20) (0,19) (0,4) (0,28) (0,27) (0,2) (0,31) (1,22) (1,5) (1,32) (2,16) (2,7) (2,20) (2,18) (2,9) (2,4) (2,28) (2,27) (2,31) (3,29) (3,26) (4,16) (4,10) (4,7) (4,12) (4,23) (4,14) (4,15) (4,20) (4,18) (4,19) (4,9) (4,28) (4,27) (5,22) (5,6) (5,32) (6,22) (6,24) (6,32) (7,16) (7,25) (7,12) (7,23) (7,14) (7,17) (7,15) (7,21) (7,19) (7,9) (7,28) (7,27) (7,31) (8,13) (8,26) (9,16) (9,10) (9,25) (9,12) (9,23) (9,14) (9,15) (9,21) (9,20) (9,19) (9,31) (10,16) (10,12) (10,23) (10,17) (10,15) (10,21) (10,18) (10,19) (10,28) (10,27) (11,24) (11,32) (12,23) (12,14) (12,15) (12,21) (12,20) (12,18) (12,19) (12,28) (12,31) (13,29) (13,26) (14,16) (14,23) (14,17) (14,20) (14,18) (14,19) (14,28) (14,27) (14,31) (15,16) (15,25) (15,23) (15,17) (15,18) (15,28) (15,27) (15,31) (16,25) (16,23) (16,17) (16,20) (16,18) (16,19) (16,27) (17,20) (17,18) (17,28) (17,27) (18,25) (18,21) (18,20) (18,28) (18,31) (19,25) (19,21) (19,20) (19,27) (19,31) (20,23) (20,21) (20,28) (21,25) (21,23) (21,27) (21,31) (22,32) (23,25) (23,28) (23,31) (24,32) (25,28) (27,28) (28,31)\nIs there a path between node 14 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph693-29_33", + "image": "data/connectivity/graph_visual/hard/graph693.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,14) (0,13) (0,12) (0,26) (0,34) (0,28) (0,32) (0,5) (0,19) (0,3) (0,2) (0,6) (0,1) (0,23) (0,15) (0,9) (0,22) (0,7) (0,16) (0,31) (1,13) (1,12) (1,26) (1,34) (1,28) (1,32) (1,10) (1,5) (1,27) (1,19) (1,3) (1,18) (1,21) (1,2) (1,6) (1,23) (1,15) (1,9) (1,17) (1,22) (1,7) (1,16) (1,31) (2,14) (2,13) (2,12) (2,34) (2,28) (2,4) (2,5) (2,27) (2,25) (2,19) (2,3) (2,18) (2,21) (2,23) (2,15) (2,9) (2,30) (2,22) (2,7) (2,16) (2,31) (3,14) (3,12) (3,26) (3,4) (3,10) (3,5) (3,27) (3,25) (3,18) (3,21) (3,6) (3,15) (3,9) (3,17) (3,30) (3,7) (3,16) (3,31) (4,14) (4,13) (4,12) (4,26) (4,28) (4,32) (4,10) (4,5) (4,27) (4,25) (4,19) (4,23) (4,9) (4,30) (4,22) (4,7) (4,16) (4,31) (5,13) (5,12) (5,26) (5,34) (5,28) (5,32) (5,10) (5,25) (5,19) (5,18) (5,6) (5,23) (5,9) (5,30) (5,16) (5,31) (6,14) (6,12) (6,26) (6,34) (6,28) (6,32) (6,27) (6,19) (6,21) (6,15) (6,17) (6,22) (6,7) (6,31) (7,14) (7,13) (7,12) (7,26) (7,34) (7,28) (7,32) (7,10) (7,27) (7,19) (7,18) (7,21) (7,23) (7,15) (7,9) (7,17) (7,30) (7,22) (7,16) (8,20) (8,33) (8,11) (8,24) (9,14) (9,13) (9,12) (9,26) (9,34) (9,28) (9,10) (9,27) (9,19) (9,18) (9,23) (9,15) (9,17) (9,30) (9,22) (9,16) (10,14) (10,13) (10,12) (10,26) (10,25) (10,18) (10,21) (10,23) (10,15) (10,17) (10,30) (10,31) (11,20) (11,33) (11,24) (11,29) (12,26) (12,28) (12,32) (12,25) (12,18) (12,21) (12,23) (12,17) (12,30) (13,14) (13,26) (13,34) (13,28) (13,32) (13,27) (13,25) (13,19) (13,21) (13,23) (13,15) (13,17) (13,16) (13,31) (14,34) (14,28) (14,32) (14,27) (14,25) (14,18) (14,21) (14,23) (14,15) (14,17) (14,30) (14,22) (14,31) (15,34) (15,28) (15,32) (15,27) (15,25) (15,19) (15,21) (15,23) (15,22) (15,16) (15,31) (16,26) (16,28) (16,32) (16,25) (16,18) (16,21) (16,23) (16,17) (16,30) (17,26) (17,34) (17,28) (17,32) (17,27) (17,19) (17,18) (17,23) (17,30) (17,22) (17,31) (18,26) (18,32) (18,27) (18,25) (18,19) (18,23) (18,30) (18,31) (19,26) (19,34) (19,32) (19,21) (19,23) (19,30) (19,22) (19,31) (20,33) (20,29) (21,26) (21,34) (21,28) (21,25) (21,30) (21,22) (21,31) (22,28) (22,27) (22,25) (22,30) (22,31) (23,26) (23,34) (23,32) (23,27) (23,25) (23,30) (23,31) (24,33) (25,26) (25,32) (25,27) (25,30) (25,31) (26,28) (26,27) (26,31) (27,28) (27,32) (27,30) (27,31) (28,34) (29,33) (30,34) (30,32) (30,31) (31,34) (31,32)\nIs there a path between node 29 and node 33 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph247-27_3", + "image": "data/connectivity/graph_visual/hard/graph247.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,12) (0,22) (0,14) (0,30) (0,18) (0,17) (0,16) (0,10) (0,1) (0,11) (0,9) (0,7) (0,21) (0,2) (1,14) (1,30) (1,17) (1,6) (1,29) (1,16) (1,11) (1,9) (1,7) (1,8) (1,2) (2,12) (2,22) (2,14) (2,30) (2,18) (2,17) (2,6) (2,16) (2,10) (2,11) (2,7) (2,21) (3,24) (3,25) (3,5) (3,19) (4,24) (4,28) (4,25) (4,5) (4,19) (4,13) (4,20) (4,26) (5,28) (5,25) (5,19) (5,23) (5,20) (5,26) (6,22) (6,14) (6,17) (6,29) (6,10) (6,11) (6,9) (6,7) (6,8) (7,22) (7,14) (7,30) (7,17) (7,29) (7,9) (7,21) (8,12) (8,22) (8,14) (8,30) (8,18) (8,17) (8,29) (8,10) (9,22) (9,14) (9,18) (9,17) (9,29) (9,10) (9,21) (10,12) (10,22) (10,14) (10,18) (10,29) (10,16) (10,11) (10,21) (11,12) (11,22) (11,14) (11,30) (11,18) (11,16) (11,21) (12,22) (12,14) (12,30) (12,17) (12,29) (12,16) (12,21) (13,24) (13,28) (13,25) (13,19) (13,23) (13,20) (14,22) (14,17) (14,29) (15,27) (15,28) (15,19) (15,20) (15,26) (16,22) (16,30) (16,18) (16,17) (17,22) (17,21) (18,22) (18,30) (18,29) (18,21) (19,24) (19,28) (19,25) (19,23) (19,26) (20,24) (20,27) (20,28) (20,23) (20,26) (21,22) (21,30) (21,29) (22,30) (22,29) (23,24) (23,28) (23,25) (24,28) (24,25) (25,28) (26,27) (26,28)\nIs there a path between node 27 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph271-22_9", + "image": "data/connectivity/graph_visual/hard/graph271.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,20) (1,3) (1,27) (1,23) (1,9) (1,26) (1,29) (1,15) (1,11) (1,24) (1,22) (1,10) (1,21) (1,18) (1,17) (1,2) (1,5) (1,4) (1,28) (1,7) (1,25) (2,20) (2,19) (2,3) (2,27) (2,23) (2,26) (2,29) (2,11) (2,24) (2,22) (2,21) (2,30) (2,18) (2,5) (2,4) (2,28) (2,7) (2,13) (2,25) (3,20) (3,19) (3,9) (3,26) (3,29) (3,15) (3,11) (3,24) (3,22) (3,10) (3,21) (3,30) (3,8) (3,28) (3,12) (3,7) (3,13) (3,25) (4,20) (4,19) (4,27) (4,26) (4,29) (4,15) (4,11) (4,24) (4,10) (4,30) (4,18) (4,17) (4,12) (4,7) (4,13) (4,25) (5,20) (5,19) (5,27) (5,26) (5,29) (5,24) (5,22) (5,30) (5,18) (5,8) (5,17) (5,6) (5,12) (5,13) (5,25) (6,19) (6,27) (6,23) (6,9) (6,26) (6,29) (6,15) (6,11) (6,22) (6,21) (6,30) (6,17) (6,28) (6,12) (6,7) (6,13) (6,25) (7,19) (7,27) (7,9) (7,26) (7,29) (7,15) (7,11) (7,22) (7,21) (7,30) (7,18) (7,8) (7,17) (7,28) (7,12) (7,13) (7,25) (8,20) (8,19) (8,27) (8,23) (8,9) (8,29) (8,15) (8,24) (8,22) (8,10) (8,30) (8,18) (8,17) (8,28) (8,13) (8,25) (9,20) (9,19) (9,27) (9,23) (9,11) (9,24) (9,22) (9,10) (9,30) (9,17) (9,12) (9,13) (9,25) (10,27) (10,23) (10,29) (10,15) (10,11) (10,24) (10,21) (10,30) (10,17) (10,28) (10,13) (10,25) (11,20) (11,27) (11,23) (11,29) (11,15) (11,24) (11,22) (11,21) (11,30) (11,12) (11,13) (11,25) (12,19) (12,27) (12,23) (12,26) (12,29) (12,15) (12,24) (12,22) (12,30) (12,18) (12,13) (12,25) (13,20) (13,19) (13,27) (13,26) (13,29) (13,24) (13,21) (13,18) (13,28) (14,16) (15,20) (15,19) (15,23) (15,26) (15,29) (15,24) (15,22) (15,21) (15,18) (15,28) (15,25) (17,20) (17,23) (17,24) (17,22) (17,21) (17,30) (17,28) (17,25) (18,20) (18,19) (18,23) (18,26) (18,24) (18,22) (18,30) (18,28) (18,25) (19,27) (19,29) (19,22) (19,21) (19,30) (19,25) (20,27) (20,26) (20,29) (20,24) (20,22) (20,21) (21,27) (21,23) (21,22) (21,30) (21,28) (21,25) (22,27) (22,23) (22,29) (22,24) (22,30) (22,28) (22,25) (23,27) (23,26) (23,29) (23,30) (23,28) (23,25) (24,27) (24,25) (25,26) (25,29) (25,30) (25,28) (26,30) (27,30) (27,28) (29,30)\nIs there a path between node 22 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph637-26_1", + "image": "data/connectivity/graph_visual/hard/graph637.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,24) (0,28) (0,32) (0,1) (0,27) (0,13) (0,9) (1,31) (1,8) (1,15) (1,14) (1,21) (1,28) (1,4) (1,6) (2,3) (2,11) (2,24) (2,31) (2,14) (2,32) (2,4) (2,27) (2,9) (3,22) (3,14) (3,32) (3,20) (3,9) (4,11) (4,24) (4,34) (4,7) (4,19) (4,18) (4,29) (4,28) (4,32) (4,27) (4,13) (5,22) (5,7) (5,18) (5,6) (5,27) (5,13) (6,15) (6,29) (6,27) (6,13) (7,22) (7,33) (7,24) (7,8) (7,19) (7,25) (7,18) (7,30) (7,21) (7,28) (8,11) (8,33) (8,14) (8,25) (8,30) (8,32) (9,27) (9,20) (10,23) (11,22) (11,31) (11,15) (11,19) (11,30) (11,29) (12,17) (13,22) (13,33) (13,19) (13,16) (13,30) (13,21) (13,20) (14,34) (14,30) (15,22) (15,33) (15,24) (15,31) (15,18) (15,30) (15,21) (15,27) (16,24) (16,30) (18,22) (18,33) (18,31) (18,32) (19,22) (19,26) (19,25) (19,28) (19,32) (20,33) (20,24) (20,28) (21,25) (21,30) (21,29) (22,31) (22,28) (22,27) (24,34) (24,31) (24,26) (25,26) (25,29) (25,28) (26,34) (26,30) (26,28) (27,34) (27,28) (28,31) (30,31) (31,34) (32,33) (33,34)\nIs there a path between node 26 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph436-22_25", + "image": "data/connectivity/graph_visual/hard/graph436.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,16) (0,21) (0,28) (0,12) (0,18) (0,1) (0,7) (0,3) (0,2) (0,17) (0,27) (0,30) (0,6) (0,8) (0,9) (0,15) (1,21) (1,28) (1,23) (1,11) (1,20) (1,7) (1,2) (1,17) (1,27) (1,30) (1,6) (1,8) (1,15) (2,21) (2,28) (2,12) (2,23) (2,18) (2,11) (2,20) (2,7) (2,17) (2,27) (2,30) (2,8) (2,9) (2,15) (3,16) (3,21) (3,28) (3,12) (3,23) (3,18) (3,17) (3,27) (3,8) (3,15) (4,5) (4,10) (4,25) (4,26) (4,29) (4,13) (4,24) (4,22) (4,14) (5,10) (5,25) (5,13) (5,31) (5,24) (5,22) (6,16) (6,21) (6,28) (6,12) (6,18) (6,11) (6,20) (6,17) (6,27) (6,8) (6,15) (7,16) (7,28) (7,12) (7,23) (7,18) (7,20) (7,30) (7,8) (7,9) (7,15) (8,16) (8,18) (8,11) (8,30) (8,9) (8,15) (9,21) (9,12) (9,23) (9,18) (9,20) (9,27) (9,15) (10,19) (10,25) (10,26) (10,32) (10,29) (10,13) (10,31) (10,24) (10,22) (10,14) (11,16) (11,28) (11,23) (11,18) (11,17) (11,27) (11,30) (11,15) (12,16) (12,21) (12,28) (12,18) (12,20) (12,27) (12,15) (13,19) (13,25) (13,26) (13,31) (13,22) (13,14) (14,25) (14,26) (14,32) (14,29) (14,31) (14,24) (14,22) (15,16) (15,21) (15,23) (15,20) (15,17) (15,27) (15,30) (16,18) (16,20) (16,17) (16,27) (16,30) (17,21) (17,28) (17,23) (17,18) (17,20) (17,27) (17,30) (18,28) (18,23) (18,20) (18,30) (19,25) (19,26) (19,29) (19,31) (19,22) (20,28) (20,23) (20,27) (21,28) (21,27) (21,30) (22,26) (22,32) (22,29) (22,31) (22,24) (23,28) (23,27) (24,25) (24,26) (24,29) (24,31) (25,26) (25,32) (25,31) (26,32) (26,31) (27,28) (27,30) (28,30) (29,31)\nIs there a path between node 22 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph572-7_26", + "image": "data/connectivity/graph_visual/hard/graph572.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,10) (0,4) (1,15) (1,11) (1,24) (1,5) (2,6) (2,7) (2,9) (2,30) (3,9) (3,20) (3,14) (3,23) (3,18) (4,10) (4,6) (4,29) (4,9) (4,17) (4,8) (4,23) (4,18) (4,30) (5,15) (5,22) (5,24) (6,10) (6,7) (6,14) (6,21) (6,30) (7,28) (7,29) (7,9) (7,27) (7,17) (7,21) (7,30) (8,10) (8,9) (8,27) (8,14) (8,23) (8,21) (9,10) (9,28) (9,27) (9,17) (10,28) (10,29) (10,18) (12,16) (12,31) (12,33) (13,19) (14,27) (14,17) (14,18) (15,24) (16,31) (16,33) (16,24) (17,29) (18,28) (18,30) (19,22) (20,27) (20,21) (21,28) (22,33) (22,24) (24,31) (24,33) (25,26)\nIs there a path between node 7 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph53-21_14", + "image": "data/connectivity/graph_visual/hard/graph53.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,2) (0,10) (0,17) (0,15) (0,4) (0,12) (0,24) (0,9) (0,3) (0,13) (0,23) (0,7) (0,19) (0,16) (0,6) (0,25) (0,8) (1,10) (1,17) (1,4) (1,12) (1,24) (1,3) (1,13) (1,23) (1,26) (1,22) (1,19) (1,6) (1,14) (1,25) (1,8) (1,20) (2,10) (2,17) (2,11) (2,4) (2,24) (2,9) (2,3) (2,13) (2,23) (2,26) (2,7) (2,22) (2,19) (2,6) (2,14) (2,25) (2,8) (3,10) (3,17) (3,11) (3,15) (3,4) (3,12) (3,24) (3,9) (3,13) (3,26) (3,7) (3,19) (3,16) (3,14) (3,25) (3,8) (3,20) (4,10) (4,17) (4,11) (4,15) (4,12) (4,24) (4,9) (4,7) (4,19) (4,16) (4,6) (4,25) (4,20) (5,18) (6,10) (6,17) (6,15) (6,12) (6,24) (6,9) (6,23) (6,7) (6,16) (6,25) (6,8) (7,10) (7,11) (7,15) (7,12) (7,13) (7,22) (7,19) (7,16) (7,25) (7,8) (7,20) (8,10) (8,17) (8,11) (8,15) (8,12) (8,24) (8,9) (8,23) (8,22) (8,19) (8,16) (8,14) (8,25) (8,20) (9,10) (9,17) (9,11) (9,12) (9,24) (9,13) (9,23) (9,26) (9,22) (9,19) (9,16) (9,20) (10,17) (10,11) (10,15) (10,12) (10,24) (10,13) (10,23) (10,26) (10,19) (10,14) (10,20) (11,15) (11,12) (11,24) (11,13) (11,23) (11,26) (11,19) (11,16) (11,14) (11,20) (12,15) (12,24) (12,23) (12,22) (12,19) (12,16) (12,14) (12,25) (12,20) (13,15) (13,24) (13,23) (13,19) (13,16) (13,14) (13,25) (13,20) (14,17) (14,15) (14,24) (14,23) (14,26) (14,22) (14,19) (14,16) (14,25) (14,20) (15,17) (15,24) (15,23) (15,26) (15,16) (15,20) (16,24) (16,23) (16,26) (16,19) (16,25) (16,20) (17,23) (17,20) (18,21) (19,23) (19,22) (19,25) (19,20) (20,24) (20,23) (20,22) (20,25) (22,26) (22,25) (23,24) (23,26) (23,25) (24,26) (24,25) (25,26)\nIs there a path between node 21 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph394-30_6", + "image": "data/connectivity/graph_visual/hard/graph394.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,12) (0,24) (0,5) (0,32) (0,18) (0,23) (0,25) (1,20) (2,21) (2,13) (2,29) (3,12) (3,7) (3,11) (3,23) (3,25) (4,27) (4,12) (4,32) (5,30) (5,14) (7,10) (7,11) (7,23) (7,25) (8,27) (8,18) (8,30) (8,11) (8,25) (9,28) (10,27) (10,24) (10,32) (10,18) (10,23) (11,22) (11,14) (12,27) (12,24) (12,25) (13,15) (13,21) (13,29) (14,27) (14,32) (14,23) (15,21) (19,20) (22,30) (22,23) (23,30) (24,32) (24,30) (24,25) (25,27)\nIs there a path between node 30 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph72-1_9", + "image": "data/connectivity/graph_visual/hard/graph72.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,13) (0,14) (0,10) (0,19) (0,8) (0,26) (0,15) (0,1) (0,4) (1,22) (1,14) (1,23) (1,5) (1,26) (1,15) (1,11) (2,20) (2,14) (2,10) (2,15) (2,6) (2,17) (2,3) (2,11) (3,13) (3,12) (3,10) (3,5) (3,7) (3,4) (4,12) (4,14) (4,10) (4,23) (4,7) (4,26) (4,15) (4,17) (4,11) (5,12) (5,19) (5,26) (5,17) (6,20) (6,13) (6,14) (6,10) (6,19) (6,8) (6,26) (6,15) (6,21) (6,17) (7,13) (7,16) (7,21) (7,17) (7,24) (8,22) (8,15) (8,21) (10,19) (10,23) (10,11) (11,16) (11,21) (12,13) (12,14) (12,23) (12,26) (12,15) (12,24) (13,23) (13,26) (13,17) (14,20) (14,23) (14,17) (14,24) (15,20) (16,20) (16,21) (17,21) (19,22) (20,23) (20,26) (22,23) (24,26)\nIs there a path between node 1 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph449-8_6", + "image": "data/connectivity/graph_visual/hard/graph449.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (0,8) (0,32) (0,4) (0,26) (0,9) (0,5) (1,23) (1,19) (1,26) (1,29) (2,20) (2,6) (3,19) (3,32) (3,22) (3,9) (4,8) (4,10) (4,7) (4,24) (4,9) (5,23) (5,18) (5,31) (5,9) (6,16) (7,13) (7,32) (7,29) (8,28) (8,19) (8,18) (8,32) (8,10) (8,31) (8,22) (9,19) (9,29) (10,23) (10,19) (10,18) (10,13) (10,32) (10,22) (11,25) (11,21) (12,16) (12,30) (13,28) (13,23) (13,18) (13,31) (15,20) (15,16) (15,30) (15,21) (16,17) (17,25) (18,28) (18,23) (19,32) (19,24) (20,30) (22,26) (23,26) (23,31) (24,29) (26,32) (28,32) (29,32) (29,31)\nIs there a path between node 8 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph64-17_25", + "image": "data/connectivity/graph_visual/hard/graph64.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,15) (0,8) (0,25) (0,1) (1,4) (1,8) (2,16) (2,5) (2,24) (2,22) (4,23) (4,7) (4,17) (5,9) (5,19) (5,20) (6,9) (6,20) (7,14) (7,17) (8,18) (8,17) (9,24) (9,22) (10,19) (10,20) (10,24) (11,16) (12,14) (12,26) (14,23) (14,18) (14,25) (14,17) (15,18) (16,22) (18,26) (19,24) (19,22) (21,23) (22,24) (25,26)\nIs there a path between node 17 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph691-13_2", + "image": "data/connectivity/graph_visual/hard/graph691.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,17) (0,8) (0,34) (0,14) (0,16) (0,5) (0,22) (0,9) (0,25) (0,3) (0,32) (1,10) (2,21) (2,33) (2,30) (2,20) (3,6) (3,17) (3,26) (3,8) (3,14) (3,23) (3,16) (3,5) (3,22) (3,25) (4,11) (4,28) (4,15) (4,13) (4,19) (4,12) (5,6) (5,26) (5,8) (5,14) (5,23) (5,16) (5,27) (5,25) (6,26) (6,34) (6,16) (6,27) (6,22) (6,9) (6,25) (6,32) (7,33) (7,18) (7,29) (7,30) (7,20) (8,26) (8,34) (8,23) (8,16) (8,27) (8,9) (8,25) (8,32) (9,17) (9,26) (9,34) (9,16) (9,25) (9,32) (11,28) (11,15) (11,13) (11,19) (11,12) (12,28) (12,24) (12,15) (12,19) (13,28) (13,24) (13,19) (14,17) (14,26) (14,34) (14,16) (14,27) (14,25) (14,32) (15,24) (15,19) (16,17) (16,34) (16,23) (16,27) (16,25) (16,32) (17,26) (17,23) (17,27) (17,22) (17,25) (18,21) (18,33) (18,30) (18,20) (19,28) (19,24) (20,21) (20,33) (21,33) (21,29) (21,30) (21,31) (22,26) (22,34) (22,27) (23,26) (23,34) (23,27) (23,32) (24,28) (25,26) (25,34) (25,32) (26,27) (26,32) (27,32) (29,33) (29,31) (30,33) (30,31) (32,34)\nIs there a path between node 13 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph620-12_28", + "image": "data/connectivity/graph_visual/hard/graph620.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,20) (0,34) (0,1) (0,10) (0,12) (1,12) (2,24) (3,31) (3,30) (3,25) (4,19) (4,6) (5,8) (7,26) (10,20) (10,28) (10,17) (10,18) (12,20) (12,32) (12,17) (13,14) (13,15) (13,21) (13,26) (13,23) (14,15) (14,21) (15,26) (15,23) (16,21) (16,30) (17,20) (17,27) (17,32) (18,27) (18,34) (19,33) (20,27) (21,31) (21,22) (22,26) (22,31) (23,31) (26,31) (28,34) (30,31)\nIs there a path between node 12 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph348-6_2", + "image": "data/connectivity/graph_visual/hard/graph348.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,31) (0,20) (0,13) (0,6) (0,9) (0,3) (0,21) (0,29) (1,16) (1,20) (1,6) (1,22) (1,30) (2,10) (2,5) (2,20) (2,19) (2,30) (3,16) (3,19) (3,23) (3,22) (3,21) (3,29) (3,28) (5,31) (5,25) (5,28) (5,30) (6,31) (6,19) (6,14) (7,27) (7,18) (8,27) (8,11) (8,18) (9,12) (9,23) (9,30) (10,16) (10,23) (10,15) (10,14) (10,30) (11,26) (11,18) (12,16) (12,13) (12,23) (12,21) (12,14) (13,16) (13,31) (13,20) (13,15) (13,21) (13,30) (14,21) (14,28) (14,30) (15,17) (15,31) (15,20) (15,19) (15,30) (16,20) (16,23) (16,22) (16,21) (17,31) (17,25) (17,30) (18,27) (19,31) (19,23) (19,25) (19,29) (19,28) (19,30) (21,23) (21,28) (22,31) (22,25) (22,29) (23,31) (23,28) (23,30) (24,27) (25,28) (26,27) (28,31) (28,29) (29,31) (30,31)\nIs there a path between node 6 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph289-19_14", + "image": "data/connectivity/graph_visual/hard/graph289.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,6) (0,21) (0,23) (0,2) (0,8) (1,18) (1,3) (1,16) (2,4) (2,5) (3,25) (3,13) (4,6) (4,27) (4,17) (4,8) (5,26) (5,19) (5,30) (5,28) (5,23) (5,15) (5,8) (6,26) (6,19) (6,30) (6,8) (8,26) (8,21) (8,23) (8,27) (9,14) (11,20) (11,16) (12,19) (12,30) (13,18) (13,29) (15,28) (16,24) (16,20) (16,29) (17,30) (17,21) (17,27) (19,30) (19,27) (20,25) (21,26) (21,28) (23,27) (25,29) (27,30) (27,28)\nIs there a path between node 19 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph11-9_6", + "image": "data/connectivity/graph_visual/hard/graph11.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,15) (0,2) (0,1) (0,23) (0,8) (0,24) (0,6) (0,22) (0,4) (0,11) (1,15) (1,14) (1,2) (1,8) (1,12) (1,17) (1,19) (2,15) (2,14) (2,23) (2,8) (2,20) (2,6) (2,22) (2,4) (2,17) (2,11) (2,19) (2,7) (3,18) (3,9) (3,10) (3,21) (3,13) (3,16) (4,15) (4,14) (4,5) (4,23) (4,24) (4,12) (4,17) (4,11) (4,19) (4,7) (5,15) (5,14) (5,8) (5,20) (5,6) (5,22) (5,12) (5,17) (5,11) (5,19) (5,7) (6,15) (6,14) (6,23) (6,8) (6,20) (6,22) (6,12) (6,11) (6,19) (7,15) (7,23) (7,22) (7,12) (7,17) (7,19) (8,15) (8,14) (8,23) (8,24) (8,12) (8,17) (9,18) (9,21) (9,13) (9,16) (10,25) (10,16) (11,15) (11,14) (11,23) (11,24) (11,17) (11,19) (12,14) (12,22) (12,19) (13,25) (13,18) (13,21) (13,16) (14,15) (14,23) (14,22) (14,17) (14,19) (15,23) (15,24) (15,20) (15,22) (15,17) (15,19) (16,18) (17,23) (17,24) (17,19) (18,25) (18,21) (19,23) (19,24) (19,20) (20,23) (20,22) (21,25) (23,24)\nIs there a path between node 9 and node 6 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph603-5_0", + "image": "data/connectivity/graph_visual/hard/graph603.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,27) (0,22) (0,15) (1,32) (1,29) (1,16) (1,17) (1,4) (1,11) (2,26) (2,25) (2,14) (3,26) (3,19) (3,14) (4,24) (4,16) (4,9) (4,8) (5,10) (5,16) (5,17) (5,33) (5,9) (5,6) (5,23) (6,24) (6,31) (6,9) (6,21) (6,23) (6,11) (7,20) (7,22) (7,28) (7,30) (8,32) (8,29) (8,16) (8,17) (8,31) (8,9) (9,29) (9,17) (9,21) (9,11) (10,24) (10,31) (10,33) (10,21) (11,24) (11,29) (11,16) (11,31) (12,27) (13,18) (13,15) (14,19) (15,20) (15,28) (15,30) (16,21) (17,33) (17,21) (18,20) (18,34) (18,28) (20,22) (21,32) (21,29) (21,33) (23,29) (24,31) (25,26) (27,34) (29,33) (31,33)\nIs there a path between node 5 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph243-15_10", + "image": "data/connectivity/graph_visual/hard/graph243.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,26) (0,20) (0,10) (0,25) (0,16) (0,1) (0,3) (0,2) (0,17) (1,11) (1,22) (1,6) (1,24) (1,9) (1,30) (1,16) (1,17) (1,13) (2,11) (2,8) (2,19) (2,6) (2,12) (2,27) (2,3) (2,17) (3,5) (3,18) (3,24) (3,12) (3,25) (3,30) (4,21) (5,26) (5,22) (5,24) (5,12) (5,29) (5,25) (5,14) (5,30) (6,26) (6,18) (6,15) (8,20) (8,22) (8,12) (8,9) (8,13) (9,20) (9,18) (9,15) (9,23) (9,17) (9,13) (10,11) (10,15) (10,14) (10,30) (10,13) (11,22) (11,30) (11,27) (11,23) (11,17) (12,26) (12,19) (12,15) (12,25) (12,23) (12,17) (13,19) (13,15) (13,30) (14,22) (14,16) (14,17) (15,26) (15,19) (15,18) (15,25) (16,24) (16,25) (16,23) (17,26) (18,25) (19,26) (19,20) (19,22) (19,24) (20,26) (20,24) (20,25) (20,27) (21,28) (22,26) (22,29) (22,30) (22,27) (22,23) (23,30) (24,30) (25,29) (25,27) (26,30) (26,27) (29,30)\nIs there a path between node 15 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph102-3_20", + "image": "data/connectivity/graph_visual/hard/graph102.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,14) (0,27) (0,17) (0,9) (0,10) (0,2) (0,4) (0,20) (1,22) (1,13) (1,7) (1,21) (1,12) (1,19) (1,6) (1,26) (1,5) (1,16) (1,8) (2,14) (2,24) (2,17) (2,9) (2,15) (2,10) (2,18) (3,14) (3,24) (3,15) (3,10) (3,18) (4,14) (4,27) (4,9) (4,15) (4,10) (4,18) (4,20) (5,13) (5,7) (5,23) (5,25) (5,12) (5,19) (5,6) (5,26) (5,11) (5,16) (6,22) (6,13) (6,7) (6,23) (6,21) (6,12) (6,19) (6,11) (6,16) (6,8) (7,22) (7,13) (7,23) (7,12) (7,19) (7,26) (7,11) (7,16) (7,8) (8,22) (8,13) (8,23) (8,25) (8,21) (8,19) (8,16) (9,14) (9,24) (9,17) (9,10) (9,20) (10,14) (10,24) (10,17) (10,18) (11,22) (11,13) (11,12) (11,19) (11,26) (11,16) (12,22) (12,13) (12,21) (12,19) (12,26) (12,16) (13,22) (13,23) (13,19) (14,24) (14,17) (14,15) (14,18) (14,20) (15,27) (15,17) (15,18) (16,22) (16,23) (16,25) (16,21) (16,26) (17,27) (17,18) (17,20) (18,27) (18,20) (19,22) (19,23) (19,25) (19,21) (20,24) (20,27) (21,22) (21,23) (21,25) (21,26) (22,25) (22,26) (23,26) (24,27) (25,26)\nIs there a path between node 3 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph33-20_23", + "image": "data/connectivity/graph_visual/hard/graph33.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,22) (0,7) (0,18) (0,14) (0,20) (0,13) (0,24) (0,17) (1,25) (1,9) (1,21) (1,15) (1,23) (1,19) (1,16) (1,8) (2,9) (2,21) (2,23) (2,19) (2,6) (2,3) (2,8) (2,5) (3,25) (3,21) (3,15) (3,23) (3,4) (3,19) (4,25) (4,10) (4,9) (4,21) (4,23) (4,19) (4,6) (4,5) (5,25) (5,10) (5,9) (5,23) (5,16) (5,8) (6,9) (6,21) (6,15) (6,19) (6,16) (7,22) (7,14) (7,13) (7,24) (7,17) (8,25) (8,10) (8,9) (8,21) (8,15) (8,23) (8,19) (8,16) (9,10) (9,15) (9,19) (9,16) (10,23) (10,16) (11,22) (11,18) (11,14) (11,20) (11,12) (11,13) (11,24) (11,17) (12,22) (12,18) (12,20) (12,24) (12,17) (13,18) (13,14) (13,20) (13,24) (13,17) (14,22) (14,18) (14,20) (14,24) (14,17) (15,25) (15,21) (15,19) (15,16) (16,25) (16,21) (16,23) (17,18) (17,20) (17,24) (18,22) (18,20) (18,24) (19,25) (19,21) (20,22) (20,24) (21,25) (21,23) (23,25)\nIs there a path between node 20 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph207-1_19", + "image": "data/connectivity/graph_visual/hard/graph207.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,1) (0,18) (0,29) (1,18) (1,25) (2,28) (2,4) (2,14) (2,19) (2,12) (3,17) (4,5) (4,21) (5,22) (5,24) (5,11) (5,28) (5,7) (5,12) (6,22) (6,24) (6,28) (6,19) (7,11) (7,19) (7,21) (7,17) (8,16) (9,16) (9,20) (9,13) (9,15) (10,22) (10,14) (11,27) (11,14) (11,12) (12,24) (12,14) (12,19) (13,18) (13,26) (14,22) (15,16) (15,25) (17,22) (17,24) (17,27) (17,19) (17,21) (18,23) (19,22) (19,24) (20,29) (20,23) (20,25) (22,24) (22,27) (24,27) (24,28) (25,29)\nIs there a path between node 1 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph635-18_34", + "image": "data/connectivity/graph_visual/hard/graph635.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,25) (0,21) (0,13) (0,34) (0,12) (0,32) (0,31) (0,24) (0,15) (0,29) (1,23) (1,31) (1,14) (1,24) (1,15) (2,5) (2,25) (2,13) (2,17) (2,15) (2,29) (2,16) (3,6) (3,10) (4,20) (4,19) (5,7) (5,13) (5,17) (5,12) (5,14) (5,30) (5,26) (6,19) (6,8) (6,18) (6,27) (7,22) (7,21) (7,34) (7,32) (7,14) (7,24) (8,11) (8,19) (8,10) (9,11) (9,19) (9,10) (10,28) (11,19) (11,18) (12,21) (12,34) (12,14) (12,15) (12,30) (13,22) (13,33) (13,32) (14,34) (14,31) (14,24) (14,15) (14,29) (15,22) (15,25) (15,34) (15,31) (15,30) (16,25) (16,21) (17,23) (17,33) (17,32) (17,29) (18,20) (18,28) (20,28) (20,27) (21,25) (21,33) (21,24) (22,23) (22,33) (22,34) (23,29) (26,30) (27,28) (29,33) (30,31) (31,32) (32,33)\nIs there a path between node 18 and node 34 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph646-25_26", + "image": "data/connectivity/graph_visual/hard/graph646.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,13) (0,16) (0,5) (0,12) (0,29) (0,33) (0,18) (0,8) (0,15) (0,10) (0,34) (0,14) (0,21) (0,25) (1,11) (1,9) (1,19) (1,20) (1,7) (1,3) (1,28) (1,4) (1,24) (1,32) (1,26) (1,22) (2,6) (2,13) (2,17) (2,5) (2,31) (2,23) (2,27) (2,12) (2,29) (2,33) (2,18) (2,8) (2,15) (2,10) (2,30) (2,21) (2,25) (3,11) (3,9) (3,19) (3,28) (3,4) (3,24) (3,32) (3,26) (4,11) (4,9) (4,19) (4,20) (4,7) (4,28) (4,32) (4,26) (4,22) (5,17) (5,16) (5,23) (5,27) (5,12) (5,29) (5,33) (5,18) (5,8) (5,10) (5,25) (6,13) (6,17) (6,16) (6,31) (6,27) (6,12) (6,29) (6,8) (6,15) (6,10) (6,30) (6,14) (6,25) (7,11) (7,28) (7,24) (7,32) (7,22) (8,13) (8,16) (8,31) (8,27) (8,12) (8,29) (8,33) (8,18) (8,15) (8,10) (8,34) (8,14) (8,25) (9,11) (9,19) (9,20) (9,24) (9,22) (10,13) (10,17) (10,27) (10,12) (10,33) (10,18) (10,30) (10,14) (10,25) (11,19) (11,20) (11,28) (11,32) (11,26) (11,22) (12,13) (12,17) (12,31) (12,23) (12,29) (12,15) (12,30) (12,34) (12,21) (12,25) (13,16) (13,31) (13,29) (13,33) (13,30) (13,34) (13,14) (13,25) (14,17) (14,16) (14,31) (14,27) (14,29) (14,33) (14,18) (14,15) (14,34) (14,25) (15,17) (15,23) (15,27) (15,33) (15,30) (15,34) (15,21) (16,23) (16,27) (16,33) (16,18) (16,34) (17,23) (17,27) (17,33) (17,30) (17,34) (17,21) (17,25) (18,31) (18,27) (18,29) (18,34) (19,20) (19,28) (19,24) (19,32) (19,26) (19,22) (20,28) (20,24) (20,22) (21,31) (21,27) (21,33) (21,30) (21,25) (22,24) (22,32) (23,31) (23,27) (23,29) (23,33) (23,34) (23,25) (24,28) (24,32) (24,26) (25,27) (25,30) (25,34) (27,29) (27,33) (27,30) (28,32) (29,31) (29,33) (29,30) (29,34) (30,31) (30,33) (30,34) (33,34)\nIs there a path between node 25 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph432-14_28", + "image": "data/connectivity/graph_visual/hard/graph432.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,23) (0,28) (0,2) (0,26) (0,6) (0,8) (0,10) (0,16) (0,5) (0,21) (0,7) (0,24) (0,27) (1,9) (1,15) (1,17) (1,30) (1,3) (1,31) (1,25) (2,23) (2,28) (2,26) (2,6) (2,8) (2,18) (2,10) (2,16) (2,21) (2,7) (2,24) (3,13) (3,9) (3,15) (3,17) (3,12) (3,30) (3,31) (3,25) (4,20) (4,32) (4,29) (4,22) (4,14) (4,11) (5,28) (5,6) (5,18) (5,24) (5,27) (6,23) (6,28) (6,8) (6,18) (6,16) (6,7) (6,24) (6,27) (7,23) (7,28) (7,26) (7,8) (7,10) (7,21) (7,24) (7,27) (8,26) (8,18) (8,16) (8,21) (8,24) (8,27) (9,17) (9,12) (9,30) (9,31) (10,23) (10,26) (10,18) (10,16) (10,21) (11,29) (11,22) (11,14) (12,13) (12,17) (12,30) (12,31) (13,15) (13,17) (13,25) (14,20) (14,32) (14,29) (14,19) (14,22) (15,17) (15,31) (15,25) (16,23) (16,21) (16,24) (17,30) (17,31) (17,25) (18,23) (18,28) (18,26) (18,21) (18,24) (18,27) (19,20) (19,32) (19,29) (19,22) (20,29) (20,22) (21,26) (22,32) (22,29) (23,28) (23,26) (23,27) (24,28) (24,26) (24,27) (25,30) (25,31) (26,27) (27,28) (29,32)\nIs there a path between node 14 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph344-12_11", + "image": "data/connectivity/graph_visual/hard/graph344.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,19) (0,22) (0,8) (0,14) (1,9) (1,11) (1,21) (1,16) (1,28) (1,25) (1,6) (1,10) (2,12) (2,18) (2,25) (2,20) (2,10) (3,18) (3,23) (3,5) (4,24) (5,26) (5,21) (5,29) (5,25) (5,20) (5,31) (6,12) (6,18) (6,17) (7,15) (7,14) (8,30) (8,19) (8,13) (9,21) (9,28) (9,25) (9,17) (10,26) (10,11) (10,25) (10,17) (11,18) (11,23) (11,25) (11,20) (12,21) (12,18) (12,23) (13,24) (13,19) (13,15) (13,14) (14,27) (14,22) (15,24) (15,22) (16,23) (16,17) (18,26) (18,28) (18,23) (18,20) (19,24) (19,30) (20,21) (20,28) (21,26) (21,25) (23,26) (24,30) (25,31) (26,28) (26,31) (28,31)\nIs there a path between node 12 and node 11 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph706-9_8", + "image": "data/connectivity/graph_visual/hard/graph706.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,21) (0,17) (0,24) (0,27) (0,4) (0,10) (0,7) (1,29) (1,14) (1,5) (1,26) (1,18) (1,23) (1,28) (1,34) (1,8) (1,6) (2,29) (2,16) (2,30) (2,5) (2,26) (2,19) (2,25) (2,11) (2,18) (2,23) (2,28) (2,20) (2,9) (2,8) (2,6) (3,33) (3,32) (4,13) (4,17) (4,22) (4,24) (4,15) (4,27) (4,12) (4,10) (4,7) (5,29) (5,14) (5,26) (5,19) (5,25) (5,11) (5,31) (5,28) (5,34) (5,6) (6,29) (6,14) (6,30) (6,26) (6,19) (6,25) (6,11) (6,18) (6,28) (6,20) (6,9) (6,8) (7,13) (7,21) (7,17) (7,22) (7,24) (7,27) (7,10) (8,16) (8,14) (8,30) (8,26) (8,25) (8,11) (8,31) (8,18) (8,23) (8,20) (8,9) (8,34) (9,29) (9,16) (9,30) (9,26) (9,19) (9,25) (9,11) (9,31) (9,23) (10,13) (10,21) (10,17) (10,24) (10,15) (10,27) (11,29) (11,16) (11,14) (11,30) (11,26) (11,19) (11,25) (11,23) (12,13) (12,17) (12,22) (12,27) (13,21) (13,17) (13,22) (13,24) (13,15) (13,27) (14,29) (14,16) (14,30) (14,26) (14,25) (14,31) (14,18) (14,28) (14,34) (15,22) (15,24) (15,27) (16,29) (16,30) (16,26) (16,25) (16,31) (16,23) (17,21) (17,24) (17,27) (18,29) (18,30) (18,26) (18,19) (18,25) (18,31) (18,23) (18,34) (19,29) (19,30) (19,26) (19,31) (19,23) (19,20) (19,34) (20,29) (20,30) (20,31) (20,23) (20,28) (20,34) (21,22) (21,24) (22,24) (22,27) (23,29) (23,26) (23,34) (24,27) (25,29) (25,30) (25,31) (25,28) (25,34) (26,29) (26,30) (26,31) (26,28) (26,34) (28,29) (28,31) (29,30) (29,31) (29,34) (30,31) (30,34) (31,34)\nIs there a path between node 9 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph217-7_24", + "image": "data/connectivity/graph_visual/hard/graph217.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,17) (0,13) (0,2) (0,27) (0,24) (0,6) (0,28) (0,10) (0,9) (1,25) (1,13) (1,24) (1,21) (1,16) (2,14) (2,16) (2,8) (2,23) (2,9) (3,18) (3,17) (3,25) (3,29) (3,27) (3,12) (3,28) (3,10) (3,8) (3,20) (4,17) (4,13) (4,5) (4,24) (4,21) (4,16) (5,14) (5,27) (5,28) (5,8) (5,20) (6,18) (6,13) (6,12) (7,26) (8,14) (8,17) (8,25) (8,27) (8,21) (8,11) (8,20) (9,14) (9,27) (9,11) (9,28) (9,10) (10,13) (10,29) (10,27) (10,24) (10,21) (10,16) (11,17) (12,21) (13,14) (13,18) (13,17) (13,25) (13,24) (14,18) (14,27) (14,16) (16,28) (16,20) (17,29) (17,21) (17,23) (17,20) (18,23) (20,23) (21,25) (21,28) (23,25) (23,27) (23,24) (23,28) (24,29) (24,27) (25,29) (25,28) (27,28)\nIs there a path between node 7 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph128-10_8", + "image": "data/connectivity/graph_visual/hard/graph128.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,12) (0,14) (0,10) (0,17) (0,18) (0,1) (0,13) (0,11) (0,23) (0,4) (1,19) (1,12) (1,14) (1,6) (1,17) (1,18) (1,13) (1,7) (1,27) (1,23) (2,5) (2,8) (3,21) (3,20) (3,15) (3,25) (4,19) (4,22) (4,10) (4,6) (4,17) (4,18) (4,13) (4,7) (4,27) (5,8) (6,22) (6,12) (6,14) (6,10) (6,17) (6,18) (6,13) (6,11) (6,23) (7,22) (7,26) (7,14) (7,10) (7,17) (7,18) (7,9) (9,26) (9,14) (9,10) (9,17) (9,13) (9,11) (9,27) (9,23) (10,19) (10,26) (10,14) (10,17) (10,18) (10,13) (10,27) (10,23) (11,19) (11,22) (11,26) (11,12) (11,14) (11,17) (11,13) (11,27) (12,19) (12,22) (12,14) (12,17) (12,18) (12,27) (13,19) (13,26) (13,14) (13,17) (13,18) (14,19) (14,18) (14,23) (15,21) (15,16) (15,20) (15,25) (16,21) (17,23) (18,19) (18,22) (18,26) (19,27) (20,21) (20,24) (21,25) (22,26) (22,27) (22,23) (23,26) (23,27) (24,25) (26,27)\nIs there a path between node 10 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph74-1_14", + "image": "data/connectivity/graph_visual/hard/graph74.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,4) (0,12) (0,1) (0,13) (0,14) (0,11) (0,20) (0,7) (0,21) (1,4) (1,13) (1,14) (1,16) (1,7) (1,21) (2,5) (2,22) (2,8) (2,15) (2,25) (2,9) (2,17) (2,26) (3,11) (3,20) (3,7) (4,13) (4,14) (4,11) (4,20) (4,21) (5,22) (5,18) (5,15) (5,23) (5,25) (5,17) (5,26) (5,24) (6,19) (7,12) (7,13) (7,14) (7,11) (7,20) (7,21) (8,22) (8,15) (8,23) (8,9) (8,17) (8,24) (9,18) (9,15) (9,23) (9,25) (9,17) (11,13) (11,14) (11,16) (11,20) (12,13) (12,14) (12,16) (12,20) (12,21) (13,16) (13,20) (14,16) (14,20) (14,21) (15,22) (15,18) (15,23) (15,25) (15,26) (15,24) (16,21) (17,22) (17,18) (17,23) (17,25) (18,25) (18,24) (20,21) (22,23) (22,25) (22,26) (22,24) (23,26) (23,24) (24,25) (25,26)\nIs there a path between node 1 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph348-7_25", + "image": "data/connectivity/graph_visual/hard/graph348.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (0,31) (0,20) (0,13) (0,6) (0,9) (0,3) (0,21) (0,29) (1,16) (1,20) (1,6) (1,22) (1,30) (2,10) (2,5) (2,20) (2,19) (2,30) (3,16) (3,19) (3,23) (3,22) (3,21) (3,29) (3,28) (5,31) (5,25) (5,28) (5,30) (6,31) (6,19) (6,14) (7,27) (7,18) (8,27) (8,11) (8,18) (9,12) (9,23) (9,30) (10,16) (10,23) (10,15) (10,14) (10,30) (11,26) (11,18) (12,16) (12,13) (12,23) (12,21) (12,14) (13,16) (13,31) (13,20) (13,15) (13,21) (13,30) (14,21) (14,28) (14,30) (15,17) (15,31) (15,20) (15,19) (15,30) (16,20) (16,23) (16,22) (16,21) (17,31) (17,25) (17,30) (18,27) (19,31) (19,23) (19,25) (19,29) (19,28) (19,30) (21,23) (21,28) (22,31) (22,25) (22,29) (23,31) (23,28) (23,30) (24,27) (25,28) (26,27) (28,31) (28,29) (29,31) (30,31)\nIs there a path between node 7 and node 25 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph564-33_21", + "image": "data/connectivity/graph_visual/hard/graph564.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,16) (1,3) (1,28) (1,21) (1,29) (1,27) (1,26) (3,28) (3,20) (3,26) (4,31) (4,8) (4,23) (4,17) (4,29) (4,33) (4,13) (4,26) (4,18) (4,9) (5,16) (6,11) (7,20) (7,29) (7,9) (7,12) (7,25) (8,30) (8,17) (8,14) (8,13) (8,18) (9,19) (9,21) (9,27) (9,26) (9,12) (12,30) (12,22) (12,19) (12,17) (12,14) (12,33) (13,20) (13,14) (13,27) (14,19) (14,21) (14,33) (14,25) (17,24) (17,21) (17,29) (17,27) (17,33) (17,26) (17,18) (18,31) (18,24) (18,27) (18,33) (18,25) (19,30) (19,23) (20,31) (20,24) (20,29) (20,27) (20,26) (21,31) (21,24) (21,28) (21,29) (22,30) (22,23) (22,28) (22,27) (23,30) (23,24) (23,25) (25,31) (25,27) (25,33) (26,29) (27,31) (27,28) (27,33) (28,31) (28,29) (29,31) (29,30)\nIs there a path between node 33 and node 21 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph36-18_10", + "image": "data/connectivity/graph_visual/hard/graph36.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,19) (0,18) (0,23) (0,22) (0,1) (0,21) (0,24) (0,7) (0,4) (0,3) (0,15) (0,12) (0,5) (1,22) (1,7) (1,4) (1,15) (1,12) (2,17) (2,9) (2,11) (2,25) (2,14) (3,19) (3,22) (3,21) (3,7) (3,4) (3,15) (3,12) (3,5) (4,19) (4,23) (4,7) (4,15) (4,12) (4,5) (5,19) (5,23) (5,22) (5,21) (5,7) (5,12) (6,20) (7,19) (7,23) (7,24) (7,15) (7,12) (8,10) (8,13) (9,17) (9,11) (9,25) (9,16) (10,13) (10,20) (11,17) (11,16) (11,14) (12,18) (12,22) (12,21) (12,15) (13,20) (14,25) (14,16) (15,19) (15,18) (15,23) (15,22) (15,21) (15,24) (16,17) (16,25) (17,25) (18,19) (18,23) (18,22) (18,21) (18,24) (19,23) (19,21) (19,24) (21,23) (21,22) (21,24) (22,24) (23,24)\nIs there a path between node 18 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph61-9_8", + "image": "data/connectivity/graph_visual/hard/graph61.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,15) (1,10) (1,16) (1,26) (1,3) (1,12) (2,7) (3,5) (3,10) (3,21) (3,9) (3,24) (3,20) (3,25) (3,12) (3,14) (4,23) (4,22) (4,18) (5,17) (5,16) (5,14) (6,8) (6,21) (6,26) (6,12) (8,11) (8,10) (8,13) (8,16) (8,20) (8,12) (9,13) (9,19) (9,25) (9,14) (10,15) (10,11) (10,16) (10,25) (11,24) (11,20) (11,25) (12,17) (12,16) (12,19) (13,17) (13,24) (13,26) (14,17) (14,21) (15,16) (15,26) (16,19) (17,21) (17,25) (18,22) (19,21) (20,24) (20,26) (21,24) (24,26) (25,26)\nIs there a path between node 9 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph73-16_1", + "image": "data/connectivity/graph_visual/hard/graph73.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,7) (0,16) (0,14) (0,13) (0,25) (0,4) (0,19) (0,9) (0,10) (2,13) (2,15) (2,10) (3,18) (3,14) (3,25) (3,23) (3,15) (3,10) (3,24) (4,16) (4,23) (4,19) (4,15) (4,11) (5,21) (5,8) (5,26) (6,20) (6,19) (6,15) (6,10) (6,24) (7,20) (7,11) (8,21) (9,20) (9,22) (9,25) (9,11) (9,24) (10,17) (10,25) (11,17) (11,13) (11,23) (12,16) (12,14) (12,25) (12,15) (13,17) (13,25) (14,17) (14,16) (14,25) (14,15) (15,17) (15,16) (15,20) (15,24) (16,18) (16,17) (16,20) (16,22) (16,19) (17,23) (18,22) (18,23) (19,22) (19,25) (22,23) (24,25)\nIs there a path between node 16 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph170-1_27", + "image": "data/connectivity/graph_visual/hard/graph170.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,26) (0,12) (0,7) (0,13) (0,3) (0,8) (0,21) (0,18) (0,22) (0,6) (0,28) (0,11) (0,24) (0,4) (0,5) (0,15) (0,20) (0,19) (1,26) (1,12) (1,13) (1,21) (1,18) (1,22) (1,6) (1,17) (1,23) (1,14) (1,11) (1,27) (1,24) (1,4) (1,5) (1,20) (2,25) (2,9) (2,16) (3,7) (3,13) (3,8) (3,18) (3,22) (3,17) (3,23) (3,14) (3,11) (3,27) (3,24) (3,15) (3,20) (3,19) (4,26) (4,12) (4,13) (4,8) (4,21) (4,6) (4,17) (4,23) (4,28) (4,27) (4,24) (4,5) (4,20) (5,12) (5,7) (5,13) (5,8) (5,21) (5,18) (5,22) (5,17) (5,28) (5,27) (5,15) (5,20) (5,19) (6,12) (6,7) (6,13) (6,8) (6,21) (6,22) (6,17) (6,14) (6,28) (6,27) (6,15) (6,20) (6,19) (7,26) (7,12) (7,13) (7,8) (7,21) (7,22) (7,17) (7,23) (7,28) (7,11) (7,24) (7,15) (8,26) (8,13) (8,22) (8,17) (8,11) (8,27) (8,24) (9,25) (9,16) (11,12) (11,13) (11,21) (11,22) (11,17) (11,23) (11,28) (11,27) (11,24) (11,15) (11,20) (11,19) (12,26) (12,18) (12,22) (12,17) (12,14) (12,28) (12,24) (12,15) (12,20) (12,19) (13,26) (13,18) (13,17) (13,23) (13,14) (13,28) (13,15) (13,20) (13,19) (14,22) (14,17) (14,23) (14,28) (14,24) (14,15) (14,19) (15,26) (15,21) (15,17) (15,28) (15,24) (15,20) (16,25) (17,26) (17,21) (17,18) (17,22) (17,27) (17,24) (17,20) (17,19) (18,21) (18,28) (18,27) (18,24) (19,21) (19,22) (19,28) (19,27) (19,24) (19,20) (20,26) (20,22) (20,24) (21,26) (21,22) (21,28) (21,27) (21,24) (22,23) (22,28) (22,27) (22,24) (23,26) (23,27) (23,24) (24,27) (26,27) (27,28)\nIs there a path between node 1 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph12-10_18", + "image": "data/connectivity/graph_visual/hard/graph12.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,25) (0,7) (0,15) (0,3) (0,17) (0,23) (0,2) (0,19) (0,16) (0,6) (0,4) (0,22) (0,1) (0,8) (0,13) (0,21) (1,25) (1,11) (1,7) (1,20) (1,5) (1,15) (1,3) (1,23) (1,12) (1,18) (1,2) (1,19) (1,9) (1,16) (1,4) (1,22) (1,13) (1,21) (2,11) (2,5) (2,3) (2,17) (2,23) (2,12) (2,19) (2,9) (2,16) (2,6) (2,22) (2,8) (2,13) (2,21) (3,25) (3,11) (3,5) (3,15) (3,23) (3,12) (3,18) (3,19) (3,9) (3,16) (3,4) (3,22) (3,8) (3,13) (4,11) (4,20) (4,5) (4,15) (4,17) (4,23) (4,12) (4,18) (4,19) (4,9) (4,16) (4,6) (4,22) (5,15) (5,17) (5,18) (5,19) (5,9) (5,16) (5,6) (5,22) (5,13) (5,21) (6,11) (6,7) (6,20) (6,15) (6,23) (6,12) (6,19) (6,9) (6,16) (6,22) (6,8) (6,13) (6,21) (7,11) (7,15) (7,23) (7,12) (7,19) (7,9) (7,16) (7,8) (7,13) (8,25) (8,11) (8,15) (8,17) (8,12) (8,18) (8,19) (8,9) (8,22) (8,13) (8,21) (9,25) (9,11) (9,15) (9,17) (9,23) (9,12) (9,18) (9,19) (9,16) (9,22) (10,24) (10,14) (11,25) (11,20) (11,23) (11,12) (11,18) (11,19) (11,13) (11,21) (12,25) (12,20) (12,15) (12,17) (12,23) (12,18) (12,19) (12,16) (12,21) (13,25) (13,20) (13,15) (13,23) (13,18) (13,16) (13,22) (14,24) (15,20) (15,17) (15,23) (15,18) (15,19) (15,16) (15,22) (15,21) (16,25) (16,20) (16,17) (16,23) (16,18) (16,19) (16,22) (17,25) (17,20) (17,23) (17,19) (17,22) (17,21) (18,25) (18,20) (19,25) (19,20) (19,22) (20,25) (20,21) (21,25) (21,22) (22,25) (23,25)\nIs there a path between node 10 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph635-28_34", + "image": "data/connectivity/graph_visual/hard/graph635.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,25) (0,21) (0,13) (0,34) (0,12) (0,32) (0,31) (0,24) (0,15) (0,29) (1,23) (1,31) (1,14) (1,24) (1,15) (2,5) (2,25) (2,13) (2,17) (2,15) (2,29) (2,16) (3,6) (3,10) (4,20) (4,19) (5,7) (5,13) (5,17) (5,12) (5,14) (5,30) (5,26) (6,19) (6,8) (6,18) (6,27) (7,22) (7,21) (7,34) (7,32) (7,14) (7,24) (8,11) (8,19) (8,10) (9,11) (9,19) (9,10) (10,28) (11,19) (11,18) (12,21) (12,34) (12,14) (12,15) (12,30) (13,22) (13,33) (13,32) (14,34) (14,31) (14,24) (14,15) (14,29) (15,22) (15,25) (15,34) (15,31) (15,30) (16,25) (16,21) (17,23) (17,33) (17,32) (17,29) (18,20) (18,28) (20,28) (20,27) (21,25) (21,33) (21,24) (22,23) (22,33) (22,34) (23,29) (26,30) (27,28) (29,33) (30,31) (31,32) (32,33)\nIs there a path between node 28 and node 34 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph257-21_30", + "image": "data/connectivity/graph_visual/hard/graph257.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,10) (0,8) (0,15) (0,12) (0,27) (0,23) (0,29) (1,20) (1,7) (1,27) (1,4) (1,2) (1,3) (1,5) (1,29) (2,15) (2,7) (2,27) (2,17) (2,26) (2,30) (3,27) (3,25) (3,13) (3,26) (3,29) (3,30) (4,7) (4,27) (4,23) (4,5) (4,29) (5,20) (5,8) (5,14) (5,12) (5,26) (5,21) (5,30) (6,16) (6,28) (6,22) (7,8) (7,27) (7,9) (7,17) (7,29) (7,30) (8,20) (8,23) (8,25) (8,13) (8,26) (9,12) (9,27) (10,14) (10,23) (11,24) (11,16) (12,27) (12,13) (13,14) (13,21) (13,29) (14,20) (14,27) (14,23) (15,23) (15,26) (16,24) (16,18) (17,23) (17,26) (18,28) (18,22) (19,22) (21,23) (23,26) (25,27) (25,26) (26,27) (26,29) (27,30)\nIs there a path between node 21 and node 30 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph467-26_29", + "image": "data/connectivity/graph_visual/hard/graph467.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,29) (0,10) (0,18) (0,21) (0,30) (0,28) (0,15) (1,27) (1,24) (1,22) (1,32) (1,14) (1,5) (2,29) (2,10) (2,18) (2,21) (2,19) (2,30) (2,16) (2,28) (2,15) (3,24) (3,13) (3,22) (3,20) (3,5) (4,17) (4,11) (4,6) (4,26) (4,23) (4,31) (4,25) (5,27) (5,13) (5,22) (5,20) (5,32) (5,14) (6,17) (6,9) (6,23) (6,31) (6,25) (7,29) (7,10) (7,18) (7,19) (7,30) (7,16) (7,15) (8,17) (8,11) (8,26) (8,23) (8,31) (9,17) (9,26) (9,23) (9,31) (9,25) (10,29) (10,18) (10,21) (10,30) (10,28) (10,15) (11,17) (11,26) (11,23) (12,27) (12,24) (12,13) (12,22) (12,32) (13,27) (13,24) (13,22) (13,20) (13,32) (13,14) (14,27) (14,22) (14,32) (15,29) (15,18) (15,21) (15,19) (15,28) (16,29) (16,21) (16,19) (16,28) (17,23) (18,29) (18,21) (18,30) (18,28) (19,29) (19,21) (19,30) (19,28) (20,24) (20,22) (20,32) (21,29) (21,30) (21,28) (22,27) (22,24) (22,32) (23,31) (24,27) (25,26) (26,31) (28,30)\nIs there a path between node 26 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph566-27_9", + "image": "data/connectivity/graph_visual/hard/graph566.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,33) (0,17) (1,5) (1,18) (1,25) (1,23) (2,13) (2,28) (2,9) (2,21) (2,22) (2,20) (3,16) (3,20) (4,6) (4,19) (4,15) (4,18) (4,30) (4,17) (5,6) (5,32) (5,10) (5,18) (5,33) (6,32) (6,19) (6,15) (6,27) (6,26) (6,18) (6,17) (6,24) (6,25) (8,12) (9,21) (9,22) (10,32) (10,18) (10,30) (10,17) (10,25) (10,23) (11,28) (11,31) (11,16) (11,20) (13,22) (15,19) (15,27) (15,18) (15,33) (15,30) (15,24) (15,25) (15,23) (16,20) (17,27) (17,18) (17,33) (17,24) (17,29) (18,26) (18,33) (18,25) (19,27) (20,21) (21,31) (23,30) (23,25) (24,32) (24,29) (24,25) (25,33) (26,33) (26,29) (27,30) (27,29) (29,30) (30,32) (30,33) (32,33)\nIs there a path between node 27 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph556-0_32", + "image": "data/connectivity/graph_visual/hard/graph556.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,2) (0,20) (0,30) (0,26) (0,15) (0,32) (0,13) (1,25) (2,31) (2,3) (2,30) (2,12) (2,11) (2,23) (2,27) (2,15) (2,6) (2,21) (3,31) (3,14) (3,33) (3,18) (3,11) (3,26) (3,23) (3,27) (3,16) (3,32) (3,29) (4,7) (4,25) (5,33) (5,12) (5,29) (5,6) (5,8) (6,33) (6,22) (6,18) (6,19) (6,16) (7,10) (8,22) (8,19) (8,11) (8,15) (8,32) (9,33) (9,19) (9,15) (9,29) (9,13) (11,27) (11,15) (11,32) (11,29) (13,33) (13,22) (13,23) (13,28) (13,21) (14,31) (14,33) (14,22) (14,18) (14,26) (14,15) (14,16) (14,21) (15,33) (15,19) (15,21) (16,20) (16,33) (16,27) (18,22) (18,30) (18,19) (18,32) (18,29) (19,26) (19,23) (19,21) (20,31) (20,30) (20,23) (20,28) (21,31) (21,26) (21,32) (22,26) (22,32) (22,29) (22,28) (23,33) (23,30) (23,27) (26,32) (28,31) (28,30) (28,29) (29,31) (29,32) (30,32) (31,33)\nIs there a path between node 0 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph94-25_8", + "image": "data/connectivity/graph_visual/hard/graph94.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,20) (0,24) (0,3) (0,19) (0,9) (0,21) (1,2) (2,13) (2,6) (3,24) (3,8) (3,12) (4,20) (4,8) (4,19) (4,17) (4,23) (4,21) (5,7) (5,25) (5,18) (6,13) (7,25) (8,20) (8,24) (8,14) (8,11) (8,23) (9,26) (9,15) (9,24) (9,14) (9,11) (9,23) (10,26) (10,15) (10,12) (10,23) (11,26) (11,15) (11,27) (11,12) (11,17) (11,23) (12,20) (12,24) (12,14) (13,22) (14,19) (14,17) (14,21) (15,19) (15,23) (15,21) (16,24) (16,19) (16,21) (17,24) (18,25) (19,26) (19,24) (20,27) (21,24) (21,27) (23,26) (23,24) (24,26)\nIs there a path between node 25 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph655-15_16", + "image": "data/connectivity/graph_visual/hard/graph655.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,9) (0,3) (0,34) (0,12) (0,2) (0,13) (0,24) (0,31) (0,17) (0,6) (1,7) (1,10) (1,20) (1,22) (1,15) (1,16) (2,9) (2,27) (2,11) (2,34) (2,18) (2,31) (2,28) (2,17) (3,9) (3,27) (3,34) (3,21) (3,12) (3,13) (3,24) (3,31) (3,28) (3,17) (4,7) (4,10) (4,20) (4,22) (4,15) (5,7) (5,10) (5,30) (5,20) (5,16) (6,9) (6,34) (6,21) (6,12) (6,13) (6,31) (6,33) (6,17) (7,10) (7,30) (7,15) (7,16) (8,19) (8,29) (8,23) (9,27) (9,11) (9,34) (9,18) (9,13) (9,24) (9,31) (9,33) (9,28) (9,17) (10,30) (10,20) (10,15) (10,16) (11,27) (11,34) (11,21) (11,18) (11,12) (11,24) (11,31) (11,33) (11,28) (11,17) (12,34) (12,21) (12,18) (12,13) (12,24) (12,31) (12,33) (12,28) (12,17) (13,27) (13,34) (13,21) (13,18) (13,24) (13,33) (13,28) (13,17) (14,19) (14,29) (14,23) (14,25) (15,30) (15,20) (15,22) (16,30) (16,20) (16,22) (17,34) (17,21) (17,18) (17,31) (17,33) (17,28) (18,24) (18,33) (18,28) (19,29) (19,32) (19,25) (20,22) (21,27) (21,34) (21,24) (21,31) (21,28) (22,30) (23,26) (23,29) (24,27) (24,34) (24,31) (24,33) (24,28) (25,26) (25,32) (26,29) (26,32) (27,34) (27,31) (27,33) (28,34) (28,31) (29,32) (31,34) (33,34)\nIs there a path between node 15 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph316-28_23", + "image": "data/connectivity/graph_visual/hard/graph316.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,19) (0,31) (0,15) (0,18) (1,24) (1,19) (1,31) (1,5) (2,30) (2,23) (2,4) (2,17) (3,30) (3,23) (3,12) (3,17) (5,28) (5,6) (5,14) (5,9) (5,31) (5,18) (6,10) (6,13) (6,19) (6,31) (6,21) (6,18) (7,28) (7,14) (7,25) (7,20) (8,26) (8,23) (8,12) (8,17) (9,22) (9,13) (9,29) (9,31) (9,15) (9,21) (9,18) (10,13) (10,19) (10,14) (10,15) (10,18) (11,12) (11,16) (12,30) (12,17) (13,28) (13,29) (13,15) (13,21) (13,20) (13,18) (14,22) (14,24) (14,29) (15,29) (15,25) (16,26) (17,30) (18,25) (18,20) (19,29) (19,21) (19,20) (20,22) (20,28) (20,29) (20,25) (21,27) (21,31) (22,28) (22,29) (23,30) (23,26) (24,29) (24,31) (27,31)\nIs there a path between node 28 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph580-28_10", + "image": "data/connectivity/graph_visual/hard/graph580.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,5) (0,29) (0,21) (0,24) (0,15) (0,16) (0,27) (0,33) (0,11) (0,8) (0,19) (0,32) (1,22) (1,18) (2,9) (2,29) (2,4) (2,21) (2,20) (2,15) (2,16) (2,27) (2,33) (2,8) (2,19) (2,30) (2,32) (3,14) (3,23) (3,17) (3,12) (3,7) (3,13) (3,28) (3,31) (3,10) (4,9) (4,21) (4,20) (4,15) (4,16) (4,27) (4,11) (4,8) (4,19) (5,9) (5,29) (5,21) (5,24) (5,15) (5,33) (5,11) (5,8) (5,19) (5,32) (6,14) (6,26) (6,25) (6,12) (6,13) (6,28) (7,23) (7,17) (7,26) (7,25) (7,31) (7,10) (8,9) (8,29) (8,24) (8,15) (8,16) (8,27) (8,33) (8,11) (8,30) (8,32) (9,29) (9,21) (9,24) (9,20) (9,15) (9,16) (9,33) (9,11) (9,19) (9,30) (9,32) (10,14) (10,17) (10,26) (10,25) (10,12) (10,13) (10,28) (10,31) (11,29) (11,21) (11,24) (11,20) (11,15) (11,16) (11,27) (11,19) (11,30) (12,14) (12,17) (12,25) (12,13) (12,28) (12,31) (13,14) (13,17) (13,26) (13,31) (14,26) (14,31) (15,29) (15,20) (15,16) (15,27) (15,33) (15,19) (15,30) (15,32) (16,29) (16,21) (16,20) (16,27) (16,33) (16,19) (16,30) (16,32) (17,23) (17,25) (17,28) (18,22) (19,29) (19,21) (19,24) (19,20) (19,27) (19,33) (19,32) (20,21) (20,27) (20,33) (20,30) (21,29) (21,33) (21,30) (23,26) (23,31) (24,29) (24,27) (25,26) (26,28) (27,29) (27,33) (27,30) (27,32) (28,31) (29,33) (29,30) (30,33) (30,32) (32,33)\nIs there a path between node 28 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph343-6_8", + "image": "data/connectivity/graph_visual/hard/graph343.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,23) (0,28) (0,25) (0,17) (0,3) (0,10) (0,31) (0,7) (0,12) (0,14) (1,18) (1,28) (1,2) (1,3) (1,7) (1,30) (1,5) (2,24) (2,25) (2,29) (2,8) (2,30) (2,19) (2,5) (3,22) (3,25) (3,4) (3,29) (3,17) (3,21) (4,23) (4,21) (4,8) (4,19) (5,22) (5,9) (5,21) (5,10) (5,8) (5,30) (5,14) (6,18) (6,9) (6,10) (6,7) (6,14) (7,22) (7,18) (7,24) (7,9) (7,29) (7,8) (7,30) (7,13) (8,26) (8,23) (8,28) (8,9) (8,21) (9,26) (9,22) (9,25) (9,17) (9,31) (9,12) (9,14) (9,13) (10,22) (10,23) (10,28) (10,17) (10,21) (10,12) (10,13) (11,22) (11,24) (11,30) (12,23) (12,17) (12,30) (12,14) (13,23) (13,28) (13,30) (13,14) (14,22) (14,24) (14,25) (14,17) (14,21) (14,31) (14,30) (17,26) (17,22) (17,24) (18,26) (18,24) (18,30) (19,23) (19,29) (19,31) (21,23) (22,24) (22,29) (22,31) (23,26) (23,24) (23,28) (23,31) (24,28) (24,31) (25,28) (28,31) (29,31) (30,31)\nIs there a path between node 6 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph276-30_29", + "image": "data/connectivity/graph_visual/hard/graph276.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,15) (0,11) (0,30) (0,8) (0,25) (0,7) (0,17) (0,23) (0,3) (0,27) (0,10) (0,28) (0,26) (0,14) (0,29) (1,15) (1,11) (1,20) (1,25) (1,17) (1,23) (1,3) (1,27) (1,10) (1,28) (1,26) (1,14) (2,9) (2,13) (2,18) (2,22) (3,30) (3,8) (3,20) (3,7) (3,23) (3,27) (3,10) (3,28) (3,26) (3,14) (3,29) (4,21) (4,19) (4,12) (4,24) (4,16) (5,9) (5,18) (5,22) (6,21) (6,19) (6,12) (6,24) (7,15) (7,11) (7,8) (7,17) (7,23) (7,10) (7,28) (7,26) (7,14) (8,15) (8,11) (8,30) (8,17) (8,10) (8,26) (8,29) (9,13) (9,18) (10,11) (10,30) (10,20) (10,25) (10,17) (10,28) (10,26) (10,14) (10,29) (11,15) (11,25) (11,17) (11,23) (11,27) (11,29) (12,21) (12,19) (13,18) (13,22) (14,15) (14,20) (14,25) (14,17) (14,23) (14,28) (14,26) (14,29) (15,30) (15,20) (15,25) (15,17) (15,23) (15,27) (15,29) (16,19) (17,20) (17,25) (17,23) (17,27) (17,28) (17,29) (20,30) (20,25) (20,27) (20,28) (20,26) (20,29) (21,24) (23,30) (23,25) (23,28) (23,26) (23,29) (25,27) (25,26) (26,29) (27,30) (27,29) (28,30) (28,29) (29,30)\nIs there a path between node 30 and node 29 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph12-10_13", + "image": "data/connectivity/graph_visual/hard/graph12.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,25) (0,7) (0,15) (0,3) (0,17) (0,23) (0,2) (0,19) (0,16) (0,6) (0,4) (0,22) (0,1) (0,8) (0,13) (0,21) (1,25) (1,11) (1,7) (1,20) (1,5) (1,15) (1,3) (1,23) (1,12) (1,18) (1,2) (1,19) (1,9) (1,16) (1,4) (1,22) (1,13) (1,21) (2,11) (2,5) (2,3) (2,17) (2,23) (2,12) (2,19) (2,9) (2,16) (2,6) (2,22) (2,8) (2,13) (2,21) (3,25) (3,11) (3,5) (3,15) (3,23) (3,12) (3,18) (3,19) (3,9) (3,16) (3,4) (3,22) (3,8) (3,13) (4,11) (4,20) (4,5) (4,15) (4,17) (4,23) (4,12) (4,18) (4,19) (4,9) (4,16) (4,6) (4,22) (5,15) (5,17) (5,18) (5,19) (5,9) (5,16) (5,6) (5,22) (5,13) (5,21) (6,11) (6,7) (6,20) (6,15) (6,23) (6,12) (6,19) (6,9) (6,16) (6,22) (6,8) (6,13) (6,21) (7,11) (7,15) (7,23) (7,12) (7,19) (7,9) (7,16) (7,8) (7,13) (8,25) (8,11) (8,15) (8,17) (8,12) (8,18) (8,19) (8,9) (8,22) (8,13) (8,21) (9,25) (9,11) (9,15) (9,17) (9,23) (9,12) (9,18) (9,19) (9,16) (9,22) (10,24) (10,14) (11,25) (11,20) (11,23) (11,12) (11,18) (11,19) (11,13) (11,21) (12,25) (12,20) (12,15) (12,17) (12,23) (12,18) (12,19) (12,16) (12,21) (13,25) (13,20) (13,15) (13,23) (13,18) (13,16) (13,22) (14,24) (15,20) (15,17) (15,23) (15,18) (15,19) (15,16) (15,22) (15,21) (16,25) (16,20) (16,17) (16,23) (16,18) (16,19) (16,22) (17,25) (17,20) (17,23) (17,19) (17,22) (17,21) (18,25) (18,20) (19,25) (19,20) (19,22) (20,25) (20,21) (21,25) (21,22) (22,25) (23,25)\nIs there a path between node 10 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph629-13_17", + "image": "data/connectivity/graph_visual/hard/graph629.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,1) (0,28) (0,7) (0,32) (0,34) (0,29) (1,16) (1,9) (1,27) (1,4) (1,22) (1,34) (2,16) (2,28) (2,9) (2,5) (2,31) (2,22) (3,13) (3,17) (3,26) (3,12) (4,24) (4,11) (4,7) (4,5) (4,27) (4,22) (5,16) (5,9) (5,31) (5,23) (6,17) (6,12) (7,24) (7,32) (7,31) (7,23) (8,21) (9,28) (9,11) (11,31) (11,19) (11,23) (12,18) (12,17) (13,20) (13,26) (14,24) (14,32) (14,27) (14,19) (14,29) (15,30) (16,24) (16,23) (19,27) (20,33) (21,25) (22,32) (22,29) (23,28) (23,24) (23,27) (24,27) (24,31) (27,32) (27,34) (31,34)\nIs there a path between node 13 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph694-9_20", + "image": "data/connectivity/graph_visual/hard/graph694.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,29) (0,33) (0,25) (0,14) (0,16) (0,4) (0,26) (0,5) (0,27) (0,20) (0,1) (0,7) (0,30) (0,2) (0,9) (0,13) (0,23) (1,29) (1,33) (1,25) (1,14) (1,26) (1,5) (1,20) (1,7) (1,31) (1,30) (1,9) (1,13) (1,23) (2,29) (2,33) (2,25) (2,14) (2,16) (2,4) (2,26) (2,5) (2,27) (2,20) (2,7) (2,31) (2,12) (2,9) (2,23) (3,32) (3,10) (3,6) (3,19) (3,8) (3,15) (3,17) (3,22) (3,21) (3,28) (4,29) (4,33) (4,25) (4,16) (4,26) (4,5) (4,27) (4,31) (4,30) (4,12) (4,13) (4,34) (4,23) (5,29) (5,25) (5,26) (5,27) (5,20) (5,7) (5,31) (5,30) (5,12) (5,9) (5,13) (5,34) (5,23) (6,11) (6,32) (6,19) (6,8) (6,24) (6,18) (6,17) (6,22) (6,21) (6,28) (7,29) (7,33) (7,25) (7,14) (7,16) (7,26) (7,31) (7,30) (7,12) (7,9) (7,13) (7,34) (7,23) (8,11) (8,10) (8,19) (8,15) (8,24) (8,17) (8,22) (8,21) (9,33) (9,25) (9,14) (9,16) (9,26) (9,20) (9,31) (9,12) (9,34) (9,23) (10,11) (10,32) (10,24) (10,18) (10,28) (11,32) (11,19) (11,15) (11,24) (11,18) (11,17) (11,21) (12,29) (12,33) (12,25) (12,16) (12,26) (12,27) (12,31) (12,30) (12,13) (12,34) (13,33) (13,25) (13,27) (13,20) (13,31) (13,30) (13,34) (14,29) (14,33) (14,25) (14,16) (14,27) (14,31) (14,34) (14,23) (15,32) (15,19) (15,22) (15,21) (15,28) (16,33) (16,25) (16,26) (16,27) (16,30) (17,32) (17,24) (17,18) (17,22) (17,28) (18,32) (18,19) (18,24) (18,22) (18,21) (18,28) (19,32) (19,24) (19,22) (19,21) (20,25) (20,26) (20,27) (20,31) (20,30) (20,23) (21,24) (21,22) (21,28) (22,24) (22,28) (23,29) (23,33) (23,26) (23,31) (23,34) (24,32) (24,28) (25,29) (25,33) (25,27) (25,31) (25,30) (25,34) (26,33) (26,27) (26,30) (26,34) (27,29) (27,31) (27,30) (27,34) (28,32) (29,33) (29,30) (29,34) (30,33) (30,31) (30,34) (31,33) (31,34) (33,34)\nIs there a path between node 9 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph167-22_24", + "image": "data/connectivity/graph_visual/hard/graph167.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,15) (0,8) (0,7) (0,4) (0,28) (0,18) (1,21) (1,15) (1,19) (1,25) (1,10) (1,4) (1,27) (1,5) (2,6) (2,14) (2,12) (2,8) (2,4) (2,11) (2,17) (3,21) (3,15) (3,6) (3,20) (3,23) (3,10) (3,7) (3,16) (3,28) (3,5) (3,18) (4,15) (4,14) (4,24) (4,20) (4,10) (4,11) (5,8) (5,27) (5,16) (5,11) (6,20) (6,16) (6,26) (6,18) (7,14) (7,19) (7,25) (7,12) (7,23) (7,8) (7,17) (7,13) (8,20) (8,16) (8,13) (10,25) (10,11) (10,26) (11,20) (11,28) (11,17) (11,18) (12,20) (12,28) (13,19) (13,27) (13,18) (14,21) (14,15) (14,23) (15,21) (15,19) (15,24) (15,16) (16,21) (16,20) (16,23) (16,26) (17,24) (17,20) (17,27) (18,19) (18,28) (19,21) (19,27) (19,28) (19,26) (20,28) (23,25) (24,25) (24,28) (25,28)\nIs there a path between node 22 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph124-5_20", + "image": "data/connectivity/graph_visual/hard/graph124.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,1) (0,16) (0,23) (0,12) (1,20) (1,18) (1,23) (1,12) (1,6) (2,24) (2,7) (2,15) (2,11) (2,25) (2,26) (2,14) (2,27) (2,10) (2,8) (2,21) (2,17) (2,4) (3,7) (3,9) (3,15) (3,11) (3,25) (3,14) (3,21) (3,17) (3,5) (3,4) (4,24) (4,7) (4,9) (4,15) (4,11) (4,26) (4,14) (4,27) (4,10) (4,8) (4,5) (5,15) (5,11) (5,25) (5,14) (5,27) (5,10) (5,21) (5,13) (5,17) (6,16) (6,12) (7,19) (7,9) (7,15) (7,25) (7,14) (7,21) (7,13) (7,17) (8,24) (8,9) (8,15) (8,25) (8,26) (8,27) (8,10) (8,13) (8,17) (9,24) (9,15) (9,25) (9,26) (9,14) (9,10) (9,21) (9,13) (10,19) (10,15) (10,11) (10,25) (10,26) (10,21) (10,13) (10,17) (11,19) (11,24) (11,15) (11,26) (11,14) (11,21) (11,13) (12,20) (12,16) (12,18) (13,19) (13,15) (13,14) (13,21) (13,17) (14,15) (14,25) (14,26) (14,27) (14,17) (15,19) (15,24) (15,25) (15,26) (15,21) (15,17) (16,23) (17,24) (17,25) (17,27) (18,20) (18,23) (19,24) (19,25) (19,26) (19,27) (20,23) (21,24) (21,26) (21,27) (24,25) (24,27) (25,27) (26,27)\nIs there a path between node 5 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph280-29_19", + "image": "data/connectivity/graph_visual/hard/graph280.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,12) (0,14) (0,16) (0,20) (0,8) (0,13) (0,18) (0,10) (0,29) (0,3) (0,7) (0,9) (1,26) (1,5) (1,11) (1,19) (1,28) (1,24) (1,6) (2,12) (2,14) (2,16) (2,20) (2,8) (2,13) (2,23) (2,18) (2,25) (2,3) (2,7) (2,9) (3,16) (3,8) (3,13) (3,18) (3,25) (3,10) (3,29) (3,7) (4,15) (4,27) (5,28) (5,24) (5,22) (6,26) (6,11) (6,19) (6,28) (6,24) (6,22) (7,14) (7,16) (7,20) (7,13) (7,23) (7,25) (7,10) (7,21) (7,9) (8,14) (8,20) (8,13) (8,23) (8,10) (9,14) (9,16) (9,20) (9,13) (9,18) (9,25) (9,21) (9,29) (10,14) (10,16) (10,20) (10,13) (10,23) (10,25) (10,21) (11,26) (11,17) (11,24) (11,22) (12,14) (12,16) (12,13) (12,23) (12,18) (12,25) (12,21) (12,29) (13,14) (13,16) (13,18) (13,21) (13,29) (14,16) (14,20) (14,23) (14,18) (14,21) (14,29) (15,30) (15,27) (16,20) (16,23) (16,25) (16,21) (16,29) (17,26) (17,19) (17,28) (17,22) (18,23) (18,25) (18,21) (18,29) (19,26) (20,23) (20,25) (20,29) (21,23) (21,25) (21,29) (22,26) (22,28) (22,24) (23,25) (23,29) (24,26) (24,28) (25,29) (26,28)\nIs there a path between node 29 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph41-5_20", + "image": "data/connectivity/graph_visual/hard/graph41.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,17) (0,2) (0,25) (0,14) (0,9) (0,15) (0,12) (0,1) (0,7) (0,16) (0,18) (0,11) (0,10) (0,5) (1,17) (1,2) (1,21) (1,14) (1,9) (1,15) (1,12) (1,19) (1,8) (1,7) (1,18) (1,11) (1,10) (1,5) (2,17) (2,21) (2,14) (2,9) (2,13) (2,3) (2,12) (2,6) (2,19) (2,7) (2,18) (2,11) (2,5) (3,17) (3,22) (3,21) (3,9) (3,15) (3,13) (3,6) (3,19) (3,8) (3,7) (3,16) (3,18) (3,11) (4,20) (4,23) (4,24) (5,17) (5,22) (5,21) (5,9) (5,15) (5,12) (5,19) (5,8) (5,16) (5,11) (5,10) (6,22) (6,25) (6,9) (6,15) (6,13) (6,12) (6,19) (6,8) (6,7) (6,16) (7,17) (7,22) (7,25) (7,9) (7,15) (7,13) (7,12) (7,19) (7,8) (7,16) (7,11) (7,10) (8,17) (8,22) (8,14) (8,12) (8,16) (8,18) (8,11) (9,17) (9,22) (9,25) (9,15) (9,13) (9,12) (9,19) (9,16) (9,18) (9,11) (10,17) (10,22) (10,25) (10,13) (10,19) (10,11) (11,17) (11,25) (11,14) (11,15) (11,13) (11,12) (11,19) (12,22) (12,21) (12,14) (12,19) (12,16) (13,22) (13,25) (13,21) (13,14) (13,16) (14,17) (14,21) (14,15) (14,19) (14,16) (14,18) (15,17) (15,25) (15,21) (15,16) (16,22) (16,25) (16,21) (16,19) (16,18) (17,22) (17,25) (17,21) (17,19) (17,18) (18,22) (18,21) (18,19) (19,22) (19,25) (19,21) (20,23) (20,24) (21,22) (21,25) (23,24)\nIs there a path between node 5 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph236-11_9", + "image": "data/connectivity/graph_visual/hard/graph236.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,2) (1,26) (2,26) (2,30) (2,6) (3,19) (4,29) (4,8) (4,11) (4,9) (5,25) (6,30) (6,19) (6,13) (6,25) (7,23) (7,29) (7,10) (7,28) (7,14) (8,23) (8,15) (8,27) (8,18) (8,11) (8,28) (8,9) (9,23) (9,29) (9,15) (9,18) (9,12) (10,15) (11,29) (11,27) (11,28) (11,14) (12,27) (13,16) (13,26) (14,17) (15,29) (15,21) (15,28) (16,25) (17,23) (17,29) (17,18) (19,20) (19,22) (20,22) (21,27) (21,28) (22,26) (23,29) (23,28) (24,26) (24,30) (25,26) (25,30) (27,28)\nIs there a path between node 11 and node 9 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph317-31_24", + "image": "data/connectivity/graph_visual/hard/graph317.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,31) (0,12) (0,22) (0,2) (1,18) (1,31) (1,30) (1,10) (1,2) (2,9) (2,31) (2,30) (2,12) (2,17) (2,16) (2,24) (3,20) (3,28) (3,14) (4,27) (4,29) (4,28) (4,7) (4,26) (5,29) (5,28) (6,8) (6,27) (6,15) (6,29) (7,20) (7,19) (7,29) (8,19) (8,11) (8,21) (8,29) (8,28) (9,18) (9,23) (9,16) (9,22) (10,30) (11,25) (11,19) (11,14) (11,26) (12,31) (13,25) (13,27) (13,29) (14,20) (14,28) (14,26) (15,20) (15,27) (15,26) (16,31) (16,30) (17,18) (18,31) (18,30) (18,22) (19,28) (20,21) (20,29) (20,28) (20,26) (21,25) (21,27) (22,24) (23,31) (24,31) (26,29)\nIs there a path between node 31 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph420-7_24", + "image": "data/connectivity/graph_visual/hard/graph420.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,14) (0,12) (0,5) (0,20) (0,28) (1,14) (1,27) (2,21) (2,16) (3,29) (3,31) (3,22) (3,17) (4,13) (4,9) (5,12) (5,32) (5,11) (6,14) (6,12) (6,32) (6,28) (7,10) (7,20) (7,27) (8,21) (8,15) (9,26) (9,31) (9,30) (9,17) (10,20) (10,28) (11,14) (11,12) (12,20) (12,32) (12,28) (13,29) (13,31) (13,22) (14,28) (15,16) (15,24) (16,19) (17,26) (17,18) (20,23) (21,24) (22,26) (22,31) (26,30)\nIs there a path between node 7 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph245-5_7", + "image": "data/connectivity/graph_visual/hard/graph245.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,3) (0,14) (0,17) (0,2) (0,25) (0,8) (0,21) (0,10) (0,18) (0,19) (0,26) (0,4) (0,29) (0,20) (0,13) (0,12) (1,3) (1,14) (1,17) (1,25) (1,8) (1,21) (1,16) (1,15) (1,10) (1,19) (1,9) (1,4) (1,5) (1,29) (1,30) (1,27) (1,13) (1,12) (2,3) (2,17) (2,24) (2,8) (2,16) (2,15) (2,26) (2,4) (2,29) (2,30) (2,27) (2,13) (3,14) (3,17) (3,24) (3,25) (3,8) (3,21) (3,16) (3,10) (3,9) (3,26) (3,29) (3,30) (3,27) (3,20) (3,13) (3,12) (4,25) (4,8) (4,21) (4,16) (4,10) (4,18) (4,19) (4,9) (4,5) (4,30) (4,27) (4,20) (5,14) (5,17) (5,24) (5,8) (5,21) (5,16) (5,15) (5,10) (5,18) (5,19) (5,9) (5,26) (5,30) (5,27) (5,20) (6,22) (6,7) (6,23) (8,14) (8,17) (8,25) (8,16) (8,15) (8,18) (8,19) (8,9) (8,26) (8,29) (8,30) (8,27) (8,13) (9,14) (9,17) (9,24) (9,25) (9,16) (9,15) (9,10) (9,26) (9,30) (9,20) (9,13) (10,14) (10,17) (10,24) (10,25) (10,21) (10,18) (10,29) (10,30) (10,27) (10,20) (10,13) (10,12) (11,28) (12,14) (12,25) (12,21) (12,16) (12,18) (12,19) (12,29) (12,27) (13,14) (13,17) (13,24) (13,16) (13,15) (13,19) (13,29) (13,30) (13,27) (14,17) (14,25) (14,21) (14,18) (14,19) (14,26) (14,29) (14,27) (14,20) (15,17) (15,24) (15,25) (15,16) (15,18) (15,19) (15,26) (15,29) (15,30) (15,20) (16,17) (16,24) (16,19) (16,26) (16,29) (16,30) (16,27) (16,20) (17,24) (17,21) (17,19) (17,30) (17,27) (18,24) (18,25) (18,21) (18,19) (18,26) (18,29) (18,30) (18,27) (19,25) (19,26) (19,29) (19,27) (19,20) (20,24) (20,25) (20,26) (20,29) (20,30) (20,27) (21,25) (21,26) (21,29) (21,30) (21,27) (24,25) (24,26) (24,29) (24,27) (25,26) (25,30) (25,27) (26,30) (26,27) (27,29) (29,30)\nIs there a path between node 5 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph504-20_18", + "image": "data/connectivity/graph_visual/hard/graph504.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,23) (0,22) (0,17) (0,15) (0,9) (0,8) (0,6) (0,13) (0,7) (0,18) (0,12) (0,20) (0,24) (0,33) (0,27) (0,11) (0,30) (1,2) (1,16) (2,16) (2,5) (3,23) (3,19) (3,25) (3,22) (3,32) (3,15) (3,21) (3,8) (3,10) (3,14) (3,6) (3,13) (3,7) (3,18) (3,24) (3,31) (3,33) (3,27) (3,11) (3,30) (4,16) (4,5) (6,23) (6,28) (6,19) (6,25) (6,26) (6,29) (6,22) (6,17) (6,8) (6,10) (6,14) (6,13) (6,18) (6,12) (6,20) (6,24) (6,31) (6,33) (6,27) (6,30) (7,23) (7,28) (7,19) (7,26) (7,29) (7,22) (7,17) (7,21) (7,9) (7,10) (7,14) (7,13) (7,18) (7,12) (7,31) (7,33) (7,27) (7,11) (8,23) (8,25) (8,26) (8,29) (8,32) (8,17) (8,21) (8,9) (8,10) (8,14) (8,13) (8,18) (8,12) (8,20) (8,24) (8,31) (8,33) (8,27) (8,11) (9,25) (9,26) (9,29) (9,22) (9,32) (9,17) (9,21) (9,14) (9,13) (9,18) (9,12) (9,20) (9,24) (9,33) (9,11) (10,28) (10,19) (10,26) (10,22) (10,32) (10,17) (10,15) (10,13) (10,18) (10,12) (10,24) (10,33) (10,27) (10,30) (11,23) (11,28) (11,25) (11,26) (11,29) (11,32) (11,17) (11,13) (11,12) (11,20) (11,24) (11,27) (11,30) (12,28) (12,25) (12,26) (12,29) (12,32) (12,13) (12,18) (12,20) (12,31) (12,27) (12,30) (13,23) (13,19) (13,25) (13,26) (13,29) (13,22) (13,32) (13,17) (13,14) (13,24) (13,31) (13,33) (13,27) (14,23) (14,28) (14,19) (14,25) (14,22) (14,15) (14,21) (14,18) (14,20) (14,24) (14,27) (14,30) (15,28) (15,26) (15,29) (15,22) (15,20) (15,31) (15,33) (15,27) (15,30) (17,23) (17,28) (17,19) (17,25) (17,26) (17,22) (17,32) (17,21) (17,18) (17,20) (17,24) (17,27) (17,30) (18,23) (18,28) (18,19) (18,25) (18,26) (18,32) (18,21) (18,20) (18,24) (18,31) (18,33) (18,27) (18,30) (19,23) (19,28) (19,25) (19,26) (19,29) (19,22) (19,32) (19,21) (19,30) (20,22) (20,32) (20,21) (20,31) (20,33) (20,27) (21,23) (21,25) (21,26) (21,22) (21,32) (21,24) (21,31) (21,33) (21,27) (21,30) (22,23) (22,26) (22,29) (22,32) (22,31) (22,33) (22,30) (23,26) (23,29) (23,32) (23,24) (23,31) (23,33) (24,25) (24,26) (24,29) (24,32) (24,31) (24,33) (24,27) (24,30) (25,26) (25,32) (25,31) (25,33) (25,30) (26,28) (26,29) (26,32) (26,31) (26,27) (27,28) (27,29) (27,31) (27,33) (27,30) (28,29) (28,31) (28,33) (29,32) (29,33) (29,30) (30,32) (30,31) (30,33) (31,32) (31,33) (32,33)\nIs there a path between node 20 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph367-4_12", + "image": "data/connectivity/graph_visual/hard/graph367.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,5) (0,11) (0,22) (0,20) (0,17) (0,13) (0,6) (0,8) (0,23) (0,18) (0,29) (0,10) (0,2) (0,21) (0,9) (0,25) (1,22) (1,20) (1,17) (1,13) (1,6) (1,12) (1,23) (1,19) (1,18) (1,14) (1,29) (1,10) (1,2) (1,21) (1,30) (1,3) (1,26) (1,25) (2,20) (2,15) (2,13) (2,6) (2,23) (2,29) (2,10) (2,3) (2,26) (2,25) (3,5) (3,11) (3,22) (3,20) (3,15) (3,6) (3,19) (3,18) (3,14) (3,21) (3,30) (3,9) (3,26) (4,28) (4,7) (4,16) (5,11) (5,20) (5,17) (5,13) (5,6) (5,8) (5,18) (5,14) (5,10) (5,21) (5,26) (5,25) (6,11) (6,22) (6,15) (6,17) (6,8) (6,23) (6,19) (6,18) (6,14) (6,29) (6,10) (6,21) (6,9) (6,25) (7,31) (7,28) (7,27) (8,22) (8,15) (8,17) (8,13) (8,23) (8,19) (8,18) (8,29) (8,10) (8,21) (8,30) (8,9) (8,26) (9,11) (9,22) (9,15) (9,17) (9,12) (9,14) (9,29) (9,21) (9,25) (10,22) (10,20) (10,15) (10,17) (10,12) (10,23) (10,19) (10,18) (10,14) (10,29) (10,21) (10,26) (10,25) (11,22) (11,15) (11,12) (11,19) (11,18) (11,14) (11,29) (11,21) (11,30) (11,26) (12,22) (12,20) (12,15) (12,17) (12,13) (12,23) (12,19) (12,18) (12,29) (12,30) (12,26) (12,25) (13,22) (13,20) (13,15) (13,17) (13,23) (13,14) (13,29) (13,21) (13,30) (13,26) (13,25) (14,20) (14,15) (14,17) (14,19) (14,29) (14,30) (14,26) (14,25) (15,22) (15,20) (15,23) (15,19) (15,29) (15,21) (15,30) (16,24) (16,28) (17,22) (17,20) (17,23) (17,19) (17,18) (17,29) (17,30) (18,20) (18,23) (18,19) (18,21) (18,26) (19,20) (19,23) (19,29) (19,21) (19,26) (19,25) (20,22) (20,23) (20,21) (20,30) (20,26) (20,25) (21,22) (21,25) (22,30) (22,26) (22,25) (23,29) (23,26) (24,31) (24,28) (24,27) (25,29) (26,29) (27,28) (29,30)\nIs there a path between node 4 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph201-28_23", + "image": "data/connectivity/graph_visual/hard/graph201.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,28) (0,3) (0,20) (0,27) (0,24) (0,12) (0,5) (0,17) (0,26) (0,10) (0,11) (0,7) (0,1) (0,19) (0,9) (0,14) (1,28) (1,16) (1,3) (1,15) (1,20) (1,21) (1,27) (1,24) (1,12) (1,25) (1,5) (1,17) (1,6) (1,26) (1,11) (1,2) (1,19) (1,14) (1,23) (2,28) (2,16) (2,15) (2,20) (2,21) (2,27) (2,24) (2,12) (2,25) (2,5) (2,17) (2,26) (2,10) (2,9) (2,23) (3,28) (3,16) (3,20) (3,27) (3,25) (3,5) (3,6) (3,11) (3,7) (3,9) (3,14) (4,18) (4,29) (4,22) (4,8) (5,16) (5,20) (5,21) (5,27) (5,24) (5,12) (5,25) (5,17) (5,6) (5,26) (5,10) (5,11) (5,19) (5,9) (5,14) (5,23) (6,28) (6,16) (6,15) (6,20) (6,21) (6,27) (6,12) (6,17) (6,26) (6,10) (6,11) (6,7) (6,19) (6,9) (6,23) (7,28) (7,16) (7,20) (7,24) (7,25) (7,17) (7,10) (7,11) (7,19) (7,9) (7,23) (8,18) (8,29) (8,22) (9,15) (9,20) (9,27) (9,24) (9,17) (9,19) (9,14) (9,23) (10,16) (10,15) (10,27) (10,24) (10,12) (10,17) (10,26) (10,11) (10,19) (10,23) (11,28) (11,16) (11,15) (11,20) (11,21) (11,24) (11,25) (11,17) (11,26) (11,14) (11,23) (12,16) (12,15) (12,20) (12,21) (12,27) (12,25) (12,26) (12,19) (12,14) (12,23) (13,18) (14,16) (14,15) (14,20) (14,21) (14,27) (14,25) (14,26) (14,19) (14,23) (15,21) (15,27) (15,24) (15,25) (15,17) (15,26) (15,23) (16,20) (16,27) (16,24) (16,17) (16,19) (16,23) (17,28) (17,20) (17,21) (17,27) (17,24) (17,25) (17,19) (18,29) (18,22) (19,28) (19,20) (19,21) (19,27) (19,24) (19,23) (20,21) (20,27) (20,25) (20,26) (20,23) (21,28) (21,24) (21,25) (21,26) (21,23) (22,29) (23,28) (23,25) (23,26) (24,27) (24,25) (24,26) (25,27) (25,26) (26,28) (26,27) (27,28)\nIs there a path between node 28 and node 23 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph233-24_22", + "image": "data/connectivity/graph_visual/hard/graph233.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,8) (0,16) (0,2) (0,21) (0,12) (0,22) (0,14) (0,1) (0,5) (0,27) (0,10) (0,23) (0,20) (1,8) (1,18) (1,26) (1,21) (1,22) (1,14) (1,6) (1,27) (1,3) (1,15) (1,10) (1,7) (1,23) (1,20) (2,18) (2,26) (2,21) (2,22) (2,14) (2,6) (2,3) (2,15) (2,10) (2,13) (2,7) (2,23) (2,20) (3,21) (3,14) (3,6) (3,15) (3,13) (3,7) (3,23) (4,11) (4,17) (4,9) (4,19) (5,8) (5,16) (5,21) (5,12) (5,14) (5,6) (5,15) (5,10) (5,13) (5,7) (6,16) (6,26) (6,21) (6,12) (6,27) (6,13) (6,7) (6,23) (7,8) (7,16) (7,18) (7,12) (7,22) (7,14) (7,27) (7,15) (7,10) (7,13) (7,23) (7,20) (8,16) (8,18) (8,26) (8,21) (8,22) (8,14) (8,27) (8,15) (8,13) (8,23) (8,20) (9,17) (10,16) (10,18) (10,26) (10,21) (10,12) (10,22) (10,14) (10,23) (10,20) (11,17) (11,28) (11,25) (11,19) (11,29) (12,16) (12,21) (12,22) (12,14) (12,27) (12,15) (12,13) (12,20) (13,16) (13,26) (13,21) (13,22) (13,14) (13,15) (13,23) (13,20) (14,16) (14,26) (14,21) (14,27) (14,15) (15,16) (15,18) (15,26) (15,21) (15,27) (15,23) (16,18) (16,26) (16,21) (16,22) (16,27) (16,20) (17,28) (17,25) (17,19) (17,29) (18,23) (19,28) (19,25) (20,26) (20,21) (20,27) (20,23) (21,26) (21,23) (22,26) (22,27) (23,26) (25,28) (25,29) (26,27) (28,29)\nIs there a path between node 24 and node 22 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph618-5_24", + "image": "data/connectivity/graph_visual/hard/graph618.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,34) (0,19) (0,17) (0,16) (0,31) (0,2) (0,7) (0,25) (0,22) (0,14) (1,28) (1,19) (1,16) (1,31) (1,8) (1,2) (1,7) (1,25) (1,14) (1,15) (2,28) (2,19) (2,17) (2,3) (2,31) (2,8) (2,7) (2,25) (2,20) (2,22) (2,14) (3,34) (3,19) (3,17) (3,16) (3,31) (3,7) (3,25) (3,22) (3,14) (4,18) (4,10) (4,24) (4,11) (4,6) (4,12) (4,26) (4,27) (4,13) (4,30) (4,21) (4,29) (5,18) (5,9) (5,11) (5,6) (5,26) (5,27) (5,30) (5,29) (6,18) (6,9) (6,24) (6,33) (6,12) (6,23) (6,27) (6,30) (7,34) (7,19) (7,16) (7,31) (7,8) (7,20) (7,14) (7,15) (8,28) (8,17) (8,16) (8,31) (8,25) (8,15) (9,18) (9,10) (9,24) (9,11) (9,33) (9,12) (9,32) (9,23) (9,13) (9,30) (9,29) (10,18) (10,24) (10,11) (10,33) (10,12) (10,32) (10,13) (10,30) (10,21) (10,29) (11,18) (11,12) (11,32) (11,23) (11,26) (11,27) (11,13) (11,30) (11,21) (12,18) (12,24) (12,33) (12,32) (12,23) (12,26) (12,27) (12,13) (12,21) (12,29) (13,18) (13,24) (13,33) (13,32) (13,23) (13,26) (13,27) (13,29) (14,34) (14,28) (14,19) (14,25) (14,22) (14,15) (15,34) (15,28) (15,19) (15,17) (15,16) (15,25) (15,20) (16,28) (16,31) (16,25) (16,22) (17,28) (17,19) (17,31) (17,25) (17,20) (17,22) (18,33) (18,32) (18,23) (18,26) (18,27) (19,34) (19,31) (19,22) (20,34) (20,31) (20,25) (20,22) (21,24) (21,33) (21,32) (21,27) (21,30) (21,29) (22,28) (22,31) (22,25) (23,24) (23,33) (23,32) (23,26) (23,27) (23,30) (24,32) (24,27) (24,30) (24,29) (25,28) (26,32) (26,27) (26,29) (28,34) (28,31) (29,32) (29,30) (30,33) (30,32) (31,34) (32,33)\nIs there a path between node 5 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph318-25_15", + "image": "data/connectivity/graph_visual/hard/graph318.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,22) (0,20) (0,21) (0,12) (0,4) (1,27) (1,9) (1,14) (1,25) (2,17) (2,14) (2,31) (3,13) (3,6) (3,20) (3,21) (3,19) (4,13) (5,11) (5,8) (5,7) (7,29) (7,16) (7,30) (8,29) (8,11) (8,10) (9,17) (9,27) (9,25) (10,16) (12,21) (12,19) (13,28) (13,20) (13,21) (14,27) (14,23) (14,31) (15,27) (15,23) (15,26) (17,23) (17,26) (18,21) (21,28) (23,31) (25,31) (25,26) (27,31) (29,30)\nIs there a path between node 25 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph320-0_10", + "image": "data/connectivity/graph_visual/hard/graph320.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,13) (0,6) (0,28) (1,30) (1,7) (1,26) (1,29) (1,8) (2,19) (2,22) (2,9) (2,20) (3,13) (3,23) (3,26) (3,17) (3,8) (3,4) (4,5) (4,28) (4,17) (5,10) (5,27) (5,26) (5,6) (6,15) (6,7) (6,27) (6,21) (6,23) (6,29) (6,28) (7,30) (7,10) (7,23) (7,26) (7,29) (8,15) (8,30) (8,29) (8,28) (9,18) (10,15) (10,27) (10,23) (10,26) (10,28) (11,14) (11,16) (11,18) (12,19) (12,20) (13,17) (14,19) (14,24) (14,25) (14,31) (15,21) (15,28) (16,22) (16,24) (17,30) (17,23) (17,29) (18,19) (18,22) (18,31) (19,31) (20,24) (21,30) (21,28) (26,30) (26,29) (28,30)\nIs there a path between node 0 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph587-13_17", + "image": "data/connectivity/graph_visual/hard/graph587.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,21) (0,30) (0,33) (0,6) (0,24) (0,25) (0,1) (0,17) (0,11) (0,16) (1,10) (1,30) (1,4) (1,33) (1,6) (1,25) (1,31) (1,5) (1,17) (1,11) (1,16) (2,27) (3,15) (3,28) (3,12) (3,32) (3,14) (3,20) (3,13) (4,21) (4,33) (4,6) (4,24) (4,25) (4,31) (4,5) (4,17) (4,11) (5,10) (5,21) (5,30) (5,33) (5,6) (5,24) (5,25) (5,31) (5,17) (5,11) (6,30) (6,33) (6,24) (6,25) (6,31) (6,17) (6,11) (6,16) (7,19) (7,29) (7,22) (7,18) (7,9) (8,23) (8,15) (8,28) (8,32) (8,14) (8,20) (9,19) (9,29) (9,22) (9,18) (10,30) (10,33) (10,24) (10,25) (10,31) (10,17) (10,11) (11,21) (11,30) (11,33) (11,24) (11,25) (11,17) (11,16) (12,23) (12,15) (12,32) (12,14) (12,13) (13,15) (13,28) (13,32) (13,14) (14,15) (14,28) (14,32) (15,23) (15,28) (15,32) (15,20) (16,30) (16,25) (16,17) (17,33) (17,31) (18,19) (18,29) (18,22) (19,29) (20,28) (20,32) (21,33) (21,24) (21,25) (21,31) (23,32) (24,30) (24,33) (24,25) (24,31) (25,33) (25,31) (26,27) (30,31)\nIs there a path between node 13 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph552-11_26", + "image": "data/connectivity/graph_visual/hard/graph552.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,27) (0,26) (0,3) (0,13) (0,22) (0,12) (0,31) (0,17) (1,2) (1,20) (1,23) (1,13) (1,4) (1,29) (2,20) (2,5) (2,6) (2,22) (2,16) (2,31) (2,17) (2,29) (3,27) (3,5) (3,23) (3,24) (3,15) (3,13) (3,4) (3,17) (4,7) (4,5) (4,15) (4,13) (4,10) (4,22) (4,16) (4,18) (4,12) (4,21) (5,27) (5,20) (5,14) (5,23) (5,6) (5,15) (5,13) (5,28) (5,12) (5,21) (5,8) (5,25) (6,26) (6,20) (6,23) (6,24) (6,15) (6,9) (6,28) (6,22) (6,16) (6,8) (7,9) (7,19) (7,12) (7,21) (7,25) (8,24) (8,15) (8,32) (8,31) (8,25) (9,23) (9,22) (9,19) (9,12) (9,17) (10,26) (10,14) (10,23) (10,28) (10,29) (11,33) (12,15) (12,28) (12,16) (12,29) (13,14) (13,24) (13,32) (13,18) (13,17) (14,27) (14,26) (14,15) (14,31) (14,17) (14,25) (15,27) (15,26) (15,28) (15,19) (15,25) (16,20) (16,19) (16,18) (16,25) (17,20) (17,24) (17,32) (17,18) (17,25) (18,27) (18,24) (18,22) (18,31) (18,29) (19,26) (19,29) (19,25) (20,27) (20,23) (20,24) (20,22) (20,31) (21,22) (22,32) (22,28) (22,29) (22,25) (23,32) (23,25) (24,31) (26,27) (26,32) (27,29) (28,32) (28,31) (29,31)\nIs there a path between node 11 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph574-19_26", + "image": "data/connectivity/graph_visual/hard/graph574.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,16) (0,28) (0,26) (0,7) (0,22) (0,6) (0,1) (0,30) (0,3) (1,16) (1,28) (1,26) (1,22) (1,10) (1,30) (2,4) (2,29) (2,24) (2,14) (2,21) (2,25) (2,13) (2,12) (2,31) (2,19) (2,33) (2,27) (2,23) (2,8) (2,18) (3,16) (3,28) (3,26) (3,9) (3,7) (3,10) (4,29) (4,32) (4,24) (4,21) (4,25) (4,15) (4,12) (4,31) (4,19) (4,33) (4,27) (4,17) (4,23) (4,18) (5,32) (5,14) (5,21) (5,15) (5,12) (5,19) (5,33) (5,27) (5,23) (5,8) (6,28) (6,26) (6,7) (6,22) (6,10) (7,16) (7,9) (7,22) (7,10) (8,29) (8,32) (8,24) (8,21) (8,15) (8,13) (8,33) (8,27) (8,23) (8,18) (9,16) (9,28) (9,26) (9,22) (9,10) (10,28) (10,22) (10,30) (12,29) (12,14) (12,21) (12,25) (12,15) (12,13) (12,31) (12,19) (12,33) (12,17) (12,23) (12,18) (13,20) (13,29) (13,24) (13,21) (13,25) (13,15) (13,31) (13,19) (13,33) (13,27) (13,17) (13,23) (13,18) (14,20) (14,29) (14,32) (14,24) (14,21) (14,15) (14,31) (14,19) (14,33) (14,17) (14,18) (15,20) (15,29) (15,32) (15,24) (15,21) (15,25) (15,31) (15,19) (15,33) (15,27) (15,17) (15,23) (15,18) (16,28) (16,26) (16,22) (16,30) (17,20) (17,29) (17,32) (17,24) (17,21) (17,25) (17,31) (17,19) (17,18) (18,20) (18,29) (18,32) (18,24) (18,21) (18,25) (18,31) (18,19) (18,27) (18,23) (19,32) (19,24) (19,33) (19,27) (19,23) (20,29) (20,32) (20,24) (20,21) (20,25) (20,31) (20,33) (20,27) (20,23) (21,32) (21,24) (21,25) (21,31) (21,33) (21,27) (21,23) (22,26) (22,30) (23,29) (23,32) (23,24) (23,25) (23,31) (23,33) (23,27) (24,32) (24,25) (24,31) (24,27) (25,29) (25,33) (25,27) (26,28) (26,30) (27,29) (27,31) (27,33) (28,30) (29,32) (29,31) (29,33) (31,32) (31,33) (32,33)\nIs there a path between node 19 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph354-25_7", + "image": "data/connectivity/graph_visual/hard/graph354.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,28) (1,7) (1,14) (1,13) (1,3) (1,5) (1,2) (1,21) (2,8) (2,27) (2,22) (3,8) (3,6) (3,7) (3,14) (4,30) (4,10) (5,14) (5,25) (5,23) (5,19) (6,11) (6,14) (6,22) (6,9) (6,16) (7,27) (7,9) (7,31) (7,23) (8,11) (8,20) (8,16) (8,19) (8,21) (9,25) (9,13) (9,31) (9,23) (9,19) (10,30) (10,12) (10,26) (11,31) (11,19) (11,21) (12,15) (12,30) (13,14) (13,23) (13,21) (14,20) (14,17) (14,23) (15,26) (16,22) (16,31) (17,20) (18,29) (19,23) (20,25) (21,25) (21,22) (22,31) (23,25) (23,31) (24,28) (24,30) (25,31) (26,30) (28,30) (28,29)\nIs there a path between node 25 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph382-2_17", + "image": "data/connectivity/graph_visual/hard/graph382.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,9) (0,16) (0,4) (0,22) (0,1) (0,23) (0,11) (0,21) (0,2) (0,13) (0,31) (0,19) (0,27) (0,17) (0,14) (0,3) (0,6) (0,12) (1,15) (1,9) (1,16) (1,4) (1,22) (1,23) (1,11) (1,21) (1,30) (1,13) (1,31) (1,19) (1,27) (1,17) (1,14) (1,12) (1,10) (2,9) (2,4) (2,23) (2,21) (2,30) (2,13) (2,31) (2,26) (2,19) (2,14) (2,3) (2,18) (3,15) (3,9) (3,16) (3,4) (3,22) (3,23) (3,11) (3,13) (3,31) (3,19) (3,17) (3,6) (4,15) (4,9) (4,16) (4,11) (4,21) (4,30) (4,13) (4,19) (4,27) (4,17) (4,14) (4,18) (4,12) (5,24) (5,20) (5,29) (5,8) (5,28) (6,15) (6,16) (6,22) (6,23) (6,21) (6,27) (6,14) (6,12) (6,10) (7,25) (8,24) (8,20) (8,28) (9,15) (9,16) (9,23) (9,30) (9,31) (9,26) (9,17) (9,14) (9,12) (9,10) (10,15) (10,16) (10,22) (10,11) (10,21) (10,30) (10,13) (10,31) (10,26) (10,19) (10,27) (10,18) (10,12) (11,16) (11,22) (11,23) (11,21) (11,30) (11,13) (11,31) (11,19) (11,17) (12,16) (12,22) (12,23) (12,30) (12,13) (12,31) (12,26) (12,19) (12,27) (12,17) (12,14) (13,15) (13,16) (13,22) (13,23) (13,30) (13,26) (13,19) (13,27) (13,17) (13,14) (14,16) (14,23) (14,21) (14,30) (14,31) (14,26) (14,19) (14,27) (14,17) (14,18) (15,16) (15,22) (15,23) (15,21) (15,26) (15,19) (15,17) (15,18) (16,22) (16,23) (16,30) (16,31) (16,26) (16,19) (16,27) (16,17) (16,18) (17,23) (17,21) (17,30) (17,31) (17,26) (17,19) (18,22) (18,23) (18,30) (18,26) (18,27) (19,22) (19,23) (19,21) (19,30) (19,26) (20,24) (20,29) (20,28) (21,22) (21,30) (21,27) (22,23) (22,31) (22,27) (23,30) (23,31) (23,26) (23,27) (24,28) (26,30) (26,31) (27,30) (27,31) (28,29) (30,31)\nIs there a path between node 2 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph15-7_3", + "image": "data/connectivity/graph_visual/hard/graph15.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,14) (0,7) (0,6) (0,23) (0,25) (1,4) (1,3) (1,5) (1,13) (1,10) (1,20) (1,16) (1,22) (1,8) (1,18) (1,15) (2,7) (2,12) (2,6) (2,25) (2,17) (2,9) (3,11) (3,20) (3,16) (3,22) (3,8) (4,11) (4,13) (4,10) (4,16) (4,8) (4,18) (4,15) (5,11) (5,13) (5,16) (5,22) (5,8) (5,18) (6,7) (6,12) (6,23) (6,25) (6,9) (7,14) (7,12) (7,23) (7,25) (7,21) (7,17) (7,9) (8,11) (8,13) (8,10) (8,20) (8,16) (8,22) (8,15) (9,14) (9,25) (9,21) (9,17) (10,11) (10,20) (10,22) (10,15) (11,20) (11,16) (11,22) (11,18) (12,14) (12,23) (12,25) (12,21) (12,17) (13,16) (14,23) (14,21) (14,17) (15,20) (15,22) (15,18) (16,20) (16,22) (16,18) (17,23) (17,21) (18,20) (18,22) (20,22) (23,25)\nIs there a path between node 7 and node 3 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph214-9_18", + "image": "data/connectivity/graph_visual/hard/graph214.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,5) (0,4) (0,22) (0,15) (2,28) (4,9) (4,15) (5,20) (5,22) (5,18) (6,25) (6,12) (7,10) (7,11) (8,21) (8,20) (8,15) (9,22) (9,18) (10,11) (11,24) (11,17) (11,27) (12,19) (12,13) (12,25) (13,25) (14,17) (15,20) (16,28) (18,21) (19,26) (21,22) (24,27) (25,29) (26,29)\nIs there a path between node 9 and node 18 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph45-21_24", + "image": "data/connectivity/graph_visual/hard/graph45.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,18) (0,10) (0,23) (0,3) (0,9) (0,26) (1,8) (1,20) (1,6) (1,4) (1,19) (1,16) (1,13) (1,24) (2,8) (2,20) (2,4) (2,19) (2,16) (2,13) (2,24) (2,12) (3,10) (3,9) (3,21) (3,22) (4,6) (4,19) (4,13) (4,24) (4,12) (5,15) (5,25) (5,11) (5,7) (6,8) (6,20) (6,19) (6,16) (6,13) (6,24) (7,15) (7,25) (7,14) (8,19) (8,13) (8,24) (8,12) (9,18) (9,23) (10,18) (10,23) (10,21) (10,26) (11,15) (11,17) (11,25) (12,20) (12,19) (12,16) (12,24) (13,20) (13,19) (13,16) (13,24) (14,17) (14,25) (15,17) (15,25) (16,20) (16,24) (17,25) (18,21) (18,22) (19,20) (19,24) (20,24) (21,23) (22,23) (22,26) (23,26)\nIs there a path between node 21 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph359-4_2", + "image": "data/connectivity/graph_visual/hard/graph359.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,13) (0,12) (0,15) (1,18) (1,31) (1,20) (1,30) (2,6) (2,14) (2,17) (2,5) (3,9) (3,29) (3,23) (3,17) (4,9) (4,21) (4,8) (4,14) (4,10) (5,16) (5,9) (5,21) (5,8) (5,10) (5,28) (6,11) (6,29) (6,22) (6,27) (7,18) (7,30) (7,26) (7,19) (8,29) (8,22) (8,14) (8,17) (8,10) (8,27) (9,16) (9,11) (9,14) (9,10) (10,16) (10,27) (11,21) (11,17) (12,30) (12,13) (12,25) (13,18) (13,24) (13,25) (13,19) (14,21) (14,22) (15,24) (16,21) (16,22) (16,28) (17,29) (17,21) (18,20) (19,20) (19,30) (19,25) (21,27) (22,28) (22,27) (23,29) (25,26)\nIs there a path between node 4 and node 2 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph417-30_27", + "image": "data/connectivity/graph_visual/hard/graph417.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,27) (1,2) (1,17) (2,10) (2,29) (2,31) (2,17) (2,24) (2,32) (3,27) (3,29) (3,32) (4,22) (4,23) (4,18) (4,12) (4,13) (4,6) (4,26) (5,15) (5,9) (5,13) (6,23) (6,20) (6,18) (6,9) (6,26) (7,10) (7,25) (7,21) (7,31) (8,27) (8,31) (8,30) (8,24) (8,11) (9,22) (9,20) (9,18) (9,15) (9,12) (9,26) (10,29) (11,31) (11,30) (11,32) (12,23) (12,20) (12,19) (13,28) (13,22) (13,20) (13,15) (13,26) (14,20) (14,18) (15,22) (15,19) (15,26) (16,24) (17,29) (17,21) (17,30) (17,32) (18,22) (18,19) (19,26) (20,28) (20,22) (21,25) (21,31) (21,24) (22,23) (24,27) (24,32) (26,28)\nIs there a path between node 30 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph357-22_14", + "image": "data/connectivity/graph_visual/hard/graph357.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,7) (0,22) (0,27) (1,18) (1,21) (1,15) (1,6) (1,29) (1,9) (1,4) (1,8) (1,28) (1,17) (2,13) (2,24) (2,14) (2,30) (2,12) (2,17) (2,5) (3,20) (3,14) (3,23) (3,15) (3,26) (3,9) (3,25) (3,8) (3,28) (3,17) (4,20) (4,18) (4,23) (4,15) (4,10) (4,30) (4,6) (4,26) (4,12) (4,16) (5,24) (5,14) (5,15) (5,6) (5,29) (5,12) (5,9) (5,8) (6,18) (6,10) (6,29) (6,28) (6,17) (7,27) (8,18) (8,21) (8,13) (8,23) (8,12) (8,25) (8,19) (8,17) (9,15) (9,30) (9,29) (9,25) (9,19) (9,17) (10,29) (10,26) (10,28) (10,17) (11,18) (11,15) (11,30) (11,26) (11,28) (11,17) (12,20) (12,14) (12,23) (13,18) (13,30) (13,29) (13,26) (13,25) (13,19) (13,28) (13,17) (14,20) (14,19) (15,18) (16,20) (16,26) (16,25) (16,19) (17,30) (17,26) (17,19) (18,21) (18,24) (18,30) (18,25) (18,28) (19,21) (19,23) (20,24) (20,26) (20,28) (21,24) (21,30) (24,30) (24,26) (25,30) (26,29) (26,28)\nIs there a path between node 22 and node 14 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph632-24_26", + "image": "data/connectivity/graph_visual/hard/graph632.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,6) (0,24) (0,12) (0,2) (2,30) (2,22) (3,7) (3,23) (3,15) (3,30) (3,24) (4,11) (4,28) (5,19) (5,31) (5,24) (5,25) (6,19) (6,31) (6,22) (6,17) (7,18) (7,24) (8,14) (8,32) (8,33) (9,14) (10,32) (12,30) (13,19) (13,30) (13,31) (15,18) (15,19) (15,17) (16,29) (17,30) (17,31) (17,24) (17,25) (18,24) (18,22) (19,30) (20,26) (22,23) (22,31) (25,30) (26,27) (30,31)\nIs there a path between node 24 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph583-8_27", + "image": "data/connectivity/graph_visual/hard/graph583.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,19) (0,16) (0,14) (0,22) (0,3) (0,21) (0,28) (0,1) (0,10) (0,8) (0,30) (0,18) (0,4) (0,25) (0,26) (0,23) (0,6) (0,24) (0,20) (0,11) (0,29) (0,33) (1,16) (1,14) (1,3) (1,21) (1,8) (1,30) (1,18) (1,4) (1,26) (1,23) (1,6) (1,24) (1,20) (1,32) (1,11) (1,29) (1,33) (1,12) (2,19) (2,14) (2,22) (2,28) (2,10) (2,8) (2,30) (2,18) (2,4) (2,25) (2,5) (2,26) (2,23) (2,6) (2,24) (2,20) (2,32) (2,29) (2,33) (2,9) (2,12) (3,19) (3,16) (3,10) (3,8) (3,30) (3,18) (3,4) (3,25) (3,5) (3,26) (3,23) (3,6) (3,32) (3,11) (3,29) (4,16) (4,22) (4,21) (4,28) (4,10) (4,18) (4,25) (4,26) (4,20) (4,11) (4,29) (4,33) (4,9) (4,12) (5,19) (5,16) (5,14) (5,22) (5,21) (5,28) (5,10) (5,8) (5,30) (5,18) (5,25) (5,26) (5,6) (5,24) (5,20) (5,32) (5,11) (5,33) (5,9) (5,12) (6,16) (6,14) (6,21) (6,10) (6,30) (6,18) (6,25) (6,24) (6,20) (6,32) (6,11) (6,12) (7,17) (7,13) (8,19) (8,16) (8,22) (8,10) (8,18) (8,23) (8,24) (8,32) (8,11) (8,29) (8,33) (8,9) (9,16) (9,14) (9,28) (9,10) (9,30) (9,18) (9,25) (9,26) (9,11) (9,29) (9,33) (10,19) (10,16) (10,14) (10,22) (10,28) (10,30) (10,18) (10,25) (10,26) (10,32) (10,11) (10,29) (10,12) (11,19) (11,16) (11,22) (11,21) (11,28) (11,18) (11,26) (11,23) (11,24) (11,20) (11,32) (11,29) (11,12) (12,16) (12,14) (12,22) (12,21) (12,28) (12,30) (12,18) (12,25) (12,23) (12,24) (12,32) (12,33) (14,16) (14,22) (14,21) (14,28) (14,18) (14,25) (14,26) (14,20) (14,32) (14,33) (15,31) (15,27) (16,19) (16,22) (16,28) (16,30) (16,18) (16,26) (16,23) (16,24) (16,20) (16,32) (16,33) (18,19) (18,22) (18,21) (18,28) (18,25) (18,26) (18,20) (18,32) (18,33) (19,22) (19,21) (19,28) (19,30) (19,25) (19,26) (19,20) (19,33) (20,22) (20,28) (20,25) (20,26) (20,24) (20,32) (20,33) (21,22) (21,28) (21,30) (21,25) (21,26) (21,24) (21,32) (21,29) (21,33) (22,26) (22,23) (22,24) (22,32) (23,30) (23,25) (23,24) (23,29) (23,33) (24,28) (24,32) (24,29) (25,28) (25,26) (25,33) (26,30) (26,29) (26,33) (27,31) (28,30) (28,32) (28,29) (29,30) (30,32)\nIs there a path between node 8 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph497-5_13", + "image": "data/connectivity/graph_visual/hard/graph497.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,19) (0,32) (0,26) (0,31) (0,9) (0,8) (0,18) (1,27) (1,23) (1,31) (1,9) (1,8) (1,7) (1,22) (1,10) (1,29) (1,28) (2,12) (2,23) (2,9) (2,13) (2,7) (2,3) (2,28) (3,16) (3,32) (3,21) (3,27) (3,14) (3,20) (3,31) (3,24) (3,7) (3,10) (3,4) (4,19) (4,32) (4,21) (4,26) (4,24) (4,9) (4,8) (4,13) (4,28) (6,12) (6,15) (6,22) (6,29) (6,18) (7,32) (7,26) (7,18) (8,32) (8,14) (8,15) (8,22) (8,28) (9,16) (9,27) (9,31) (9,24) (9,15) (9,29) (9,18) (9,28) (10,12) (10,19) (10,32) (10,21) (10,33) (10,17) (10,15) (10,22) (10,18) (11,16) (11,32) (11,26) (11,20) (11,31) (11,24) (11,22) (11,29) (12,16) (12,19) (12,14) (12,26) (12,23) (12,20) (12,22) (12,18) (13,16) (13,19) (13,24) (13,15) (14,32) (14,21) (14,27) (14,20) (14,31) (14,24) (14,15) (14,29) (15,32) (15,21) (15,24) (15,28) (16,21) (16,23) (16,22) (16,28) (17,23) (17,29) (17,28) (18,31) (18,22) (19,26) (19,23) (19,20) (19,31) (20,28) (21,33) (21,31) (22,28) (23,27) (23,28) (24,26) (24,31) (25,30) (26,32) (27,31) (28,32) (28,33) (32,33)\nIs there a path between node 5 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph195-10_5", + "image": "data/connectivity/graph_visual/hard/graph195.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,28) (0,13) (0,26) (0,17) (0,6) (0,29) (0,18) (0,27) (1,12) (1,9) (1,20) (1,4) (1,7) (1,22) (1,11) (1,15) (2,12) (2,9) (2,23) (2,20) (2,24) (2,22) (2,11) (2,15) (3,8) (3,28) (3,26) (3,17) (3,6) (3,29) (3,25) (3,18) (3,27) (4,12) (4,9) (4,20) (4,24) (4,22) (4,11) (5,10) (5,21) (6,8) (6,28) (6,13) (6,26) (6,17) (6,25) (6,18) (7,24) (7,22) (7,11) (7,15) (8,13) (8,19) (8,29) (8,25) (8,27) (9,23) (9,20) (9,24) (9,22) (10,16) (10,14) (10,21) (11,12) (11,23) (11,20) (11,24) (12,23) (12,20) (12,24) (13,28) (13,26) (13,17) (13,19) (13,29) (13,25) (13,18) (13,27) (14,16) (15,23) (15,20) (15,24) (15,22) (17,28) (17,26) (17,19) (17,29) (17,25) (17,18) (17,27) (18,28) (18,26) (18,19) (18,25) (18,27) (19,28) (19,26) (19,29) (19,25) (20,23) (20,22) (22,23) (22,24) (23,24) (25,26) (25,29) (25,27) (26,28) (26,29) (27,28)\nIs there a path between node 10 and node 5 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph50-19_7", + "image": "data/connectivity/graph_visual/hard/graph50.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,14) (0,17) (0,12) (0,9) (0,8) (1,11) (1,24) (1,15) (1,10) (1,13) (2,14) (2,17) (2,8) (2,3) (3,12) (4,15) (4,25) (4,6) (5,17) (5,12) (5,23) (6,11) (6,24) (6,20) (7,24) (7,20) (7,15) (7,18) (7,26) (8,9) (9,12) (10,20) (10,13) (11,24) (11,26) (11,13) (12,16) (13,26) (15,24) (15,20) (15,25) (15,22) (16,19) (16,21) (17,19) (17,23) (22,26) (24,25)\nIs there a path between node 19 and node 7 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph689-20_26", + "image": "data/connectivity/graph_visual/hard/graph689.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,17) (0,16) (0,10) (0,7) (1,2) (1,13) (1,7) (2,22) (2,13) (2,17) (2,9) (3,8) (3,31) (3,25) (3,20) (3,21) (3,34) (3,18) (3,23) (3,27) (3,12) (3,28) (3,29) (3,24) (3,5) (3,6) (4,15) (5,8) (5,31) (5,25) (5,21) (5,34) (5,11) (5,18) (5,27) (5,28) (5,29) (5,6) (6,8) (6,31) (6,25) (6,21) (6,26) (6,30) (6,18) (6,23) (6,14) (6,12) (6,33) (6,24) (6,19) (7,22) (7,13) (7,17) (7,16) (7,9) (7,10) (8,21) (8,26) (8,11) (8,18) (8,23) (8,14) (8,27) (8,28) (8,29) (8,19) (9,13) (9,17) (9,10) (10,22) (10,13) (10,17) (10,16) (11,31) (11,25) (11,20) (11,21) (11,26) (11,34) (11,18) (11,23) (11,14) (11,27) (11,12) (11,33) (11,28) (11,29) (11,24) (11,19) (12,31) (12,25) (12,20) (12,21) (12,26) (12,34) (12,30) (12,14) (12,27) (12,28) (13,22) (13,17) (14,31) (14,25) (14,20) (14,21) (14,26) (14,30) (14,18) (14,23) (14,27) (14,28) (14,29) (14,19) (15,32) (16,17) (18,34) (18,30) (18,23) (18,27) (18,33) (18,28) (18,29) (18,24) (18,19) (19,31) (19,20) (19,21) (19,34) (19,30) (19,23) (19,27) (19,33) (19,28) (19,29) (19,24) (20,31) (20,25) (20,21) (20,26) (20,34) (20,23) (20,33) (20,28) (20,24) (21,31) (21,25) (21,34) (21,27) (21,33) (21,29) (21,24) (23,34) (23,27) (23,33) (23,28) (24,31) (24,26) (24,34) (24,30) (24,27) (24,28) (24,29) (25,31) (25,26) (25,34) (25,30) (25,27) (25,33) (25,29) (26,30) (26,27) (26,33) (26,28) (26,29) (27,34) (27,30) (27,33) (27,28) (27,29) (28,31) (28,30) (28,33) (28,29) (29,31) (29,34) (29,33) (30,31) (30,34) (31,33) (33,34)\nIs there a path between node 20 and node 26 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph356-11_27", + "image": "data/connectivity/graph_visual/hard/graph356.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,12) (0,7) (0,13) (0,25) (0,26) (0,10) (0,15) (1,12) (1,16) (1,7) (1,4) (1,13) (1,26) (1,17) (1,18) (1,15) (3,12) (3,16) (3,4) (3,13) (3,25) (3,17) (3,8) (3,21) (3,15) (4,12) (4,22) (4,16) (4,13) (4,9) (4,11) (4,19) (4,26) (5,29) (5,31) (5,6) (6,24) (6,29) (7,12) (7,20) (7,13) (7,10) (7,23) (7,18) (7,15) (8,16) (8,13) (8,27) (8,19) (8,26) (8,28) (8,10) (8,21) (9,16) (9,20) (9,11) (9,19) (9,18) (10,16) (10,13) (10,25) (10,19) (10,26) (10,28) (10,23) (10,21) (11,12) (11,22) (11,25) (11,21) (11,15) (12,19) (12,26) (12,28) (12,21) (13,16) (13,20) (13,27) (13,25) (13,19) (13,28) (14,31) (14,30) (15,16) (15,20) (15,25) (15,17) (15,28) (16,22) (16,20) (16,27) (16,19) (16,21) (16,18) (17,22) (17,26) (17,21) (17,18) (18,19) (18,23) (19,22) (19,25) (19,26) (20,27) (20,25) (20,21) (21,28) (22,26) (22,23) (23,25) (24,30) (25,28) (26,27)\nIs there a path between node 11 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph7-18_8", + "image": "data/connectivity/graph_visual/hard/graph7.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,5) (0,1) (0,4) (0,12) (0,23) (0,19) (0,14) (0,21) (0,15) (0,7) (0,22) (1,24) (1,6) (1,20) (1,23) (1,25) (1,3) (1,9) (1,16) (1,7) (2,6) (2,19) (2,14) (2,10) (2,3) (2,8) (2,9) (2,7) (3,5) (3,24) (3,14) (3,25) (3,22) (4,24) (4,19) (4,10) (4,16) (5,24) (5,14) (5,15) (5,9) (6,23) (6,14) (6,15) (7,24) (7,23) (7,14) (7,15) (7,10) (7,22) (8,19) (8,14) (8,21) (8,25) (8,22) (9,23) (10,24) (10,16) (11,18) (11,17) (12,20) (12,14) (12,25) (12,16) (14,24) (14,23) (14,19) (14,15) (15,20) (15,19) (15,21) (15,22) (16,25) (17,18) (19,21) (20,24) (20,23) (20,25) (21,23) (22,23)\nIs there a path between node 18 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph527-32_15", + "image": "data/connectivity/graph_visual/hard/graph527.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,33) (0,21) (0,2) (0,19) (1,11) (2,17) (3,18) (3,10) (4,12) (4,7) (4,13) (5,14) (5,32) (6,10) (6,14) (7,12) (7,21) (8,14) (8,28) (10,32) (10,28) (12,33) (12,17) (12,19) (13,21) (13,29) (14,18) (14,32) (16,21) (16,19) (17,29) (18,26) (19,33) (19,29) (20,23) (23,31) (24,32) (25,30) (26,32) (26,28)\nIs there a path between node 32 and node 15 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph128-4_13", + "image": "data/connectivity/graph_visual/hard/graph128.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (0,12) (0,14) (0,10) (0,17) (0,18) (0,1) (0,13) (0,11) (0,23) (0,4) (1,19) (1,12) (1,14) (1,6) (1,17) (1,18) (1,13) (1,7) (1,27) (1,23) (2,5) (2,8) (3,21) (3,20) (3,15) (3,25) (4,19) (4,22) (4,10) (4,6) (4,17) (4,18) (4,13) (4,7) (4,27) (5,8) (6,22) (6,12) (6,14) (6,10) (6,17) (6,18) (6,13) (6,11) (6,23) (7,22) (7,26) (7,14) (7,10) (7,17) (7,18) (7,9) (9,26) (9,14) (9,10) (9,17) (9,13) (9,11) (9,27) (9,23) (10,19) (10,26) (10,14) (10,17) (10,18) (10,13) (10,27) (10,23) (11,19) (11,22) (11,26) (11,12) (11,14) (11,17) (11,13) (11,27) (12,19) (12,22) (12,14) (12,17) (12,18) (12,27) (13,19) (13,26) (13,14) (13,17) (13,18) (14,19) (14,18) (14,23) (15,21) (15,16) (15,20) (15,25) (16,21) (17,23) (18,19) (18,22) (18,26) (19,27) (20,21) (20,24) (21,25) (22,26) (22,27) (22,23) (23,26) (23,27) (24,25) (26,27)\nIs there a path between node 4 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph617-15_20", + "image": "data/connectivity/graph_visual/hard/graph617.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,22) (0,19) (0,23) (0,18) (0,2) (0,24) (0,14) (0,6) (0,7) (0,33) (0,30) (0,21) (0,11) (0,29) (0,10) (1,25) (1,31) (1,16) (1,34) (1,28) (2,22) (2,23) (2,18) (2,24) (2,32) (2,14) (2,6) (2,33) (2,8) (2,27) (2,21) (2,4) (2,29) (3,9) (3,13) (3,15) (3,5) (3,26) (4,19) (4,23) (4,18) (4,24) (4,12) (4,32) (4,6) (4,7) (4,33) (4,8) (4,27) (4,30) (4,17) (4,10) (5,9) (5,13) (5,15) (5,26) (6,19) (6,12) (6,32) (6,14) (6,33) (6,27) (6,10) (7,22) (7,19) (7,18) (7,24) (7,32) (7,14) (7,27) (7,30) (7,11) (7,10) (8,22) (8,19) (8,23) (8,12) (8,33) (8,30) (8,17) (8,11) (8,29) (8,10) (9,13) (9,15) (9,26) (10,19) (10,18) (10,12) (10,32) (10,33) (10,27) (10,17) (10,11) (10,29) (11,19) (11,23) (11,18) (11,24) (11,32) (11,33) (11,27) (11,21) (11,29) (12,19) (12,23) (12,18) (12,32) (12,14) (12,33) (12,27) (12,30) (12,21) (12,17) (13,26) (14,22) (14,19) (14,23) (14,18) (14,32) (14,30) (14,21) (14,29) (15,26) (16,25) (16,31) (16,34) (16,28) (17,19) (17,23) (17,18) (17,24) (17,33) (17,27) (17,29) (18,22) (18,19) (18,23) (18,33) (18,27) (18,21) (18,29) (19,22) (19,23) (19,33) (19,27) (19,29) (20,25) (20,31) (20,34) (21,22) (21,23) (21,32) (21,33) (21,27) (21,30) (21,29) (22,33) (22,27) (22,30) (23,24) (23,32) (23,33) (23,27) (23,29) (24,32) (24,33) (24,27) (24,30) (24,29) (25,31) (25,34) (27,32) (27,33) (27,29) (29,33) (30,32) (30,33) (31,34) (32,33)\nIs there a path between node 15 and node 20 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph61-12_24", + "image": "data/connectivity/graph_visual/hard/graph61.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,15) (1,10) (1,16) (1,26) (1,3) (1,12) (2,7) (3,5) (3,10) (3,21) (3,9) (3,24) (3,20) (3,25) (3,12) (3,14) (4,23) (4,22) (4,18) (5,17) (5,16) (5,14) (6,8) (6,21) (6,26) (6,12) (8,11) (8,10) (8,13) (8,16) (8,20) (8,12) (9,13) (9,19) (9,25) (9,14) (10,15) (10,11) (10,16) (10,25) (11,24) (11,20) (11,25) (12,17) (12,16) (12,19) (13,17) (13,24) (13,26) (14,17) (14,21) (15,16) (15,26) (16,19) (17,21) (17,25) (18,22) (19,21) (20,24) (20,26) (21,24) (24,26) (25,26)\nIs there a path between node 12 and node 24 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph466-28_8", + "image": "data/connectivity/graph_visual/hard/graph466.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,26) (0,17) (0,32) (0,5) (0,31) (0,29) (0,27) (0,1) (0,18) (0,13) (0,2) (0,23) (1,7) (1,17) (1,20) (1,14) (1,13) (1,28) (2,3) (2,26) (2,32) (2,20) (2,31) (2,27) (2,23) (3,17) (3,25) (3,5) (3,19) (3,31) (3,14) (3,29) (3,11) (3,27) (3,18) (3,13) (3,22) (3,9) (4,20) (4,31) (4,14) (4,11) (4,16) (4,27) (4,18) (4,10) (4,9) (5,7) (5,17) (5,25) (5,32) (5,20) (5,18) (6,15) (6,12) (7,20) (7,19) (7,9) (7,23) (8,17) (8,32) (8,19) (8,29) (8,11) (8,22) (8,21) (9,17) (9,25) (9,28) (10,25) (10,20) (10,31) (10,14) (11,26) (11,17) (11,13) (11,22) (11,28) (11,21) (12,30) (13,19) (13,16) (13,28) (13,23) (14,29) (14,16) (14,18) (14,22) (15,30) (15,24) (16,19) (16,27) (16,28) (17,32) (17,20) (17,31) (17,23) (18,25) (18,31) (19,20) (19,28) (19,21) (20,25) (20,32) (20,27) (20,21) (21,23) (22,26) (22,31) (22,23) (23,26) (23,32) (23,29) (24,30) (26,32) (26,29) (26,28) (27,31) (28,32) (29,32) (29,31)\nIs there a path between node 28 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph470-2_13", + "image": "data/connectivity/graph_visual/hard/graph470.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,29) (0,16) (0,15) (0,25) (0,23) (0,24) (1,5) (1,2) (1,21) (1,19) (1,30) (1,27) (1,9) (1,18) (1,31) (1,13) (1,32) (1,12) (1,22) (1,8) (2,4) (2,5) (2,21) (2,11) (2,6) (2,30) (2,3) (2,9) (2,7) (2,18) (2,31) (2,13) (2,32) (2,12) (2,22) (2,8) (3,4) (3,5) (3,21) (3,11) (3,19) (3,30) (3,9) (3,7) (3,31) (3,13) (3,32) (3,12) (3,26) (3,8) (4,21) (4,11) (4,30) (4,27) (4,9) (4,18) (4,13) (4,17) (4,32) (4,12) (4,26) (4,22) (5,21) (5,11) (5,6) (5,19) (5,30) (5,27) (5,18) (5,31) (5,13) (5,17) (5,32) (5,12) (5,26) (5,8) (6,21) (6,11) (6,19) (6,30) (6,27) (6,7) (6,31) (6,13) (6,17) (6,12) (6,26) (7,21) (7,19) (7,30) (7,9) (7,18) (7,31) (7,13) (7,17) (7,32) (7,12) (8,21) (8,11) (8,27) (8,9) (8,18) (8,31) (8,13) (8,17) (8,32) (8,12) (8,22) (9,19) (9,27) (9,31) (9,13) (9,32) (9,12) (9,26) (9,22) (10,14) (10,28) (11,19) (11,30) (11,31) (11,17) (11,12) (11,26) (12,21) (12,19) (12,30) (12,31) (12,13) (12,17) (12,32) (13,21) (13,27) (13,18) (13,31) (13,22) (14,28) (15,29) (15,16) (15,25) (15,20) (15,23) (15,24) (16,25) (16,20) (16,24) (17,21) (17,30) (17,31) (17,32) (17,26) (17,22) (18,21) (18,19) (18,31) (18,32) (18,26) (18,22) (19,21) (19,30) (19,27) (19,32) (19,26) (19,22) (20,29) (20,25) (20,23) (20,24) (21,30) (21,27) (21,31) (21,32) (21,26) (21,22) (22,30) (22,27) (22,26) (23,29) (23,25) (23,24) (24,29) (24,25) (25,29) (26,30) (26,27) (26,32) (27,31) (27,32) (30,32) (31,32)\nIs there a path between node 2 and node 13 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph370-0_8", + "image": "data/connectivity/graph_visual/hard/graph370.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,24) (0,20) (0,26) (0,29) (0,27) (0,5) (0,30) (0,6) (0,1) (0,21) (0,10) (0,11) (0,16) (0,23) (1,24) (1,20) (1,13) (1,26) (1,29) (1,9) (1,27) (1,5) (1,30) (1,21) (1,16) (1,23) (1,22) (2,3) (2,28) (3,28) (4,24) (4,20) (4,26) (4,9) (4,27) (4,15) (4,5) (4,30) (4,16) (4,12) (4,22) (5,24) (5,26) (5,9) (5,27) (5,15) (5,30) (5,21) (5,10) (5,16) (5,12) (5,23) (6,24) (6,20) (6,9) (6,27) (6,30) (6,10) (6,11) (6,12) (6,23) (7,18) (7,25) (7,8) (7,14) (7,17) (8,18) (8,14) (8,17) (9,24) (9,20) (9,29) (9,27) (9,15) (9,21) (9,16) (9,12) (9,23) (9,22) (10,24) (10,13) (10,27) (10,15) (10,30) (10,21) (10,11) (10,16) (10,23) (10,22) (11,20) (11,13) (11,26) (11,29) (11,15) (11,30) (11,12) (11,23) (11,22) (12,20) (12,13) (12,29) (12,27) (12,15) (12,30) (12,21) (12,16) (12,23) (13,24) (13,20) (13,26) (13,30) (13,16) (14,18) (14,25) (15,20) (15,26) (15,29) (15,27) (15,30) (15,21) (15,22) (16,24) (16,20) (16,29) (16,27) (16,23) (17,18) (19,31) (19,28) (20,24) (20,27) (20,30) (20,21) (20,22) (21,26) (21,29) (21,30) (21,22) (22,24) (22,29) (22,27) (22,30) (23,26) (23,30) (24,26) (24,29) (24,27) (24,30) (26,29) (26,27) (26,30) (27,29) (27,30) (28,31) (29,30)\nIs there a path between node 0 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph163-17_28", + "image": "data/connectivity/graph_visual/hard/graph163.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,8) (0,11) (0,14) (0,13) (0,3) (1,28) (1,10) (1,21) (1,18) (1,14) (1,13) (2,28) (2,8) (2,27) (2,23) (2,7) (2,4) (2,25) (2,20) (2,26) (2,9) (3,28) (3,6) (3,11) (3,23) (3,21) (3,14) (4,19) (4,23) (4,18) (4,20) (4,9) (5,15) (6,28) (6,8) (6,23) (6,21) (6,25) (6,20) (6,26) (7,27) (7,25) (7,20) (7,13) (7,24) (7,26) (8,28) (8,19) (8,14) (8,26) (8,12) (9,19) (9,21) (9,14) (9,26) (10,14) (10,13) (10,12) (11,28) (11,16) (11,27) (11,14) (11,20) (11,13) (11,24) (11,26) (11,12) (12,20) (13,16) (13,21) (13,18) (14,28) (14,19) (14,23) (14,21) (14,25) (14,24) (15,17) (16,23) (16,24) (18,28) (18,27) (18,26) (19,27) (19,24) (19,26) (20,28) (20,27) (20,23) (21,23) (21,25) (21,26) (23,26) (26,27)\nIs there a path between node 17 and node 28 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph19-20_12", + "image": "data/connectivity/graph_visual/hard/graph19.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,21) (0,9) (0,6) (0,8) (1,21) (1,19) (1,13) (1,9) (1,3) (2,17) (3,21) (3,16) (3,19) (3,13) (3,8) (4,12) (4,13) (4,6) (4,7) (6,12) (6,16) (6,20) (6,13) (6,18) (6,11) (6,7) (7,20) (7,9) (8,12) (8,16) (8,20) (8,18) (8,11) (9,21) (10,25) (10,24) (11,20) (12,19) (12,13) (13,21) (13,19) (15,23) (18,21) (18,20) (19,20) (23,24)\nIs there a path between node 20 and node 12 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph555-7_32", + "image": "data/connectivity/graph_visual/hard/graph555.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,5) (0,7) (0,22) (0,1) (1,5) (1,7) (1,22) (2,31) (2,28) (2,18) (3,19) (3,23) (3,33) (4,26) (4,19) (4,31) (4,27) (5,21) (5,7) (6,24) (6,29) (7,21) (8,32) (8,26) (8,28) (8,23) (9,32) (9,26) (9,17) (9,16) (9,12) (9,19) (9,27) (11,21) (12,25) (12,27) (13,22) (14,29) (15,26) (15,17) (15,25) (15,20) (15,19) (15,18) (16,20) (16,19) (16,31) (16,18) (17,32) (17,28) (18,27) (19,31) (19,27) (19,33) (20,32) (20,27) (23,30) (23,27) (26,32) (27,28) (28,31) (28,33) (30,32) (30,33) (32,33)\nIs there a path between node 7 and node 32 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph695-17_0", + "image": "data/connectivity/graph_visual/hard/graph695.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,21) (0,22) (0,25) (0,23) (0,10) (0,16) (0,3) (0,4) (0,7) (0,34) (0,27) (0,28) (0,19) (0,1) (0,20) (1,14) (1,6) (1,12) (1,25) (1,8) (1,16) (1,4) (1,7) (1,34) (1,27) (1,28) (1,26) (2,5) (2,17) (2,18) (2,15) (2,11) (3,14) (3,13) (3,6) (3,21) (3,12) (3,25) (3,33) (3,8) (3,10) (3,4) (3,7) (3,34) (3,28) (3,19) (3,26) (4,13) (4,6) (4,21) (4,22) (4,12) (4,8) (4,23) (4,10) (4,16) (4,34) (4,29) (4,28) (4,20) (5,30) (5,24) (5,9) (5,31) (5,15) (5,11) (6,14) (6,13) (6,21) (6,25) (6,23) (6,16) (6,7) (6,34) (6,27) (6,29) (6,28) (6,19) (7,14) (7,22) (7,12) (7,33) (7,23) (7,10) (7,16) (7,28) (7,19) (7,26) (7,20) (8,14) (8,13) (8,22) (8,12) (8,25) (8,33) (8,23) (8,10) (8,16) (8,34) (8,27) (8,19) (8,26) (8,20) (9,30) (9,24) (9,18) (9,31) (9,32) (10,14) (10,21) (10,22) (10,12) (10,23) (10,34) (10,27) (10,28) (10,19) (10,26) (11,30) (11,24) (11,17) (11,18) (11,31) (11,15) (11,32) (12,14) (12,13) (12,22) (12,25) (12,33) (12,23) (12,34) (12,27) (12,29) (12,28) (12,19) (12,26) (13,21) (13,22) (13,25) (13,33) (13,23) (13,16) (13,34) (13,27) (13,26) (13,20) (14,21) (14,33) (14,16) (14,34) (14,27) (14,29) (14,26) (14,20) (15,30) (15,24) (15,31) (16,25) (16,33) (16,23) (16,27) (16,19) (16,26) (16,20) (18,30) (18,24) (18,31) (18,32) (19,25) (19,33) (19,23) (19,34) (19,27) (19,29) (19,26) (19,20) (20,22) (20,25) (20,33) (20,23) (20,34) (20,27) (20,28) (20,26) (21,33) (21,23) (21,34) (21,27) (21,29) (22,33) (22,23) (22,27) (22,28) (23,25) (23,33) (23,34) (23,29) (23,28) (23,26) (24,31) (25,33) (25,34) (25,27) (25,28) (25,26) (26,33) (26,34) (26,27) (26,28) (27,33) (27,34) (27,29) (27,28) (28,33) (28,34) (29,33) (29,34) (30,32)\nIs there a path between node 17 and node 0 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph469-26_31", + "image": "data/connectivity/graph_visual/hard/graph469.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,29) (0,16) (0,3) (0,25) (0,26) (0,13) (0,14) (0,5) (0,4) (0,22) (0,20) (0,21) (0,24) (0,17) (0,32) (0,2) (0,10) (0,7) (0,12) (1,28) (1,16) (1,6) (1,25) (1,13) (1,14) (1,18) (1,5) (1,23) (1,4) (1,22) (1,20) (1,21) (1,24) (1,15) (1,2) (1,10) (1,7) (1,12) (2,28) (2,29) (2,16) (2,6) (2,3) (2,25) (2,26) (2,13) (2,14) (2,18) (2,5) (2,23) (2,8) (2,4) (2,19) (2,20) (2,21) (2,24) (2,17) (2,15) (2,12) (3,29) (3,6) (3,25) (3,13) (3,14) (3,5) (3,23) (3,8) (3,4) (3,19) (3,20) (3,21) (3,24) (3,17) (3,32) (3,15) (3,10) (3,7) (3,12) (4,28) (4,29) (4,16) (4,6) (4,25) (4,26) (4,14) (4,5) (4,8) (4,27) (4,22) (4,19) (4,21) (4,15) (4,10) (4,7) (5,28) (5,25) (5,13) (5,18) (5,23) (5,8) (5,27) (5,19) (5,20) (5,21) (5,24) (5,32) (5,15) (5,10) (5,7) (5,12) (6,28) (6,29) (6,16) (6,14) (6,18) (6,8) (6,22) (6,19) (6,20) (6,21) (6,17) (6,12) (7,28) (7,23) (7,8) (7,22) (7,19) (7,21) (7,32) (7,15) (7,10) (7,12) (8,29) (8,16) (8,26) (8,13) (8,22) (8,19) (8,20) (8,24) (8,17) (8,32) (8,15) (8,10) (8,12) (9,31) (10,28) (10,16) (10,25) (10,26) (10,13) (10,18) (10,23) (10,22) (10,19) (10,21) (10,17) (10,32) (10,15) (10,12) (11,31) (11,30) (12,28) (12,29) (12,16) (12,14) (12,22) (12,20) (12,24) (12,17) (12,32) (12,15) (13,29) (13,16) (13,26) (13,14) (13,23) (13,27) (13,22) (13,19) (13,20) (13,21) (13,32) (14,28) (14,29) (14,26) (14,18) (14,27) (14,19) (14,20) (14,21) (14,17) (14,15) (15,28) (15,29) (15,16) (15,25) (15,26) (15,18) (15,27) (15,22) (15,21) (15,24) (15,32) (16,25) (16,26) (16,18) (16,27) (16,22) (16,19) (16,20) (16,21) (16,24) (16,17) (16,32) (17,28) (17,25) (17,27) (17,22) (17,19) (17,21) (17,32) (18,28) (18,29) (18,26) (18,27) (18,19) (18,20) (18,21) (18,24) (18,32) (19,29) (19,25) (19,26) (19,23) (19,27) (19,20) (19,21) (19,24) (19,32) (20,28) (20,29) (20,27) (20,22) (20,24) (20,32) (21,26) (21,24) (22,28) (22,29) (22,25) (22,26) (22,23) (22,27) (22,24) (23,28) (23,29) (23,25) (23,26) (23,24) (24,28) (24,25) (25,28) (25,26) (25,27) (25,32) (26,29) (26,32) (27,28) (27,29) (27,32) (28,29) (28,32) (29,32) (30,31)\nIs there a path between node 26 and node 31 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph145-13_10", + "image": "data/connectivity/graph_visual/hard/graph145.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,3) (0,24) (0,15) (0,16) (0,19) (0,7) (0,25) (0,26) (1,28) (1,23) (3,6) (3,18) (3,11) (3,24) (3,22) (3,4) (3,7) (3,25) (4,27) (4,24) (4,22) (4,12) (4,21) (4,16) (4,19) (5,6) (5,13) (5,22) (5,12) (5,16) (6,11) (6,21) (6,15) (6,25) (6,26) (7,14) (7,25) (8,23) (9,11) (9,13) (10,11) (10,15) (10,19) (11,27) (11,18) (11,22) (11,12) (11,21) (11,19) (11,25) (12,27) (12,14) (13,27) (13,18) (13,14) (13,21) (14,18) (14,24) (14,15) (15,22) (15,16) (15,26) (16,18) (16,22) (17,28) (17,23) (17,20) (18,27) (19,27) (19,24) (21,26) (22,25) (22,26) (23,28) (24,25) (24,26)\nIs there a path between node 13 and node 10 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph192-17_16", + "image": "data/connectivity/graph_visual/hard/graph192.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,20) (0,5) (0,18) (0,6) (1,29) (1,21) (1,14) (1,23) (1,4) (1,27) (1,3) (2,28) (2,13) (2,16) (2,12) (2,14) (2,23) (2,4) (2,17) (2,11) (2,22) (2,15) (3,26) (4,29) (4,28) (4,12) (4,7) (4,22) (5,24) (5,20) (6,24) (7,11) (7,10) (8,24) (9,28) (9,14) (9,22) (9,10) (10,27) (10,22) (11,28) (11,12) (11,27) (11,26) (11,15) (12,29) (12,19) (12,28) (12,14) (12,23) (12,26) (13,29) (13,28) (13,14) (13,17) (13,26) (14,29) (14,19) (14,28) (14,26) (15,29) (15,19) (15,21) (15,17) (16,29) (16,21) (16,23) (16,22) (17,29) (17,19) (17,25) (17,27) (18,24) (19,21) (19,27) (19,22) (21,27) (22,28) (22,27) (23,29) (23,28) (23,25) (25,27) (25,26) (26,29) (27,28)\nIs there a path between node 17 and node 16 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph285-18_17", + "image": "data/connectivity/graph_visual/hard/graph285.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,3) (0,11) (0,15) (0,25) (0,31) (0,23) (0,14) (1,28) (1,20) (1,12) (1,21) (1,19) (1,24) (1,27) (1,13) (1,6) (2,20) (2,22) (2,21) (2,19) (2,13) (2,6) (3,15) (3,4) (3,25) (3,23) (4,9) (4,15) (4,14) (5,8) (5,17) (5,10) (5,26) (5,7) (5,16) (6,20) (6,21) (6,19) (6,27) (6,13) (7,17) (7,16) (7,29) (8,17) (9,11) (9,15) (9,31) (9,23) (9,14) (10,17) (11,15) (11,30) (11,23) (11,14) (12,20) (12,22) (12,19) (12,27) (12,13) (12,18) (13,28) (13,22) (13,21) (13,24) (13,27) (13,18) (14,15) (14,25) (14,31) (14,23) (15,25) (15,30) (15,23) (16,26) (17,26) (17,29) (18,28) (18,20) (18,22) (18,21) (18,19) (18,24) (18,27) (19,22) (19,21) (19,24) (19,27) (20,28) (20,22) (20,21) (20,24) (20,27) (21,28) (21,22) (21,24) (22,24) (22,27) (23,30) (23,31) (24,28) (25,31) (27,28) (30,31)\nIs there a path between node 18 and node 17 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph360-27_8", + "image": "data/connectivity/graph_visual/hard/graph360.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,26) (0,28) (0,24) (0,31) (0,30) (0,27) (0,20) (1,21) (1,6) (1,19) (1,12) (1,22) (1,4) (1,17) (1,13) (1,30) (2,23) (2,3) (2,14) (3,25) (4,5) (4,17) (4,27) (5,17) (5,31) (5,20) (6,26) (6,16) (6,28) (6,10) (6,19) (6,12) (6,22) (6,13) (7,21) (7,28) (7,19) (7,17) (7,13) (7,18) (7,27) (8,23) (8,11) (8,25) (10,26) (10,28) (10,22) (10,31) (10,18) (11,23) (12,30) (13,21) (13,19) (13,31) (15,26) (15,16) (15,17) (15,18) (15,20) (16,21) (16,28) (16,19) (16,30) (16,27) (16,20) (17,24) (17,22) (17,18) (18,22) (19,22) (19,31) (19,20) (20,28) (21,22) (21,31) (22,30) (24,31) (27,28) (28,31)\nIs there a path between node 27 and node 8 in this undirected graph?" + }, + { + "from": "gpt", + "value": "No." + } + ] + }, + { + "id": "connectivity-hard-graph506-25_27", + "image": "data/connectivity/graph_visual/hard/graph506.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,32) (0,10) (0,4) (0,11) (0,24) (0,14) (0,21) (0,8) (0,18) (0,27) (0,13) (0,1) (0,29) (0,16) (0,28) (0,12) (0,20) (1,32) (1,4) (1,26) (1,11) (1,24) (1,8) (1,18) (1,13) (1,31) (1,29) (1,25) (1,15) (1,28) (1,12) (1,20) (2,6) (2,33) (4,10) (4,18) (4,27) (4,31) (4,22) (4,29) (4,25) (4,16) (4,15) (4,28) (4,12) (5,17) (5,23) (5,30) (5,9) (6,19) (7,19) (8,32) (8,10) (8,26) (8,11) (8,24) (8,14) (8,21) (8,18) (8,22) (8,29) (8,15) (8,20) (9,30) (10,11) (10,24) (10,14) (10,18) (10,27) (10,13) (10,31) (10,22) (10,29) (10,25) (10,28) (10,12) (10,20) (11,32) (11,26) (11,24) (11,14) (11,21) (11,27) (11,13) (11,31) (11,29) (11,16) (11,28) (11,12) (12,32) (12,24) (12,14) (12,18) (12,27) (12,31) (12,16) (12,15) (12,20) (13,32) (13,26) (13,14) (13,18) (13,22) (13,29) (13,25) (13,16) (13,15) (13,28) (13,20) (14,26) (14,24) (14,18) (14,31) (14,22) (14,29) (14,25) (14,16) (14,28) (14,20) (15,26) (15,24) (15,21) (15,18) (15,27) (15,31) (15,22) (15,25) (15,28) (15,20) (16,26) (16,24) (16,21) (16,31) (16,22) (16,25) (16,28) (16,20) (18,24) (18,21) (18,22) (18,28) (19,33) (20,32) (20,26) (20,24) (20,21) (20,31) (20,22) (20,29) (20,25) (20,28) (21,32) (21,24) (21,27) (21,31) (21,22) (21,29) (22,32) (22,26) (22,24) (22,27) (22,31) (22,29) (22,25) (22,28) (23,30) (24,32) (24,27) (24,31) (24,25) (24,28) (25,32) (25,31) (25,28) (26,32) (26,27) (26,31) (26,29) (26,28) (27,32) (27,31) (27,29) (27,28) (31,32)\nIs there a path between node 25 and node 27 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph228-9_19", + "image": "data/connectivity/graph_visual/hard/graph228.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,18) (0,15) (0,8) (0,20) (1,22) (1,4) (1,25) (1,11) (1,7) (1,24) (1,28) (1,21) (2,23) (2,27) (2,18) (2,16) (2,3) (2,8) (2,5) (2,20) (3,27) (3,16) (3,12) (3,15) (3,8) (3,5) (4,29) (4,22) (4,6) (4,10) (4,17) (4,14) (4,25) (4,11) (4,7) (4,24) (4,28) (4,21) (4,26) (5,23) (5,27) (5,18) (5,16) (5,12) (5,15) (5,8) (5,20) (6,29) (6,22) (6,19) (6,10) (6,25) (6,9) (6,7) (6,13) (6,24) (6,28) (6,26) (7,10) (7,17) (7,14) (7,25) (7,9) (7,13) (7,24) (7,28) (7,21) (7,26) (8,23) (8,18) (8,12) (8,20) (9,29) (9,22) (9,19) (9,10) (9,25) (9,11) (9,13) (9,24) (9,28) (9,26) (10,29) (10,22) (10,19) (10,14) (10,25) (10,11) (10,13) (10,24) (10,26) (11,22) (11,19) (11,17) (11,25) (11,13) (11,24) (11,21) (11,26) (12,23) (12,27) (12,18) (12,16) (12,15) (13,29) (13,19) (13,17) (13,14) (13,25) (13,28) (13,21) (13,26) (14,19) (14,17) (14,25) (14,28) (14,21) (14,26) (15,23) (15,27) (15,18) (15,16) (15,20) (16,23) (16,18) (16,20) (17,22) (17,19) (17,25) (17,28) (17,26) (18,23) (18,27) (19,22) (19,25) (19,28) (19,26) (21,29) (21,25) (21,24) (21,28) (21,26) (22,29) (22,25) (22,28) (22,26) (23,27) (24,29) (24,25) (24,28) (24,26) (25,29) (25,28) (25,26) (26,29) (26,28)\nIs there a path between node 9 and node 19 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + }, + { + "id": "connectivity-hard-graph251-22_1", + "image": "data/connectivity/graph_visual/hard/graph251.png", + "conversations": [ + { + "from": "human", + "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,17) (1,8) (1,29) (1,10) (1,7) (1,11) (1,25) (1,18) (1,14) (1,30) (1,16) (1,5) (1,26) (1,4) (1,23) (1,27) (2,21) (3,21) (4,17) (4,29) (4,9) (4,10) (4,6) (4,7) (4,11) (4,14) (4,22) (4,26) (4,13) (4,24) (4,23) (4,19) (5,17) (5,29) (5,9) (5,10) (5,6) (5,7) (5,11) (5,18) (5,14) (5,30) (5,16) (5,26) (5,15) (5,13) (5,24) (5,19) (5,27) (6,17) (6,9) (6,10) (6,11) (6,18) (6,14) (6,30) (6,16) (6,22) (6,15) (6,24) (6,19) (6,27) (7,17) (7,8) (7,29) (7,9) (7,10) (7,25) (7,18) (7,30) (7,16) (7,22) (7,24) (7,23) (7,19) (7,27) (8,17) (8,11) (8,25) (8,18) (8,14) (8,30) (8,16) (8,15) (8,13) (8,24) (8,19) (8,27) (9,17) (9,29) (9,10) (9,11) (9,25) (9,14) (9,30) (9,16) (9,22) (9,15) (9,13) (9,24) (9,19) (9,27) (10,17) (10,11) (10,25) (10,18) (10,14) (10,30) (10,16) (10,22) (10,15) (10,13) (10,24) (10,23) (10,27) (11,29) (11,25) (11,14) (11,30) (11,16) (11,26) (11,15) (11,13) (11,24) (11,23) (11,19) (11,27) (12,28) (13,29) (13,18) (13,14) (13,30) (13,16) (13,22) (13,26) (13,15) (13,24) (13,19) (13,27) (14,17) (14,25) (14,18) (14,30) (14,16) (14,22) (14,26) (14,15) (14,19) (14,27) (15,17) (15,25) (15,18) (15,30) (15,16) (15,22) (15,26) (15,24) (15,23) (15,19) (15,27) (16,29) (16,25) (16,30) (16,23) (16,27) (17,29) (17,25) (17,18) (17,30) (17,26) (17,19) (17,27) (18,22) (18,26) (18,24) (18,23) (18,19) (19,29) (19,25) (19,22) (19,26) (19,24) (19,23) (19,27) (22,29) (22,25) (22,26) (22,24) (22,23) (22,27) (23,25) (23,30) (23,24) (24,29) (24,25) (24,26) (24,27) (25,29) (25,30) (25,26) (25,27) (26,29) (26,30) (29,30)\nIs there a path between node 22 and node 1 in this undirected graph?" + }, + { + "from": "gpt", + "value": "Yes." + } + ] + } +] \ No newline at end of file