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@@ -438,3 +438,4 @@ deepseek/lib/python3.10/site-packages/timm/models/__pycache__/vision_transformer
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 deepseek/lib/python3.10/site-packages/pyarrow/_s3fs.cpython-310-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text
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+janus/lib/libtinfow.so.6 filter=lfs diff=lfs merge=lfs -text

janus/lib/libtinfow.so.6

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janus/lib/python3.10/site-packages/networkx/generators/atlas.dat.gz

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janus/lib/python3.10/site-packages/networkx/generators/tests/test_classic.py

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+"""
+====================
+Generators - Classic
+====================
+
+Unit tests for various classic graph generators in generators/classic.py
+"""
+
+import itertools
+import typing
+
+import pytest
+
+import networkx as nx
+from networkx.algorithms.isomorphism.isomorph import graph_could_be_isomorphic
+from networkx.utils import edges_equal, nodes_equal
+
+is_isomorphic = graph_could_be_isomorphic
+
+
+class TestGeneratorClassic:
+    def test_balanced_tree(self):
+        # balanced_tree(r,h) is a tree with (r**(h+1)-1)/(r-1) edges
+        for r, h in [(2, 2), (3, 3), (6, 2)]:
+            t = nx.balanced_tree(r, h)
+            order = t.order()
+            assert order == (r ** (h + 1) - 1) / (r - 1)
+            assert nx.is_connected(t)
+            assert t.size() == order - 1
+            dh = nx.degree_histogram(t)
+            assert dh[0] == 0  # no nodes of 0
+            assert dh[1] == r**h  # nodes of degree 1 are leaves
+            assert dh[r] == 1  # root is degree r
+            assert dh[r + 1] == order - r**h - 1  # everyone else is degree r+1
+            assert len(dh) == r + 2
+
+    def test_balanced_tree_star(self):
+        # balanced_tree(r,1) is the r-star
+        t = nx.balanced_tree(r=2, h=1)
+        assert is_isomorphic(t, nx.star_graph(2))
+        t = nx.balanced_tree(r=5, h=1)
+        assert is_isomorphic(t, nx.star_graph(5))
+        t = nx.balanced_tree(r=10, h=1)
+        assert is_isomorphic(t, nx.star_graph(10))
+
+    def test_balanced_tree_path(self):
+        """Tests that the balanced tree with branching factor one is the
+        path graph.
+
+        """
+        # A tree of height four has five levels.
+        T = nx.balanced_tree(1, 4)
+        P = nx.path_graph(5)
+        assert is_isomorphic(T, P)
+
+    def test_full_rary_tree(self):
+        r = 2
+        n = 9
+        t = nx.full_rary_tree(r, n)
+        assert t.order() == n
+        assert nx.is_connected(t)
+        dh = nx.degree_histogram(t)
+        assert dh[0] == 0  # no nodes of 0
+        assert dh[1] == 5  # nodes of degree 1 are leaves
+        assert dh[r] == 1  # root is degree r
+        assert dh[r + 1] == 9 - 5 - 1  # everyone else is degree r+1
+        assert len(dh) == r + 2
+
+    def test_full_rary_tree_balanced(self):
+        t = nx.full_rary_tree(2, 15)
+        th = nx.balanced_tree(2, 3)
+        assert is_isomorphic(t, th)
+
+    def test_full_rary_tree_path(self):
+        t = nx.full_rary_tree(1, 10)
+        assert is_isomorphic(t, nx.path_graph(10))
+
+    def test_full_rary_tree_empty(self):
+        t = nx.full_rary_tree(0, 10)
+        assert is_isomorphic(t, nx.empty_graph(10))
+        t = nx.full_rary_tree(3, 0)
+        assert is_isomorphic(t, nx.empty_graph(0))
+
+    def test_full_rary_tree_3_20(self):
+        t = nx.full_rary_tree(3, 20)
+        assert t.order() == 20
+
+    def test_barbell_graph(self):
+        # number of nodes = 2*m1 + m2 (2 m1-complete graphs + m2-path + 2 edges)
+        # number of edges = 2*(nx.number_of_edges(m1-complete graph) + m2 + 1
+        m1 = 3
+        m2 = 5
+        b = nx.barbell_graph(m1, m2)
+        assert nx.number_of_nodes(b) == 2 * m1 + m2
+        assert nx.number_of_edges(b) == m1 * (m1 - 1) + m2 + 1
+
+        m1 = 4
+        m2 = 10
+        b = nx.barbell_graph(m1, m2)
+        assert nx.number_of_nodes(b) == 2 * m1 + m2
+        assert nx.number_of_edges(b) == m1 * (m1 - 1) + m2 + 1
+
+        m1 = 3
+        m2 = 20
+        b = nx.barbell_graph(m1, m2)
+        assert nx.number_of_nodes(b) == 2 * m1 + m2
+        assert nx.number_of_edges(b) == m1 * (m1 - 1) + m2 + 1
+
+        # Raise NetworkXError if m1<2
+        m1 = 1
+        m2 = 20
+        pytest.raises(nx.NetworkXError, nx.barbell_graph, m1, m2)
+
+        # Raise NetworkXError if m2<0
+        m1 = 5
+        m2 = -2
+        pytest.raises(nx.NetworkXError, nx.barbell_graph, m1, m2)
+
+        # nx.barbell_graph(2,m) = nx.path_graph(m+4)
+        m1 = 2
+        m2 = 5
+        b = nx.barbell_graph(m1, m2)
+        assert is_isomorphic(b, nx.path_graph(m2 + 4))
+
+        m1 = 2
+        m2 = 10
+        b = nx.barbell_graph(m1, m2)
+        assert is_isomorphic(b, nx.path_graph(m2 + 4))
+
+        m1 = 2
+        m2 = 20
+        b = nx.barbell_graph(m1, m2)
+        assert is_isomorphic(b, nx.path_graph(m2 + 4))
+
+        pytest.raises(
+            nx.NetworkXError, nx.barbell_graph, m1, m2, create_using=nx.DiGraph()
+        )
+
+        mb = nx.barbell_graph(m1, m2, create_using=nx.MultiGraph())
+        assert edges_equal(mb.edges(), b.edges())
+
+    def test_binomial_tree(self):
+        graphs = (None, nx.Graph, nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)
+        for create_using in graphs:
+            for n in range(4):
+                b = nx.binomial_tree(n, create_using)
+                assert nx.number_of_nodes(b) == 2**n
+                assert nx.number_of_edges(b) == (2**n - 1)
+
+    def test_complete_graph(self):
+        # complete_graph(m) is a connected graph with
+        # m nodes and  m*(m+1)/2 edges
+        for m in [0, 1, 3, 5]:
+            g = nx.complete_graph(m)
+            assert nx.number_of_nodes(g) == m
+            assert nx.number_of_edges(g) == m * (m - 1) // 2
+
+        mg = nx.complete_graph(m, create_using=nx.MultiGraph)
+        assert edges_equal(mg.edges(), g.edges())
+
+        g = nx.complete_graph("abc")
+        assert nodes_equal(g.nodes(), ["a", "b", "c"])
+        assert g.size() == 3
+
+        # creates a self-loop... should it? <backward compatible says yes>
+        g = nx.complete_graph("abcb")
+        assert nodes_equal(g.nodes(), ["a", "b", "c"])
+        assert g.size() == 4
+
+        g = nx.complete_graph("abcb", create_using=nx.MultiGraph)
+        assert nodes_equal(g.nodes(), ["a", "b", "c"])
+        assert g.size() == 6
+
+    def test_complete_digraph(self):
+        # complete_graph(m) is a connected graph with
+        # m nodes and  m*(m+1)/2 edges
+        for m in [0, 1, 3, 5]:
+            g = nx.complete_graph(m, create_using=nx.DiGraph)
+            assert nx.number_of_nodes(g) == m
+            assert nx.number_of_edges(g) == m * (m - 1)
+
+        g = nx.complete_graph("abc", create_using=nx.DiGraph)
+        assert len(g) == 3
+        assert g.size() == 6
+        assert g.is_directed()
+
+    def test_circular_ladder_graph(self):
+        G = nx.circular_ladder_graph(5)
+        pytest.raises(
+            nx.NetworkXError, nx.circular_ladder_graph, 5, create_using=nx.DiGraph
+        )
+        mG = nx.circular_ladder_graph(5, create_using=nx.MultiGraph)
+        assert edges_equal(mG.edges(), G.edges())
+
+    def test_circulant_graph(self):
+        # Ci_n(1) is the cycle graph for all n
+        Ci6_1 = nx.circulant_graph(6, [1])
+        C6 = nx.cycle_graph(6)
+        assert edges_equal(Ci6_1.edges(), C6.edges())
+
+        # Ci_n(1, 2, ..., n div 2) is the complete graph for all n
+        Ci7 = nx.circulant_graph(7, [1, 2, 3])
+        K7 = nx.complete_graph(7)
+        assert edges_equal(Ci7.edges(), K7.edges())
+
+        # Ci_6(1, 3) is K_3,3 i.e. the utility graph
+        Ci6_1_3 = nx.circulant_graph(6, [1, 3])
+        K3_3 = nx.complete_bipartite_graph(3, 3)
+        assert is_isomorphic(Ci6_1_3, K3_3)
+
+    def test_cycle_graph(self):
+        G = nx.cycle_graph(4)
+        assert edges_equal(G.edges(), [(0, 1), (0, 3), (1, 2), (2, 3)])
+        mG = nx.cycle_graph(4, create_using=nx.MultiGraph)
+        assert edges_equal(mG.edges(), [(0, 1), (0, 3), (1, 2), (2, 3)])
+        G = nx.cycle_graph(4, create_using=nx.DiGraph)
+        assert not G.has_edge(2, 1)
+        assert G.has_edge(1, 2)
+        assert G.is_directed()
+
+        G = nx.cycle_graph("abc")
+        assert len(G) == 3
+        assert G.size() == 3
+        G = nx.cycle_graph("abcb")
+        assert len(G) == 3
+        assert G.size() == 2
+        g = nx.cycle_graph("abc", nx.DiGraph)
+        assert len(g) == 3
+        assert g.size() == 3
+        assert g.is_directed()
+        g = nx.cycle_graph("abcb", nx.DiGraph)
+        assert len(g) == 3
+        assert g.size() == 4
+
+    def test_dorogovtsev_goltsev_mendes_graph(self):
+        G = nx.dorogovtsev_goltsev_mendes_graph(0)
+        assert edges_equal(G.edges(), [(0, 1)])
+        assert nodes_equal(list(G), [0, 1])
+        G = nx.dorogovtsev_goltsev_mendes_graph(1)
+        assert edges_equal(G.edges(), [(0, 1), (0, 2), (1, 2)])
+        assert nx.average_clustering(G) == 1.0
+        assert nx.average_shortest_path_length(G) == 1.0
+        assert sorted(nx.triangles(G).values()) == [1, 1, 1]
+        assert nx.is_planar(G)
+        G = nx.dorogovtsev_goltsev_mendes_graph(2)
+        assert nx.number_of_nodes(G) == 6
+        assert nx.number_of_edges(G) == 9
+        assert nx.average_clustering(G) == 0.75
+        assert nx.average_shortest_path_length(G) == 1.4
+        assert nx.is_planar(G)
+        G = nx.dorogovtsev_goltsev_mendes_graph(10)
+        assert nx.number_of_nodes(G) == 29526
+        assert nx.number_of_edges(G) == 59049
+        assert G.degree(0) == 1024
+        assert G.degree(1) == 1024
+        assert G.degree(2) == 1024
+
+        with pytest.raises(nx.NetworkXError, match=r"n must be greater than"):
+            nx.dorogovtsev_goltsev_mendes_graph(-1)
+        with pytest.raises(nx.NetworkXError, match=r"directed graph not supported"):
+            nx.dorogovtsev_goltsev_mendes_graph(7, create_using=nx.DiGraph)
+        with pytest.raises(nx.NetworkXError, match=r"multigraph not supported"):
+            nx.dorogovtsev_goltsev_mendes_graph(7, create_using=nx.MultiGraph)
+        with pytest.raises(nx.NetworkXError):
+            nx.dorogovtsev_goltsev_mendes_graph(7, create_using=nx.MultiDiGraph)
+
+    def test_create_using(self):
+        G = nx.empty_graph()
+        assert isinstance(G, nx.Graph)
+        pytest.raises(TypeError, nx.empty_graph, create_using=0.0)
+        pytest.raises(TypeError, nx.empty_graph, create_using="Graph")
+
+        G = nx.empty_graph(create_using=nx.MultiGraph)
+        assert isinstance(G, nx.MultiGraph)
+        G = nx.empty_graph(create_using=nx.DiGraph)
+        assert isinstance(G, nx.DiGraph)
+
+        G = nx.empty_graph(create_using=nx.DiGraph, default=nx.MultiGraph)
+        assert isinstance(G, nx.DiGraph)
+        G = nx.empty_graph(create_using=None, default=nx.MultiGraph)
+        assert isinstance(G, nx.MultiGraph)
+        G = nx.empty_graph(default=nx.MultiGraph)
+        assert isinstance(G, nx.MultiGraph)
+
+        G = nx.path_graph(5)
+        H = nx.empty_graph(create_using=G)
+        assert not H.is_multigraph()
+        assert not H.is_directed()
+        assert len(H) == 0
+        assert G is H
+
+        H = nx.empty_graph(create_using=nx.MultiGraph())
+        assert H.is_multigraph()
+        assert not H.is_directed()
+        assert G is not H
+
+        # test for subclasses that also use typing.Protocol. See gh-6243
+        class Mixin(typing.Protocol):
+            pass
+
+        class MyGraph(Mixin, nx.DiGraph):
+            pass
+
+        G = nx.empty_graph(create_using=MyGraph)
+
+    def test_empty_graph(self):
+        G = nx.empty_graph()
+        assert nx.number_of_nodes(G) == 0
+        G = nx.empty_graph(42)
+        assert nx.number_of_nodes(G) == 42
+        assert nx.number_of_edges(G) == 0
+
+        G = nx.empty_graph("abc")
+        assert len(G) == 3
+        assert G.size() == 0
+
+        # create empty digraph
+        G = nx.empty_graph(42, create_using=nx.DiGraph(name="duh"))
+        assert nx.number_of_nodes(G) == 42
+        assert nx.number_of_edges(G) == 0
+        assert isinstance(G, nx.DiGraph)
+
+        # create empty multigraph
+        G = nx.empty_graph(42, create_using=nx.MultiGraph(name="duh"))
+        assert nx.number_of_nodes(G) == 42
+        assert nx.number_of_edges(G) == 0
+        assert isinstance(G, nx.MultiGraph)
+
+        # create empty graph from another
+        pete = nx.petersen_graph()
+        G = nx.empty_graph(42, create_using=pete)
+        assert nx.number_of_nodes(G) == 42
+        assert nx.number_of_edges(G) == 0
+        assert isinstance(G, nx.Graph)
+
+    def test_ladder_graph(self):
+        for i, G in [
+            (0, nx.empty_graph(0)),
+            (1, nx.path_graph(2)),
+            (2, nx.hypercube_graph(2)),
+            (10, nx.grid_graph([2, 10])),
+        ]:
+            assert is_isomorphic(nx.ladder_graph(i), G)
+
+        pytest.raises(nx.NetworkXError, nx.ladder_graph, 2, create_using=nx.DiGraph)
+
+        g = nx.ladder_graph(2)
+        mg = nx.ladder_graph(2, create_using=nx.MultiGraph)
+        assert edges_equal(mg.edges(), g.edges())
+
+    @pytest.mark.parametrize(("m", "n"), [(3, 5), (4, 10), (3, 20)])
+    def test_lollipop_graph_right_sizes(self, m, n):
+        G = nx.lollipop_graph(m, n)
+        assert nx.number_of_nodes(G) == m + n
+        assert nx.number_of_edges(G) == m * (m - 1) / 2 + n
+
+    @pytest.mark.parametrize(("m", "n"), [("ab", ""), ("abc", "defg")])
+    def test_lollipop_graph_size_node_sequence(self, m, n):
+        G = nx.lollipop_graph(m, n)
+        assert nx.number_of_nodes(G) == len(m) + len(n)
+        assert nx.number_of_edges(G) == len(m) * (len(m) - 1) / 2 + len(n)
+
+    def test_lollipop_graph_exceptions(self):
+        # Raise NetworkXError if m<2
+        pytest.raises(nx.NetworkXError, nx.lollipop_graph, -1, 2)
+        pytest.raises(nx.NetworkXError, nx.lollipop_graph, 1, 20)
+        pytest.raises(nx.NetworkXError, nx.lollipop_graph, "", 20)
+        pytest.raises(nx.NetworkXError, nx.lollipop_graph, "a", 20)
+
+        # Raise NetworkXError if n<0
+        pytest.raises(nx.NetworkXError, nx.lollipop_graph, 5, -2)
+
+        # raise NetworkXError if create_using is directed
+        with pytest.raises(nx.NetworkXError):
+            nx.lollipop_graph(2, 20, create_using=nx.DiGraph)
+        with pytest.raises(nx.NetworkXError):
+            nx.lollipop_graph(2, 20, create_using=nx.MultiDiGraph)
+
+    @pytest.mark.parametrize(("m", "n"), [(2, 0), (2, 5), (2, 10), ("ab", 20)])
+    def test_lollipop_graph_same_as_path_when_m1_is_2(self, m, n):
+        G = nx.lollipop_graph(m, n)
+        assert is_isomorphic(G, nx.path_graph(n + 2))
+
+    def test_lollipop_graph_for_multigraph(self):
+        G = nx.lollipop_graph(5, 20)
+        MG = nx.lollipop_graph(5, 20, create_using=nx.MultiGraph)
+        assert edges_equal(MG.edges(), G.edges())
+
+    @pytest.mark.parametrize(
+        ("m", "n"),
+        [(4, "abc"), ("abcd", 3), ([1, 2, 3, 4], "abc"), ("abcd", [1, 2, 3])],
+    )
+    def test_lollipop_graph_mixing_input_types(self, m, n):
+        expected = nx.compose(nx.complete_graph(4), nx.path_graph(range(100, 103)))
+        expected.add_edge(0, 100)  # Connect complete graph and path graph
+        assert is_isomorphic(nx.lollipop_graph(m, n), expected)
+
+    def test_lollipop_graph_non_builtin_ints(self):
+        np = pytest.importorskip("numpy")
+        G = nx.lollipop_graph(np.int32(4), np.int64(3))
+        expected = nx.compose(nx.complete_graph(4), nx.path_graph(range(100, 103)))
+        expected.add_edge(0, 100)  # Connect complete graph and path graph
+        assert is_isomorphic(G, expected)
+
+    def test_null_graph(self):
+        assert nx.number_of_nodes(nx.null_graph()) == 0
+
+    def test_path_graph(self):
+        p = nx.path_graph(0)
+        assert is_isomorphic(p, nx.null_graph())
+
+        p = nx.path_graph(1)
+        assert is_isomorphic(p, nx.empty_graph(1))
+
+        p = nx.path_graph(10)
+        assert nx.is_connected(p)
+        assert sorted(d for n, d in p.degree()) == [1, 1, 2, 2, 2, 2, 2, 2, 2, 2]
+        assert p.order() - 1 == p.size()
+
+        dp = nx.path_graph(3, create_using=nx.DiGraph)
+        assert dp.has_edge(0, 1)
+        assert not dp.has_edge(1, 0)
+
+        mp = nx.path_graph(10, create_using=nx.MultiGraph)
+        assert edges_equal(mp.edges(), p.edges())
+
+        G = nx.path_graph("abc")
+        assert len(G) == 3
+        assert G.size() == 2
+        G = nx.path_graph("abcb")
+        assert len(G) == 3
+        assert G.size() == 2
+        g = nx.path_graph("abc", nx.DiGraph)
+        assert len(g) == 3
+        assert g.size() == 2
+        assert g.is_directed()
+        g = nx.path_graph("abcb", nx.DiGraph)
+        assert len(g) == 3
+        assert g.size() == 3
+
+        G = nx.path_graph((1, 2, 3, 2, 4))
+        assert G.has_edge(2, 4)
+
+    def test_star_graph(self):
+        assert is_isomorphic(nx.star_graph(""), nx.empty_graph(0))
+        assert is_isomorphic(nx.star_graph([]), nx.empty_graph(0))
+        assert is_isomorphic(nx.star_graph(0), nx.empty_graph(1))
+        assert is_isomorphic(nx.star_graph(1), nx.path_graph(2))
+        assert is_isomorphic(nx.star_graph(2), nx.path_graph(3))
+        assert is_isomorphic(nx.star_graph(5), nx.complete_bipartite_graph(1, 5))
+
+        s = nx.star_graph(10)
+        assert sorted(d for n, d in s.degree()) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10]
+
+        pytest.raises(nx.NetworkXError, nx.star_graph, 10, create_using=nx.DiGraph)
+
+        ms = nx.star_graph(10, create_using=nx.MultiGraph)
+        assert edges_equal(ms.edges(), s.edges())
+
+        G = nx.star_graph("abc")
+        assert len(G) == 3
+        assert G.size() == 2
+
+        G = nx.star_graph("abcb")
+        assert len(G) == 3
+        assert G.size() == 2
+        G = nx.star_graph("abcb", create_using=nx.MultiGraph)
+        assert len(G) == 3
+        assert G.size() == 3
+
+        G = nx.star_graph("abcdefg")
+        assert len(G) == 7
+        assert G.size() == 6
+
+    def test_non_int_integers_for_star_graph(self):
+        np = pytest.importorskip("numpy")
+        G = nx.star_graph(np.int32(3))
+        assert len(G) == 4
+        assert G.size() == 3
+
+    @pytest.mark.parametrize(("m", "n"), [(3, 0), (3, 5), (4, 10), (3, 20)])
+    def test_tadpole_graph_right_sizes(self, m, n):
+        G = nx.tadpole_graph(m, n)
+        assert nx.number_of_nodes(G) == m + n
+        assert nx.number_of_edges(G) == m + n - (m == 2)
+
+    @pytest.mark.parametrize(("m", "n"), [("ab", ""), ("ab", "c"), ("abc", "defg")])
+    def test_tadpole_graph_size_node_sequences(self, m, n):
+        G = nx.tadpole_graph(m, n)
+        assert nx.number_of_nodes(G) == len(m) + len(n)
+        assert nx.number_of_edges(G) == len(m) + len(n) - (len(m) == 2)
+
+    def test_tadpole_graph_exceptions(self):
+        # Raise NetworkXError if m<2
+        pytest.raises(nx.NetworkXError, nx.tadpole_graph, -1, 3)
+        pytest.raises(nx.NetworkXError, nx.tadpole_graph, 0, 3)
+        pytest.raises(nx.NetworkXError, nx.tadpole_graph, 1, 3)
+
+        # Raise NetworkXError if n<0
+        pytest.raises(nx.NetworkXError, nx.tadpole_graph, 5, -2)
+
+        # Raise NetworkXError for digraphs
+        with pytest.raises(nx.NetworkXError):
+            nx.tadpole_graph(2, 20, create_using=nx.DiGraph)
+        with pytest.raises(nx.NetworkXError):
+            nx.tadpole_graph(2, 20, create_using=nx.MultiDiGraph)
+
+    @pytest.mark.parametrize(("m", "n"), [(2, 0), (2, 5), (2, 10), ("ab", 20)])
+    def test_tadpole_graph_same_as_path_when_m_is_2(self, m, n):
+        G = nx.tadpole_graph(m, n)
+        assert is_isomorphic(G, nx.path_graph(n + 2))
+
+    @pytest.mark.parametrize("m", [4, 7])
+    def test_tadpole_graph_same_as_cycle_when_m2_is_0(self, m):
+        G = nx.tadpole_graph(m, 0)
+        assert is_isomorphic(G, nx.cycle_graph(m))
+
+    def test_tadpole_graph_for_multigraph(self):
+        G = nx.tadpole_graph(5, 20)
+        MG = nx.tadpole_graph(5, 20, create_using=nx.MultiGraph)
+        assert edges_equal(MG.edges(), G.edges())
+
+    @pytest.mark.parametrize(
+        ("m", "n"),
+        [(4, "abc"), ("abcd", 3), ([1, 2, 3, 4], "abc"), ("abcd", [1, 2, 3])],
+    )
+    def test_tadpole_graph_mixing_input_types(self, m, n):
+        expected = nx.compose(nx.cycle_graph(4), nx.path_graph(range(100, 103)))
+        expected.add_edge(0, 100)  # Connect cycle and path
+        assert is_isomorphic(nx.tadpole_graph(m, n), expected)
+
+    def test_tadpole_graph_non_builtin_integers(self):
+        np = pytest.importorskip("numpy")
+        G = nx.tadpole_graph(np.int32(4), np.int64(3))
+        expected = nx.compose(nx.cycle_graph(4), nx.path_graph(range(100, 103)))
+        expected.add_edge(0, 100)  # Connect cycle and path
+        assert is_isomorphic(G, expected)
+
+    def test_trivial_graph(self):
+        assert nx.number_of_nodes(nx.trivial_graph()) == 1
+
+    def test_turan_graph(self):
+        assert nx.number_of_edges(nx.turan_graph(13, 4)) == 63
+        assert is_isomorphic(
+            nx.turan_graph(13, 4), nx.complete_multipartite_graph(3, 4, 3, 3)
+        )
+
+    def test_wheel_graph(self):
+        for n, G in [
+            ("", nx.null_graph()),
+            (0, nx.null_graph()),
+            (1, nx.empty_graph(1)),
+            (2, nx.path_graph(2)),
+            (3, nx.complete_graph(3)),
+            (4, nx.complete_graph(4)),
+        ]:
+            g = nx.wheel_graph(n)
+            assert is_isomorphic(g, G)
+
+        g = nx.wheel_graph(10)
+        assert sorted(d for n, d in g.degree()) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 9]
+
+        pytest.raises(nx.NetworkXError, nx.wheel_graph, 10, create_using=nx.DiGraph)
+
+        mg = nx.wheel_graph(10, create_using=nx.MultiGraph())
+        assert edges_equal(mg.edges(), g.edges())
+
+        G = nx.wheel_graph("abc")
+        assert len(G) == 3
+        assert G.size() == 3
+
+        G = nx.wheel_graph("abcb")
+        assert len(G) == 3
+        assert G.size() == 4
+        G = nx.wheel_graph("abcb", nx.MultiGraph)
+        assert len(G) == 3
+        assert G.size() == 6
+
+    def test_non_int_integers_for_wheel_graph(self):
+        np = pytest.importorskip("numpy")
+        G = nx.wheel_graph(np.int32(3))
+        assert len(G) == 3
+        assert G.size() == 3
+
+    def test_complete_0_partite_graph(self):
+        """Tests that the complete 0-partite graph is the null graph."""
+        G = nx.complete_multipartite_graph()
+        H = nx.null_graph()
+        assert nodes_equal(G, H)
+        assert edges_equal(G.edges(), H.edges())
+
+    def test_complete_1_partite_graph(self):
+        """Tests that the complete 1-partite graph is the empty graph."""
+        G = nx.complete_multipartite_graph(3)
+        H = nx.empty_graph(3)
+        assert nodes_equal(G, H)
+        assert edges_equal(G.edges(), H.edges())
+
+    def test_complete_2_partite_graph(self):
+        """Tests that the complete 2-partite graph is the complete bipartite
+        graph.
+
+        """
+        G = nx.complete_multipartite_graph(2, 3)
+        H = nx.complete_bipartite_graph(2, 3)
+        assert nodes_equal(G, H)
+        assert edges_equal(G.edges(), H.edges())
+
+    def test_complete_multipartite_graph(self):
+        """Tests for generating the complete multipartite graph."""
+        G = nx.complete_multipartite_graph(2, 3, 4)
+        blocks = [(0, 1), (2, 3, 4), (5, 6, 7, 8)]
+        # Within each block, no two vertices should be adjacent.
+        for block in blocks:
+            for u, v in itertools.combinations_with_replacement(block, 2):
+                assert v not in G[u]
+                assert G.nodes[u] == G.nodes[v]
+        # Across blocks, all vertices should be adjacent.
+        for block1, block2 in itertools.combinations(blocks, 2):
+            for u, v in itertools.product(block1, block2):
+                assert v in G[u]
+                assert G.nodes[u] != G.nodes[v]
+        with pytest.raises(nx.NetworkXError, match="Negative number of nodes"):
+            nx.complete_multipartite_graph(2, -3, 4)
+
+    def test_kneser_graph(self):
+        # the petersen graph is a special case of the kneser graph when n=5 and k=2
+        assert is_isomorphic(nx.kneser_graph(5, 2), nx.petersen_graph())
+
+        # when k is 1, the kneser graph returns a complete graph with n vertices
+        for i in range(1, 7):
+            assert is_isomorphic(nx.kneser_graph(i, 1), nx.complete_graph(i))
+
+        # the kneser graph of n and n-1 is the empty graph with n vertices
+        for j in range(3, 7):
+            assert is_isomorphic(nx.kneser_graph(j, j - 1), nx.empty_graph(j))
+
+        # in general the number of edges of the kneser graph is equal to
+        # (n choose k) times (n-k choose k) divided by 2
+        assert nx.number_of_edges(nx.kneser_graph(8, 3)) == 280

janus/lib/python3.10/site-packages/networkx/generators/tests/test_community.py

@@ -0,0 +1,362 @@
+import pytest
+
+import networkx as nx
+
+
+def test_random_partition_graph():
+    G = nx.random_partition_graph([3, 3, 3], 1, 0, seed=42)
+    C = G.graph["partition"]
+    assert C == [{0, 1, 2}, {3, 4, 5}, {6, 7, 8}]
+    assert len(G) == 9
+    assert len(list(G.edges())) == 9
+
+    G = nx.random_partition_graph([3, 3, 3], 0, 1)
+    C = G.graph["partition"]
+    assert C == [{0, 1, 2}, {3, 4, 5}, {6, 7, 8}]
+    assert len(G) == 9
+    assert len(list(G.edges())) == 27
+
+    G = nx.random_partition_graph([3, 3, 3], 1, 0, directed=True)
+    C = G.graph["partition"]
+    assert C == [{0, 1, 2}, {3, 4, 5}, {6, 7, 8}]
+    assert len(G) == 9
+    assert len(list(G.edges())) == 18
+
+    G = nx.random_partition_graph([3, 3, 3], 0, 1, directed=True)
+    C = G.graph["partition"]
+    assert C == [{0, 1, 2}, {3, 4, 5}, {6, 7, 8}]
+    assert len(G) == 9
+    assert len(list(G.edges())) == 54
+
+    G = nx.random_partition_graph([1, 2, 3, 4, 5], 0.5, 0.1)
+    C = G.graph["partition"]
+    assert C == [{0}, {1, 2}, {3, 4, 5}, {6, 7, 8, 9}, {10, 11, 12, 13, 14}]
+    assert len(G) == 15
+
+    rpg = nx.random_partition_graph
+    pytest.raises(nx.NetworkXError, rpg, [1, 2, 3], 1.1, 0.1)
+    pytest.raises(nx.NetworkXError, rpg, [1, 2, 3], -0.1, 0.1)
+    pytest.raises(nx.NetworkXError, rpg, [1, 2, 3], 0.1, 1.1)
+    pytest.raises(nx.NetworkXError, rpg, [1, 2, 3], 0.1, -0.1)
+
+
+def test_planted_partition_graph():
+    G = nx.planted_partition_graph(4, 3, 1, 0, seed=42)
+    C = G.graph["partition"]
+    assert len(C) == 4
+    assert len(G) == 12
+    assert len(list(G.edges())) == 12
+
+    G = nx.planted_partition_graph(4, 3, 0, 1)
+    C = G.graph["partition"]
+    assert len(C) == 4
+    assert len(G) == 12
+    assert len(list(G.edges())) == 54
+
+    G = nx.planted_partition_graph(10, 4, 0.5, 0.1, seed=42)
+    C = G.graph["partition"]
+    assert len(C) == 10
+    assert len(G) == 40
+
+    G = nx.planted_partition_graph(4, 3, 1, 0, directed=True)
+    C = G.graph["partition"]
+    assert len(C) == 4
+    assert len(G) == 12
+    assert len(list(G.edges())) == 24
+
+    G = nx.planted_partition_graph(4, 3, 0, 1, directed=True)
+    C = G.graph["partition"]
+    assert len(C) == 4
+    assert len(G) == 12
+    assert len(list(G.edges())) == 108
+
+    G = nx.planted_partition_graph(10, 4, 0.5, 0.1, seed=42, directed=True)
+    C = G.graph["partition"]
+    assert len(C) == 10
+    assert len(G) == 40
+
+    ppg = nx.planted_partition_graph
+    pytest.raises(nx.NetworkXError, ppg, 3, 3, 1.1, 0.1)
+    pytest.raises(nx.NetworkXError, ppg, 3, 3, -0.1, 0.1)
+    pytest.raises(nx.NetworkXError, ppg, 3, 3, 0.1, 1.1)
+    pytest.raises(nx.NetworkXError, ppg, 3, 3, 0.1, -0.1)
+
+
+def test_relaxed_caveman_graph():
+    G = nx.relaxed_caveman_graph(4, 3, 0)
+    assert len(G) == 12
+    G = nx.relaxed_caveman_graph(4, 3, 1)
+    assert len(G) == 12
+    G = nx.relaxed_caveman_graph(4, 3, 0.5)
+    assert len(G) == 12
+    G = nx.relaxed_caveman_graph(4, 3, 0.5, seed=42)
+    assert len(G) == 12
+
+
+def test_connected_caveman_graph():
+    G = nx.connected_caveman_graph(4, 3)
+    assert len(G) == 12
+
+    G = nx.connected_caveman_graph(1, 5)
+    K5 = nx.complete_graph(5)
+    K5.remove_edge(3, 4)
+    assert nx.is_isomorphic(G, K5)
+
+    # need at least 2 nodes in each clique
+    pytest.raises(nx.NetworkXError, nx.connected_caveman_graph, 4, 1)
+
+
+def test_caveman_graph():
+    G = nx.caveman_graph(4, 3)
+    assert len(G) == 12
+
+    G = nx.caveman_graph(5, 1)
+    E5 = nx.empty_graph(5)
+    assert nx.is_isomorphic(G, E5)
+
+    G = nx.caveman_graph(1, 5)
+    K5 = nx.complete_graph(5)
+    assert nx.is_isomorphic(G, K5)
+
+
+def test_gaussian_random_partition_graph():
+    G = nx.gaussian_random_partition_graph(100, 10, 10, 0.3, 0.01)
+    assert len(G) == 100
+    G = nx.gaussian_random_partition_graph(100, 10, 10, 0.3, 0.01, directed=True)
+    assert len(G) == 100
+    G = nx.gaussian_random_partition_graph(
+        100, 10, 10, 0.3, 0.01, directed=False, seed=42
+    )
+    assert len(G) == 100
+    assert not isinstance(G, nx.DiGraph)
+    G = nx.gaussian_random_partition_graph(
+        100, 10, 10, 0.3, 0.01, directed=True, seed=42
+    )
+    assert len(G) == 100
+    assert isinstance(G, nx.DiGraph)
+    pytest.raises(
+        nx.NetworkXError, nx.gaussian_random_partition_graph, 100, 101, 10, 1, 0
+    )
+    # Test when clusters are likely less than 1
+    G = nx.gaussian_random_partition_graph(10, 0.5, 0.5, 0.5, 0.5, seed=1)
+    assert len(G) == 10
+
+
+def test_ring_of_cliques():
+    for i in range(2, 20, 3):
+        for j in range(2, 20, 3):
+            G = nx.ring_of_cliques(i, j)
+            assert G.number_of_nodes() == i * j
+            if i != 2 or j != 1:
+                expected_num_edges = i * (((j * (j - 1)) // 2) + 1)
+            else:
+                # the edge that already exists cannot be duplicated
+                expected_num_edges = i * (((j * (j - 1)) // 2) + 1) - 1
+            assert G.number_of_edges() == expected_num_edges
+    with pytest.raises(
+        nx.NetworkXError, match="A ring of cliques must have at least two cliques"
+    ):
+        nx.ring_of_cliques(1, 5)
+    with pytest.raises(
+        nx.NetworkXError, match="The cliques must have at least two nodes"
+    ):
+        nx.ring_of_cliques(3, 0)
+
+
+def test_windmill_graph():
+    for n in range(2, 20, 3):
+        for k in range(2, 20, 3):
+            G = nx.windmill_graph(n, k)
+            assert G.number_of_nodes() == (k - 1) * n + 1
+            assert G.number_of_edges() == n * k * (k - 1) / 2
+            assert G.degree(0) == G.number_of_nodes() - 1
+            for i in range(1, G.number_of_nodes()):
+                assert G.degree(i) == k - 1
+    with pytest.raises(
+        nx.NetworkXError, match="A windmill graph must have at least two cliques"
+    ):
+        nx.windmill_graph(1, 3)
+    with pytest.raises(
+        nx.NetworkXError, match="The cliques must have at least two nodes"
+    ):
+        nx.windmill_graph(3, 0)
+
+
+def test_stochastic_block_model():
+    sizes = [75, 75, 300]
+    probs = [[0.25, 0.05, 0.02], [0.05, 0.35, 0.07], [0.02, 0.07, 0.40]]
+    G = nx.stochastic_block_model(sizes, probs, seed=0)
+    C = G.graph["partition"]
+    assert len(C) == 3
+    assert len(G) == 450
+    assert G.size() == 22160
+
+    GG = nx.stochastic_block_model(sizes, probs, range(450), seed=0)
+    assert G.nodes == GG.nodes
+
+    # Test Exceptions
+    sbm = nx.stochastic_block_model
+    badnodelist = list(range(400))  # not enough nodes to match sizes
+    badprobs1 = [[0.25, 0.05, 1.02], [0.05, 0.35, 0.07], [0.02, 0.07, 0.40]]
+    badprobs2 = [[0.25, 0.05, 0.02], [0.05, -0.35, 0.07], [0.02, 0.07, 0.40]]
+    probs_rect1 = [[0.25, 0.05, 0.02], [0.05, -0.35, 0.07]]
+    probs_rect2 = [[0.25, 0.05], [0.05, -0.35], [0.02, 0.07]]
+    asymprobs = [[0.25, 0.05, 0.01], [0.05, -0.35, 0.07], [0.02, 0.07, 0.40]]
+    pytest.raises(nx.NetworkXException, sbm, sizes, badprobs1)
+    pytest.raises(nx.NetworkXException, sbm, sizes, badprobs2)
+    pytest.raises(nx.NetworkXException, sbm, sizes, probs_rect1, directed=True)
+    pytest.raises(nx.NetworkXException, sbm, sizes, probs_rect2, directed=True)
+    pytest.raises(nx.NetworkXException, sbm, sizes, asymprobs, directed=False)
+    pytest.raises(nx.NetworkXException, sbm, sizes, probs, badnodelist)
+    nodelist = [0] + list(range(449))  # repeated node name in nodelist
+    pytest.raises(nx.NetworkXException, sbm, sizes, probs, nodelist)
+
+    # Extra keyword arguments test
+    GG = nx.stochastic_block_model(sizes, probs, seed=0, selfloops=True)
+    assert G.nodes == GG.nodes
+    GG = nx.stochastic_block_model(sizes, probs, selfloops=True, directed=True)
+    assert G.nodes == GG.nodes
+    GG = nx.stochastic_block_model(sizes, probs, seed=0, sparse=False)
+    assert G.nodes == GG.nodes
+
+
+def test_generator():
+    n = 250
+    tau1 = 3
+    tau2 = 1.5
+    mu = 0.1
+    G = nx.LFR_benchmark_graph(
+        n, tau1, tau2, mu, average_degree=5, min_community=20, seed=10
+    )
+    assert len(G) == 250
+    C = {frozenset(G.nodes[v]["community"]) for v in G}
+    assert nx.community.is_partition(G.nodes(), C)
+
+
+def test_invalid_tau1():
+    with pytest.raises(nx.NetworkXError, match="tau2 must be greater than one"):
+        n = 100
+        tau1 = 2
+        tau2 = 1
+        mu = 0.1
+        nx.LFR_benchmark_graph(n, tau1, tau2, mu, min_degree=2)
+
+
+def test_invalid_tau2():
+    with pytest.raises(nx.NetworkXError, match="tau1 must be greater than one"):
+        n = 100
+        tau1 = 1
+        tau2 = 2
+        mu = 0.1
+        nx.LFR_benchmark_graph(n, tau1, tau2, mu, min_degree=2)
+
+
+def test_mu_too_large():
+    with pytest.raises(nx.NetworkXError, match="mu must be in the interval \\[0, 1\\]"):
+        n = 100
+        tau1 = 2
+        tau2 = 2
+        mu = 1.1
+        nx.LFR_benchmark_graph(n, tau1, tau2, mu, min_degree=2)
+
+
+def test_mu_too_small():
+    with pytest.raises(nx.NetworkXError, match="mu must be in the interval \\[0, 1\\]"):
+        n = 100
+        tau1 = 2
+        tau2 = 2
+        mu = -1
+        nx.LFR_benchmark_graph(n, tau1, tau2, mu, min_degree=2)
+
+
+def test_both_degrees_none():
+    with pytest.raises(
+        nx.NetworkXError,
+        match="Must assign exactly one of min_degree and average_degree",
+    ):
+        n = 100
+        tau1 = 2
+        tau2 = 2
+        mu = 1
+        nx.LFR_benchmark_graph(n, tau1, tau2, mu)
+
+
+def test_neither_degrees_none():
+    with pytest.raises(
+        nx.NetworkXError,
+        match="Must assign exactly one of min_degree and average_degree",
+    ):
+        n = 100
+        tau1 = 2
+        tau2 = 2
+        mu = 1
+        nx.LFR_benchmark_graph(n, tau1, tau2, mu, min_degree=2, average_degree=5)
+
+
+def test_max_iters_exceeded():
+    with pytest.raises(
+        nx.ExceededMaxIterations,
+        match="Could not assign communities; try increasing min_community",
+    ):
+        n = 10
+        tau1 = 2
+        tau2 = 2
+        mu = 0.1
+        nx.LFR_benchmark_graph(n, tau1, tau2, mu, min_degree=2, max_iters=10, seed=1)
+
+
+def test_max_deg_out_of_range():
+    with pytest.raises(
+        nx.NetworkXError, match="max_degree must be in the interval \\(0, n\\]"
+    ):
+        n = 10
+        tau1 = 2
+        tau2 = 2
+        mu = 0.1
+        nx.LFR_benchmark_graph(
+            n, tau1, tau2, mu, max_degree=n + 1, max_iters=10, seed=1
+        )
+
+
+def test_max_community():
+    n = 250
+    tau1 = 3
+    tau2 = 1.5
+    mu = 0.1
+    G = nx.LFR_benchmark_graph(
+        n,
+        tau1,
+        tau2,
+        mu,
+        average_degree=5,
+        max_degree=100,
+        min_community=50,
+        max_community=200,
+        seed=10,
+    )
+    assert len(G) == 250
+    C = {frozenset(G.nodes[v]["community"]) for v in G}
+    assert nx.community.is_partition(G.nodes(), C)
+
+
+def test_powerlaw_iterations_exceeded():
+    with pytest.raises(
+        nx.ExceededMaxIterations, match="Could not create power law sequence"
+    ):
+        n = 100
+        tau1 = 2
+        tau2 = 2
+        mu = 1
+        nx.LFR_benchmark_graph(n, tau1, tau2, mu, min_degree=2, max_iters=0)
+
+
+def test_no_scipy_zeta():
+    zeta2 = 1.6449340668482264
+    assert abs(zeta2 - nx.generators.community._hurwitz_zeta(2, 1, 0.0001)) < 0.01
+
+
+def test_generate_min_degree_itr():
+    with pytest.raises(
+        nx.ExceededMaxIterations, match="Could not match average_degree"
+    ):
+        nx.generators.community._generate_min_degree(2, 2, 1, 0.01, 0)

janus/lib/python3.10/site-packages/networkx/generators/tests/test_directed.py

@@ -0,0 +1,163 @@
+"""Generators - Directed Graphs
+----------------------------
+"""
+
+import pytest
+
+import networkx as nx
+from networkx.classes import Graph, MultiDiGraph
+from networkx.generators.directed import (
+    gn_graph,
+    gnc_graph,
+    gnr_graph,
+    random_k_out_graph,
+    random_uniform_k_out_graph,
+    scale_free_graph,
+)
+
+
+class TestGeneratorsDirected:
+    def test_smoke_test_random_graphs(self):
+        gn_graph(100)
+        gnr_graph(100, 0.5)
+        gnc_graph(100)
+        scale_free_graph(100)
+
+        gn_graph(100, seed=42)
+        gnr_graph(100, 0.5, seed=42)
+        gnc_graph(100, seed=42)
+        scale_free_graph(100, seed=42)
+
+    def test_create_using_keyword_arguments(self):
+        pytest.raises(nx.NetworkXError, gn_graph, 100, create_using=Graph())
+        pytest.raises(nx.NetworkXError, gnr_graph, 100, 0.5, create_using=Graph())
+        pytest.raises(nx.NetworkXError, gnc_graph, 100, create_using=Graph())
+        G = gn_graph(100, seed=1)
+        MG = gn_graph(100, create_using=MultiDiGraph(), seed=1)
+        assert sorted(G.edges()) == sorted(MG.edges())
+        G = gnr_graph(100, 0.5, seed=1)
+        MG = gnr_graph(100, 0.5, create_using=MultiDiGraph(), seed=1)
+        assert sorted(G.edges()) == sorted(MG.edges())
+        G = gnc_graph(100, seed=1)
+        MG = gnc_graph(100, create_using=MultiDiGraph(), seed=1)
+        assert sorted(G.edges()) == sorted(MG.edges())
+
+        G = scale_free_graph(
+            100,
+            alpha=0.3,
+            beta=0.4,
+            gamma=0.3,
+            delta_in=0.3,
+            delta_out=0.1,
+            initial_graph=nx.cycle_graph(4, create_using=MultiDiGraph),
+            seed=1,
+        )
+        pytest.raises(ValueError, scale_free_graph, 100, 0.5, 0.4, 0.3)
+        pytest.raises(ValueError, scale_free_graph, 100, alpha=-0.3)
+        pytest.raises(ValueError, scale_free_graph, 100, beta=-0.3)
+        pytest.raises(ValueError, scale_free_graph, 100, gamma=-0.3)
+
+    def test_parameters(self):
+        G = nx.DiGraph()
+        G.add_node(0)
+
+        def kernel(x):
+            return x
+
+        assert nx.is_isomorphic(gn_graph(1), G)
+        assert nx.is_isomorphic(gn_graph(1, kernel=kernel), G)
+        assert nx.is_isomorphic(gnc_graph(1), G)
+        assert nx.is_isomorphic(gnr_graph(1, 0.5), G)
+
+
+def test_scale_free_graph_negative_delta():
+    with pytest.raises(ValueError, match="delta_in must be >= 0."):
+        scale_free_graph(10, delta_in=-1)
+    with pytest.raises(ValueError, match="delta_out must be >= 0."):
+        scale_free_graph(10, delta_out=-1)
+
+
+def test_non_numeric_ordering():
+    G = MultiDiGraph([("a", "b"), ("b", "c"), ("c", "a")])
+    s = scale_free_graph(3, initial_graph=G)
+    assert len(s) == 3
+    assert len(s.edges) == 3
+
+
+@pytest.mark.parametrize("ig", (nx.Graph(), nx.DiGraph([(0, 1)])))
+def test_scale_free_graph_initial_graph_kwarg(ig):
+    with pytest.raises(nx.NetworkXError):
+        scale_free_graph(100, initial_graph=ig)
+
+
+class TestRandomKOutGraph:
+    """Unit tests for the
+    :func:`~networkx.generators.directed.random_k_out_graph` function.
+
+    """
+
+    def test_regularity(self):
+        """Tests that the generated graph is `k`-out-regular."""
+        n = 10
+        k = 3
+        alpha = 1
+        G = random_k_out_graph(n, k, alpha)
+        assert all(d == k for v, d in G.out_degree())
+        G = random_k_out_graph(n, k, alpha, seed=42)
+        assert all(d == k for v, d in G.out_degree())
+
+    def test_no_self_loops(self):
+        """Tests for forbidding self-loops."""
+        n = 10
+        k = 3
+        alpha = 1
+        G = random_k_out_graph(n, k, alpha, self_loops=False)
+        assert nx.number_of_selfloops(G) == 0
+
+    def test_negative_alpha(self):
+        with pytest.raises(ValueError, match="alpha must be positive"):
+            random_k_out_graph(10, 3, -1)
+
+
+class TestUniformRandomKOutGraph:
+    """Unit tests for the
+    :func:`~networkx.generators.directed.random_uniform_k_out_graph`
+    function.
+
+    """
+
+    def test_regularity(self):
+        """Tests that the generated graph is `k`-out-regular."""
+        n = 10
+        k = 3
+        G = random_uniform_k_out_graph(n, k)
+        assert all(d == k for v, d in G.out_degree())
+        G = random_uniform_k_out_graph(n, k, seed=42)
+        assert all(d == k for v, d in G.out_degree())
+
+    def test_no_self_loops(self):
+        """Tests for forbidding self-loops."""
+        n = 10
+        k = 3
+        G = random_uniform_k_out_graph(n, k, self_loops=False)
+        assert nx.number_of_selfloops(G) == 0
+        assert all(d == k for v, d in G.out_degree())
+
+    def test_with_replacement(self):
+        n = 10
+        k = 3
+        G = random_uniform_k_out_graph(n, k, with_replacement=True)
+        assert G.is_multigraph()
+        assert all(d == k for v, d in G.out_degree())
+        n = 10
+        k = 9
+        G = random_uniform_k_out_graph(n, k, with_replacement=False, self_loops=False)
+        assert nx.number_of_selfloops(G) == 0
+        assert all(d == k for v, d in G.out_degree())
+
+    def test_without_replacement(self):
+        n = 10
+        k = 3
+        G = random_uniform_k_out_graph(n, k, with_replacement=False)
+        assert not G.is_multigraph()
+        assert all(d == k for v, d in G.out_degree())

janus/lib/python3.10/site-packages/networkx/generators/tests/test_lattice.py

@@ -0,0 +1,246 @@
+"""Unit tests for the :mod:`networkx.generators.lattice` module."""
+
+from itertools import product
+
+import pytest
+
+import networkx as nx
+from networkx.utils import edges_equal
+
+
+class TestGrid2DGraph:
+    """Unit tests for :func:`networkx.generators.lattice.grid_2d_graph`"""
+
+    def test_number_of_vertices(self):
+        m, n = 5, 6
+        G = nx.grid_2d_graph(m, n)
+        assert len(G) == m * n
+
+    def test_degree_distribution(self):
+        m, n = 5, 6
+        G = nx.grid_2d_graph(m, n)
+        expected_histogram = [0, 0, 4, 2 * (m + n) - 8, (m - 2) * (n - 2)]
+        assert nx.degree_histogram(G) == expected_histogram
+
+    def test_directed(self):
+        m, n = 5, 6
+        G = nx.grid_2d_graph(m, n)
+        H = nx.grid_2d_graph(m, n, create_using=nx.DiGraph())
+        assert H.succ == G.adj
+        assert H.pred == G.adj
+
+    def test_multigraph(self):
+        m, n = 5, 6
+        G = nx.grid_2d_graph(m, n)
+        H = nx.grid_2d_graph(m, n, create_using=nx.MultiGraph())
+        assert list(H.edges()) == list(G.edges())
+
+    def test_periodic(self):
+        G = nx.grid_2d_graph(0, 0, periodic=True)
+        assert dict(G.degree()) == {}
+
+        for m, n, H in [
+            (2, 2, nx.cycle_graph(4)),
+            (1, 7, nx.cycle_graph(7)),
+            (7, 1, nx.cycle_graph(7)),
+            (2, 5, nx.circular_ladder_graph(5)),
+            (5, 2, nx.circular_ladder_graph(5)),
+            (2, 4, nx.cubical_graph()),
+            (4, 2, nx.cubical_graph()),
+        ]:
+            G = nx.grid_2d_graph(m, n, periodic=True)
+            assert nx.could_be_isomorphic(G, H)
+
+    def test_periodic_iterable(self):
+        m, n = 3, 7
+        for a, b in product([0, 1], [0, 1]):
+            G = nx.grid_2d_graph(m, n, periodic=(a, b))
+            assert G.number_of_nodes() == m * n
+            assert G.number_of_edges() == (m + a - 1) * n + (n + b - 1) * m
+
+    def test_periodic_directed(self):
+        G = nx.grid_2d_graph(4, 2, periodic=True)
+        H = nx.grid_2d_graph(4, 2, periodic=True, create_using=nx.DiGraph())
+        assert H.succ == G.adj
+        assert H.pred == G.adj
+
+    def test_periodic_multigraph(self):
+        G = nx.grid_2d_graph(4, 2, periodic=True)
+        H = nx.grid_2d_graph(4, 2, periodic=True, create_using=nx.MultiGraph())
+        assert list(G.edges()) == list(H.edges())
+
+    def test_exceptions(self):
+        pytest.raises(nx.NetworkXError, nx.grid_2d_graph, -3, 2)
+        pytest.raises(nx.NetworkXError, nx.grid_2d_graph, 3, -2)
+        pytest.raises(TypeError, nx.grid_2d_graph, 3.3, 2)
+        pytest.raises(TypeError, nx.grid_2d_graph, 3, 2.2)
+
+    def test_node_input(self):
+        G = nx.grid_2d_graph(4, 2, periodic=True)
+        H = nx.grid_2d_graph(range(4), range(2), periodic=True)
+        assert nx.is_isomorphic(H, G)
+        H = nx.grid_2d_graph("abcd", "ef", periodic=True)
+        assert nx.is_isomorphic(H, G)
+        G = nx.grid_2d_graph(5, 6)
+        H = nx.grid_2d_graph(range(5), range(6))
+        assert edges_equal(H, G)
+
+
+class TestGridGraph:
+    """Unit tests for :func:`networkx.generators.lattice.grid_graph`"""
+
+    def test_grid_graph(self):
+        """grid_graph([n,m]) is a connected simple graph with the
+        following properties:
+        number_of_nodes = n*m
+        degree_histogram = [0,0,4,2*(n+m)-8,(n-2)*(m-2)]
+        """
+        for n, m in [(3, 5), (5, 3), (4, 5), (5, 4)]:
+            dim = [n, m]
+            g = nx.grid_graph(dim)
+            assert len(g) == n * m
+            assert nx.degree_histogram(g) == [
+                0,
+                0,
+                4,
+                2 * (n + m) - 8,
+                (n - 2) * (m - 2),
+            ]
+
+        for n, m in [(1, 5), (5, 1)]:
+            dim = [n, m]
+            g = nx.grid_graph(dim)
+            assert len(g) == n * m
+            assert nx.is_isomorphic(g, nx.path_graph(5))
+
+    #        mg = nx.grid_graph([n,m], create_using=MultiGraph())
+    #        assert_equal(mg.edges(), g.edges())
+
+    def test_node_input(self):
+        G = nx.grid_graph([range(7, 9), range(3, 6)])
+        assert len(G) == 2 * 3
+        assert nx.is_isomorphic(G, nx.grid_graph([2, 3]))
+
+    def test_periodic_iterable(self):
+        m, n, k = 3, 7, 5
+        for a, b, c in product([0, 1], [0, 1], [0, 1]):
+            G = nx.grid_graph([m, n, k], periodic=(a, b, c))
+            num_e = (m + a - 1) * n * k + (n + b - 1) * m * k + (k + c - 1) * m * n
+            assert G.number_of_nodes() == m * n * k
+            assert G.number_of_edges() == num_e
+
+
+class TestHypercubeGraph:
+    """Unit tests for :func:`networkx.generators.lattice.hypercube_graph`"""
+
+    def test_special_cases(self):
+        for n, H in [
+            (0, nx.null_graph()),
+            (1, nx.path_graph(2)),
+            (2, nx.cycle_graph(4)),
+            (3, nx.cubical_graph()),
+        ]:
+            G = nx.hypercube_graph(n)
+            assert nx.could_be_isomorphic(G, H)
+
+    def test_degree_distribution(self):
+        for n in range(1, 10):
+            G = nx.hypercube_graph(n)
+            expected_histogram = [0] * n + [2**n]
+            assert nx.degree_histogram(G) == expected_histogram
+
+
+class TestTriangularLatticeGraph:
+    "Tests for :func:`networkx.generators.lattice.triangular_lattice_graph`"
+
+    def test_lattice_points(self):
+        """Tests that the graph is really a triangular lattice."""
+        for m, n in [(2, 3), (2, 2), (2, 1), (3, 3), (3, 2), (3, 4)]:
+            G = nx.triangular_lattice_graph(m, n)
+            N = (n + 1) // 2
+            assert len(G) == (m + 1) * (1 + N) - (n % 2) * ((m + 1) // 2)
+        for i, j in G.nodes():
+            nbrs = G[(i, j)]
+            if i < N:
+                assert (i + 1, j) in nbrs
+            if j < m:
+                assert (i, j + 1) in nbrs
+            if j < m and (i > 0 or j % 2) and (i < N or (j + 1) % 2):
+                assert (i + 1, j + 1) in nbrs or (i - 1, j + 1) in nbrs
+
+    def test_directed(self):
+        """Tests for creating a directed triangular lattice."""
+        G = nx.triangular_lattice_graph(3, 4, create_using=nx.Graph())
+        H = nx.triangular_lattice_graph(3, 4, create_using=nx.DiGraph())
+        assert H.is_directed()
+        for u, v in H.edges():
+            assert v[1] >= u[1]
+            if v[1] == u[1]:
+                assert v[0] > u[0]
+
+    def test_multigraph(self):
+        """Tests for creating a triangular lattice multigraph."""
+        G = nx.triangular_lattice_graph(3, 4, create_using=nx.Graph())
+        H = nx.triangular_lattice_graph(3, 4, create_using=nx.MultiGraph())
+        assert list(H.edges()) == list(G.edges())
+
+    def test_periodic(self):
+        G = nx.triangular_lattice_graph(4, 6, periodic=True)
+        assert len(G) == 12
+        assert G.size() == 36
+        # all degrees are 6
+        assert len([n for n, d in G.degree() if d != 6]) == 0
+        G = nx.triangular_lattice_graph(5, 7, periodic=True)
+        TLG = nx.triangular_lattice_graph
+        pytest.raises(nx.NetworkXError, TLG, 2, 4, periodic=True)
+        pytest.raises(nx.NetworkXError, TLG, 4, 4, periodic=True)
+        pytest.raises(nx.NetworkXError, TLG, 2, 6, periodic=True)
+
+
+class TestHexagonalLatticeGraph:
+    "Tests for :func:`networkx.generators.lattice.hexagonal_lattice_graph`"
+
+    def test_lattice_points(self):
+        """Tests that the graph is really a hexagonal lattice."""
+        for m, n in [(4, 5), (4, 4), (4, 3), (3, 2), (3, 3), (3, 5)]:
+            G = nx.hexagonal_lattice_graph(m, n)
+            assert len(G) == 2 * (m + 1) * (n + 1) - 2
+        C_6 = nx.cycle_graph(6)
+        hexagons = [
+            [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2)],
+            [(0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4)],
+            [(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3)],
+            [(2, 0), (2, 1), (2, 2), (3, 0), (3, 1), (3, 2)],
+            [(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)],
+        ]
+        for hexagon in hexagons:
+            assert nx.is_isomorphic(G.subgraph(hexagon), C_6)
+
+    def test_directed(self):
+        """Tests for creating a directed hexagonal lattice."""
+        G = nx.hexagonal_lattice_graph(3, 5, create_using=nx.Graph())
+        H = nx.hexagonal_lattice_graph(3, 5, create_using=nx.DiGraph())
+        assert H.is_directed()
+        pos = nx.get_node_attributes(H, "pos")
+        for u, v in H.edges():
+            assert pos[v][1] >= pos[u][1]
+            if pos[v][1] == pos[u][1]:
+                assert pos[v][0] > pos[u][0]
+
+    def test_multigraph(self):
+        """Tests for creating a hexagonal lattice multigraph."""
+        G = nx.hexagonal_lattice_graph(3, 5, create_using=nx.Graph())
+        H = nx.hexagonal_lattice_graph(3, 5, create_using=nx.MultiGraph())
+        assert list(H.edges()) == list(G.edges())
+
+    def test_periodic(self):
+        G = nx.hexagonal_lattice_graph(4, 6, periodic=True)
+        assert len(G) == 48
+        assert G.size() == 72
+        # all degrees are 3
+        assert len([n for n, d in G.degree() if d != 3]) == 0
+        G = nx.hexagonal_lattice_graph(5, 8, periodic=True)
+        HLG = nx.hexagonal_lattice_graph
+        pytest.raises(nx.NetworkXError, HLG, 2, 7, periodic=True)
+        pytest.raises(nx.NetworkXError, HLG, 1, 4, periodic=True)
+        pytest.raises(nx.NetworkXError, HLG, 2, 1, periodic=True)

janus/lib/python3.10/site-packages/networkx/generators/tests/test_spectral_graph_forge.py

@@ -0,0 +1,49 @@
+import pytest
+
+pytest.importorskip("numpy")
+pytest.importorskip("scipy")
+
+
+from networkx import is_isomorphic
+from networkx.exception import NetworkXError
+from networkx.generators import karate_club_graph
+from networkx.generators.spectral_graph_forge import spectral_graph_forge
+from networkx.utils import nodes_equal
+
+
+def test_spectral_graph_forge():
+    G = karate_club_graph()
+
+    seed = 54321
+
+    # common cases, just checking node number preserving and difference
+    # between identity and modularity cases
+    H = spectral_graph_forge(G, 0.1, transformation="identity", seed=seed)
+    assert nodes_equal(G, H)
+
+    I = spectral_graph_forge(G, 0.1, transformation="identity", seed=seed)
+    assert nodes_equal(G, H)
+    assert is_isomorphic(I, H)
+
+    I = spectral_graph_forge(G, 0.1, transformation="modularity", seed=seed)
+    assert nodes_equal(G, I)
+
+    assert not is_isomorphic(I, H)
+
+    # with all the eigenvectors, output graph is identical to the input one
+    H = spectral_graph_forge(G, 1, transformation="modularity", seed=seed)
+    assert nodes_equal(G, H)
+    assert is_isomorphic(G, H)
+
+    # invalid alpha input value, it is silently truncated in [0,1]
+    H = spectral_graph_forge(G, -1, transformation="identity", seed=seed)
+    assert nodes_equal(G, H)
+
+    H = spectral_graph_forge(G, 10, transformation="identity", seed=seed)
+    assert nodes_equal(G, H)
+    assert is_isomorphic(G, H)
+
+    # invalid transformation mode, checking the error raising
+    pytest.raises(
+        NetworkXError, spectral_graph_forge, G, 0.1, transformation="unknown", seed=seed
+    )

janus/lib/python3.10/site-packages/networkx/generators/tests/test_time_series.py

@@ -0,0 +1,64 @@
+"""Unit tests for the :mod:`networkx.generators.time_series` module."""
+
+import itertools
+
+import networkx as nx
+
+
+def test_visibility_graph__empty_series__empty_graph():
+    null_graph = nx.visibility_graph([])  # move along nothing to see here
+    assert nx.is_empty(null_graph)
+
+
+def test_visibility_graph__single_value_ts__single_node_graph():
+    node_graph = nx.visibility_graph([10])  # So Lonely
+    assert node_graph.number_of_nodes() == 1
+    assert node_graph.number_of_edges() == 0
+
+
+def test_visibility_graph__two_values_ts__single_edge_graph():
+    edge_graph = nx.visibility_graph([10, 20])  # Two of Us
+    assert list(edge_graph.edges) == [(0, 1)]
+
+
+def test_visibility_graph__convex_series__complete_graph():
+    series = [i**2 for i in range(10)]  # no obstructions
+    expected_series_length = len(series)
+
+    actual_graph = nx.visibility_graph(series)
+
+    assert actual_graph.number_of_nodes() == expected_series_length
+    assert actual_graph.number_of_edges() == 45
+    assert nx.is_isomorphic(actual_graph, nx.complete_graph(expected_series_length))
+
+
+def test_visibility_graph__concave_series__path_graph():
+    series = [-(i**2) for i in range(10)]  # Slip Slidin' Away
+    expected_node_count = len(series)
+
+    actual_graph = nx.visibility_graph(series)
+
+    assert actual_graph.number_of_nodes() == expected_node_count
+    assert actual_graph.number_of_edges() == expected_node_count - 1
+    assert nx.is_isomorphic(actual_graph, nx.path_graph(expected_node_count))
+
+
+def test_visibility_graph__flat_series__path_graph():
+    series = [0] * 10  # living in 1D flatland
+    expected_node_count = len(series)
+
+    actual_graph = nx.visibility_graph(series)
+
+    assert actual_graph.number_of_nodes() == expected_node_count
+    assert actual_graph.number_of_edges() == expected_node_count - 1
+    assert nx.is_isomorphic(actual_graph, nx.path_graph(expected_node_count))
+
+
+def test_visibility_graph_cyclic_series():
+    series = list(itertools.islice(itertools.cycle((2, 1, 3)), 17))  # It's so bumpy!
+    expected_node_count = len(series)
+
+    actual_graph = nx.visibility_graph(series)
+
+    assert actual_graph.number_of_nodes() == expected_node_count
+    assert actual_graph.number_of_edges() == 25

janus/lib/python3.10/site-packages/networkx/linalg/__init__.py

@@ -0,0 +1,13 @@
+from networkx.linalg.attrmatrix import *
+from networkx.linalg import attrmatrix
+from networkx.linalg.spectrum import *
+from networkx.linalg import spectrum
+from networkx.linalg.graphmatrix import *
+from networkx.linalg import graphmatrix
+from networkx.linalg.laplacianmatrix import *
+from networkx.linalg import laplacianmatrix
+from networkx.linalg.algebraicconnectivity import *
+from networkx.linalg.modularitymatrix import *
+from networkx.linalg import modularitymatrix
+from networkx.linalg.bethehessianmatrix import *
+from networkx.linalg import bethehessianmatrix

janus/lib/python3.10/site-packages/networkx/linalg/algebraicconnectivity.py

@@ -0,0 +1,657 @@
+"""
+Algebraic connectivity and Fiedler vectors of undirected graphs.
+"""
+
+from functools import partial
+
+import networkx as nx
+from networkx.utils import (
+    not_implemented_for,
+    np_random_state,
+    reverse_cuthill_mckee_ordering,
+)
+
+__all__ = [
+    "algebraic_connectivity",
+    "fiedler_vector",
+    "spectral_ordering",
+    "spectral_bisection",
+]
+
+
+class _PCGSolver:
+    """Preconditioned conjugate gradient method.
+
+    To solve Ax = b:
+        M = A.diagonal() # or some other preconditioner
+        solver = _PCGSolver(lambda x: A * x, lambda x: M * x)
+        x = solver.solve(b)
+
+    The inputs A and M are functions which compute
+    matrix multiplication on the argument.
+    A - multiply by the matrix A in Ax=b
+    M - multiply by M, the preconditioner surrogate for A
+
+    Warning: There is no limit on number of iterations.
+    """
+
+    def __init__(self, A, M):
+        self._A = A
+        self._M = M
+
+    def solve(self, B, tol):
+        import numpy as np
+
+        # Densifying step - can this be kept sparse?
+        B = np.asarray(B)
+        X = np.ndarray(B.shape, order="F")
+        for j in range(B.shape[1]):
+            X[:, j] = self._solve(B[:, j], tol)
+        return X
+
+    def _solve(self, b, tol):
+        import numpy as np
+        import scipy as sp
+
+        A = self._A
+        M = self._M
+        tol *= sp.linalg.blas.dasum(b)
+        # Initialize.
+        x = np.zeros(b.shape)
+        r = b.copy()
+        z = M(r)
+        rz = sp.linalg.blas.ddot(r, z)
+        p = z.copy()
+        # Iterate.
+        while True:
+            Ap = A(p)
+            alpha = rz / sp.linalg.blas.ddot(p, Ap)
+            x = sp.linalg.blas.daxpy(p, x, a=alpha)
+            r = sp.linalg.blas.daxpy(Ap, r, a=-alpha)
+            if sp.linalg.blas.dasum(r) < tol:
+                return x
+            z = M(r)
+            beta = sp.linalg.blas.ddot(r, z)
+            beta, rz = beta / rz, beta
+            p = sp.linalg.blas.daxpy(p, z, a=beta)
+
+
+class _LUSolver:
+    """LU factorization.
+
+    To solve Ax = b:
+        solver = _LUSolver(A)
+        x = solver.solve(b)
+
+    optional argument `tol` on solve method is ignored but included
+    to match _PCGsolver API.
+    """
+
+    def __init__(self, A):
+        import scipy as sp
+
+        self._LU = sp.sparse.linalg.splu(
+            A,
+            permc_spec="MMD_AT_PLUS_A",
+            diag_pivot_thresh=0.0,
+            options={"Equil": True, "SymmetricMode": True},
+        )
+
+    def solve(self, B, tol=None):
+        import numpy as np
+
+        B = np.asarray(B)
+        X = np.ndarray(B.shape, order="F")
+        for j in range(B.shape[1]):
+            X[:, j] = self._LU.solve(B[:, j])
+        return X
+
+
+def _preprocess_graph(G, weight):
+    """Compute edge weights and eliminate zero-weight edges."""
+    if G.is_directed():
+        H = nx.MultiGraph()
+        H.add_nodes_from(G)
+        H.add_weighted_edges_from(
+            ((u, v, e.get(weight, 1.0)) for u, v, e in G.edges(data=True) if u != v),
+            weight=weight,
+        )
+        G = H
+    if not G.is_multigraph():
+        edges = (
+            (u, v, abs(e.get(weight, 1.0))) for u, v, e in G.edges(data=True) if u != v
+        )
+    else:
+        edges = (
+            (u, v, sum(abs(e.get(weight, 1.0)) for e in G[u][v].values()))
+            for u, v in G.edges()
+            if u != v
+        )
+    H = nx.Graph()
+    H.add_nodes_from(G)
+    H.add_weighted_edges_from((u, v, e) for u, v, e in edges if e != 0)
+    return H
+
+
+def _rcm_estimate(G, nodelist):
+    """Estimate the Fiedler vector using the reverse Cuthill-McKee ordering."""
+    import numpy as np
+
+    G = G.subgraph(nodelist)
+    order = reverse_cuthill_mckee_ordering(G)
+    n = len(nodelist)
+    index = dict(zip(nodelist, range(n)))
+    x = np.ndarray(n, dtype=float)
+    for i, u in enumerate(order):
+        x[index[u]] = i
+    x -= (n - 1) / 2.0
+    return x
+
+
+def _tracemin_fiedler(L, X, normalized, tol, method):
+    """Compute the Fiedler vector of L using the TraceMIN-Fiedler algorithm.
+
+    The Fiedler vector of a connected undirected graph is the eigenvector
+    corresponding to the second smallest eigenvalue of the Laplacian matrix
+    of the graph. This function starts with the Laplacian L, not the Graph.
+
+    Parameters
+    ----------
+    L : Laplacian of a possibly weighted or normalized, but undirected graph
+
+    X : Initial guess for a solution. Usually a matrix of random numbers.
+        This function allows more than one column in X to identify more than
+        one eigenvector if desired.
+
+    normalized : bool
+        Whether the normalized Laplacian matrix is used.
+
+    tol : float
+        Tolerance of relative residual in eigenvalue computation.
+        Warning: There is no limit on number of iterations.
+
+    method : string
+        Should be 'tracemin_pcg' or 'tracemin_lu'.
+        Otherwise exception is raised.
+
+    Returns
+    -------
+    sigma, X : Two NumPy arrays of floats.
+        The lowest eigenvalues and corresponding eigenvectors of L.
+        The size of input X determines the size of these outputs.
+        As this is for Fiedler vectors, the zero eigenvalue (and
+        constant eigenvector) are avoided.
+    """
+    import numpy as np
+    import scipy as sp
+
+    n = X.shape[0]
+
+    if normalized:
+        # Form the normalized Laplacian matrix and determine the eigenvector of
+        # its nullspace.
+        e = np.sqrt(L.diagonal())
+        # TODO: rm csr_array wrapper when spdiags array creation becomes available
+        D = sp.sparse.csr_array(sp.sparse.spdiags(1 / e, 0, n, n, format="csr"))
+        L = D @ L @ D
+        e *= 1.0 / np.linalg.norm(e, 2)
+
+    if normalized:
+
+        def project(X):
+            """Make X orthogonal to the nullspace of L."""
+            X = np.asarray(X)
+            for j in range(X.shape[1]):
+                X[:, j] -= (X[:, j] @ e) * e
+
+    else:
+
+        def project(X):
+            """Make X orthogonal to the nullspace of L."""
+            X = np.asarray(X)
+            for j in range(X.shape[1]):
+                X[:, j] -= X[:, j].sum() / n
+
+    if method == "tracemin_pcg":
+        D = L.diagonal().astype(float)
+        solver = _PCGSolver(lambda x: L @ x, lambda x: D * x)
+    elif method == "tracemin_lu":
+        # Convert A to CSC to suppress SparseEfficiencyWarning.
+        A = sp.sparse.csc_array(L, dtype=float, copy=True)
+        # Force A to be nonsingular. Since A is the Laplacian matrix of a
+        # connected graph, its rank deficiency is one, and thus one diagonal
+        # element needs to modified. Changing to infinity forces a zero in the
+        # corresponding element in the solution.
+        i = (A.indptr[1:] - A.indptr[:-1]).argmax()
+        A[i, i] = np.inf
+        solver = _LUSolver(A)
+    else:
+        raise nx.NetworkXError(f"Unknown linear system solver: {method}")
+
+    # Initialize.
+    Lnorm = abs(L).sum(axis=1).flatten().max()
+    project(X)
+    W = np.ndarray(X.shape, order="F")
+
+    while True:
+        # Orthonormalize X.
+        X = np.linalg.qr(X)[0]
+        # Compute iteration matrix H.
+        W[:, :] = L @ X
+        H = X.T @ W
+        sigma, Y = sp.linalg.eigh(H, overwrite_a=True)
+        # Compute the Ritz vectors.
+        X = X @ Y
+        # Test for convergence exploiting the fact that L * X == W * Y.
+        res = sp.linalg.blas.dasum(W @ Y[:, 0] - sigma[0] * X[:, 0]) / Lnorm
+        if res < tol:
+            break
+        # Compute X = L \ X / (X' * (L \ X)).
+        # L \ X can have an arbitrary projection on the nullspace of L,
+        # which will be eliminated.
+        W[:, :] = solver.solve(X, tol)
+        X = (sp.linalg.inv(W.T @ X) @ W.T).T  # Preserves Fortran storage order.
+        project(X)
+
+    return sigma, np.asarray(X)
+
+
+def _get_fiedler_func(method):
+    """Returns a function that solves the Fiedler eigenvalue problem."""
+    import numpy as np
+
+    if method == "tracemin":  # old style keyword <v2.1
+        method = "tracemin_pcg"
+    if method in ("tracemin_pcg", "tracemin_lu"):
+
+        def find_fiedler(L, x, normalized, tol, seed):
+            q = 1 if method == "tracemin_pcg" else min(4, L.shape[0] - 1)
+            X = np.asarray(seed.normal(size=(q, L.shape[0]))).T
+            sigma, X = _tracemin_fiedler(L, X, normalized, tol, method)
+            return sigma[0], X[:, 0]
+
+    elif method == "lanczos" or method == "lobpcg":
+
+        def find_fiedler(L, x, normalized, tol, seed):
+            import scipy as sp
+
+            L = sp.sparse.csc_array(L, dtype=float)
+            n = L.shape[0]
+            if normalized:
+                # TODO: rm csc_array wrapping when spdiags array becomes available
+                D = sp.sparse.csc_array(
+                    sp.sparse.spdiags(
+                        1.0 / np.sqrt(L.diagonal()), [0], n, n, format="csc"
+                    )
+                )
+                L = D @ L @ D
+            if method == "lanczos" or n < 10:
+                # Avoid LOBPCG when n < 10 due to
+                # https://github.com/scipy/scipy/issues/3592
+                # https://github.com/scipy/scipy/pull/3594
+                sigma, X = sp.sparse.linalg.eigsh(
+                    L, 2, which="SM", tol=tol, return_eigenvectors=True
+                )
+                return sigma[1], X[:, 1]
+            else:
+                X = np.asarray(np.atleast_2d(x).T)
+                # TODO: rm csr_array wrapping when spdiags array becomes available
+                M = sp.sparse.csr_array(sp.sparse.spdiags(1.0 / L.diagonal(), 0, n, n))
+                Y = np.ones(n)
+                if normalized:
+                    Y /= D.diagonal()
+                sigma, X = sp.sparse.linalg.lobpcg(
+                    L, X, M=M, Y=np.atleast_2d(Y).T, tol=tol, maxiter=n, largest=False
+                )
+                return sigma[0], X[:, 0]
+
+    else:
+        raise nx.NetworkXError(f"unknown method {method!r}.")
+
+    return find_fiedler
+
+
+@not_implemented_for("directed")
+@np_random_state(5)
+@nx._dispatchable(edge_attrs="weight")
+def algebraic_connectivity(
+    G, weight="weight", normalized=False, tol=1e-8, method="tracemin_pcg", seed=None
+):
+    r"""Returns the algebraic connectivity of an undirected graph.
+
+    The algebraic connectivity of a connected undirected graph is the second
+    smallest eigenvalue of its Laplacian matrix.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        An undirected graph.
+
+    weight : object, optional (default: None)
+        The data key used to determine the weight of each edge. If None, then
+        each edge has unit weight.
+
+    normalized : bool, optional (default: False)
+        Whether the normalized Laplacian matrix is used.
+
+    tol : float, optional (default: 1e-8)
+        Tolerance of relative residual in eigenvalue computation.
+
+    method : string, optional (default: 'tracemin_pcg')
+        Method of eigenvalue computation. It must be one of the tracemin
+        options shown below (TraceMIN), 'lanczos' (Lanczos iteration)
+        or 'lobpcg' (LOBPCG).
+
+        The TraceMIN algorithm uses a linear system solver. The following
+        values allow specifying the solver to be used.
+
+        =============== ========================================
+        Value           Solver
+        =============== ========================================
+        'tracemin_pcg'  Preconditioned conjugate gradient method
+        'tracemin_lu'   LU factorization
+        =============== ========================================
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    algebraic_connectivity : float
+        Algebraic connectivity.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    NetworkXError
+        If G has less than two nodes.
+
+    Notes
+    -----
+    Edge weights are interpreted by their absolute values. For MultiGraph's,
+    weights of parallel edges are summed. Zero-weighted edges are ignored.
+
+    See Also
+    --------
+    laplacian_matrix
+
+    Examples
+    --------
+    For undirected graphs algebraic connectivity can tell us if a graph is connected or not
+    `G` is connected iff  ``algebraic_connectivity(G) > 0``:
+
+    >>> G = nx.complete_graph(5)
+    >>> nx.algebraic_connectivity(G) > 0
+    True
+    >>> G.add_node(10)  # G is no longer connected
+    >>> nx.algebraic_connectivity(G) > 0
+    False
+
+    """
+    if len(G) < 2:
+        raise nx.NetworkXError("graph has less than two nodes.")
+    G = _preprocess_graph(G, weight)
+    if not nx.is_connected(G):
+        return 0.0
+
+    L = nx.laplacian_matrix(G)
+    if L.shape[0] == 2:
+        return 2.0 * float(L[0, 0]) if not normalized else 2.0
+
+    find_fiedler = _get_fiedler_func(method)
+    x = None if method != "lobpcg" else _rcm_estimate(G, G)
+    sigma, fiedler = find_fiedler(L, x, normalized, tol, seed)
+    return float(sigma)
+
+
+@not_implemented_for("directed")
+@np_random_state(5)
+@nx._dispatchable(edge_attrs="weight")
+def fiedler_vector(
+    G, weight="weight", normalized=False, tol=1e-8, method="tracemin_pcg", seed=None
+):
+    """Returns the Fiedler vector of a connected undirected graph.
+
+    The Fiedler vector of a connected undirected graph is the eigenvector
+    corresponding to the second smallest eigenvalue of the Laplacian matrix
+    of the graph.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        An undirected graph.
+
+    weight : object, optional (default: None)
+        The data key used to determine the weight of each edge. If None, then
+        each edge has unit weight.
+
+    normalized : bool, optional (default: False)
+        Whether the normalized Laplacian matrix is used.
+
+    tol : float, optional (default: 1e-8)
+        Tolerance of relative residual in eigenvalue computation.
+
+    method : string, optional (default: 'tracemin_pcg')
+        Method of eigenvalue computation. It must be one of the tracemin
+        options shown below (TraceMIN), 'lanczos' (Lanczos iteration)
+        or 'lobpcg' (LOBPCG).
+
+        The TraceMIN algorithm uses a linear system solver. The following
+        values allow specifying the solver to be used.
+
+        =============== ========================================
+        Value           Solver
+        =============== ========================================
+        'tracemin_pcg'  Preconditioned conjugate gradient method
+        'tracemin_lu'   LU factorization
+        =============== ========================================
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    fiedler_vector : NumPy array of floats.
+        Fiedler vector.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    NetworkXError
+        If G has less than two nodes or is not connected.
+
+    Notes
+    -----
+    Edge weights are interpreted by their absolute values. For MultiGraph's,
+    weights of parallel edges are summed. Zero-weighted edges are ignored.
+
+    See Also
+    --------
+    laplacian_matrix
+
+    Examples
+    --------
+    Given a connected graph the signs of the values in the Fiedler vector can be
+    used to partition the graph into two components.
+
+    >>> G = nx.barbell_graph(5, 0)
+    >>> nx.fiedler_vector(G, normalized=True, seed=1)
+    array([-0.32864129, -0.32864129, -0.32864129, -0.32864129, -0.26072899,
+            0.26072899,  0.32864129,  0.32864129,  0.32864129,  0.32864129])
+
+    The connected components are the two 5-node cliques of the barbell graph.
+    """
+    import numpy as np
+
+    if len(G) < 2:
+        raise nx.NetworkXError("graph has less than two nodes.")
+    G = _preprocess_graph(G, weight)
+    if not nx.is_connected(G):
+        raise nx.NetworkXError("graph is not connected.")
+
+    if len(G) == 2:
+        return np.array([1.0, -1.0])
+
+    find_fiedler = _get_fiedler_func(method)
+    L = nx.laplacian_matrix(G)
+    x = None if method != "lobpcg" else _rcm_estimate(G, G)
+    sigma, fiedler = find_fiedler(L, x, normalized, tol, seed)
+    return fiedler
+
+
+@np_random_state(5)
+@nx._dispatchable(edge_attrs="weight")
+def spectral_ordering(
+    G, weight="weight", normalized=False, tol=1e-8, method="tracemin_pcg", seed=None
+):
+    """Compute the spectral_ordering of a graph.
+
+    The spectral ordering of a graph is an ordering of its nodes where nodes
+    in the same weakly connected components appear contiguous and ordered by
+    their corresponding elements in the Fiedler vector of the component.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        A graph.
+
+    weight : object, optional (default: None)
+        The data key used to determine the weight of each edge. If None, then
+        each edge has unit weight.
+
+    normalized : bool, optional (default: False)
+        Whether the normalized Laplacian matrix is used.
+
+    tol : float, optional (default: 1e-8)
+        Tolerance of relative residual in eigenvalue computation.
+
+    method : string, optional (default: 'tracemin_pcg')
+        Method of eigenvalue computation. It must be one of the tracemin
+        options shown below (TraceMIN), 'lanczos' (Lanczos iteration)
+        or 'lobpcg' (LOBPCG).
+
+        The TraceMIN algorithm uses a linear system solver. The following
+        values allow specifying the solver to be used.
+
+        =============== ========================================
+        Value           Solver
+        =============== ========================================
+        'tracemin_pcg'  Preconditioned conjugate gradient method
+        'tracemin_lu'   LU factorization
+        =============== ========================================
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    spectral_ordering : NumPy array of floats.
+        Spectral ordering of nodes.
+
+    Raises
+    ------
+    NetworkXError
+        If G is empty.
+
+    Notes
+    -----
+    Edge weights are interpreted by their absolute values. For MultiGraph's,
+    weights of parallel edges are summed. Zero-weighted edges are ignored.
+
+    See Also
+    --------
+    laplacian_matrix
+    """
+    if len(G) == 0:
+        raise nx.NetworkXError("graph is empty.")
+    G = _preprocess_graph(G, weight)
+
+    find_fiedler = _get_fiedler_func(method)
+    order = []
+    for component in nx.connected_components(G):
+        size = len(component)
+        if size > 2:
+            L = nx.laplacian_matrix(G, component)
+            x = None if method != "lobpcg" else _rcm_estimate(G, component)
+            sigma, fiedler = find_fiedler(L, x, normalized, tol, seed)
+            sort_info = zip(fiedler, range(size), component)
+            order.extend(u for x, c, u in sorted(sort_info))
+        else:
+            order.extend(component)
+
+    return order
+
+
+@nx._dispatchable(edge_attrs="weight")
+def spectral_bisection(
+    G, weight="weight", normalized=False, tol=1e-8, method="tracemin_pcg", seed=None
+):
+    """Bisect the graph using the Fiedler vector.
+
+    This method uses the Fiedler vector to bisect a graph.
+    The partition is defined by the nodes which are associated with
+    either positive or negative values in the vector.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+
+    weight : str, optional (default: weight)
+        The data key used to determine the weight of each edge. If None, then
+        each edge has unit weight.
+
+    normalized : bool, optional (default: False)
+        Whether the normalized Laplacian matrix is used.
+
+    tol : float, optional (default: 1e-8)
+        Tolerance of relative residual in eigenvalue computation.
+
+    method : string, optional (default: 'tracemin_pcg')
+        Method of eigenvalue computation. It must be one of the tracemin
+        options shown below (TraceMIN), 'lanczos' (Lanczos iteration)
+        or 'lobpcg' (LOBPCG).
+
+        The TraceMIN algorithm uses a linear system solver. The following
+        values allow specifying the solver to be used.
+
+        =============== ========================================
+        Value           Solver
+        =============== ========================================
+        'tracemin_pcg'  Preconditioned conjugate gradient method
+        'tracemin_lu'   LU factorization
+        =============== ========================================
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    bisection : tuple of sets
+        Sets with the bisection of nodes
+
+    Examples
+    --------
+    >>> G = nx.barbell_graph(3, 0)
+    >>> nx.spectral_bisection(G)
+    ({0, 1, 2}, {3, 4, 5})
+
+    References
+    ----------
+    .. [1] M. E. J Newman 'Networks: An Introduction', pages 364-370
+       Oxford University Press 2011.
+    """
+    import numpy as np
+
+    v = nx.fiedler_vector(G, weight, normalized, tol, method, seed)
+    nodes = np.array(list(G))
+    pos_vals = v >= 0
+
+    return set(nodes[~pos_vals].tolist()), set(nodes[pos_vals].tolist())

janus/lib/python3.10/site-packages/networkx/linalg/attrmatrix.py

@@ -0,0 +1,465 @@
+"""
+Functions for constructing matrix-like objects from graph attributes.
+"""
+
+import networkx as nx
+
+__all__ = ["attr_matrix", "attr_sparse_matrix"]
+
+
+def _node_value(G, node_attr):
+    """Returns a function that returns a value from G.nodes[u].
+
+    We return a function expecting a node as its sole argument. Then, in the
+    simplest scenario, the returned function will return G.nodes[u][node_attr].
+    However, we also handle the case when `node_attr` is None or when it is a
+    function itself.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph
+
+    node_attr : {None, str, callable}
+        Specification of how the value of the node attribute should be obtained
+        from the node attribute dictionary.
+
+    Returns
+    -------
+    value : function
+        A function expecting a node as its sole argument. The function will
+        returns a value from G.nodes[u] that depends on `edge_attr`.
+
+    """
+    if node_attr is None:
+
+        def value(u):
+            return u
+
+    elif not callable(node_attr):
+        # assume it is a key for the node attribute dictionary
+        def value(u):
+            return G.nodes[u][node_attr]
+
+    else:
+        # Advanced:  Allow users to specify something else.
+        #
+        # For example,
+        #     node_attr = lambda u: G.nodes[u].get('size', .5) * 3
+        #
+        value = node_attr
+
+    return value
+
+
+def _edge_value(G, edge_attr):
+    """Returns a function that returns a value from G[u][v].
+
+    Suppose there exists an edge between u and v.  Then we return a function
+    expecting u and v as arguments.  For Graph and DiGraph, G[u][v] is
+    the edge attribute dictionary, and the function (essentially) returns
+    G[u][v][edge_attr].  However, we also handle cases when `edge_attr` is None
+    and when it is a function itself. For MultiGraph and MultiDiGraph, G[u][v]
+    is a dictionary of all edges between u and v.  In this case, the returned
+    function sums the value of `edge_attr` for every edge between u and v.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    edge_attr : {None, str, callable}
+        Specification of how the value of the edge attribute should be obtained
+        from the edge attribute dictionary, G[u][v].  For multigraphs, G[u][v]
+        is a dictionary of all the edges between u and v.  This allows for
+        special treatment of multiedges.
+
+    Returns
+    -------
+    value : function
+        A function expecting two nodes as parameters. The nodes should
+        represent the from- and to- node of an edge. The function will
+        return a value from G[u][v] that depends on `edge_attr`.
+
+    """
+
+    if edge_attr is None:
+        # topological count of edges
+
+        if G.is_multigraph():
+
+            def value(u, v):
+                return len(G[u][v])
+
+        else:
+
+            def value(u, v):
+                return 1
+
+    elif not callable(edge_attr):
+        # assume it is a key for the edge attribute dictionary
+
+        if edge_attr == "weight":
+            # provide a default value
+            if G.is_multigraph():
+
+                def value(u, v):
+                    return sum(d.get(edge_attr, 1) for d in G[u][v].values())
+
+            else:
+
+                def value(u, v):
+                    return G[u][v].get(edge_attr, 1)
+
+        else:
+            # otherwise, the edge attribute MUST exist for each edge
+            if G.is_multigraph():
+
+                def value(u, v):
+                    return sum(d[edge_attr] for d in G[u][v].values())
+
+            else:
+
+                def value(u, v):
+                    return G[u][v][edge_attr]
+
+    else:
+        # Advanced:  Allow users to specify something else.
+        #
+        # Alternative default value:
+        #     edge_attr = lambda u,v: G[u][v].get('thickness', .5)
+        #
+        # Function on an attribute:
+        #     edge_attr = lambda u,v: abs(G[u][v]['weight'])
+        #
+        # Handle Multi(Di)Graphs differently:
+        #     edge_attr = lambda u,v: numpy.prod([d['size'] for d in G[u][v].values()])
+        #
+        # Ignore multiple edges
+        #     edge_attr = lambda u,v: 1 if len(G[u][v]) else 0
+        #
+        value = edge_attr
+
+    return value
+
+
+@nx._dispatchable(edge_attrs={"edge_attr": None}, node_attrs="node_attr")
+def attr_matrix(
+    G,
+    edge_attr=None,
+    node_attr=None,
+    normalized=False,
+    rc_order=None,
+    dtype=None,
+    order=None,
+):
+    """Returns the attribute matrix using attributes from `G` as a numpy array.
+
+    If only `G` is passed in, then the adjacency matrix is constructed.
+
+    Let A be a discrete set of values for the node attribute `node_attr`. Then
+    the elements of A represent the rows and columns of the constructed matrix.
+    Now, iterate through every edge e=(u,v) in `G` and consider the value
+    of the edge attribute `edge_attr`.  If ua and va are the values of the
+    node attribute `node_attr` for u and v, respectively, then the value of
+    the edge attribute is added to the matrix element at (ua, va).
+
+    Parameters
+    ----------
+    G : graph
+        The NetworkX graph used to construct the attribute matrix.
+
+    edge_attr : str, optional
+        Each element of the matrix represents a running total of the
+        specified edge attribute for edges whose node attributes correspond
+        to the rows/cols of the matrix. The attribute must be present for
+        all edges in the graph. If no attribute is specified, then we
+        just count the number of edges whose node attributes correspond
+        to the matrix element.
+
+    node_attr : str, optional
+        Each row and column in the matrix represents a particular value
+        of the node attribute.  The attribute must be present for all nodes
+        in the graph. Note, the values of this attribute should be reliably
+        hashable. So, float values are not recommended. If no attribute is
+        specified, then the rows and columns will be the nodes of the graph.
+
+    normalized : bool, optional
+        If True, then each row is normalized by the summation of its values.
+
+    rc_order : list, optional
+        A list of the node attribute values. This list specifies the ordering
+        of rows and columns of the array. If no ordering is provided, then
+        the ordering will be random (and also, a return value).
+
+    Other Parameters
+    ----------------
+    dtype : NumPy data-type, optional
+        A valid NumPy dtype used to initialize the array. Keep in mind certain
+        dtypes can yield unexpected results if the array is to be normalized.
+        The parameter is passed to numpy.zeros(). If unspecified, the NumPy
+        default is used.
+
+    order : {'C', 'F'}, optional
+        Whether to store multidimensional data in C- or Fortran-contiguous
+        (row- or column-wise) order in memory. This parameter is passed to
+        numpy.zeros(). If unspecified, the NumPy default is used.
+
+    Returns
+    -------
+    M : 2D NumPy ndarray
+        The attribute matrix.
+
+    ordering : list
+        If `rc_order` was specified, then only the attribute matrix is returned.
+        However, if `rc_order` was None, then the ordering used to construct
+        the matrix is returned as well.
+
+    Examples
+    --------
+    Construct an adjacency matrix:
+
+    >>> G = nx.Graph()
+    >>> G.add_edge(0, 1, thickness=1, weight=3)
+    >>> G.add_edge(0, 2, thickness=2)
+    >>> G.add_edge(1, 2, thickness=3)
+    >>> nx.attr_matrix(G, rc_order=[0, 1, 2])
+    array([[0., 1., 1.],
+           [1., 0., 1.],
+           [1., 1., 0.]])
+
+    Alternatively, we can obtain the matrix describing edge thickness.
+
+    >>> nx.attr_matrix(G, edge_attr="thickness", rc_order=[0, 1, 2])
+    array([[0., 1., 2.],
+           [1., 0., 3.],
+           [2., 3., 0.]])
+
+    We can also color the nodes and ask for the probability distribution over
+    all edges (u,v) describing:
+
+        Pr(v has color Y | u has color X)
+
+    >>> G.nodes[0]["color"] = "red"
+    >>> G.nodes[1]["color"] = "red"
+    >>> G.nodes[2]["color"] = "blue"
+    >>> rc = ["red", "blue"]
+    >>> nx.attr_matrix(G, node_attr="color", normalized=True, rc_order=rc)
+    array([[0.33333333, 0.66666667],
+           [1.        , 0.        ]])
+
+    For example, the above tells us that for all edges (u,v):
+
+        Pr( v is red  | u is red)  = 1/3
+        Pr( v is blue | u is red)  = 2/3
+
+        Pr( v is red  | u is blue) = 1
+        Pr( v is blue | u is blue) = 0
+
+    Finally, we can obtain the total weights listed by the node colors.
+
+    >>> nx.attr_matrix(G, edge_attr="weight", node_attr="color", rc_order=rc)
+    array([[3., 2.],
+           [2., 0.]])
+
+    Thus, the total weight over all edges (u,v) with u and v having colors:
+
+        (red, red)   is 3   # the sole contribution is from edge (0,1)
+        (red, blue)  is 2   # contributions from edges (0,2) and (1,2)
+        (blue, red)  is 2   # same as (red, blue) since graph is undirected
+        (blue, blue) is 0   # there are no edges with blue endpoints
+
+    """
+    import numpy as np
+
+    edge_value = _edge_value(G, edge_attr)
+    node_value = _node_value(G, node_attr)
+
+    if rc_order is None:
+        ordering = list({node_value(n) for n in G})
+    else:
+        ordering = rc_order
+
+    N = len(ordering)
+    undirected = not G.is_directed()
+    index = dict(zip(ordering, range(N)))
+    M = np.zeros((N, N), dtype=dtype, order=order)
+
+    seen = set()
+    for u, nbrdict in G.adjacency():
+        for v in nbrdict:
+            # Obtain the node attribute values.
+            i, j = index[node_value(u)], index[node_value(v)]
+            if v not in seen:
+                M[i, j] += edge_value(u, v)
+                if undirected:
+                    M[j, i] = M[i, j]
+
+        if undirected:
+            seen.add(u)
+
+    if normalized:
+        M /= M.sum(axis=1).reshape((N, 1))
+
+    if rc_order is None:
+        return M, ordering
+    else:
+        return M
+
+
+@nx._dispatchable(edge_attrs={"edge_attr": None}, node_attrs="node_attr")
+def attr_sparse_matrix(
+    G, edge_attr=None, node_attr=None, normalized=False, rc_order=None, dtype=None
+):
+    """Returns a SciPy sparse array using attributes from G.
+
+    If only `G` is passed in, then the adjacency matrix is constructed.
+
+    Let A be a discrete set of values for the node attribute `node_attr`. Then
+    the elements of A represent the rows and columns of the constructed matrix.
+    Now, iterate through every edge e=(u,v) in `G` and consider the value
+    of the edge attribute `edge_attr`.  If ua and va are the values of the
+    node attribute `node_attr` for u and v, respectively, then the value of
+    the edge attribute is added to the matrix element at (ua, va).
+
+    Parameters
+    ----------
+    G : graph
+        The NetworkX graph used to construct the NumPy matrix.
+
+    edge_attr : str, optional
+        Each element of the matrix represents a running total of the
+        specified edge attribute for edges whose node attributes correspond
+        to the rows/cols of the matrix. The attribute must be present for
+        all edges in the graph. If no attribute is specified, then we
+        just count the number of edges whose node attributes correspond
+        to the matrix element.
+
+    node_attr : str, optional
+        Each row and column in the matrix represents a particular value
+        of the node attribute.  The attribute must be present for all nodes
+        in the graph. Note, the values of this attribute should be reliably
+        hashable. So, float values are not recommended. If no attribute is
+        specified, then the rows and columns will be the nodes of the graph.
+
+    normalized : bool, optional
+        If True, then each row is normalized by the summation of its values.
+
+    rc_order : list, optional
+        A list of the node attribute values. This list specifies the ordering
+        of rows and columns of the array. If no ordering is provided, then
+        the ordering will be random (and also, a return value).
+
+    Other Parameters
+    ----------------
+    dtype : NumPy data-type, optional
+        A valid NumPy dtype used to initialize the array. Keep in mind certain
+        dtypes can yield unexpected results if the array is to be normalized.
+        The parameter is passed to numpy.zeros(). If unspecified, the NumPy
+        default is used.
+
+    Returns
+    -------
+    M : SciPy sparse array
+        The attribute matrix.
+
+    ordering : list
+        If `rc_order` was specified, then only the matrix is returned.
+        However, if `rc_order` was None, then the ordering used to construct
+        the matrix is returned as well.
+
+    Examples
+    --------
+    Construct an adjacency matrix:
+
+    >>> G = nx.Graph()
+    >>> G.add_edge(0, 1, thickness=1, weight=3)
+    >>> G.add_edge(0, 2, thickness=2)
+    >>> G.add_edge(1, 2, thickness=3)
+    >>> M = nx.attr_sparse_matrix(G, rc_order=[0, 1, 2])
+    >>> M.toarray()
+    array([[0., 1., 1.],
+           [1., 0., 1.],
+           [1., 1., 0.]])
+
+    Alternatively, we can obtain the matrix describing edge thickness.
+
+    >>> M = nx.attr_sparse_matrix(G, edge_attr="thickness", rc_order=[0, 1, 2])
+    >>> M.toarray()
+    array([[0., 1., 2.],
+           [1., 0., 3.],
+           [2., 3., 0.]])
+
+    We can also color the nodes and ask for the probability distribution over
+    all edges (u,v) describing:
+
+        Pr(v has color Y | u has color X)
+
+    >>> G.nodes[0]["color"] = "red"
+    >>> G.nodes[1]["color"] = "red"
+    >>> G.nodes[2]["color"] = "blue"
+    >>> rc = ["red", "blue"]
+    >>> M = nx.attr_sparse_matrix(G, node_attr="color", normalized=True, rc_order=rc)
+    >>> M.toarray()
+    array([[0.33333333, 0.66666667],
+           [1.        , 0.        ]])
+
+    For example, the above tells us that for all edges (u,v):
+
+        Pr( v is red  | u is red)  = 1/3
+        Pr( v is blue | u is red)  = 2/3
+
+        Pr( v is red  | u is blue) = 1
+        Pr( v is blue | u is blue) = 0
+
+    Finally, we can obtain the total weights listed by the node colors.
+
+    >>> M = nx.attr_sparse_matrix(G, edge_attr="weight", node_attr="color", rc_order=rc)
+    >>> M.toarray()
+    array([[3., 2.],
+           [2., 0.]])
+
+    Thus, the total weight over all edges (u,v) with u and v having colors:
+
+        (red, red)   is 3   # the sole contribution is from edge (0,1)
+        (red, blue)  is 2   # contributions from edges (0,2) and (1,2)
+        (blue, red)  is 2   # same as (red, blue) since graph is undirected
+        (blue, blue) is 0   # there are no edges with blue endpoints
+
+    """
+    import numpy as np
+    import scipy as sp
+
+    edge_value = _edge_value(G, edge_attr)
+    node_value = _node_value(G, node_attr)
+
+    if rc_order is None:
+        ordering = list({node_value(n) for n in G})
+    else:
+        ordering = rc_order
+
+    N = len(ordering)
+    undirected = not G.is_directed()
+    index = dict(zip(ordering, range(N)))
+    M = sp.sparse.lil_array((N, N), dtype=dtype)
+
+    seen = set()
+    for u, nbrdict in G.adjacency():
+        for v in nbrdict:
+            # Obtain the node attribute values.
+            i, j = index[node_value(u)], index[node_value(v)]
+            if v not in seen:
+                M[i, j] += edge_value(u, v)
+                if undirected:
+                    M[j, i] = M[i, j]
+
+        if undirected:
+            seen.add(u)
+
+    if normalized:
+        M *= 1 / M.sum(axis=1)[:, np.newaxis]  # in-place mult preserves sparse
+
+    if rc_order is None:
+        return M, ordering
+    else:
+        return M

janus/lib/python3.10/site-packages/networkx/linalg/bethehessianmatrix.py

@@ -0,0 +1,79 @@
+"""Bethe Hessian or deformed Laplacian matrix of graphs."""
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = ["bethe_hessian_matrix"]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def bethe_hessian_matrix(G, r=None, nodelist=None):
+    r"""Returns the Bethe Hessian matrix of G.
+
+    The Bethe Hessian is a family of matrices parametrized by r, defined as
+    H(r) = (r^2 - 1) I - r A + D where A is the adjacency matrix, D is the
+    diagonal matrix of node degrees, and I is the identify matrix. It is equal
+    to the graph laplacian when the regularizer r = 1.
+
+    The default choice of regularizer should be the ratio [2]_
+
+    .. math::
+      r_m = \left(\sum k_i \right)^{-1}\left(\sum k_i^2 \right) - 1
+
+    Parameters
+    ----------
+    G : Graph
+       A NetworkX graph
+    r : float
+       Regularizer parameter
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by ``G.nodes()``.
+
+    Returns
+    -------
+    H : scipy.sparse.csr_array
+      The Bethe Hessian matrix of `G`, with parameter `r`.
+
+    Examples
+    --------
+    >>> k = [3, 2, 2, 1, 0]
+    >>> G = nx.havel_hakimi_graph(k)
+    >>> H = nx.bethe_hessian_matrix(G)
+    >>> H.toarray()
+    array([[ 3.5625, -1.25  , -1.25  , -1.25  ,  0.    ],
+           [-1.25  ,  2.5625, -1.25  ,  0.    ,  0.    ],
+           [-1.25  , -1.25  ,  2.5625,  0.    ,  0.    ],
+           [-1.25  ,  0.    ,  0.    ,  1.5625,  0.    ],
+           [ 0.    ,  0.    ,  0.    ,  0.    ,  0.5625]])
+
+    See Also
+    --------
+    bethe_hessian_spectrum
+    adjacency_matrix
+    laplacian_matrix
+
+    References
+    ----------
+    .. [1] A. Saade, F. Krzakala and L. Zdeborová
+       "Spectral Clustering of Graphs with the Bethe Hessian",
+       Advances in Neural Information Processing Systems, 2014.
+    .. [2] C. M. Le, E. Levina
+       "Estimating the number of communities in networks by spectral methods"
+       arXiv:1507.00827, 2015.
+    """
+    import scipy as sp
+
+    if nodelist is None:
+        nodelist = list(G)
+    if r is None:
+        r = sum(d**2 for v, d in nx.degree(G)) / sum(d for v, d in nx.degree(G)) - 1
+    A = nx.to_scipy_sparse_array(G, nodelist=nodelist, format="csr")
+    n, m = A.shape
+    # TODO: Rm csr_array wrapper when spdiags array creation becomes available
+    D = sp.sparse.csr_array(sp.sparse.spdiags(A.sum(axis=1), 0, m, n, format="csr"))
+    # TODO: Rm csr_array wrapper when eye array creation becomes available
+    I = sp.sparse.csr_array(sp.sparse.eye(m, n, format="csr"))
+    return (r**2 - 1) * I - r * A + D

janus/lib/python3.10/site-packages/networkx/linalg/graphmatrix.py

@@ -0,0 +1,168 @@
+"""
+Adjacency matrix and incidence matrix of graphs.
+"""
+
+import networkx as nx
+
+__all__ = ["incidence_matrix", "adjacency_matrix"]
+
+
+@nx._dispatchable(edge_attrs="weight")
+def incidence_matrix(
+    G, nodelist=None, edgelist=None, oriented=False, weight=None, *, dtype=None
+):
+    """Returns incidence matrix of G.
+
+    The incidence matrix assigns each row to a node and each column to an edge.
+    For a standard incidence matrix a 1 appears wherever a row's node is
+    incident on the column's edge.  For an oriented incidence matrix each
+    edge is assigned an orientation (arbitrarily for undirected and aligning to
+    direction for directed).  A -1 appears for the source (tail) of an edge and
+    1 for the destination (head) of the edge.  The elements are zero otherwise.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    nodelist : list, optional   (default= all nodes in G)
+       The rows are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    edgelist : list, optional (default= all edges in G)
+       The columns are ordered according to the edges in edgelist.
+       If edgelist is None, then the ordering is produced by G.edges().
+
+    oriented: bool, optional (default=False)
+       If True, matrix elements are +1 or -1 for the head or tail node
+       respectively of each edge.  If False, +1 occurs at both nodes.
+
+    weight : string or None, optional (default=None)
+       The edge data key used to provide each value in the matrix.
+       If None, then each edge has weight 1.  Edge weights, if used,
+       should be positive so that the orientation can provide the sign.
+
+    dtype : a NumPy dtype or None (default=None)
+        The dtype of the output sparse array. This type should be a compatible
+        type of the weight argument, eg. if weight would return a float this
+        argument should also be a float.
+        If None, then the default for SciPy is used.
+
+    Returns
+    -------
+    A : SciPy sparse array
+      The incidence matrix of G.
+
+    Notes
+    -----
+    For MultiGraph/MultiDiGraph, the edges in edgelist should be
+    (u,v,key) 3-tuples.
+
+    "Networks are the best discrete model for so many problems in
+    applied mathematics" [1]_.
+
+    References
+    ----------
+    .. [1] Gil Strang, Network applications: A = incidence matrix,
+       http://videolectures.net/mit18085f07_strang_lec03/
+    """
+    import scipy as sp
+
+    if nodelist is None:
+        nodelist = list(G)
+    if edgelist is None:
+        if G.is_multigraph():
+            edgelist = list(G.edges(keys=True))
+        else:
+            edgelist = list(G.edges())
+    A = sp.sparse.lil_array((len(nodelist), len(edgelist)), dtype=dtype)
+    node_index = {node: i for i, node in enumerate(nodelist)}
+    for ei, e in enumerate(edgelist):
+        (u, v) = e[:2]
+        if u == v:
+            continue  # self loops give zero column
+        try:
+            ui = node_index[u]
+            vi = node_index[v]
+        except KeyError as err:
+            raise nx.NetworkXError(
+                f"node {u} or {v} in edgelist but not in nodelist"
+            ) from err
+        if weight is None:
+            wt = 1
+        else:
+            if G.is_multigraph():
+                ekey = e[2]
+                wt = G[u][v][ekey].get(weight, 1)
+            else:
+                wt = G[u][v].get(weight, 1)
+        if oriented:
+            A[ui, ei] = -wt
+            A[vi, ei] = wt
+        else:
+            A[ui, ei] = wt
+            A[vi, ei] = wt
+    return A.asformat("csc")
+
+
+@nx._dispatchable(edge_attrs="weight")
+def adjacency_matrix(G, nodelist=None, dtype=None, weight="weight"):
+    """Returns adjacency matrix of `G`.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in `nodelist`.
+       If ``nodelist=None`` (the default), then the ordering is produced by
+       ``G.nodes()``.
+
+    dtype : NumPy data-type, optional
+        The desired data-type for the array.
+        If `None`, then the NumPy default is used.
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to provide each value in the matrix.
+       If None, then each edge has weight 1.
+
+    Returns
+    -------
+    A : SciPy sparse array
+      Adjacency matrix representation of G.
+
+    Notes
+    -----
+    For directed graphs, entry ``i, j`` corresponds to an edge from ``i`` to ``j``.
+
+    If you want a pure Python adjacency matrix representation try
+    :func:`~networkx.convert.to_dict_of_dicts` which will return a
+    dictionary-of-dictionaries format that can be addressed as a
+    sparse matrix.
+
+    For multigraphs with parallel edges the weights are summed.
+    See :func:`networkx.convert_matrix.to_numpy_array` for other options.
+
+    The convention used for self-loop edges in graphs is to assign the
+    diagonal matrix entry value to the edge weight attribute
+    (or the number 1 if the edge has no weight attribute).  If the
+    alternate convention of doubling the edge weight is desired the
+    resulting SciPy sparse array can be modified as follows::
+
+        >>> G = nx.Graph([(1, 1)])
+        >>> A = nx.adjacency_matrix(G)
+        >>> A.toarray()
+        array([[1]])
+        >>> A.setdiag(A.diagonal() * 2)
+        >>> A.toarray()
+        array([[2]])
+
+    See Also
+    --------
+    to_numpy_array
+    to_scipy_sparse_array
+    to_dict_of_dicts
+    adjacency_spectrum
+    """
+    return nx.to_scipy_sparse_array(G, nodelist=nodelist, dtype=dtype, weight=weight)

janus/lib/python3.10/site-packages/networkx/linalg/laplacianmatrix.py

@@ -0,0 +1,617 @@
+"""Laplacian matrix of graphs.
+
+All calculations here are done using the out-degree. For Laplacians using
+in-degree, use `G.reverse(copy=False)` instead of `G` and take the transpose.
+
+The `laplacian_matrix` function provides an unnormalized matrix,
+while `normalized_laplacian_matrix`, `directed_laplacian_matrix`,
+and `directed_combinatorial_laplacian_matrix` are all normalized.
+"""
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = [
+    "laplacian_matrix",
+    "normalized_laplacian_matrix",
+    "total_spanning_tree_weight",
+    "directed_laplacian_matrix",
+    "directed_combinatorial_laplacian_matrix",
+]
+
+
+@nx._dispatchable(edge_attrs="weight")
+def laplacian_matrix(G, nodelist=None, weight="weight"):
+    """Returns the Laplacian matrix of G.
+
+    The graph Laplacian is the matrix L = D - A, where
+    A is the adjacency matrix and D is the diagonal matrix of node degrees.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to compute each value in the matrix.
+       If None, then each edge has weight 1.
+
+    Returns
+    -------
+    L : SciPy sparse array
+      The Laplacian matrix of G.
+
+    Notes
+    -----
+    For MultiGraph, the edges weights are summed.
+
+    This returns an unnormalized matrix. For a normalized output,
+    use `normalized_laplacian_matrix`, `directed_laplacian_matrix`,
+    or `directed_combinatorial_laplacian_matrix`.
+
+    This calculation uses the out-degree of the graph `G`. To use the
+    in-degree for calculations instead, use `G.reverse(copy=False)` and
+    take the transpose.
+
+    See Also
+    --------
+    :func:`~networkx.convert_matrix.to_numpy_array`
+    normalized_laplacian_matrix
+    directed_laplacian_matrix
+    directed_combinatorial_laplacian_matrix
+    :func:`~networkx.linalg.spectrum.laplacian_spectrum`
+
+    Examples
+    --------
+    For graphs with multiple connected components, L is permutation-similar
+    to a block diagonal matrix where each block is the respective Laplacian
+    matrix for each component.
+
+    >>> G = nx.Graph([(1, 2), (2, 3), (4, 5)])
+    >>> print(nx.laplacian_matrix(G).toarray())
+    [[ 1 -1  0  0  0]
+     [-1  2 -1  0  0]
+     [ 0 -1  1  0  0]
+     [ 0  0  0  1 -1]
+     [ 0  0  0 -1  1]]
+
+    >>> edges = [
+    ...     (1, 2),
+    ...     (2, 1),
+    ...     (2, 4),
+    ...     (4, 3),
+    ...     (3, 4),
+    ... ]
+    >>> DiG = nx.DiGraph(edges)
+    >>> print(nx.laplacian_matrix(DiG).toarray())
+    [[ 1 -1  0  0]
+     [-1  2 -1  0]
+     [ 0  0  1 -1]
+     [ 0  0 -1  1]]
+
+    Notice that node 4 is represented by the third column and row. This is because
+    by default the row/column order is the order of `G.nodes` (i.e. the node added
+    order -- in the edgelist, 4 first appears in (2, 4), before node 3 in edge (4, 3).)
+    To control the node order of the matrix, use the `nodelist` argument.
+
+    >>> print(nx.laplacian_matrix(DiG, nodelist=[1, 2, 3, 4]).toarray())
+    [[ 1 -1  0  0]
+     [-1  2  0 -1]
+     [ 0  0  1 -1]
+     [ 0  0 -1  1]]
+
+    This calculation uses the out-degree of the graph `G`. To use the
+    in-degree for calculations instead, use `G.reverse(copy=False)` and
+    take the transpose.
+
+    >>> print(nx.laplacian_matrix(DiG.reverse(copy=False)).toarray().T)
+    [[ 1 -1  0  0]
+     [-1  1 -1  0]
+     [ 0  0  2 -1]
+     [ 0  0 -1  1]]
+
+    References
+    ----------
+    .. [1] Langville, Amy N., and Carl D. Meyer. Google’s PageRank and Beyond:
+       The Science of Search Engine Rankings. Princeton University Press, 2006.
+
+    """
+    import scipy as sp
+
+    if nodelist is None:
+        nodelist = list(G)
+    A = nx.to_scipy_sparse_array(G, nodelist=nodelist, weight=weight, format="csr")
+    n, m = A.shape
+    # TODO: rm csr_array wrapper when spdiags can produce arrays
+    D = sp.sparse.csr_array(sp.sparse.spdiags(A.sum(axis=1), 0, m, n, format="csr"))
+    return D - A
+
+
+@nx._dispatchable(edge_attrs="weight")
+def normalized_laplacian_matrix(G, nodelist=None, weight="weight"):
+    r"""Returns the normalized Laplacian matrix of G.
+
+    The normalized graph Laplacian is the matrix
+
+    .. math::
+
+        N = D^{-1/2} L D^{-1/2}
+
+    where `L` is the graph Laplacian and `D` is the diagonal matrix of
+    node degrees [1]_.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to compute each value in the matrix.
+       If None, then each edge has weight 1.
+
+    Returns
+    -------
+    N : SciPy sparse array
+      The normalized Laplacian matrix of G.
+
+    Notes
+    -----
+    For MultiGraph, the edges weights are summed.
+    See :func:`to_numpy_array` for other options.
+
+    If the Graph contains selfloops, D is defined as ``diag(sum(A, 1))``, where A is
+    the adjacency matrix [2]_.
+
+    This calculation uses the out-degree of the graph `G`. To use the
+    in-degree for calculations instead, use `G.reverse(copy=False)` and
+    take the transpose.
+
+    For an unnormalized output, use `laplacian_matrix`.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> edges = [
+    ...     (1, 2),
+    ...     (2, 1),
+    ...     (2, 4),
+    ...     (4, 3),
+    ...     (3, 4),
+    ... ]
+    >>> DiG = nx.DiGraph(edges)
+    >>> print(nx.normalized_laplacian_matrix(DiG).toarray())
+    [[ 1.         -0.70710678  0.          0.        ]
+     [-0.70710678  1.         -0.70710678  0.        ]
+     [ 0.          0.          1.         -1.        ]
+     [ 0.          0.         -1.          1.        ]]
+
+    Notice that node 4 is represented by the third column and row. This is because
+    by default the row/column order is the order of `G.nodes` (i.e. the node added
+    order -- in the edgelist, 4 first appears in (2, 4), before node 3 in edge (4, 3).)
+    To control the node order of the matrix, use the `nodelist` argument.
+
+    >>> print(nx.normalized_laplacian_matrix(DiG, nodelist=[1, 2, 3, 4]).toarray())
+    [[ 1.         -0.70710678  0.          0.        ]
+     [-0.70710678  1.          0.         -0.70710678]
+     [ 0.          0.          1.         -1.        ]
+     [ 0.          0.         -1.          1.        ]]
+    >>> G = nx.Graph(edges)
+    >>> print(nx.normalized_laplacian_matrix(G).toarray())
+    [[ 1.         -0.70710678  0.          0.        ]
+     [-0.70710678  1.         -0.5         0.        ]
+     [ 0.         -0.5         1.         -0.70710678]
+     [ 0.          0.         -0.70710678  1.        ]]
+
+    See Also
+    --------
+    laplacian_matrix
+    normalized_laplacian_spectrum
+    directed_laplacian_matrix
+    directed_combinatorial_laplacian_matrix
+
+    References
+    ----------
+    .. [1] Fan Chung-Graham, Spectral Graph Theory,
+       CBMS Regional Conference Series in Mathematics, Number 92, 1997.
+    .. [2] Steve Butler, Interlacing For Weighted Graphs Using The Normalized
+       Laplacian, Electronic Journal of Linear Algebra, Volume 16, pp. 90-98,
+       March 2007.
+    .. [3] Langville, Amy N., and Carl D. Meyer. Google’s PageRank and Beyond:
+       The Science of Search Engine Rankings. Princeton University Press, 2006.
+    """
+    import numpy as np
+    import scipy as sp
+
+    if nodelist is None:
+        nodelist = list(G)
+    A = nx.to_scipy_sparse_array(G, nodelist=nodelist, weight=weight, format="csr")
+    n, _ = A.shape
+    diags = A.sum(axis=1)
+    # TODO: rm csr_array wrapper when spdiags can produce arrays
+    D = sp.sparse.csr_array(sp.sparse.spdiags(diags, 0, n, n, format="csr"))
+    L = D - A
+    with np.errstate(divide="ignore"):
+        diags_sqrt = 1.0 / np.sqrt(diags)
+    diags_sqrt[np.isinf(diags_sqrt)] = 0
+    # TODO: rm csr_array wrapper when spdiags can produce arrays
+    DH = sp.sparse.csr_array(sp.sparse.spdiags(diags_sqrt, 0, n, n, format="csr"))
+    return DH @ (L @ DH)
+
+
+@nx._dispatchable(edge_attrs="weight")
+def total_spanning_tree_weight(G, weight=None, root=None):
+    """
+    Returns the total weight of all spanning trees of `G`.
+
+    Kirchoff's Tree Matrix Theorem [1]_, [2]_ states that the determinant of any
+    cofactor of the Laplacian matrix of a graph is the number of spanning trees
+    in the graph. For a weighted Laplacian matrix, it is the sum across all
+    spanning trees of the multiplicative weight of each tree. That is, the
+    weight of each tree is the product of its edge weights.
+
+    For unweighted graphs, the total weight equals the number of spanning trees in `G`.
+
+    For directed graphs, the total weight follows by summing over all directed
+    spanning trees in `G` that start in the `root` node [3]_.
+
+    .. deprecated:: 3.3
+
+       ``total_spanning_tree_weight`` is deprecated and will be removed in v3.5.
+       Use ``nx.number_of_spanning_trees(G)`` instead.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+
+    weight : string or None, optional (default=None)
+        The key for the edge attribute holding the edge weight.
+        If None, then each edge has weight 1.
+
+    root : node (only required for directed graphs)
+       A node in the directed graph `G`.
+
+    Returns
+    -------
+    total_weight : float
+        Undirected graphs:
+            The sum of the total multiplicative weights for all spanning trees in `G`.
+        Directed graphs:
+            The sum of the total multiplicative weights for all spanning trees of `G`,
+            rooted at node `root`.
+
+    Raises
+    ------
+    NetworkXPointlessConcept
+        If `G` does not contain any nodes.
+
+    NetworkXError
+        If the graph `G` is not (weakly) connected,
+        or if `G` is directed and the root node is not specified or not in G.
+
+    Examples
+    --------
+    >>> G = nx.complete_graph(5)
+    >>> round(nx.total_spanning_tree_weight(G))
+    125
+
+    >>> G = nx.Graph()
+    >>> G.add_edge(1, 2, weight=2)
+    >>> G.add_edge(1, 3, weight=1)
+    >>> G.add_edge(2, 3, weight=1)
+    >>> round(nx.total_spanning_tree_weight(G, "weight"))
+    5
+
+    Notes
+    -----
+    Self-loops are excluded. Multi-edges are contracted in one edge
+    equal to the sum of the weights.
+
+    References
+    ----------
+    .. [1] Wikipedia
+       "Kirchhoff's theorem."
+       https://en.wikipedia.org/wiki/Kirchhoff%27s_theorem
+    .. [2] Kirchhoff, G. R.
+        Über die Auflösung der Gleichungen, auf welche man
+        bei der Untersuchung der linearen Vertheilung
+        Galvanischer Ströme geführt wird
+        Annalen der Physik und Chemie, vol. 72, pp. 497-508, 1847.
+    .. [3] Margoliash, J.
+        "Matrix-Tree Theorem for Directed Graphs"
+        https://www.math.uchicago.edu/~may/VIGRE/VIGRE2010/REUPapers/Margoliash.pdf
+    """
+    import warnings
+
+    warnings.warn(
+        (
+            "\n\ntotal_spanning_tree_weight is deprecated and will be removed in v3.5.\n"
+            "Use `nx.number_of_spanning_trees(G)` instead."
+        ),
+        category=DeprecationWarning,
+        stacklevel=3,
+    )
+
+    return nx.number_of_spanning_trees(G, weight=weight, root=root)
+
+
+###############################################################################
+# Code based on work from https://github.com/bjedwards
+
+
+@not_implemented_for("undirected")
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def directed_laplacian_matrix(
+    G, nodelist=None, weight="weight", walk_type=None, alpha=0.95
+):
+    r"""Returns the directed Laplacian matrix of G.
+
+    The graph directed Laplacian is the matrix
+
+    .. math::
+
+        L = I - \frac{1}{2} \left (\Phi^{1/2} P \Phi^{-1/2} + \Phi^{-1/2} P^T \Phi^{1/2} \right )
+
+    where `I` is the identity matrix, `P` is the transition matrix of the
+    graph, and `\Phi` a matrix with the Perron vector of `P` in the diagonal and
+    zeros elsewhere [1]_.
+
+    Depending on the value of walk_type, `P` can be the transition matrix
+    induced by a random walk, a lazy random walk, or a random walk with
+    teleportation (PageRank).
+
+    Parameters
+    ----------
+    G : DiGraph
+       A NetworkX graph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to compute each value in the matrix.
+       If None, then each edge has weight 1.
+
+    walk_type : string or None, optional (default=None)
+       One of ``"random"``, ``"lazy"``, or ``"pagerank"``. If ``walk_type=None``
+       (the default), then a value is selected according to the properties of `G`:
+       - ``walk_type="random"`` if `G` is strongly connected and aperiodic
+       - ``walk_type="lazy"`` if `G` is strongly connected but not aperiodic
+       - ``walk_type="pagerank"`` for all other cases.
+
+    alpha : real
+       (1 - alpha) is the teleportation probability used with pagerank
+
+    Returns
+    -------
+    L : NumPy matrix
+      Normalized Laplacian of G.
+
+    Notes
+    -----
+    Only implemented for DiGraphs
+
+    The result is always a symmetric matrix.
+
+    This calculation uses the out-degree of the graph `G`. To use the
+    in-degree for calculations instead, use `G.reverse(copy=False)` and
+    take the transpose.
+
+    See Also
+    --------
+    laplacian_matrix
+    normalized_laplacian_matrix
+    directed_combinatorial_laplacian_matrix
+
+    References
+    ----------
+    .. [1] Fan Chung (2005).
+       Laplacians and the Cheeger inequality for directed graphs.
+       Annals of Combinatorics, 9(1), 2005
+    """
+    import numpy as np
+    import scipy as sp
+
+    # NOTE: P has type ndarray if walk_type=="pagerank", else csr_array
+    P = _transition_matrix(
+        G, nodelist=nodelist, weight=weight, walk_type=walk_type, alpha=alpha
+    )
+
+    n, m = P.shape
+
+    evals, evecs = sp.sparse.linalg.eigs(P.T, k=1)
+    v = evecs.flatten().real
+    p = v / v.sum()
+    # p>=0 by Perron-Frobenius Thm. Use abs() to fix roundoff across zero gh-6865
+    sqrtp = np.sqrt(np.abs(p))
+    Q = (
+        # TODO: rm csr_array wrapper when spdiags creates arrays
+        sp.sparse.csr_array(sp.sparse.spdiags(sqrtp, 0, n, n))
+        @ P
+        # TODO: rm csr_array wrapper when spdiags creates arrays
+        @ sp.sparse.csr_array(sp.sparse.spdiags(1.0 / sqrtp, 0, n, n))
+    )
+    # NOTE: This could be sparsified for the non-pagerank cases
+    I = np.identity(len(G))
+
+    return I - (Q + Q.T) / 2.0
+
+
+@not_implemented_for("undirected")
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def directed_combinatorial_laplacian_matrix(
+    G, nodelist=None, weight="weight", walk_type=None, alpha=0.95
+):
+    r"""Return the directed combinatorial Laplacian matrix of G.
+
+    The graph directed combinatorial Laplacian is the matrix
+
+    .. math::
+
+        L = \Phi - \frac{1}{2} \left (\Phi P + P^T \Phi \right)
+
+    where `P` is the transition matrix of the graph and `\Phi` a matrix
+    with the Perron vector of `P` in the diagonal and zeros elsewhere [1]_.
+
+    Depending on the value of walk_type, `P` can be the transition matrix
+    induced by a random walk, a lazy random walk, or a random walk with
+    teleportation (PageRank).
+
+    Parameters
+    ----------
+    G : DiGraph
+       A NetworkX graph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to compute each value in the matrix.
+       If None, then each edge has weight 1.
+
+    walk_type : string or None, optional (default=None)
+        One of ``"random"``, ``"lazy"``, or ``"pagerank"``. If ``walk_type=None``
+        (the default), then a value is selected according to the properties of `G`:
+        - ``walk_type="random"`` if `G` is strongly connected and aperiodic
+        - ``walk_type="lazy"`` if `G` is strongly connected but not aperiodic
+        - ``walk_type="pagerank"`` for all other cases.
+
+    alpha : real
+       (1 - alpha) is the teleportation probability used with pagerank
+
+    Returns
+    -------
+    L : NumPy matrix
+      Combinatorial Laplacian of G.
+
+    Notes
+    -----
+    Only implemented for DiGraphs
+
+    The result is always a symmetric matrix.
+
+    This calculation uses the out-degree of the graph `G`. To use the
+    in-degree for calculations instead, use `G.reverse(copy=False)` and
+    take the transpose.
+
+    See Also
+    --------
+    laplacian_matrix
+    normalized_laplacian_matrix
+    directed_laplacian_matrix
+
+    References
+    ----------
+    .. [1] Fan Chung (2005).
+       Laplacians and the Cheeger inequality for directed graphs.
+       Annals of Combinatorics, 9(1), 2005
+    """
+    import scipy as sp
+
+    P = _transition_matrix(
+        G, nodelist=nodelist, weight=weight, walk_type=walk_type, alpha=alpha
+    )
+
+    n, m = P.shape
+
+    evals, evecs = sp.sparse.linalg.eigs(P.T, k=1)
+    v = evecs.flatten().real
+    p = v / v.sum()
+    # NOTE: could be improved by not densifying
+    # TODO: Rm csr_array wrapper when spdiags array creation becomes available
+    Phi = sp.sparse.csr_array(sp.sparse.spdiags(p, 0, n, n)).toarray()
+
+    return Phi - (Phi @ P + P.T @ Phi) / 2.0
+
+
+def _transition_matrix(G, nodelist=None, weight="weight", walk_type=None, alpha=0.95):
+    """Returns the transition matrix of G.
+
+    This is a row stochastic giving the transition probabilities while
+    performing a random walk on the graph. Depending on the value of walk_type,
+    P can be the transition matrix induced by a random walk, a lazy random walk,
+    or a random walk with teleportation (PageRank).
+
+    Parameters
+    ----------
+    G : DiGraph
+       A NetworkX graph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to compute each value in the matrix.
+       If None, then each edge has weight 1.
+
+    walk_type : string or None, optional (default=None)
+       One of ``"random"``, ``"lazy"``, or ``"pagerank"``. If ``walk_type=None``
+       (the default), then a value is selected according to the properties of `G`:
+        - ``walk_type="random"`` if `G` is strongly connected and aperiodic
+        - ``walk_type="lazy"`` if `G` is strongly connected but not aperiodic
+        - ``walk_type="pagerank"`` for all other cases.
+
+    alpha : real
+       (1 - alpha) is the teleportation probability used with pagerank
+
+    Returns
+    -------
+    P : numpy.ndarray
+      transition matrix of G.
+
+    Raises
+    ------
+    NetworkXError
+        If walk_type not specified or alpha not in valid range
+    """
+    import numpy as np
+    import scipy as sp
+
+    if walk_type is None:
+        if nx.is_strongly_connected(G):
+            if nx.is_aperiodic(G):
+                walk_type = "random"
+            else:
+                walk_type = "lazy"
+        else:
+            walk_type = "pagerank"
+
+    A = nx.to_scipy_sparse_array(G, nodelist=nodelist, weight=weight, dtype=float)
+    n, m = A.shape
+    if walk_type in ["random", "lazy"]:
+        # TODO: Rm csr_array wrapper when spdiags array creation becomes available
+        DI = sp.sparse.csr_array(sp.sparse.spdiags(1.0 / A.sum(axis=1), 0, n, n))
+        if walk_type == "random":
+            P = DI @ A
+        else:
+            # TODO: Rm csr_array wrapper when identity array creation becomes available
+            I = sp.sparse.csr_array(sp.sparse.identity(n))
+            P = (I + DI @ A) / 2.0
+
+    elif walk_type == "pagerank":
+        if not (0 < alpha < 1):
+            raise nx.NetworkXError("alpha must be between 0 and 1")
+        # this is using a dense representation. NOTE: This should be sparsified!
+        A = A.toarray()
+        # add constant to dangling nodes' row
+        A[A.sum(axis=1) == 0, :] = 1 / n
+        # normalize
+        A = A / A.sum(axis=1)[np.newaxis, :].T
+        P = alpha * A + (1 - alpha) / n
+    else:
+        raise nx.NetworkXError("walk_type must be random, lazy, or pagerank")
+
+    return P

janus/lib/python3.10/site-packages/networkx/linalg/modularitymatrix.py

@@ -0,0 +1,166 @@
+"""Modularity matrix of graphs."""
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = ["modularity_matrix", "directed_modularity_matrix"]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def modularity_matrix(G, nodelist=None, weight=None):
+    r"""Returns the modularity matrix of G.
+
+    The modularity matrix is the matrix B = A - <A>, where A is the adjacency
+    matrix and <A> is the average adjacency matrix, assuming that the graph
+    is described by the configuration model.
+
+    More specifically, the element B_ij of B is defined as
+
+    .. math::
+        A_{ij} - {k_i k_j \over 2 m}
+
+    where k_i is the degree of node i, and where m is the number of edges
+    in the graph. When weight is set to a name of an attribute edge, Aij, k_i,
+    k_j and m are computed using its value.
+
+    Parameters
+    ----------
+    G : Graph
+       A NetworkX graph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight : string or None, optional (default=None)
+       The edge attribute that holds the numerical value used for
+       the edge weight.  If None then all edge weights are 1.
+
+    Returns
+    -------
+    B : Numpy array
+      The modularity matrix of G.
+
+    Examples
+    --------
+    >>> k = [3, 2, 2, 1, 0]
+    >>> G = nx.havel_hakimi_graph(k)
+    >>> B = nx.modularity_matrix(G)
+
+
+    See Also
+    --------
+    to_numpy_array
+    modularity_spectrum
+    adjacency_matrix
+    directed_modularity_matrix
+
+    References
+    ----------
+    .. [1] M. E. J. Newman, "Modularity and community structure in networks",
+           Proc. Natl. Acad. Sci. USA, vol. 103, pp. 8577-8582, 2006.
+    """
+    import numpy as np
+
+    if nodelist is None:
+        nodelist = list(G)
+    A = nx.to_scipy_sparse_array(G, nodelist=nodelist, weight=weight, format="csr")
+    k = A.sum(axis=1)
+    m = k.sum() * 0.5
+    # Expected adjacency matrix
+    X = np.outer(k, k) / (2 * m)
+
+    return A - X
+
+
+@not_implemented_for("undirected")
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def directed_modularity_matrix(G, nodelist=None, weight=None):
+    """Returns the directed modularity matrix of G.
+
+    The modularity matrix is the matrix B = A - <A>, where A is the adjacency
+    matrix and <A> is the expected adjacency matrix, assuming that the graph
+    is described by the configuration model.
+
+    More specifically, the element B_ij of B is defined as
+
+    .. math::
+        B_{ij} = A_{ij} - k_i^{out} k_j^{in} / m
+
+    where :math:`k_i^{in}` is the in degree of node i, and :math:`k_j^{out}` is the out degree
+    of node j, with m the number of edges in the graph. When weight is set
+    to a name of an attribute edge, Aij, k_i, k_j and m are computed using
+    its value.
+
+    Parameters
+    ----------
+    G : DiGraph
+       A NetworkX DiGraph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight : string or None, optional (default=None)
+       The edge attribute that holds the numerical value used for
+       the edge weight.  If None then all edge weights are 1.
+
+    Returns
+    -------
+    B : Numpy array
+      The modularity matrix of G.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_edges_from(
+    ...     (
+    ...         (1, 2),
+    ...         (1, 3),
+    ...         (3, 1),
+    ...         (3, 2),
+    ...         (3, 5),
+    ...         (4, 5),
+    ...         (4, 6),
+    ...         (5, 4),
+    ...         (5, 6),
+    ...         (6, 4),
+    ...     )
+    ... )
+    >>> B = nx.directed_modularity_matrix(G)
+
+
+    Notes
+    -----
+    NetworkX defines the element A_ij of the adjacency matrix as 1 if there
+    is a link going from node i to node j. Leicht and Newman use the opposite
+    definition. This explains the different expression for B_ij.
+
+    See Also
+    --------
+    to_numpy_array
+    modularity_spectrum
+    adjacency_matrix
+    modularity_matrix
+
+    References
+    ----------
+    .. [1] E. A. Leicht, M. E. J. Newman,
+        "Community structure in directed networks",
+        Phys. Rev Lett., vol. 100, no. 11, p. 118703, 2008.
+    """
+    import numpy as np
+
+    if nodelist is None:
+        nodelist = list(G)
+    A = nx.to_scipy_sparse_array(G, nodelist=nodelist, weight=weight, format="csr")
+    k_in = A.sum(axis=0)
+    k_out = A.sum(axis=1)
+    m = k_in.sum()
+    # Expected adjacency matrix
+    X = np.outer(k_out, k_in) / m
+
+    return A - X