Assertion: graph's vertex | /r/HasProperty | edge
Facets:
value: between two people
type: OTHER
value: within w
type: LOCATION
value: from person a
type: OTHER
value: within x.
type: LOCATION
Source sentences:
text: While we considered in the "Eulerian graph" section a way of going and returning including every edge of a graph, we consider here a similar problem of going around on a graph including every "vertex" (not "edge").
text: For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person A can shake hands with a person B only if B also shakes hands with A.
text: Two vertices, v and w, of a graph are ADJACENT if there is an edge, vx, joining theem; the vertices are then considered INCIDENT to the edge, vx.
text: For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this is an undirected graph, because if person A shook hands with person B, then person B also shook hands with person A.
text: In contrast, if the vertices represent people at a party, and there is an edge from person A to person B when person A knows of person B, then this graph is directed, because knowledge of someone is not necessarily a symmetric relation.
text: A vertex v adjacent to u is called a neighbor of u, and (in a directed graph) is a predecessor of u if (v,u) is an edge and a successor of u if (u,v) is an edge.
text: In a complete bipartite graph, the vertex set is the union of two disjoint sets, W and X, so that every vertex in W is adjacent to every vertex in X but there are no edges within W or X.