VertexCoverQ[g, c] yields True if the vertices in list c define a vertex cover of graph g.

Backtrack[s, partialQ, solutionQ] performs a backtrack search of the state space s, expanding a partial solution so long as partialQ is True and returning the first complete ...

NumberOfKPaths[g, v, k] returns a sorted list that contains the number of paths of length k to different vertices of g from v.NumberOfKPaths[al, v, k] behaves identically, ...

ChangeEdges[g, e] replaces the edges of graph g with the edges in e. e can have the form {{s_1, t_1}, {s_2, t_2}, ...} or the form {{{s_1, t_1}, gr_1}, {{s_2, t_2}, gr_2}, ...

ChangeVertices[g, v] replaces the vertices of graph g with the vertices in the given list v. v can have the form {{x_1, y_1}, {x_2, y_2}, ...} or the form {{{x_1, y_1}, ...

FindShortestPath[g, s, t] finds the shortest path from source vertex s to target vertex t in the graph g.FindShortestPath[g, s, All] generates a ShortestPathFunction[...] ...

CirculantGraph[n, l] constructs a circulant graph on n vertices, meaning the i\[Null]^th vertex is adjacent to the (i + j)\[Null]^th and (i - j)\[Null]^th vertices, for each ...

MakeDirected[g] constructs a directed graph from a given undirected graph g by replacing each undirected edge in g by two directed edges pointing in opposite directions.

KatzCentrality[g, \[Alpha]] gives a list of Katz centralities for the vertices in the graph g and weight \[Alpha].KatzCentrality[g, \[Alpha], \[Beta]] gives a list of Katz ...

InversionPoset[n] returns a Hasse diagram of the partially ordered set on size-n permutations in which p < q if q can be obtained from p by an adjacent transposition that ...