PageRanks[g] give the page rank of the graph g as a rule list.

GraphIntersection[g_1, g_2, ...] constructs the graph defined by the edges that are in all the graphs g_1, g_2, ....

GraphSum[g_1, g_2, ...] constructs the graph resulting from joining the edge lists of graphs g_1, g_2, and so forth.

MaximalBipartiteMatching[g] gives the maximal matching of the bipartite graph g.

ShortestPath[g, start, end] finds a shortest path between vertices start and end in graph g.

ShortestPathSpanningTree[g, v] constructs a shortest-path spanning tree rooted at v, so that a shortest path in graph g from v to any other vertex is a path in the tree.

EdgeIndex[g, e] gives the integer index for the edge e in the graph g.

NetworkFlow[g, source, sink] returns the value of a maximum flow through graph g from source to sink. NetworkFlow[g, source, sink, Edge] returns the edges in g that have ...

GraphPolynomial[n, x] returns a polynomial in x in which the coefficient of x^m is the number of nonisomorphic graphs with n vertices and m edges. GraphPolynomial[n, x, ...

BellmanFord[g, v] gives a shortest-path spanning tree and associated distances from vertex v of graph g. The shortest-path spanning tree is given by a list in which element i ...