LinkRanks[g] gives the link ranks of the directed graph g as a rule list.

ShowGraph[g] displays the graph g. ShowGraph[g, Directed] is obsolete and it is currently identical to ShowGraph[g].

ListGraphs[n, m] returns all nonisomorphic undirected graphs with n vertices and m edges. ListGraphs[n, m, Directed] returns all nonisomorphic directed graphs with n vertices ...

FiniteGraphs produces a convenient list of all the interesting, finite, parameterless graphs built into Combinatorica.

IsomorphismQ[g, h, p] tests if permutation p defines an isomorphism between graphs g and h.

When Mathematica plots a graph for you, it has to make many choices. It has to work out what the scales should be, where the function should be sampled, how the axes should ...

AlternatingPaths[g, start, ME] returns the alternating paths in graph g with respect to the matching ME, starting at the vertices in the list start. The paths are returned in ...

ChromaticPolynomial[g, z] gives the chromatic polynomial P(z) of graph g, which counts the number of ways to color g with, at most, z colors.

CompleteQ[g] yields True if graph g is complete. This means that between any pair of vertices there is an undirected edge or two directed edges going in opposite directions.

Diameter[g] gives the diameter of graph g, the maximum length, among all pairs of vertices in g, of a shortest path between each pair.