FiniteGraphs produces a convenient list of all the interesting, finite, parameterless graphs built into Combinatorica.
FirstLexicographicTableau[p] constructs the first Young tableau with shape described by partition p.
FolkmanGraph returns a smallest graph that is edge-transitive but not vertex-transitive.
FromInversionVector[v] reconstructs the unique permutation with inversion vector v.
FruchtGraph returns the smallest 3-regular graph whose automorphism group consists of only the identity.
GraphCenter[g] gives a list of the vertices of graph g with minimum eccentricity.
GraphComplement[g] gives the complement of graph g.
GraphDifference[g, h] constructs the graph resulting from subtracting the edges of graph h from the edges of graph g.
GraphIntersection[g_1, g_2, ...] constructs the graph defined by the edges that are in all the graphs g_1, g_2, ....
GraphProduct[g_1, g_2, ...] constructs the product of graphs g_1, g_2, and so forth.