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

FolkmanGraph returns a smallest graph that is edge-transitive but not vertex-transitive.

GraphCenter[g] gives a list of the vertices of graph g with minimum eccentricity.

GrayCodeSubsets[l] constructs a binary reflected Gray code on set l.

GrayGraph returns a 3-regular, 54-vertex graph that is edge-transitive but not vertex-transitive\[LongDash]the smallest known such example.

HamiltonianPath[g] finds a Hamiltonian path in graph g if one exists. HamiltonianPath[g, All] gives all Hamiltonian paths of graph g.

HasseDiagram[g] constructs a Hasse diagram of the relation defined by directed acyclic graph g.

Heapify[p] builds a heap from permutation p.

HeapSort[l] performs a heap sort on the items of list l.

IcosahedralGraph returns the graph corresponding to the icosahedron, a Platonic solid.