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

HamiltonianQ[g] yields True if there exists a Hamiltonian cycle in graph g, or in other words, if there exists a cycle that visits each vertex exactly once.

Harary[k, n] constructs the minimal k-connected graph on n vertices.

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.

HeawoodGraph returns a smallest (6, 3)-cage, a 3-regular graph with girth 6.

HerschelGraph returns a graph object that represents a Herschel graph.

HideCycles[c] canonically encodes the cycle structure c into a unique permutation.

HighlightedEdgeColors is an option to Highlight that determines which colors are used for the highlighted edges.