GetVertexLabels[g] returns the list of labels of vertices of g. GetVertexLabels[g, v] returns the list of labels in graph g of the vertices specified in list v.
GetVertexWeights[g] returns the list of weights of vertices of g. GetVertexWeights[g, v] returns the list of weights in graph g of the vertices in v.
Girth
(Combinatorica Package Symbol) Girth[g] gives the length of a shortest cycle in a simple graph g.
GraphicQ[s] yields True if the list of integers s is a graphic sequence, and thus represents a degree sequence of some graph.
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
(Combinatorica Package Symbol) Harary[k, n] constructs the minimal k-connected graph on n vertices.
HideCycles[c] canonically encodes the cycle structure c into a unique permutation.
IdenticalQ[g, h] yields True if graphs g and h have identical edge lists, even though the associated graphics information need not be the same.
InDegree[g, n] returns the in-degree of vertex n in directed graph g. InDegree[g] returns the sequence of in-degrees of the vertices in directed graph g.
Index
(Combinatorica Package Symbol) Index[p] gives the index of permutation p, the sum of all subscripts j such that p[[j]] is greater than p[[j + 1]].