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[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.

GreedyVertexCover[g] returns a vertex cover of graph g constructed using the greedy algorithm. This is a natural heuristic for constructing a vertex cover, but it can produce ...

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.

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.