FromCycles[{c_1, c_2, ...}] gives the permutation that has the given cycle structure.

GetEdgeLabels[g] returns the list of labels of the edges of g. GetEdgeLabels[g, e] returns the list of labels in graph g of the edges in e.

GetEdgeWeights[g] returns the list of weights of the edges of g. GetEdgeWeights[g, e] returns the list of weights in graph g of the edges in e.

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.

GraphOptions[g] returns the display options associated with g. GraphOptions[g, v] returns the display options associated with vertex v in g. GraphOptions[g, {u, v}] returns ...

GraphUnion[g_1, g_2, ...] constructs the union of graphs g_1, g_2, and so forth. GraphUnion[n, g] constructs n copies of graph g, for any nonnegative integer n.

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 ...