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

FranklinGraph returns a 12-vertex graph that represents a 6-chromatic map on the Klein bottle. It is the sole counterexample to Heawood's map-coloring conjecture.

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

FruchtGraph returns the smallest 3-regular graph whose automorphism group consists of only the identity.

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.

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