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.

FromAdjacencyLists[l] constructs an edge list representation for a graph from the given adjacency lists l, using a circular embedding. FromAdjacencyLists[l, v] uses v as the ...

FromAdjacencyMatrix[m] constructs a graph from a given adjacency matrix m, using a circular embedding. FromAdjacencyMatrix[m, v] uses v as the embedding for the resulting ...

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

FromOrderedPairs[l] constructs an edge list representation from a list of ordered pairs l, using a circular embedding. FromOrderedPairs[l, v] uses v as the embedding for the ...

FromUnorderedPairs[l] constructs an edge list representation from a list of unordered pairs l, using a circular embedding.FromUnorderedPairs[l, v] uses v as the embedding for ...

FunctionalGraph[f, v] takes a set v and a function f from v to v and constructs a directed graph with vertex set v and edges (x, f[x]) for each x in v. FunctionalGraph[{f_1, ...

GraphIntersection[g_1, g_2, ...] constructs the graph defined by the edges that are in all the graphs g_1, g_2, ....

Graph[e, v, opts] represents a graph object where e is the list of edges annotated with graphics options, v is a list of vertices annotated with graphics options, and opts is ...