GeneralizedPetersenGraph[n, k] returns the generalized Petersen graph, for integers n > 1 and k > 0, which is the graph with vertices {u_1, u_2, ..., u_n} and {v_1, v_2, ..., ...

GraphRadius[g] gives the minimum eccentricity of the vertices in the graph g.

VertexEccentricity[g, s] gives the length of the longest shortest path from the source s to every other vertex in the graph g.

Contract[g, {x, y}] gives the graph resulting from contracting the pair of vertices {x, y} of graph g.

MakeSimple[g] gives the undirected graph, free of multiple edges and self-loops derived from graph g.

RegularGraph[k, n] constructs a semirandom k-regular graph on n vertices, if such a graph exists.

RobertsonGraph returns a 19-vertex graph that is the unique (4, 5)-cage graph.

TutteGraph returns the Tutte graph, the first known example of a 3-connected, 3-regular, planar graph that is non-Hamiltonian.

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 ...

PetersenGraph[n, k] gives the generalized Petersen graph P n, k.