OddGraph[n] returns the graph whose vertices are the size-(n - 1) subsets of a size-(2 nTraditionalForm\`\[Dash]1) set and whose edges connect pairs of vertices that ...

PetersenGraph returns the Petersen graph, a graph whose vertices can be viewed as the size-2 subsets of a size-5 set with edges connecting disjoint subsets.

ThomassenGraph returns a hypotraceable graph, a graph G that has no Hamiltonian path but whose subgraph G - v for every vertex v has a Hamiltonian path.

Turan[n, p] constructs the Turán graph, the extremal graph on n vertices that does not contain CompleteGraph[p].

LinkRankMatrix[g] returns the link rank of the graph g, in the form of a sparse matrix. The link rank of an edge u -> v is defined as the PageRanks of u, divided by the ...

EdgeCoverQ[g, elist] yields True if the edge list elist is an edge cover of the graph g and False otherwise.

FindEulerianCycle[g] finds an Eulerian cycle in the graph g if one exists.FindEulerianCycle[g, k] finds at most k Eulerian cycles.

ClosenessCentrality[g] gives a list of closeness centralities for the vertices in the graph g.

Equivalences[g, h] lists the vertex equivalence classes between graphs g and h defined by their vertex degrees. Equivalences[g] lists the vertex equivalences for graph g ...

MaximalIndependentVertexSet[g] gives a maximal independent vertex set of an undirected graph g.MaximalIndependentVertexSet[g, w] gives a maximal independent vertex set of g ...