FindCycle[g] finds a list of vertices that define a cycle in graph g.

Girth[g] gives the length of a shortest cycle in a simple graph g.

GraphPower[g, k] gives the k\[Null]^th power of graph g. This is the graph whose vertex set is identical to the vertex set of g and that contains an edge between vertices i ...

HamiltonianCycle[g] finds a Hamiltonian cycle in graph g if one exists. HamiltonianCycle[g, All] gives all Hamiltonian cycles of graph g.

KSubsetGroupIndex[g, s, x] returns the cycle index of the k-subset group on s expressed as a polynomial in x[1], x[2], .... This function also takes the optional argument ...

M[g] gives the number of edges in the graph g. M[g, Directed] is obsolete because M[g] works for directed as well as undirected graphs.

Neighborhood[g, v, k] returns the subset of vertices in g that are at a distance of k or less from vertex v. Neighborhood[al, v, k] behaves identically, except that it takes ...

NextBinarySubset[l, s] constructs the subset of l following subset s in the order obtained by interpreting subsets as binary string representations of integers.

NonLineGraphs returns a graph whose connected components are the 9 graphs whose presence as a vertex-induced subgraph in a graph g makes g a nonline graph.

NthPair[n] returns the n\[Null]^th unordered pair of distinct positive integers, when sequenced to minimize the size of the larger integer. Pairs that have the same larger ...