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

RegularQ[g] yields True if g is a regular graph.

RemoveMultipleEdges[g] returns the graph obtained by deleting multiple edges from g.

RemoveSelfLoops[g] returns the graph obtained by deleting self-loops in g.

RevealCycles[p] unveils the canonical hidden cycle structure of permutation p.

ReverseEdges[g] flips the directions of all edges in a directed graph.

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

Runs[p] partitions p into contiguous increasing subsequences.

SelfLoopsQ[g] yields True if graph g has self-loops.

SignaturePermutation[p] gives the signature of permutation p.