ShakeGraph[g, d] performs a random perturbation of the vertices of graph g, with each vertex moving, at most, a distance d from its original position.

SignaturePermutation[p] gives the signature of permutation p.

SimpleQ[g] yields True if g is a simple graph, meaning it has no multiple edges and contains no self-loops.

SmallestCyclicGroupGraph returns a smallest nontrivial graph whose automorphism group is cyclic.

StableMarriage[mpref, fpref] finds the male optimal stable marriage defined by lists of permutations describing male and female preferences.

StronglyConnectedComponents[g] gives the strongly connected components of directed graph g as lists of vertices.

SymmetricGroupIndex[n, x] returns the cycle index of the symmetric group on n symbols, expressed as a polynomial in x[1], x[2], ..., x[n].

TableauClasses[p] partitions the elements of permutation p into classes according to their initial columns during Young tableaux construction.

TableauQ[t] yields True if and only if t represents a Young tableau.

Tableaux[p] constructs all tableaux having a shape given by integer partition p.