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.

Spectrum[g] gives the eigenvalues of graph g.

SpringEmbedding[g] beautifies the embedding of graph g by modeling the embedding as a system of springs. SpringEmbedding[g, step, increment] can be used to refine the ...

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

StirlingSecond[n, k] returns the Stirling number of the second kind.

Strings[l, n] constructs all possible combinatorial strings of length n from the elements of list l.

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

Strong is an option to ConnectedQ that seeks to determine if a directed graph is strongly connected.