EquivalenceClasses[r] identifies the equivalence classes among the elements of matrix r.

FindSet[n, s] gives the root of the set containing n in union-find data structure s.

InitializeUnionFind[n] initializes a union-find data structure for n elements.

MaximumAntichain[g] gives a largest set of unrelated vertices in partial order g.

MinimumChainPartition[g] partitions partial-order g into a minimum number of chains.

MinimumVertexColoring[g] returns a minimum vertex coloring of g. MinimumVertexColoring[g, k] returns a k-coloring of g, if one exists.

MultipleEdgesQ[g] yields True if g has multiple edges between pairs of vertices. It yields False otherwise.

NumberOf2Paths[g, v] returns a sorted list that contains the number of paths of length 2 to different vertices of g from v.

UnionSet[a, b, s] merges the sets containing a and b in union-find data structure s.

UnweightedQ[g] yields True if all edge weights are 1 and False otherwise.