EquivalenceRelationQ[r] yields True if the matrix r defines an equivalence relation. EquivalenceRelationQ[g] tests whether the adjacency matrix of graph g defines an ...

EulerianCycle[g] finds an Eulerian cycle of g if one exists.

Eulerian[n, k] gives the number of permutations of length n with k runs.

EulerianQ[g] yields True if graph g is Eulerian, meaning there exists a tour that includes each edge exactly once.

ExactRandomGraph[n, e] constructs a random labeled graph of exactly e edges and n vertices.

ExtractCycles[g] gives a maximal list of edge-disjoint cycles in graph g.

FerrersDiagram[p] draws a Ferrers diagram of integer partition p.

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

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

FiniteGraphs produces a convenient list of all the interesting, finite, parameterless graphs built into Combinatorica.