Edge is an optional argument to inform certain functions to work with edges instead of vertices.

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

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

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.

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.

FruchtGraph returns the smallest 3-regular graph whose automorphism group consists of only the identity.

GraphComplement[g] gives the complement of graph g.