EdgeWeight is an option that allows the user to associate weights with edges. 1 is the default weight. EdgeWeight can be set as part of the graph data structure.

EmptyGraph[n] generates an empty graph on n vertices. An option Type that can take on values Directed or Undirected is provided. The default setting is Type -> Undirected.

EmptyQ[g] yields True if graph g contains no edges.

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

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.