Eccentricity[g] gives the eccentricity of each vertex v of graph g, the maximum length among all shortest paths from v.

EdgeConnectivity[g] gives the minimum number of edges whose deletion from graph g disconnects it. EdgeConnectivity[g, Cut] gives a set of edges of minimum size whose deletion ...

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.

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

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

FromCycles[{c_1, c_2, ...}] gives the permutation that has the given cycle structure.

Girth[g] gives the length of a shortest cycle in a simple graph g.

GraphOptions[g] returns the display options associated with g. GraphOptions[g, v] returns the display options associated with vertex v in g. GraphOptions[g, {u, v}] returns ...

GraphUnion[g_1, g_2, ...] constructs the union of graphs g_1, g_2, and so forth. GraphUnion[n, g] constructs n copies of graph g, for any nonnegative integer n.

GreedyVertexCover[g] returns a vertex cover of graph g constructed using the greedy algorithm. This is a natural heuristic for constructing a vertex cover, but it can produce ...