EdgeDirection is an option that takes on values True or False allowing the user to specify whether the graph is directed or not. EdgeDirection can be set as part of the graph ...

EdgeLabelColor is an option that allows the user to associate different colors to edge labels. Black is the default color. EdgeLabelColor can be set as part of the graph data ...

EdgeLabel is an option that can take on values True or False, allowing the user to associate labels to edges. By default, there are no edge labels. The EdgeLabel option can ...

EdgeLabelPosition is an option that allows the user to place an edge label in a certain position relative to the midpoint of the edge. LowerLeft is the default value of this ...

EdgeStyle is an option that allows the user to associate different sizes and shapes to edges. A line segment is the default edge. EdgeStyle can be set as part of the graph ...

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.

Equivalences[g, h] lists the vertex equivalence classes between graphs g and h defined by their vertex degrees. Equivalences[g] lists the vertex equivalences for graph g ...

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

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