graphs are automatically symmetric, by definition.

A {{mvar-arc}} is defined to be a sequence of vertices, such that any two consecutive vertices in the sequence are adjacent, and with any repeated vertices being more than 2 steps apart. A {{mvar-transitive}} graph is a graph such that the automorphism group acts transitively on {{mvar-arcs}}, but not on ({{math + 1}})-arcs}}. Since 1-arcs are simply edges, every symmetric graph of degree 3 or more must be {{mvar-transitive}} for some , and the