Definition:Directed Graph

Definition
A directed graph or digraph is a graph each of whose edges has a direction:



In the above graph, the vertices are $v_1, v_2, v_3$ and $v_4$.

Arc
In the above graph, the arcs are $v_1 v_2, v_2 v_4, v_4 v_3, v_4 v_1$ and $v_1 v_4$.

As can be seen, in this general definition it is allowable for an arc to go in both directions between a given pair of vertices.