Definition:Directed Graph/Formal Definition

Definition


A directed graph or digraph $D$ is a non-empty set $V$ together with an antireflexive relation $E$ on $V$.

The elements of $E$ are the arcs.

Thus the above digraph can be defined as:


 * $D = \struct {V, E}: V = \set {v_1, v_2, v_3, v_4}$
 * $E = \set {\tuple {v_1, v_2}, \tuple {v_2, v_4}, \tuple {v_4, v_3}, \tuple {v_4, v_1}, \tuple {v_1, v_4} }$