\begin{definition}[Definition:Directed Graph/Formal Definition]
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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:
:$D = \struct {V, E}:$
::$V = \set {v_1, v_2, v_3, v_4}$
::$E = \set {\tuple {v_1, v_2}, \tuple {v_2, v_4}, \tuple {v_4, v_3}, \tuple {v_4, v_1}, \tuple {v_1, v_4} }$
\end{definition}