Definition:Directed Graph/Simple Digraph

Definition
Let $D = \struct {V, E}$ be a digraph. If the relation $E$ in $D$ is also specifically asymmetric, then $D$ is called a simple digraph.

That is, in a simple digraph there are no pairs of arcs (like there are between $v_1$ and $v_4$ in the diagram above) which go in both directions between two vertices.