Which terms are used for the digraph of the edges of a digraph?

Question

For any digraph $G = (V,E)$, consider the digraph $H = (E,F)$ with $F = \{ee' \in E \times E\ |\ \exists u,v,w \in V: e = uv \wedge e' = vw\}$, that is, the digraph $H$ whose nodes are the edges of the digraph $G$ and whose edges connect any two edges of $G$ which, together, form a directed path.

Which term is used in the literature for the digraph $H$ wrt. the digraph $G$?

Answer 1

For undirected graphs this is called the line graph. In the link there is a short section on the line digraph.