# Ambigous line graph definition

While reading the openbook "Algorithmic Graph Theory " I came by Definition 1.7 which is supposed to define what a line graph is , here is the definition:

Definition 1.7. Let $G=(V,E,h)$ be an unweighted multidigraph.The line graph of $G$ , denoted $\mathcal{L}(G)$, is the multidigraph whose vertices are the edges of $G$ and whose edges are $(e,e')$ where $h(e)=t(e')($for $e, e' \in E)$.A similar definition holds if $G$ is undirected.

The above did not make any sense to me especially the whose vertices are edges of $G$

could anyone please clear up this definition?

• As a start, to define $\mathcal L(G)$, the required datafor a graph must be specified. Among these is a set of vertices. We are allowed to take the set $E$ as this set. – Hagen von Eitzen Apr 3 '13 at 21:06
• $h(e)$ is the start vertex of an edge, and $t(e)$ its target ? – Vincent Nivoliers Apr 3 '13 at 21:09
• @HagenvonEitzen can a set of ordered pairs taken up as a set of vertices ? – metric-space Apr 3 '13 at 21:12
• @VincentNivoliers $t(e)$ refers to the tail ,$h(e)$ refers to the head. – metric-space Apr 3 '13 at 21:13