Definition 1.1.5.1. A *directed graph* $G$ consists of the following data:

A set $\operatorname{Vert}(G)$, whose elements we refer to as

*vertices of $G$*.A set $\operatorname{Edge}(G)$, whose elements we refer to as

*edges of $G$*.A pair of functions $s,t: \operatorname{Edge}(G) \rightarrow \operatorname{Vert}(G)$ which assign to each edge $e \in \operatorname{Edge}(G)$ a pair of vertices $s(e)$, $t(e) \in \operatorname{Vert}(G)$ that we refer to as the

*source*and*target*of $e$, respectively.