Definition 1.1.6.1. 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.