Digraphs

Digraphs (Directed Graphs)

Definition: A Digraph (or directed graph) $D$ is a type of graph containing a set of vertices, and a set of arcs (or directed edges), where each arc joins two vertices in a specific direction. $V(D)$ is a set containing elements known as Vertices, while $E(D) \subseteq (V x V)$ such that $V x V = \left\{(a, b) : a, b \in V \right\}$ is the set where the elements are ordered pairs called Arcs.

For example, let's look at the following directed graph. Arrows on the arcs indicate the direction of the arc:

This digraph contains $4$ vertices and $4$ arcs.