Directed graph - Alex's public notes

Directed graph

Let $V$ be a set of vertices and let $E \subset V \times V$ an edge $e = (x,y)$ is a directed edge from $x \in V$ to $y \in V$. The directed graph is the pair $(V,E)$.

This is similar to a graph but the edges now have a direction. Depending on the definition you can allow loops or disallow them. Also some may allow repeated edges where you can switch to a more formal definition of a directed graph.