Directed graph

Let $V$ be a set of vertices and let $E \subset V \times V$ be a set of edges. 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 or disallow self-loops. Additionally, some definitions allow multiple edges between the same pair of vertices, which leads to more formal definitions such as multigraphs.

# Directed graph