Directed graph

Definition

A directed graph, or digraph, is a pair $D = (V, A)$ of a set $V$ and a relation $A \subseteq V \times V$. The elements of $V$ are the vertices of $D$. The elements of $A$ are the arcs, or directed edges, of $D$. An arc $(u, v)$ goes from its tail $u$ to its head $v$.

Remarks

With this definition a digraph can have loops $(v, v)$, and it has at most one arc from $u$ to $v$. Some authors exclude loops. A graph is the same as a digraph whose relation is symmetric and irreflexive. The out-degree of $v$ is the number of arcs with tail $v$, and the in-degree is the number of arcs with head $v$.

Explanations

L1 human

A directed graph is a graph whose lines are arrows. One-way streets between crossings form a directed graph.