--- ## Definition > [!tldr] Definition > In a [[Directed graph|digraph]] $G$, the **out-degree** of a vertex $v$ is the number of edges for which $v$ is the head. The **in-degree** of a vertex $v$ is the number of edges for which $v$ is the tail. We use $d_G^+(v)$ to denote the out-degree and $d_G^-(v)$ to denote the in-degree. Notes: - If $v$ is the head and tail of a loop, then the loop contributes 1 to both the in- and out-degrees of $v$. ## Examples and Non-Examples Consider the digraph below: ![[digraph-example.png|400]] The in- and out-degrees are as follows: | $v$ | In-degree $d_G^-(v)$ | Out-degree $d_G^+(v)$ | | :-: | -------------------- | --------------------- | | 1 | 1 | 1 | | 2 | 0 | 3 | | 3 | 3 | 0 | | 4 | 0 | 1 | | 5 | 1 | 0 | ## Resources