Out-degree

In graph theory, the out-degree ^[1][2] of a vertex $v$ in a directed graph $G$ is the number of directed edges with $v$ as tail. Its counterpart is the in-degree, the number of directed edges with $v$ as head.

Definition

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Definition 1 (Out-degree)

Let $G=(V,E)$ be a directed graph and $v\in V$ a vertex. The out-degree ${\mathrm{deg}}^{+}(v)$ of $v$ is

$${\mathrm{deg}}^{+}(v):=|\{u\in V:(v,u)\in E\}|$$

the number of directed edges in $E$ with $v$ as tail.

Notation

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The out-degree of $v$ is denoted ${\mathrm{deg}}^{+}(v)$.

References

1. [1]

   “Indegree and outdegree”, Wikipedia, Available: https://en.wikipedia.org/wiki/Directed_graph#Indegree_and_outdegree, Accessed: 2026-07-31 ↩

2. [2]

   “Outdegree”, Wolfram MathWorld, Available: https://mathworld.wolfram.com/Outdegree.html, Accessed: 2026-08-28 ↩