Definition:Degree (Vertex)

Definition
Let $G = \struct {V, E}$ be an undirected graph.

Let $v \in V$ be a vertex of $G$.

The degree of $v$ in $G$ is the number of edges to which it is incident.

It is denoted $\map {\deg_G} v$, or just $\map \deg v$ if it is clear from the context which graph is being referred to.

That is:
 * $\map {\deg_G} v = \card {\set {u \in V : \set {u, v} \in E} }$

Also see

 * Out-Degree and In-Degree in the context of directed graphs.