\begin{definition}[Definition:Degree (Vertex)]
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:
:$\map {\deg_G} v = \card {\set {u \in V : \set {u, v} \in E} }$
\end{definition}