Definition:Neighborhood (Graph Theory)

Definition
Let $G = \left({V, E}\right)$ be a graph.

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

The neighborhood of $v$ in $G$ is:


 * $\Gamma_G \left({v}\right) = \left\{{u \in V : u v \in E}\right\}$

That is, it is the set of all vertices which are adjacent to $v$.

Linguistic Note
The UK English spelling of this is neighbourhood.