Definition:Neighborhood (Graph Theory)

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

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

Then the neighborhood of $v$ in $G$ is:


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

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

Linguistic Note
The UK English spelling of this is neighbourhood.