Definition:Neighborhood (Graph Theory)

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This page is about Neighborhood in the context of Graph Theory. For other uses, see Neighborhood.


Let $G = \struct {V, E}$ be a graph.

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

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

$\map {\Gamma_G} v = \set {u \in V : u v \in E}$

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


Neighborhood is translated:

In Dutch: nabuurschap
In French: voisinage

Linguistic Note

The UK English spelling of neighborhood is neighbourhood.