The neighbourhood N_G(v) of a vertex v of a graph G consists of those vertices which are adjacent to v. For a subset W of the vertex set, N_G(W) consists of those vertices which are adjacent to some vertex in W.

On the real line, a neighbourhood of the real number a is a subset which contains an open interval (a−δ‎, a + δ‎) for some δ‎ > 0.

In a Euclidean space or metric space, a neighbourhood of a point is a subset which contains an open ball centred at the point. More generally, in a topological space, a neighbourhood of a point is a subset which contains an open set which includes the point.