Neighbourhood (graph theory)

In graph theory, the neighbourhood of a vertex v in a graph G is the subgraph of G induced by all the vertices that are connected to v by an edge (vertices that are adjacent to v), i.e., the graph composed of all the vertices adjacent to v and all the edges connecting them. The neighbourhood is often denoted by ⁠ N G ( v ) {\displaystyle N_{G}(v)} ⁠ or (when the graph is unambiguous) ⁠ N ( v ) {\displaystyle N(v)} ⁠.

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