Graph Neighborhood

The graph neighborhood of a graph vertex is terminology whose convention must be specified. The open graph neighborhood consists of the vertices adjacent to , excluding itself. The closed neighborhood also includes . Some sources use "graph neighborhood" specifically for , while others use "neighborhood" for .

More generally, the th neighborhood of is the set of all vertices at graph distance from .

The subgraph induced by the neighborhood of a graph from vertex is called the neighborhood graph.

The term "graph neighbors" generally means vertices adjacent to excluding itself (Brouwer et al. 1989).