BUILT-IN MATHEMATICA SYMBOL

NeighborhoodGraph

NeighborhoodGraph[g, v]
gives the graph neighborhood of a vertex v in the graph g.

NeighborhoodGraph[g, {a₁, a₂, ...}]
gives the graph neighborhood of the that can be vertices, edges, or subgraphs of g.

NeighborhoodGraph[g, patt]
gives the graph neighborhood of the vertices and edges that match the pattern patt.

NeighborhoodGraph[g, ..., d]
gives the neighborhood up to distance d.

Details and Options Details and Options

The neighborhood graph for a vertex v is given by vertices adjacent to v and the edges connecting them.
The neighborhood graph for an edge e is the neighborhood graph for the vertices of e.
The neighborhood graph for a subgraph h is the neighborhood graph for the vertices in h.
The neighborhood graph at distance d is the neighborhood graph for the vertices of the neighborhood graph at distance d-1.
The default value for d is .