# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE 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.

NeighborhoodGraph[{vw,},]
uses rules to specify the graph g.

## Details and OptionsDetails 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 .
• NeighborhoodGraph works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

Give the neighborhood from vertex 1 in a graph:

 Out[1]=
 Out[2]=

From a set of vertices:

 Out[3]=

Give the neighborhood up to distance k from the vertices:

 Out[1]=
 Out[2]=