# 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 ai 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 vw to specify the graph g.

# 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 1.
• NeighborhoodGraph works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

# Examples

open allclose all

## Basic Examples(2)

Give the neighborhood from vertex 1 in a graph:

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From a set of vertices:

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Give the neighborhood up to distance k from the vertices:

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