# 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:

From a set of vertices:

Give the neighborhood up to distance k from the vertices:

## Scope(8)

NeighborhoodGraph works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

NeighborhoodGraph works with vertices:

Edges:

Use rules to specify the graph:

Use patterns to specify a set of vertices:

NeighborhoodGraph works with large graphs:

## Applications(2)

Highlight the neighborhood from the vertices in CompleteGraph:

Manipulate the neighborhood of vertices:

## Properties & Relations(2)

Use Subgraph to find the neighborhood graph of a set of vertices:

Highlight the subgraph:

This is equivalent to:

The neighborhood of a vertex in a complete graph is the graph itself:

## Neat Examples(2)

Pick out random neighborhoods from a grid:

Subtract random neighborhoods from a grid:

Introduced in 2010
(8.0)
|
Updated in 2014
(10.0)
2015
(10.3)