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 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 .

## ExamplesExamplesopen allclose all

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

Give the neighborhood from vertex 1 in a graph:

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From a set of vertices:

 Out[3]=

Give the neighborhood up to distance k from the vertices:

 Out[1]=
 Out[2]=