BUILT-IN MATHEMATICA SYMBOL

NeighborhoodGraph

gives the graph neighborhood vertex v in the graph g.

NeighborhoodGraph

gives the graph neighborhood of the

that can be vertices, edges, or subgraphs of g.

NeighborhoodGraph

gives the graph neighborhood of the vertices and edges that match the pattern patt.

NeighborhoodGraph

gives the neighborhood up to distance k.

MORE INFORMATION

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 k is the neighborhood graph for the vertices of the neighborhood graph at distance k-1.

The default value for k is .

EXAMPLES

CLOSE 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:

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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Scope (5)

NeighborhoodGraph works with undirected graphs:

Directed graphs:

NeighborhoodGraph works with vertices:

Edges:

Use patterns to specify a set of vertices:

Works with large graphs:

Applications (2)

Highlight the neighborhood from the vertices in CompleteGraph:

Manipulate the neighborhood of vertices:

Properties & Relations (1)

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: