gives the graph neighborhood of a vertex v in the graph g.
gives the graph neighborhood of the ai that can be vertices, edges, or subgraphs of g.
gives the graph neighborhood of the vertices and edges that match the pattern patt.
gives the neighborhood up to distance d.
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.
Examplesopen allclose all
Basic Examples (2)
NeighborhoodGraph works with undirected graphs:
NeighborhoodGraph works with vertices:
Use rules to specify the graph:
Use patterns to specify a set of vertices:
NeighborhoodGraph works with large graphs:
Highlight the neighborhood from the vertices in CompleteGraph:
Properties & Relations (2)
Use Subgraph to find the neighborhood graph of a set of vertices:
The neighborhood of a vertex in a complete graph is the graph itself:
Wolfram Research (2010), NeighborhoodGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/NeighborhoodGraph.html (updated 2015).
Wolfram Language. 2010. "NeighborhoodGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/NeighborhoodGraph.html.
Wolfram Language. (2010). NeighborhoodGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NeighborhoodGraph.html