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NeighborhoodVertices[g,i,r]

gives vertices that can be reached from vertex i within r hops.

NeighborhoodVertices[g,i]

gives vertices that can be reached from vertex i.

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Details and Options Details and Options
Examples  
Basic Examples  
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GraphUtilities`
GraphUtilities`

NeighborhoodVertices

As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System. »

NeighborhoodVertices[g,i,r]

gives vertices that can be reached from vertex i within r hops.

NeighborhoodVertices[g,i]

gives vertices that can be reached from vertex i.

Details and Options

  • NeighborhoodVertices functionality is now available in the built-in Wolfram Language function NeighborhoodGraph.
  • To use NeighborhoodVertices, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
  • NeighborhoodVertices returns the vertices that can be reached from a given vertex within certain hops.

Examples

Basic Examples  (2)

Wolfram Language code: Needs["GraphUtilities`"]

This defines a simple directed graph:

Wolfram Language code: g = {1 -> 2, 2 -> 3, 1 -> 3, 2 -> 4, 4 -> 5, 5 -> 6, 6 -> 4};
Wolfram Language code: GraphPlot[g, VertexLabeling -> True, DirectedEdges -> True]

This finds all vertices that can be reached from vertex 2 within 1 hop:

Wolfram Language code: NeighborhoodVertices[g, 2, 1]

This finds all vertices that can be reached from vertex 2:

Wolfram Language code: NeighborhoodVertices[g, 2]

NeighborhoodVertices has been superseded by NeighborhoodGraph:

Wolfram Language code: g = Graph[{1 -> 2, 2 -> 3, 1 -> 3, 2 -> 4, 4 -> 5, 5 -> 6, 6 -> 4}]
Wolfram Language code: VertexList[NeighborhoodGraph[g, 2, 1, DirectedEdges -> True]]
Wolfram Language code: VertexList[NeighborhoodGraph[g, 2, DirectedEdges -> True]]
Wolfram Research (2007), NeighborhoodVertices, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/NeighborhoodVertices.html.

Text

Wolfram Research (2007), NeighborhoodVertices, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/NeighborhoodVertices.html.

CMS

Wolfram Language. 2007. "NeighborhoodVertices." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/GraphUtilities/ref/NeighborhoodVertices.html.

APA

Wolfram Language. (2007). NeighborhoodVertices. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/GraphUtilities/ref/NeighborhoodVertices.html

BibTeX

@misc{reference.wolfram_2026_neighborhoodvertices, author="Wolfram Research", title="{NeighborhoodVertices}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/NeighborhoodVertices.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_neighborhoodvertices, organization={Wolfram Research}, title={NeighborhoodVertices}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/NeighborhoodVertices.html}, note=[Accessed: 13-June-2026]}