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CommunityStructureAssignment[g]

gives the assignment of vertices of a graph g into communities.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Options  
Weighted  
See Also
Tech Notes
Related Guides
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GraphUtilities`
GraphUtilities`

CommunityStructureAssignment

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

CommunityStructureAssignment[g]

gives the assignment of vertices of a graph g into communities.

Details and Options

  • CommunityStructureAssignment functionality is now available in the built-in Wolfram Language function FindGraphCommunities.
  • To use CommunityStructureAssignment, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
  • The assignment groups the vertices into communities, such that there is a higher density of edges within communities than between them.
  • The following option can be given:
  • Weighted Falsewhether edges with higher weights are preferred during matching

Examples

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Basic Examples  (2)

This defines a small graph:

Wolfram Language code: Needs["GraphUtilities`"]
Wolfram Language code: g = {3 -> 2, 2 -> 1, 1 -> 3, 3 -> 5, 5 -> 6, 6 -> 7, 7 -> 5}; GraphPlot[g, VertexLabeling -> True]

This finds that the network is grouped into two communities:

Wolfram Language code: CommunityStructureAssignment[g]

CommunityStructureAssignment has been superseded by FindGraphCommunities:

Wolfram Language code: g = Graph[{3 -> 2, 2 -> 1, 1 -> 3, 3 -> 5, 5 -> 6, 6 -> 7, 7 -> 5}]
Wolfram Language code: FindGraphCommunities[g]
Wolfram Language code: Map[Position[%, #, {2}, 1][[1, 1]]&, VertexList[g]]

Options  (1)

Weighted  (1)

This specifies a weighted graph:

Wolfram Language code: Needs["GraphUtilities`"]
Wolfram Language code: g = SparseArray[{{1, 2} -> 10, {2, 1} -> 10, {2, 3} -> 1, {3, 2} -> 1, {3, 1} -> 1, {1, 3} -> 1, {3, 5} -> 10, {5, 3} -> 10, {5, 6} -> 1, {6, 5} -> 1, {6, 4} -> 10, {4, 6} -> 10, {5, 4} -> 1, {4, 5} -> 1}, {6, 6}]

This plots the graph with edge weights shown:

Wolfram Language code: GraphPlot[g, VertexLabeling -> True, EdgeRenderingFunction -> ({Line[#1], Text[g[[First[#4], Last[#4]]], LineScaledCoordinate[#1], Background -> White]}&)]

This finds the community structure, ignoring edge weights:

Wolfram Language code: cs = CommunityStructureAssignment[g]

This plots the graph, coloring the vertices based on community assignment:

Wolfram Language code: GraphPlot[g, EdgeRenderingFunction -> ({Line[#1], Text[g[[First[#4], Last[#4]]], LineScaledCoordinate[#1], Background -> White]}&), VertexRenderingFunction -> ({Text[Framed[#2, Background -> Hue[cs[[#3]] / 4], FrameStyle -> RGBColor[0.94, 0.85, 0.36]], #1]}&)]

This finds the community structure, taking into account the edge weights:

Wolfram Language code: cs = CommunityStructureAssignment[g, Weighted -> True]

This plots the graph, coloring the vertices based on community assignment:

Wolfram Language code: GraphPlot[g, EdgeRenderingFunction -> ({Line[#1], Text[g[[First[#4], Last[#4]]], LineScaledCoordinate[#1], Background -> White]}&), VertexRenderingFunction -> ({Text[Framed[#2, Background -> Hue[cs[[#3]] / 4], FrameStyle -> RGBColor[0.94, 0.85, 0.36]], #1]}&)]
Wolfram Research (2007), CommunityStructureAssignment, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/CommunityStructureAssignment.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_communitystructureassignment, author="Wolfram Research", title="{CommunityStructureAssignment}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/CommunityStructureAssignment.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_communitystructureassignment, organization={Wolfram Research}, title={CommunityStructureAssignment}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/CommunityStructureAssignment.html}, note=[Accessed: 13-June-2026]}