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CommunityModularity[g,partition]

gives the community modularity of a partition.

CommunityModularity[g,assignment]

gives the community modularity of an assignment.

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`

CommunityModularity

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

CommunityModularity[g,partition]

gives the community modularity of a partition.

CommunityModularity[g,assignment]

gives the community modularity of an assignment.

Details and Options

  • CommunityModularity functionality is now available in the built-in Wolfram Language function GraphAssortativity.
  • To use CommunityModularity, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
  • A community in a network is a group of vertices such that there is a higher density of edges within the group than between them.
  • Given a graph , let the vertex set be partitioned into subsets such that each subset belongs to one community. The community modularity of this partition is defined as , where is the percentage of edges that have both ends in community , and is the percentage of edges that start from community . In other words, and .
  • The community modularity is a number less than or equal to 1. A large positive value indicates that the vertex partition gives significant community structure.
  • 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 = {1 -> 2, 2 -> 3, 3 -> 1, 3 -> 4, 4 -> 5, 5 -> 6, 6 -> 4};
Wolfram Language code: GraphPlot[g, VertexLabeling -> True]

This gives the community modularity, assuming a partition {{1,2,3},{4,5,6}}:

Wolfram Language code: CommunityModularity[g, {{1, 2, 3}, {4, 5, 6}}]

CommunityModularity has been superseded by GraphAssortativity:

Wolfram Language code: g = Graph[{1 -> 2, 2 -> 3, 3 -> 1, 3 -> 4, 4 -> 5, 5 -> 6, 6 -> 4}]
Wolfram Language code: N[GraphAssortativity[g, {{1, 2, 3}, {4, 5, 6}}, "Normalized" -> False]]

Options  (1)

Weighted  (1)

This defines a graph with edge weights:

Wolfram Language code: Needs["GraphUtilities`"]
Wolfram Language code: m = {{0, 1, 0, 10}, {1, 0, 0, 0}, {0, 0, 0, 1}, {10, 0, 1, 0}};
Wolfram Language code: GraphPlot[m, VertexLabeling -> True, EdgeRenderingFunction -> ({Line[#], Text[m[[First[#4], Last[#4]]], LineScaledCoordinate[#], Background -> White]}&)]

The community modularity of partition {{1,2},{3,4}}, ignoring edge weights:

Wolfram Language code: CommunityModularity[m, {{1, 2}, {3, 4}}]

The community modularity of partition {{1,2},{3,4}}, taking into account edge weights:

Wolfram Language code: CommunityModularity[m, {{1, 2}, {3, 4}}, Weighted -> True]

When taking into account edge weights, partition {{1,4},{2,3}} has higher community modularity:

Wolfram Language code: CommunityModularity[m, {{1, 4}, {2, 3}}, Weighted -> True]
Wolfram Research (2007), CommunityModularity, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/CommunityModularity.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_communitymodularity, author="Wolfram Research", title="{CommunityModularity}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/CommunityModularity.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_communitymodularity, organization={Wolfram Research}, title={CommunityModularity}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/CommunityModularity.html}, note=[Accessed: 13-June-2026]}