WOLFRAM

Wolfram Language & System Documentation Center

FindGraphCommunities[g]

finds communities in the graph g.

FindGraphCommunities[{vw,…}]

uses rules vw to specify the graph g.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
Method  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

FindGraphCommunities

FindGraphCommunities[g]

finds communities in the graph g.

FindGraphCommunities[{vw,…}]

uses rules vw to specify the graph g.

Details and Options

  • FindGraphCommunities finds communities with many edges joining vertices of the same community and comparatively few edges joining vertices of different communities.
  • FindGraphCommunities returns a list of communities {c1,c2,…}, where each community ci is a list of vertices.
  • The communities are ordered by their length, with the largest community first.
  • FindGraphCommunities supports a Method option that specifies the detailed method to use.
  • Possible settings for the Method option include:
  • "Modularity"modularity-based clustering
    "Centrality"centrality-based clustering
    "CliquePercolation"clique percolation-based clustering
    "Hierarchical"hierarchical-based clustering
    "Spectral"spectral-based clustering
  • FindGraphCommunities works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.

Examples

open all close all

Basic Examples  (2)

Find communities in a graph:

Wolfram Language code: g = Graph[{12, 23, 13, 34, 45, 76, 86, 57, 78}]
Wolfram Language code: FindGraphCommunities[g]

Highlight the communities:

Wolfram Language code: HighlightGraph[g, Map[Subgraph[g, #]&, %]]

Visualize communities:

Wolfram Language code: RandomGraph[WattsStrogatzGraphDistribution[30, 0.3, 3]]
Wolfram Language code: CommunityGraphPlot[%, FindGraphCommunities[%]]

Scope  (7)

FindGraphCommunities works with undirected graphs:

Wolfram Language code: FindGraphCommunities[[image]]

Directed graphs:

Wolfram Language code: FindGraphCommunities[[image]]

Weighted graphs:

Wolfram Language code: FindGraphCommunities[[image]]

Multigraphs:

Wolfram Language code: FindGraphCommunities[[image]]

Mixed graphs:

Wolfram Language code: FindGraphCommunities[[image]]

Use rules to specify the graph:

Wolfram Language code: FindGraphCommunities[{1 -> 2, 1 -> 3, 2 -> 4, 3 -> 4, 3 -> 5, 4 -> 6, 5 -> 6, 5 -> 7, 6 -> 8, 7 -> 8}]

FindGraphCommunities works with large graphs:

Wolfram Language code: g = RandomGraph[WattsStrogatzGraphDistribution[10 ^ 4, 0.25, 5]];
Wolfram Language code: Timing[Length[FindGraphCommunities[g]]]

Options  (6)

Method  (6)

By default, FindGraphCommunities uses modularity maximization methods:

Wolfram Language code: FindGraphCommunities[[image]]

This can also be obtained with Method->"Modularity":

Wolfram Language code: FindGraphCommunities[[image], Method -> "Modularity"]

Use Method->"Hierarchical" for hierarchical clustering based on vertex similarity:

Wolfram Language code: FindGraphCommunities[[image], Method -> "Hierarchical"]

Use Method->"Spectral" for spectral partitioning:

Wolfram Language code: FindGraphCommunities[[image], Method -> "Spectral"]

Use Method->"Centrality" for partitioning based on edge centrality:

Wolfram Language code: FindGraphCommunities[[image], Method -> "Centrality"]

Use Method->"CliquePercolation" for k-clique percolation:

Wolfram Language code: FindGraphCommunities[[image], Method -> "CliquePercolation"]

Use Method->"VertexMoving" to improve the result obtained by default:

Wolfram Language code: g = GridGraph[{3, 7}]
Wolfram Language code: N[GraphAssortativity[g, FindGraphCommunities[g]]]
Wolfram Language code: N[GraphAssortativity[g, FindGraphCommunities[g, Method -> "VertexMoving"]]]

Applications  (2)

Find communities in a friendship network between members of a karate club:

Wolfram Language code: g = ExampleData[{"NetworkGraph", "ZacharyKarateClub"}];
Wolfram Language code: FindGraphCommunities[g, Method -> "Hierarchical"]

Predict the split of the network in case of an internal conflict:

Wolfram Language code: HighlightGraph[g, Subgraph[g, #]& /@ %, GraphHighlightStyle -> "DehighlightHide"]

A weighted network of wins in the National Hockey League during regular season 2010–2011. Group teams by conferences:

Wolfram Language code: g = ExampleData[{"NetworkGraph", "NationalHockeyLeague"}];
Wolfram Language code: conferences = FindGraphCommunities[g]

Partition teams in six divisions:

Wolfram Language code: divisions = FindGraphPartition[g, 6]

Properties & Relations  (5)

Communities are ordered by their length, with the largest community first:

Wolfram Language code: g = RandomGraph[SpatialGraphDistribution[100, 0.15]];
Wolfram Language code: Length /@ FindGraphCommunities[g]

By default, FindGraphCommunities gives communities with high modularity:

Wolfram Language code: g = ExampleData[{"NetworkGraph", "ZacharyKarateClub"}];
Wolfram Language code: FindGraphCommunities[g]

Use GraphAssortativity to compute the modularity:

Wolfram Language code: N[GraphAssortativity[g, %, "Normalized" -> False]]

Use FindGraphPartition to find partitions of vertices into k parts of approximately equal size:

Wolfram Language code: g = RandomGraph[WattsStrogatzGraphDistribution[20, 0.1, 3]];
Wolfram Language code: FindGraphPartition[g, 3]

The size of communities in the Watts–Strogatz model:

Wolfram Language code: 𝒟[p_] := GraphPropertyDistribution[Length[FindGraphCommunities[g]], gWattsStrogatzGraphDistribution[1000, p]]
Wolfram Language code: ListPlot[Table[{p, RandomVariate[𝒟[p]]}, {p, 0, 1, 0.01}]]

In random spatial graphs:

Wolfram Language code: 𝒟[r_] := GraphPropertyDistribution[Length[FindGraphCommunities[g]], gSpatialGraphDistribution[100, r]]
Wolfram Language code: ListPlot[Table[{r, RandomVariate[𝒟[r]]}, {r, 0, 0.25, 0.001}]]

CommunityGraphPlot finds and visualizes communities:

Wolfram Language code: g = RandomGraph[WattsStrogatzGraphDistribution[30, 0.3, 3]];
Wolfram Language code: CommunityGraphPlot[g]

Specify communities:

Wolfram Language code: CommunityGraphPlot[g, FindGraphCommunities[g, Method -> "Spectral"]]
Wolfram Research (2012), FindGraphCommunities, Wolfram Language function, https://reference.wolfram.com/language/ref/FindGraphCommunities.html (updated 2015).

Text

Wolfram Research (2012), FindGraphCommunities, Wolfram Language function, https://reference.wolfram.com/language/ref/FindGraphCommunities.html (updated 2015).

CMS

Wolfram Language. 2012. "FindGraphCommunities." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/FindGraphCommunities.html.

APA

Wolfram Language. (2012). FindGraphCommunities. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindGraphCommunities.html

BibTeX

@misc{reference.wolfram_2026_findgraphcommunities, author="Wolfram Research", title="{FindGraphCommunities}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindGraphCommunities.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_findgraphcommunities, organization={Wolfram Research}, title={FindGraphCommunities}, year={2015}, url={https://reference.wolfram.com/language/ref/FindGraphCommunities.html}, note=[Accessed: 12-June-2026]}