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FindGraphCommunities
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FindGraphCommunities

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finds communities in the graph g.

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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 allclose all

Basic Examples  (2)Summary of the most common use cases

Find communities in a graph:

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-1sby6
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0tp745bytirzzu-sismj8
Out[2]=2

Highlight the communities:

In[3]:=3
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https://wolfram.com/xid/0tp745bytirzzu-emyblc
Out[3]=3

Visualize communities:

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-k0xus1
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0tp745bytirzzu-xznnu2
Out[2]=2

Scope  (7)Survey of the scope of standard use cases

FindGraphCommunities works with undirected graphs:

In[3]:=3
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https://wolfram.com/xid/0tp745bytirzzu-ez8fmf
Out[3]=3

Directed graphs:

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-dpe04v
Out[1]=1

Weighted graphs:

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-uocid0
Out[1]=1

Multigraphs:

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-15kl6n
Out[1]=1

Mixed graphs:

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-czvddh
Out[1]=1

Use rules to specify the graph:

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-t96r7
Out[1]=1

FindGraphCommunities works with large graphs:

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-cddhqp
In[2]:=2
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https://wolfram.com/xid/0tp745bytirzzu-ozq2m5
Out[2]=2

Options  (6)Common values & functionality for each option

Method  (6)

By default, FindGraphCommunities uses modularity maximization methods:

In[18]:=18
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https://wolfram.com/xid/0tp745bytirzzu-9cy3t
Out[18]=18

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

In[19]:=19
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https://wolfram.com/xid/0tp745bytirzzu-jtdtac
Out[19]=19

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

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-k5uwhz
Out[1]=1

Use Method->"Spectral" for spectral partitioning:

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-3zhjc1
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-rm0kp5
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-ujpr77
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-047kxu
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0tp745bytirzzu-ns2gqf
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0tp745bytirzzu-u2pwpj
Out[3]=3

Applications  (2)Sample problems that can be solved with this function

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

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-uowy3o
In[2]:=2
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https://wolfram.com/xid/0tp745bytirzzu-vdn3wc
Out[2]=2

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

In[3]:=3
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https://wolfram.com/xid/0tp745bytirzzu-deykiq
Out[3]=3

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

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-bdkpsm
In[2]:=2
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https://wolfram.com/xid/0tp745bytirzzu-tphwdv
Out[2]=2

Partition teams in six divisions:

In[3]:=3
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https://wolfram.com/xid/0tp745bytirzzu-c0enfy
Out[3]=3

Properties & Relations  (5)Properties of the function, and connections to other functions

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

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-pmxx5l
In[2]:=2
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https://wolfram.com/xid/0tp745bytirzzu-38jxwz
Out[2]=2

By default, FindGraphCommunities gives communities with high modularity:

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-ne1mi7
In[2]:=2
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https://wolfram.com/xid/0tp745bytirzzu-e43ji3
Out[2]=2

Use GraphAssortativity to compute the modularity:

In[3]:=3
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https://wolfram.com/xid/0tp745bytirzzu-g0rf8d
Out[3]=3

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

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-pombu9
In[2]:=2
✖
https://wolfram.com/xid/0tp745bytirzzu-bpem8
Out[2]=2

The size of communities in the Watts–Strogatz model:

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-xarxvx
In[2]:=2
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https://wolfram.com/xid/0tp745bytirzzu-0edlcv
Out[2]=2

In random spatial graphs:

In[3]:=3
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https://wolfram.com/xid/0tp745bytirzzu-0nxaa0
In[4]:=4
✖
https://wolfram.com/xid/0tp745bytirzzu-f9stea
Out[4]=4

CommunityGraphPlot finds and visualizes communities:

In[1]:=1
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https://wolfram.com/xid/0tp745bytirzzu-irifvs
In[2]:=2
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https://wolfram.com/xid/0tp745bytirzzu-yl96db
Out[2]=2

Specify communities:

In[3]:=3
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https://wolfram.com/xid/0tp745bytirzzu-7f2wir
Out[3]=3
Wolfram Research (2012), FindGraphCommunities, Wolfram Language function, https://reference.wolfram.com/language/ref/FindGraphCommunities.html (updated 2015).
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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).

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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.

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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

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

BibTeX

@misc{reference.wolfram_2025_findgraphcommunities, author="Wolfram Research", title="{FindGraphCommunities}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindGraphCommunities.html}", note=[Accessed: 15-April-2025 ]}

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@misc{reference.wolfram_2025_findgraphcommunities, author="Wolfram Research", title="{FindGraphCommunities}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindGraphCommunities.html}", note=[Accessed: 15-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_findgraphcommunities, organization={Wolfram Research}, title={FindGraphCommunities}, year={2015}, url={https://reference.wolfram.com/language/ref/FindGraphCommunities.html}, note=[Accessed: 15-April-2025 ]}

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@online{reference.wolfram_2025_findgraphcommunities, organization={Wolfram Research}, title={FindGraphCommunities}, year={2015}, url={https://reference.wolfram.com/language/ref/FindGraphCommunities.html}, note=[Accessed: 15-April-2025 ]}