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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

open allclose all

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

This defines a small graph:

In[1]:=1
✖
https://wolfram.com/xid/0pj5t9ohsqwrubvd0lu-m5blrz
In[2]:=2
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https://wolfram.com/xid/0pj5t9ohsqwrubvd0lu-f4a055
Out[2]=2

This finds that the network is grouped into two communities:

In[3]:=3
✖
https://wolfram.com/xid/0pj5t9ohsqwrubvd0lu-inm3sf
Out[3]=3

CommunityStructureAssignment has been superseded by FindGraphCommunities:

In[1]:=1
✖
https://wolfram.com/xid/0pj5t9ohsqwrubvd0lu-qs9cop
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0pj5t9ohsqwrubvd0lu-bjx69d
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0pj5t9ohsqwrubvd0lu-twuj07
Out[3]=3

Options  (1)Common values & functionality for each option

Weighted  (1)

This specifies a weighted graph:

In[1]:=1
✖
https://wolfram.com/xid/0pj5t9ohsqwrubvd0lu-303bxx
In[2]:=2
✖
https://wolfram.com/xid/0pj5t9ohsqwrubvd0lu-24a4ho
Out[2]=2

This plots the graph with edge weights shown:

In[3]:=3
✖
https://wolfram.com/xid/0pj5t9ohsqwrubvd0lu-se9jnu
Out[3]=3

This finds the community structure, ignoring edge weights:

In[4]:=4
✖
https://wolfram.com/xid/0pj5t9ohsqwrubvd0lu-zgwqjl
Out[4]=4

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

In[5]:=5
✖
https://wolfram.com/xid/0pj5t9ohsqwrubvd0lu-d42605
Out[5]=5

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

In[6]:=6
✖
https://wolfram.com/xid/0pj5t9ohsqwrubvd0lu-ddncdx
Out[6]=6

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

In[7]:=7
✖
https://wolfram.com/xid/0pj5t9ohsqwrubvd0lu-gunbj5
Out[7]=7
Wolfram Research (2007), CommunityStructureAssignment, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/CommunityStructureAssignment.html.
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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.

✖
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.

✖
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

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

BibTeX

@misc{reference.wolfram_2025_communitystructureassignment, author="Wolfram Research", title="{CommunityStructureAssignment}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/CommunityStructureAssignment.html}", note=[Accessed: 04-April-2025 ]}

✖
@misc{reference.wolfram_2025_communitystructureassignment, author="Wolfram Research", title="{CommunityStructureAssignment}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/CommunityStructureAssignment.html}", note=[Accessed: 04-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_communitystructureassignment, organization={Wolfram Research}, title={CommunityStructureAssignment}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/CommunityStructureAssignment.html}, note=[Accessed: 04-April-2025 ]}

✖
@online{reference.wolfram_2025_communitystructureassignment, organization={Wolfram Research}, title={CommunityStructureAssignment}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/CommunityStructureAssignment.html}, note=[Accessed: 04-April-2025 ]}