Resolution limit in community detection
- Santo Fortunato † , ‡ , § and
- Marc Barthélemy † , ¶ , ‖
+ Author Affiliations
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Edited by David O. Siegmund, Stanford University, Stanford, CA, and approved November 6, 2006 (received for review July 17, 2006)
Abstract
Detecting community structure is fundamental for uncovering the links between structure and function in complex networks and for practical applications in many disciplines such as biology and sociology. A popular method now widely used relies on the optimization of a quantity called modularity, which is a quality index for a partition of a network into communities. We find that modularity optimization may fail to identify modules smaller than a scale which depends on the total size of the network and on the degree of interconnectedness of the modules, even in cases where modules are unambiguously defined. This finding is confirmed through several examples, both in artificial and in real social, biological, and technological networks, where we show that modularity optimization indeed does not resolve a large number of modules. A check of the modules obtained through modularity optimization is thus necessary, and we provide here key elements for the assessment of the reliability of this community detection method.
Footnotes
- ‖To whom correspondence should be addressed. E-mail: marc.barthelemy@cea.fr
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Author contributions: S.F. and M.B. designed research, performed research, analyzed data, and wrote the paper.
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The authors declare no conflict of interest.
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This article is a PNAS direct submission.
- © 2006 by The National Academy of Sciences of the USA
