Resolution limit in community detection

Details Resolution limit in community detection Resolution limit in community detection

2006-07-11

arxiv.org/abs/physics/0607100v2

Proc. Natl. Acad. Sci. USA 104 (1), 36-41 (2007)

Physics

Physics and Society

8 pages, 3 figures. Clarification of definition of community in Section II + minor revisions

Scientific paper

10.1073/pnas.0605965104

Detecting community structure is fundamental to clarify the link between structure and function in complex networks and is used for practical applications in many disciplines. A successful method relies on the optimization of a quantity called modularity [Newman and Girvan, Phys. Rev. E 69, 026113 (2004)], which is a quality index of 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 number L of links of the network and on the degree of interconnectedness of the modules, even in cases where modules are unambiguously defined. The probability that a module conceals well-defined substructures is the highest if the number of links internal to the module is of the order of \sqrt{2L} or smaller. We discuss the practical consequences of this result by analyzing partitions obtained through modularity optimization in artificial and real networks.

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