dorsal/arxiv
View SchemaResolution limit in community detection
| Authors | Santo Fortunato, Marc Barthelemy |
|---|---|
| Categories | |
| ArXiv ID | physics/0607100 |
| URL | https://arxiv.org/abs/physics/0607100 |
| DOI | 10.1073/pnas.0605965104 |
| Journal | Proc. Natl. Acad. Sci. USA 104 (1), 36-41 (2007) |
Abstract
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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"abstract": "Detecting community structure is fundamental to clarify the link between\nstructure and function in complex networks and is used for practical\napplications in many disciplines. A successful method relies on the\noptimization of a quantity called modularity [Newman and Girvan, Phys. Rev. E\n69, 026113 (2004)], which is a quality index of a partition of a network into\ncommunities. We find that modularity optimization may fail to identify modules\nsmaller than a scale which depends on the total number L of links of the\nnetwork and on the degree of interconnectedness of the modules, even in cases\nwhere modules are unambiguously defined. The probability that a module conceals\nwell-defined substructures is the highest if the number of links internal to\nthe module is of the order of \\sqrt{2L} or smaller. We discuss the practical\nconsequences of this result by analyzing partitions obtained through modularity\noptimization in artificial and real networks.",
"arxiv_id": "physics/0607100",
"authors": [
"Santo Fortunato",
"Marc Barthelemy"
],
"categories": [
"physics.soc-ph",
"cond-mat.dis-nn"
],
"doi": "10.1073/pnas.0605965104",
"journal_ref": "Proc. Natl. Acad. Sci. USA 104 (1), 36-41 (2007)",
"title": "Resolution limit in community detection",
"url": "https://arxiv.org/abs/physics/0607100"
},
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