dorsal/arxiv
View SchemaMaximizing Modularity is hard
| Authors | U. Brandes, D. Delling, M. Gaertler, R. Goerke, M. Hoefer, Z. Nikoloski, D. Wagner |
|---|---|
| Categories | |
| ArXiv ID | physics/0608255 |
| URL | https://arxiv.org/abs/physics/0608255 |
Abstract
Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to emphasize the plausibility of results, none of these algorithms has been shown to actually compute optimal partitions. We here settle the unknown complexity status of modularity maximization by showing that the corresponding decision version is NP-complete in the strong sense. As a consequence, any efficient, i.e. polynomial-time, algorithm is only heuristic and yields suboptimal partitions on many instances.
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"date_created": "2026-03-02T18:01:11.463000Z",
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"abstract": "Several algorithms have been proposed to compute partitions of networks into\ncommunities that score high on a graph clustering index called modularity.\nWhile publications on these algorithms typically contain experimental\nevaluations to emphasize the plausibility of results, none of these algorithms\nhas been shown to actually compute optimal partitions. We here settle the\nunknown complexity status of modularity maximization by showing that the\ncorresponding decision version is NP-complete in the strong sense. As a\nconsequence, any efficient, i.e. polynomial-time, algorithm is only heuristic\nand yields suboptimal partitions on many instances.",
"arxiv_id": "physics/0608255",
"authors": [
"U. Brandes",
"D. Delling",
"M. Gaertler",
"R. Goerke",
"M. Hoefer",
"Z. Nikoloski",
"D. Wagner"
],
"categories": [
"physics.data-an",
"cond-mat.stat-mech",
"physics.soc-ph"
],
"title": "Maximizing Modularity is hard",
"url": "https://arxiv.org/abs/physics/0608255"
},
"schema_id": "dorsal/arxiv",
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"type": "Model",
"variant": "snapshot-2026-03-01",
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