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Performance of modularity maximization in practical contexts
Open accessAbstract
Although widely used in practice, the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts. Here, we present a broad characterization of its performance in such situations. First, we revisit and clarify the resolution limit phenomenon for modularity maximization. Second, we show that the modularity function Q exhibits extreme degeneracies: it typically admits an exponential number of distinct high-scoring solutions and typically lacks a clear global maximum. Third, we derive the limiting behavior of the maximum modularity Qmax for one model of infinitely modular networks, showing that it depends strongly both on the size of the network and on the number of modules it contains. Finally, using three real-world metabolic networks as examples, we show that the degenerate solutions can fundamentally disagree on many, but not all, partition properties such as the composition of the largest modules and the distribution of module sizes. These results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts. They also explain why many heuristics are often successful at finding high-scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network. We conclude by discussing avenues for mitigating some of these behaviors, such as combining information from many degenerate solutions or using generative models.
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“One recent study has shown that, even in relatively small networks, a large number of good solutions exist for the standard modularity criterion [51], [52].”
From Spatial Guilds in the Serengeti Food Web Revealed by a Bayesian Group Model (2011) · cites this paper as [52]
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“However, as of today, a common method for dealing with this degeneracy is to examine statistics averaged over the 100 repetitions of the optimization, with equal weight being placed on each solution, rather than just on the unique solutions.”
From Dynamic reconfiguration of frontal brain networks during executive cognition in humans (2015) · cites this paper as [51]
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Cites
(1979) · Cited by 43,841
Fast unfolding of communities in large networks
Blondel, V. D., Guillaume, J.-L., Lambiotte, R., & Lefebvre, E. (2008) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2008/10/p10008 · Cited by 21,424
The Structure and Function of Complex Networks
Newman, M. E. J. (2003) · SIAM Review · doi:10.1137/s003614450342480 · Cited by 18,719
Numerical recipes in C: the art of scientific computing
(1993) · Choice Reviews Online · doi:10.5860/choice.30-5638 · Cited by 17,933
Social Network Analysis: Methods and Applications
Wasserman, S., & Faust, K. (1994) · doi:10.1017/cbo9780511815478 · Cited by 17,557
Advances in Neural Information Processing Systems 19
(2007) · The MIT Press eBooks · doi:10.52202/085713 · Cited by 16,043
Community structure in social and biological networks
Girvan, M., & Newman, M. E. J. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.122653799 · Cited by 15,502
Finding and evaluating community structure in networks
Newman, M. E. J., & Girvan, M. (2004) · Physical Review E · doi:10.1103/physreve.69.026113 · Cited by 13,931
Modularity and community structure in networks
Newman, M. E. J. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0601602103 · Cited by 12,256
Fortunato, S. (2010) · Physics Reports · doi:10.1016/j.physrep.2009.11.002 · Cited by 11,293
Research works printed but not linked: 4
- M. A. Porter, 2009, Not. Am. Math. Soc., 59, 1082
- L. K. Branting, Proceedings of the 2nd Workshop on Social Network Mining and Analysis
- E. M. Airoldi, 2008, J. Mach. Learn. Res., 9, 1981
- P. Demartines, 1995, Proceedings of 15th workshop GRETSI. Juan-Les-Pins France
Cited by
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A Game Theoretic Framework for Community Detection
McSweeney, P. J., Mehrotra, K., & Oh, J. C. (2012) · IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM) · doi:10.1109/asonam.2012.47 · Cited by 31
Online Community Detection for Large Complex Networks
Pan, G., Zhang, W., Wu, Z., & Li, S. (2014) · PLoS ONE · doi:10.1371/journal.pone.0102799 · Cited by 31
Community Detection Using Cooperative Co-evolutionary Differential Evolution
Huang, Q., White, T., Jia, G., Musolesi, M., Turan, N., Tang, K., He, S., Heath, J. K., & Yao, X. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-32964-7_24 · Cited by 31
MULTI-SCALE COMMUNITY DETECTION USING STABILITY AS OPTIMISATION CRITERION IN A GREEDY ALGORITHM
Martelot, E. L., & Hankin, C. (2011) · International Conference on Knowledge Discovery and Information Retrieval · doi:10.5220/0003655002160225 · Cited by 31
Gorsich, E. E., Luis, A. D., Buhnerkempe, M., Grear, D. A., Portacci, K., Miller, R. S., & Webb, C. T. (2016) · Preventive Veterinary Medicine · doi:10.1016/j.prevetmed.2016.09.023 · Cited by 31
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Rosvall, M., Delvenne, J., Schaub, M. T., & Lambiotte, R. (2019) · Wiley eBooks · doi:10.1002/9781119483298.ch4 · Cited by 34
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Esfahlani, F. Z., Bertolero, M. A., Bassett, D. S., & Betzel, R. F. (2020) · NeuroImage · doi:10.1016/j.neuroimage.2020.116612 · Cited by 32
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Lee, T.-W., Northoff, G., & Wu, Y.-T. (2014) · Neuroscience · doi:10.1016/j.neuroscience.2014.05.035 · Cited by 26
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Granell, C., Gómez, S., & Arenas, À. (2011) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.3560932 · Cited by 29
Tien, J. H., Eisenberg, M. C., Cherng, S. T., & Porter, M. A. (2020) · Applied Network Science · doi:10.1007/s41109-019-0223-3 · Cited by 34
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Speidel, L., Takaguchi, T., & Masuda, N. (2015) · The European Physical Journal B · doi:10.1140/epjb/e2015-60226-y · Cited by 31
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Costa, L. D. F., Villas-Boas, P. R., Silva, F. N., & Rodrigues, F. A. (2010) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2010/11/p11015 · Cited by 29
Fang, Y., & Zio, E. (2013) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2013.02.021 · Cited by 29
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Kawamoto, T., & Kabashima, Y. (2015) · Physical Review E · doi:10.1103/physreve.91.062803 · Cited by 27
Global features of functional brain networks change with contextual disorder
Andric, M., & Hasson, U. (2015) · NeuroImage · doi:10.1016/j.neuroimage.2015.05.025 · Cited by 29
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Škrlj, B., Kralj, J., & Nada Lavrač, A. (2020) · Machine Learning · doi:10.1007/s10994-020-05882-8 · Cited by 28
MILP formulations for the modularity density maximization problem
Costa, A. (2015) · European Journal of Operational Research · doi:10.1016/j.ejor.2015.03.012 · Cited by 28
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Liu, D., Jin, D., Baquero, C., He, D., Yang, B., & Yu, Q. (2013) · International Journal of Computational Intelligence Systems · doi:10.1080/18756891.2013.773175 · Cited by 28
YASCA: An Ensemble-Based Approach for Community Detection in Complex Networks
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Liu, Y., Hong, X., Bengson, J. J., Kelley, T. A., Ding, M., & Mangun, G. R. (2017) · NeuroImage · doi:10.1016/j.neuroimage.2017.05.048 · Cited by 31
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Kovács, B., & Palla, G. (2021) · Scientific Reports · doi:10.1038/s41598-021-93921-2 · Cited by 27
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Kirkley, A., & Newman, M. E. J. (2022) · Communications Physics · doi:10.1038/s42005-022-00816-3 · Cited by 27
Boroujeni, R. J., & Soleimani, S. (2022) · Expert Systems with Applications · doi:10.1016/j.eswa.2022.117452 · Cited by 27
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Betzel, R. F., Mišić, B., He, Y., Rumschlag, J. A., Zuo, X., & Sporns, O. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1510.08045 · Cited by 35
Kristanto, Y. D., & Padmi, R. S. (2020) · Jurnal Penelitian dan Evaluasi Pendidikan · doi:10.21831/pep.v24i2.33912 · Cited by 31
Michael, C., Tillem, S., Sripada, C., Burt, S. A., Klump, K. L., & Hyde, L. W. (2023) · Developmental Cognitive Neuroscience · doi:10.1016/j.dcn.2023.101316 · Cited by 30
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Langone, R., Alzate, C., & Suykens, J. A. K. (2013) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2013.01.058 · Cited by 25
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Fornito, A. (2016) · Neuromethods · doi:10.1007/978-1-4939-5611-1_10 · Cited by 26
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de Santiago, R., & Lamb, L. C. (2016) · European Journal of Operational Research · doi:10.1016/j.ejor.2016.10.033 · Cited by 25
Global vs local modularity for network community detection
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Humphries, M. D. (2017) · Network Neuroscience · doi:10.1162/netn_a_00020 · Cited by 27
He, M., Glasser, J., Pritchard, N., Bhamidi, S., & Kaza, N. (2020) · PLoS ONE · doi:10.1371/journal.pone.0230941 · Cited by 25
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Darst, R. K., Nussinov, Z., & Fortunato, S. (2014) · Physical Review E · doi:10.1103/physreve.89.032809 · Cited by 24
Schmidt, C. Q., Piper, D., Pester, B., Mierau, A., & Witte, H. (2017) · International Journal of Neural Systems · doi:10.1142/s0129065717500514 · Cited by 24
Li, H., He, F., & Chen, Y. (2020) · Applied Soft Computing · doi:10.1016/j.asoc.2020.106593 · Cited by 24
Community detection in network neuroscience
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Community evolution in retweet networks
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Multi-resolution modularity methods and their limitations in community detection
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Online community detection for large complex networks
Zhang, W., Pan, G., Wu, Z., & Li, S. (2013) · International Joint Conference on Artificial Intelligence · Cited by 20
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Cui, X., Ding, C., Wei, J., Xue, J., Wang, X., Wang, B., & Xiang, J. (2021) · Cerebral Cortex · doi:10.1093/cercor/bhab133 · Cited by 21
Maximizing Barber’s bipartite modularity is also hard
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Costa, A., & Hansen, P. (2013) · Optimization Letters · doi:10.1007/s11590-013-0621-x · Cited by 20
van Laarhoven, T., & Marchiori, E. (2013) · Physical Review E · doi:10.1103/physreve.87.012812 · Cited by 19
McDonnell, E. M., Stoltz, D. S., & Taylor, M. A. (2020) · Socio-Economic Review · doi:10.1093/ser/mwaa034 · Cited by 18
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Maserrat, H., & Pei, J. (2012) · Proceedings · doi:10.1109/icdm.2012.14 · Cited by 19
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Core of communities in bipartite networks
Bongiorno, C., London, A., Miccichè, S., & Mantegna, R. N. (2017) · Physical review. E · doi:10.1103/physreve.96.022321 · Cited by 19
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Adaptive rewiring in weighted networks
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A density-based statistical analysis of graph clustering algorithm performance
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Science Mapping and the Identification of Topics: Theoretical and Methodological Considerations
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Gene communities in co-expression networks across different tissues
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Metadata
- Authors
- Good, B. H., de Montjoye, Y.-A., & Clauset, A.
- Affiliations
- Swarthmore College (US)
- Santa Fe Institute (US)
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2010-04-15
- Volume
- 81
- Issue
- 4
- Pages
- 046106-046106
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W2061099285
- Cited by
- 937
- References
- 66
- Citations by year
- 2026: 18 · 2025: 38 · 2024: 36 · 2023: 36 · 2022: 35 · 2021: 45 · 2020: 58 · 2019: 57 · 2018: 94 · 2017: 76 · 2016: 59 · 2015: 71 · 2014: 80 · 2013: 79 · 2012: 70
- FWCI
- 52.48
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review E (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Digital Access to Libraries (Université catholique de Louvain (UCL), l'Université de Namur (UNamur) and the Université Saint-Louis (USL-B)) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Bioinformatics and Genomic Networks
- Physical Sciences › Computer Science › Artificial Intelligence › Advanced Clustering Algorithms Research
- Keywords
- modularity optimization, resolution limit, network module identification, degenerate solutions, modularity function, metabolic networks, community detection
- MeSH terms
- Models, Theoretical
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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