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International Workshop on Algorithms and Models for the Web-Graph

WAW 2023: Algorithms and Models for the Web Graph pp 52–67Cite as

Modularity Based Community Detection in Hypergraphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13894))

Abstract

In this paper, we make a significant step toward designing a scalable community detection algorithm using hypergraph modularity function. The main obstacle with adjusting the initial stage of the classical Louvain algorithm is dealt via carefully adjusted linear combination of the graph modularity function of the corresponding two-section graph and the desired hypergraph modularity function. It remains to properly tune the algorithm and design a mechanism to adjust the weights in the modularity function (in an unsupervised way), depending on how often nodes in one community share hyperedges with nodes from other communities. It will be done in the journal version of this paper.

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Notes

  1. 1.

    https://github.com/bkamins/ABCDGraphGenerator.jl/.

  2. 2.

    https://github.com/tolcz/ABCDeGraphGenerator.jl/.

  3. 3.

    https://math.torontomu.ca/~pralat/research.html.

  4. 4.

    https://math.torontomu.ca/~pralat/research.html.

References

  1. Ahn, K., Lee, K., Suh, C.: Hypergraph spectral clustering in the weighted stochastic block model. IEEE J. Sel. Top. Signal Process. 12(5), 959–974 (2018)

    Article  Google Scholar 

  2. Battiston, F., et al.: Networks beyond pairwise interactions: structure and dynamics. Phys. Rep. 874, 1–92 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  3. Benson, A.R., Abebe, R., Schaub, M.T., Jadbabaie, A., Kleinberg, J.: Simplicial closure and higher-order link prediction. Proc. Natl. Acad. Sci. 115(48), E11221–E11230 (2018)

    Article  Google Scholar 

  4. Benson, A.R., Gleich, D.F., Higham, D.J.: Higher-order network analysis takes off, fueled by classical ideas and new data. arXiv preprint arXiv:2103.05031 (2021)

  5. Benson, A.R., Gleich, D.F., Leskovec, J.: Tensor spectral clustering for partitioning higher-order network structures. In: Proceedings of the 2015 SIAM International Conference on Data Mining, pp. 118–126. SIAM (2015)

    Google Scholar 

  6. Benson, A.R., Gleich, D.F., Leskovec, J.: Higher-order organization of complex networks. Science 353(6295), 163–166 (2016)

    Article  Google Scholar 

  7. Blondel, V.D., Guillaume, J.L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Stat. Mech: Theory Exp. 2008(10), P10008 (2008)

    Article  MATH  Google Scholar 

  8. Chien, I., Lin, C.Y., Wang, I.H.: Community detection in hypergraphs: optimal statistical limit and efficient algorithms. In: International Conference on Artificial Intelligence and Statistics, pp. 871–879. PMLR (2018)

    Google Scholar 

  9. Chodrow, P.S., Veldt, N., Benson, A.R.: Generative hypergraph clustering: from blockmodels to modularity. Sci. Adv. 7(28), eabh1303 (2021)

    Google Scholar 

  10. Chung Graham, F., Lu, L.: Complex graphs and networks. No. 107, American Mathematical Society (2006)

    Google Scholar 

  11. Clauset, A., Newman, M.E., Moore, C.: Finding community structure in very large networks. Phys. Rev. E 70(6), 066111 (2004)

    Article  Google Scholar 

  12. Demšar, J.: Statistical comparisons of classifiers over multiple data sets. J. Mach. Learn. Res. 7, 1–30 (2006)

    MathSciNet  MATH  Google Scholar 

  13. Easley, D., Kleinberg, J.: Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Cambridge University Press, Cambridge (2010)

    Google Scholar 

  14. Fortunato, S., Barthelemy, M.: Resolution limit in community detection. Proc. Natl. Acad. Sci. 104(1), 36–41 (2007)

    Article  Google Scholar 

  15. Jackson, M.O.: Social and Economic Networks. Princeton University Press, Princeton (2010)

    Google Scholar 

  16. Juul, J.L., Benson, A.R., Kleinberg, J.: Hypergraph patterns and collaboration structure. arXiv preprint arXiv:2210.02163 (2022)

  17. Kamiński, B., Pankratz, B., Prałat, P., Théberge, F.: Modularity of the abcd random graph model with community structure. preprint arXiv:2203.01480 (2022)

  18. Kamiński, B., Poulin, V., Prałat, P., Szufel, P., Théberge, F.: Clustering via hypergraph modularity. PLoS ONE 14(11), e0224307 (2019)

    Article  Google Scholar 

  19. Kamiński, B., Prałat, P., Théberge, F.: Community detection algorithm using hypergraph modularity. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds.) Complex Networks and Their Applications, pp. 152–163. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-65347-7_13

    Chapter  Google Scholar 

  20. Kamiński, B., Prałat, P., Théberge, F.: Artificial benchmark for community detection (ABCD)-fast random graph model with community structure. Netw. Sci. 1–26 (2021)

    Google Scholar 

  21. Kamiński, B., Prałat, P., Théberge, F.: Mining Complex Networks. Chapman and Hall/CRC, Boca Raton (2021)

    Google Scholar 

  22. Kamiński, B., Prałat, P., Théberge, F.: Hypergraph artificial benchmark for community detection (h-ABCD). arXiv preprint arXiv:2210.15009 (2022)

  23. Kamiński, B., Prałat, P., Théberge, F.: Outliers in the ABCD random graph model with community structure (ABCD+O). In: Proceedings of the 11th International Conference on Complex Networks and their Applications (2022, in press)

    Google Scholar 

  24. Kamiński, B., Olczak, T., Pankratz, B., Prałat, P., Théberge, F.: Properties and performance of the ABCDE random graph model with community structure. Big Data Res. 30, 100348 (2022)

    Article  Google Scholar 

  25. Kumar, T., Vaidyanathan, S., Ananthapadmanabhan, H., Parthasarathy, S., Ravindran, B.: Hypergraph clustering by iteratively reweighted modularity maximization. Appl. Netw. Sci. 5(1), 1–22 (2020)

    Article  Google Scholar 

  26. Kumar, T., Vaidyanathan, S., Ananthapadmanabhan, H., Parthasarathy, S., Ravindran, B.: A new measure of modularity in hypergraphs: theoretical insights and implications for effective clustering. In: Cherifi, H., Gaito, S., Mendes, J.F., Moro, E., Rocha, L.M. (eds.) COMPLEX NETWORKS 2019. SCI, vol. 881, pp. 286–297. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-36687-2_24

    Chapter  Google Scholar 

  27. Lancichinetti, A., Fortunato, S.: Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. Phys. Rev. E 80(1), 016118 (2009)

    Article  Google Scholar 

  28. Lancichinetti, A., Fortunato, S.: Limits of modularity maximization in community detection. Phys. Rev. E 84(6), 066122 (2011)

    Article  Google Scholar 

  29. Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78(4), 046110 (2008)

    Article  Google Scholar 

  30. Lee, G., Choe, M., Shin, K.: How do hyperedges overlap in real-world hypergraphs?-patterns, measures, and generators. In: Proceedings of the Web Conference 2021, pp. 3396–3407 (2021)

    Google Scholar 

  31. Newman, M.: Networks. Oxford University Press, Oxford (2018)

    Google Scholar 

  32. Newman, M.E.: Fast algorithm for detecting community structure in networks. Phys. Rev. E 69(6), 066133 (2004)

    Article  Google Scholar 

  33. Newman, M.E., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69(2), 026113 (2004)

    Article  Google Scholar 

  34. Yin, H., Benson, A.R., Leskovec, J.: Higher-order clustering in networks. Phys. Rev. E 97(5), 052306 (2018)

    Article  Google Scholar 

  35. Yin, H., Benson, A.R., Leskovec, J., Gleich, D.F.: Local higher-order graph clustering. In: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 555–564 (2017)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Decision Analysis and Support Unit, SGH Warsaw School of Economics, Warsaw, Poland

    Bogumił Kamiński

  2. Institute of Computer Sciences, Poznan University of Technology, Poznan, Poland

    Paweł Misiorek

  3. Department of Mathematics, Toronto Metropolitan University, Toronto, ON, Canada

    Paweł Prałat

  4. Tutte Institute for Mathematics and Computing, Ottawa, ON, Canada

    François Théberge

Authors
  1. Bogumił Kamiński
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  2. Paweł Misiorek
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  3. Paweł Prałat
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  4. François Théberge
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Corresponding author

Correspondence to Paweł Prałat .

Editor information

Editors and Affiliations

  1. Tutte Institute for Mathematics and Computing, Ottawa, ON, Canada

    Megan Dewar

  2. Toronto Metropolitan University, Toronto, ON, Canada

    Paweł Prałat

  3. SGH Warsaw School of Economics, Warsaw, Poland

    Przemysław Szufel

  4. Tutte Institute for Mathematics and Computing, Ottawa, ON, Canada

    François Théberge

  5. SGH Warsaw School of Economics, Warsaw, Poland

    Małgorzata Wrzosek

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Kamiński, B., Misiorek, P., Prałat, P., Théberge, F. (2023). Modularity Based Community Detection in Hypergraphs. In: Dewar, M., Prałat, P., Szufel, P., Théberge, F., Wrzosek, M. (eds) Algorithms and Models for the Web Graph. WAW 2023. Lecture Notes in Computer Science, vol 13894. Springer, Cham. https://doi.org/10.1007/978-3-031-32296-9_4

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  • DOI: https://doi.org/10.1007/978-3-031-32296-9_4

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  • Online ISBN: 978-3-031-32296-9

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