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International Conference on Computational Science and Its Applications

ICCSA 2022: Computational Science and Its Applications – ICCSA 2022 pp 19–33Cite as

Network Size Reduction Preserving Optimal Modularity and Clique Partition

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13375))

Abstract

Graph clustering and community detection are significant and actively developing topics in network science. Uncovering community structure can provide essential information about the underlying system. In this work, we consider two closely related graph clustering problems. One is the clique partitioning problem, and the other is the maximization of partition quality function called modularity. We are interested in the exact solution. However, both problems are NP-hard. Thus the computational complexity of any existing algorithm makes it impossible to solve the problems exactly for the networks larger than several hundreds of nodes. That is why even a small reduction of network size can significantly improve the speed of finding the solution to these problems. We propose a new method for reducing the network size that preserves the optimal partition in terms of modularity score or the clique partitioning objective function. Furthermore, we prove that the optimal partition of the reduced network has the same quality as the optimal partition of the initial network. We also address the cases where a previously proposed method could provide incorrect results. Finally, we evaluate our method by finding the optimal partitions for two sets of networks. Our results show that the proposed method reduces the network size by 40% on average, decreasing the computation time by about 54%.

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Notes

  1. 1.

    https://github.com/Alexander-Belyi/best-partition.

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Acknowledgement

This research was supported by the MUNI Award in Science and Humanities (MASH) of the Grant Agency of Masaryk University under the Digital City project (MUNI/J/0008/2021).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic

    Alexander Belyi & Stanislav Sobolevsky

  2. Center for Urban Science and Progress, New York University, Brooklyn, NY, USA

    Stanislav Sobolevsky

Authors
  1. Alexander Belyi
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  2. Stanislav Sobolevsky
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Corresponding author

Correspondence to Alexander Belyi .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Universidad de Málaga, Malaga, Spain

    Eligius M. T. Hendrix

  4. Monash University, Clayton, VIC, Australia

    David Taniar

  5. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

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Belyi, A., Sobolevsky, S. (2022). Network Size Reduction Preserving Optimal Modularity and Clique Partition. In: Gervasi, O., Murgante, B., Hendrix, E.M.T., Taniar, D., Apduhan, B.O. (eds) Computational Science and Its Applications – ICCSA 2022. ICCSA 2022. Lecture Notes in Computer Science, vol 13375. Springer, Cham. https://doi.org/10.1007/978-3-031-10522-7_2

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  • DOI: https://doi.org/10.1007/978-3-031-10522-7_2

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