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Finding community structures in complex networks using mixed integer optimisation

Author

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  • G. Xu
  • S. Tsoka
  • L. G. Papageorgiou

Abstract

The detection of community structure has been used to reveal the relationships between individual objects and their groupings in networks. This paper presents a mathematical programming approach to identify the optimal community structures in complex networks based on the maximisation of a network modularity metric for partitioning a network into modules. The overall problem is formulated as a mixed integer quadratic programming (MIQP) model, which can then be solved to global optimality using standard optimisation software. The solution procedure is further enhanced by developing special symmetry-breaking constraints to eliminate equivalent solutions. It is shown that additional features such as minimum/maximum module size and balancing among modules can easily be incorporated in the model. The applicability of the proposed optimisation-based approach is demonstrated by four examples. Comparative results with other approaches from the literature show that the proposed methodology has superior performance while global optimum is guaranteed. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • G. Xu & S. Tsoka & L. G. Papageorgiou, 2007. "Finding community structures in complex networks using mixed integer optimisation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(2), pages 231-239, November.
    • Handle: RePEc:spr:eurphb:v:60:y:2007:i:2:p:231-239
    DOI: 10.1140/epjb/e2007-00331-0
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    Citations

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    Cited by:

    1. Wu, Jianshe & Zhang, Long & Li, Yong & Jiao, Yang, 2016. "Partition signed social networks via clustering dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 568-582.
    2. Harun Pirim & Burak Eksioglu & Fred W. Glover, 2018. "A Novel Mixed Integer Linear Programming Model for Clustering Relational Networks," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 492-508, February.
    3. Costa, Alberto, 2015. "MILP formulations for the modularity density maximization problem," European Journal of Operational Research, Elsevier, vol. 245(1), pages 14-21.
    4. Santiago, Rafael & Lamb, Luís C., 2017. "Efficient modularity density heuristics for large graphs," European Journal of Operational Research, Elsevier, vol. 258(3), pages 844-865.
    5. Li, Zhangtao & Liu, Jing, 2016. "A multi-agent genetic algorithm for community detection in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 336-347.
    6. Sonia Cafieri & Alberto Costa & Pierre Hansen, 2014. "Reformulation of a model for hierarchical divisive graph modularity maximization," Annals of Operations Research, Springer, vol. 222(1), pages 213-226, November.
    7. Liu, X. & Murata, T., 2010. "Advanced modularity-specialized label propagation algorithm for detecting communities in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1493-1500.
    8. Leo Liberti, 2020. "Distance geometry and data science," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 271-339, July.

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