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.
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Xu, G., Tsoka, S. & Papageorgiou, L. Finding community structures in complex networks using mixed integer optimisation. Eur. Phys. J. B 60, 231–239 (2007). https://doi.org/10.1140/epjb/e2007-00331-0
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DOI: https://doi.org/10.1140/epjb/e2007-00331-0