DETECTION OF DISJOINT AND OVERLAPPING MODULES IN WEIGHTED COMPLEX NETWORKS

Laura Bennett, Songsong Liu, Lazaros G. Papageorgiou () and Sophia Tsoka ()
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Laura Bennett: Department of Informatics, School of Natural and Mathematical Sciences, King's College London, Strand, London, WC2R 2LS, United Kingdom
Songsong Liu: Centre for Process Systems Engineering, Department of Chemical Engineering, University College London, Torrington Place, London, WC1E 7JE, United Kingdom
Lazaros G. Papageorgiou: Centre for Process Systems Engineering, Department of Chemical Engineering, University College London, Torrington Place, London, WC1E 7JE, United Kingdom
Sophia Tsoka: Department of Informatics, School of Natural and Mathematical Sciences, King's College London, Strand, London, WC2R 2LS, United Kingdom

Advances in Complex Systems (ACS), 2012, vol. 15, issue 05, 1-20

Abstract: Community structure detection is widely accepted as a means of elucidating the functional properties of complex networks. The problem statement is ever evolving, with the aim of developing more flexible and realistic modeling procedures. For example, a first step in developing a more informative model is the inclusion of weighted interactions. In addition to the standard community structure problem, interest has increased in the detection of overlapping communities. Adopting such constraints may, in some cases, represent a more true to life abstraction of the system under study. In this paper, two novel mathematical programming algorithms for module detection are presented. First, disjoint modules in weighted and unweighted networks are detected by formulating modularity maximization as a mixed integer nonlinear programming (MINLP) model. The solution obtained is then used to detect overlapping modules through a further MINLP model. The inclusion of two parameters controlling the extent of overlapping offers flexibility in user requirements. Comparative results show that these methodologies perform competitively to previously proposed methods. The methodologies proposed here promote the detection of topological relationships in complex systems. Together with the amenable nature of mathematical programming models, we show that both algorithms offer a versatile solution to the community detection problem.

Keywords: Module detection; complex network; modularity; weighted networks; overlapping communities; mixed integer optimization (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S0219525911500238

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