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Self-organizing map of complex networks for community detection

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Abstract

Detecting communities from complex networks is an important issue and has attracted attention of researchers in many fields. It is relevant to social tasks, biological inquiries, and technological problems since various networks exist in these systems. This paper proposes a new self-organizing map (SOM) based approach to community detection. By adopting a new operation and a new weight-updating scheme, a complex network can be organized into dense subgraphs according to the topological connection of each node by the SOM algorithm. Extensive numerical experiments show that the performance of the SOM algorithm is good. It can identify communities more accurately than existing methods. This method can be used to detect communities not only in undirected networks, but also in directed networks and bipartite networks.

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References

  1. L. Chen, R. S. Wang, and X. S. Zhang, Biomolecular Networks: Methods and Applications in Systems Biology, John Wiley and Sons, Hoboken, NJ, 2009.

    Google Scholar 

  2. R. Albert and A. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys., 2002, 74: 47–97.

    Article  Google Scholar 

  3. M. Girvan and M. Newman, Community structure in social and biological networks, Proc. Natl. Acad. Sci., 2002, 99: 7821–7826.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. Palla, I. Derényi, I. Farkas, and T. Vicsek, Uncovering the overlapping community structure of complex networks in nature and society, Nature, 2005, 435: 814–818.

    Article  Google Scholar 

  5. A. Lancichinetti, S. Fortunato, and J. Kertesz, Detecting the overlapping and hierarchical community structure in complex networks, New J. Phys., 2009, 11: 033015.

    Article  Google Scholar 

  6. S. Zhang, R. S. Wang, and X. S. Zhang, Uncovering fuzzy community structure in complex networks, Phys. Rev. E, 2007, 76: 046103.

    Article  Google Scholar 

  7. R. S. Wang, S. Zhang, Y. Wang, et al., Clustering complex networks and biological networks by nonnegative matrix factorization with various similarity measures, Neurocomputing, 2008, 72: 134–141.

    Article  Google Scholar 

  8. J. Reichardt and S. Bornholdt, Detecting fuzzy community structures in complex networks with a Potts model, Phys. Rev. Lett., 2004, 93(21): 218701.

    Article  Google Scholar 

  9. M. Rosvall and C. Bergstrom, An information-theoretic framework for resolving community structure in complex networks, Proc. Natl. Acad. Sci., 2007, 104: 7327–7331.

    Article  Google Scholar 

  10. M. Rosvall and C. Bergstrom, Maps of random walks on complex networks reveal community structure, Proc. Natl. Acad. Sci., 2008, 105: 1118–1123.

    Article  Google Scholar 

  11. M. Newman and M. Girvan, Finding and evaluating community structure in networks, Phys. Rev. E, 2004, 69: 26113.

    Article  Google Scholar 

  12. Z. Li, S. Zhang, R. S. Wang, et al., Quantitative function for community detection, Phys. Rev. E, 2008, 77: 36109.

    Article  Google Scholar 

  13. M. Newman, Modularity and community structure in networks, Proc. Natl. Acad. Sci., 2006, 103: 8577–8582.

    Article  Google Scholar 

  14. P. Schuetz and A. Caflisch, Multistep greedy algorithm identifies community structure, Phys. Rev. E, 2008, 78: 026112.

    Article  Google Scholar 

  15. S. Jalan and J. Bandyopadhyay, Random matrix analysis of complex networks, Phys. Rev. E, 2007, 76: 46107.

    Article  MathSciNet  Google Scholar 

  16. R. Guimera, S. Mossa, A. Turtschi, and L. Amaral, The worldwide air transportation network: Anomalous centrality, community structure, and cities’ global roles, Proc. Natl. Acad. Sci., 2005, 102: 7794–7799.

    Article  MATH  MathSciNet  Google Scholar 

  17. R. Guimerà and L. Amaral, Functional cartography of complex metabolic networks, Nature, 2005, 433: 895–900.

    Article  Google Scholar 

  18. X. S. Zhang and R. S. Wang, Optimization analysis of modularity measures for network community detection, Lect. Notes Oper. Res., 2008, 9: 13–20.

    Google Scholar 

  19. X. S. Zhang, R. S. Wang, Y. Wang, et al., Modularity optimization in community detection of complex networks, Europhys. Lett., 2009, 87: 38002.

    Article  Google Scholar 

  20. X. S. Zhang, Neural Networks in Optimization, Kluwer Academic Publishers, 2000.

  21. L. Danon, A. Daz-Guilera, J. Duch, and A. Arenas, Comparing community structure identification, J. Statist. Mech.: Theory Exp., 2005, 9: P09008.

    Article  Google Scholar 

  22. S. Fortunato and M. Barthelemy, Resolution limit in community detection, Proc. Natl. Acad. Sci. USA, 2007, 104: 36–41.

    Article  Google Scholar 

  23. A. Lancichinetti, S. Fortunato, and F. Radicchi, Benchmark graphs for testing community detection algorithms, Phys. Rev. E, 2008, 78: 046110.

    Article  Google Scholar 

  24. P. Gleiser and L. Danon, Community structure in jazz, Advances in Complex Systems, 2003, 6: 565–573.

    Article  Google Scholar 

  25. A. Davis, B. B. Gardner, and M. R. Gardner, Deep South, University of Chicago Press, Chicago, 1941.

    Google Scholar 

  26. R. Guimerà, M. Sales-Pardo, and L. A. N. Amaral, Module identification in bipartite and directed networks, Phys. Rev. E, 2007, 76: 036102.

    Article  Google Scholar 

  27. M. Gustafsson, M. Hörnquista, and A. Lombardi, Comparison and validation of community structures in complex networks, Physica A, 2006, 367: 559–576.

    Article  Google Scholar 

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Correspondence to Zhenping Li.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant Nos 10631070, 60873205, 10701080, and the Beijing Natural Science Foundation under Grant No. 1092011. It is also partially supported by the Foundation of Beijing Education Commission under Grant No. SM200910037005, the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHR201006217), and the Foundation of WYJD200902.

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Li, Z., Wang, R., Zhang, XS. et al. Self-organizing map of complex networks for community detection. J Syst Sci Complex 23, 931–941 (2010). https://doi.org/10.1007/s11424-010-0202-3

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  • DOI: https://doi.org/10.1007/s11424-010-0202-3

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