Skip to main content

Scalably revealing the dynamics of soft community structure in complex networks

Journal of Systems Science and Complexity volume 29, pages 1071–1088 (2016)Cite this article

Abstract

Revealing the dynamics of community structure is of great concern for scientists from many fields. Specifically, how to quantify the dynamic details of soft community structure is a very interesting topic. In this paper, the authors propose a novel framework to study the scalable dynamic behavior of the soft community structure. First, the authors model the Potts dynamics to detect community structure using a “soft” Markov process. Then the soft stability of in a multiscale view is proposed to naturally uncover the local uniform behavior of spin values across multiple hierarchical levels. Finally, a new partition index is developed to detect fuzzy communities based on the stability and the dynamical information. Experiments on the both synthetically generated and real-world networks verify that the framework can be used to uncover hierarchical community structures effectively and efficiently.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. Newman M E J, Fast algorithm for detecting community structure in networks, Phys. Rev. E, 2004, 69: 066133.

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. Chen D B, Shang M S, and Fu Y, Detecting overlapping communities of weighted networks via a local algorithm, Physica A, 2010, 389: 4177–4187.

    Article  Google Scholar 

  4. Zhang X S, Wang R S, Wang Y, Wang J, Qiu Y, Wang L, and Chen L, Modularity optimization in community detection of complex networks, Europhys. Lett., 2009, 87: 38002.

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. Ahn Y Y, Bagrow J P, and Lehmann S, Link communities reveal multiscale complexity in networks, Nature, 2010, 466: 761–764.

    Article  Google Scholar 

  7. Zhang S, Wang R S, and Zhang X S, Identification of overlapping community structure in complex networks using fuzzy c-means clustering, Physica A, 2007, 374: 483–490.

    Article  Google Scholar 

  8. Blatt M, Wiseman S, and Domany E, Superparamagnetic clustering of data, Phys. Rev. Lett., 1996, 76: 3251–3255.

    Article  Google Scholar 

  9. Reichardt J and Bornholdt S, Detecting fuzzy community structures in complex networks with a potts model, Phys. Rev. Lett., 2004, 93: 218701.

    Article  Google Scholar 

  10. Clauset A, Newman M E J, and Moore C, Finding community structure in very large networks, Phys. Rev. E, 2004, 70: 066111.

    Article  Google Scholar 

  11. Newman M E J, Finding community structure in networks using the eigenvectors of matrices, Phys. Rev. E, 2006, 74: 036104.

    MathSciNet  Article  Google Scholar 

  12. Li H J, Wang Y, Wu L Y, Liu Z P, Chen L, and Zhang X S, Community structure detection based on Potts model and spectral characterization, Europhys. Lett., 2012, 97: 48005.

    Article  Google Scholar 

  13. Li H J, Wang Y, Wu L Y, Zhang J, and Zhang X S, Potts model based on a Markov process computation solves the community structure problem effectively, Phys. Rev. E, 2012, 86: 016109.

    Article  Google Scholar 

  14. Li H J and Zhang X S, Analysis of stability of community structure across multiple hierarchical levels, Europhys. Lett., 2013, 103: 58002.

    Article  Google Scholar 

  15. Xia Z and Bu Z, Community detection based on a semantic network, Knowl-Based Syst., 2012, 26: 30–39.

    Article  Google Scholar 

  16. Bu Z, Zhang C, Xia Z, and Wang J, A fast parallel modularity optimization algorithm (FPMQA) for community detection in online social network, Knowl-Based Syst., 2013, 50: 246–259.

    Article  Google Scholar 

  17. Von Luxburg U, A tutorial on spectral clustering, Tech. Rep., 2006, 149, Max Planck Institute for Biological Cybernetics.

    Google Scholar 

  18. Bach F R and Jordan M I, Advances in Neural Information Processing Systems, NIPS*, Eds. by Thrun S, Saul L, and Schoelkopf B, MIT Press, Cambridge, MA, 2003, 16.

  19. Zha H, He X, Ding C, Gu M, and Simon H, Spectral relaxation for k-mean, NIPS*, 2001, 14: 1057–1064.

    Google Scholar 

  20. Shi J and Malik J, Normalized cuts and image segmentation, IEEE Trans. Pattern Anal. Mach. Intell., 2000, 22: 8888.

    Google Scholar 

  21. Rosvall M and Bergstrom C T, Maps of random walks on complex networks reveal community structure, Proc. Natl. Acad. Sci., 2008, 105(4): 1118–1123.

    Article  Google Scholar 

  22. Zhou H, Distance, dissimilarity index, and network community structure, Phys. Rev. E, 2003, 67: 041908.

    Article  Google Scholar 

  23. Ravasz E and Barabási A L, Hierarchical organization in complex networks, Phys. Rev. E, 2003, 67: 026112.

    Article  MATH  Google Scholar 

  24. Arenas A, Fernandez A, and Gomez S, Analysis of the structure of complex networks at different resolution levels, New. J. Phys., 2008, 10: 053039.

    Article  Google Scholar 

  25. Lancichinetti A and Fortunato S, Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities, Phys. Rev. E, 2009, 80: 016118.

    Article  Google Scholar 

  26. Zachary W W, An information flow model for conflict and fission in small groups, J. Anthropol. Res., 1977, 33: 452–473.

    Article  Google Scholar 

  27. Girvan M and Newman M E J, Community structure in social and biological networks, Proc. Natl. Acad. Sci., 2002, 99: 7821.

    MathSciNet  Article  MATH  Google Scholar 

  28. Shen H, Cheng X, Cai K, and Hu M B, Detect overlapping and hierarchical community structure in networks, Physica A, 2009, 388: 1706–1712.

    Article  Google Scholar 

  29. Lancichinetti A and Fortunato S, Community detection algorithms: A comparative analysis, Phys. Rev. E, 2009, 80: 056117.

    Article  Google Scholar 

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

    Article  Google Scholar 

  31. Liu J, Fuzzy modularity and fuzzy community structure in networks, Eur. Phys. J. B, 2010, 77: 547–557.

    Article  Google Scholar 

  32. Li H J and Jasmine J Daniels, Social significance of community structure: Statistical view, Phys. Rev. E, 2015, 91: 012801.

    MathSciNet  Article  Google Scholar 

  33. Li H J, Wang H, and Chen L, Measuring robustness of community structure in complex networks, Europhys. Lett., 2015, 108: 68009.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Management Science and Engineering, Central University of Finance and Economics, Beijing, 100081, China

    Huijia Li

  2. Department of Automation, Tsinghua University, Beijing, 100084, China

    Huiying Li

Authors
  1. Huijia Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huiying Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huijia Li.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 71401194, 91324203 and 11131009, and “121” Youth Development Fund of CUFE under Grant No. QBJ1410.

This paper was recommended for publication by Editor DI Zengru.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, H., Li, H. Scalably revealing the dynamics of soft community structure in complex networks. J Syst Sci Complex 29, 1071–1088 (2016). https://doi.org/10.1007/s11424-015-4145-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-015-4145-6

Keywords

  • Community detection
  • dynamical behavior
  • Markov process
  • Potts model
  • soft partition