Exploratory Analysis of the Structural Regularities in Networks

  • Hua-Wei Shen
Part of the Springer Theses book series (Springer Theses)

Abstract

In this chapter, we explore various types of structural regularities in networks. For this aim, we divide network nodes into groups such that the members of each group have similar patterns of connections to other groups. Then, we leverage generative model to describe network structure. The structural regularities are then naturally obtained by statistical inference using expectation maximization algorithm. The most prominent strength of our model is the high flexibility, which enables it to possess the advantages of existing models and to overcome their shortcomings in a unified way. Not only can broad types of structure be detected without prior knowledge of the type of intrinsic regularities existing in the target network, but also the type of identified structure can be directly learned from the network. Our model outperforms the state-of-the-art model in shedding light on various structural regularities of networks, which are beyond the capability of existing models.

References

  1. 1.
    Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99, 7821–7826 (2002) MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45, 167–256 (2003) MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Flake, G.W., Lawrence, S.R., Giles, C.L., Coetzee, F.M.: Self-organization and identification of Web communities. IEEE Comput. 35, 66–71 (2002) CrossRefGoogle Scholar
  4. 4.
    Cheng, X.Q., Ren, F.X., Zhou, S., Hu, M.B.: Triangular clustering in document networks. New J. Phys. 11, 033019 (2009) CrossRefGoogle Scholar
  5. 5.
    Guimerà, R., Amaral, L.A.N.: Functional cartography of complex metabolic networks. Nature 433, 895–900 (2005) CrossRefGoogle Scholar
  6. 6.
    Cheng, X.Q., Ren, F.X., Shen, H.W., Zhang, Z.K., Zhou, T.: Bridgeness: A local index on edge significance in maintaining global connectivity. J. Stat. Mech. P10011 (2010) Google Scholar
  7. 7.
    Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004) CrossRefGoogle Scholar
  8. 8.
    Newman, M.E.J.: Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E 74, 036104 (2006) MathSciNetCrossRefGoogle Scholar
  9. 9.
    Ramasco, J.J., Mungan, M.: Inversion method for content-based networks. Phys. Rev. E 77, 036122 (2008) MathSciNetCrossRefGoogle Scholar
  10. 10.
    Vazquez, A.: Population stratification using a statistical model on hypergraphs. Phys. Rev. E 77, 066106 (2008) CrossRefGoogle Scholar
  11. 11.
    Ren, W., Yan, G.Y., Liao, X.P., Xiao, L.: Simple probabilistic algorithm for detecting community structure. Phys. Rev. E 79, 036111 (2009) CrossRefGoogle Scholar
  12. 12.
    Zhang, H.Z., Qiu, B.J., Giles, C.L., Foley, H.C., Yen, J.: An lda-based community structure discovery approach for large-scale social networks. In: Proceedings of the IEEE Conference on Intelligence and Security Informatics, pp. 200–207 (2007) Google Scholar
  13. 13.
    Clauset, A., Moore, C., Newman, M.E.J.: Hierarchical structure and the prediction of missing links in networks. Nature 453, 98–101 (2008) CrossRefGoogle Scholar
  14. 14.
    Newman, M.E.J., Leicht, E.A.: Mixture models and exploratory analysis in networks. Proc. Natl. Acad. Sci. USA 104, 9564–9569 (2007) MATHCrossRefGoogle Scholar
  15. 15.
    Karrer, B., Newman, M.E.J.: Stochastic blockmodels and community structure in networks. Phys. Rev. E 83, 016107 (2011) MathSciNetCrossRefGoogle Scholar
  16. 16.
    Airoldi, E.M., Blei, D.M., Fienberg, S.E., Xing, E.P.: Mixed membership stochastic blockmodels. J. Mach. Learn. Res. 9, 1981–2014 (2008) MATHGoogle Scholar
  17. 17.
    Newman, M.E.J., Strogatz, S.H., Watts, D.J.: Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64, 026118 (2001) CrossRefGoogle Scholar
  18. 18.
    Ball, B., Karrer, B., Newman, M.E.J.: Efficient and principled method for detecting communities in networks. Phys. Rev. E 84, 036103 (2011) CrossRefGoogle Scholar
  19. 19.
    Shen, H.W., Cheng, X.Q., Guo, J.F.: Exploring the structural regularities in networks. Phys. Rev. E 84, 056111 (2011) CrossRefGoogle Scholar
  20. 20.
    Zachary, W.W.: An information flow model for conflict and fission in small groups. J. Anthropol. Res. 33, 452–473 (1977) Google Scholar
  21. 21.
    Rosvall, M., Bergstrom, C.T.: An information-theoretic framework for resolving community structure in complex networks. Proc. Natl. Acad. Sci. USA 104, 7327–7331 (2007) CrossRefGoogle Scholar
  22. 22.
    Szell, M., Lambiotte, R., Thurner, S.: Multirelational organization of large-scale social networks in an online world. Proc. Natl. Acad. Sci. USA 107, 13636–13641 (2010) CrossRefGoogle Scholar
  23. 23.
    Heider, F.: Attitudes and cognitive organization. J. Psychol. 21, 107–112 (1946) CrossRefGoogle Scholar
  24. 24.
    Marvel, S.A., Kleinberg, J., Kleinberg, R.D., Strogatz, S.H.: Continuous-time model of structural balance. Proc. Natl. Acad. Sci. USA 108, 1771–1776 (2011) CrossRefGoogle Scholar
  25. 25.
    Gómez, S., Jensen, P., Arenas, A.: Analysis of community structure in networks of correlated data. Phys. Rev. E 80, 016114 (2009) CrossRefGoogle Scholar
  26. 26.
    Traag, V.A., Bruggeman, J.: Community detection in networks with positive and negative links. Phys. Rev. E 80, 036115 (2009) CrossRefGoogle Scholar
  27. 27.
    Rubinov, M., Sporns, O.: Weight-conserving characterization of complex functional brain networks. NeuroImage 56, 2068–2079 (2011) CrossRefGoogle Scholar
  28. 28.
    Yang, B., Cheung, W.K., Liu, J.M.: Community mining from signed social networks. IEEE Trans. Knowl. Data Eng. 19, 1333–1348 (2007) CrossRefGoogle Scholar
  29. 29.
    Lusseau, D., Schneider, K., Boisseau, O.J., Haase, P., Slooten, E., Dawson, S.M.: The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations. Can geographic isolation explain this unique trait? Behav. Ecol. Sociobiol. 54, 396–405 (2003) CrossRefGoogle Scholar
  30. 30.
    Guimerà, R., Sales-Pardo, M., Amaral, L.A.N.: Module identification in bipartite and directed networks. Phys. Rev. E 76, 036102 (2007) CrossRefGoogle Scholar
  31. 31.
    Kropivnik, S., Mrvar, A.: An analysis of the Slovene parliamentary parties network. In: Developments in Statistics and Methodology, pp. 209–216 (1996) Google Scholar
  32. 32.
    Doreian, P., Mrvar, A.: A partitioning approach to structural balance. Soc. Netw. 18, 149–168 (1996) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hua-Wei Shen
    • 1
  1. 1.Institute of Computing TechnologyChinese Academy of SciencesBeijingChina

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