The Small Community Phenomenon in Networks: Models, Algorithms and Applications

  • Pan Peng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7287)

Abstract

We survey a recent new line of research on the small community phenomenon in networks, which characterizes the intuition and observation that in a broad class of networks, a significant fraction of nodes belong to some small communities. We propose the formal definition of this phenomenon as well as the definition of communities, based on which we are able to both study the community structure of network models, i.e., whether a model exhibits the small community phenomenon or not, and design new models that embrace this phenomenon in a natural way while preserving some other typical network properties such as the small diameter and the power law degree distribution. We also introduce the corresponding community detection algorithms, which not only are used to identify true communities and confirm the existence of the small community phenomenon in real networks but also have found other applications, e.g., the classification of networks and core extraction of networks.

Keywords

Small Community Real Network Community Detection Preferential Attachment Collaboration Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Andersen, R., Chung, F., Lang, K.: Local graph partitioning using pagerank vectors. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, pp. 475–486. IEEE Computer Society, Washington, DC, USA (2006)Google Scholar
  2. 2.
    Andersen, R., Lang, K.J.: Communities from seed sets. In: Proceedings of the 15th International Conference on World Wide Web, WWW 2006, pp. 223–232. ACM, New York (2006)CrossRefGoogle Scholar
  3. 3.
    Andersen, R., Peres, Y.: Finding sparse cuts locally using evolving sets. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009, pp. 235–244. ACM, New York (2009)CrossRefGoogle Scholar
  4. 4.
    Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Clauset, A., Moore, C., Newman, M.E.: Hierarchical structure and the prediction of missing links in networks. Nature 453(7191), 98–101 (2008)CrossRefGoogle Scholar
  6. 6.
    Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Physical Review E, 1–6 (2004)Google Scholar
  7. 7.
    Doerr, B., Fouz, M., Friedrich, T.: Social networks spread rumors in sublogarithmic time. In: Proceedings of the 43rd Annual ACM Symposium on Theory of Computing, STOC 2011, pp. 21–30 (2011)Google Scholar
  8. 8.
    Ravasz, E., Somera, A.L., D.M.Z.O., Barabási, A.L.: Hierarchical organization of modularity in metabolic networks. Science 297, 1551 (2002)CrossRefGoogle Scholar
  9. 9.
    Easley, D., Kleinberg, J.: Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Cambridge University Press (July 2010)Google Scholar
  10. 10.
    Flaxman, A.D., Frieze, A., Vera, J.: A geometric preferential attachment model of networks. Internet Mathematics 3(2) (2007)Google Scholar
  11. 11.
    Flaxman, A.D., Frieze, A.M., Vera, J.: A geometric preferential attachment model of networks II. Internet Mathematics 4(1), 87–111 (2007)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Fortunato, S.: Community detection in graphs. Physics Reports 486 (2010)Google Scholar
  13. 13.
    Hodgkinson, L., Karp, R.M.: Algorithms to Detect Multiprotein Modularity Conserved during Evolution. In: Chen, J., Wang, J., Zelikovsky, A. (eds.) ISBRA 2011. LNCS, vol. 6674, pp. 111–122. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Kannan, R., Vempala, S., Vetta, A.: On clusterings: Good, bad and spectral. J. ACM 51(3), 497–515 (2004)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: KDD 2003: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 137–146 (2003)Google Scholar
  16. 16.
    Kleinberg, J.: The small-world phenomenon: an algorithmic perspective. In: Proceedings of the 32nd ACM Symposium on the Theory of Computing (2000)Google Scholar
  17. 17.
    Lancichinetti, A., Kivelä, M., Saramäki, J., Fortunato, S.: Characterizing the community structure of complex networks. PLoS ONE 5(8), e11976 (2010)CrossRefGoogle Scholar
  18. 18.
    Leskovec, J., Lang, K.J., Dasgupta, A., Mahoney, M.W.: Community structure in large networks: Natural cluster sizes and the absence of large well-defined clusters. CoRR abs/0810.1355 (2008)Google Scholar
  19. 19.
    Leskovec, J., Lang, K.J., Mahoney, M.: Empirical comparison of algorithms for network community detection. In: Proceedings of the 19th International Conference on World Wide Web, WWW 2010, pp. 631–640 (2010)Google Scholar
  20. 20.
    Li, A., Li, J., Pan, Y., Peng, P.: Homophily law of networks: Principles, methods and experiments (2012) (manuscript submitted for publication)Google Scholar
  21. 21.
    Li, A., Li, J., Pan, Y., Peng, P., Zhang, W.: Small core phenomenon of networks: Global influence core of the collaboration networks (2012) (unpublished manuscript)Google Scholar
  22. 22.
    Li, A., Li, J., Peng, P.: Small community phenomenon in social networks: Local dimension (2012) (unpublished manuscript)Google Scholar
  23. 23.
    Li, A., Peng, P.: Communities structures in classical network models. Internet Mathematics 7(2), 81–106 (2011)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Li, A., Peng, P.: The small-community phenomenon in networks. Mathematical Structures in Computer Science, Available on CJO doi:10.1017/S0960129511000570Google Scholar
  25. 25.
    Liao, C.S., Lu, K., Baym, M., Singh, R., Berger, B.: IsoRankN: spectral methods for global alignment of multiple protein networks. Bioinformatics 25(12), i253–i258 (2009)CrossRefGoogle Scholar
  26. 26.
    Mihail, M., Papadimitriou, C., Saberi, A.: On certain connectivity properties of the internet topology. J. Comput. Syst. Sci. 72(2), 239–251 (2006)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Morris, S.: Contagion. The Review of Economic Studies 67(1), 57–78 (2000)CrossRefMATHGoogle Scholar
  28. 28.
    Newman, M.E.J.: Detecting community structure in networks. The European Physical Journal B 38 (2004)Google Scholar
  29. 29.
    Newman, M.E.J., Barabási, A.L., Watts, D.J. (eds.): The Structure and Dynamics of Networks. Princeton University Press (2006)Google Scholar
  30. 30.
    Onnela, J.P., Fenn, D.J., Reid, S., Porter, M.A., Mucha, P.J., Fricker, M.D., Jones, N.S.: A Taxonomy of Networks. CoRR abs/1006.5731 (June 2010)Google Scholar
  31. 31.
    Palla, G., Derenyi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435(7043), 814–818 (2005)CrossRefGoogle Scholar
  32. 32.
    Porter, M.A., Onnela, J.P., Mucha, P.J.: Communities in networks. Notices of the American Mathematical Society 56, 1082–1097 (2009)MathSciNetMATHGoogle Scholar
  33. 33.
    Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., Parisi, D.: Defining and identifying communities in networks. Proceedings of the National Academy of Sciences 101(9), 2658 (2004)CrossRefGoogle Scholar
  34. 34.
    Ravasz, E., Barabási, A.L.: Hierarchical organization in complex networks. Physical Review E 67, 026112 (2003)CrossRefGoogle Scholar
  35. 35.
    Schaeffer, S.: Graph clustering. Computer Science Review (1), 27–64Google Scholar
  36. 36.
    Spielman, D.A., Teng, S.H.: Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems. In: Proceedings of the Thirty-Sixth Annual ACM Symposium on Theory of Computing, STOC 2004, pp. 81–90. ACM, New York (2004)CrossRefGoogle Scholar
  37. 37.
    Voevodski, K., Teng, S.H., Xia, Y.: Finding local communities in protein networks. BMC Bioinformatics 10(1), 297 (2009)CrossRefGoogle Scholar
  38. 38.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Pan Peng
    • 1
    • 2
  1. 1.State Key Laboratory of Computer Science, Institute of SoftwareChinese Academy of SciencesChina
  2. 2.School of Information Science and EngineeringGraduate University of China Academy of SciencesBeijingChina

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