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Modeling and Detecting Community Hierarchies

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Similarity-Based Pattern Recognition (SIMBAD 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7953))

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Abstract

Community detection has in recent years emerged as an invaluable tool for describing and quantifying interactions in networks. In this paper we propose a theoretical model that explicitly formalizes both the tight connections within each community and the hierarchical nature of the communities. We further present an efficient algorithm that provably detects all the communities in our model. Experiments demonstrate that our definition successfully models real world communities, and our algorithm compares favorably with existing approaches.

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References

  1. Airoldi, E.M., Blei, D.M., Fienberg, S.E., Xing, E.P.: Mixed membership stochastic blockmodels. J. Mach. Learn. Res. 9, 1981–2014 (2008)

    MATH  Google Scholar 

  2. Arora, S., Ge, R., Sachdeva, S., Schoenebeck, G.: Finding overlapping communities in social networks: toward a rigorous approach. In: Proceedings of the 13th ACM Conference on Electronic Commerce (2012)

    Google Scholar 

  3. Balcan, M.F., Borgs, C., Braverman, M., Chayes, J., Teng, S.H.: Finding endogenously formed communities. In: SODA 2013 (2013)

    Google Scholar 

  4. Balcan, M.F., Gupta, P.: Robust hierarchical clustering. In: Proceedings of the Conference on Learning Theory, COLT (2010)

    Google Scholar 

  5. Bounova, G., de Weck, O.L.: Overview of metrics and their correlation patterns for multiple-metric topology analysis on heterogeneous graph ensembles. Phys. Rev. E 85(016117) (2012)

    Google Scholar 

  6. Clauset, A., Moore, C., Newman, M.E.J.: Hierarchical structure and the prediction of missing links in networks. Nature 453(7191), 98–101 (2008)

    Article  Google Scholar 

  7. Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Physical Review E 70(6), 066111+ (2004)

    Article  Google Scholar 

  8. Fortunato, S.: Community detection in graphs. Physics Reports 486(3-5), 75–174 (2010)

    Article  MathSciNet  Google Scholar 

  9. Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proceedings of the National Academy of Sciences 99(12), 7821–7826 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proceedings of the National Academy of Sciences 99(12) (2002)

    Google Scholar 

  11. Gleiser, P., Danon, L.: Community Structure in Jazz. Advances in Complex Systems 6(4), 565–573 (2003)

    Article  Google Scholar 

  12. He, J., Hopcroft, J., Liang, H., Suwajanakorn, S., Wang, L.: Detecting the structure of social networks using (α, β)-communities. In: Frieze, A., Horn, P., Prałat, P. (eds.) WAW 2011. LNCS, vol. 6732, pp. 26–37. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  13. Ho, Q., Parikh, A.P., Xing, E.P.: A Multiscale Community Blockmodel for Network Exploration. Journal of the American Statistical Association 107(499), 916–934 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Huang, J., Sun, H., Han, J., Deng, H., Sun, Y., Liu, Y.: Shrink: a structural clustering algorithm for detecting hierarchical communities in networks. In: Proceedings of the 19th ACM International Conference on Information and Knowledge Management, pp. 219–228. ACM (2010)

    Google Scholar 

  15. Kim, M., Leskovec, J.: Latent multi-group membership graph model. In: ICML (2012)

    Google Scholar 

  16. Kleinberg, J.: Complex networks and decentralized search algorithms. In: Proceedings of the International Congress of Mathematicians, ICM (2006)

    Google Scholar 

  17. Knuth, D.E.: The Stanford GraphBase: a platform for combinatorial computing. ACM, New York (1993)

    Google Scholar 

  18. Krebs, V.: http://www.orgnet.com/ (unpublished)

  19. Cosentino Lagomarsino, M., Jona, P., Bassetti, B., Isambert, H.: Hierarchy and feedback in the evolution of the Escherichia coli transcription network. Proceedings of the National Academy of Sciences 104(13), 5516–5520 (2007)

    Article  Google Scholar 

  20. Lancichinetti, A., Fortunato, S.: Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. Physical Review E 80(1), 016118 (2009)

    Google Scholar 

  21. Lancichinetti, A., Fortunato, S., Kertész, J.: Detecting the overlapping and hierarchical community structure in complex networks. New Journal of Physics 11(3), 033015 (2009)

    Google Scholar 

  22. 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. ACM, New York (2010)

    Chapter  Google Scholar 

  23. Lusseau, D., Schneider, K., Boisseau, O.J., Haase, P., Slooten, E., Dawson, S.M.: Behavioral Ecology and Sociobiology 54, 396–405 (2003)

    Google Scholar 

  24. McAuley, J., Leskovec, J.: Learning to discover social circles in ego networks. In: Advances in Neural Information Processing Systems 25, pp. 548–556 (2012)

    Google Scholar 

  25. Mishra, N., Schreiber, R., Stanton, I., Tarjan, R.E.: Clustering social networks. In: Bonato, A., Chung, F.R.K. (eds.) WAW 2007. LNCS, vol. 4863, pp. 56–67. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  26. Mishra, N., Schreiber, R., Stanton, I., Tarjan, R.E.: Finding strongly knit clusters in social networks. Internet Mathematics 5(1), 155–174 (2008)

    Article  MathSciNet  Google Scholar 

  27. Narasimhan, G., Smid, M.: Geometric spanning networks. Cambridge University Press (2007)

    Google Scholar 

  28. Newman, M.E.J.: Detecting community structure in networks. The European Physical Journal B - Condensed Matter and Complex Systems 38(2), 321–330 (2004)

    Article  Google Scholar 

  29. Newman, M.E.J.: Modularity and community structure in networks. Proceedings of the National Academy of Sciences 103(23), 8577–8582 (2006)

    Article  Google Scholar 

  30. Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., Parisi, D.: Defining and identifying communities in networks. Proceedings of the National Academy of Sciences of the United States of America 101(9), 2658–2663 (2004)

    Article  Google Scholar 

  31. Ravasz, E., Somera, A.L., Mongru, D.A., Oltvai, Z.N., Barabási, A.L.: Hierarchical Organization of Modularity in Metabolic Networks. Science 297(5586), 1551–1555 (2002)

    Article  Google Scholar 

  32. Schweinberger, M., Snijders, T.A.B.: Settings in social networks: A measurement model. Sociological Methodology 33, 307–341 (2003)

    Article  Google Scholar 

  33. Shen, K., Song, L., Yang, X., Zhang, W.: A hierarchical diffusion algorithm for community detection in social networks. In: 2010 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC), pp. 276–283. IEEE (2010)

    Google Scholar 

  34. 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)

    Chapter  Google Scholar 

  35. Yang, B., Di, J., Liu, J., Liu, D.: Hierarchical community detection with applications to real-world network analysis. Data & Knowledge Engineering (2012)

    Google Scholar 

  36. Zachary, W.W.: An information flow model for conflict and fission in small groups. Journal of Anthropological Research 33, 452–473 (1977)

    Google Scholar 

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Balcan, M.F., Liang, Y. (2013). Modeling and Detecting Community Hierarchies. In: Hancock, E., Pelillo, M. (eds) Similarity-Based Pattern Recognition. SIMBAD 2013. Lecture Notes in Computer Science, vol 7953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39140-8_11

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  • DOI: https://doi.org/10.1007/978-3-642-39140-8_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39139-2

  • Online ISBN: 978-3-642-39140-8

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