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Robustness of Social Networks: Comparative Results Based on Distance Distributions

  • Paolo Boldi
  • Marco Rosa
  • Sebastiano Vigna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6984)

Abstract

Given a social network, which of its nodes have a stronger impact in determining its structure? More formally: which node-removal order has the greatest impact on the network structure? We approach this well-known problem for the first time in a setting that combines both web graphs and social networks, using datasets that are orders of magnitude larger than those appearing in the previous literature, thanks to some recently developed algorithms and software tools that make it possible to approximate accurately the number of reachable pairs and the distribution of distances in a graph. Our experiments highlight deep differences in the structure of social networks and web graphs, show significant limitations of previous experimental results, and at the same time reveal clustering by label propagation as a new and very effective way of locating nodes that are important from a structural viewpoint.

Keywords

Social Network Betweenness Centrality Distance Distribution Label Propagation Neighbourhood Function 
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. [AJB00]
    Albert, R., Jeong, H., Barabási, A.-L.: Error and attack tolerance of complex networks. Nature 406, 378–382 (2000)CrossRefGoogle Scholar
  2. [BCK06]
    Borgatti, S.P., Carley, K.M., Krackhardt, D.: On the robustness of centrality measures under conditions of imperfect data. Social Networks 28(2), 124–136 (2006)CrossRefGoogle Scholar
  3. [BE05]
    Brandes, U., Erlebach, T. (eds.): Network Analysis. LNCS, vol. 3418, pp. 1–6. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. [Bor05]
    Borgatti, S.P.: Centrality and network flow. Social Networks 27(1), 55–71 (2005)MathSciNetCrossRefGoogle Scholar
  5. [Bor06]
    Borgatti, S.P.: Identifying sets of key players in a social network. Comput. Math. Organ. Theory 12, 21–34 (2006)CrossRefzbMATHGoogle Scholar
  6. [Bra01]
    Brandes, U.: A faster algorithm for betweenness centrality. Journal of Mathematical Sociology 25(2), 163–177 (2001)CrossRefzbMATHGoogle Scholar
  7. [BRV11]
    Boldi, P., Rosa, M., Vigna, S.: HyperANF: Approximating the neighbourhood function of very large graphs on a budget. In: Proceedings of the 20th International Conference on World Wide Web, pp. 625–634. ACM, New York (2011)Google Scholar
  8. [BSV09]
    Boldi, P., Santini, M., Vigna, S.: PageRank: Functional dependencies. ACM Trans. Inf. Sys. 27(4), 1–23 (2009)CrossRefGoogle Scholar
  9. [CH10]
    Cohen, R., Havlin, S.: Complex Networks: Structure, Robustness and Function. Cambridge University Press, Cambridge (2010)CrossRefzbMATHGoogle Scholar
  10. [CKL+09]
    Chierichetti, F., Kumar, R., Lattanzi, S., Mitzenmacher, M., Panconesi, A., Raghavan, P.: On compressing social networks. In: KDD 2009, pp. 219–228. ACM, New York (2009)Google Scholar
  11. [DLMT08]
    Donato, D., Leonardi, S., Millozzi, S., Tsaparas, P.: Mining the inner structure of the web graph. Journal of Physics A: Mathematical and Theoretical 41(22), 224017 (2008)MathSciNetCrossRefGoogle Scholar
  12. [Fog03]
    Fogaras, D.: Where to Start Browsing the Web? In: Böhme, T., Heyer, G., Unger, H. (eds.) IICS 2003. LNCS, vol. 2877, pp. 65–79. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. [LADW05]
    Li, L., Alderson, D.L., Doyle, J., Willinger, W.: Towards a theory of scale-free graphs: Definition, properties, and implications. Internet Math. 2(4) (2005)Google Scholar
  14. [LM04]
    Langville, A.N., Meyer, C.D.: Deeper inside PageRank. Internet Math. 1(3), 355–400 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  15. [Mil67]
    Milgram, S.: The small world problem. Psychology Today 2, 60–67 (1967)Google Scholar
  16. [ML00]
    Marchiori, M., Latora, V.: Harmony in the small-world. Physica A 285(3-4), 539–546 (2000)CrossRefzbMATHGoogle Scholar
  17. [NP03]
    Newman, M.E.J., Park, J.: Why social networks are different from other types of networks. Phys. Rev. E 68(3), 036122 (2003)CrossRefGoogle Scholar
  18. [PBMW98]
    Page, L., Brin, S., Motwani, R., Winograd, T.: The PageRank citation ranking: Bringing order to the web. Technical report, Stanford Digital Library Technologies Project, Stanford University, USA (1998)Google Scholar
  19. [PGF02]
    Palmer, C.R., Gibbons, P.B., Faloutsos, C.: Anf: a fast and scalable tool for data mining in massive graphs. In: KDD 2002, pp. 81–90. ACM, New York (2002)Google Scholar
  20. [RAK07]
    Raghavan, U.N., Albert, R., Kumara, S.: Near linear time algorithm to detect community structures in large-scale networks. Phys. Rev. E 76(3) (2007)Google Scholar
  21. [WF94]
    Wasserman, S., Faust, K.: Social network analysis: Methods and applications. Cambridge Univ. Press, Cambridge (1994)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Paolo Boldi
    • 1
  • Marco Rosa
    • 1
  • Sebastiano Vigna
    • 1
  1. 1.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoItalia

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