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Indirect Estimation of Shortest Path Distributions with Small-World Experiments

  • Antti Ukkonen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8819)

Abstract

The distribution of shortest path lenghts is a useful characterisation of the connectivity in a network. The small-world experiment is a classical way to study the shortest path distribution in real-world social networks that cannot be directly observed. However, the data observed in these experiments are distorted by two factors: attrition and routing (in)efficiency. This leads to inaccuracies in the estimates of shortest path lenghts. In this paper we propose a model to analyse small-world experiments that corrects for both of the aforementioned sources of bias. Under suitable circumstances the model gives accurate estimates of the true underlying shortest path distribution without directly observing the network. It can also quantify the routing efficiency of the underlying population. We study the model by using simulations, and apply it to real data from previous small-world experiments.

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References

  1. 1.
    Backstrom, L., Boldi, P., Rosa, M., Ugander, J., Vigna, S.: Four degrees of separation. In: WebSci., pp. 33–42 (2012)Google Scholar
  2. 2.
    Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bauckhage, C., Kersting, K., Rastegarpanah, B.: The Weibull as a model of shortest path distributions in random networks. In: MLG (2013)Google Scholar
  4. 4.
    Bonchi, F., De Francisci Morales, G., Gionis, A., Ukkonen, A.: Activity preserving graph simplification. Data Min. Knowl. Discov. 27(3), 321–343 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Dodds, P.S., Muhamad, R., Watts, D.J.: An experimental study of search in global social networks. Science 301(5634), 827–829 (2003)CrossRefGoogle Scholar
  6. 6.
    Erdős, P., Rényi, A.: On random graphs. Publicationes Mathematicae Debrecen 6, 290–297 (1959)MathSciNetGoogle Scholar
  7. 7.
    Goel, S., Muhamad, R., Watts, D.J.: Social search in ”small-world” experiments. In: WWW, pp. 701–710 (2009)Google Scholar
  8. 8.
    Gomez-Rodriguez, M., Leskovec, J., Krause, A.: Inferring networks of diffusion and influence. Transactions on Knowledge Discovery from Data 5(4), 21 (2012)Google Scholar
  9. 9.
    Gomez-Rodriguez, M., Schölkopf, B.: Submodular inference of diffusion networks from multiple trees. In: ICML (2012)Google Scholar
  10. 10.
    Killworth, P.D., McCarty, C., Bernard, H.R., House, M.: The accuracy of small world chains in social networks. Social Networks 28(1), 85–96 (2006)CrossRefGoogle Scholar
  11. 11.
    Kleinberg, J.M.: Navigation in a small world. Nature 406(6798), 845 (2000)CrossRefGoogle Scholar
  12. 12.
    Korte, C., Milgram, S.: Acquaintance links between white and negro populations: Application of the small world method. Journal of Personality and Social Psychology 15(2), 101–108 (1970)CrossRefGoogle Scholar
  13. 13.
    Liben-Nowell, D., Novak, J., Kumar, R., Raghavan, P., Tomkins, A.: Geographic routing in social networks. Proceedings of the National Academy of Sciences 102(33), 11623–11628 (2005)CrossRefGoogle Scholar
  14. 14.
    Mathioudakis, M., Bonchi, F., Castillo, C., Gionis, A., Ukkonen, A.: Sparsification of influence networks. In: KDD, pp. 529–537 (2011)Google Scholar
  15. 15.
    Travers, J., Milgram, S.: An experimental study of the small world problem. Sociometry 32(4), 425–443 (1969)CrossRefGoogle Scholar
  16. 16.
    Watts, D.J., Dodds, P.S., Newman, M.E.J.: Identity and search in social networks. Science 296(5571), 1302–1305 (2002)CrossRefGoogle Scholar
  17. 17.
    Zachary, W.: An information flow model for conflict and fission in small groups. Journal of Anthropological Research 33(4), 452–473 (1977)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Antti Ukkonen
    • 1
  1. 1.Helsinki Institute for Information Technology HIITAalto UniversityFinland

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