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The Geometric Protean Model for On-Line Social Networks

  • Anthony Bonato
  • Jeannette Janssen
  • Pawel Prałat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6516)

Abstract

We introduce a new geometric, rank-based model for the link structure of on-line social networks (OSNs). In the geo-protean (GEO-P) model for OSNs nodes are identified with points in Euclidean space, and edges are stochastically generated by a mixture of the relative distance of nodes and a ranking function. With high probability, the GEO-P model generates graphs satisfying many observed properties of OSNs, such as power law degree distributions, the small world property, densification power law, and bad spectral expansion. We introduce the dimension of an OSN based on our model, and examine this new parameter using actual OSN data.

Keywords

Degree Distribution Average Degree Ranking Function Link Structure Expansion Property 
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.
    Adamic, L.A., Buyukkokten, O., Adar, E.: A social network caught in the web. First Monday 8 (2003)Google Scholar
  2. 2.
    Ahn, Y., Han, S., Kwak, H., Moon, S., Jeong, H.: Analysis of topological characteristics of huge on-line social networking services. In: Proceedings of the 16th International Conference on World Wide Web (2007)Google Scholar
  3. 3.
    Aiello, W., Bonato, A., Cooper, C., Janssen, J., Prałat, P.: A spatial web graph model with local influence regions. Internet Mathematics 5, 175–196 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bonato, A.: A Course on the Web Graph. American Mathematical Society Graduate Studies Series in Mathematics, Providence, Rhode Island (2008)Google Scholar
  5. 5.
    Bonato, A., Hadi, N., Horn, P., Prałat, P., Wang, C.: Models of on-line social networks. Accepted to Internet Mathematics (2010)Google Scholar
  6. 6.
    Chierichetti, F., Kumar, R., Lattanzi, S., Mitzenmacher, M., Panconesi, A., Raghavan, P.: On compressing social networks. In: Proceedings of the 15th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2009 (2009)Google Scholar
  7. 7.
    Chung, F.R.K.: Spectral Graph Theory. American Mathematical Society, Providence (1997)zbMATHGoogle Scholar
  8. 8.
    Chung, F.R.K., Lu, L.: Complex Graphs and Networks. American Mathematical Society, U.S.A. (2004)zbMATHGoogle Scholar
  9. 9.
    Estrada, E.: Spectral scaling and good expansion properties in complex networks. Europhys. Lett. 73, 649–655 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Flaxman, A., Frieze, A., Vera, J.: A geometric preferential attachment model of networks. Internet Mathematics 3, 187–205 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Janssen, J., Prałat, P.: Protean graphs with a variety of ranking schemes. Theoretical Computer Science 410, 5491–5504 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Java, A., Song, X., Finin, T., Tseng, B.: Why we twitter: understanding microblogging usage and communities. In: Proceedings of the Joint 9th WEBKDD and 1st SNA-KDD Workshop 2007 (2007)Google Scholar
  13. 13.
    Kleinberg, J.: The small-world phenomenon: An algorithmic perspective. In: Proceedings of the 32nd ACM Symposium on Theory of Computing (2000)Google Scholar
  14. 14.
    Kumar, R., Novak, J., Tomkins, A.: Structure and evolution of on-line social networks. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2006)Google Scholar
  15. 15.
    Kwak, H., Lee, C., Park, H., Moon, S.: What is Twitter, a social network or a news media? In: Proceedings of the 19th International World Wide Web Conference (2010)Google Scholar
  16. 16.
    Lattanzi, S., Sivakumar, D.: Affiliation Networks. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing (2009)Google Scholar
  17. 17.
    Leskovec, J., Kleinberg, J., Faloutsos, C.: Graphs over time: densification Laws, shrinking diameters and possible explanations. In: Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2005)Google Scholar
  18. 18.
    Leskovec, J., Chakrabarti, D., Kleinberg, J., Faloutsos, C.: Realistic, mathematically tractable graph generation and evolution, using Kronecker multiplication. In: Jorge, A.M., Torgo, L., Brazdil, P.B., Camacho, R., Gama, J. (eds.) PKDD 2005. LNCS (LNAI), vol. 3721, pp. 133–145. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
    Liben-Nowell, D., Novak, J., Kumar, R., Raghavan, P., Tomkins, A.: Geographic routing in social networks. Proceedings of the National Academy of Sciences 102, 11623–11628 (2005)CrossRefGoogle Scholar
  20. 20.
    Łuczak, T., Prałat, P.: Protean graphs. Internet Mathematics 3, 21–40 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Mislove, A., Marcon, M., Gummadi, K., Druschel, P., Bhattacharjee, B.: Measurement and analysis of on-line social networks. In: Proceedings of the 7th ACM SIGCOMM Conference on Internet Measurement (2007)Google Scholar
  22. 22.
    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
  23. 23.
    Twitterholic, http://twitterholic.com/ (accessed September 12, 2010)
  24. 24.
    Watts, D.J., Dodds, P.S., Newman, M.E.J.: Identity and search in social networks. Science 296, 1302–1305 (2002)CrossRefGoogle Scholar
  25. 25.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)CrossRefzbMATHGoogle Scholar
  26. 26.
    Wikipedia: List of social networking websites, http://en.wikipedia.org/wiki/List_of_social_networking_websites (accessed September 12, 2010)
  27. 27.
    YouTube, Advertising and Targeting, http://www.youtube.com/t/advertising_targeting (accessed September 12, 2010)

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Anthony Bonato
    • 1
  • Jeannette Janssen
    • 2
  • Pawel Prałat
    • 3
  1. 1.Department of MathematicsRyerson UniversityTorontoCanada
  2. 2.Department of Mathematics and StatisticsDalhousie UniversityHalifaxCanada
  3. 3.Department of MathematicsWest Virginia UniversityMorgantownUSA

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