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Random Dot Product Graph Models for Social Networks

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Algorithms and Models for the Web-Graph (WAW 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4863))

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Inspired by the recent interest in combining geometry with random graph models, we explore in this paper two generalizations of the random dot product graph model proposed by Kraetzl, Nickel and Scheinerman, and Tucker [1,2]. In particular we consider the properties of clustering, diameter and degree distribution with respect to these models. Additionally we explore the conductance of these models and show that in a geometric sense, the conductance is constant.

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  1. Kraetzl, M., Nickel, C., Scheinerman, E.R.: Random dot product graphs: A model for social netowrks. Preliminary Manuscript (2005)

    Google Scholar 

  2. Kraetzl, M., Nickel, C., Scheinerman, E.R., Tucker, K.: Random dot product graphs (July 2005),

  3. Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Modern Phys. 74(1), 47–97 (2002)

    Article  MathSciNet  Google Scholar 

  4. Achlioptas, D., Kempe, D., Clasuet, A., Moore, C.: On the bias of traceroute sampling or, power-law degree distributions in regular graphs. In: STOC 2005. Proc. of the 37th ACM Symposium on the Theory of Computer Science (2005)

    Google Scholar 

  5. Lakhina, A., Byers, J.W., Crovella, M., Xie, P.: Sampling biases in IP topology measurements. In: INFOCOM 2003. 22nd Joint Conference of the IEEE Computer and Communications Societies (2003)

    Google Scholar 

  6. Durrett, R.: Random graph dynamics. In: Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge (2007)

    Google Scholar 

  7. Chung, F., Galas, D.J., Dewey, T.G., Lu, L.: Duplication models for biological networks. Journal of Computational Biology (2003)

    Google Scholar 

  8. Kumar, R., Raghavan, P., Rajagopalan, S., Sivakumar, D., Tompkins, A., Upfal, E.: The web as a graph. In: PODS 2000. Proc. of the 19th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pp. 1–10. ACM Press, New York (2000)

    Chapter  Google Scholar 

  9. Bornholdt, S., Schuster, H.G. (eds.): Handbook of graphs and networks. From the genome to the internet. Wiley-VCH, Weinheim (2003)

    MATH  Google Scholar 

  10. Newman, M.E.J.: Assortative mixing in networks. Physical Review Letters 89 (2002)

    Google Scholar 

  11. Flaxman, A.D., Frieze, A.M., Vera, J.: A geometric preferential attachment model of networks. Internet Math. 3(2), 187–205 (2006)

    MATH  MathSciNet  Google Scholar 

  12. Caldarelli, G., Capocci, A., de Los Rios, P., Muñoz, M.A.: Scale-Free Networks from Varying Vertex Intrinsic Fitness. Physical Review Letters 89(25) (2002)

    Google Scholar 

  13. Azar, Y., Fiat, A., Karlin, A., McSherry, F., Saia, J.: Spectral analysis of data. In: STOC 2001. Proc. of the 33rd ACM Symposium on Theory of Computing, pp. 619–626. ACM Press, New York (2001)

    Chapter  Google Scholar 

  14. Leskovec, J., Kleinberg, J., Faloutsos, C.: Graph evolution: Densification and shrinking diameters. ACM Trans. Knowl. Discov. Data 1(1) (2007)

    Google Scholar 

  15. 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), 11623–1162 (2005)

    Google Scholar 

  16. Bollobás, B.: Modern graph theory. In: Bollobás, B. (ed.) Graduate Texts in Mathematics, vol. 184, Springer, New York (1998)

    Google Scholar 

  17. Ben-Tal, A., Nemirovski, A.: Lectures on Modern Convex Optimization; Analysis, Algorithms, and Engineering Applications, SIAM, Philadelphia, PA (2001)

    Google Scholar 

  18. Hörmnn, W., Leydold, J.: Random-number and random-variate generation: automatic random variate generation for simulation input. In: Winter Simulation Conference, pp. 675–682 (2000)

    Google Scholar 

  19. Scheinerman, E.R., Tucker, K.: Exact and asymptotic dot product representations of graphs i: Fundamentals (Submitted, 2007)

    Google Scholar 

  20. Scheinerman, E.R., Tucker, K.: Exact and asymptotic dot product representations of graphs ii: Characterization and recognition (Submitted, 2007)

    Google Scholar 

  21. Scheinerman, E.R., Tucker, K.: Modelling graphs using dot product representations. (preparation, 2007)

    Google Scholar 

  22. Alon, N., Spencer, J.H.: The Probabilistic Method. In: Wiley-Interscience Series in Discrete Mathematics and Optimization, 2nd edn., Wiley-Interscience, New York (2000)

    Google Scholar 

  23. Mihail, M., Papadimitriou, C., Saberi, A.: On certain connectivity properties of the internet topology. J. Comput. System Sci. 72(2), 239–251 (2006) (FOCS 2003 Special Issue)

    Article  MATH  MathSciNet  Google Scholar 

  24. Young, S.J.: Sparse random dot product graphs. (preparation, 2007)

    Google Scholar 

  25. Milgram, S.: The small world problem. Psychology Today (1967)

    Google Scholar 

  26. Milgram, S., Travers, J.: An experimental study of the small world problem. Sociometry 32(4), 425–443 (1969)

    Article  Google Scholar 

  27. Kleinberg, J.M.: The small world phenomenon: an algorithmic perspective. In: STOC 1999. Proc. of the 32nd ACM Symposium on the Theory of Computer Science (1999)

    Google Scholar 

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Anthony Bonato Fan R. K. Chung

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Young, S.J., Scheinerman, E.R. (2007). Random Dot Product Graph Models for Social Networks. In: Bonato, A., Chung, F.R.K. (eds) Algorithms and Models for the Web-Graph. WAW 2007. Lecture Notes in Computer Science, vol 4863. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77003-9

  • Online ISBN: 978-3-540-77004-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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