Abstract
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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Kraetzl, M., Nickel, C., Scheinerman, E.R.: Random dot product graphs: A model for social netowrks. Preliminary Manuscript (2005)
Kraetzl, M., Nickel, C., Scheinerman, E.R., Tucker, K.: Random dot product graphs (July 2005), http://www.ipam.ucla.edu/abstract.aspx?tid=5498
Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Modern Phys. 74(1), 47–97 (2002)
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)
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)
Durrett, R.: Random graph dynamics. In: Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge (2007)
Chung, F., Galas, D.J., Dewey, T.G., Lu, L.: Duplication models for biological networks. Journal of Computational Biology (2003)
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)
Bornholdt, S., Schuster, H.G. (eds.): Handbook of graphs and networks. From the genome to the internet. Wiley-VCH, Weinheim (2003)
Newman, M.E.J.: Assortative mixing in networks. Physical Review Letters 89 (2002)
Flaxman, A.D., Frieze, A.M., Vera, J.: A geometric preferential attachment model of networks. Internet Math. 3(2), 187–205 (2006)
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)
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)
Leskovec, J., Kleinberg, J., Faloutsos, C.: Graph evolution: Densification and shrinking diameters. ACM Trans. Knowl. Discov. Data 1(1) (2007)
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)
Bollobás, B.: Modern graph theory. In: Bollobás, B. (ed.) Graduate Texts in Mathematics, vol. 184, Springer, New York (1998)
Ben-Tal, A., Nemirovski, A.: Lectures on Modern Convex Optimization; Analysis, Algorithms, and Engineering Applications, SIAM, Philadelphia, PA (2001)
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)
Scheinerman, E.R., Tucker, K.: Exact and asymptotic dot product representations of graphs i: Fundamentals (Submitted, 2007)
Scheinerman, E.R., Tucker, K.: Exact and asymptotic dot product representations of graphs ii: Characterization and recognition (Submitted, 2007)
Scheinerman, E.R., Tucker, K.: Modelling graphs using dot product representations. (preparation, 2007)
Alon, N., Spencer, J.H.: The Probabilistic Method. In: Wiley-Interscience Series in Discrete Mathematics and Optimization, 2nd edn., Wiley-Interscience, New York (2000)
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)
Young, S.J.: Sparse random dot product graphs. (preparation, 2007)
Milgram, S.: The small world problem. Psychology Today (1967)
Milgram, S., Travers, J.: An experimental study of the small world problem. Sociometry 32(4), 425–443 (1969)
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)
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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. https://doi.org/10.1007/978-3-540-77004-6_11
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DOI: https://doi.org/10.1007/978-3-540-77004-6_11
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