Limit theorems for the number of multiple edges in the configuration graph Irina Cheplyukova Karelian Research Centre of Russian Academy of Sciences

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Presentation transcript:

Limit theorems for the number of multiple edges in the configuration graph Irina Cheplyukova Karelian Research Centre of Russian Academy of Sciences

CONFUGURATION MODEL B,Bollobas (1980). A Probabilistic proof of an asymptotic formula for the number of labeled regular graphs. European Journal of Combinatorics. Vol.1. P model with fixed degree sequence M.Molloy and B.Reed (1995). A critical point for random graphs given degree sequence. Random Structures and Algorithms. Vol.6. P model with independent identically distributed vertex degrees M.E.J. Newman, S.H. Strogatz, D.J. Watts.(2001) Random graphs with arbitrary degree distribution and their applications, Phys. Rev. E A.-L. Barabasi, R. Albert.(1999) Emergence of scaling in random network, Science 286, P Faloutsos C., Faloutsos P.,Faloutsos M. (1999) On power-law relationships of the internet topology. Computer Communications. Rev. 29. P. 251−262.

H. Reittu, I. Norros (2004). On the power-law random graph model of massive data networks. Performance Evaluation. 55, 3-23.

Erdös P., Rényi A.Erdös P., Rényi A. (1960) On the evolution of random graphs. Magyar Tud. Akad. Mat. Kutató Int. Közl. Vol.5. P. 17−61. Hofstad R., Hooghiemsra G., Znamenski D.Hofstad R., Hooghiemsra G., Znamenski D. (2007) Distances in random graphs with finite mean and infinite variance degrees. Electronic Journal of Probability. Vol.12. P.703−766. Janson S., Luczak T., Rucinski A.Janson S., Luczak T., Rucinski A. (2000) Random graphs. New York: Wiley, 348p. Pavlov Yu.L. Pavlov Yu.L. (2007) On power-law random graphs and branching processes. Proceedings of the Eight International Conference CDAM. Minsk: Publishing center BSU. Vol.1. P. 92−98.

Bollobas B.( 1980 ) A probabilistic proof of an asymptotic formula for the number of labeled regular graphs. European Journal of Combinatorics. Vol.1. P. 311−316.

Hofstad R. Random graphs and complex networks

The first configuration graph

Power-law random graph Aiello W., Chung F., Lu L. A random graph model for power-law graphs. Experiment Math., 10, 1, 2001, Newman M.E.J., Strogats S.H., Wats D.J. Random graphs with arbitrary degree distribution and their appliсations. Phys. Rev. E., 64, , 2000.

The second random graph

Yu.Pavlov, M.Stepanov. Limit distribution of the number of loops in a random graph. (2013) Proceeding of Steklov Institute of Mathematics. Volume 282. Issue 1. Pp

Thanks for your attention.