1. Limit theorems for the number of multiple edges in the configuration graph Irina Cheplyukova Karelian Research Centre of Russian Academy of Sciences chia@krc.karelia.ru

2. 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. 311-316. 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.161-179. 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 64 026118. A.-L. Barabasi, R. Albert.(1999) Emergence of scaling in random network, Science 286, P.509-512. Faloutsos C., Faloutsos P.,Faloutsos M. (1999) On power-law relationships of the internet topology. Computer Communications. Rev. 29. P. 251−262.

3. 1 0 2 3 4 5 6 H. Reittu, I. Norros (2004). On the power-law random graph model of massive data networks. Performance Evaluation. 55, 3-23.

4. 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.

5. 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.

6. Hofstad R. Random graphs and complex networks. 2011.

7. The first configuration graph

8. Power-law random graph Aiello W., Chung F., Lu L. A random graph model for power-law graphs. Experiment Math., 10, 1, 2001, 53-66. Newman M.E.J., Strogats S.H., Wats D.J. Random graphs with arbitrary degree distribution and their appliсations. Phys. Rev. E., 64, 026118, 2000.

9. The second random graph

10. 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.209-219.

16. Thanks for your attention.