Geodesic
Conditional configuration graphs with discrete power-law distribution of vertex degrees
Sbornik. Mathematics, Tome 209 (2018) no. 2, pp. 258-275 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is concerned with configuration graphs with discrete power-law distribution of vertex degrees. The parameter of this distribution is a random variable, which is unknown except that it imposes relatively weak constraints on the asymptotic behaviour of the probabilities of large values of degrees. For such graphs with the known number of edges, we find the limiting distributions of the maximal degree of a vertex and of the number of vertices of a given degree for various laws of convergence to infinity of the numbers of vertices and edges. The results in the present paper, which are proved using the generalized scheme of allocation of particles to cells, demonstrate the potency of this method in the case of independent random variables with known limiting behaviour of the tail of the distribution. Bibliography: 13 titles.
Keywords: configuration graphs, vertex degree, limit theorem, conditional random graph, generalized allocation scheme. 
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     title = {Conditional configuration graphs with discrete power-law distribution of vertex degrees},
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Yu. L. Pavlov. Conditional configuration graphs with discrete power-law distribution of vertex degrees. Sbornik. Mathematics, Tome 209 (2018) no. 2, pp. 258-275. http://geodesic.mathdoc.fr/item/SM_2018_209_2_a6/

[1] B. Bollobas, “A probabilistic proof of an asymptotic formula of the number of labelled regular graphs”, European J. Combin., 1:4 (1980), 311–316 | DOI | MR | Zbl

[2] C. Faloutsos, P. Faloutsos, M. Faloutsos, “On power-law relationships of the Internet topology”, Comput. Commun. Rev., 29:4 (1999), 251–262 | DOI

[3] R. Durrett, Random graph dynamics, Camb. Ser. Stat. Probab. Math., Cambridge Univ. Press, Cambridge, 2007, x+212 pp. | DOI | MR | Zbl

[4] H. Reittu, I. Norros, “On the power-law random graph model of massive data networks”, Performance Evaluation, 55:1-2 (2004), 3–23 | DOI

[5] M. Leri, Yu. Pavlov, “Power-law random graphs robustness: link saving and forest fire model”, Austrian J. Stat., 43:4 (2014), 229–236 | DOI

[6] Yu. L. Pavlov, I. A. Cheplyukova, “Random graphs of Internet type and the generalised allocation scheme”, Discrete Math. Appl., 18:5 (2008), 447–463 | DOI | DOI | MR | Zbl

[7] Yu. L. Pavlov, “On conditional Internet graphs whose vertex degrees have no mathematical expectation”, Discrete Math. Appl., 20:5-6 (2010), 509–524 | DOI | DOI | MR | Zbl

[8] G. Bianconi, A.-L. Barabási, “Bose–Einstein condensation in complex networks”, Phys. Rev. Lett., 86:24 (2001), 5632–5635 | DOI

[9] Yu. L. Pavlov, “Predelnye raspredeleniya chisla vershin zadannoi stepeni uslovnogo konfiguratsionnogo grafa”, Tr. Kar. NTs RAN, 8 (2016), 73–80

[10] Yu. L. Pavlov, E. V. Feklistova, “On limit behavior of maximum vertex degree in a conditional configuration graph near critical points”, Discrete Math. Appl., 27:4 (2017), 213–222 | DOI | DOI | MR

[11] Yu. L. Pavlov, “Ob uslovnykh konfiguratsionnykh grafakh so sluchainym raspredeleniem stepenei vershin”, Tr. Kar. NTs RAN, 8 (2016), 62–72

[12] V. F. Kolchin, Random graphs, Encyclopedia Math. Appl., 53, Cambridge Univ. Press, Cambridge, 1999, xii+252 pp. | MR | MR | Zbl | Zbl

[13] A. Erdélyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Higher transcendental functions, Based, in part, on notes left by H. Bateman, v. I, McGraw-Hill Book Company, Inc., New York–Toronto–London, 1953, xxvi+302 pp. | MR | MR | Zbl | Zbl