Abstract:
We consider the random graphs modelling the structure of large data transmission networks including Internet. We investigate the subset of such graphs consisting of $N$ vertices under the condition that the number of edges is equal to $n$. We obtain the limit distributions of the maximum degree of vertices and the number of vertices of a given degree as $N,n\to\infty$ so that $n/N\to\lambda$, where $\lambda$ is a positive constant.
Citation:
Yu. L. Pavlov, “On the limit distributions of the vertex degrees of conditional Internet graphs”, Diskr. Mat., 21:3 (2009), 14–23; Discrete Math. Appl., 19:4 (2009), 349–359
\Bibitem{Pav09}
\by Yu.~L.~Pavlov
\paper On the limit distributions of the vertex degrees of conditional Internet graphs
\jour Diskr. Mat.
\yr 2009
\vol 21
\issue 3
\pages 14--23
\mathnet{http://mi.mathnet.ru/dm1057}
\crossref{https://doi.org/10.4213/dm1057}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2588649}
\elib{https://elibrary.ru/item.asp?id=20730297}
\transl
\jour Discrete Math. Appl.
\yr 2009
\vol 19
\issue 4
\pages 349--359
\crossref{https://doi.org/10.1515/DMA.2009.023}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350518864}
Linking options:
https://www.mathnet.ru/eng/dm1057
https://doi.org/10.4213/dm1057
https://www.mathnet.ru/eng/dm/v21/i3/p14
This publication is cited in the following 15 articles:
Yu Miao, Qian Du, Zhen Wang, “Some Limit Theorems for the Cell Load in the Generalized Allocation Scheme”, Lith Math J, 62:3 (2022), 372
E. G. Grigoreva, V. A. Klyachin, “Issledovanie statisticheskikh kharakteristik teksta na osnove grafovoi modeli lingvisticheskogo korpusa”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 20:1 (2020), 116–126
Yu. L. Pavlov, “On the connectivity of configuration graphs”, Discrete Math. Appl., 31:1 (2021), 43–49
Yu. L. Pavlov, I. A. Cheplyukova, “On the asymptotics of degree structure of configuration graphs with bounded number of edges”, Discrete Math. Appl., 29:4 (2019), 219–232
Goldaeva A.A. Lebedev A.V., “On Extremal Indices Greater Than One For a Scheme of Series”, Lith. Math. J., 58:4 (2018), 384–398
Yu. L. Pavlov, E. V. Khvorostyanskaya, “On the limit distributions of the degrees of vertices in configuration graphs with a bounded number of edges”, Sb. Math., 207:3 (2016), 400–417
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
A. V. Lebedev, “Activity maxima in some models of information networks with random weights and heavy tails”, Problems Inform. Transmission, 51:1 (2015), 66–74
A. V. Lebedev, “Ekstremalnye indeksy v skheme serii i ikh prilozheniya”, Inform. i ee primen., 9:3 (2015), 39–54
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