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Diskr. Mat., 2009, Volume 21, Issue 3, Pages 14–23 (Mi dm1057)  

This article is cited in 13 scientific papers (total in 13 papers)

On the limit distributions of the vertex degrees of conditional Internet graphs

Yu. L. Pavlov


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.

DOI: https://doi.org/10.4213/dm1057

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English version:
Discrete Mathematics and Applications, 2009, 19:4, 349–359

Bibliographic databases:

UDC: 519.2
Received: 24.03.2008

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

Citation in format AMSBIB
\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://www.ams.org/mathscinet-getitem?mr=2588649}
\elib{http://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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350518864}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. L. Pavlov, “On conditional Internet graphs whose vertex degrees have no mathematical expectation”, Discrete Math. Appl., 20:5-6 (2010), 509–524  mathnet  crossref  crossref  mathscinet  elib
    2. Pavlov Yu.L., Dertishnikova E.N., “O predelnom raspredelenii maksimalnoi stepeni vershiny v sluchainom grafe internet-tipa”, Trudy Karelskogo nauchnogo tsentra RAN, 2010, no. 3, 59–65  elib
    3. Pavlov Yu.L., Cheplyukova I.A., “Ob asimptotike statistiki tipa $\chi^2$ dlya internet-grafov”, Trudy Karelskogo nauchnogo tsentra RAN, 2010, no. 3, 66–71  elib
    4. Pavlov Yu.L., “O tipichnoi strukture konfiguratsionnogo internet-grafa s izvestnym chislom svyazei”, Trudy Karelskogo nauchnogo tsentra RAN, 2011, no. 5, 86–96  elib
    5. Cheplyukova I.A., “O predelnykh raspredeleniyakh nekotorykh chislovykh kharakteristik internet-grafov”, Trudy Karelskogo nauchnogo tsentra RAN, 2012, no. 5, 110–121  elib
    6. Pavlov Yu.L., “O predelnykh raspredeleniyakh stepenei vershin uslovnogo konfiguratsionnogo sluchainogo grafa”, Trudy Karelskogo nauchnogo tsentra RAN, 2012, no. 5, 78–88  elib
    7. 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  mathnet  crossref  isi  elib
    8. A. V. Lebedev, “Ekstremalnye indeksy v skheme serii i ikh prilozheniya”, Inform. i ee primen., 9:3 (2015), 39–54  mathnet  crossref  elib
    9. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    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  mathnet  crossref  crossref  mathscinet  isi  elib
    11. 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  mathnet  crossref  crossref  isi  elib
    12. 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  crossref  mathscinet  zmath  isi  scopus
    13. Yu. L. Pavlov, “O svyaznosti konfiguratsionnykh grafov”, Diskret. matem., 31:2 (2019), 114–122  mathnet  crossref  elib
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