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Matematicheskoe modelirovanie, 2021, Volume 33, Number 9, Pages 3–21
DOI: https://doi.org/10.20948/mm-2021-09-01
(Mi mm4316)
 

Model for the evolution of the degree distributions of the vertices of social network graphs

A. A. Kislitsyn, Yu. N. Orlov

Keldysh Institute of Applied Mathematics RAS
References:
Abstract: The paper presents a study of the structure of the network graph formed by friendships of the social network «VKontakte» between Russian cities, taking into account the gender and age structure of participants. This graph is interesting because its vertices are not points, but multidimensional objects corresponding to the amount of parameters the user is described by. In this case, we consider three-dimensional vertexes that correspond to gender, age, and region of residence. It turned out that the distribution of graph vertices by degrees strongly depends on which parameter the vertex corresponds to. Thus, the distribution of regional relationships without gender and age is close to uniform, and the distribution of age relationships without gender and region is triangular. As a result, the «urban» graph has a large fully connected core and sparse periphery, and the «age» graph has fully connected communities of 5–7 vertices that are weakly connected to each other. In this paper, model distributions of degrees of multidimensional vertices of a network graph are constructed and the dependence of the graph density on the rank of vertex parameters (large city, medium city, small city, popular age etc.) is studied. Various methods of vertex clustering and matrix evolution are also considered.
Keywords: network graph evolution, strongly connected component, multidimensional vertices, vertex degree distribution, clustering.
Received: 19.04.2021
Revised: 19.04.2021
Accepted: 24.05.2021
English version:
Mathematical Models and Computer Simulations, 2022, Volume 14, Issue 2, Pages 270–280
DOI: https://doi.org/10.1134/S2070048222020089
Document Type: Article
Language: Russian
Citation: A. A. Kislitsyn, Yu. N. Orlov, “Model for the evolution of the degree distributions of the vertices of social network graphs”, Matem. Mod., 33:9 (2021), 3–21; Math. Models Comput. Simul., 14:2 (2022), 270–280
Citation in format AMSBIB
\Bibitem{KisOrl21}
\by A.~A.~Kislitsyn, Yu.~N.~Orlov
\paper Model for the evolution of the degree distributions of the vertices of social network graphs
\jour Matem. Mod.
\yr 2021
\vol 33
\issue 9
\pages 3--21
\mathnet{http://mi.mathnet.ru/mm4316}
\crossref{https://doi.org/10.20948/mm-2021-09-01}
\transl
\jour Math. Models Comput. Simul.
\yr 2022
\vol 14
\issue 2
\pages 270--280
\crossref{https://doi.org/10.1134/S2070048222020089}
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    References:34
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