chebЧебышевский сборникChebyshevskii Sbornik2226-8383Tula State Lev Tolstoy Pedagogical University10.22405/2226-8383-2025-26-2-218-231cheb-1970Research ArticleСтатьиArticleЦентральности в классических графах и зависимости между нимиCentralities in classical graphs and relations between themТужилинМихаил АлексеевичTuzhilinMikhail Alekseevich

кандидат физико-математических наук

candidate of physical and mathematical sciences

mtu93@mail.ruМосковский государственный университет им. М. В. ЛомоносоваРоссияLomonosov Moscow State UniversityRussian Federation202510072025262218231Copyright © Тужилин М.А., 20252025Тужилин М.А.Tuzhilin M.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.chebsbornik.ru/jour/article/view/1970

В статье доказываются оценки зависимостей между средним кластерным коэффициентом и глобальным кластерным коэффициентом, центральностью по близости, централь-ностью по посредничеству и центральностью напряжения для простых графов. Также уточняется теорема о зависимости между средним кластерным коэффициентом и радиальной центральностью и проводится подсчет этих центральностей для 3-х бесконечных серий классических графов.

In the paper relations between average clustering coefficient and global clustering coefficient, closeness, betweenness and stress centralities were proved for simple graphs. Also the theorem about the realtion between average clustering coefficient and radiality is clarified and thesecentralities are calculated for 3 classical series of graphs.

сетицентральностилокальные и глобальные характеристики графовкластерный коэффициент Уоттса – Строгацаглобальный кластерный коэффициент.networkscentralitieslocal and global properties of graphsWatts – Strogatz clustering coefficientglobal clustering coefficient.ReferencesBonacich P. Factoring and weighting approaches to status scores and clique identification // Journal of mathematical sociology. 1972. Vol. 2, no. 1. P. 113-120.Bonacich, P., 1972, “Factoring and weighting approaches to status scores and clique identification”, Journal of Mathematical Sociology, vol. 2, no. 1, pp. 113–120.Borgatti S.P., Everett M.G. A graph-theoretic perspective on centrality // Social networks. 2006. Vol. 28, no. 4. P. 466-484.Borgatti, S.P., Everett, M.G., 2006, “A graph-theoretic perspective on centrality”, Social Networks, vol. 28, no. 4, pp. 466–484.Kiss C., Bichler M. Identification of influencers - measuring influence in customer networks // Decision Support Systems. 2008. Vol. 46, no. 1. P. 233-253.Kiss, C., Bichler, M., 2008, “Identification of influencers - measuring influence in customer networks”, Decision Support Systems, vol. 46, no. 1, pp. 233–253.Lee S.H.M., Cotte J., Noseworthy T.J. The role of network centrality in the flow of consumer influence // Journal of Consumer Psychology. 2010. Vol. 20, no. 1. P. 66-77.Lee, S.H.M., Cotte, J., Noseworthy, T.J., 2010, “The role of network centrality in the flow of consumer influence”, Journal of Consumer Psychology, vol. 20, no. 1, pp. 66–77.You J. [et al.] Identity-aware graph neural networks // Proceedings of the AAAI conference on artificial intelligence. 2021. Vol. 35, no. 12. P. 10737-10745.You, J., Gomes-Selman, J.M., Ying, R., Leskovec, J., 2021, “Identity-aware graph neural networks”, Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35, no. 12, pp. 10737–10745.Yuan M.M. [et al.] Climate warming enhances microbial network complexity and stability // Nature Climate Change. 2021. Vol. 11, no. 4. P. 343-348.Yuan, M.M., Guo, X., Wu, L., Zhang, Y.A., Xiao, N., Ning, D., Zhou, J., 2021, “Climate warming enhances microbial network complexity and stability”, Nature Climate Change, vol. 11, no. 4, pp. 343–348.Watts D.J., Strogatz S.H. Collective dynamics of ’small-world’ networks // Nature. 1998. Vol. 393, no. 6684. P. 440-442.Watts, D.J., Strogatz, S.H., 1998, “Collective dynamics of ’small-world’ networks”, Nature, vol. 393, no. 6684, pp. 440–442.Luce R.D., Perry A.D. A method of matrix analysis of group structure // Psychometrika. 1949. Vol. 14, no. 2. P. 95-116.Luce, R.D., Perry, A.D., 1949, “A method of matrix analysis of group structure”, Psychometrika, vol. 14, no. 2, pp. 95–116.Estrada E. When local and global clustering of networks diverge // Linear Algebra and its Applications. 2016. Vol. 488. P. 249-263.Estrada, E., 2016, “When local and global clustering of networks diverge”, Linear Algebra and its Applications, vol. 488, pp. 249–263.Harary F. Graph Theory. Reading, MA: Addison-Wesley, 1994. 46 p.Harary, F., 1994, Graph Theory, Reading, MA: Addison-Wesley, p. 46.Pemmaraju S., Skiena S. Computational Discrete Mathematics: Combinatorics and Graph Theory in Mathematica. Cambridge: Cambridge University Press, 2003. P. 248-249.Pemmaraju, S., Skiena, S., 2003, “Cycles, Stars, and Wheels”, in Computational Discrete Mathematics: Combinatorics and Graph Theory in Mathematica, Cambridge: Cambridge University Press, pp. 248–249.Tutte W.T. Graph Theory. Cambridge: Cambridge University Press, 2005. 340 p.Tutte, W.T., 2005, Graph Theory, Cambridge: Cambridge University Press.Dolev D., Leighton F.T., Trickey H. Planar embedding of planar graphs // Advances in Computing Research. 1983. Vol. 2. P. 147-161.Dolev, D., Leighton, F.T., Trickey, H., 1983, “Planar embedding of planar graphs”, Advances in Computing Research, vol. 2, pp. 147–161.Frati F., Patrignani M. A note on minimum-area straight-line drawings of planar graphs // Graph Drawing: 15th International Symposium. Berlin: Springer, 2008. P. 339-344.Frati, F., Patrignani, M., 2008, “A note on minimum-area straight-line drawings of planar graphs”, in Graph Drawing: 15th International Symposium, Berlin: Springer, pp. 339–344.Тужилин М.А. Зависимости между средним кластерным коэффициентом и другими центральностями в графах // Вестник Московского университета. Серия 1: Математика. Механика. 2024. (В печати).Tuzhilin, M.A., 2024, “Relations between average clustering coefficient and other centralities in graphs”, Moscow University Mathematics Bulletin, in press.

The authors declare that there are no conflicts of interest present.