IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i5p643-d1343713.html
   My bibliography  Save this article

Network Evolution Model with Preferential Attachment at Triadic Formation Step

Author

Listed:
  • Sergei Sidorov

    (Faculty of Mathematics and Mechanics, Saratov State University, 410012 Saratov, Russia)

  • Timofei Emelianov

    (Faculty of Computer Science and Informatics, Saratov State University, 410012 Saratov, Russia)

  • Sergei Mironov

    (Faculty of Computer Science and Informatics, Saratov State University, 410012 Saratov, Russia)

  • Elena Sidorova

    (Faculty of Tax, Audit and Business Analysis, Financial University under the Government of the Russian Federation, 125993 Moscow, Russia
    Finance and Credit Department, Peoples’ Friendship University of Russia (RUDN University), 117198 Moscow, Russia)

  • Yuri Kostyukhin

    (Engineering Business and Management Faculty, Bauman Moscow State Technical University, 105005 Moscow, Russia
    Industrial Management Department, National University of Science & Technology (MISIS), 119049 Moscow, Russia)

  • Alexandr Volkov

    (Educational and Methodological Department, National University of Science & Technology (MISIS), 119049 Moscow, Russia)

  • Anna Ostrovskaya

    (Higher School of Management, Peoples’ Friendship University of Russia (RUDN University), 117198 Moscow, Russia)

  • Lyudmila Polezharova

    (Faculty of Tax, Audit and Business Analysis, Financial University under the Government of the Russian Federation, 125993 Moscow, Russia)

Abstract

It is recognized that most real systems and networks exhibit a much higher clustering with comparison to a random null model, which can be explained by a higher probability of the triad formation—a pair of nodes with a mutual neighbor have a greater possibility of having a link between them. To catch the more substantial clustering of real-world networks, the model based on the triadic closure mechanism was introduced by P. Holme and B. J. Kim in 2002. It includes a “triad formation step” in which a newly added node links both to a preferentially chosen node and to its randomly chosen neighbor, therefore forming a triad. In this study, we propose a new model of network evolution in which the triad formation mechanism is essentially changed in comparison to the model of P. Holme and B. J. Kim. In our proposed model, the second node is also chosen preferentially , i.e., the probability of its selection is proportional to its degree with respect to the sum of the degrees of the neighbors of the first selected node. The main goal of this paper is to study the properties of networks generated by this model. Using both analytical and empirical methods, we show that the networks are scale-free with power-law degree distributions, but their exponent γ is tunable which is distinguishable from the networks generated by the model of P. Holme and B. J. Kim. Moreover, we show that the degree dynamics of individual nodes are described by a power law.

Suggested Citation

  • Sergei Sidorov & Timofei Emelianov & Sergei Mironov & Elena Sidorova & Yuri Kostyukhin & Alexandr Volkov & Anna Ostrovskaya & Lyudmila Polezharova, 2024. "Network Evolution Model with Preferential Attachment at Triadic Formation Step," Mathematics, MDPI, vol. 12(5), pages 1-21, February.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:643-:d:1343713
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/5/643/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/5/643/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Emily M. Jin & Michelle Girvan & M. E. J. Newman, 2001. "The Structure of Growing Social Networks," Working Papers 01-06-032, Santa Fe Institute.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Johansson, Tobias, 2017. "Gossip spread in social network Models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 126-134.
    2. Russell Golman & Aditi Jain & Sonica Saraf, 2019. "Hipsters and the Cool: A Game Theoretic Analysis of Social Identity, Trends and Fads," Papers 1910.13385, arXiv.org.
    3. Shiau, Wen-Lung & Dwivedi, Yogesh K. & Yang, Han Suan, 2017. "Co-citation and cluster analyses of extant literature on social networks," International Journal of Information Management, Elsevier, vol. 37(5), pages 390-399.
    4. Lipari, Francesca & Lázaro-Touza, Lara & Escribano, Gonzalo & Sánchez, Ángel & Antonioni, Alberto, 2024. "When the design of climate policy meets public acceptance: An adaptive multiplex network model," Ecological Economics, Elsevier, vol. 217(C).
    5. Karan, Rituraj & Biswal, Bibhu, 2017. "A model for evolution of overlapping community networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 380-390.
    6. Hackney, Jeremy & Marchal, Fabrice, 2011. "A coupled multi-agent microsimulation of social interactions and transportation behavior," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(4), pages 296-309, May.
    7. Huang, Chung-Yuan & Tsai, Yu-Shiuan, 2010. "Effects of friend-making resources/costs and remembering on acquaintance networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 604-622.
    8. Konc, Théo & Savin, Ivan & van den Bergh, Jeroen C.J.M., 2021. "The social multiplier of environmental policy: Application to carbon taxation," Journal of Environmental Economics and Management, Elsevier, vol. 105(C).
    9. Gergő Tóth & Balázs Lengyel, 2021. "Inter-firm inventor mobility and the role of co-inventor networks in producing high-impact innovation," The Journal of Technology Transfer, Springer, vol. 46(1), pages 117-137, February.
    10. P.B., Divya & Lekha, Divya Sindhu & Johnson, T.P. & Balakrishnan, Kannan, 2022. "Vulnerability of link-weighted complex networks in central attacks and fallback strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    11. ChristianR. Jaramillo H., 2005. "The Role Of Networks In Collective Action With Costly Communication," Documentos CEDE 3625, Universidad de los Andes, Facultad de Economía, CEDE.
    12. Inoue, Hiroyasu, 2014. "A two-layer team-assembly model for invention networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 181-188.
    13. Claes Andersson & Koen Frenken & Alexander Hellervik, 2006. "A Complex Network Approach to Urban Growth," Environment and Planning A, , vol. 38(10), pages 1941-1964, October.
    14. Haizheng Zhang & Baojun Qiu & Kristinka Ivanova & C. Lee Giles & Henry C. Foley & John Yen, 2010. "Locality and attachedness‐based temporal social network growth dynamics analysis: A case study of evolving nanotechnology scientific collaboration networks," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 61(5), pages 964-977, May.
    15. Ronald, Nicole & Arentze, Theo & Timmermans, Harry, 2012. "Modeling social interactions between individuals for joint activity scheduling," Transportation Research Part B: Methodological, Elsevier, vol. 46(2), pages 276-290.
    16. Hendrik Ludolph & Gilbert Babin & Peter Kropf, 2003. "A Communication Framework Towards Flexible Associations of Business Entities Within Evolving Environments," CIRANO Working Papers 2003s-43, CIRANO.
    17. Liang Chen & Guy G. Gable & Haibo Hu, 2013. "Communication and organizational social networks: a simulation model," Computational and Mathematical Organization Theory, Springer, vol. 19(4), pages 460-479, December.
    18. Perc, Matjaž, 2010. "Growth and structure of Slovenia’s scientific collaboration network," Journal of Informetrics, Elsevier, vol. 4(4), pages 475-482.
    19. Junlong Zhao & Xiumin Liu & Hansheng Wang & Chenlei Leng, 2022. "Dimension reduction for covariates in network data [On semidefinite relaxations for the block model]," Biometrika, Biometrika Trust, vol. 109(1), pages 85-102.
    20. Tian, Lixin & Huang, Yi & Dong, Gaogao & Du, Ruijin & Shi, Liu, 2014. "Robustness of interdependent and interconnected clustered networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 120-126.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:643-:d:1343713. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.