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A Continuous-Time Network Evolution Model Describing 2- and 3-Interactions

Author

Listed:
  • István Fazekas

    (Faculty of Informatics, University of Debrecen, Kassai Street 26, 4028 Debrecen, Hungary)

  • Attila Barta

    (Faculty of Informatics, University of Debrecen, Kassai Street 26, 4028 Debrecen, Hungary)

Abstract

A continuous-time network evolution model is considered. The evolution of the network is based on 2- and 3-interactions. 2-interactions are described by edges, and 3-interactions are described by triangles. The evolution of the edges and triangles is governed by a multi-type continuous-time branching process. The limiting behaviour of the network is studied by mathematical methods. We prove that the number of triangles and edges have the same magnitude on the event of non-extinction, and it is e α t , where α is the Malthusian parameter. The probability of the extinction and the degree process of a fixed vertex are also studied. The results are illustrated by simulations.

Suggested Citation

  • István Fazekas & Attila Barta, 2021. "A Continuous-Time Network Evolution Model Describing 2- and 3-Interactions," Mathematics, MDPI, vol. 9(23), pages 1-26, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3143-:d:696059
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    References listed on IDEAS

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    1. Iksanov, Alexander & Meiners, Matthias, 2015. "Rate of convergence in the law of large numbers for supercritical general multi-type branching processes," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 708-738.
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    Cited by:

    1. Feng, Qunqiang & Li, Xing & Hu, Zhishui, 2023. "Asymptotic degree distribution in a homogeneous evolving network model," Statistics & Probability Letters, Elsevier, vol. 193(C).

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