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Evolutionary Model of Signed Edges in Online Networks Based on Infinite One-Dimensional Uniform Lattice

Author

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  • Zhenpeng Li

    (School of Electronics and Information Engineering, Taizhou University, Taizhou 318000, Zhejiang, China)

  • Zhihua Yan

    (School of Management Science and Engineering, Shanxi University of Finance and Economics, Taiyuan 030006, China)

  • Xijin Tang

    (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100039, China
    University of Chinese Academy of Sciences, Beijing 100039, China)

Abstract

The aim of this paper is to study the evolutionary dynamic model for signed edges as observed in online signed social networks. We introduce the incremental mechanism of signed edges behind a simple random walk and explain how this relates to Brownian motion and the diffusive process. We prove how a one-dimensional thermal diffusion equation can be obtained to describe such edge-generating mechanism, and moreover obtain a macroscopic probability distribution of positive and negative edges. The result reveals that the signed edge growth dynamics process can be regarded as a thermodynamic diffusion process. Both empirically and theoretically, we validate that signed network links follow the classic statistic mechanism, i.e., local Brownian motion gives rise to the global emergence pattern of the Gaussian process. The investigation might discover a new and universal characteristic for signed networks, and shed light on some potential applications, such as information spreading, evolutionary games, trust transmission, and dynamic structural balance.

Suggested Citation

  • Zhenpeng Li & Zhihua Yan & Xijin Tang, 2024. "Evolutionary Model of Signed Edges in Online Networks Based on Infinite One-Dimensional Uniform Lattice," Mathematics, MDPI, vol. 12(7), pages 1-9, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1026-:d:1366756
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    References listed on IDEAS

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    1. Zhong, Xiaowen & Fan, Ying & Di, Zengru, 2021. "The evolution of cooperation in public goods games on signed networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    2. Duncan J. Watts & Steven H. Strogatz, 1998. "Collective dynamics of ‘small-world’ networks," Nature, Nature, vol. 393(6684), pages 440-442, June.
    3. Viswanathan, G.M & Afanasyev, V & Buldyrev, Sergey V & Havlin, Shlomo & da Luz, M.G.E & Raposo, E.P & Stanley, H.Eugene, 2000. "Lévy flights in random searches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(1), pages 1-12.
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