IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i7p1026-d1366756.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/7/1026/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/7/1026/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Duncan J. Watts & Steven H. Strogatz, 1998. "Collective dynamics of ‘small-world’ networks," Nature, Nature, vol. 393(6684), pages 440-442, June.
    2. 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.
    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. Huan Wang & Chuang Ma & Han-Shuang Chen & Ying-Cheng Lai & Hai-Feng Zhang, 2022. "Full reconstruction of simplicial complexes from binary contagion and Ising data," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    2. Vinayak, & Raghuvanshi, Adarsh & kshitij, Avinash, 2023. "Signatures of capacity development through research collaborations in artificial intelligence and machine learning," Journal of Informetrics, Elsevier, vol. 17(1).
    3. Supriya Tiwari & Pallavi Basu, 2024. "Quasi-randomization tests for network interference," Papers 2403.16673, arXiv.org, revised Oct 2024.
    4. Anzhi Sheng & Qi Su & Aming Li & Long Wang & Joshua B. Plotkin, 2023. "Constructing temporal networks with bursty activity patterns," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    5. Samrachana Adhikari & Beau Dabbs, 2018. "Social Network Analysis in R: A Software Review," Journal of Educational and Behavioral Statistics, , vol. 43(2), pages 225-253, April.
    6. Wang, Xiaojie & Slamu, Wushour & Guo, Wenqiang & Wang, Sixiu & Ren, Yan, 2022. "A novel semi local measure of identifying influential nodes in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    7. Lin, Dan & Wu, Jiajing & Xuan, Qi & Tse, Chi K., 2022. "Ethereum transaction tracking: Inferring evolution of transaction networks via link prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    8. Ferreira, D.S.R. & Ribeiro, J. & Oliveira, P.S.L. & Pimenta, A.R. & Freitas, R.P. & Dutra, R.S. & Papa, A.R.R. & Mendes, J.F.F., 2022. "Spatiotemporal analysis of earthquake occurrence in synthetic and worldwide data," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    9. Mario V. Tomasello & Mauro Napoletano & Antonios Garas & Frank Schweitzer, 2017. "The rise and fall of R&D networks," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 26(4), pages 617-646.
    10. Qinghu Liao & Wenwen Dong & Boxin Zhao, 2023. "A New Strategy to Solve “the Tragedy of the Commons” in Sustainable Grassland Ecological Compensation: Experience from Inner Mongolia, China," Sustainability, MDPI, vol. 15(12), pages 1-24, June.
    11. Xinyu Huang & Dongming Chen & Dongqi Wang & Tao Ren, 2020. "MINE: Identifying Top- k Vital Nodes in Complex Networks via Maximum Influential Neighbors Expansion," Mathematics, MDPI, vol. 8(9), pages 1-25, August.
    12. Xueguo Xu & Chen Xu & Wenxin Zhang, 2022. "Research on the Destruction Resistance of Giant Urban Rail Transit Network from the Perspective of Vulnerability," Sustainability, MDPI, vol. 14(12), pages 1-26, June.
    13. Jianhong Chen & Hongcai Ma & Shan Yang, 2023. "SEIOR Rumor Propagation Model Considering Hesitating Mechanism and Different Rumor-Refuting Ways in Complex Networks," Mathematics, MDPI, vol. 11(2), pages 1-22, January.
    14. Xiaokun Su & Chenrouyu Zheng & Yefei Yang & Yafei Yang & Wen Zhao & Yue Yu, 2022. "Spatial Structure and Development Patterns of Urban Traffic Flow Network in Less Developed Areas: A Sustainable Development Perspective," Sustainability, MDPI, vol. 14(13), pages 1-18, July.
    15. Daniel Reisinger & Fabian Tschofenig & Raven Adam & Marie Lisa Kogler & Manfred Füllsack & Fabian Veider & Georg Jäger, 2024. "Patterns of stability in complex contagions," Journal of Computational Social Science, Springer, vol. 7(2), pages 1895-1911, October.
    16. Manisha Sawant & Rupali Patil & Tanmay Shikhare & Shreyas Nagle & Sakshi Chavan & Shivang Negi & Neeraj Dhanraj Bokde, 2022. "A Selective Review on Recent Advancements in Long, Short and Ultra-Short-Term Wind Power Prediction," Energies, MDPI, vol. 15(21), pages 1-24, October.
    17. Vincenza Carchiolo & Marco Grassia & Michele Malgeri & Giuseppe Mangioni, 2022. "Co-Authorship Networks Analysis to Discover Collaboration Patterns among Italian Researchers," Future Internet, MDPI, vol. 14(6), pages 1-15, June.
    18. Gregory Gutin & Tomohiro Hirano & Sung-Ha Hwang & Philip R. Neary & Alexis Akira Toda, 2021. "The effect of social distancing on the reach of an epidemic in social networks," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(3), pages 629-647, July.
    19. Jie, Ke-Wei & Liu, San-Yang & Sun, Xiao-Jun & Xu, Yun-Cheng, 2023. "A dynamic ripple-spreading algorithm for solving mean–variance of shortest path model in uncertain random networks," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    20. Anna Concas & Lothar Reichel & Giuseppe Rodriguez & Yunzi Zhang, 2021. "Iterative Methods for the Computation of the Perron Vector of Adjacency Matrices," Mathematics, MDPI, vol. 9(13), pages 1-16, June.

    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:7:p:1026-:d:1366756. 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.