IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v201y2025ip3s0960077925013918.html

The effect of adding one edge between two chain networks on the consensus convergence rate

Author

Listed:
  • Ping, Chao
  • Zhang, Shenggui
  • Chen, Xinzhuang
  • Jia, Jiajia

Abstract

Where to add edges between interacting networks of multiple multi-agent systems (MAS) to make the resulting MAS achieve consensus and have the fastest consensus convergence rate is an meaningful work in the study of the consensus problem of MASs. However, there are few works considering this theme. For a first-order MAS with the interaction network represented as an undirected graph, improving the system’s consensus convergence rate is equivalent to increasing the algebraic connectivity of the undirected graph. This paper investigates the effect of adding one edge between two chain networks on the consensus convergence rate. Firstly, all optimal approaches of adding one edge that maximize the algebraic connectivity are given. Then, considering the case where one of the end-vertices of the edge added is fixed, not only all optimal approaches to adding an edge that maximize algebraic connectivity are given, but also an ordering of all possible approaches to adding an edge based on algebraic connectivity. The ordering can be used as a criterion on how to choose an optimal one among the feasible approaches to adding one edge when the optimal approaches are not achievable. Finally, numerical examples are provided to verify the theoretical results, and potential directions for further research are discussed.

Suggested Citation

  • Ping, Chao & Zhang, Shenggui & Chen, Xinzhuang & Jia, Jiajia, 2025. "The effect of adding one edge between two chain networks on the consensus convergence rate," Chaos, Solitons & Fractals, Elsevier, vol. 201(P3).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p3:s0960077925013918
    DOI: 10.1016/j.chaos.2025.117378
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925013918
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.117378?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Ma, Shan & Shen, Binda & Ma, Junfeng & Hu, Wenfeng & Peng, Tao, 2023. "Improvement of network robustness against cascading failures based on the min–max edge-adding strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    2. Zhang, Jianhua & Wu, Zhihai & Hong, Liu & Xu, Xiaoming, 2011. "Connectivity recovery of multi-agent systems based on connecting neighbor set," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4596-4601.
    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. Wang, Luyao & Chen, Libin & Yang, Zhiwei & Yang, Kewei, 2026. "Research on network robustness analysis method of combat system-of-systems considering collaborative reconfiguration," Reliability Engineering and System Safety, Elsevier, vol. 265(PB).
    2. Wang, Shuliang & Zhang, Jianhua & Yue, Xin, 2018. "Multiple robustness assessment method for understanding structural and functional characteristics of the power network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 261-270.
    3. Geng, Liang & Xiao, Renbin, 2017. "Outer synchronization and parameter identification approach to the resilient recovery of supply network with uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 407-421.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:chsofr:v:201:y:2025:i:p3:s0960077925013918. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.