\begin{document}$\mu $\end{document}, is set for these edge-dependent clusters. When the failure rate of an edge-dependent cluster exceeds \begin{document}$\mu $\end{document}, the failure of the nodes in network A that depends on it, will happen. Based on the self-balancing probability method, a theoretical analysis framework is established. Through computer simulation verification of BINNEC under three classical network structures, the model's phase transition behavior and critical thresholds in the face of random attacks are analyzed. The results reveal that BINNEC under three network structures is as fragile as a single-element coupled network, exhibiting a first-order phase transition behavior. As the size of edge-dependent cluster \begin{document}$m$\end{document} increases, network robustness is enhanced. Moreover, with a constant size of edge-dependent cluster, a larger tolerance for node failure \begin{document}$\mu $\end{document} leads to stronger network robustness. Finally, this research reveals that under the same conditions of \begin{document}$m$\end{document} and \begin{document}$\mu $\end{document}, when the tolerance for node failure \begin{document}$\mu $\end{document} is insufficient to withstand the failure of a single edge, the degree distribution widens, and network robustness weakens. However, when the tolerance for node failure is sufficient to withstand the failure of at least one edge, the network robustness actually strengthens as the degree distribution increases. These findings provide a theoretical basis for studying such binary coupled models and also for guiding the secure design of real-world networks."> - 必威体育下载

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Citation:

    Gao Yan-Li, Xu Wei-Nan, Zhou Jie, Chen Shi-Ming
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    • Abstract views:255
    • PDF Downloads:4
    • Cited By:0
    Publishing process
    • Received Date:01 April 2024
    • Accepted Date:14 June 2024
    • Available Online:16 July 2024
    • Published Online:20 August 2024

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