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<p>Network coherence, which measures the steady-state variance of a network in maintaining consensus under stochastic disturbances, is a fundamental performance measure for distributed algorithms. This paper investigates the coherence of extended polygonal networks, focusing on how network parameters influence coherence. Firstly, an extended polygon network is constructed by introducing an expansion factor. It is characterized by three parameters: <i>m</i>, <i>n</i>, and <i>z</i>, which represent the expansion factor, the initial network size, and the number of iterations, respectively. Secondly, using spectral graph theory, an expression for first-order coherence in terms of the three parameters is derived, along with the exact solution for the Kirchhoff index. Thirdly, numerical simulations and robustness analysis on the effects of topology on coherence and the Kirchhoff index indicate that increasing <i>z</i> and <i>n</i> improves both coherence and the Kirchhoff index, while increasing <i>m</i> reduces coherence but increases the Kirchhoff index. These findings provide a theoretical basis for understanding the performance limitations and topological design of distributed systems.</p>

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Network Coherence and Robustness Analysis of Extended Polygonal Networks

  • 期刊论文

  • 发表日期：

    2026年3月7日

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  • Jia-Bao Liu,
  • Fen Zou,
  • Guo-Jun Cai,
  • Jinde Cao

摘要

Network coherence, which measures the steady-state variance of a network in maintaining consensus under stochastic disturbances, is a fundamental performance measure for distributed algorithms. This paper investigates the coherence of extended polygonal networks, focusing on how network parameters influence coherence. Firstly, an extended polygon network is constructed by introducing an expansion factor. It is characterized by three parameters: m, n, and z, which represent the expansion factor, the initial network size, and the number of iterations, respectively. Secondly, using spectral graph theory, an expression for first-order coherence in terms of the three parameters is derived, along with the exact solution for the Kirchhoff index. Thirdly, numerical simulations and robustness analysis on the effects of topology on coherence and the Kirchhoff index indicate that increasing z and n improves both coherence and the Kirchhoff index, while increasing m reduces coherence but increases the Kirchhoff index. These findings provide a theoretical basis for understanding the performance limitations and topological design of distributed systems.