Abstract
We study the impact of the distance between two hubs on network coherence defined by Laplacian eigenvalues. Network coherence is a measure of the extent of consensus in a linear system with additive noise. To obtain an exact determination of coherence based on the distance, we choose a family of tree networks with two hubs controlled by two parameters. Using the tree’s regular structure, we obtain analytical expressions of the coherences with regard to network parameters and the network size. We then demonstrate that a shorter distance and a larger difference in the degrees of the two hubs lead to a higher coherence. With the same network size and distance, the best coherence occurs in the tree with the largest difference in the hub’s degrees. Finally, we establish a correlation between network coherence and average path length and find that they behave linearly.
摘要
本文研究了两个中心节点之间的距离对网络一致性的影响。网络一致性由拉普拉斯特征值所量化, 可用来衡量线性系统对外部噪声的一致性程度。为获得网络一致性关于距离的精确表达式, 选取一类由网络参数控制的具有两个中心节点的树状网络。利用其规则的拓扑结构, 得到一致性关于网络参数和网络规模的解析表达式。证明两个中心节点距离越短, 度的差异性越大, 网络一致性越好。在相同网络规模和距离下, 最大的中心节点度差异会导致最优的一致性。最后, 建立了网络一致性与平均路径长度之间的联系, 发现它们呈线性关系。
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The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Weigang SUN guided the research. Daquan LI, Weigang SUN, and Hongxiang HU contributed to the conceptualization and methodology of the study. Daquan LI and Weigang SUN performed the formal analysis and drafted the paper. Weigang SUN and Hongxiang HU revised and finalized the paper.
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Daquan LI, Weigang SUN, and Hongxiang HU declare that they have no conflict of interest.
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Project supported by the National Natural Science Foundation of China (Nos. 71932005 and 62376079), the Zhejiang Provincial Natural Science Foundation of China (No. LR22F030004), and the Fundamental Research Funds for the Provincial Universities of Zhejiang, China (No. GK219909299001-004)
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Li, D., Sun, W. & Hu, H. Impact of distance between two hubs on the network coherence of tree networks. Front Inform Technol Electron Eng 24, 1349–1356 (2023). https://doi.org/10.1631/FITEE.2200400
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DOI: https://doi.org/10.1631/FITEE.2200400