The article focuses on the problem of maximizing the degree correlation of a network through a finite number of rewirings, using the assortativity coefficient as the measure. The authors analyze the changes in the assortativity coefficient under degree-preserving rewiring and establish its relationship with the s-metric. They prove that under their assumptions, the problem is monotonic and submodular, leading to the proposal of the GA (Greedy Assortative) method to enhance network degree correlation. The authors also introduce three heuristic rewiring strategies, EDA (Edge Difference Assortative), TA (Targeted Assortative), and PEA (Probability Edge Assortative), and demonstrate their applicability to different types of networks. Furthermore, the authors extend the application of their proposed rewiring strategies to investigate their impact on several spectral robustness metrics based on the adjacency matrix, revealing that GA effectively improves network robustness, while TA and PEA perform well in enhancing the robustness of power and routing networks, respectively. Finally, the authors explore the robustness of several centrality metrics in the network while enhancing network degree correlation using the GA method, finding that in disassortative real networks, closeness centrality and eigenvector centrality are typically robust, and all centrality metrics remain robust when focusing on the top-ranked nodes.
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by Shuo Zou,Bo ... at arxiv.org 04-12-2024
https://arxiv.org/pdf/2404.07779.pdfDeeper Inquiries