AI 中文总结
研究人员提出邻居限制盒覆盖方法重正化无向加权移动网络，应用该方法揭示中国城市间人员与货运网络多尺度结构，发现其拓扑等呈现自相似性，重正化节点有空间凝聚力，该方法适用于不同规模网络，为复杂系统多尺度分析提供工具。
AI 中文摘要
人员和货物的移动系统本质上是多尺度的，涵盖从单个城市到地区和国家的组织层次。了解移动网络在这些尺度上是否呈现相似模式很重要，因为这种相似性将指向共同的组织原则。尽管人们越来越努力在多尺度上分析移动性，但这种跨尺度相似性仍知之甚少，重正化提供了一个解决此问题的自然框架。本文提出一种邻居限制盒覆盖方法对无向加权移动网络进行重正化。该方法按节点强度降序迭代选择盒中心，将每个中心与其固定数量的最高权重邻居合并形成一个重正化节点，并聚合重正化节点之间的边权重以生成下一级尺度的网络。我们将此技术应用于揭示中国现实世界中城市间人员移动和货运网络的多尺度结构，发现拓扑结构、加权结构特征和动态过程在这些多尺度移动网络中都呈现自相似性。此外，我们发现大多数重正化节点中的组成节点表现出很强的空间凝聚力，其边界紧密遵循现有的政治和社会经济边界，尽管该方法没有明确纳入任何空间信息。我们的研究不仅揭示了多尺度城市间移动模式的一致性，还为其空间组织提供了重要见解。此外，我们的方法适用于不同规模的移动网络，有潜力成为分析各种其他现实世界复杂系统多尺度的强大工具。
英文摘要
Mobility systems of people and goods are inherently multi-scale, spanning levels of organization from individual cities to regions and nations. Understanding whether mobility networks exhibit similar patterns across these scales is important. Such similarity would point to common organizing principles, enabling insights gained at one scale to inform planning and management at others. Despite growing efforts to analyze mobility at multiple scales, such cross-scale similarity remains poorly understood, and renormalization provides a natural framework for addressing this question. Here, we propose a Neighbor-Limited Box Covering method to renormalize undirected weighted mobility networks. This method iteratively selects box centers in descending order of node strength, merges each center with a fixed number of its highest-weight neighbors to form a renormalized node, and aggregates edge weights between renormalized nodes to generate the network at the next scale. We apply this technique to uncover multi-scale structures of real-world inter-city human mobility and freight trip networks in China and find that the topological structures, weighted structural features, and dynamic processes all exhibit self-similarity across these multi-scale mobility networks. Moreover, we find that the constituent nodes in most renormalized nodes show a strong spatial cohesion, and the boundaries of them closely follow existing political and socio-economic borders, even though the method does not explicitly incorporate any spatial information. Our study not only reveals the consistency of multi-scale inter-city mobility patterns, but also provides important insights into their spatial organization. Furthermore, our method is applicable to mobility networks of different sizes and has potential as a powerful tool for the multi-scale analysis of various other real-world complex systems.
Comments29 pages, 15 figures, including supplementary material
