人员与货物的移动系统本质上具有多尺度特征,涵盖从单个城市到区域乃至国家的不同组织层级。理解移动网络是否在这些尺度上呈现相似模式至关重要:若存在此类相似性,则表明其背后存在共通的组织原理,从而使某一尺度上获得的认知可用于指导其他尺度上的规划与管理。尽管针对多尺度移动性的分析日益增多,跨尺度相似性仍缺乏深入理解,而重正化(renormalization)为此问题提供了天然的分析框架。本文提出一种邻域受限的盒覆盖(Neighbor-Limited Box Covering)方法,用于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取盒中心,将每个中心与其权重最高的固定数量邻节点合并为一个重正化节点,并聚合重正化节点之间的边权重以生成下一尺度的网络。我们将该方法应用于中国真实世界的城市间人类移动网络与货运出行网络,发现其拓扑结构、加权结构特征及动态过程均在多尺度移动网络中表现出自相似性。此外,我们发现绝大多数重正化节点所包含的原始节点展现出强烈的空间凝聚性,且其边界与既有的行政及社会经济边界高度吻合,尽管该方法并未显式引入任何空间信息。本研究不仅揭示了城市间多尺度移动模式的一致性,也为理解其空间组织提供了重要洞见。此外,本方法适用于不同规模的移动网络,并具备潜在应用价值。
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.