Quantifying the overall characteristics of urban mobility considering spatial information

Quantification of the overall characteristics of urban mobility using coarse-grained methods is crucial for urban management, planning and sustainable development. Although some recent studies have provided quantification methods for coarse-grained numerical information regarding urban mobility, a method that can simultaneously capture numerical and spatial information remains an outstanding problem. Here, we use mathematical vectors to depict human mobility, with mobility magnitude representing numerical information and mobility direction representing spatial information. We then define anisotropy and centripetality metrics by vector computation to measure imbalance in direction distribution and orientation toward the city center of mobility flows, respectively. As a case study, we apply our method to 60 Chinese cities and identify three mobility patterns: strong monocentric, weak monocentric and polycentric. To better understand mobility pattern, we further study the allometric scaling of the average commuting distance and the spatiotemporal variations of the two metrics in different patterns. Finally, we build a microscopic model to explain the key mechanisms driving the diversity in anisotropy and centripetality. Our work offers a comprehensive method that considers both numerical and spatial information to quantify and classify the overall characteristics of urban mobility, enhancing our understanding of the structure and evolution of urban mobility systems.