Torque work of origin-destination flows: Quantifying urban place centrality from a physical perspective

Quantifying urban place centrality, defined as its relative importance in serving its peripheral areas, provides insights into urban structures, optimizes resource allocation, and supports strategic urban planning. Centrality is shaped by three aspects: service volume, spatial reach, and directional diversity. However, existing measures often assess these factors separately and few integrate them simultaneously. Additionally, centrality analyses often overlook local perspectives and intra-day dynamics. To this end, we propose a novel origin-destination flow-based centrality measure, namely Total Torque Work (TTW), that integrates these three aspects into a single value, conceptualized as “Torque work of flow”, where flow volume, length, and direction correspond to the force magnitude, lever arm, and angular displacement. The effectiveness of the TTW is validated by simulation experiments. We apply this measure to analyze macro- and micro-centralities in Beijing, using taxi and shared bike flow data. Macro-centrality shows a monocentric structure, with higher values near railway stations, airports, and business and commercial centers. Micro-centrality is more polycentric, with subway stations exhibiting higher centrality. Time series clustering identifies three temporal patterns in both macro- and micro-centralities: two “daytime-dominant” patterns linked to multifunctional activities and commuting, and a “nighttime-dominant” pattern in residential areas. The study concludes with several implications for urban planning, emphasizing the importance of incorporating multi-spatiotemporal scales.