Universal expansion of human mobility across urban scales

Human mobility is a fundamental process underpinning socioeconomic life and urban structure. Classic theories, such as egocentric activity spaces and central place theory, provide crucial insights into specific facets of movement, like home-centricity and hierarchical spatial organization. However, identifying universal characteristics or an underlying principle that quantitatively links these disparate perspectives has remained a challenge. Here, we reveal such a connection by analyzing the spatial structure of individual daily mobility trajectories using network-based modules. We discover a universal scaling law: the spatial extent (radius) of these mobility modules expands sublinearly with increasing distance from home, a pattern consistent across three orders of magnitude. Furthermore, we demonstrate that these modules precisely map onto the nested hierarchy of urban systems, corresponding to local, city-level, and regional scales as distance from home increases. These findings deepen our understanding of human mobility dynamics and demonstrate the profound connection between classical urban theory, human geography, and mobility studies.