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Universal expansion of human mobility across urban scales

Nature Cities volume 2, pages 603–607 (2025)Cite this article

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Abstract

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, including 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.

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Fig. 1: The spatial expansion of modules.
Fig. 2: Spatial hierarchical levels and expansion law.

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Data availability

The US dataset is anonymized location-based service records provided by Cuebiq Inc. (https://www.cuebiq.com/). The Senegal and the Ivory Coast dataset is anonymized call detail records provided by the Data for Development (D4D) Senegal/Ivory Coast Challenge. These datasets are not publicly available owing to data-sharing restrictions. To analyze the influence of demographic characteristics on mobility patterns, we additionally use publicly available data from the American Community Survey (https://www.census.gov/programs-surveys/acs).

Code availability

The codes used for data processing and analysis are available via GitHub at https://github.com/lucinezhong/Spatial_Expansion_Human_Mobility.

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Acknowledgements

We thank J. Yu for his assistance with preprocessing the Senegal dataset and fruitful discussion. J.G. and L.Z. acknowledge the support of the US National Science Foundation under grant no. 2047488. L.D. acknowledges the support of the National Natural Science Foundation of China (grant no. 42422110) and the Fundamental Research Funds for the Central Universities, Peking University. Q.R.W. acknowledges the support of the US National Science Foundation under grant nos. 2125326, and 2402438.

Author information

Author notes

  1. These authors contributed equally: Lu Zhong, Lei Dong.

Authors and Affiliations

  1. Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, USA

    Lu Zhong & Jianxi Gao

  2. Network Science and Technology Center, Rensselaer Polytechnic Institute, Troy, NY, USA

    Lu Zhong & Jianxi Gao

  3. Institute of Remote Sensing and Geographical Information Systems, School of Earth and Space Sciences, Peking University, Beijing, China

    Lei Dong

  4. Department of Civil and Environmental Engineering, Northeastern University, Boston, MA, USA

    Qi R. Wang

  5. Department of Physics, University of Miami, Coral Gables, FL, USA

    Chaoming Song

Authors
  1. Lu Zhong
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  2. Lei Dong
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  5. Jianxi Gao
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Contributions

L.Z., L.D., Q.R.W. and J.G. conceived the project and designed the experiments; Q.R.W. collected and analyzed the raw data; L.Z., L.D., J.G. and C.S. carried out theoretical calculations and performed the experiments; all authors wrote and edited the paper.

Corresponding author

Correspondence to Jianxi Gao.

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Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Cities thanks Carmen Cabrera-Arnau and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 The spatial expansion of modules regarding convex hull area size.

Module convex hull area size, Ac, increases sub-linearly with its distance from home dc. (a, b, d, e) For US data in the West, Northeast, Midwest, and South regions, the exponent of expansion is around 0.57. (c) For Senegal data, the exponent of expansion is 0.49. (f) For Ivory Coast data, the exponent of expansion is 0.46.

Extended Data Fig. 2 Part-1-Module radius versus distance from home, for populations in different states.

By categorizing users based on the states of their home locations, the spatial expansion of the module remains consistent.

Extended Data Fig. 3 Part-2-Module radius versus distance from home, for populations in different states.

By categorizing users based on the states of their home locations, the spatial expansion of the module remains consistent.

Extended Data Fig. 4 Module radius versus distance from home, for populations in different demographic attributes.

By categorizing users based on the proportions of the poverty population in their home locations (a), the elderly population (age 65 and older) (b), the black population (c), the female population (d), the urban population (e), the spatial expansion of module remains consistent across various user groups.

Supplementary information

Supplementary Information

Supplementary Figs. 1–13 and Tables 1–3.

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Zhong, L., Dong, L., Wang, Q.R. et al. Universal expansion of human mobility across urban scales. Nat Cities 2, 603–607 (2025). https://doi.org/10.1038/s44284-025-00268-0

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