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  • Open Access

Renormalization of human mobility based on a revised electric circuit model and a new gravity relation

Zhihua Zhong, Hideki Takayasu, and Misako Takayasu*

  • *Contact author: takayasu@comp.isct.ac.jp
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Phys. Rev. Research 7, 013235 – Published 3 March, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.013235

Abstract

Human movement in an urban environment consists of a complex system where the results and observations of an analysis may be dependent on the choice of resolutions. In this study, a two-dimensional lattice weighted undirected graph embedded in Euclidean space is constructed to represent human flow in an urban environment. Specifically, each node represents an area whereas a link consists of a road connecting two adjacent areas. People moving in a grid under a specific resolution are aggregated, and the sum of their velocity is assigned as the link weight. Based on the analysis of real-world GPS data, we first find that the human potential in the revised electric circuit model (RECM) can characterize the spatial-temporal human movement trends in an urban environment independent of different observation resolutions. Second, we propose several renormalization methods for three analogical concepts in the RECM, namely, human current, human resistance, and human potential. Each of these can be used to describe spatial-temporal flow patterns, infrastructure level, and movement trends, respectively, to reveal their relation under different spatial resolutions. Third, we find a nontrivial scaling relation, which may be regarded as a new type of gravity relation, to characterize the heterogeneous spatial distribution of human conductivity. Although the power exponent of distance γ in the above relation slightly changes at different spatial scales, a nontrivial relation is derived to explain and estimate the exponent automatically. Overall, these discoveries may lead to new approaches for establishing a cross-scale human mobility description framework.

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Phys. Rev. Research 7, 013235– Published 3 March, 2025
  • Received 30 August 2024
  • Accepted 6 February 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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