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Scaling law of individual urban tour behavior

Xu-Jie Lin1, Yitao Yang2, Wei-Peng Nie1,*, and Xiao-Yong Yan1,†

  • *Contact author: wpnie@bjtu.edu.cn
  • †Contact author: yanxy@bjtu.edu.cn

Phys. Rev. E 113, 034303 – Published 6 March, 2026

DOI: https://doi.org/10.1103/9d5z-9xxt

Abstract

Analyzing and modeling the mobility process with tour behavior is fundamental to understanding a wide range of complex systems, including animal foraging, human mobility, and freight transportation. However, despite their importance, the distribution of tour length has long been neglected in individual human mobility models. To fill this gap, we analyze Foursquare users' check-in data and find that the distribution of urban tour length follows a truncated power-law distribution. To reproduce the universal scaling law for human mobility in urban areas, we introduce a tour terminate-continue model. Our model reproduces not only the urban tour length distribution, but also Heaps' law, Zipf's law, and the distribution of the radius of gyration, providing an additional perspective for characterizing individual human mobility.

Physics Subject Headings (PhySH)

synopsis

A Scaling Law for Tours

Published 6 March, 2026

A simple model can reproduce the distribution of tour lengths harvested by a social media app used by thousands of visitors to Los Angeles and New York.

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