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Hierarchy, cities size distribution and Zipf's law

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  • F. Semboloni

Abstract

We show that a hierarchical cities structure can be generated by a self-organized process which grows with a bottom-up mechanism, and that the resulting distribution is power law. First we analytically prove that the power law distribution satisfies the balance between the offer of the city and the demand of its basin of attraction, and that the exponent in the Zipf's law corresponds to the multiplier linking the population of the central city to the population of its basin of attraction. Moreover, the corresponding hierarchical structure shows a variable spanning factor, and the population of the cities linked to the same city up in the hierarchy is variable as well. Second a stochastic dynamic spatial model is proposed, whose numerical results confirm the analytical findings. In this model, inhabitants minimize the transportation cost, so that the greater the importance of this cost, the more stable is the system in its microscopic aspect. After a comparison with the existent methods for the generation of a power law distribution, conclusions are drawn on the connection of hierarchical structure, and power law distribution, with the functioning of the system of cities. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Suggested Citation

  • F. Semboloni, 2008. "Hierarchy, cities size distribution and Zipf's law," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 63(3), pages 295-301, June.
    • Handle: RePEc:spr:eurphb:v:63:y:2008:i:3:p:295-301
    DOI: 10.1140/epjb/e2008-00203-1
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    Citations

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    Cited by:

    1. Rafael González-Val, 2011. "Deviations from Zipf’s Law for American Cities," Urban Studies, Urban Studies Journal Limited, vol. 48(5), pages 1017-1035, April.
    2. Chen, Yanguang, 2012. "The rank-size scaling law and entropy-maximizing principle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 767-778.
    3. Chen, Yanguang, 2012. "Zipf’s law, 1/f noise, and fractal hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 63-73.
    4. Liao, Cong & Scheuer, Bronte, 2022. "Evaluating the performance of transit-oriented development in Beijing metro station areas: Integrating morphology and demand into the node-place model," Journal of Transport Geography, Elsevier, vol. 100(C).
    5. Adele Sateriano & Giovanni Quaranta & Rosanna Salvia & Francisco Escrivà Saneugenio & Alvaro Marucci & Luca Salvati & Barbara Zagaglia & Francesco Chelli, 2024. "Envisaging the Intrinsic Departure from Zipf’s Law as an Indicator of Economic Concentration along Urban–Rural Gradients," Land, MDPI, vol. 13(4), pages 1-15, March.

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