IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v63y2008i3p295-301.html
   My bibliography  Save this article

Hierarchy, cities size distribution and Zipf's law

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1140/epjb/e2008-00203-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1140/epjb/e2008-00203-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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 1-16, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:eurphb:v:63:y:2008:i:3:p:295-301. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.