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Distance distributions of human settlements

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  • Fernández-Rosales, Iván Yair
  • Angulo-Brown, Fernando
  • Pérez-Campuzano, Enrique
  • Guzmán-Vargas, Lev

Abstract

City-size distributions have been studied from different perspectives in past decades. However, spatial properties of city distributions have not been widely explored. Here, we study distance distribution between pairs of cities by considering their sizes for data from ten countries. We find that distance distributions present different shapes, from quasi-symmetrical to right-skewed, which exhibit changes as the lower threshold of the city size is increased. The Gini index G and the normalized Shannon entropy ES were calculated to evaluate the inequality and heterogeneity (diversity) in the distance distributions. Our results show that quasi-symmetrical distributions are characterized by a low inequality and intermediate value of entropy, while right-skewed distributions lead to higher inequality indexes with different levels of diversity. We introduce the big-club (set of the largest cities) coefficient to evaluate the tendency of big settlements to be located close to (or far away from) each other, finding that most of the countries have a high big-club value. Finally, we consider a simple model based on node sizes to generate three configurations with different spatial correlations (random, correlated and anti-correlated), which roughly reproduce similar values of G and ES to those found in actual distance distributions.

Suggested Citation

  • Fernández-Rosales, Iván Yair & Angulo-Brown, Fernando & Pérez-Campuzano, Enrique & Guzmán-Vargas, Lev, 2020. "Distance distributions of human settlements," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    • Handle: RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920302095
    DOI: 10.1016/j.chaos.2020.109808
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    1. Eaton, Jonathan & Eckstein, Zvi, 1997. "Cities and growth: Theory and evidence from France and Japan," Regional Science and Urban Economics, Elsevier, vol. 27(4-5), pages 443-474, August.
    2. Gilles Duranton, 2007. "Urban Evolutions: The Fast, the Slow, and the Still," American Economic Review, American Economic Association, vol. 97(1), pages 197-221, March.
    3. John B. Parr, 2017. "Central Place Theory: An Evaluation," Review of Urban & Regional Development Studies, Wiley Blackwell, vol. 29(3), pages 151-164, November.
    4. Clémentine Cottineau, 2017. "MetaZipf. A dynamic meta-analysis of city size distributions," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-22, August.
    5. Chen, Yanguang, 2011. "Fractal systems of central places based on intermittency of space-filling," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 619-632.
    6. Wen‐Tai Hsu, 2012. "Central Place Theory and City Size Distribution," Economic Journal, Royal Economic Society, vol. 122(563), pages 903-932, September.
    7. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
    8. Chen, Yanguang & Zhou, Yixing, 2008. "Scaling laws and indications of self-organized criticality in urban systems," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 85-98.
    9. Chen, Yanguang, 2015. "The distance-decay function of geographical gravity model: Power law or exponential law?," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 174-189.
    10. Chen, Yanguang, 2014. "Multifractals of central place systems: Models, dimension spectrums, and empirical analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 266-282.
    11. Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
    12. Gabaix, Xavier & Ioannides, Yannis M., 2004. "The evolution of city size distributions," Handbook of Regional and Urban Economics, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 53, pages 2341-2378, Elsevier.
    13. Moura, Newton J. & Ribeiro, Marcelo B., 2006. "Zipf law for Brazilian cities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 441-448.
    14. Pérez-Campuzano, Enrique & Guzmán-Vargas, Lev & Angulo-Brown, F., 2015. "Distributions of city sizes in Mexico during the 20th century," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 64-70.
    15. Arshad, Sidra & Hu, Shougeng & Ashraf, Badar Nadeem, 2018. "Zipf’s law and city size distribution: A survey of the literature and future research agenda," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 75-92.
    16. Chen, Yanguang & Huang, Linshan, 2018. "A scaling approach to evaluating the distance exponent of the urban gravity model," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 303-313.
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