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A spatial network explanation for a hierarchy of urban power laws

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  • Andersson, Claes
  • Hellervik, Alexander
  • Lindgren, Kristian

Abstract

Power laws in socioeconomic systems are generally explained as being generated by multiplicative growth of aggregate objects. In this paper we formulate a model of geographic activity distribution with spatial correlations on the level of land lots where multiplicative growth is assumed to be dominant but not exclusive. The purpose is to retain the explanatory power of earlier models due to Simon, Gibrat and others while attaining some additional properties that are attractive for both empirical and modelling purposes. In this sense, the model presented here is a combination of the two factors that have been identified as central to urban evolution but rarely appear unified in the same model: transportation costs and multiplicative growth. The model is an elaboration of a previously reported complex network model of geographical land value evolution. We reproduce statistical properties of an empirical geographical distribution of land values on multiple hierarchical levels: land value per unit area, cluster areas, aggregated land value per cluster and cluster area/perimeter ratios. It is found that transportation effects are not strong enough to disturb the power law distribution of land values per unit area but strong enough to sort nodes to generate a new set of power laws on a higher level of aggregation. The main hypothesis is that all these relations can be understood as consequences of an underlying growing scale-free network of geographic economic interdependencies.

Suggested Citation

  • Andersson, Claes & Hellervik, Alexander & Lindgren, Kristian, 2005. "A spatial network explanation for a hierarchy of urban power laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(1), pages 227-244.
    • Handle: RePEc:eee:phsmap:v:345:y:2005:i:1:p:227-244
    DOI: 10.1016/j.physa.2004.07.027
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    References listed on IDEAS

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    1. Kaizoji, Taisei, 2003. "Scaling behavior in land markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 326(1), pages 256-264.
    2. Ergün, G. & Rodgers, G.J., 2002. "Growing random networks with fitness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 303(1), pages 261-272.
    3. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    4. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    5. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
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    Cited by:

    1. Yicheol Han & Stephan J. Goetz & Claudia Schmidt, 2021. "Visualizing Spatial Economic Supply Chains to Enhance Sustainability and Resilience," Sustainability, MDPI, vol. 13(3), pages 1-15, February.
    2. Hernán D. Rozenfeld & Diego Rybski & Xavier Gabaix & Hernán A. Makse, 2011. "The Area and Population of Cities: New Insights from a Different Perspective on Cities," American Economic Review, American Economic Association, vol. 101(5), pages 2205-2225, August.
    3. Arthur Huang & David Levinson, 2008. "An Agent-based Model of Retail Location with Complementary Goods," Working Papers 000056, University of Minnesota: Nexus Research Group.
    4. Claes Andersson & Koen Frenken & Alexander Hellervik, 2006. "A Complex Network Approach to Urban Growth," Environment and Planning A, , vol. 38(10), pages 1941-1964, October.
    5. César Ducruet & Laurent Beauguitte, 2014. "Spatial Science and Network Science: Review and Outcomes of a Complex Relationship," Networks and Spatial Economics, Springer, vol. 14(3), pages 297-316, December.
    6. Bono, Flavio & Gutiérrez, Eugenio & Poljansek, Karmen, 2010. "Road traffic: A case study of flow and path-dependency in weighted directed networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5287-5297.

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