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A spatial network explanation for a hierarchy of urban power laws

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

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.

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File URL: http://www.sciencedirect.com/science/article/pii/S0378437104009926
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Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 345 (2005)
Issue (Month): 1 ()
Pages: 227-244

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Handle: RePEc:eee:phsmap:v:345:y:2005:i:1:p:227-244
Contact details of provider: Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

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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. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
  3. K C Clarke & S Hoppen & L Gaydos, 1997. "A self-modifying cellular automaton model of historical urbanization in the San Francisco Bay area," Environment and Planning B: Planning and Design, Pion Ltd, London, vol. 24(2), pages 247-261, March.
  4. 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.
  5. 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.
  6. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
  7. Paul M Torrens & David O'Sullivan, 2001. "Cellular automata and urban simulation: where do we go from here?," Environment and Planning B: Planning and Design, Pion Ltd, London, vol. 28(2), pages 163-168, March.
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