A scale-free transportation network explains the city-size distribution

Berliant, Marcus and Watanabe, Hiroki (2014): A scale-free transportation network explains the city-size distribution.

Abstract

Zipf’s law is one of the best-known empirical regularities in urban economics. There is extensive research on the subject, where each city is treated symmetrically in terms of the cost of transactions with other cities. Recent developments in network theory facilitate the examination of an asymmetric transport network. In a scale-free network, the chance of observing extremes in network connections becomes higher than the Gaussian distribution predicts and therefore it explains the emergence of large clusters. The city-size distribution shares the same pattern. This paper decodes how accessibility of a city to other cities on the transportation network can boost its local economy and explains the city-size distribution as a result of its underlying transportation network structure.

• Item Type: MPRA Paper
• Language: English
• Keywords: Zipf’s law; City-size distribution; Scale-free network
• Subjects: R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R12 - Size and Spatial Distributions of Regional Economic Activity; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R4 - Transportation Economics > R40 - General

References

Réka Albert and Albert-László Barabási. Statistical mechanics of complex networks. Reviews of Modern Physics, 2002.

Albert-László Barabási and Réka Albert. Emergence of scaling in random networks. Science, 1999.

Albert-László Barabási and Eric Bonabeau. Scale-free networks. Scientific American, 2003.

Duncan Black and Vernon Henderson. Urban evolution in the USA. Journal of Economic Geography, 2003.

Kristian Behrens, Giordano Mion, Yasusada Murata, and Jens Südekum. Spatial frictions. Working Paper, 2013.

Marcus Berliant and Hiroki Watanabe. Explaining the size distribution of cities: X-treme economies. Quantitative Economics, 2014.

Nicholas A. Christakis, James H. Fowler, Guido W. Imbens, and Karthik Kalyanaraman. An empirical model for strategic network formation. mimeo, 2010.

S. N. Dorogovtsev, J. F. F. Mendes, and J. G. Oliveira. Degree-dependent intervertex separation in complex networks. Phyisical Review E, 2006.

Gilles Duranton. Some foundations for zipf’s law: Product proliferation and local spillovers. Regional Science & Urban Economics, 2006.

Jan Eeckhout. Gibrat’s law for (all) cities. American Economic Review, 2004.

Paul Erdos and Alfréd Rényi. On random graphs. Publicationes Mathematicae, 1959.

Agata Fronczak, Piotr Fronczak, and Janusz A. Hołyst. Average path length in random networks. Physical Review E, 2004.

Masahisa Fujita, Paul Krugman, and Anthony J. Venables. The Spatial Economy. The MIT Press, 1999.

Masahisa Fujita and Jacques-François Thisse. Economics of Agglomeration. Cambridge University Press, 2002.

Janusz A. Hołyst, Julian Sienkiewicz, Agata Fronczak, Piotr Fronczak, and Krzysztof Suchecki. Universal scaling of distances in complex networks. Physical Review E, 2005.

Matthew O. Jackson and Brian W. Rogers. Meeting strangers and friends of friends: How random are social networks? The American Economic Review, 2007.

Eckhard Limpert, Werner A. Stahel, and Markus Abbt. Log-normal distributions across the sciences: Keys and clues. BioScience, 2001.

Philip McCann. Transport costs and new economic geography. Journal of Economic Geography, 2005.

Angelo Mele. A structural model of segregation in social networks. mimeo, 2011.

M. E. J. Newman, C. Moore, and D. J. Watts. Mean-field solution of the small-world network model. Physical Review Letters, 2000.

M. E. J. Newman, S. H. Strogatz, and D. J. Watts. Random graphs with arbitrary degree distributions and their applications. Physical Review E, 2001.

M. E. J. Newman and D. J. Watts. Renormalization group analysis of the small-world network model. Physics Letters A, 1999.

Bo Ranneby. The maximum spacing method. an estimation method related to the maximum likelihood method. Scandinavian Journal of Statistics, 1984.

Esteban Rossi-Hansberg and Mark L. J. Wright. Urban structure and growth. The Review of Economic Studies, 2007.

Kwok Tong Soo. Zipf’s law for cities: a cross-country investigation. Regional Science and Urban Economics, 2005.

Zhongzhi Zhang, Yuan Lin, Shuyang Gao, Shuigeng Zhou, and Jihong Guan. Average distance in a hierarchical scale-free network: an exact solution. Journal of Statistical Mechanics: Theory and Experiment, 2009.