Hierarchy, cities size distribution and Zipf's law

Semboloni, Ferdinando

doi:10.1140/epjb/e2008-00203-1

Cited by 16 publications

(12 citation statements)

References 17 publications

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“…Empirically, q values always approach to 1 (Basu and Bandyapadhyay, 2009;Gabaix, 1999a;Gabaix, 1999b;Ioannides and Overman, 2003;Jiang and Yao, 2010;Krugman, 1996;Saichev et al, 2011;Zipf, 1949). The rank-size regularity is associated with fractals, and the power exponent indicates the fractal dimension of city-size distributions (Batty, 2006;Batty and Longley, 1994;Chen and Zhou, 2003;Frankhauser, 1998;Mandelbrot, 1983;Salingaros and West, 1999;Semboloni, 2008).…”

Section: Introductionmentioning

confidence: 99%

The rank-size scaling law and entropy-maximizing principle

Chen¹

2012

Physica A: Statistical Mechanics and its Applications

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Abstract:The rank-size regularity known as Zipf's law is one of scaling laws and frequently observed within the natural living world and in social institutions. Many scientists tried to derive the rank-size scaling relation by entropy-maximizing methods, but the problem failed to be resolved thoroughly. By introducing a pivotal constraint condition, I present here a set of new derivations based on the self-similar hierarchy of cities. First, I derive a pair of exponent laws by postulating local entropy maximizing. From the two exponential laws follows a general hierarchical scaling law, which implies general Zipf's law. Second, I derive a special hierarchical scaling law with exponent equal to 1 by postulating global entropy maximizing, and this implies the strong form of Zipf's law. The rank-size scaling law proved to be one of the special cases of the hierarchical law, and the derivation suggests a certain scaling range with the first or last data point as an outlier. The entropy maximization of social systems differs from the notion of entropy increase in thermodynamics. For urban systems, entropy maximizing suggests the best equilibrium state of equity for parts/individuals and efficiency for the whole.

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Section: Introductionmentioning

confidence: 99%

The rank-size scaling law and entropy-maximizing principle

Chen¹

2012

Physica A: Statistical Mechanics and its Applications

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“…Introduction. -Power law behaviors are now pervasive in various kinds of studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14], which give an important class of complex networks, namely the scale-free networks. However, in some cases, such a single property is insufficient to describe the distributions in real-world systems in which scaling law is absent in some regions or, even more peculiar, changed at some critical points [15,16].…”

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confidence: 99%

Emergence of double scaling law in complex systems

Han¹,

Qian²,

Ma³

2011

EPL

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We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness consideration and noise fluctuation. We find that if the number of variables (e.g. the degree of nodes in complex networks or people's incomes) grows exponentially, normal distributed fitness coupled with exponentially increasing variable is responsible for the emergence of the double power-law distribution. Fluctuations do not change the result qualitatively but contribute to the second-part scaling exponent. The evolution of Chinese airline network is taken as an example to show a nice agreement with our stochastic model.

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“…Metropolitan areas are usually associated with incomplete coverage, as they are based on centers of spatial concentration that are not exhaustive in space. In addition, within a given country or territory, such urban areas present a hierarchycal structure (Batty, 2006;Mazzeo, 2012;Semboloni, 2008;and Soto & Paredes, 2016). We find different approaches to defining integrated areas as spatial clusters.…”

Section: Functional Urban Areasmentioning

confidence: 88%

Identifying Functional Urban Areas in Ecuador Using a Varying Travel Time Approach

Obaco

Royuela

Vítores

2019

Geographical Analysis

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Identifying integrated urban areas is an important issue for urban analysis and policy evaluation. In this paper, we extend the OECD's methodology to identify Functional Urban Areas to countries where there is not commuting data. We do so substituting such socioeconomic flows by available information on road structure, which allow us to work with accessibility based on travel time. The main advantage of our procedure is its applicability to most countries in the world, as it only uses GIS data. In this paper we apply the procedure two border countries: Colombia, which has a recent census with commuting data, to calibrate our approach, and Ecuador, where there is not commuting census. We perform several sensitivity analysis and robustness checks to Ecuador with alternative sources of socioeconomic flows.

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Hierarchy, cities size distribution and Zipf's law

Cited by 16 publications

References 17 publications

The rank-size scaling law and entropy-maximizing principle

The rank-size scaling law and entropy-maximizing principle

Emergence of double scaling law in complex systems

Identifying Functional Urban Areas in Ecuador Using a Varying Travel Time Approach

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