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A rank-size rule following Zipf's law was tested along a complete urban–rural hierarchy in Greece using 2021 census data released at different administrative levels. Testing five econometric specifications (linear, quadratic, and cubic forms, together with refined logistic and Gompertz forms) on log-transformed population numbers, deviations from the rank-size rule were assumed as an indicator of economic concentration (considering settlements, population, and activities jointly) along the density gradient in Greece. This hypothesis was verified using progressively disaggregated population numbers at (i) regional units (n = 75), (ii) 'Kallikratis' municipalities (n = 333), (iii) 'Kapodistrian' municipalities (n = 1037), and (iv) local communities (n = 6126). Econometric results were stable across geographical levels and indicate a relatively poor fit of linear specifications, the classical formulation of Zipf's law. Quadratic specifications displayed a good fit for all territorial levels outperforming cubic specifications. Gompertz specifications outperformed logistic specifications under aggregate partitions (e.g., regional units and 'Kallikratis' municipalities). Quadratic specifications outperformed both logistic and Gompertz specifications under disaggregated levels of investigation ('Kapodistrian' municipalities and local communities). Altogether, these findings indicate the persistence of non-linear rank-size relationships estimated over a cross-section of population data at progressively detailed observational units. Such evidence enriches the recent literature on Zipf's law, demonstrating the inherent complexity of rank-size rules tested on real data along the whole density gradient in a given country. [ABSTRACT FROM AUTHOR]

Effectively monitoring the size of a city in real time enables the scientific planning of urban development. Models that utilize the distribution and variations in city size generally use population data as inputs, which cannot be obtained in a timely and rapid manner. However, night-time light (NTL) remote sensing may be an alternative method. A case study was carried out on the Yangtze River Delta (YRD) in China, and the rank–size rule, the law of primate cities, and the Gini coefficient were employed to monitor the variation in city size in the study area. The urban areas extracted based on NTL remote sensing were utilized instead of the traditionally used population data to evaluate the variations in city size from 2012 to 2017. Considering the empiricism and subjectivity of the thresholding method, urban areas were extracted from NTL data combined with the normalized differential vegetation index and land-surface temperature data based on the artificial neural network algorithm. Based on the results, the YRD did not fit the distribution of the primate cities from 2012 to 2017. However, this region satisfied the rank–size rule well, which indicated that the development of medium–small cities was more prominent than that of larger cities, and the dispersed force was larger than the concentrated force. Notably, the city size reached a relatively balanced level in the study area. Further, sensitivity analysis revealed that the relatively low extraction accuracy of urban areas of few small cities had little effect on the results of city size variations. Moreover, the validation of city size computed from statistical population data and its comparison with results calculated based on the statistical data of urban areas aligned with the results of this study, which indicates the rationality and applicability of monitoring the variations in city size using the urban areas extracted from NTL remote sensing instead of population data. [ABSTRACT FROM AUTHOR]

One piece of evidence of the inefficiency of the spatial economy of modern Russia presented in the seminal work of Hill and Gaddy (2004) is that Russian urban agglomerations are non-viable. This was demonstrated using Zipf's rank-size distribution, which does not hold for Russian urban systems. Hill and Gaddy explained this through the legacy of the Soviet command-administrative planning. Having constructed an original dataset, which incorporated comprehensive historical data for all the cities in the former Soviet Union republics and tested the rank-size distributions for the respective years, the study yielded more nuanced findings. First, unlike the modern Russian hierarchical urban systems, the Soviet ones followed rank-size distribution fairly well. Second, the Soviet urban systems were evolving. In the late Imperial era and early Soviet period, they followed the Zipf's law prediction. However, between 1939 and 1959, the rank-size distribution diverged from the predicted one. Yet again, the Soviet hierarchical urban systems revealed a trend of convergence toward the traditional rank-size distribution in the late Soviet era. A corollary to such evidence from data trajectory appears that the evolution of the Soviet hierarchical urban systems was not necessarily the ultimate product of the urban development policies of the command-administrative system. It can be thus presumed that, contrary to the established belief, command administrative urban development might be ineffectual even in centrally planned socialist economies. [ABSTRACT FROM AUTHOR]

Urban sprawl is the most prominent characteristic of urbanization, and increasingly affects local and regional sustainable development. The observation and analysis of urban sprawl dynamics and their relationship with urbanization quality are essential for framing integrative urban planning. In this study, the urban areas of the West Taiwan Strait Urban Agglomeration (WTSUA) were extracted using nighttime light imagery from 1992 to 2013. The spatio-temporal characteristics and pattern of urban sprawl were quantitatively analyzed by combining an urban expansion rate index and a standard deviation ellipse model. The urbanization quality was assessed using an entropy weight model, and its relationship with urban sprawl was calculated by a coupling coordination degree model. The results showed that the urban area in the WTSUA experienced a significant increase, i.e., 18,806.73 km2, during the period 1992–2013. The central cities grew by 11.08% and noncentral cities by 27.43%, with a general uneven city rank-size distribution. The urban sprawl showed a circular expansion pattern, accompanied by a gradual centroid migration of urban areas from the southeast coast to the central-western regions. The coupling coordination level between urban expansion and urbanization quality increased from serious incoordination in 1992 to basic coordination in 2013. Dual driving forces involving state-led policies and market-oriented land reform had a positive influence on the harmonious development of urban sprawl and urbanization quality of the WTSUA. This research offers an effective approach to monitor changes in urban sprawl and explore the coupling coordination relationship between urban sprawl and urbanization quality. The study provides important scientific references for the formulation of future policies and planning for sustainable development in urban agglomerations. [ABSTRACT FROM AUTHOR]

This paper maps out the structure and relative dynamics of cities of various size classes in India. It aims to address their hierarchical distribution, by employing the rank-size rule, Gibrat's law, and a primacy index. The implications of urban concentrations for GDP, banking system, FDI, civic amenities, and various urban externalities (such as pollution and spatial exclusion) are also examined. It shows that India's urban system, though it follows the rank-size rule, is huge and top-heavy. It follows also Gibrat's law of proportionate growth. Although India's cities collectively account for less than one third of the total population, they command more than three fourths of the country's GDP. Megacities have become congested, clogged, polluted, and also show significant social polarization. There is a gridlock situation for the cities, inhibiting their potential for becoming effective economic and social change sites. The top-heavy character of India's urban system also adversely impacts the balanced regional development of the country. [ABSTRACT FROM AUTHOR]

This paper analyzes the basic characteristics of Serbia's urban system after World War II. The term urban system is largely determined by the use and functioning of the space in which it exists. We used the methods common in urban geography, notably the Rank-Size Rule and the Law of the Primate City with the aim of identifying the basic regularities, as the first step in an in-depth study of an under-researched topic. The research seeks to contribute to explaining the causes of the previous and current situation in the national settlement network, as a prerequisite for planning the future organization of the settlement network. Our study, conducted in Serbia, finds polarization apparent in the prominent domination of the capital city in terms of population, and this is a key feature of Serbia's urban system. The current situation is the result of an intensive process of urbanization, but also of the establishment of new administrative boundaries after the disintegration of Yugoslavia. The study also seeks to suggest the most appropriate development model for Serbia's urban system that could help overcome the extreme population concentration in Belgrade and create a basis for organizing an optimal system of centers. Keeping in mind that uneven regional development is determined by the features of the urban system, polycentric development is a common model for overcoming extreme polarization on a global level. [ABSTRACT FROM AUTHOR]