Superlinear and sublinear urban scaling in geographical networks modeling cities

Abstract

Using a geographical scale-free network to describe relations between people in a city, we explain both superlinear and sublinear allometric scaling of urban indicators that quantify activities or performances of the city. The urban indicator Y (N ) of a city with the population size N is analytically calculated by summing up all individual activities produced by person-to-person relationships. Our results show that the urban indicator scales superlinearly with the population, namely, Y (N ) ∝ N β with β > 1, if Y (N ) represents a creative productivity and the indicator scales sublinearly (β < 1) if Y (N ) is related to the degree of infrastructure development. These results coincide with allometric scaling observed in real-world urban indicators. We also show how the scaling exponent β depends on the strength of the geographical constraint in the network formation.

The Scale-Dependent Behaviour of Cities: A Cross-Cities Multiscale Driver Analysis of Urban Energy Use

“…Based on univariate correlations on real-world data, this research community provides a theoretical framework capable of predicting the evolution of a series of urban characteristics based on cities' sizes. More specifically, these studies focus on analysing how urban infrastructure, socio-economic or metabolic indicators change with either the population or the mean population density (e.g., [14,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]). These studies suggest that, even though cities seem to be very complex, different from one another and being located in very different regions of the world, they might share common macroscale (city-scale) simple behaviours.…”

Productivity, Infrastructure and Urban Density—An Allometric Comparison of Three European City Regions Across Scales

“…(Although the first two assumptions may appear contentious, the first is supported by current empirical observations and generally agreed on across other urban scaling models (Yakubo et al ., ; Sim et al ., ; Gomez‐Lievano et al ., ) whereas the second is ultimately an idealized and stylized assumption that affects the value of the scaling exponent and not the existence of an overall population power law relationship. )…”

Urban performance at different boundaries in England and Wales through the settlement scaling theory

“…These include models rooted in probabilistic conceptualisations of activities taking place in cities and the portion of population contributing towards them (Gomez-Lievano, Patterson-Lomba, & Hausmann, 2016) and those that are based on network realisations of the interactions between inhabitants and/or the geographical embedding of such networks within cities (Yakubo, Saijo, & Korošak, 2014).…”

“…We would be remiss, however, if we did not point out the remaining shortcomings and potential direction. The majority of models from the same family of the one used here start from the assumption that the units under study are in fact uniformly urban and functional economic catchments (Bettencourt, 2013;Yakubo et al, 2014;Gomez-Lievano et al, 2016). Unfortunately, this leaves them highly sensitive to the urban population count at each spatial scale and hence the choice of boundary used in that scale (Arcaute et al, 2015).…”