On the problem of boundaries and scaling for urban street networks.

A Paolo Masucci,Kiril Stanilov,Michael Batty,Erez Hatna,Elsa Arcaute

doi:10.1098/rsif.2015.0763

A Paolo Masucci, Kiril Stanilov + Show 3 more

Open Access

https://doi.org/10.1098/rsif.2015.0763

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Abstract

Urban morphology has presented significant intellectual challenges to mathematicians and physicists ever since the eighteenth century, when Euler first explored the famous Königsberg bridges problem. Many important regularities and scaling laws have been observed in urban studies, including Zipf's law and Gibrat's law, rendering cities attractive systems for analysis within statistical physics. Nevertheless, a broad consensus on how cities and their boundaries are defined is still lacking. Applying an elementary clustering technique to the street intersection space, we show that growth curves for the maximum cluster size of the largest cities in the UK and in California collapse to a single curve, namely the logistic. Subsequently, by introducing the concept of the condensation threshold, we show that natural boundaries of cities can be well defined in a universal way. This allows us to study and discuss systematically some of the regularities that are present in cities. We show that some scaling laws present consistent behaviour in space and time, thus suggesting the presence of common principles at the basis of the evolution of urban systems.

Highlights

Since the middle of the twentieth century, universal properties of cities have been identified, including Zipf’s and Gibrat’s laws [1,2]
Street networks provide a good representation to characterize the morphology of a city, where a street network is defined as that planar graph where the street intersections N are the vertices and the street segments E are the links
We provided a methodology to define city boundaries through spatial urban networks in a universal way

Summary

Introduction

Since the middle of the twentieth century, universal properties of cities have been identified, including Zipf’s and Gibrat’s laws [1,2]. Many different techniques to define cities have been suggested based on the analysis of urban growth [3,4,5], and recently a method using demographic and commuting data has been proposed [6] Clustering techniques such as the City Clustering Algorithm have been applied, mostly to analyse satellite images and demographic data [7,8,9], but these are rarely parameter free. As pointed out in [6], a broad range of exponents based on different allometries inferred from urban studies [10,11] can be observed for different boundary definitions. This further supports the urgent need for an operational and context-free definition of the city. Such universality in the spatial properties of cities prompts us to look at the spatial and temporal behaviour of important properties of urban street networks, and investigate whether some scaling laws could display a general behaviour

Results

The condensation threshold

Space and time scaling relations

Discussion