On the problem of boundaries and scaling for urban street networks

TL;DR

This paper investigates the boundaries and scaling laws of urban street networks, proposing a universal method to define city boundaries and revealing consistent spatial and temporal regularities in urban growth.

Contribution

It introduces a clustering-based approach to define city boundaries universally and demonstrates the presence of common scaling laws in urban evolution.

Findings

Growth curves collapse to a logistic form

Natural city boundaries can be universally defined

Scaling laws show consistent behavior in space and time

Abstract

Urban morphology has presented significant intellectual challenges to mathematicians and physicists ever since the eighteenth century, when Euler first explored the famous Konigsberg 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.