title: On the problem of boundaries and scaling for urban street networks.
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.
authors.affiliation: Centre for Advanced Spatial Analysis, University College London, 90 Tottenham Court Road, London W1N 6TR, UK a.masucci@ucl.ac.uk.
authors.forename: A Paolo
authors.initials: AP
authors.lastname: Masucci
authors.affiliation: Centre for Advanced Spatial Analysis, University College London, 90 Tottenham Court Road, London W1N 6TR, UK.
authors.forename: Elsa
authors.initials: E
authors.lastname: Arcaute
authors.affiliation: Center for Advanced Modeling, The Johns Hopkins University, Baltimore, MD, USA.
authors.forename: Erez
authors.initials: E
authors.lastname: Hatna
authors.affiliation: Centre for Advanced Spatial Analysis, University College London, 90 Tottenham Court Road, London W1N 6TR, UK Centre for Sustainable Infrastructure and Construction, University of Cambridge, Cambridge CB2 1TN, UK.
authors.forename: Kiril
authors.initials: K
authors.lastname: Stanilov
authors.affiliation: Centre for Advanced Spatial Analysis, University College London, 90 Tottenham Court Road, London W1N 6TR, UK.
authors.forename: Michael
authors.initials: M
authors.lastname: Batty
mesh_terms: D000465:Algorithms; D002140:California; D002947:Cities; D016000:Cluster Analysis; D005843:Geography; D008131:London; D008433:Mathematics; D015233:Models, Statistical; D011157:Population Dynamics; D013997:Time Factors; D006113:United Kingdom; D014505:Urban Population
keywords: complex systems; scaling laws; street networks