Great cities look small

TL;DR

This paper introduces a mathematical model to quantify urban connectivity based on human interaction strategies constrained by travel time, validated with economic and health data, and applied to assess transport infrastructure impacts.

Contribution

The paper develops a novel model of city connectivity that incorporates real transport data and explains urban indicator scaling through mechanistic interactions.

Findings

Connectivity correlates with GDP and health outcomes.

Transport developments significantly impact city connectivity.

Model explains urban scaling laws mechanistically.

Abstract

Great cities connect people; failed cities isolate people. Despite the fundamental importance of physical, face-to-face social-ties in the functioning of cities, these connectivity networks are not explicitly observed in their entirety. Attempts at estimating them often rely on unrealistic over-simplifications such as the assumption of spatial homogeneity. Here we propose a mathematical model of human interactions in terms of a local strategy of maximising the number of beneficial connections attainable under the constraint of limited individual travelling-time budgets. By incorporating census and openly-available online multi-modal transport data, we are able to characterise the connectivity of geometrically and topologically complex cities. Beyond providing a candidate measure of greatness, this model allows one to quantify and assess the impact of transport developments, population growth, and other infrastructure and demographic changes on a city. Supported by validations of GDP and HIV infection rates across United States metropolitan areas, we illustrate the effect of changes in local and city-wide connectivities by considering the economic impact of two contemporary inter- and intra-city transport developments in the United Kingdom: High Speed Rail 2 and London Crossrail. This derivation of the model suggests that the scaling of different urban indicators with population size has an explicitly mechanistic origin.