title: Great cities look small.
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 maximizing 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 characterize 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 gross domestic product and human immunodeficiency virus infection rates across US 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 UK: High Speed 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.
authors.affiliation: Department of Mathematics, Imperial College London, London SW7 2AZ, UK Department of Life Sciences, Imperial College London, London SW7 2AZ, UK.
authors.forename: Aaron
authors.initials: A
authors.lastname: Sim
authors.affiliation: Department of Chemistry, Imperial College London, London SW7 2AZ, UK.
authors.forename: Sophia N
authors.initials: SN
authors.lastname: Yaliraki
authors.affiliation: Department of Mathematics, Imperial College London, London SW7 2AZ, UK m.barahona@imperial.ac.uk.
authors.forename: Mauricio
authors.initials: M
authors.lastname: Barahona
authors.affiliation: Department of Life Sciences, Imperial College London, London SW7 2AZ, UK m.stumpf@imperial.ac.uk.
authors.forename: Michael P H
authors.initials: MP
authors.lastname: Stumpf
mesh_terms: D006801:Humans; D008962:Models, Theoretical; D014506:Urban Renewal
keywords: infrastructure; population models; social networks