title: The scaling of human interactions with city size.
abstract: The size of cities is known to play a fundamental role in social and economic life. Yet, its relation to the structure of the underlying network of human interactions has not been investigated empirically in detail. In this paper, we map society-wide communication networks to the urban areas of two European countries. We show that both the total number of contacts and the total communication activity grow superlinearly with city population size, according to well-defined scaling relations and resulting from a multiplicative increase that affects most citizens. Perhaps surprisingly, however, the probability that an individual's contacts are also connected with each other remains largely unaffected. These empirical results predict a systematic and scale-invariant acceleration of interaction-based spreading phenomena as cities get bigger, which is numerically confirmed by applying epidemiological models to the studied networks. Our findings should provide a microscopic basis towards understanding the superlinear increase of different socioeconomic quantities with city size, that applies to almost all urban systems and includes, for instance, the creation of new inventions or the prevalence of certain contagious diseases.
authors.affiliation: Senseable City Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Santa Fe Institute, Santa Fe, NM 87501, USA schlmark@mit.edu.
authors.forename: Markus
authors.initials: M
authors.lastname: Schläpfer
authors.affiliation: Santa Fe Institute, Santa Fe, NM 87501, USA.
authors.forename: Luís M A
authors.initials: LM
authors.lastname: Bettencourt
authors.affiliation: Senseable City Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
authors.forename: Sébastian
authors.initials: S
authors.lastname: Grauwin
authors.affiliation: Raschke Software Engineering, 65195 Wiesbaden, Germany.
authors.forename: Mathias
authors.initials: M
authors.lastname: Raschke
authors.affiliation: British Telecommunications PLC, Ipswich IP5 3RE, UK.
authors.forename: Rob
authors.initials: R
authors.lastname: Claxton
authors.affiliation: Orange Labs, 92794 Issy-les-Moulineaux Cedex 9, France.
authors.forename: Zbigniew
authors.initials: Z
authors.lastname: Smoreda
authors.affiliation: Santa Fe Institute, Santa Fe, NM 87501, USA.
authors.forename: Geoffrey B
authors.initials: GB
authors.lastname: West
authors.affiliation: Senseable City Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
authors.forename: Carlo
authors.initials: C
authors.lastname: Ratti
mesh_terms: D040421:Cell Phone; D002947:Cities; D003142:Communication; D006801:Humans; D015233:Models, Statistical; D011156:Population Density; D011174:Portugal; D012919:Social Behavior; D012959:Socioeconomic Factors; D006113:United Kingdom; D014505:Urban Population; D014507:Urbanization
keywords: epidemiology; human interactions; mobile phone data; networks; urban scaling