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The scaling of human interactions with city size
Open accessAbstract
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.
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Metadata
- Authors
- Schläpfer, M., Bettencourt, L. M. A., Grauwin, S., Raschke, M., Claxton, R., Smoreda, Z., West, G. B., & Ratti, C.
- Affiliations
- Santa Fe Institute (US)
- Massachusetts Institute of Technology (US)
- Raschke Software Engineering, 65195 Wiesbaden, Germany
- BT Group (United Kingdom) (GB)
- Orange (France) (FR)
- Corresponding author
- Schläpfer, Markus
- ORCID
- Venue
- Journal of The Royal Society Interface
- Publisher
- The Royal Society
- Published
- 2014-09-06
- Volume
- 11
- Issue
- 98
- Pages
- 20130789-20130789
- ISSN
- 1742-5662 (ISSN-L)
- 1742-5689
- PMC
- PMC4233681
- OpenAlex
- W2099610463
- Cited by
- 356
- References
- 60
- Citations by year
- 2026: 20 · 2025: 21 · 2024: 23 · 2023: 20 · 2022: 28 · 2021: 37 · 2020: 64 · 2019: 30 · 2018: 25 · 2017: 22 · 2016: 26 · 2015: 24 · 2014: 14
- FWCI
- 18.89
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of The Royal Society Interface (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- Rockefeller Foundation
- James S. McDonnell Foundation (220020195)
- John Templeton Foundation (15705)
- Banco Bilbao Vizcaya Argentaria
- Army Research Office (W911NF1210097)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Social Sciences › Urban Studies › Global Urban Networks and Dynamics
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Agglomeration and Urban Systems
- Keywords
- city size, superlinear scaling, communication networks, urban population, contact networks, scale invariance, epidemic spread, disease transmission
- MeSH terms
- Cities, Communication, United Kingdom, Humans, Population Density, Portugal, Social Behavior, Socioeconomic Factors, Urban Population, Urbanization, Models, Statistical, Cell Phone
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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