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Evidence for a conserved quantity in human mobility

Nature Human Behaviourvolume 2pages485491 (2018) | Download Citation


Recent seminal works on human mobility have shown that individuals constantly exploit a small set of repeatedly visited locations1,2,3. A concurrent study has emphasized the explorative nature of human behaviour, showing that the number of visited places grows steadily over time4,5,6,7. How to reconcile these seemingly contradicting facts remains an open question. Here, we analyse high-resolution multi-year traces of ~40,000 individuals from 4 datasets and show that this tension vanishes when the long-term evolution of mobility patterns is considered. We reveal that mobility patterns evolve significantly yet smoothly, and that the number of familiar locations an individual visits at any point is a conserved quantity with a typical size of ~25. We use this finding to improve state-of-the-art modelling of human mobility4,8. Furthermore, shifting the attention from aggregated quantities to individual behaviour, we show that the size of an individual’s set of preferred locations correlates with their number of social interactions. This result suggests a connection between the conserved quantity we identify, which as we show cannot be understood purely on the basis of time constraints, and the ‘Dunbar number’9,10 describing a cognitive upper limit to an individual’s number of social relations. We anticipate that our work will spark further research linking the study of human mobility and the cognitive and behavioural sciences.

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This work was partially supported by the Villum Foundation (High Resolution Networks project, for which S.L. is the principal investigator), a UCPH-2016 grant (Social Fabric project, for which S.L. is a co-principal investigator) and the Danish Council for Independent Research (Microdynamics of Influence in Social Systems project, for which S.L. is the principal investigator; grant ID 4184-00556). Portions of the research in this paper used the MDC Database made available by the Idiap Research Institute, Switzerland and owned by Nokia. V.S. was supported by Sony Mobile Communications. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. V.S. thanks H. Jonsson for invaluable technical assistance.

Author information


  1. Department of Mathematics, City, University of London, London, United Kingdom

    • Laura Alessandretti
    •  & Andrea Baronchelli
  2. Technical University of Denmark, Lyngby, Denmark

    • Laura Alessandretti
    • , Piotr Sapiezynski
    • , Vedran Sekara
    •  & Sune Lehmann
  3. Sony Mobile Communications, Lund, Sweden

    • Vedran Sekara
  4. Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

    • Sune Lehmann


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L.A., S.L. and A.B. designed the research. L.A., P.S. and V.S. pre-processed the data. L.A. performed the data analysis. L.A., S.L. and A.B. analysed the results and wrote the paper.

Competing interests

The authors declare no competing interests.

Corresponding authors

Correspondence to Sune Lehmann or Andrea Baronchelli.

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    Supplementary Notes, Supplementary Figures 1–38, Supplementary Tables 1–7, Supplementary References 1–16

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