Article

Memory in network flows and its effects on spreading dynamics and community detection

  • Nature Communications 5, Article number: 4630 (2014)
  • doi:10.1038/ncomms5630
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Abstract

Random walks on networks is the standard tool for modelling spreading processes in social and biological systems. This first-order Markov approach is used in conventional community detection, ranking and spreading analysis, although it ignores a potentially important feature of the dynamics: where flow moves to may depend on where it comes from. Here we analyse pathways from different systems, and although we only observe marginal consequences for disease spreading, we show that ignoring the effects of second-order Markov dynamics has important consequences for community detection, ranking and information spreading. For example, capturing dynamics with a second-order Markov model allows us to reveal actual travel patterns in air traffic and to uncover multidisciplinary journals in scientific communication. These findings were achieved only by using more available data and making no additional assumptions, and therefore suggest that accounting for higher-order memory in network flows can help us better understand how real systems are organized and function.

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Acknowledgements

We thank F. Liljeros for extracting the patient data and JSTOR for providing the journal citation data. We also thank D. Edler, A. Eklöf, D. Kolp, C. Poletto and D. Vilhena for many discussions. M.R. was supported by the Swedish Research Council grant 2012-3729. R.L. was supported by the Belgian Network DYSCO, funded by the IAP Programme initiated by Belspo.

Author information

Affiliations

  1. Integrated Science Lab, Department of Physics, Umeå University, Linnaeus va¨g 24 , SE-901 87 Umeå, Sweden

    • Martin Rosvall
    • , Alcides V. Esquivel
    • , Andrea Lancichinetti
    •  & Jevin D. West
  2. Department of Chemical and Biological Engineering, Howard Hughes Medical Institute (HHMI), Northwestern University, Evanston, Illinois 60208, USA

    • Andrea Lancichinetti
  3. Information School, University of Washington, Seattle, Washington 98195, USA

    • Jevin D. West
  4. Department of Mathematics and Naxys, University of Namur, 5000 Namur, Belgium

    • Renaud Lambiotte

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Contributions

M.R., A.V.E. and R.L. conceived the project. M.R. developed the community-detection algorithm. A.V.E. assembled the data and carried out the significance analysis. A.L. developed the epidemic and memory models. J.D.W. performed the ranking analysis. R.L. derived the analytical results. M.R. wrote the manuscript and all authors wrote the Supplementary Information. All authors were involved in interpreting the results and commented on the manuscript at all stages.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Martin Rosvall.

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    Supplementary Figures 1-9, Supplementary Tables 1-4, Supplementary Notes 1-4 and Supplementary References

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