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Phase transitions in information spreading on structured populations


Mathematical models of social contagion that incorporate networks of human interactions have become increasingly popular, however, very few approaches have tackled the challenges of including complex and realistic properties of socio-technical systems. Here, we define a framework to characterize the dynamics of the Maki–Thompson rumour spreading model in structured populations, and analytically find a previously uncharacterized dynamical phase transition that separates the local and global contagion regimes. We validate our threshold prediction through extensive Monte Carlo simulations. Furthermore, we apply this framework in two real-world systems, the European commuting and transportation network and the Digital Bibliography and Library Project collaboration network. Our findings highlight the importance of the underlying population structure in understanding social contagion phenomena and have the potential to define new intervention strategies aimed at hindering or facilitating the diffusion of information in socio-technical systems.

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Fig. 1: Types of structured population considered in the modelling framework.
Fig. 2: Results from numerical simulations of the rumour spreading process in homogeneous structured populations.
Fig. 3: Results from numerical simulations of a rumour spreading in real-world networks.

Data availability

The data represented in Fig. 3b are available through the Stanford Network Analysis Project (SNAP)48. All other data that supports the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

Code is available upon request from the corresponding author.


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N.P. was supported in part by the US Army Research Laboratory and the US Army Research Office under contract/grant number W911NF-18-1-0376. Y.M. acknowledges partial support from the Government of Aragón, Spain through grant E36-17R, by MINECO and FEDER funds (grant FIS2017-87519-P) and from Intesa Sanpaolo Innovation Center. The funder had no role in study design, data collection, and analysis, decision to publish, or preparation of the manuscript.

Author information




J.T.D., N.P., Y.M. and A.V. designed the research. J.T.D., A.V. and Q.Z. performed research and analysed data. All authors wrote the manuscript.

Corresponding author

Correspondence to Alessandro Vespignani.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Damon Centola, Chris Danforth and Hawoong Jeong for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Source data

Source Data Fig. 2

Data to remake Fig. 2 plots.

Source Data Fig. 3

Data to remake Fig. 3a,b.

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Davis, J.T., Perra, N., Zhang, Q. et al. Phase transitions in information spreading on structured populations. Nat. Phys. 16, 590–596 (2020).

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