A major achievement in the study of complex networks is the realization that diverse systems, from sub-cellular biology to social networks, exhibit universal topological characteristics. Yet, such universality does not naturally translate to the dynamics of these systems, as dynamic behaviour cannot be uniquely predicted from topology alone. Rather, it depends on the interplay of the network’s topology with the dynamic mechanisms of interaction between the nodes. Hence, systems with similar structure may exhibit profoundly different dynamic behaviour. We therefore seek a general theoretical framework to help us systematically translate topological elements into their predicted dynamic outcome. Here, we offer such a translation in the context of signal propagation, linking the topology of a network to the observed spatiotemporal spread of perturbative signals across it, thus capturing the network’s role in propagating local information. For a range of nonlinear dynamic models, we predict that the propagation rules condense into three highly distinctive dynamic regimes, characterized by the interplay between network paths, degree distribution and the interaction dynamics. As a result, classifying a system’s intrinsic interaction mechanisms into the relevant dynamic regime allows us to systematically translate topology into dynamic patterns of information propagation.

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All data and codes to reproduce the results presented here are freely accessible at https://github.com/CRHENS/Spatio-Temporal-/blob/master/README.md. Additional information is available from the corresponding author upon reasonable request. The only exception is the air-traffic network data, which the authors are restricted from sharing.

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C.H. thanks the Planning and Budgeting Committee (PBC) of the Council for Higher Education, Israel, and the INSPIRE-Faculty grant (code: IFA17-PH193) for support. This work was supported by the US National Science Foundation-CRISP award no. 1735505, the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Directorate in the Prime Minister’s office, and by a grant from the Ministry of Science & Technology, Israel & Ministry of Foreign Affairs and International Cooperation General Directorate for Country Promotion, Italian Republic.

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Author notes

  1. These authors contributed equally: Chittaranjan Hens, Uzi Harush.


  1. Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

    • Chittaranjan Hens
    • , Uzi Harush
    • , Simi Haber
    • , Reuven Cohen
    •  & Baruch Barzel
  2. Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India

    • Chittaranjan Hens


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All authors designed and conducted the research. C.H. and U.H. analysed the data and performed the numerical simulations. B.B. was the lead principal investigator.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Baruch Barzel.

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  1. Supplementary Information

    Supplementary Methods, Supplementary Tables 1–5, Supplementary Figures 1–17 and Supplementary References 1–36.

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