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Long ties accelerate noisy threshold-based contagions

Nature Human Behaviour (2024)Cite this article

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Abstract

In widely used models of biological contagion, interventions that randomly rewire edges (generally making them ‘longer’) accelerate spread. However, recent work has argued that highly clustered, rather than random, networks facilitate the spread of threshold-based contagions, such as those motivated by myopic best response for adoption of new innovations, norms and products in games of strategic complement. Here we show that minor modifications to this model reverse this result, thereby harmonizing qualitative facts about how network structure affects contagion. We analyse the rate of spread over circular lattices with rewired edges and show that having a small probability of adoption below the threshold probability is enough to ensure that random rewiring accelerates the spread of a noisy threshold-based contagion. This conclusion is verified in simulations of empirical networks and remains valid with partial but frequent enough rewiring and when adoption decisions are reversible but infrequently so, as well as in high-dimensional lattice structures.

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Fig. 1: Illustration of activation functions and local network structure.
Fig. 2: Network structures combining lattices and random graphs.
Fig. 3: Spread time of noisy complex contagion over rewired \({{{{{\mathcal{C}}}}}}_{{2}}\) graphs.
Fig. 4: Noisy threshold-based contagions on empirical networks and their structural variations.

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Data availability

The simulations on the empirical networks use data that were publicly released8,33,34,40. The data from ref. 8 are available at https://doi.org/10.17863/CAM.26430. The data from ref. 34 are available in the associated journal replication package. The data from ref. 33 are available at https://doi.org/10.7910/DVN/U3BIHX. The data from ref. 40 are available at https://archive.org/details/oxford-2005-facebook-matrix.

Code availability

The code for the reported simulations can be accessed from https://github.com/aminrahimian/social-contagion.

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Acknowledgements

E.M. was partially supported by a National Science Foundation (NSF) grant no. CCF 1665252, Department of Defense Office of Naval Research (ONR) grant no. N00014-17-1-2598, NSF grant no. DMS-1737944, Vannevar Bush Faculty Fellowship (ONR-N00014-20-1-2826), Simons Investigator award (no. 622132), ARO Multidisciplinary University Initiative W911NF1910217 and NSF award no. CCF 1918421. M.A.R. was partially supported by the NSF (SaTC-2318844), a Pitt Momentum Funds award and a Pitt Cyber Accelerator grant. This research was supported in part by the University of Pittsburgh Center for Research Computing, research resource identifier SCR_022735, through the resources provided. Specifically, this work used the H2P cluster, which is supported by NSF award no. OAC-2117681. During his postdoctoral work at the Massachusetts Institute of Technology, M.A.R. was supported by an Amazon Research Award to D.E. S.S. was partially supported by the NSF (DMS CAREER 2239234), ONR (N00014-23-1-2489) and Air Force Office of Scientific Research (FA9950-23-1-0429). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. We thank C. Hurtado, Y. Long and C. S. Reid for research assistance. We thank S. Aral, S. Morris and D. G. Rand for helpful comments. We also thank R. Cohen and J. Moody for their reviews.

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Authors and Affiliations

  1. Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA, USA

    Dean Eckles

  2. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Elchanan Mossel

  3. Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, USA

    M. Amin Rahimian

  4. Department of Statistics, Harvard University, Cambridge, MA, USA

    Subhabrata Sen

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Contributions

D.E., E.M., M.A.R. and S.S. conceived the research and contributed to the analysis. M.A.R. led the writing of the paper, with input from all authors. All authors approved the final paper.

Corresponding authors

Correspondence to Dean Eckles or M. Amin Rahimian.

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Competing interests

Meta (which operates Facebook) has sponsored a conference co-organized by D.E. and has funded some of his other research. M.A.R. has served on the advisory committee of a vaccine confidence fund created by Meta and Merck; some of his research has also been funded by Meta. The other authors declare no competing interests.

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Nature Human Behaviour thanks Reuven Cohen, James Moody and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Eckles, D., Mossel, E., Rahimian, M.A. et al. Long ties accelerate noisy threshold-based contagions. Nat Hum Behav (2024). https://doi.org/10.1038/s41562-024-01865-0

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