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Influential groups for seeding and sustaining nonlinear contagion in heterogeneous hypergraphs

St-Onge, Guillaume; Iacopini, Iacopo; Latora, Vito; Barrat, Alain; Petri, Giovanni; Allard, Antoine; Hébert-Dufresne, Laurent; (2022) Influential groups for seeding and sustaining nonlinear contagion in heterogeneous hypergraphs. Communications Physics , 5 , Article 25. 10.1038/s42005-021-00788-w. Green open access

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Abstract

Contagion phenomena are often the results of multibody interactions—such as superspreading events or social reinforcement—describable as hypergraphs. We develop an approximate master equation framework to study contagions on hypergraphs with a heterogeneous structure in terms of group size (hyperedge cardinality) and of node membership (hyperdegree). By mapping multibody interactions to nonlinear infection rates, we demonstrate the influence of large groups in two ways. First, we characterize the phase transition, which can be continuous or discontinuous with a bistable regime. Our analytical expressions for the critical and tricritical points highlight the influence of the first three moments of the membership distribution. We also show that heterogeneous group sizes and nonlinear contagion promote a mesoscopic localization regime where contagion is sustained by the largest groups, thereby inhibiting bistability. Second, we formulate an optimal seeding problem for hypergraph contagion and compare two strategies: allocating seeds according to node or group properties. We find that, when the contagion is sufficiently nonlinear, groups are more effective seeds than individual hubs.

Type: Article
Title: Influential groups for seeding and sustaining nonlinear contagion in heterogeneous hypergraphs
Open access status: An open access version is available from UCL Discovery
DOI: 10.1038/s42005-021-00788-w
Publisher version: https://doi.org/10.1038/s42005-021-00788-w
Language: English
Additional information: Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
UCL classification: UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment > Centre for Advanced Spatial Analysis
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL
URI: https://discovery.ucl.ac.uk/id/eprint/10144070
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