Social contagion models on hypergraphs: a new look on an emerging field

Accumulating evidence in showing that several biological and social contagion phenomena, such as superspreading events or social reinforcement, are the results of multi-body interactions. These are group interactions among more than two of the fundamental elements of a system, for example people in a social network, or neurons in a brain region. The standard paradigm so far has however been based on networks, which only allow interactions between pairs of nodes. To overcome these limitations, researchers have started focusing more and more on hypergraphs which instead offer a natural mathematical description of multi-body interactions (as described also in a recent Nature Perspective ).
In a new paper  out in Communications Physics, a scientific team led by Dr. Guillaume St-Onge (Université Laval) and coordinated by Prof. Laurent Hébert-Dufresne (University of Vermont) and including ISI Foundation Senior Research Scientist Giovanni Petri, develops a novel mathematical framework based on approximate master equations to study contagions on hypergraphs characterize by heterogeneity in the size of the groups defining the interactions and in the number of groups a node is part of. Using this contagion model where multi-body interactions are mapped onto a nonlinear infection rates between nodes within the same group, researchers demonstrate the influence of large groups in two ways. First, they highlight how large groups drive both the early spread of a contagion and its endemic state (i.e., its stationary state). Second, scientists find that, when the contagion is sufficiently nonlinear, groups are more effective seeds of contagion than individual nodes. Putting together these two effects, the researchers found a complex tradeoff between the efficacy of node and group seeding strategies on the evolution of the contagion process.

This new paper follows, resonates with, and expands previous works on related models, like Nature Communications ( june 2019, conducted by a similar scientific team), and Physical Review Research (april 2020, authored by an ISI Foundation team), opening new horizons in the exploration of a very exciting, fast-advancing and forward-looking field: the one around social contagion modelling on hypergraphs.
«Influential groups for seeding and sustaining nonlinear contagion in heterogeneous hypergraphs», Guillaume St-Onge, Iacopo Iacopini, Vito Latora, Alain Barrat, Giovanni Petri, Antoine Allard, Laurent Hébert-Dufresne, Nature Communications Physics, 17th January 2022.