Influential groups in hypergraph contagions

Contagion on higher-order networks provides a natural basis for the study of social reinforcement effects through group interactions. In this presentation, I will introduce group-based approximate master equations for hypergraph contagion. Compared to a standard heterogeneous mean-field theory, this compartmental approach preserves the dynamical correlations within groups of arbitrary size. Consequently, it provides extremely accurate predictions for contagions on random heterogeneous hypergraphs, while still being analytically tractable.

This approach helps us to better understand the important role of group interactions in two ways: (1) Dynamical correlations can induce localization of the contagion in the largest groups, which significantly affects the critical properties of the system. (2) When trying to maximize the early spread, if the contagion is sufficiently nonlinear (strong social reinforcement) it is more effective to engineer the initial configuration of groups than to infect the most central nodes. This is interpreted as influential groups being more important than influential spreaders for highly nonlinear contagion processes.