From pairwise to higher-order representations of complex systems and processes
Alain Barrat (CPT, Marseille)
Many complex systems find a convenient representation as networks, where nodes represent the system’s elements, and links their (pairwise) interactions. However, interactions involving more than two elements occur commonly: for instance, a group discussion is usually not reducible to a series of pairwise interactions. In recent years, an important activity has thus been devoted to the study of group (« higher-order) interactions in complex systems, using in particular the framework of hypergraphs (in which hyperedges can naturally encode group interactions of any size).
In this talk, I will address several recent developments in this context, focusing on contagion processes taking explicitly group processes into account. I will show how these group processes change the phenomenology of the epidemic transition, from a continuous to a discontinuous transition with the appearance of a bistable parameter region; I will discuss the similarities and differences in the propagation patterns of pairwise and group contagion, and whether it is possible to determine which process is at play by observing a propagation. Finally I will show how adaptive effects, which model change in behaviour occurring during an epidemic, can impact the higher-order contagion processes, suppressing the bistability region and effectively reverting a higher-order contagion process into a pairwise one.