Network science provides a powerful framework for the modelling and description of interacting systems. Its strength comes from its minimalism and generality, dissecting the notion of connectivity into core elements, nodes and edges, that may then be combined to form indirect connections. Yet, interactions may not always be sufficiently captured by independent, pairwise links. Addressing this issue, researchers have developed a variety of higher-order models for complex systems in order to enrich the standard network formalism when it is not sufficient to capture their structure and function. Among those, multi-body models, sometimes called combinatorial models, focus on the importance of group interactions, that is situations when the basic unit of interaction involves more than two nodes. This becomes particularly relevant for applications in sociology. It is a well known phenomenon that the dynamics in a social clique are determined not just by the pairwise relationships of its members, but often by complex mechanisms of peer influence and reinforcement. This requires to develop models that capture these multi-body mechanisms to better understand phenomena such as hate communities, echo chambers and polarisation in society.
In this talk, I will provide an overview of the main research streams of higher-order models and then derive and analyse a model for consensus dynamics on hypergraphs that incorporates reinforcing group dynamics such as peer pressure.