#hypergraph

The raison d’être of complexity science—in fact of science in general—is to find simple mechanisms that explain seemingly complex behavior. If the best one can do to model reality is to represent it as, say, a multilayer, time-varying, simplicial complex, I think this counts mostly as a failure of this program. But, the above considerations should be put in the background if nature demands it. Indeed, this is how the HON [higher order networks] literature frames things, insisting on the following very specific set of claims, often stated explicitly and repeatedly: 1. Graphs encode only “pairwise interactions,” 2. Hypergraphs encode “group interactions,” indivisible interaction units with more than two elements that cannot be represented by graphs. 3. Many systems are better modeled with “group interactions,” and hence hypergraphs. 4. “Group interactions” give rise to new phenomenology, not explainable by graph-based models. The central observation we make is that this set of claims rests on a rather elementary conflation between structure and function: A graph does not define interactions; it merely constrains them.