Disentangling high-order mechanisms and high-order behaviours in complex systems

Battiston et al. (arXiv:2110.06023) provide a comprehensive overview of how investigations complex systems should take into account interactions between more than two elements, which can be modelled by hypergraphs and studied via topological data analysis. Following separate line enquiry, broad literature has developed information-theoretic tools to characterize high-order interdependencies from observed data. While these could seem competing approaches aiming address the same question, in this correspondence we clarify that is not case, complete higher-order phenomena needs embrace both.