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Many real-world complex systems are characterized by interactions in groupsthat change in time. Current temporal network approaches, however, are unableto describe group dynamics, as they are based on pairwise interactions only.Here, we use time-varying hypergraphs to describe such systems, and weintroduce a framework based on higher-order correlations to characterize theirtemporal organization. We analyze various social systems, finding that groupsof different sizes have typical patterns of long-range temporal correlations.Moreover, our method reveals the presence of non-trivial temporalinterdependencies between different group sizes. We introduce a model oftemporal hypergraphs with non-Markovian group interactions, which revealscomplex memory as a fundamental mechanism underlying the pattern in the data.

Higher-order correlations reveal complex memory in temporal hypergraphs