Higher-order correlations reveal complex memory in temporal hypergraphs.

Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we use time-varying hypergraphs to describe such systems, and we introduce a framework based on higher-order correlations to characterize their temporal organization. The analysis of human interaction data reveals the existence of coherent and interdependent mesoscopic structures, thus capturing aggregation, fragmentation and nucleation processes in social systems. We introduce a model of temporal hypergraphs with non-Markovian group interactions, which reveals complex memory as a fundamental mechanism underlying the emerging pattern in the data. Network memory impacts dynamical processes emerging in real-world social systems, however little is known about memory of temporal networks beyond pairwise interactions. The authors develop a framework to characterize the temporal organization of higher-order networks and propose a model of temporal hypergraphs with higher-order memory to reproduce the patterns emerging in real-world complex systems. [ABSTRACT FROM AUTHOR]