Higher-order correlations reveal complex memory in temporal hypergraphs

TL;DR

This paper introduces a framework using time-varying hypergraphs and higher-order correlations to analyze complex group dynamics and memory effects in temporal systems, surpassing traditional pairwise interaction models.

Contribution

It presents a novel approach to characterize temporal organization in systems with group interactions using higher-order correlations and models non-Markovian group dynamics.

Findings

Groups of different sizes exhibit long-range temporal correlations.

Non-trivial temporal interdependencies exist between different group sizes.

The model reveals complex memory as a key mechanism in temporal hypergraphs.

Abstract

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. We analyze various social systems, finding that groups of different sizes have typical patterns of long-range temporal correlations. Moreover, our method reveals the presence of non-trivial temporal interdependencies between different group sizes. We introduce a model of temporal hypergraphs with non-Markovian group interactions, which reveals complex memory as a fundamental mechanism underlying the pattern in the data.