Abstract

The proliferation of large-scale interaction datasets, from scientific collaboration networks and legislative records to online communication platforms, has made the analysis of group-based, time-varying systems one of the central challenges of modern data analytics. Hypergraphs provide a natural formalism for such systems, where interactions involve arbitrary groups of agents rather than isolated pairs, and temporal hypergraphs extend this to sequential data by capturing how group interactions evolve over time. Yet quantifying how complex, predictable, or volatile this evolution is remains an open problem: existing entropy-based measures either operate on pairwise projections and thus discard multi-way dependencies or are not naturally defined for varying hyperedge sizes. In this paper, we propose an information–theoretic framework for characterizing how the diversity of interaction orders in a temporal hypergraph evolves over time. We introduce the hyperedge-size distribution entropy of a snapshot and, building on the theory of entropy rates for stochastic processes, we define the temporal hypergraph entropy rate as a principled, dataset-agnostic measure of the average diversity of interaction orders exhibited by the snapshot sequence over time. We further equip the framework with a bias-corrected sliding-window estimator and a lightweight change-point detector, assembling a complete pipeline that runs in time linear in the total number of hyperedges and requires no node alignment across datasets or snapshots. We prove that the measure collapses to zero under clique expansion, demonstrating that it captures interaction-order information that is discarded by the standard size-blind pairwise projection. Experiments on six small and large publicly available benchmark datasets show that the entropy rate spans 1.60 bits across domains, detects unsupervised structural change points, and discriminates between structurally distinct interaction cultures even within the same domain. Our framework is computationally lightweight and applicable to any dataset that can be represented as a temporal sequence of hypergraphs, paving the way for practical, scalable, interaction-order-aware analysis of large-scale higher-order temporal data.

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