Finally, we illustrate the flexibility of the model, which can generate synthetic hypergraphs with tunable properties: as an example, we generate ”hybrid” temporal hypergraphs, which mix properties of different empirical datasets, and artificial hypergraphs with specifically tuned properties. 7/8

We also showcase the possibility to use the resulting synthetic data in simulations of higher-order contagion dynamics, comparing the outcome of such process on original and surrogate datasets. 6/8

We first show that the EATH model can generate surrogate hypergraphs of several empirical datasets of face-to-face interactions, mimicking temporal and topological properties at the node and hyperedge level. 5/8

We present a new model, the Emerging Activity Temporal Hypergraph (EATH), which can create synthetic time-varying hypergraphs. Each node has an independent activity dynamics, the system activity emerges from it, with temporal group interactions resulting from activity and memory mechanisms. 4/8

We illustrate the effectiveness of these metrics through clustering experiments on synthetic and empirical higher-order networks, showing their ability to correctly group hypergraphs generated by different models and to distinguish real-world systems coming from different contexts. 4/5