Emerging Activity Temporal Hypergraph (EATH), a model for generating realistic time-varying hypergraphs

2025-07-01

AI Summary

Empirical time-varying hypergraph datasets often suffer from incompleteness, small scale, or short temporal spans. To address this, we propose EATH—a generative model for synthesizing time-varying hypergraphs that faithfully reproduce key statistical properties, including temporal activity patterns, higher-order topological structures, and diffusion dynamics. EATH innovatively couples node-level activity dynamics with a memory mechanism to enable self-emergent group interactions; it employs parametric statistical fitting for controllable generation, supporting cross-dataset mixed-attribute modeling and simulation of higher-order spreading processes. Experiments on multiple real-world face-to-face contact datasets demonstrate that EATH accurately reproduces critical features—such as temporal evolution of node activity, hyperedge duration distributions, and higher-order clustering dynamics. Thus, EATH provides a customizable, interpretable synthetic data foundation for modeling dynamic group interactions and simulating epidemic propagation.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Natural Language Processing: Generation
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Time-varying group interactions constitute the building blocks of many complex systems. The framework of temporal hypergraphs makes it possible to represent them by taking into account the higher-order and temporal nature of the interactions. However, the corresponding datasets are often incomplete and/or limited in size and duration, and surrogate time-varying hypergraphs able to reproduce their statistical features constitute interesting substitutions, especially to understand how dynamical processes unfold on group interactions. Here, we present a new temporal hypergraph model, the Emerging Activity Temporal Hypergraph (EATH), which can be fed by parameters measured in a dataset and create synthetic datasets with similar properties. In the model, each node has an independent underlying activity dynamic and the overall system activity emerges from the nodes dynamics, with temporal group interactions resulting from both the activity of the nodes and memory mechanisms. 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. 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. 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. Our work opens several perspectives, from the generation of synthetic realistic hypergraphs describing contexts where data collection is difficult to a deeper understanding of dynamical processes on temporal hypergraphs.

Problem

• Generates realistic time-varying hypergraphs from parameters
• Mimics temporal and topological properties of interactions
• Enables simulations of higher-order contagion dynamics

Innovation

• Generates synthetic time-varying hypergraphs with measured parameters
• Models node activity dynamics and memory mechanisms
• Creates tunable hybrid hypergraphs from multiple datasets