Generalizing Hypergraph Ego-Networks and Their Temporal Stability

Ego-networks provide a local perspective on networked systems by focusing on a central entity and its immediate relational context. While extensively studied in static pairwise interaction models, their analysis in dynamic and higher-order interaction contexts remains limited. In this paper, we introduce a formal analytical framework to generalize ego-networks to temporal hypergraphs, capable of modeling complex, non-dyadic group interactions over time. Our framework consists of two main components, namely, the concept of Rooted Ego-Networks (RENs), and generalized similarity criterion. RENs extend traditional ego-networks by capturing temporal and structural characteristics of groups centered on one or more nodes. We define multiple inclusion functions and similarity criteria to compare RENs across time, and we introduce the notion of stability to identify persistent local structures. Through empirical evaluation on real-world temporal hypergraphs from the SocioPatterns database, we illustrate the expressiveness of our approach in capturing and analyzing the evolution of localized group dynamics. To the best of our knowledge, this is the first comprehensive framework for analyzing the temporal and non-monotonic evolution of ego structures in higher-order networks.