Structure and Dynamics of Temporal Hypergraphs via Multi-Rooted Ego Networks

Ego-networks capture the local structure around a central entity. In this paper, we propose a framework that extends static pairwise settings to temporal hypergraphs and consists of two main components, namely, \textit{(i)} the concept of Multi-Rooted Ego-Network (REN), which generalizes traditional ego-networks centered on a single node to potentially multiple nodes; and, \textit{(ii)} similarity criteria for comparing consecutive RENs across time. The framework also enables the formalization of events such as \textsf{STABILITY}, allowing the identification and categorization of persistent local structures. Through empirical evaluation on real-world temporal hypergraphs from the SocioPatterns database, we highlight the expressiveness of our approach in capturing and analyzing the evolution of localized group dynamics. Moreover, we focus on a case study involving diachronic word embeddings, highlighting correlations between statistical descriptors of RENs' similarity time series and standard polysemy measures. This shows the flexibility of our framework across many application domains.