Higher-order homophily analysis for hypergraphs with time-varying node categories

Homophily has recently been studied in higher-order networks such as hypergraphs, yet existing measures are mostly limited to static settings and do not address cases in which node categories vary over time. In many real-world applications, nodes have basic categories, while their relevance to group interactions may change with time-varying activation levels, suggesting the need to treat categories in a temporal manner. In this paper, by naturally extending homophily indices developed for static hypergraphs, we propose an analytical framework for measuring higher-order homophily in temporal hypergraphs with time-varying node categories. The proposed method enables the quantification of higher-order homophily for individual categories and further for category pairs in a unified manner. We first conduct experiments on synthetic temporal hypergraphs where categories are associated with fluctuating activation levels. These experiments highlight differences between higher-order homophily patterns evaluated under the proposed framework and those evaluated on the aggregated static hypergraph, revealing situations in which conventional static indices may overlook important time-dependent characteristics. We then apply the framework to real-world hypergraphs derived from collective human activities observed in social media, demonstrating that explicitly accounting for temporal variations in node categories reveals higher-order homophily patterns that remain hidden in conventional static approaches.