Identifying Vital Nodes in Hypergraphs Under Time-Decaying Contagion Dynamics

Identifying vital nodes in hypergraphs is a fundamental problem with wide-ranging applications, including epidemic mitigation, rumor suppression, and public awareness promotion. Since node influence is shaped by the underlying spreading dynamics, it is crucial to consider temporal attenuation, where user interest in a topic on social platforms typically declines over time. Motivated by this observation, we study a novel problem of identifying vital nodes in hypergraphs under time-decaying (TD) spreading dynamics. To this end, we first introduce a TD spreading model on hypergraphs and analyze its dynamical behaviors using a mean-field approximation (MFA). The analysis reveals unique features such as delayed phase transitions and low steady-state infection densities under decay. Building on these insights, we propose a decay-aware structural-dynamical hybrid algorithm that integrates spectral characteristics with temporal decay information to tackle the problem. We validate the performance of proposed method on six real-world hypergraphs from diverse domains, including online social platforms, offline contact networks, and legislative co-bill systems. Experimental results demonstrate that our approach consistently outperforms eight state-of-the-art baselines, achieving up to a 10.04% improvement in influential node ranking. Further analysis reveals that the performance gains arise from the effective balance of topological structure and decaying temporal dynamics. In addition, the superior performance of our method leveraging paths of increasing order, over existing path-based ranking benchmarks, highlights the significance of incorporating dynamical information for identifying crucial nodes under decaying dynamics in higher order networks.