A unified framework for identifying influential nodes in hypergraphs

Abstract

Identifying influential nodes plays a pivotal role in understanding, controlling, and optimizing the behavior of complex systems, ranging from social to biological and technological domains. Yet most centrality-based approaches rely on pairwise topology and are purely structural, neglecting the higher-order interactions and the coupling between structure and dynamics. Consequently, the practical effectiveness of existing approaches remains uncertain when applied to complex spreading processes. To bridge this gap, we propose a unified framework, Initial Propagation Score (IPS), to directly embed propagation dynamics into influence assessment on higher-order networks. We analytically derive mechanism-aware influence measures by relating the early-stage dynamics and local topological characteristics to long-term outbreak sizes, and such explicit physical context endows IPS with robustness, transferability, and interpretability. Extensive experiments across multiple dynamics and more than 20 real-world hypergraphs show that IPS consistently outperforms other leading baseline centralities. Furthermore, IPS estimates node influence with only local neighborhood information, yielding computational efficiency and scalability to large-scale networks. This work underscores the necessity of considering dynamics for reliable identification of influential nodes and provides a concise principled basis for optimizing interventions in epidemiology, information diffusion, and collective intelligence.