A geometric-dynamic paradigm for identifying influential nodes in complex networks

Identifying influential nodes in complex networks is one of the core issues in network science, with wide applications in fields such as public opinion control, viral propagation inhibition, and identification of key disease-related genes. Dynamics is a major research direction in this field; dynamical processes inherently contain geometric properties, yet current dynamics-based methods for key node identification in complex networks do not incorporate geometric research. To address this issue, this paper proposes a geometry-enhanced hybrid framework for influential node identification. First, the framework maps discrete networks to a continuous geometric space via Riemannian manifold embedding, thereby converting the topological states of nodes into computable geometric coordinates. The embedded coordinates are combined with Ricci curvature to derive edge weights, which are used to construct geometric features for quantifying the local influence of nodes. By using geometric features to enhance thermodynamic diffusion between nodes and integrating classical centrality metrics with local influence, we form a new indicator for influential node identification. Systematic comparisons with 9 classic and cutting-edge algorithms on 9 real-world network datasets show that the proposed method significantly outperforms existing baselines in most cases and can accurately identify the most influential nodes. This study not only confirms the profound connection between geometric structures and network functions but also provides a novel and powerful paradigm for the analysis of influential nodes in complex networks. Our code is also publicly available at https://gitee.com/zlwlovv/gahc-algorithm-code.git • We proposed geometric diffusion model to achieves fine-grained quantification of node. • We propose a novel hybrid centrality metric for accurately identifying key nodes. • Geometric embedding makes key node identification more interpretable and realistic.