Identifying critical nodes in complex networks via a Multi-Scale Influence Spread method

Evaluating the propagation influence of nodes is crucial for understanding the survival and robustness of networks. In recent years, numerous methods have been widely applied to identify high-influence nodes, such as degree centrality and K-shell decomposition, which are based on single network features. However, these methods often fail to fully capture the propagation potential of nodes. To improve upon existing methods, we propose a novel heuristic method based on the Multi-Scale Influence Spread (MSIS). MSIS integrates various network characteristics, including node degree, clustering coefficient, and the influence and propagation distance of neighboring nodes, providing a more comprehensive evaluation of node influence. The main advantage of MSIS is its multi-scale method, which integrates both local and global network features to more effectively assess node propagation influence. Furthermore, MSIS eliminates the need for parameter tuning, enhancing its robustness and applicability across different network scenarios. Experiments conducted on eight real-world networks indicate that MSIS surpasses seven other methods in terms of node ranking performance, identifying influential nodes, and maintaining ranking monotonicity. MSIS also exhibits strong robustness and adaptability across diverse network topologies, effectively identifying critical nodes and assessing influence propagation. We offers a novel approach for identifying critical nodes in complex networks. Future research could focus on reducing computational complexity, enhancing adaptability to complex topologies, and deriving more universal global metrics from local features to optimize performance.