Detecting cardinal nodes in unweighted complex networks by examining their trajectories within Krylov subspace and various topological features

Network Science, delving into complex networks with intricate topologies and structural interactions, plays a pivotal role in understanding various natural systems. Computational studies highlight the importance of influential nodes in capturing network characteristics and functionalities. Previous research underscores the inadequacy of relying on a single node characteristic to identify influence, emphasizing the need for integrating multiple characteristics. In this study, we propose an indicator by incorporating the network’s topological features into the Krylov subspace to effectively capture influence propagation among nodes and their neighbors. This new indicator, in an asymmetric form, considers distinct node influence effects and inherent dynamics asymmetry. Furthermore, when integrated with other locality-based measures, it enhances the cohesion of a unified model. This model is employed to identify influential nodes within complex networks. Empirical evaluations of Susceptible–Infected–Recovered (SIR) propagation dynamics across ten authentic networks demonstrate that our proposed unified model operates within polynomial time and surpasses numerous traditional methods in terms of accuracy. Utilizing this approach to identify influential nodes offers potential applications across a range of domains, such as social networks, malware analysis, and neuro-perception networks.