A Key Node Ranking Method in Complex Networks by Integrating Semi-Local and Global Influence

The existing key node identification methods in complex networks rely on local topological information or global structural features, which are difficult to fully integrate multi-order local structural information and global propagation characteristics, resulting in the limitation of the accuracy and discrimination ability of node influence evaluation. In this paper, a key node ranking method combining semi-local and global influence, named SGIR, is proposed. Firstly, in the semi-local influence calculation stage, the second-order neighborhood, the third-order neighborhood, and the triangular closed structure of the node are used to construct the structural correlation matrix, and the structural energy migration mechanism is combined to quantify the local structural influence of the node, so as to enhance the expression ability of the semi-local structural features of the node. Secondly, in the global influence calculation stage, based on K-shell decomposition, a distance attenuation mechanism is introduced to weighted aggregate the influence of core nodes within the limited propagation range, and an adaptive propagation radius is designed by combining the average shortest path length of the network to effectively describe the global propagation ability of nodes. The semi-local influence and the global influence are fused to obtain the comprehensive influence ranking of nodes. Finally, comparative experiments are carried out on nine real complex networks from different fields such as communication, PowerGrid, and biological and social networks. The experimental results show that the proposed SGIR method achieves the best Kendall's τb on most data sets, and produces a highly discriminative ranking, which verifies the rationality, effectiveness, and stability of the proposed method and provides an effective solution for the identification of critical nodes in complex networks that takes into account both semi-local structural information and global propagation ability.