Enhanced Key Node Identification in Complex Networks Based on Fractal Dimension and Entropy-Driven Spring Model

How to identify the key nodes in a complex network is a major challenge. In this paper, we propose a Second-Order Neighborhood Entropy Fuzzy Local Dimension Spring Model (SNEFLD-SM). SNEFLD-SM model combines a variety of centrality methods based on spring model, such as second-order neighborhood centrality, betweenness centrality, and fractal dimension, to evaluate the importance of nodes. Fractal technology can effectively boost the framework's proficiency in understanding network self-similarity and hierarchical structure in multi-scale complex networks. It overcomes the limitation of the traditional centrality method which only focuses on local or global information. The method introduces information entropy and node influence range; information entropy can effectively capture the local and global features of the network. The node influence rangecan increase the node importance distinction and reduce the calculation cost. Meanwhile, an attenuation factor is introduced to suppress the "rich-club" phenomenon. Tests on six networks show that SNEFLD-SM has higher accuracy in critical node detection than traditional methods. Furthermore, the application of information entropy further strengthens the model's capability to recognize key nodes.