Key node identification for a network topology using hierarchical comprehensive importance coefficients

Key nodes are similar to important hubs in a network structure, which can directly determine the robustness and stability of the network. By effectively identifying and protecting these critical nodes, the robustness of the network can be improved, making it more resistant to external interference and attacks. There are various topology analysis methods for a given network, but key node identification methods often focus on either local attributes or global attributes. Designing an algorithm that combines both attributes can improve the accuracy of key node identification. In this paper, the constraint coefficient of a weakly connected network is calculated based on the Salton indicator, and a hierarchical tenacity global coefficient is obtained by an improved K-Shell decomposition method. Then, a hierarchical comprehensive key node identification algorithm is proposed which can comprehensively indicate the local and global attributes of the network nodes. Experimental results on real network datasets show that the proposed algorithm outperforms the other classic algorithms in terms of connectivity, average remaining edges, sensitivity and monotonicity.