# A Key Node Mining Method Based on K-Shell and Neighborhood Information
## 5 Conclusions  
This paper introduces an innovative method for identifying key nodes in the network based on K-shell and node neighborhood information, referred to as KCH. KCH posits that the importance of a node within the network is jointly determined by the node's own information and its neighborhood information. KCH is based on the K-shell method and considers the overall information of the network to quickly identify the global position of nodes within the network. Additionally, it enhances the importance score of bridge nodes and similar nodes by combining structural hole information and utilizing local clustering coefficient information of the network's local structure. As a result, the KCH method not only resolves the monotonicity issue of the KS method but also achieves a high degree of accuracy.  
The experimental results demonstrate that the KCH method possesses better accuracy, monotonicity, and universality, enabling it to better identify the influence of nodes within the network. This paper evaluates the performance of the KCH method through experimental comparisons with six centrality methods, such as CI, SC, and HKS, on ten networks. Among them, KCH exhibits the minimum robustness in nine networks, and in the remaining network, KCH ranks second but with a very small gap from the first. In the constructed null model experiments, the KCH method demonstrates excellent universality, with good results in both real and random networks. In terms of monotonicity, KCH can effectively identify important nodes and can almost uniquely measure the importance of each node in most networks. However, there are still some limitations in special networks where KCH cannot well-distinguish peripheral nodes that lack local characteristics. Overall, in a comprehensive assessment of accuracy, monotonicity, and universality, KCH is the best compared to other benchmark methods, and it can better identify the influence of nodes in the network.  
As research continues, we will consider designing a new method that addresses the limitations of the current approach and offers high performance. Additionally, KCH has the potential to be extended to weighted and directed networks. The insights gained from this study will play a key role in advancing effective techniques for the identification and protection of critical nodes in network systems, and we hope our work will provide some inspiration for future researchers in the field.  
Conceptualization, N.Z. and Q.F.; methodology, Q.F.; software, J.W.; validation, Q.F., M.J. and H.W.; formal analysis, N.Z.; investigation, J.W.; resources, H.W.; data curation, H.W. and M.J.; writing--original draft preparation, Q.F.; writing--review and editing, Q.F.; visualization, N.Z.; supervision, J.W. and Z.L.; project administration, Z.L. and M.J.; funding acquisition, J.W. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the National Natural Science Foundation of China under Grant No. 62066048 and No. 62366057 and the Li Zhengqiang Expert Workstation of Yunnan Province Grant No. 202205 AF150031.  
Not applicable.  
The data presented in this study are available from the corresponding author upon request. The data are not publicly available due to the following reasons. The information contained in the data is proprietary to the funding organization that supported this research, and public sharing is restricted to protect their intellectual property and competitive interests.  
The authors declare no conflicts of interest.