# A Complex Network Important Node Identification Based on the KPDN Method
## 6 Conclusions  
This study aims to find a more general important node-sorting method suitable for complex networks with different characteristics. The proposed KPDN method comprehensively considers the global K-shell properties of nodes as well as the neighborhood properties of target nodes. Experiments show that the proposed method in this paper fully takes into account the local and global characteristics of nodes and performs well in identifying important nodes in most networks. At the same time, since the global characteristics are based on the K-shell method, there is no excessive time and computational burden in the overall consideration. Therefore, in general, the proposed method in this paper can better distinguish important nodes in most real-world networks. Meanwhile, it also has an obvious effect on identifying important nodes in similar community networks or networks satisfying the small-world property. Moreover, this paper analyzes the importance of nodes from the perspective of network structure collapse. The work is mainly organized around the method of static node deletion in networks. Complex network models of real scenarios, such as virus propagation, have strong dynamic characteristics. According to the literature [32; 33], the network structure status will change after each node deletion (for example, some indicators in Figures 2 and 3 will show a curve with a slow decrease). Whether the changed network can inspire us to dynamically update the screening of nodes based on the initial node sorting method is worth further exploring. In recent years, the representation and analysis of multilayer networks and research on propagation dynamics based on complex networks have also been popular topics. These directions are also worth our in-depth exploration in the future. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app13148303/s1](https://www.mdpi.com/article/10.3390/app13148303/s1)]([https://www.mdpi.com/article/10.3390/app13148303/s1](https://www.mdpi.com/article/10.3390/app13148303/s1)). Supplementary File S1: The code and datasets used in this paper. Supplementary File S2: The time and space complexity proofs of various algorithms; Supplementary File S3: The statistics of results on real networks under different node removal strategies. Conceptualization, L.Z. and P.S. ; methodology, L.Z., W.L., J.Z. and Y.Z. ; software, L.Z. ; validation, L.Z. ; formal analysis, L.Z., P.S., J.Z. and M.P. ; investigation, L.Z. and M.P. ; resources, P.S. ; data curation, L.Z. ; writing--original draft preparation, L.Z., P.S. and J.Z. ; writing--review and editing, L.Z., P.S., J.Z., Y.Z., W.L. and M.P. ; visualization, L.Z. ; supervision, P.S., J.Z. and M.P. ; project administration, P.S. ; funding acquisition, P.S. and J.Z. All authors have read and agreed to the published version of the manuscript. This work was supported in part by the National Natural Science Foundation of China under grant 61773396. Not applicable. All datasets mentioned in this paper can be obtained free of charge from [[https://networkrepository.com](https://networkrepository.com)]([https://networkrepository.com](https://networkrepository.com)). The authors declare no conflict of interest. \begin{table}
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**Methods** & **Dimacs10-Astro-ph** & **Ca-Astroph** & **Gottron-Reuters** & **Prosper-Loans** & **Facebook-Wosn-Links** \\ \hline KPD & 99.6912\% & 99.8508\% & 99.8725\% & 99.9987\% & 99.8928\% \\ KPDN & **99.8386\%** & **99.9151\%** & 99.9940\% & **99.9998\%** & 99.9967\% \\ DC & 90.3604\% & 92.6562\% & 86.4161\% & 97.5723\% & 92.4147\% \\ KSHELL & 87.7731\% & 90.8483\% & 86.2097\% & 97.1114\% & 90.5103\% \\ DWT & 98.5433\% & 99.0495\% & 87.1266\% & 98.9777\% & 96.0803\% \\ WL & 99.6638\% & 99.8277\% & 99.9144\% & 99.9971\% & 99.8639\% \\ INCC & 98.2508\% & 98.8770\% & 68.5998\% & 79.2388\% & 90.3909\% \\ PR & 99.4724\% & 99.7526\% & **99.9989\%** & **99.9998\%** & **99.9971\%** \\ \hline \hline \end{tabular}
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