# A Complex Network Important Node Identification Based on the KPDN Method
## 5 Results and Analysis
### Analysis of Real Networks
#### 5.1.2 Size of Real Network from \(10^{4}\) to \(10^{5}\)  
Due to the discovery in the experimental process that for large network node attack experiments, the efficiency of centrality evaluation indicators based on path analysis is very low, so when analyzing networks of \(10^{4}\sim 10^{5}\) this scale, we will no longer participate in BC, HC, CC, and CI comparison experiments to balance the overall experiment efficiency (we will also continue to retain the BC, HC, CC, and CI methods in the original code so that interested readers can verify and try for themselves). From Figure 7, it can be clearly seen that on the newly added network data of scale \(10^{4}\sim 10^{5}\), the KPDN method proposed in this paper can achieve suitable results in terms of the largest connected component size, meaning the method proposed in this paper has strong robustness in node removal. Meanwhile, in order to describe the actual data of each point in more detail, we show the data under different thresholds in Table S1 of Supplementary File S3. As can be seen more clearly from Figure 7, the method proposed in this paper has achieved suitable performance on the five existing real-world datasets of scale \(10^{4}\sim 10^{5}\). (Note: 0% in the tables refers to the actual removal effect when the top 1 ranked node is removed according to different strategies). From Figure 8, it can be clearly seen that on the newly added network data of scale \(10^{4}\sim 10^{5}\), the KPDN method can achieve suitable results in terms of the maximum number of remaining edges, meaning the method proposed in this paper is efficient in terms of the edge drop rate metric. Meanwhile, in order to describe the actual data of each point in more detail, we show the data under different thresholds in Table S2 of Supplementary File S3. Figure 6: The decrease rate of network edges affected by different network disintegration strategies (proportion of remaining subnet edges. The horizontal axis represents the proportion of nodes removed, and the vertical axis represents the remaining ratio of edges in the subnetwork). (**a–f**) correspond to: (**a**) email-univ, (**b**) p2p-Gnutella08, (**c**) fb-pages-government, (**d**) US-airports, (**e**) power-eris1176, and (**f**) bio-grid-worm. Figure 8: The maximum number of remaining edges of the 5 newly added datasets of scale \(10^{4}\sim 10^{5}\). (**a-e**) correspond to the datasets of: (**a**) dimas10-astro-ph, (**b**) ca-Astroph, (**c**) gotron-reuters, (**d**) facebook-wosn-links, and (**e**) prosper-loans. Figure 7: The size of the largest connected component of the 5 newly added datasets of scale \(10^{4}\sim 10^{5}\). (**a-e**) correspond to the datasets of: (**a**) dimas10-astro-ph, (**b**) ca-Astroph, (**c**) gotron-reuters, (**d**) facebook-wosn-links, and (**e**) prosper-loans. As can be seen more clearly from Figure 8, although the KPDN method does not rank first across all datasets among the five existing real-world datasets of scale \(10^{4}\sim 10^{5}\), overall, it ranks relatively high in the actual demonstrations of these five datasets, which also shows the proposed method has suitable performance. (Note: 0% in the tables refers to the actual removal effect when the top 1 ranked node is removed according to different strategies). As can be clearly seen from Figure 9, on the newly added network data of scale \(10^{4}\sim 10^{5}\), the KPDN method can achieve suitable results in terms of subgraph sensitivity, meaning the proposed method has relatively high efficiency in node removal on real-world networks of scale \(10^{4}\sim 10^{5}\). Meanwhile, to describe the actual node removal ratio when different methods reach the extreme points in more detail, we summarize the extreme points obtained by the five real-world datasets under different strategies in Table S3 of Supplementary File S3.