## 4 Conclusions  
The identification of node importance in complex networks is of theoretical and practical significance for improving network robustness and invulnerability. By analyzing the neighborhood structure of the target node, we propose a node importance identification algorithm based on a node bridging feature. The algorithm just needs neighborhood information within two hops of the node for computing instead of global information, which makes it applicable in a large-scale network. The robustness simulation experiments on real networks and synthetic networks show that the proposed algorithm performs better than degree centrality, k-shell algorithm, WL algorithm, LLS algorithm and ego betweenness centrality under two network connectivity evaluation criteria whether in static or dynamic attack strategies. Especially in the real applications where the cost of network attacks is limited, the advantage of the proposed algorithm is more obvious.  
We also find that the dynamic attack effect is better than the static attack for the same node importance identification algorithm. This is due to the fact that, in the dynamic attack mode, the importance of nodes is recalculated when removing a node, ensuring that each attacked node is the most important node in the current network. Therefore, both proposed algorithms and attack strategy construction are key factors for the invulnerability of the complex network, which guides the way to construct and maintain more robust networks.  
In addition, we discover that attack effect is related to the network structure, especially the average degree of the network. This is because a less average degree corresponds to less edges of the node pairs; thus, after removing the important nodes, the connectivity of the network turns bad very fast. The Power network and the Netscience network have the lowest and second lowest average degree, respectively, and the two networks are almost down after removing the top 10% important nodes under most attack strategies.  
The algorithm designed in this paper is for the undirected and unweighted networks. In real networks, the connections between nodes usually have directions, and each connection has different weights. It is easy to know from the expression of the NBF algorithm that the algorithm can be extended to directed weighted networks, which is the focus of future research. In addition, an algorithm that is optimal for one network may get sub-optimal results in a different network, and it is almost impossible to design a universal ranking algorithm which outperforms the best in all networks. In order to get more universal conclusions, we will test our algorithm on more real and synthetic networks in the future.  
Conceptualization, L.J., Y.J. and S.H.; Methodology, L.J.; Software, L.J.; Validation, S.H.; Formal Analysis, L.J. and Y.J.; Resources, W.X.; Data Curation, L.J.; Writing--Original Draft Preparation, L.J. and Y.J.; Writing--Review and Editing, S.H. and W.X.; Visualization, L.J. and B.G.; Supervision, W.X.; Project Administration, B.G.; Funding Acquisition, S.H. and W.X.  
This research was funded by the National Natural Science Foundation of China under Grant (No. 61872446), (No. 71690233) and (No. 71331008).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Information** & **Computational Complexity** \\ \hline K-shell & Global information & \(O(m)\) \\ WL & Local information & \(O(m+n(k))\) \\ Degree & Local information & \(O(m+n(k))\) \\ EggBot & Local information & \(O(n(k)^{2})\) \\ LLS & Local information & \(O(n(k)^{2})\) \\ NBF & Local information & \(O(n(k)^{2})\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The computational complexity of six methods.  
**Acknowledgments:** We are pleased to thank the Editor and the Referees for their useful suggestions. This work was supported by the National Natural Science Foundation of China under Grant Nos. 61872446, 71690233 and 71331008.  
**Conflicts of Interest:** The authors declare no conflict of interest.