## 3 Results and Analysis
### Experimental Results on the Maximum Connectivity Coefficient  
Figure 2 shows the comparison of the network maximum connectivity coefficient \(G\) subjects with different static attack strategies on real and synthetic networks. As can be seen from Figure 2, in the static attack mode, the NBF attack strategy corresponds to the fastest decline of \(G\), that is to say, the proposed algorithm performs the best when identifying node importance. The advantage of the NBF algorithm is more obvious especially when the rate of removed nodes is small. For example, in the USAirport network from Figure 2a, when the rate of removed nodes is less than 15%, the decline speed of \(G\) is much more faster. In real applications, 15% is a very big attack rate when taking into account the cost of attack which has to be paid for. Since the NBF attack strategy can make the network fragment the most when removing a small rate of nodes, and also guarantee a great strike effect when removing a large rate of nodes, the proposed NBF algorithm performs the best on ranking node importance and has the highest application value. In addition, one can find that ego betweenness centrality attack strategy has the second best attack effect in four networks, LLS attack strategy has the second best attack effect in one network and WL attack strategy has the second best attack effect in one network. In order to further verify the efficiency of our NBF method, the experiment analyzes the changes of the network maximum connectivity coefficient in the dynamic attack mode, as shown in Figure 3. Observing the experimental results, we can also find that the maximum connectiv  
Figure 2: The network maximum connectivity coefficient (\(G\)) subjects with different dynamic attack strategies. Maximum connectivity coefficient (\(G\)) on the \(y\)-axis against the rate of removed node (\(p\)) on the \(x\)-axis. (**a**) the USAir network; (**b**) the Netscience network; (**c**) the Infectious network; (**d**) the USAirport network; (**e**) the Yeast network; (**f**) the Power network; and (**g**) the synthetic network WS. the NBF dynamic attack strategy decreases faster than other strategies, which shows that the NBF algorithm is more accurate than other algorithms for ranking node importance. The design principle of the NBF algorithm considers the bridging feature of the nodes, so the structure importance of the network nodes can be more effectively sorted. The experimental results verify this point. In addition, it can be observed that, when the network nodes are removed by k-shell method, the network has the worst fragmentation effect. This is because the k-shell method can not distinguish the importance of nodes in the same shell layer. Comparing the static attack and dynamic attack results of each algorithm in the same data set in Figures 2 and 3, it can always be observed that the dynamic attack effect is better than the static attack effect. 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. However, in the static attack mode, the network structure changes with the removal of nodes, and the importance of the nodes may be greatly reduced due to the drastic changes in the network structure. In addition, we find that the decline speed of \(G\) is related to the network structure, especially the average degree \(\langle k\rangle\) of the network. The Power network and the Netscience network have the lowest and second lowest average degree, respectively. In addition, the two networks are almost down after removing the top 10% important nodes under most attack strategies. The reason is that less average degree means less edges for the node pairs, so, after removing a small fraction of important nodes, the  
Figure 3: The network maximum connectivity coefficient (\(G\)) subjects with different dynamic attack strategies.