# Multi-Attribute Decision Making Method for Node Importance Metric in Complex Network
## 4 Experimental Results and Analysis
### Network Attack Simulation Experiment
#### 4.2.3 Discussion  
In the network experiment, the ranking of node importance in the experimental network is obtained according to the relevant node importance measurement indicators. The descending order of node importance is used for attack simulation, and the experimental results will be used as the basis to evaluate the quality of node importance metric indicator. The networks used in our experiments all have large-scale and scale-free structural properties. First, we obtained a single network property (\(H,COC,KS,\) and \(NCC\)) based on the network data separately, and after that, we combined it with the CRITIC method to obtain the composite indicator MCNDI. Next, simulated attacks were performed on these networks based on the node importance (measured by five methods) from highest  
Figure 7: This figure shows the topological distribution of the real network in our network experiment. (**a**) Simulation comparison chart of the USAir97 network subjected to deliberate attacks with different indicators, where the horizontal axis represents the ratio of failed nodes to the total number of nodes, and the vertical axis is the network efficiency ratio. (**b**) Simulation comparison chart of the technology routes networks subjected to deliberate attacks with different indicators, where the horizontal axis represents the evolutionary stage (every five nodes are a basic evolution stage) and the vertical axis is the network efficiency ratio.  
to lowest. Top 10 network node ranking is shown in Tables 1 and 2. \(M(i)\) represents the monotonicity of the set of nodes.  
In the USAir97 network, the numbers of node members with the same ranking of our method (MCNDI) and single indicators \((H,COC,KS,NCC)\) are \((7,8,4,9)\). Node 118 has the highest importance among all indicators, which means that node 118 is the most influential in the USAir97 network. Similarly, in the technology routing network, the numbers of node members with the same ranking of our method and single indicators \((H,COC,KS,NCC)\) are \((6,6,2,8)\). Combined with the monotonicity, we found that the \(k\)-shell indicator is the most different from the composite indicator, and has the worst monotonicity, which can cause difficulties in node importance decisions. I.e., the top 35 nodes in the USAir97 network have the same KS value. We also found that some of the top ten nodes of MCNDI in Table 2 do not exist in the top 10 ranking of the single indicators, which proves that their overall score is high, and such nodes with high overall importance are difficult to be measured by a single indicator. By contrast, MCNDI integrates the internal and external attributes of nodes, and the indications are accurate in decision making.  
Comparing Figure 7a with Figure 7b, we found similar network changes. According to the changes of the node network efficiency ratio, the network efficiency ratios of different networks all decrease rapidly under the MCNDI indicator attack, reflecting the stability of MCNDI's assessment of the importance of nodes in different networks, while the other indicators are affected by the network topology, and there are large fluctuations in the ability to influence the network efficiency ratio. The reason for the difference between the two figures is the different topology of the network, so the importance of the distribution of the