## 3 Experiment  
The experiments in this paper use four real network data sets. 1. The 9/11 criminal relationship network [20]. The nodes represent the terrorists who hijacked the planes and those who had contact with them; the edges represent the interpersonal relationships between them; and the set of important nodes represents the group of terrorists who hijacked the planes on 9/11. 2. SARS international aviation network [21]. Each node represents a country; the edge represents the existence of routes between two countries; and the earliest group of countries with the SARS virus is the set of important nodes. 3. Mouse protein interaction network [22]. The nodes represent mouse proteins; edges represent the existence of interactions between proteins; and the group of mouse protein kinases is the set of the important nodes. 4. Human protein interaction network [22]. The nodes represent human proteins; edges represent the existence of interactions between proteins; and the group of human protein kinases is the set of the important nodes. The topological information of these network data sets is listed in the following Table 1.  
The table header indicates the topological attributes of a network. \(N\) is the number of nodes in the network; \(N^{\prime}\) is the number of important node sets; \(M\) is the number of edges; and \(K\) and \(C\) are the average degree and clustering coefficient of the entire network, respectively. In this paper, we use \(AUC\) (Area Under Curve) to evaluate the overall results of this algorithm for mining relatively important nodes. The \(AUC\) is calculated as follows. \[AUC=\frac{0.5n_{1}+n_{2}}{n} \tag{2}\]  
where \(n_{1}\) represents the number of times that the importance score of a node selected from the unknown important node set equals that of a node selected from the unimportant node set; \(n_{2}\) represents the number of times that the importance score of a node selected from the unknown important node set is larger than that of a node selected from the unimportant node set. \(n\) represents the number of comparisons, which is the product of the size of the unknown important node set and the size of the unimportant node set. In this paper, we conduct nine rounds of experiments for each network, and the ratios (\(p\)) of known important nodes for each round are set to 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80% and 90%. Each round uses a different algorithm to calculate the relative importance of the nodes, according to which these nodes are ranked. Twenty independent experiments are conducted, and the \(AUC\) values are calculated for the ranking results. This paper uses NN [17], RD [18] and Katz [19] for comparison, and the results are as follows. In Figure 2, the horizontal axis represents the percentage of known important nodes of the set of important nodes, and the vertical axis represents the average \(AUC\) value. A higher \(AUC\) value represents a higher effectiveness. It is easy to see that the \(AUC\) values of most algorithms show an increasing trend as the ratio of important nodes in the network increases. The effect of the EG algorithm is most significant for the 9/11 network, and its \(AUC\) value remains stable at around 0.8, which is far ahead of other algorithms. In the SARS network and the Human network, our algorithm also achieved satisfactory results. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Network** & \(N\) & \(N^{\prime}\) & \(M\) & \(K\) & \(C\) \\ \hline
9/11 & 37 & 19 & 85 & 4.59 & 0.52 \\ SARS & 224 & 18 & 2247 & 20.06 & 0.65 \\ Human & 3574 & 186 & 6002 & 3.36 & 0.15 \\ Mouse & 1187 & 67 & 1557 & 2.62 & 0.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Network topology information. The _AUC_ index maintains its leading position against comparison algorithms, although the margins are not as prominent as those for 911 net.