## 4 Experimental Results and Analysis
### Experimental Analysis  
The core goal of this work is to find relatively important nodes from the target node set \(T\). Therefore, the major subjects investigated from the four real networks selected, that is, all nodes of target node set \(T\), need to be determined. From the important node set \(V_{1}\), 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90% of the nodes are selected and used as known important nodes. The experiment in this paper treats the proportion of nodes equally; that is, the number of experiments corresponding to different proportion of nodes is the same. Different algorithms are used to find the relatively important nodes in the network. At the same time, precision, recall, and AUC values corresponding to different algorithms are calculated, and their values obtained from the experiments are averaged. Finally, the proposed DDMF method is used and compared with other comparative algorithms in terms of the three evaluation indexes. The parameters of five other comparative algorithms are adjusted to be close to the optimal ones in the four networks. The specific values are as follows: \(K=3\) is taken from the Ksmar indexes, \(S=0.75\) is taken from the PPR indexes, and \(\varphi=0.0001\) is taken from the Katz indexes. In the NMF algorithm, random walk length \(walk\_length\) is valued as 10, embedded vector length \(size\) is set to 128, and hyperparameters \(p,q\in\{0.25,0.50,1,2,4\}\). In the NLD algorithm, the selection method of known important nodes \(hu\) is the same as that of the DDMF method. The experimental results of the three evaluation indexes are shown in Figures 2 and 3 and Table 2.  
In this study, different proportions of nodes are selected from the important node set \(V_{1}\) as the known important nodes \(R\). The precision, recall, and AUC values are calculated by six relatively important node mining algorithms on the basis of experiments. The average value of 50 times in the experimental results is used as the final experimental result. Figure 2 shows the precision values of six relative importance node mining methods in the four networks. The \(X\) axis represents the proportion of nodes in the target node set \(T\) while the \(Y\) axis represents the precision of different node proportions. Figure 3 shows the recall rates of the six relative importance node mining algorithms in the four networks. The \(X\) axis represents the proportion of nodes in the target node set \(T\) while the \(Y\) axis represents the recall rates of different node proportions. Table 2 shows the AUC values obtained by the six relative importance node mining algorithms in the four networks. The experimental results show that with the increase in the number of nodes in the target node set \(T\), the precision of the algorithm decreases gradually while the recall rate increases gradually. In order to better simulate the actual situation of different real-world networks and to reduce accidental error, the important nodes of different batches are selected in different proportions from the important node set. Then the relatively important nodes corresponding to the important nodes of these different batches are calculated and mined. By calculating the arithmetic average of the relatively important nodes of different batches, the final relatively important nodes are obtained. In terms of precision, the proposed DDMF method is obviously better than the other five comparative algorithms in the SARS and Genepath networks, and all of them perform well in the mouse and yeast networks. In terms of recall, the DDMF method performs well in the SARS and mouse networks. Specifically, its recall, under multiple node proportions, is better than those of the comparative algorithms. The DDMF method ranks second for the Genepath and yeast networks. In terms of the AUC, the DDMF method outperforms the others in the SARS, Genepath, and mouse networks and ranks second in the yeast network.