## 3 Solution for DRLP
### Construction of Similarity Adjacency Matrix
Details of parameter settings for synthetic networks are described in Table 2.

### Experimental Parameter Analysis

#### 4.3.1 Parameter \(\alpha\)

In the proposed algorithm, a damping factor \(\alpha\) is introduced for the node importance to evaluate the quantity and quality of a node's neighbors during each iteration. It also illustrates sudden changes in closeness or distance between nodes due to unexpected events. In addition, a higher damping factor means that the connections between nodes have a \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Networks** & **Karate** & **Dolphin** & **Polbooks** & **Football** & **PGP** & **AstroPh** & **CondMat** \\ \hline Nodes & 34 & 63 & 105 & 115 & 10,681 & 18,772 & 23,133 \\ Edges & 78 & 159 & 441 & 613 & 24,316 & 396,160 & 186,939 \\ \(C_{n}\) & 2 & 3 & 3 & 12 & -\(\backslash\)- & -\(\backslash\)- & -\(\backslash\)- \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specific information on real networks. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameter** & _Nodes_ & \(k_{\textit{average}}\) & \(k_{\textit{max}}\) & \(\tau_{1}\) & \(\tau_{2}\) & \(C_{\textit{min}}\) & \(C_{\textit{max}}\) \\ \hline LFR1 & 1000 & 20 & 50 & 2 & 1 & 10 & 50 \\ LFR2 & 5000 & 20 & 50 & 2 & 1 & 20 & 100 \\ LFR3 & 10,000 & 20 & 50 & 2 & 1 & 20 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specific information on synthetic networks. greater influence on their relationships, while sudden changes due to unexpected events have a lesser impact, which is more closely aligned with the interpersonal relationships observed in real social networks. To denote the importance, the value of the damping factor \(\alpha\) is set as 0.85 in the experiments. #### 4.3.2 Parameter \(\beta\)

In real social networks, there is a \"spillover effect\" [50]; that is, interacting with influential individuals can expand personal social networks, thus broadening the sphere of one's influence. By establishing relationships with influential individuals, a person can obtain more resources, information, and opportunities, thus enhancing personal influence. Therefore, in coordination with the above parameter \(\alpha\), we need to set another parameter \(\beta\) in the algorithm. It is the number of iterations performed when calculating node importance. The importance of each node is updated by iterative calculations. As a result, the importance of the neighbors or close connections of the nodes with higher importance also increases accordingly. The modularity \(Q\)-values and the mean modularity (\(Q\)) detected by the proposed algorithm at different \(\beta\) values on various network datasets are shown in Figure 2a,b. We show the changing of \(Q\)-values with the varying of parameter \(\beta\) on different datasets. From Figure 2a, it can be observed that the modularity tends to decrease to some extent with an increase in the number of iterations on all datasets. And in particular, as the number of iterations exceeds 25, the modularity values of the three datasets, namely, karate, Dolphin, and football, decrease by nearly 20%. Moreover, Figure 2b shows a sharp decline in the mean modularity. This is because, as the number of iterations increases, the difference in importance between individual nodes becomes smaller and smaller, and nodes with supposedly small importance gradually increase in importance after many iterations, and may even exceed the expected importance. From Figure 2a,b, we can also find that when the number of iterations ranges from four to eight, more optimal results are achieved for all datasets. Therefore, in all experiments, the value of \(\beta\) is set within the range of [4; 8]. Furthermore, to systematically validate the effectiveness of \(\beta\) parameter selection, we performed one-way ANOVA. The results are presented in Figure 2c,d, where Figure 2c illustrates the distribution of Q-values across different \(\beta\) intervals, and Figure 2d displays the mean Q-values with corresponding 95% confidence intervals for each interval.