## 3 Solution for DRLP
### Construction of Similarity Adjacency Matrix
Therefore, although the LPA_CL algorithm obtains a lower \(Q\)-value than the DRLP algorithm on the Dolphin dataset in Table 3, its \(NMI\) value is higher than that of the DRLP algorithm in Table 4. And Table 4 indicates that with the exception of the Dolphin dataset, the DRLP algorithm achieves higher \(NMI\) values across other datasets. These results illustrate that the proposed method performs well in detecting communities with higher values. The modular density values that we recorded in experiments for our algorithm and the other compared algorithms are shown in Table 5, which provides community detection results on seven real network datasets. Based on the definitions of modularity and modular density, higher values indicate tighter community connections. The difference is that Q is used to measure the quality of the global community partition of the network, while D measures the closeness of the connection within the community. Table 5 shows that the LPA algorithm achieves the highest modular density on the Karate dataset among the five algorithms. But the DRLP algorithm achieves higher modular density values than the other algorithms on other network datasets. This is because the modular density will be larger than that of the actual community due to the LPA algorithm's randomization, which produces more community division results. The experiment results \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Datasets** & **LPA** & **Lovain** & **SC** & **CNLLP** & ** LPA\_CL** & **CDEP** & **DRLP** \\ \hline KarateClub & 0.6855 & 0.6929 & 1.0000 & 0.8372 & 1.0000 & 1.0000 & **1.0000** \\ Dolphin & 0.1354 & 0.8735 & 0.1644 & 0.6011 & **0.8739** & 0.5996 & 0.5792 \\ Football & 0.2068 & 0.9014 & 0.8740 & 0.2763 & 0.8486 & 0.8691 & **0.9150** \\ Polbooks & 0.4039 & 0.4850 & 0.4382 & 0.4803 & 0.5432 & 0.5436 & **0.5754** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: NMI of community detection results in real network datasets (bold indicates maximum values across all datasets). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Datasets** & **LPA** & **Lovain** & **SC** & **CNLLP** & ** LPA\_CL** & **CDEP** & **DRLP** \\ \hline KarateClub & 0.3245 & **0.4160** & 0.3715 & 0.3718 & 0.3715 & 0.3715 & 0.3715 \\ Dolphin & 0.4832 & 0.5207 & 0.2635 & 0.5246 & 0.4826 & 0.3797 & **0.5265** \\ Football & 0.5563 & **0.6021** & 0.5752 & 0.5667 & 0.5463 & 0.3797 & 0.6020 \\ Polbooks & 0.4328 & **0.5263** & 0.4552 & 0.4569 & 0.4509 & 0.3559 & 0.4831 \\ PGP & 0.5879 & 0.7835 & 0.5351 & 0.7374 & 0.4378 & 0.5211 & **0.7974** \\ Astroph & 0.3016 & **0.5352** & 0.3158 & 0.3440 & 0.3214 & 0.5326 & 0.5015 \\ condMat & 0.5910 & 0.6252 & 0.4982 & 0.6581 & 0.4732 & 0.4714 & **0.6659** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The modular value Q of the community detection results of the real network datasets (bold indicates maximum values across all datasets). in Tables 3 and 5 show that the DRLP algorithm demonstrates more compact community structures and better structural characteristics on both large- and small-scale networks. These results illustrate the effectiveness of the proposed DRLP algorithm. #### 4.4.2 Synthetic Network Community Detection Results and Analysis

The curves of NMI variation with \(\mu\) for the DRLP algorithm and six other algorithms running 100 times on the LFR1 network are shown in Figure 3. The parameter \(\mu\) is increased from 0.1 to 0.7 with increments of 0.05 to ensure the accuracy of the test results. When the mixing parameter \(\mu\) is in the interval [0, 4.5], the community structure of the LFR network is relatively clear. In this case, the LPA, LPA_CL, Louvain, and DRLP algorithms achieve good community detection results. In particular, the DRLP and LPA_CL algorithms mostly reach the optimal NMI value of 1 within this interval. However, as \(\mu\) increases and the network's community structure becomes increasingly blurred, the accuracy of the LPA_CL algorithm drops significantly.