## 3 Solution for DRLP
### Construction of Similarity Adjacency Matrix
In contrast, although the Louvain algorithm does not reach the optimal accuracy, its NMI value remains consistently stable above 0.9. Interestingly, the CNLLP algorithm demonstrates even stronger robustness when the community structure is ambiguous, with its NMI value surpassing its performance under clear community structures. It can be obviously observed that, in the entire \(\mu\) range of 0 to 0.7, the DRLP algorithm consistently maintains excellent \(NMI\) metrics, significantly surpassing those of the comparison algorithms. This indicates that our DRLP algorithm can effectively detect meaningful community structures, whether the community structure is clear or blurred. The curves of NMI variation with \(\mu\) for the DRLP algorithm and six other algorithms running 100 times on the LFR2 network are shown in Figure 4. The parameter \(\mu\) is increased from 0.1 to 0.7 with increments of 0.05 to ensure the accuracy of the test results. From Figure 4, it can be observed that the community structure is relatively clear when the network size is 5000 and \(\mu<0.6\). The CNLLP algorithm shows a significant improvement, with \(NMI\) metrics consistently above 0.85 compared to the LFR1 network. Figure 3: Community detection results on the LFR1 network dataset. \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 & **7.7558** & 7.5295 & 6.8331 & 6.8238 & 6.8331 & 6.8331 & 6.8331 \\ Dolphin & 10.6580 & 10.2083 & 4.5377 & 10.5862 & 9.3143 & 8.4019 & **11.3823** \\ Football & 36.9792 & 37.4626 & 35.7051 & 34.1977 & 35.5773 & 33.5373 & **38.4390** \\ Polbooks & 15.6841 & 20.4789 & 15.1983 & 15.2867 & 10.1125 & 7.0234 & **17.4662** \\ PGP & 685.4679 & 299.4904 & 158.5631 & 361.1701 & 251.3371 & 13.7751 & **1103.1510** \\ AstroPh & 307.5602 & 296.4743 & 168.2516 & 155.2704 & 41.4322 & 10.3578 & **732.5882** \\ CondMat & 378.2734 & 277.3363 & 146.2851 & 222.7298 & 65.7114 & 19.8701 & **1728.8760** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Modularity density D of community detection results of real network datasets (bold indicates maximum values across all datasets). The DRLP, Louvain, and LPA_CL algorithms all maintain high community detection accuracy, with the first two algorithms having NMI values close to 1. However, when \(\mu>0.6\), the \(NMI\) value for the LPA_CL algorithm begins to drop sharply, while the CNLLP, Louvain, and DRLP algorithms continue to detect effective community structures. Although the CNLLP and Louvain algorithms maintain stability in the entire \(\mu\) range of [0, 0.7], the DRLP algorithm achieves \(NMI\) values greater than 0.9 throughout the same range. This further demonstrates that the DRLP algorithm can effectively detect meaningful community structures in networks with different connection characteristics. The curves of NMI variation with \(\mu\) for the DRLP algorithm and six other algorithms running 100 times on the LFR3 network are shown in Figure 5. The parameter \(\mu\) is increased from 0.1 to 0.8 with increments of 0.05 to ensure the accuracy of the test results. As shown in Figure 5, in large-scale LFR networks with 10,000 nodes, when the community mixing parameter \(\mu<0.5\), both the DRLP and LPA_CL algorithms demonstrate excellent performance consistent with their performance in smaller networks (LFR1 and LFR2), with their NMI metrics consistently maintained at near-optimal levels close to 1. Notably, the CNLLP algorithm shows significant improvement in the larger networks compared to its performance in smaller networks, achieving detection accuracy comparable to that of both the DRLP and LPA_CL algorithms.