## 3 Solution for DRLP
### Construction of Similarity Adjacency Matrix
The optimal performance interval is explicitly indicated by a green arrow in Figure 2c. The experimental results demonstrate that the [5; 8] interval exhibits both a concentrated and stable Q-value distribution (as shown in the boxplot of Figure 2c), with its significant superiority confirmed by 95% confidence interval analysis (Figure 2d). Therefore, based on the aforementioned experimental results and ANOVA statistical testing, we recommend configuring \(\beta\) within the [4; 8] range to simultaneously maximize system performance (Q-value) and optimal operational stability. ### Detection Result Analysis

#### 4.4.1 Analysis of Community Detection Results in Real Networks

We compare the DRLP algorithm with six other algorithms (LPA, Louvain, SC, CNLLP, LPA_CL, and CDEP) on seven real network datasets to demonstrate the efficacy of our algorithm. The experimental analysis results of the compared algorithms are shown in Table 3, which provides the corresponding modularity \(Q\)-values. Table 3 shows that the Louvain algorithm achieves a maximum Q-value of 0.4160 on the Karate dataset, and the LPA algorithm has the lowest average modularity among all algorithms. In addition, the average modularity value \(Q\) of the LPA is found to be consistent based on test results across all networks, with a significant discrepancy between the maximum modularity values and average modularity values. This is due to the high frequency of using random functions in the LPA algorithm, which leads to its low robustness. On small-scale datasets, the LPA_CL algorithm achieves stable and relatively good results. On large-scale datasets, it was unable to efficiently produce findings for community detection. As the size of the dataset increases, we can see that the time required by the LPA_CL algorithm increases significantly, and it performs poorly on large-scale datasets. The CDEP algorithm has a low time complexity and can achieve convergent community detection results on all datasets. However, its \(Q\)-values on small-scale and some large-scale networks are even lower than the LPA algorithm. The proposed DRLP algorithm achieves good community detection results on all datasets. Although it does not attain the maximum Q-value on certain datasets, its performance remains close to the maximum, even nearly identical on the football dataset. While Louvain obtains comparatively high modularity (Q) values on medium-scale networks, its effectiveness is constrained by resolution limits and randomness, and the modularity metric may obscure the loss of true community structures. On the other datasets, the DRLP algorithm consistently achieves the highest \(Q\)-values. The analysis of Q-values presented in Table 3 demonstrates the effectiveness of the DRLP algorithm. These results illustrate that the proposed DRLP algorithm performs better compared to other algorithms in this paper. Figure 2: Analysis and comparison of \(\beta\) parameter results. The normalized mutual information values that we recorded in experiments for our algorithm and the other compared algorithms are listed as Table 4, which provides community detection results on four real network datasets. The definition of NMI makes it clear that if the experimental results perfectly match the actual community division outcomes, then NMI = 1. From Table 4, the results of the experiment indicate that, when the algorithm's partitioning result matches the actual network community structure (\(NMI\) value of 1), the corresponding modularity value in Table 3 is 0.3715 for the KarateClub dataset. However, for the Louvain and CNLLP algorithms, their Q-values are greater than 0.3715 in Table 3, but their corresponding \(NMI\) values in Table 4 are both less than 1. This is because, for these two evaluation metrics, the \(Q\)-value is measured by the connections between the internal and external community structures, and the \(NMI\) is assessed according to the real network partitioning, and there is a certain inverse relationship between \(NMI\) and \(Q\)-values.