## 5 Experiments and Discussions
### Experimental Results and Analysis
#### 5.4.3 Experimental Results and Analysis on synthetic networks  
In order to better measure the performance of the algorithm, we generate networks of different sizes for experiments on the LFR test network model. In this case, the number of nodes in the LFR1 network is 1000 and the number of nodes in the LFR2 network is 4000. Since the real community structure of the LFR network is known, the performance of the algorithm is measured using NMI. Among the important parameters used to create  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Algorithm** & **Lesmis** & **Jazz** & **Email** & **Netscience** & **Power Grid** & **Facebook** & **PGP** \\ \hline Walktrap & 0.521 & 0.438 & 0.531 & 0.956 & 0.831 & 0.812 & 0.832 \\ Infomap & 0.546 & 0.442 & 0.538 & 0.930 & 0.759 & 0.706 & 0.821 \\ \hline CNM & 0.501 & 0.439 & 0.503 & 0.955 & 0.935 & 0.777 & 0.853 \\ Louvain & 0.527 & 0.282 & 0.463 & 0.907 & 0.627 & 0.835 & 0.885 \\ Leiden & 0.558 & 0.443 & 0.563 & 0.959 & 0.935 & 0.836 & 0.887 \\ \hline LPA & 0.560 & 0.445 & 0.574 & 0.960 & 0.939 & 0.737 & 0.745 \\ TS & 0.535 & 0.440 & 0.550 & 0.924 & 0.930 & 0.796 & 0.767 \\ GLLPA & 0.556 & 0.440 & 0.292 & 0.920 & 0.784 & 0.785 & 0.786 \\ SSCLPA & 0.557 & 0.406 & 0.513 & 0.906 & 0.838 & 0.779 & 0.801 \\ \hline Paris & 0.504 & 0.276 & 0.451 & 0.876 & 0.405 & 0.586 & 0.679 \\ \hline MSC & 0.544 & 0.447 & 0.565 & 0.948 & 0.890 & 0.812 & 0.872 \\ \hline SCL & 0.539 & 0.411 & 0.550 & 0.932 & 0.863 & 0.804 & 0.815 \\ \hline LNSSCL & **0.575** & **0.463** & **0.585** & **0.971** & **0.952** & **0.847** & **0.896** \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of modularity Q of each algorithm on unlabeled real network datasets. The largest Q are in bold.  
the LFR network, the mixing parameter \(\mu\) is used to represent the complexity of the community structure and determines the clarity of the community structure. As the mixing parameter \(\mu\) increases, the community structure becomes more complex and the difficulty of recognizing the community increases. The experimental results of the LFR network with different mixing parameter \(\mu\) are shown in Figure 4, where the horizontal coordinates represent the individual values of the mixing parameter \(\mu\) and the vertical coordinates represent the NMI.  
As can be seen in Figure 4, the performance of each algorithm decreases to varying degrees in both sets of networks as the mixing parameter \(\mu\) increases, but the community detection performance of the LNSSCL algorithm still outperforms most of the compared algorithms.  
When the mixing parameter \(\mu\) is less than 0.4, the algorithms have higher NMI values, except for the CNM and Paris algorithms. When \(\mu\) is greater than 0.4, the NMIs all show a decrease. Among them, label propagation-based algorithms such as LPA have very obvious changes in decline, especially the LPA algorithm, which has an NMI value of 0 in both networks when \(\mu\) is not less than 0.6. The reason for the analysis is that label propagation-based algorithms have a certain degree of randomness, which is prone to cause low performance and instability in community detection when the community structure is not clear enough. Comparing the synthetic networks LFR1 and LFR2, the NMI of most of the algorithms increased with the increase in the number of nodes. However, the performance of the CNM algorithm shows a decrease, which is attributed to the fact that the algorithm may have the problem of resolution limitation when dealing with networks with larger communities, and is unable to decompose large communities into smaller sub-communities. From Figure 4, it can be found that the NMI value of LNSSCL tends to 1 when \(\mu\) = 0.1, and the NMI value of LNSSCL is maximum when \(\mu\) = 0.8. It indicates that the performance of LNSSCL decays the slowest, i.e., the performance of LNSSCL is more stable.  
In summary, the community detection results of the LNSSCL algorithm are better on synthetic network datasets generated with different parameters.