# DMFO-CD: A Discrete Meth-Flame Optimization Algorithm for Community Detection
## 6 Conclusions and Future Works  
In this study, a discrete moth-flame optimization algorithm for community detection (DMFO-CD) was proposed for complex networks. The solution vectors representation, the distance calculation, and the spiral flight movement of the MFO algorithm were adapted for community detection. This adaptation was performed by introducing a singl \(\times\) 10 point crossover to imitate the distance calculation, a two-point crossover to alter the movement strategy, and a singl \(\times\) 10 point neighbor-based mutation to increase the exploration ability. The performance of the DMFO-CD was experimentally evaluated on eleven real-world \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**DMFO-CD vs.**} \\ \hline
**Network** & **DPSO-PDM** & **GA-Net** & **GACD** & **EGACD** & **DECS** \\ \hline Karate & \(6.02\times 10^{-7}\) & \(1.62\times 10^{-6}\) & \(1.00\times 10^{0}\) & \(1.00\times 10^{0}\) & \(8.01\times 10^{-7}\) \\ \hline Dolphins & \(3.47\times 10^{-6}\) & \(1.73\times 10^{-6}\) & \(1.70\times 10^{-6}\) & \(1.71\times 10^{-6}\) & \(1.44\times 10^{-6}\) \\ \hline Football & \(1.90\times 10^{-4}\) & \(1.73\times 10^{-6}\) & \(1.73\times 10^{-6}\) & \(1.73\times 10^{-6}\) & \(1.00\times 10^{0}\) \\ \hline Polbooks & \(1.42\times 10^{-6}\) & \(1.73\times 10^{-6}\) & \(1.73\times 10^{-6}\) & \(1.72\times 10^{-6}\) & \(1.50\times 10^{-6}\) \\ \hline WebKB-Cornell & \(1.73\times 10^{-6}\) & \(1.73\times 10^{-6}\) & \(2.58\times 10^{-3}\) & \(1.73\times 10^{-6}\) & \(1.73\times 10^{-6}\) \\ \hline WebKB-Texas & \(1.73\times 10^{-6}\) & \(1.73\times 10^{-6}\) & \(1.36\times 10^{-5}\) & \(1.96\times 10^{-3}\) & \(1.73\times 10^{-6}\) \\ \hline WebKB-Washington & \(1.73\times 10^{-6}\) & \(1.73\times 10^{-6}\) & \(3.71\times 10^{-1}\) & \(1.80\times 10^{-5}\) & \(1.73\times 10^{-6}\) \\ \hline WebKB-Wisconsin & \(1.73\times 10^{-6}\) & \(1.73\times 10^{-6}\) & \(2.16\times 10^{-5}\) & \(2.16\times 10^{-5}\) & \(1.73\times 10^{-6}\) \\ \hline AdjNoun & \(1.73\times 10^{-6}\) & \(1.73\times 10^{-6}\) & \(1.73\times 10^{-6}\) & \(3.18\times 10^{-6}\) & \(1.73\times 10^{-6}\) \\ \hline Email-Eu & \(1.95\times 10^{-3}\) & \(1.95\times 10^{-3}\) & \(1.95\times 10^{-3}\) & \(1.95\times 10^{-3}\) & \(1.93\times 10^{-1}\) \\ \hline Dblp & \(1.95\times 10^{-3}\) & \(1.95\times 10^{-3}\) & \(1.95\times 10^{-3}\) & \(1.95\times 10^{-3}\) & \(1.95\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The \(p\) values of Wilcoxon signed-rank test. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Network** & **DPSO-PDM** & **GA-Net** & **GACD** & **EGACD** & **DECS** & **DMFO-CD** \\ \hline Karate & 4.23 & 2.73 & 3.13 & 3.13 & 4.63 & 3.13 \\ \hline Dolphins & 6.00 & 4.87 & 1.75 & 2.32 & 2.77 & 3.30 \\ \hline Football & 4.28 & 5.60 & 1.37 & 1.63 & 3.90 & 4.22 \\ \hline Polbooks & 5.57 & 1.00 & 3.20 & 2.40 & 3.47 & 5.37 \\ \hline WebKB-Cornell & 3.03 & 1.00 & 5.07 & 4.13 & 2.00 & 5.77 \\ \hline WebKB-Texas & 1.03 & 2.97 & 5.80 & 4.70 & 2.00 & 4.50 \\ \hline WebKB-Washington & 1.10 & 2.87 & 5.57 & 4.10 & 2.03 & 5.33 \\ \hline WebKB-Wisconsin & 2.10 & 1.13 & 5.07 & 4.07 & 2.77 & 5.87 \\ \hline AdjNoun & 2.83 & 2.00 & 4.97 & 4.23 & 1.17 & 5.80 \\ \hline
**Avg. Rank** & 3.35 & 2.69 & 3.99 & 3.41 & 2.75 & 4.81 \\ \hline
**Overall Rank** & 4 & 6 & 2 & 3 & 5 & 1 \\ \hline Email-Eu & 5.20 & 3.80 & 1.40 & 2.80 & 2.00 & 5.80 \\ \hline Dblp & 4.40 & 2.00 & 6.00 & 3.30 & 4.30 & 1.00 \\ \hline
**Avg. Rank** & 4.8 & 2.9 & 3.7 & 3.05 & 3.15 & 3.4 \\ \hline
**Overall Rank** & 1 & 6 & 2 & 5 & 4 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The Friedman test on NMI. networks and compared with five well-known algorithms in community detection in terms of modularity, NMI, and the number of detected communities. The experimental results show that the proposed DMFO-CD can detect the correct number of communities with better modularity in comparison to other stat \(\times\) 100f-th \(\times\) 10 art algorithms.