# DMFO-CD: A Discrete Meth-Flame Optimization Algorithm for Community Detection
## 5 Experimental Evaluation
### Performance Evaluation
As per the results in Table 2 and Figure 10, DMFO-CD, GACD, and EGACD have the highest value of modularity and lowest distribution of modularity on karate network. In Figure 10, EGACD has the largest distribution of modularity than others, and GACD has the lowest average modularity that shows that they have the poorest performance on the dolphins network. The average modularity gained by GA-Net is better than EGACD and GACD; however, its distribution is near to GACD. The modularity of DMFO-CD is evident in that it is superior to other comparative algorithms for detecting communities of the dolphins network. As shown in Figure 10, GACD and EGACD have the lowest performance in the football dataset among other algorithms, while DMFO-CD and DPSO-PDM have better results than other algorithms. Figure 10 shows the results on polbooks network in which the GA-NET algorithm has the largest distribution and weak modularity, while in comparison to other algorithms, DMFO-CD has the best average modularity. Table 2 shows that DMFO-CD has mostly gained the best result of modularity among other comparative algorithms on webkb datasets. GACD and EGACD have the results near to DMFO-CD, and DPSO-PDM could not gain proper results in term of modularity. For adjnoun dataset, as shown in Figure 10, the proposed DMFO-CD has the best average of modularity than other comparative algorithms. GACD and EGACD after DMFO-CD have better results than DPSO-PDM, GA-Net, and DECS. In Table 2 the row of email-Eu represents the results of modularity on email-Eu dataset that DMFO-CD has the best results on it. DMFO-CD in compare with GA-Net and DECS has better performance and is near to EGACD. As shown in Figure 10, the performance of DMFO-CD in terms of modularity for dblp dataset is better than others, except for DPSO-PDM. The reported results show that the proposed DMFO-CD has the best performance in terms of modularity in the dolphins and polbooks datasets. In addition, DMFO-CD is competitive with GACD and EGACD on the karate dataset, and with DPSO-PDM and DECS on the football dataset. DMFO-CD in email-Eu dataset has a weak performance in terms of modularity; however, it is better than GA-Net and DECS. In dblp dataset, although DMFO-CD is not better than DPSO-PDM, it is better than other algorithms. Thus, DMFO-CD is able to provide superior and competitive results in comparison to the comparative algorithms in terms of modularity. Table 3 shows the average NMI of values gained by GA-Net, GACD, EGACD, DPSO-PDM, DECS, and DMFO-CD in karate, dolphins, football, polbooks, webkb, and adjnoun datasets from 30 runs and email-Eu and dblp datasets from 10 independent runs. In Figure 11, the bar plot of gained NMI of all algorithms is shown on each dataset. In the karate dataset, although DMFO-CD in terms of NMI obtains better results than GA-Net and DPSO-PDM, all comparative algorithms detect four communities, except for DECS, which has better NMI than others and detects the more correct community number. In the dolphins dataset, DPSO-PDM gained the most value of average NMI. In the football dataset, DPSO-PDM gained the most value of average NMI. dataset, DPSO-PDM and GA-Net have better performance than DMFO-CD, while DMFO-CD after GA-Net detects the correct number of communities. As shown in the fourth row of Table 3, in polbooks dataset, DMFO-CD and DPSO-PDM detect a more accurate and correct number of communities than the rest of the comparative algorithms. In webkb, network datasets GA-Net gained the best results of average NMI, while DMFO-CD could not gain proper results. In adjnoun dataset, GA-Net has the best result, but DMFO-CD has less good performance than other algorithms. In email-Eu dataset, DMFO-CD has the greatest value of NMI. The last row of Table 3 shows the results in dblp dataset in which DMFO-CD after GACD has the best average of NMI. Although in this experiment, DMFO-CD does not have the expected performance in terms of NMI, it practically detects the correct number of communities.