## 6 Experiments
### Maximum Number of Maximum Cliques in Noncomplete Weighted Graph  
ALGR_1 to ALGR_3 were compared with each other, and the results of these comparisons are shown in in Tables 6-8. These tables contain the averages of 10 measurements. The obtained results are the averages of the largest number of maximum cliques obtained \(nK\) and of the maximum sum of the maximum clique weights \(W\). The parameters that changed during the tests were as follows: \(q\)--the density of the graph; \(m\)--the number of vertices in one part of the graph; \(d\)--the number of graph parts; \(lm\)--the number of ants; \(lc\)--the number of cycles; \(\rho\)--the pheromone evaporation coefficient. Figure 8: Number of maximum cliques: m changes, \(d=11\), \(lc=30\), \(lm=10\), \(\rho=0.995\), \(q=0.75\). Figure 7: Number of maximum cliques: \(d\) changes, \(m=50\), \(q=0.75\), \(lc=30\), \(lm=10\), \(\rho=0.995\). Table 6 shows the results obtained when the graph density \(q\) changes while the number of vertices in each part of the graph \(m\), the number of graph parts \(d\), the number of ants \(lm\), the number of cycles \(lc\), and the evaporation rate \(\rho\) are constant. ALGR_2 is slightly better than ALGR_3 in terms of the maximum sum of clique weights and slightly worse in terms of the maximum number of cliques. Figure 9 shows the deviation in the sum of the maximum cliques and in the number of maximum cliques determined with varying graph density, fixed numbers of vertices in each part of the graph, and a constant number of graph parts. The deviation in the number of maximum cliques determined is defined as follows:  
\[\frac{nK_{ALGR\_1}-nK_{ALGR\_x}}{W_{ALGR\_1}} \tag{23}\]  
where  
nKALGR_1 represents the maximum number of all maximum clicks obtained by ALGR_1;  
nKALGR_x represents the maximum number of all maximum clicks obtained by the remaining ALGR algorithms. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline _q_: & & **0.7** & **0.75** & **0.8** & **0.85** & **0.9** \\ \hline ALGR\_1 & \(W\) & 49,897 & 67,663 & 80,004 & 85,353 & 89,199 \\  & \(nK\) & 22.1 & 29.6 & 35.1 & 37.9 & 39.1 \\ ALGR\_2 & \(W\) & 86,595 & 100,749 & 111,913 & 118,064 & 123,668 \\  & \(nK\) & 16.2 & 26.0 & 33.0 & 36.8 & 38.9 \\ ALGR\_3 & \(W\) & 87,425 & 99,223 & 110,504 & 117,409 & 123,102 \\  & \(nK\) & 16.5 & 26.4 & 33.0 & 37.0 & 39.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Weights and number of maximum cliques: \(d=10\), \(m=40\), \(lc=30\), \(lm=10\), \(\rho=0.995\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**d:**} & \multicolumn{1}{c}{**6**} & **8** & **10** & **12** & **14** \\ \hline ALGR\_1 & \(W\) & 29,930 & 53,423 & 80,004 & 99,542 & 102,656 \\  & \(nK\) & 39.6 & 37.7 & 35.1 & 30.3 & 22.4 \\ ALGR\_2 & \(W\) & 45,035 & 77,218 & 111,913 & 151,287 & 179,214 \\  & \(nK\) & 39.2 & 36.4 & 33.0 & 25.9 & 18.3 \\ ALGR\_3 & \(W\) & 45,550 & 76,077 & 110,504 & 145,867 & 178,998 \\  & \(nK\) & 39.1 & 37.0 & 33.0 & 26.1 & 18.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Weights and number of maximum cliques: \(d\) changes, \(m=40\), \(q=0.8\), \(lc=30\), \(lm=10\), \(\rho=0.995\). Figure 9 shows that ALGR_2 and ALGR_3 operate similarly, and with an increase in graph density to q = 0.8, they determine an increasingly larger number of maximum cliques, while the sum of the weights of these cliques decreases. However, above a density of q = 0.8, these two algorithms demonstrate a greater sum of the weights of maximum cliques compared to ALGR_1, while the number of cliques determined converges to the number of maximum cliques determined by ALGR_1. Table 7 shows the results obtained when the graph density \(q\) and the number of vertices in each part of the graph \(m\) are constant; the number of graph parts \(d\) changes; and the number of ants \(lm\), the number of cycles \(lc\), and the evaporation rate \(\rho\) are constant. ALGR_2 is slightly better than ALGR_3 in terms of the maximum sum of clique weights and slightly worse in terms of the maximum number of cliques.