# Distributed Average Consensus Algorithms in d-Regular Bipartite Graphs: Comparative Study
## 4 Experiments and Discussion
### Experimental Results and Discussion about Observable Phenomena  
In what follows, we focus our attention on the performance evaluation of the analyzed algorithms in regular bipartite graphs of various connectivities in order to identify whether  
Figure 8: Maximum error of used precisions of applied stopping criterion. all the algorithms can achieve the consensus and find the best-performing approach among those examined. In each connectivity graph, the algorithms were evaluated for three different precisions of the stopping criterion (the precision is provided in the right upper corner of each figure). For \(d=2\) (see Figure 9 and Table 1 in Appendix A) and the low precision of the applied stopping criterion, we can see that the best performance was achieved by GMH 0.1. The second-best-performing algorithm for this precision was CW, with \(\epsilon=\) MD 0.9. Both BC and OW achieved the same performance (as for \(d=2\), their matrices were identical) and were the third best among the analyzed algorithms. As further seen from the figure, the worst of the examined algorithms was MH. In the cases of the medium/high precision of the stopping criterion, GMH 0.1 outperformed all the other approaches again. Here, BC and OW were, however, better than CW and were, thus, the second best among the examined algorithms. The worst performance was observed for MH, like in the previous analysis. Moreover, it can be seen that the best performance for CW was achieved with the highest analyzed mixing parameter (i.e., \(e=\) MD 0.9), and its performance declined with a decrease in \(\epsilon\) (this is valid for each precision of the stopping criterion). For low values of \(\epsilon\), its performance was significantly lower than the other examined algorithms. In contrast, GMH performed the best, provided that the lowest \(\epsilon\) was applied (like for CW, this is valid for each precision of the stopping criterion). In addition, it can be seen from the figures that an increase in \(\epsilon\) resulted in performance degradation of the mentioned algorithm. For \(d=3\) (see Figure 10 and Table 2 in Appendix A), OW was the best-performing approach for each precision of the used stopping criterion, unlike the previous analysis. The second-best-performing algorithm, in this case, was GMH (however, with \(\epsilon=0.3\)), CW with \(\epsilon=\) MD 0.9 was the third best, BC was the fourth one, and MH was the worst approach once again--these statements are valid for each precision of the stopping criterion for \(d=3\). In the case of CW, we can see that an increase in \(\epsilon\) resulted in better performance of the algorithm, and the highest convergence rate was obtained with \(\epsilon=\) MD 0.9, like for \(d=2\). In contrast, GMH did not achieve the highest performance with the lowest \(\epsilon\) (like in the previous analysis), but with \(\epsilon=0.3\). In this case, we can see that an increase in \(\epsilon\) ensured the algorithm accelerated until the maximum convergence rate was achieved. Afterward, a further increase in \(\epsilon\) resulted in the deceleration of the algorithm. Figure 9: Convergence rate expressed as number of iterations required for consensus achievement in 2-regular bipartite graphs and for three precisions of applied stopping criterion. For \(d=4\) (see Figure 11 and Table A3 in Appendix A), the best-performing algorithm for each precision of the stopping criterion was OW again. The second-best one for each precision was GMH, but now with \(\epsilon=0.6\) (note that the maximum was obtained for a greater \(\epsilon\) than for \(d=3\)). Compared to the previous analysis, BC outperformed CW with the optimal mixing parameter (for \(d=4\), CW performed the best with \(\epsilon=\) MD 0.9) if the precision of the stopping criterion was medium/high. However, if its precision was low, CW performed better than BC, like in the previous analysis. MH was also the worst algorithm regarding the number of iterations required for the consensus achievement in these graphs like before.