# Distributed Average Consensus Algorithms in d-Regular Bipartite Graphs: Comparative Study
## 4 Experiments and Discussion
### Comparison with Papers Concerned with Examined Algorithms in Non-Regular Non-Bipartite Graphs  
In this section, we individually compare each of the examined algorithms in \(d\)-regular bipartite graphs with their performance in non-regular non-bipartite graphs analyzed in papers from Section 2.2. MH was the worst algorithm in many examined scenarios, as seen from the figures. However, for \(d=5\), it was the best configuration of GMH, which does not correspond to theoretical assumptions from [51]. In these graphs, it performed well and was the second-best-performing algorithm. It was also the optimal configuration of GMH for \(d=10\); however, its performance was very low in this case (it even decreased compared to the performance in sparser graphs). This significant degradation of its performance in densely connected graphs was not seen in non-regular non-bipartite graphs [65; 66]. In general, we can see that MH did not perform well in regular bipartite graphs, such as in non-regular non-bipartite graphs [63; 65; 66]. BC performed well in the densest examined graphs, which confirms the conclusions in non-regular non-bipartite graphs [66]. As identified in [63; 65; 66], BC usually performed poorly in sparse non-regular non-bipartite graphs, but its performance was high in 2-regular bipartite graphs (i.e., in graphs of the lowest examined connectivity). As shown in [65; 66], in non-regular non-bipartite graphs, BC performed much better if the precision of the stopping criterion was not low. This statement was partially confirmed in regular bipartite graphs. In general, this algorithm achieved an average performance, which was also identified in non-regular non-bipartite graphs [62; 63; 65; 66]. As already mentioned, OW can be considered the best-performing distributed average consensus algorithm since it outperformed the other algorithms in almost every executed scenario. The only exception was the graphs with \(d=2\), where this algorithm was beaten by GMH (for each precision of the applied stopping criterion) and even by CW (if the precision was low). This statement is supported by the conclusions from [64; 66], where this algorithm was identified as being slow in the transient phase--the sparse connectivity of graphs caused this phase to take a longer time, and the low precision of a stopping criterion ensured that the algorithms were stopped early on. In addition, our findings in this paper correspond to the conclusions in regular bipartite graphs, where OW was mostly the best algorithm [62; 63; 65; 66; 67; 68; 69; 70]. As shown in [63; 65; 66], its performance was not good in sparsely connected graphs or if the stopping criterion was operating at a low precision, like in this paper. According to the presented results, CW was one of the worst-performing algorithms, which corresponds to its performance in non-regular non-bipartite topologies [51; 62]. Its higher performance was only seen for \(d=2\) and the low precision of the stopping criterion. The theoretical assumption from [51] that higher values of \(\epsilon\) ensure better performance of the algorithm was only valid in sparser graphs. As seen from the figures, for higher values of \(d\), the value of \(\epsilon\) guaranteeing its maximum performance was decreased. Regarding GMH, this algorithm also achieved high performance, especially in sparsely connected graphs (confirmed by [64]). Similar to CW, the theoretical assumption about the optimal value of \(\epsilon\) was not valid again--here, a lower value of \(\epsilon\) did not ensure better performance in denser regular bipartite graphs in contrast to non-regular non-bipartite topologies [51]. As the graph connectivity grew, we can see that this algorithm did not achieve its maximum performance with the lowest examined value of \(\epsilon\). In densely connected graphs, we can see that higher connectivity caused a greater value of \(\epsilon\) to ensure maximum performance.