## 5 Evaluation Results  
In this section, we present the evaluation results for the two scenarios described in Section 4. Regarding the first scenario, the convergence time is plotted in Figure 1 as a function of the malicious nodes percentage. The latter spans from 0% to 35%.  
This is shown for various percentages of the UNL overlap, namely, 10%, 50%, 90%, and 95%. (These values are representative and adequately cover the parameter's space. That is, in-between UNL overlap percentages consistently yielded analogous performance scores. They are not depicted for the sake of plot's readability.) Overall, we observe that low convergence times (less than 1000 ms) are achieved when 90% and 95% UNL overlap is applied. A key observation deals with the broad separation of the considered operational space, in terms of UNL overlap, into two regions, \([0\%,20\%]\)  
Figure 1: Convergence time vs. percentage of malicious nodes for various UNL overlaps.  
and \((20\%,35\%)\), denoted as \(R_{1}^{1}\) and \(R_{2}^{1}\), respectively. Regarding \(R_{1}^{1}\), all convergence times lie below 1000 ms, while the utilization of 90% and 95% UNL overlaps exhibits better performance compared to the case of 10% and 50% UNL overlaps. Within the \(R_{2}^{1}\) region, the use of 10% and 50% UNL overlaps exhibits a non-robust behavior yielding convergence times that reach, and occasionally exceed, 4000 ms. These observations suggest that high UNL overlaps are needed only when the percentage of malicious nodes increases beyond a certain threshold. This threshold is (empirically) shown to be approximately equal to 20%.  
The evaluation results for the second scenario are reported in Figure 2. In this figure, NHI (defined in Section 4) is plotted as a function of the percentage of malicious nodes. As in the case of the first scenario, the percentage of malicious nodes ranges from 0% to 35%. NHI scores are shown for three percentages of UNL overlap, namely, 10%, 50%, and 90% (i.e., weak, mild, and strong UNL overlap). Overall, it is observed that, for all three UNL overlaps, higher NHI scores are reached (i.e., the performance drops) as the percentage of malicious nodes increases. The two operational regions identified in the first scenario, are also evident here, i.e., \([0\%,20\%]\) and \((20\%,35\%]\) (denoted as \(R_{1}^{2}\) and \(R_{2}^{2}\), respectively). Interestingly, in the entire \(R_{1}^{2}\) region, the lowest NHI scores (corresponding to better performance) are consistently achieved for the case of 50% UNL overlap. In \(R_{2}^{2}\), almost identical NHI scores are yielded by all three UNL overlaps. The top performance of 50% UNL overlap within \(R_{1}^{2}\), agrees with the main finding of the first scenario, which indicates that a strict (i.e., high) UNL overlap is not required when a low percentage of malicious nodes is present in the network. As before, the respective threshold is empirically found to be approximately equal to 20%.  
Overall, the aforementioned finding aligns with the theoretical foundations and analysis of [PERSON] et al. [27]. On this basis, the 90% threshold reported was not only justified in our work, but also it was further investigated. Specifically, a wide range of such thresholds (10-99%) are experimentally studied in combination with a range of malicious nodes percentages (0-35%) within the bounds of strong and weak correctness [11].