## 3 Results  
In this study, we aimed at investigating the impact of the head model accuracy on EEG-RSN connectivity estimation, particularly focusing on the role of different electrode localization techniques and head tissue segmentation methods. First, we reconstructed the functional connectivity values using our reference data. In particular, we quantified the connectivity between pairs of RSNs for each frequency band (Figure 4), and the differences between intra- and inter-network connectivity for each network and frequency band (Figure 5 and Figure S2). We observed remarkable similarities with connectivity results obtained in our recent study [49]. This was a valuable starting point for a detailed analysis of the impact of different head models on RSN connectivity. Figure 4: Functional connectivity matrices for the following frequency bands: delta (1–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), beta (13–30 Hz) and gamma (30–80 Hz). In each matrix, the diagonal values represent the group average intra-network connectivity, whereas the off-diagonal values represent the group average inter-network connectivity. Figure 5: Intra- and inter-network connectivity differences per network and frequency band. A comparison was performed by means of a Wilcoxon signed-rank paired test; the color bar represents the z-value obtained through the test, where the red colors stand for intra-network connectivity values higher than inter-network ones, and the blue colors vice-versa. The ANOVA performed on the z-values extracted for electrode positioning errors revealed significant modulations of all four factors under investigation (\(p<0.001\) for RSN, frequency band, error magnitude and type) (Table 1). Post-hoc tests showed that DMN, DAN and SMN were the most robust networks, whereas VAN and LN were the most sensitive to electrode positioning accuracy (Figure S3A). Similarly, alpha and delta bands were the most and least robust frequency bands, respectively (Figure S3B). As expected, our analyses confirmed that the difference between reference and test connectivity data increased as the magnitude of the positioning error was larger (Figure S3C). The Wilcoxon signed rank test yielded significantly lower correlations with random errors compared to systematic ones, for a magnitude level larger than 0.25 mm (Figure S3D and Figure 6 and Table S3). The ANOVA run on the z-values obtained with different head tissue segmentation methods showed significant modulations (\(p<0.001\)) of all three factors under investigation: RSN, frequency band and segmentation method (Table 2). Once again, post-hoc tests revealed that DMN, DAN and SMN were more robust in regard to head tissue segmentation variations than VAN and LN (Figure S4A), and that alpha and delta bands were the least and most sensitive frequency bands, respectively (Figure S4B). The _3-layer template_ method was found to be the least accurate. Notably, no significant differences were observed between the _12_- and _3-layer WTS_ methods (Figure S4C). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Electrode Localization Errors** & **df** & **Sum Squares** & **Mean Square** & **F** & \(p\)**-Value** \\ \hline Network & 5 & 6.58 & 1.32 & 79.39 & \textless{}0.001 \\ Band & 4 & 18.10 & 4.53 & 273.19 & \textless{}0.001 \\ Error magnitude & 3 & 7.28 & 2.43 & 146.54 & \textless{}0.001 \\ Error type & 1 & 0.46 & 0.46 & 27.72 & \textless{}0.001 \\ Residuals & 226 & 3.74 & 0.02 & & \\ Total & 239 & 36.16 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: ANOVA testing for electrode localization errors. Four factors were assessed: resting-state network (DMN, DAN, VAN, LN, SMN and VN), frequency band (delta; theta; alpha; beta; gamma), error magnitude (0.25; 0.5; 0.75; 1 cm) and error type (systematic; random). Figure 6: Correlation between the reference connectivity matrices and those obtained when introducing electrode localization errors.