## 3 Results and Discussion
### Network Characteristics  
We computed various network characteristics. As depicted in Figure 2, the coherence coefficient ranges from 0 to 19.16 across different frequency bands, reaching a distinct maximum value for each band. Table 1 displays the maximum coherences observed within each frequency band, along with the lobes between which they were identified. Figure 2: Coherence networks (**left column**) with their respective matrices (**right column**) for (**a**) delta, (**b**) theta, (**c**) alpha, (**d**) beta, and (**e**) gamma waves of the normalized F-trials. The stronger coherence is represented by wider lines. In Figure 4, we plot the global connectivity coefficient \(\kappa\) found by Equation (2) for each frequency band with respect to the threshold value \(\sigma_{th}\). A general decrease in the coherence coefficient between nodes was observed with increasing frequency. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Frequency Band** & **Maximum Coherence** & **Lobes** \\ \hline Delta & 15.5940 & Temporal Left–Temporal Right \\ Theta & 19.160 & Temporal Left–Temporal Right \\ Alpha & 4.6720 & Parietal Left–Parietal Right \\ Beta & 0.8300 & Frontal Right–Occipital Left \\ Gamma & 0.7180 & Frontal Left–Occipital Right \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Maximum coherence of each frequency band. Figure 4: Global connectivity coefficient \(\kappa\) for different frequency bands as a function of the threshold value. Figure 3: Power spectra of brain activity in different lobes: (**a**) left frontal, (**b**) right frontal, (**c**) left occipital, (**d**) right occipital, (**e**) left parietal, (**f**) right parietal, (**g**) left temporal, and (**h**) right temporal. The dotted lines marked by letters M and H denote the modulation frequency \(f_{m}\) and its second harmonic \(2f_{m}\), respectively. Additionally, it is noteworthy that our representation emphasizes the heightened connectivity of low-frequency components compared to high frequencies, aligning with previous observations by [PERSON] et al. [48]. This depiction offers a clearer insight into the variations in connectivity between lobes within each frequency band. One can see that, for each frequency range, there is a coherence threshold value \(\sigma_{th}\) at which centrality measures, shortest-path distances, and degree of nodes undergo significant changes (Figures A1-A5). This threshold value depends on the wave frequency. Specifically, as seen in Figure 4, for delta waves \(\sigma_{th}\approx 0.75\) and for theta waves, the global connectivity appears to remain constant at 1 at all these \(\sigma_{th}\) values: for alpha waves, this is \(\sigma_{th}\approx 0.42\), for beta waves, this is \(\sigma_{th}\approx 0.37\), and for gamma waves, this is \(\sigma_{th}\approx 0.3\). This means that \(\sigma_{th}\) decreases as the wave frequency increases, i.e., the brain network of functional connectivity is more stable at low frequencies. A connectivity threshold serves as a crucial parameter in delineating genuine connections within a functional network while filtering out spurious ones. This approach enables a focused examination of network properties. Analyzing a graph necessitates setting a connectivity threshold to discern valid connections among nodes and discard erroneous ones. The choice of threshold value is somewhat arbitrary, with increasing thresholds excluding weaker, potentially noisy connections. However, setting the threshold too high risks eliminating important frequency bands like beta and gamma, resulting in a connectivity coefficient of 0 for the resulting graph. Our chosen threshold value of \(\sigma_{th}=0.5\) ensures a minimum coherence of this magnitude between lobes' signals. Despite its strictness, this threshold preserves all connections across various frequency bands. Figure 5 illustrates the results of the analysis of degree centrality in the brain network of the eight lobes for different frequency ranges. The node sizes indicate their importance as a function of edge weights.