## 4 Conclusions  
In this study, we conducted a comprehensive hypergraph analysis of functional connectivity using MEG data acquired from a modulated visual stimulus. By focusing on differences within distinct frequency bands, we constructed a coherence-based hypergraph to explore functional connectivity among the frontal, parietal, temporal, and occipital brain lobes. Our findings suggest that each frequency band has a specific coherence threshold; beyond this, significant changes occur in network characteristics, such as centrality, shortest-path distances, and node degree. Interestingly, this threshold is lower for higher-frequency bands, indicating stronger connectivity between lobes at lower frequencies and greater stability in the brain network of functional connectivity. Specifically, we observed strong coherence among all eight lobes in the delta and theta bands; this was only observed among six lobes in the gamma band. Furthermore, we noted variations in global connectivity with coherence thresholds across different frequency bands. Strong coherence was observed between temporal right and left lobes for delta and theta waves, occipital right and parietal left lobes for alpha waves, frontal right and occipital left lobes for beta waves, and frontal and occipital lobes for gamma waves. These findings collectively contribute to our understanding of brain network dynamics across different frequency bands. Our results lend credence to the idea that cortico-cortical interactions can manifest at multiple levels. The resultant hypergraph exposes robust activation patterns in select brain regions across varied cognitive contexts associated with various frequency bands, hinting at possible integration or multifunctionality within these lobes. While previous studies have noted correlations between frequencies and proposed biophysical models to explain interactions, our results highlight the importance of further research to unravel potential connections between the mechanisms generating different frequencies and with a modulated visual stimulus, using coherence instead of traditional correlation. Additionally, we argue that exploring hypergraph visualizations with a focused examination of finer-grained neural ensembles or smaller regions of interest (ROIs) can reveal compelling dynamics that merit further scholarly investigation. N.P.S. : investigation, formal analysis; R.J.-R.: resources, project administration, original draft preparation; A.N.P. : conceptualization, methodology, review and editing. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Ethics Committee of the Technical University of Madrid (protocol No. 19, 3 February 2020). Informed Consent Statement:Informed consent was obtained from all subjects involved in the study. The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author. The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results. The dependencies of the main network characteristics on the coherence threshold \(\sigma\) for different brain waves are illustrated in Figures 11-15 (delta in Figure 11; theta in Figure 11; alpha in Figure 11; beta in Figure 11; gamma in Figure 11). The lobes are represented with different colors. The shortest path distances and numbers of cycles depict averages in the case of distances and totals in the case of cycles. Figure 16 illustrates the results of the analysis of the betweenness centrality coefficient, which measures the importance of a node in terms of the number of shortest paths that pass through it. Once again, the connections are less pronounced at higher frequencies (Figure 16c,d) compared to lower frequencies (Figure 16a,b).