# Hypergraph Analysis of Functional Brain Connectivity During Figurative Attention
## 7 Discussion  
Hypergraphs have been extensively studied and applied in network analysis, including node classification [71], community detection [72], and link prediction [73]. In neuroscience, hypergraphs, as a generalization of the graph theory, provide a more sophisticated framework for modeling brain connectivity by capturing high-order interactions among multiple brain regions [74]. Recent studies [21] have constructed hypergraphs using functional and structural connectivity as hyperedges. In contrast, we created hypergraphs based on three connectivity measures (coherence, cross-correlation, and mutual information) and three disconnectivity measures (anticoherence, anticorrelation, and information loss). Additionally, we employed sparsification techniques to remove less significant nodes, reducing noise and enhancing functional connectivity interpretation. By incorporating hypergraph theory into EEG-based functional connectivity analysis, our method provides a novel perspective on understanding attention and its neural correlates. Hypergraph-based models enable a subject-level representation of high-order relationships, facilitating a more refined analysis of individual differences in cognitive function. This has significant implications for identifying biomarkers of attention-related disorders and advancing personalized cognitive assessments. Recent advancements in deep learning have further amplified the potential of hypergraph-based models. [PERSON] et al. [19] introduced the hypergraph attention network (FC-HAT), while [PERSON] et al. [75] developed the hypergraph structural information aggregation generative adversarial network (HSIA-GAN) model for functional connectivity analysis. These models dynamically construct  
Figure 18: Dual clique expansions \(\mathcal{G}_{3,4}\) of hypergraphs \(\mathcal{H}_{3,4}\) associated with right-cube attention at (**left**) \(f_{1}\) and (**right**) \(f_{2}\). functional connectivity networks, extract abnormal connectivity patterns, and identify critical biomarkers for neurodevelopmental and neurodegenerative disorders. Our hypergraph analysis reveals that hyperedges associated with increased and decreased connectivity are spatially distinct and localized in different brain regions, depending on both the cognitive task and frequency. Since attention to the left-cube orientation is linked to increased spectral energy at \(f_{1}\), the hypergraph in Figure 11 highlights the key nodes involved in this cognitive process. Notably, the occipital-parietal cortex emerges as a central hub for functional connectivity, whereas the central cortex plays a predominant role in disconnectivity. An intriguing observation is the frequency-dependent nature of brain region activity: nodes that exhibit increased connectivity at one frequency tend to show decreased connectivity at another. For instance, the left parietal lobe (P3), which is highly active at \(f_{1}\) (Figure 11), demonstrates reduced activity at \(f_{2}\) (Figure 12), suggesting a dynamic reconfiguration of neural networks in response to different attentional states. A similar pattern is evident during right-cube attention. The hypergraph in Figure 14 indicates that the frontal cortex plays a central role in connectivity, while the central-parietal cortex is predominantly associated with disconnectivity. This observation aligns with the fact that right-cube attention corresponds to increased spectral energy at \(f_{2}\). Once again, the same brain regions exhibit frequency-dependent activation and deactivation, reinforcing the notion that attentional shifts are accompanied by distinct neural reorganization patterns across different frequency bands. Specifically, for right-cube attention, the frontal and prefrontal cortices demonstrate increased activity at \(f_{2}\) (Figure 14) but reduced activity at \(f_{1}\) (Figure 13). In contrast, the parietal cortices show the opposite trend, increasing their activity at \(f_{1}\) (Figure 13) while decreasing at \(f_{2}\) (Figure 14).