# Hypergraph Analysis of Functional Brain Connectivity During Figurative Attention
## 8 Conclusions  
This study presents a comprehensive hypergraph-based analysis of functional brain connectivity during figurative attention to an ambiguous visual stimulus, integrating coherence, cross-correlation, and mutual information from EEG data. Our findings support the hypothesis that figurative attention engages cortico-cortical interactions, with hypergraph representations revealing distinct frequency-dependent activation and deactivation patterns across brain regions. Notably, the parietal, frontal, and prefrontal lobes play a key role in integrating information, highlighting their functional specialization and dynamic reconfiguration in attentional processing. However, while these regions facilitate efficient cognitive functions, some information may be lost in the central cortex, underscoring the complexity of neural information processing. By leveraging a frequency-tagging approach in the context of the Necker cube illusion, we identified distinct connectivity patterns corresponding to different cube orientations. Our results emphasize the role of bilateral cortico-cortical interactions and suggest the existence of integrated processing hubs that coordinate visual attention. Hypergraph analysis, extending beyond traditional graph-based methods, provided novel insights into higher-order relationships between multiple brain regions, offering a more comprehensive understanding of dynamic neural interactions. The methodology developed in this study--incorporating three connectivity and three disconnectivity measures--enabled the identification of higher-order relationships among brain regions, facilitating a more precise characterization of functional connectivity networks underlying figurative attention. This multivariate approach allowed us to construct connectivity difference matrices, revealing both new connections induced by sustained attention and disconnections due to decreased connectivity. Additionally, by applying a sparsification method based on statistical thresholds, we filtered out spurious or noisy connections, enhancing the robustness and interpretability of our functional connectivity network. Beyond its theoretical implications, this methodological framework holds promise for practical applications in cognitive neuroscience, attention monitoring, and the clinical assessment of attention-related disorders. While this proof-of-concept study is based on a single subject, it establishes a foundation for future large-scale investigations into the neural mechanisms underlying ambiguous visual perception and attentional control. Although previous studies have explored frequency correlations and proposed biophysical models of neural interactions, our findings highlight the need for further studies investigating the mechanisms linking different frequency-dependent processes. A more refined hypergraph analysis, focusing on smaller neural ensembles or specific regions of interest, could provide deeper insights into the intricate dynamics of brain connectivity. This study lays essential groundwork for advancing our understanding of brain network dynamics and their role in cognitive function. Hypergraphs provide a powerful framework for modeling high-order interactions in EEG-based functional connectivity networks. Our findings emphasize the importance of incorporating connectivity and disconnectivity measures in hypergraph construction, enabling a more comprehensive understanding of individual differences in attention and cognitive processing. Future research should focus on further refining hypergraph learning algorithms, integrating dynamic hypergraph representations, and expanding applications to clinical populations for biomarker discovery and personalized interventions in cognitive and psychiatric disorders. While our findings demonstrate the potential of hypergraph-based models for capturing the complex neural dynamics underlying attention, several challenges must be addressed before this approach can be fully integrated into clinical practice.