Brain Connectivity Hypergraphs

Hypergraphs are a rapidly developing area of graph theory that has important applications in many fields, including cognitive neuroscience and medicine. In this paper, we review recent advances in the application of hypergraphs to brain connectivity analysis using brain imaging data. We also present our results on the construction of a hypergraph of brain connectivity during visual perception based on the analysis of magnetoencephalography (MEG) data. The hypergraph approach allowed us to identify individual differences in frequency bands, offering deeper insights into the dynamic nature of brain connectivity. Extending traditional graph theory, we defined a functional network connecting different brain regions (vertices) across time segments by generating edge time series that capture temporal fluctuations in connectivity. Using a coherence measure, we created edge time series to illustrate how connections evolve over time. These series contribute to the edge-to-edge functional connectivity network, highlighting hyperedges as connected components in the absolute value functional connectivity network. We identified key features of the brain network across the delta, theta, alpha, beta, and gamma frequency bands and examined interactions among the frontal, parietal, temporal, and occipital lobes in both hemispheres. Our findings support the existence of cortico-cortical interactions, and the resulting hypergraph revealing robust activation patterns in specific brain regions. These results suggest potential integration and multifunctionality within the lobes, providing valuable insights into brain dynamics during visual perception.