Emergence of Higher-Order Functional Brain Connectivity with Hypergraph Signal Processing

Network theory has provided remarkable insights on how the human brain works. Such insights usually originate from models based on dyadic connections between brain regions, which may be inadequate for characterizing higher-order interactions. In recent works, this issue has been addressed by using hypergraph-based models, from which the aforementioned interactions can be revealed. In this line, this paper proposes to construct (brain) hypergraphs using a multivariate information-theoretic interdependence metric called interaction information. Our methodology is applied to functional magnetic resonance imaging (fMRI) time series and employs hypergraph signal processing concepts to analyze the eigenmodes of the brain hypergraph spectrum space. This allows to associate some spectral components of hypergraph modes with well-known functional brain subsystems as well as observe that specific low-frequency eigenmodes exhibit similarity patterns of neural activity. These results are in line with recent findings regarding the redundant and synergistic properties of the brain, and indicate that our study may represent a promising pathway to characterize the dynamics of higher-order brain functional connectivity.