High-Order Triadic Functional Connectivity in the Brain and Beyond

Here, we report high-order functional network connectivity as a promising way for studying the brain connectome. Traditional functional connectivity approaches capture only pairwise relationships between brain regions, overlooking complex multivariate dependencies that underlie cognition and behavior. First, we demonstrated that high-order interactions capture more information and can distinguish between resting-state and task-state brain activity. Second, we introduce a matrix-based entropy-functional method for estimating triadic interactions, which are statistical dependencies among triplets of brain regions, and apply it to large-scale functional brain networks. The resulting triadic networks revealed distinct community patterns that complement those observed in traditional pairwise functional connectivity analyses and simultaneously capture additional connection information. Despite the potential combinatorial explosion of triadic configurations, the networks exhibited constrained and hierarchical structures that allowed computation and interpretation. These findings position triadic connectivity as a promising next-step functional connectivity framework for probing brain network organization and high-order neural interactions, while also highlighting key biological and technical challenges that require careful consideration.