Integrative, segregative, and degenerate harmonics of the structural connectome

Unifying integration and segregation in the brain has been a fundamental puzzle in neuroscience ever since the conception of the "binding problem." Here, we introduce a framework that places integration and segregation within a continuum based on a fundamental property of the brain-its structural connectivity graph Laplacian harmonics and a new feature we term the gap-spectrum. This framework organizes harmonics into three regimes-integrative, segregative, and degenerate-that together account for various group-level properties. Integrative and segregative harmonics occupy the ends of the continuum, and they share properties such as reproducibility across individuals, stability to perturbation, and involve "bottom-up" sensory networks. Degenerate harmonics are in the middle of the continuum, and they are subject-specific, flexible, and involve "top-down" networks. The proposed framework accommodates inter-subject variation, sensitivity to changes, and structure-function coupling in ways that offer promising avenues for studying cognition and consciousness in the brain.