Abstract

Connectome harmonics provide a spectral representation of structural brain connectivity that has emerged as a powerful framework for studying structure-function relationships. However, two fundamental questions remain unresolved: how should inter-individual variability in structural connectivity be incorporated into graph signal processing analyses, and at which spectral scale should connectome harmonics be interpreted? Here, using structural and functional MRI data from 875 participants, we show that subject-specific connectome harmonics reveal a reproducible hierarchical organization of the human connectome. Across the spectrum, harmonics exhibited orderly transitions in stability, graph support, sparsity and anatomical localization, and naturally organized into multiscale families sharing common structural properties. Sparse harmonic representations accurately reconstructed brain activity across resting-state and task paradigms, revealing frequency-dependent recruitment of this structural hierarchy during cognition. Finally, combining structural and functional harmonic organization enabled the prediction of individual cognitive performance, demonstrating that both representations capture complementary behaviorally relevant information. Together, our findings show that connectome harmonics should be viewed not simply as graph-frequency modes of structural connectivity, but as a hierarchically organized representation of the connectome that links brain structure, functional dynamics and cognition.