Eigenmode decomposition of asymmetries in whole-brain effective connectivity reveals multiscale hierarchical dynamics

The human brain is a complex system operating far from equilibrium, yet how whole-brain directed hierarchical patterns emerge across spatiotemporal scales remains unclear. While functional and structural hierarchies have been described, no framework has exhaustively integrated a node-level hierarchical ranking of directed brain networks with non-equilibrium dynamics decomposition across spectral scales. Here we isolate the irreversible rotational component of whole-brain effective connectivity (EC), encoding the hierarchical network derived from antisymmetric interactions, and decompose it into EC eigenmodes across spectral ranges. Hierarchy strengthens near criticality, where slow oscillatory modes dominate and reflects long-range anatomical scaffolding of whole-brain activity. Our decomposition provides the first EC eigenmode-based multiscale representation of temporal irreversibility, revealing dual counterpropagating streams along the unimodal-transmodal axis at distinct frequencies and identifying slow-mode individual-specific signatures, with unimodal networks contributing disproportionately to subject identifiability. Altogether, this work provides a unified EC-based framework for characterizing whole-brain hierarchical patterns across spectral scales and individuals.