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The brain is a complex, interconnected system in which structural wiring underpins the flow of information between functional units. After two decades of advances in connectomics, the asymmetry of edge structures in large-scale brain networks remains largely unexplored. Here, we build a directed connectome combining structure and function, and dissect its organization into bicommunities where sending and associated receiving sets of nodes, through clustering of directed-edge information, are fully acknowledged. Our findings reveal a primary directional axis from sensory to association cortices, indicative of bottom-up information flow. Validation with invasive electrophysiological measures demonstrates that these bicommunities capture an intermediate organizational scale at which connection asymmetry aligns across modalities. Finally, sets of distinct known anatomical fiber bundles and their functional mapping are recovered as specific bicommunities. This work identifies asymmetric pathways onto which neural computation can be expressed, and establishes directed connectomics as a novel framework for understanding brain organization.