Renormalization of the brain connectome: Duality of particle and wave

Networks in neuroscience determine how brain function unfolds. Perturbations of the network lead to psychiatric disorders and brain disease. Brain networks are characterized by their connectomes, which comprise the totality of all connections, and are commonly described by graph theory. This approach is deeply rooted in a particle view of information processing, based on the quantification of informational bits such as firing rates. Oscillations and brain rhythms demand, however, a wave perspective of information processing based on synchronization. We extend traditional graph theory to a dual particle-wave-perspective, integrate time delays due to finite transmission speeds and derive a renormalization of the connectome. When applied to the data base of the Human Connectome project, we explain the emergence of frequency-specific network cores including the visual and default mode networks. These findings are robust across human subjects (N=100) and are a fundamental network property within the wave picture. The renormalized connectome comprises the particle view in the limit of infinite transmission speeds and opens the applicability of graph theory to a wide range of novel network phenomena, including physiological and pathological brain rhythms.