General Relationship of Global Topology, Local Dynamics, and Directionality in Large-Scale Brain Networks

The balance of global integration and functional specialization is a critical feature of efficient brain networks, but the relationship of global topology, local node dynamics and information flow across networks has yet to be identified. One critical step in elucidating this relationship is the identification of governing principles underlying the directionality of interactions between nodes. Here, we demonstrate such principles through analytical solutions based on the phase lead/lag relationships of general oscillator models in networks. We confirm analytical results with computational simulations using general model networks and anatomical brain networks, as well as high-density electroencephalography collected from humans in the conscious and anesthetized states. Analytical, computational, and empirical results demonstrate that network nodes with more connections (i.e., higher degrees) have larger amplitudes and are directional targets (phase lag) rather than sources (phase lead). The relationship of node degree and directionality therefore appears to be a fundamental property of networks, with direct applicability to brain function. These results provide a foundation for a principled understanding of information transfer across networks and also demonstrate that changes in directionality patterns across states of human consciousness are driven by alterations of brain network topology.Author Summary: Current brain connectome projects are attempting to construct a map of the structural and functional network connections in the brain. One goal of these projects is to understand how network organization determines local functions and information transfer patterns, which is essential to achieve higher cognitive brain functions. Because of the limitation of constructing all brain maps for all cognitive states, finding a general relationship of global topology, local dynamics and the directionality of information transfer in a network is crucial. In this study, we show that inter-node directionality arises naturally from the topology of the network. Analytical, computational, and empirical results all demonstrate that network nodes with more connections (i.e., higher degree) lag in phase, while lower-degree nodes lead. Our mathematical analysis allowed us to predict the directionality patterns in general model networks as well as human brain networks across different states of consciousness. These findings may provide more straightforward approaches to dissecting how directionality between interacting nodes is shaped in complex brain networks, providing a foundation for understanding principles of information transfer. Furthermore, the underlying mathematical relationship between node connections and directionality patterns has the potential to advance network science across numerous disciplines.