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Abstract

Brain networks inferred from collective patterns of neuronal activity are cornerstones of experimental neuroscience. Modern fMRI scanners allow for high-resolution data that measures the neuronal activity underlying cognitive processes in unprecedented detail. Due to the immense size and complexity of such data sets, efficient evaluation and visualization remain data-analytic challenges. In this study, we combine recent advances in experimental neuroscience and applied mathematics to perform a mathematical characterization of complex networks constructed from fMRI data. We use task-related edge densities (G. Lohmann et al., PlosOne 2016) for constructing networks whose nodes represent voxels in the fMRI data and edges the task-related changes in synchronization between them. This construction captures the dynamic formation of patterns of neuronal activity and therefore represents effectively the connectivity structure between brain regions. Using geometric methods that utilize Forman-Ricci curvature as an edge-based network characteristic (M. Weber et al., J Complex Networks 2017), we perform a mathematical analysis of the resulting complex networks. Our results identify unique features in the network structure that significantly deviate from common observations in other real-world networks. Those include long-range connections of high curvature acting as bridges between major clusters and the absence of hubness and small-world phenomena that are considered hallmarks of real-world networks. The unique features of the networks call for new network-analytics protocols that extend the established node-based tools for real-world networks. We motivate the use of edge-based characteristics and suggest applications in biomedical research.