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 analysis 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., 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 effectively represents the connectivity structure between brain regions. Using geometric methods that utilize Forman-Ricci curvature as an edge-based network characteristic (M. Weber et al., 2017), we perform a mathematical analysis of the resulting complex networks. We motivate the use of edge-based characteristics to evaluate the network structure with geometric methods. Our results identify unique features in the network structure including long-range connections of high curvature acting as bridges between major network components.