abstract: We explore how tools from combinatorial algebraic topology can be used to better understand the structure and function of connectomes (brain networks). We use the Blue Brain model as a demonstration of these tools. We explore basic graph theory metrics of the structure and introduce some topological generalisations of these metrics that reveal different structural information. We introduce a technique for classifying input stimuli using the functional response of the connectome. We finish we by briefly looking at the difference between efficiency and reliability in connectomes.