Network neuroscience is built atop a network model in which cells, populations, and regions are linked to one another via anatomical or functional connections. Historically, this model has been approached from a node-centric perspective, emphasizing features of neural elements: the number of connections they make, their centrality, module affiliation, etc. However, brain networks can also be examined from an edge-centric perspective that explicitly focuses on properties of connections: their material and metabolic costs, the generative processes that govern connection formation, and their dynamics across time. In this talk, I will present results from several recent papers and highlight findings and advantages of edge-centric network perspectives compared with traditional node-centric network representations.