Reeb graphs and mapper graphs are tools from Applied Topology and TDA which skeletonize and summarize the shape and structure of data. In this open-directions talk, we discuss how one can view these graphs as sheaves. This particular viewpoint leaves open the possibility of using ideas from the interleaving distance for persistence modules to create a metric for the structures. We will discuss various theorems showing when the mapper graph converges to the Reeb graph and discuss open questions related to these ideas to seed discussion during the workshop.