Many optimization problems can be represented as a graph to provide useful visualization and to allow for manipulating and exploiting problem structure. We use Plasmo.jl (which extends JuMP.jl) to build optimization problems within a graph structure (where optimization model components are stored within the nodes and edges of the graph), and we use the nonlinear interior-point solver, MadNLP.jl, to solve these models and exploit some of these graph structures.