The bulk heterojunction (BHJ) nanomorphology in organic solar cells strongly affects the final efficiency of the device. Progress in experimental techniques now allows visualization of the complex 3D BHJ morphology. It is, therefore, important to characterize the topological properties of the morphology in order to quantify the link between morphology features and performance. Here, we introduce a suite of morphology descriptors which encode the complex nature of the multi-stage photovoltaic process in the BHJ. These morphology descriptors are easily determined using an approach based on converting the morphology into an equivalent weighted, labeled, undirected graph. We show how these descriptors can be used to interrogate BHJ morphologies, allow identification of bottlenecks in the photovoltaic process, and conduct quantitative comparison between morphologies with respect to each sub-process in the photovoltaic phenomena. This framework provides a simple and easy-to-use characterization tool that can be used to unravel the impact of morphology on complex transport phenomena.