Organic solar cells (OSC) have the potential for widespread usage, due to their promise of low cost, roll-to-roll manufacturability, and mechanical flexibility. However, ubiquitous deployment is impeded by their relatively low power conversion efficiencies (PCE). The last decade has seen significant progress in enhancing the PCE of these devices through various strategies. One such approach is based on morphology control. This is because morphology affects all phenomena involved in solar conversion: (1) light absorption and electron-hole pair (exciton) generation; (2) exciton diffusion and dissociation into free charges; and (3) transport of charges to the electrodes.Progress in experimental characterization and computational modeling now allow reconstruction and imaging of thin film morphology. This opens up the possibility of rationally linking fabrication processes with morphology, as well as morphology with performance. In this context, a comprehensive set of computational tools to rapidly quantify and classify the 2D/3D heterogeneous internal structure of thin films will be invaluable in linking process, structure, and property.We present a novel graph-based framework to efficiently compute a broad suite of physically meaningful morphology descriptors. These morphology descriptors are further classified according to the physical subprocesses within OSCs -photon absorption, exciton diffusion, charge separation, and charge transport. This approach is motivated by the equivalence between a discretized 2D/3D morphology and a labeled, weighted, undirected graph. We utilize this approach to pose six key questions related to structure characterization. We subsequently construct estimates and rigorous upper bounds of various efficiencies. The approach is showcased by characterizing the effect of thermal annealing on time-evolution of a thin film morphology. We conclude by formulating natural extensions of our framework to characterize crystallinity and anisotropy of the morphology using the framework.