To improve the efficiency of organic solar cells, it is essential to understand the role of morphology and to tailor fabrication process to get desired morphologies. In this context, a comprehensive set of computational tools to quantify and classify the 2D/3D heterogeneous internal structure of thin films is invaluable. We present a 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. These questions are the basis for a comprehensive suite of morphology descriptors. To advocate the appropriateness of the formulated suite, we correlate these morphology descriptors with analysis using a excitonic-drift–diffusion-based device model. A very high correlation between the fast graph-based approach and computationally intensive full scale analysis illustrates the potential of our formulation to rapidly characterize a large set of morphologies. Finally, our approach is showcased by characterizing the effect of thermal annealing on time-evolution of a model thin film morphology.