Engineering the compositional gradient for core/shell semiconductor nanocrystals improves their optical properties. To date, however, the structure of graded core/shell nanocrystal emitters has only been qualitatively described. In this paper, we demonstrate an approach to quantify nanocrystal structure, selecting graded Ag-In-Se/ZnSe core/shell nanocrystals as a proof-of-concept material. A combination of multi-energy small-angle X-ray scattering and electron microscopy techniques enables us to establish the radial distribution of ZnSe with sub-nanometer resolution. Using ab initio shape-retrieval analysis of X-ray scattering spectra, we further determine the average shape of nanocrystals. These results allow us to generate three-dimensional, atomistic reconstructions of graded core/shell nanocrystals. We use these reconstructions to calculate solid-state Zn diffusion in the Ag-In-Se nanocrystals and the lattice mismatch between nanocrystal monolayers. Finally, we apply these findings to propose design rules for optimal shell structure and record-luminescent core/shell nanocrystals.