In diabetic nephropathy (DN), hyperglycemia drives a progressive thickening of and damage to the glomerular filtration surfaces, as well as mesangial expansion and a constriction of capillary lumens. This leads at first to high blood pressure, increased glomerular filtration and micro-proteinuria, and later (if untreated) to severe proteinuria and end-stage renal disease (ESRD). Though, it is well known that DN is accompanied by marked histopathological changes, the assessment of these structural changes is to a degree subjective and hence varies between pathologists. In this work, we make a first study of glomerular changes in DN from a graph-Theoretical and distance-based standpoint, using minimal spanning trees (MSTs) and distance matrices to generate statistical distributions that can potentially provide a "fingerprint" of DN. We apply these tools to detect notable differences between normal and DN glomeruli in both human disease and in a streptozotocin-induced (STZ) mouse model. We also introduce an automated pipeline for rapidly generating MSTs and evaluating their properties with respect to DN, and make a first pass at three-dimensional MST structures. We envision these approaches may provide a better understanding not only of the processes underway in DN progression, but of key differences between actual human disease and current experimental models.