We present extensive molecular dynamics simulation results for self-diffusion and viscosity for isoparaffins between C-6 and C-16 and examine the ability of several forms of Stokes-Einstein relationships to link the transport properties in a coherent framework. Based on a hydrodynamic model for drag past prolate ellipsoids in the slip limit, much of the variation between diffusion and viscosity can be explained as a function of molecular structure. For pure species, we demonstrate how one can exploit the linearity of the Stokes-Einstein relationship to make quantitative, extrapolative predictions of viscosity from computer simulations based on the self-diffusion coefficient and systematic characterization of the molecule's gyration ellipsoid.