We report in a companion paper that in the mouse brain, in contrast to the 1,000-fold variation in local neuronal densities across sites, capillary density (measured both as capillary volume fraction and as density of endothelial cells) show very little variation, of the order of only fourfold. Here we confirm that finding in the rat brain and, using published rates of local blood flow and glucose use at rest, proceed to show that what small variation exists in capillary density across sites in the rat brain is strongly and linearly correlated to variations in local rates of brain metabolism at rest. Crucially, we show that such variations in local capillary density and brain metabolism are not correlated with local variations in neuronal density, which contradicts expectations that use-dependent self-organization would cause brain sites with more neurons to have higher capillary densities due to higher energetic demands. In fact, we show that the ratio of endothelial cells per neuron serves as a linear indicator of average blood flow and glucose use per neuron at rest, and both increase as neuronal density decreases across sites. In other words, because of the relatively tiny variation in capillary densities compared to the large variation in neuronal densities, the anatomical infrastructure of the brain is such that those sites with fewer neurons have more energy supplied per neuron, which matches a higher average rate of energy use per neuron, compared to sites with more neurons. Taken together, our data support the interpretation that resting brain metabolism is not demand-based, but rather limited by its capillary supply, and raise multiple implications for the differential vulnerability of diverse brain areas to disease and aging.