Graph models of cerebral vasculature derived from two-photon microscopy have shown to be relevant to study brain microphysiology. Automatic graphing of these microvessels remain problematic due to the vascular network complexity and two-photon sensitivity limitations with depth. In this paper, we propose a fully automatic processing pipeline to address this issue. The modeling scheme consists of a fully-convolution neural network to segment microvessels, a three-dimensional surface model generator, and a geometry contraction algorithm to produce graphical models with a single connected component. Based on a quantitative assessment using NetMets metrics, at a tolerance of 60 μm, false negative and false positive geometric error 19 rates are 3.8% and 4.2%, respectively, whereas false nega- 20 tive and false positive topological error rates are 6.1% and 4.5%, respectively. Our qualitative evaluation confirms the efficiency of our scheme in generating useful and accurate graphical models.