Accurate extraction of vascular graphs from medical images is essential for quantitative analysis of vascular morphology, enabling downstream tasks such as cognitive disease assessment, hemodynamic modeling, and temporal analysis of structural changes. Despite the importance of this task, several challenges remain, including the sparsity of graph annotations, variability across imaging modalities, and the need to preserve global topological consistency. To address these limitations, prior work has leveraged non-medical network domains, such as road networks, to provide additional supervision. However, such man-made systems are primarily shaped by planning, economic, and regulatory constraints, which differ fundamentally from biological growth processes. Building on these observations and adopting a recent single-stage image-to-graph transformer that enables end-to-end structured prediction, we show that incorporating biologically meaningful structural priors within a transfer-learning framework improves vascular graph extraction.