We present a methodology for extracting the vascular network in the human retina using Dijkstra's shortest-path algorithm. Our method preserves vessel thickness, requires no manual intervention, and follows vessel branching naturally and efficiently. To test our method, we constructed a retinal video indirect ophthalmoscopy (VIO) image database from pediatric patients and compared the segmentations achieved by our method and state-of-the-art approaches to a human-drawn gold standard. Our experimental results show that our algorithm outperforms prior state-of-the-art methods, for both single VIO frames and automatically generated, large field-of-view enhanced mosaics. We have made the corresponding dataset and source code freely available online.