Drainage network analysis includes several operations that quantify the topological organization of stream networks. Network analysis operations are frequently performed on streams that are derived from digital elevation models (DEMs). While these methods are suited to application with fine-resolution DEM data, this is not the case for coarse DEMs or low-relief landscapes. In these cases, network analysis that is based on mapped vector streams is an alternative. This study presents a novel vector drainage network analysis technique for performing stream ordering, basin tagging, the identification of main stems and tributaries, and the calculation of total upstream channel length and distance to outlet. The algorithm uses a method for automatically identifying outlet nodes and for determining the upstream-downstream connections among links within vector stream networks while using the priority-flood method. The new algorithm was applied to test stream datasets in two Canadian study areas. The tests demonstrated that the new algorithm could efficiently process large hydrographic layers containing a variety of topological errors. The approach handled topological errors in the hydrography data that have challenged previous methods, including disjoint links, conjoined channels, and heterogeneity in the digitized direction of links. The method can provide a suitable alternative to DEM-based approaches to drainage network analysis, particularly in applications where stream burning would otherwise be necessary.