To study gully spatial patterns in the badlands using a continuous thalweg vector network, this paper presents methods to extract the badlands' thalweg network from a regular grid digital terrain model (DTM) by combining terrain morphology indices with a drainage algorithm. This method will delineate a thalweg only where the DTM denotes a significant curvature with respect to DTM accuracy and relies on three major steps. First, discontinuous concave areas were detected from the DTM using morphological criteria, either the plan curvature or the convergence index. Second, the concave areas were connected using a drainage algorithm, which provides a continuous, thick, tree-structured scheme. We assumed that these areas were physically significant and corresponded to a gully floor. Finally, the thick path was reduced to its main course and vectorised to obtain a thalweg network. The methods were applied to both virtual and actual DTM cases. The actual case was a LiDAR DTM of the Draix badlands in the French Alps. The obtained networks were quantitatively compared, both with a network obtained using the usual drainage area criteria and with a reference network mapped in the field. The CI-based network showed the great potential for thalweg network extraction.