Quantitative measures of channel network geometry inform diverse applications in hydrology, sediment transport, ecology, hazard assessment, and stratigraphic prediction. These uses require a clear, objectively defined channel network. Automated techniques for extracting channels from topography are well developed for convergent channel networks and identify flow paths based on land-surface gradients. These techniques—even when they allow multiple flow paths—do not consistently capture channel networks with frequent bifurcations (e.g., in rivers, deltas, and alluvial fans). This paper uses multithread rivers as a template to develop a new approach for channel extraction suitable for channel networks with divergences. Multithread channels are commonly mapped using observed inundation extent, and I generalize this approach using a depth-resolving, reduced-complexity flow model to map inundation patterns for fixed topography across an arbitrary range of discharge. A case study for the Platte River, Nebraska, reveals that (1) the number of bars exposed above the water surface, bar area, and the number of wetted channel threads (i.e., braiding index) peak at intermediate discharge; (2) the anisotropic scaling of bar dimensions occurs for a range of discharge; and (3) the maximum braiding index occurs at a corresponding reference discharge that provides an objective basis for comparing the planform geometry of multithread rivers. Mapping by flow depth overestimates braiding index by a factor of 2. The new approach extends channel network extraction from topography to the full spectrum of channel patterns, with the potential for comparing diverse channel patterns at scales from laboratory experiments to natural landscapes.