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Here are some examples of different kinds of ordering, pointed out by Denis Boutin (NRCAN) in the GRASS documentation:

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Note that most of these schemes are built a non-divergent model of flow direction downslope. While this is fine for DEM-derived networks, it might require that the network be pre-processed (pruned, generally cleaned up) to enforce this assumption prior to applying the selected ordering scheme (from which we extract the "main stem").