We propose a characterization of hierarchical watersheds built in the framework of edge-weighted graphs. Based on the notion of binary partition hierarchy by altitude ordering, we provide sufficient and necessary conditions for a hierarchy to be a hierarchical watershed. Those conditions are further used to design an efficient algorithm to recognize hierarchical watersheds. Furthermore, as an immediate application of our theoretical results, we present experiments with the combinations of hierarchical watersheds studied in [15]. Namely, we test if combinations of hierarchical watersheds are hierarchical watersheds themselves.