arbitrary undirected graph G may be defined as the smallest number w such that there exists an interval graph H containing G as a subgraph, with the largest clique in H having w + 1 vertices. For trees (viewed as undirected graphs by forgetting their orientation and root) the pathwidth differs from the Strahler number, but is closely related to it: in a tree with pathwidth w and Strahler number s, these two numbers are related by the inequalities w ≤ s ≤ 2w + 2. The ability to handle graphs with cycles and not just trees gives pathwidth extra versatility compared to the Strahler number. However, unlike the Strahler number, the pathwidth is defined only for the whole graph, and not separately for each node in the graph. See also Main stem of a river, typically found by following the branch with the highest Strahler number Pfafstetter Coding System Notes References . . . . . . . . . . . . . Hydrology Geomorphology Physical geography Trees (graph theory) Graph invariants