Strahler number

In mathematics, the Strahler number or Horton–Strahler number of a mathematical tree is a numerical measure of its branching complexity. In mathematics, the Strahler number or Horton–Strahler number of a mathematical tree is a numerical measure of its branching complexity. These numbers were first developed in hydrology by Robert E. Horton (1945) and Arthur Newell Strahler (1952, 1957); in this application, they are referred to as the Strahler stream order and are used to define stream size based on a hierarchy of tributaries. They also arise in the analysis of L-systems and of hierarchical biological structures such as (biological) trees and animal respiratory and circulatory systems, in register allocation for compilation of high-level programming languages and in the analysis of social networks. Alternative stream ordering systems have been developed by Shreve and Hodgkinson et al. A statistical comparison of Strahler and Shreve systems, together with an analysis of stream/link lengths, is given by Smart. All trees in this context are directed graphs, oriented from the root towards the leaves; in other words, they are arborescences. The degree of a node in a tree is just its number of children. One may assign a Strahler number to all nodes of a tree, in bottom-up order, as follows: