# Strahler number

In mathematics, the **Strahler number** or **Hortonâ€“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[1][2] and Hodgkinson et al.[3] A statistical comparison of Strahler and Shreve systems, together with an analysis of stream/link lengths, is given by Smart.[4]