Strahler

The Strahler number, also known as Strahler stream order, is a numerical measure of the branching complexity of a tree, most commonly used in hydrology to classify the order of streams within a river network. It can also be applied to other branching structures, such as blood vessels in the human body or file systems.

The assignment of Strahler numbers proceeds as follows:

1. All source streams (those with no tributaries) are assigned an order of 1.
2. When two streams of order i join, the resulting stream is assigned an order of i + 1.
3. When two streams of different orders join, the resulting stream takes the higher of the two orders.
4. When three or more streams join at a single junction, and the highest two orders are i, then the resulting stream is assigned order i + 1. This rule generalizes for any number of joining streams; only the two highest orders matter.

The Strahler number of a river network is the order of the largest stream within the network. Higher Strahler numbers indicate more branching and a more complex drainage basin.

The concept was originally developed by Arthur Newell Strahler in 1952, significantly modifying an earlier ordering scheme proposed by Robert E. Horton in 1945. Strahler's system simplified Horton's system, making it more amenable to quantitative analysis.

The Strahler number is useful because it provides a relatively simple way to quantify the branching hierarchy of a tree structure. This has applications in various fields including:

• Hydrology: Characterizing river networks and estimating flood potential.
• Biology: Analyzing branching patterns in vascular systems and plant root systems.
• Computer Science: Measuring the complexity of hierarchical data structures.