is high, then there is a higher chance of flooding. There would also be a lower time of concentration. The bifurcation ratio can also show which parts of a drainage basin are more likely to flood, comparatively, by looking at the separate ratios. Most British rivers have a bifurcation ratio of between 3 and 5. describe how to compute Strahler stream order values in a GIS application. This algorithm is implemented by RivEX, an ESRI ArcGIS 10.7 tool. The input to their algorithm is a network of the centre lines of the bodies of water, represented as arcs (or edges) joined at nodes. Lake boundaries and river banks should not be used as arcs, as these will generally form a non-tree network with an incorrect topology. Other hierarchical systems The Strahler numbering may be applied in the statistical analysis of any hierarchical system, not just to rivers. describe an application of the Horton–Strahler index in the analysis of social networks. applied a variant of Strahler numbering (starting with zero at the leaves instead of one), which they called tree-rank, to the analysis of L-systems. Strahler numbering has also been applied to biological hierarchies such as the branching structures of trees and of animal respiratory and circulatory systems. Register allocation When translating a high-level programming language to assembly language the minimum number of registers required to evaluate an expression tree is exactly its Strahler number. In this context, the Strahler number may also be called the register number. For expression trees that require more registers than are available, the Sethi–Ullman algorithm may be used to translate an expression tree into a sequence of machine instructions that uses the registers as efficiently as possible, minimizing the number of times intermediate values are spilled from registers to main memory and the total number of instructions in the resulting compiled code. Related parameters Bifurcation ratio Associated with the Strahler numbers of a tree are bifurcation ratios, numbers describing how close to balanced a tree is. For each order i in a hierarchy, the ith bifurcation ratio is where ni denotes the number of nodes with order i. The bifurcation ratio of an overall hierarchy may be taken by averaging the bifurcation ratios at different orders. In a complete binary tree, the bifurcation ratio will be 2, while other trees will have larger bifurcation ratios. It is a dimensionless number. Pathwidth The pathwidth of an