avgVertDep {treebalance}

Calculation of the average vertex depth for rooted trees

Description

This function calculates the average vertex depth AVD(T) for a given rooted tree T. The tree must not necessarily be binary. AVD(T) is defined as

AVD(T)=\frac{1}{|V(T)|}\cdot\sum_{x\in V(T)} \delta(x)

in which V(T) denotes the set of vertices of T, and \delta(x) denotes the depth of the vertex x. The average vertex depth is a normalised version of the total path length and an imbalance index.

For n=1 the function returns AVD(T)=0 and a warning.

For details on the average vertex depth, see also Chapter 23 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_23).

Usage

avgVertDep(tree)

Arguments

tree

A rooted tree in phylo format.

Value

avgVertDep returns the average vertex depth of the given tree.

Author(s)

Luise Kuehn

References

A. Herrada et al. Scaling properties of protein family phylogenies. BMC Evolutionary Biology, 11(1), June 2011. doi: 10.1186/1471-2148-11-155.

Examples

tree <- ape::read.tree(text="((((,),),(,)),(((,,),),(,)));")
avgVertDep(tree)