totIntPathLen {treebalance}

Calculation of the total internal path length for rooted trees

Description

This function calculates the total internal path length TIP(T) for a given rooted tree T. The tree must not necessarily be binary. TIP(T) is defined as

TIP(T)=\sum_{x\in V_{in}(T)} \delta(x)

in which V_{in}(T) denotes the set of inner vertices of T, and \delta(x) denotes the depth of the vertex x. The total internal path length is an imbalance index.

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

Usage

totIntPathLen(tree)

Arguments

tree

A rooted tree in phylo format.

Value

totIntPathLen returns the total internal path length of the given tree.

Author(s)

Luise Kuehn

References

D. E. Knuth. The art of computer programming: fundamental algorithms, volume 1. Addison-Wesley, Reading, Mass, 3rd edition, 1997. ISBN 9780201896831.

Examples

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