maxWidth {treebalance}

Calculation of the maximum width of the tree

Description

This function calculates the maximum width maxWidth(T) for a given rooted tree T. The tree must not necessarily be binary. maxWidth(T) is defined as

maxWidth(T)=\max_{i=0,...,h(T)} w(i)

in which h(T) denotes the height of the tree T and w(i) denotes the number of vertices in T that have depth i. The maximum width is a balance index.

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

Usage

maxWidth(tree)

Arguments

tree

A rooted tree in phylo format.

Value

maxWidth returns the maximum width of a tree.

Author(s)

Sophie Kersting

References

C. Colijn and J. Gardy. Phylogenetic tree shapes resolve disease transmission patterns. Evolution, Medicine, and Public Health, 2014(1):96-108, 2014. ISSN 2050-6201. doi: 10.1093/emph/eou018.

Examples

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