symNodesI {treebalance}

Calculation of the symmetry nodes index for rooted binary trees

Description

This function calculates the symmetry nodes index SNI(T) for a given rooted binary tree T. SNI(T) is defined as the number of inner vertices v that are not symmetry nodes, i.e. the two pending subtrees rooted at the children of v do not have the same tree shape.

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

For details on the symmetry nodes index, see also Chapter 18 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_18).

Usage

symNodesI(tree)

Arguments

tree

A rooted binary tree in phylo format.

Value

symNodesI returns the symmetry nodes index of the given tree.

Author(s)

Sophie Kersting

References

S. J. Kersting, M. Fischer. Measuring tree balance using symmetry nodes — A new balance index and its extremal properties. Mathematical Biosciences, page 108690, 2021. ISSN 0025-5564. doi:https://doi.org/10.1016/j.mbs.2021.108690

Examples

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