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#' Fraction of nodes with given imbalance
#'
#' Calculate the fraction of internal nodes with an imbalance greater than or equal to a given threshold.
#'
#' @author Michelle Kendall \email{michelle.louise.kendall@@gmail.com}
#'
#' @param tree a tree of class \code{phylo} or \code{phylo4}. The tree should be binary and rooted; if not it will be coerced into a binary rooted tree using multi2di, if possible.
#' @param threshold a threshold value for node imbalance.
#'
#' @return For any internal node, the function \code{\link{nodeImb}} gives the number of tip descendants of each of the node's descending branches. The function \code{nodeImbFrac} returns the fraction of internal nodes where the difference between these numbers is greater than or equal to the threshold.
#'
#' @import ape
#'
#' @seealso \code{\link{nodeImb}}
#'
#' @examples
#' ## Find the fraction of internal nodes with an imbalance of 5 or more,
#' ## in a random tree with 20 tips:
#' tree <- rtree(20)
#' plot(tree)
#' nodeImbFrac(tree,threshold=5)
#'
#' @export
nodeImbFrac <- function(tree,threshold) {
# initial tree check
tree <- phyloCheck(tree)
ntips <- length(tree$tip.label) # number of tips
tImb <- treeImb(tree)
tImb <- tImb[(ntips+1):(2*ntips - 1),]
count <- sum(abs(tImb[,1]-tImb[,2]) >= threshold)
return(count/(ntips-1))
}
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