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#' Number of nodes at each depth
#'
#' Find the number of nodes at each depth in the tree
#'
#' @author Caroline Colijn \email{c.colijn@imperial.ac.uk}
#' @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.
#' @return A vector of widths, where entry i is the number of nodes at depth i. There is a single node at depth 0 (the root) which is not included in the vector, for simplicity.
#'
#' @import ape
#'
#' @examples
#' ## Find the node widths in a random tree with 10 tips:
#' tree <- rtree(10)
#' tree$edge.length <- rep(1,18) # to make it easier to see the width and depths in the plot
#' plot(tree)
#' widths(tree)
#'
#' @export
widths <- function(tree) {
depths <- getDepths(tree)
allDepths <- c(depths$tipDepths,depths$nodeDepths)
widths <- sapply(1:max(allDepths), function(x) sum(allDepths==x))
names(widths) <- 1:max(allDepths)
return(widths)
}
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