```
#' Calculate the f_4(W, X; Y, Z) statistics.
#'
#' Calculate the \eqn{f_4(W, X; Y, Z)} statistics.
#'
#' @param graph The admixture graph.
#' @param W A leaf node.
#' @param X A leaf node.
#' @param Y A leaf node.
#' @param Z A leaf node.
#'
#' @return The overlaps between paths from \code{W} to \code{X} and paths from
#' \code{Y} to \code{Z}.
#'
#' @export
f4 <- function(graph, W, X, Y, Z) {
if (!(W %in% graph$leaves)) stop(paste(W, "is not a leaf in the graph."))
if (!(X %in% graph$leaves)) stop(paste(X, "is not a leaf in the graph."))
if (!(Y %in% graph$leaves)) stop(paste(Y, "is not a leaf in the graph."))
if (!(Z %in% graph$leaves)) stop(paste(Z, "is not a leaf in the graph."))
WX <- all_paths(graph, W, X)
YZ <- all_paths(graph, Y, Z)
all_path_overlaps(WX, YZ)
}
#' Calculate the f_3(A; B, C) statistics.
#'
#' Calculate the \eqn{f_3(A; B, C)} statistics.
#'
#' @param graph The admixture graph.
#' @param A A leaf node.
#' @param B A leaf node.
#' @param C A leaf node.
#'
#' @return A symbolic representation of the equation for the \eqn{f_3}
#' statistics given by the admixture graph.
#'
#' @export
f3 <- function(graph, A, B, C) f4(graph, A, B, A, C)
#' Calculate the f_2(A, B) statistics.
#'
#' Calculate the \eqn{f_2(A, B)} statistics.
#'
#' @param graph The admixture graph.
#' @param A A leaf node.
#' @param B A leaf node.
#'
#' @return A symbolic representation of the equation for the \eqn{f_2}
#' statistics given by the admixture graph.
#'
#' @export
f2 <- function(graph, A, B) f4(graph, A, B, A, B)
```

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