The Kendall-Colijn distance works by measuring, for each pair of leaves,
the distance from the most recent
common ancestor of those leaves and the root node. For a given tree, this
produces a vector of values recording the distance-from-the-root of each
most recent common ancestor of each pair of leaves.
Two trees are compared by taking the Euclidian distance between the
respective vectors. This is calculated by taking the square root of the sum
of the squares of the differences between the vectors.
This metric emphasizes the position of the root; the path difference
instead measures the distance of the last common ancestor of each pair
of leaves from the leaves themselves, i.e. the length of the path from one
leaf to another.