  The magnitude of Pearson correlation between two scalar random variables can
be visually judged from the two-dimensional scatter plot of an independent and
identically distributed sample drawn from the joint distribution of the two
variables: the closer the points lie to a straight slanting line, the greater
the correlation. To the best of our knowledge, similar graphical representation
or geometric quantification of tree correlation does not exist in the
literature although tree-shaped datasets are frequently encountered in various
fields, such as academic genealogy tree and embryonic development tree. In this
paper, we introduce a geometric statistic to both represent tree correlation
intuitively and quantify its magnitude precisely. The theoretical properties of
the geometric statistic are provided. Large-scale simulations based on various
data distributions demonstrate that the geometric statistic is precise in
measuring the tree correlation. Its real application on mathematical genealogy
trees also demonstrated its usefulness.
