Imbalance Metrics.

In this table we report the definition of eight imbalance metrics defined in the literature [4], [16], [17], [10], [11], [12], [15]. The last two columns show the values of such metrics for totally balanced or totally imbalanced trees with leaves. is the set of all the leaves in the tree while is the set of all the internal nodes. For each internal node , and are respectively the number of leaves belonging to the right and left subtrees descending from , and we define and if is even, and if is odd, . is the topological distance between leaf and the root i.e., the number of internal nodes in the path connecting to the root. Given an internal node , is the maximum topological distance between and one of its descending leaves. is the number of cherry leaves within the tree, where a cherry is a couple of leaves which descend from the same internal node. We refer to the File S1 for further details about the definition of the imbalance metrics.