This function computes the balance of a phylogenetic tree, that is for each node of the tree the numbers of descendants (i.e. tips) on each of its daughter-branch. The tree must be fully dichotomous.
balance(phy)a numeric matrix with two columns and one row for each node of the
  tree. The columns give the numbers of descendants on each
  daughter-branches (the order of both columns being arbitrary). If the
  phylogeny phy has an element node.label, this is used as
  rownames for the returned matrix; otherwise the numbers (of mode
  character) of the matrix edge of phy are used as rownames.
an object of class "phylo".
Emmanuel Paradis
Aldous, D. J. (2001) Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today. Statistical Science, 16, 23--34.