Hierarchical trees in N-body simulations: Relations with cluster analysis methods

The purpose of this note is to point out that a very efficient agglomerative hierarchical clustering algorithm has been employed in tree codes for cosmological simulations. However, the agglomerative criterion used, although intuitively plausible, is not the correct one. It may be seen from the multivariate data analysis literature that the criterion used for such simulations (i) is not guaranteed to give rise to a well-defined tree structure; and (ii) on the basis of empirical evidence leads to an inefficient decomposition of the data.