  In the election of a hierarchical clustering method, theoretic properties may
give some insight to determine which method is the most suitable to treat a
clustering problem. Herein, we study some basic properties of two hierarchical
clustering methods: $\alpha$-unchaining single linkage or $SL(\alpha)$ and a
modified version of this one, $SL^*(\alpha)$. We compare the results with the
properties satisfied by the classical linkage-based hierarchical clustering
methods.
