On the properties of $\alpha$-unchaining single linkage hierarchical clustering

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.