The "richness" definition also seemed hand wavey to me so I looked at the referenced paper. The actual definition of "richness" of an algorithm is that for any

The "richness" definition also seemed hand wavey to me so I looked at the referenced paper. The actual definition of "richness" of an algorithm is that for any arbitrary partition P of your original data (singletons, one cluster, etc), there is a distance function on the data, which when used in the clustering algorithm, produces P.