Cluster analyses are often conducted with the goal to characterize an underlying probability density, for which the data-point density serves as an estimate for this probability density. We here test and benchmark the common nearest neighbor (CNN) cluster algorithm. This algorithm assigns a spherical neighborhood R to each data point and estimates the data-point density between two data points as the number of data points N in the overlapping region of their neighborhoods (step 1). The main principle in the CNN cluster algorithm is cluster growing. This grows the clusters by sequentially adding data points and thereby effectively positions the border of the clusters along an iso-surface of the underlying probability density. This yields a strict partitioning with outliers, for which the cluster represents peaks in the underlying probability density—termed core sets (step 2). The removal of the outliers on the basis of a threshold criterion is optional (step 3). The benchmark datasets address a series of typical challenges, including datasets with a very high dimensional state space and datasets in which the cluster centroids are aligned along an underlying structure (Birch sets). The performance of the CNN algorithm is evaluated with respect to these challenges. The results indicate that the CNN cluster algorithm can be useful in a wide range of settings. Cluster algorithms are particularly important for the analysis of molecular dynamics (MD) simulations. We demonstrate how the CNN cluster results can be used as a discretization of the molecular state space for the construction of a core-set model of the MD improving the accuracy compared to conventional full-partitioning models. The software for the CNN clustering is available on GitHub.