We propose a novel method for the clustering of point-cloud data that originate from single-molecule localization microscopy (SMLM). Our scheme has the ability to infer a hierarchical structure from the data. It takes a particular relevance when quantitatively analyzing the biological particles of interest at different scales. It assumes a prior neither on the shape of particles nor on the background noise. Our multiscale clustering pipeline is built upon graph theory. At each scale, we first construct a weighted graph that represents the SMLM data. Next, we find clusters using spectral clustering. We then use the output of this clustering algoritlun to build the graph in the next scale; in this way, we ensure consistency over different scales. We illustrate our method with examples that highlight some of its important properties.