Graph-based clustering algorithms are particularly suited for dealing with data that do not come from a Gaussian or a spherical distribution. They can be used for detecting clusters of any size and shape without the need of specifying the actual number of clusters; moreover, they can be profitably used in cluster detection problems. In this paper, we propose a detailed performance evaluation of four different graph-based clustering approaches. Three of the algorithms selected for comparison have been chosen from the literature. While these algorithms do not require the setting of the number of clusters, they need, however, some parameters to be provided by the user. So, as the fourth algorithm under comparison, we propose in this paper an approach that overcomes this limitation, proving to be an effective solution in real applications where a completely unsupervised method is desirable.