Self-Organizing Map (SOM) is an artificial neural network tool that is trained using unsupervised learning to produce a low dimensional representation of the input space, called a map. This map is generally the object of a clustering analysis step which aims to partition the referents vectors (map neurons) into compact and well-separated groups. In this paper, we consider the problem of the clustering self-organizing map using different aspects: partitioning, hierarchical and graph coloring based techniques. Unlike the traditional clustering SOM techniques, which use k-means or hierarchical clustering, the graph-based approaches have the advantage of providing a partitioning of the self-organizing map by simultaneously using dissimilarities and neighborhood relations provided by the map. We present the experimental results of several comparisons between these different ways of clustering.