This article explores a graph clustering method that is derived from an information theoretic method that clusters points in ${{\mathbb{R}}^{n}}$ relying on Renyi entropy, which involves computing the usual Euclidean distance between these points. Two view points are adopted: (1) the graph to be clustered is first embedded into ${\mathbb{R}}^{d}$ for some dimension d so as to minimize the distortion of the embedding, then the resulting points are clustered, and (2) the graph is clustered directly, using as distance the shortest path distance for undirected graphs, and a variation of the Jaccard distance for directed graphs. In both cases, a hierarchical approach is adopted, where both the initial clustering and the agglomeration steps are computed using Renyi entropy derived evaluation functions. Numerical examples are provided to support the study, showing the consistency of both approaches (evaluated in terms of F -scores).