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The Web graph has recently been used to model the link structure of the Web. The studies of such graphs can yield valuable insights into Web algorithms for crawling, searching and discovery of Web communities. This paper proposes a new approach to clustering the Web graph. The proposed algorithm identifies a small subset of the graph as "core" members of clusters, and then incrementally constructs the clusters by a selection criterion. Two qualitative criteria are proposed to measure the quality of graph clustering. We have implemented our algorithm and tested a set of arbitrary graphs with good results. Applications of our approach include graph drawing and Web visualization.