In this paper we introduce a dynamic algorithm for clustering undirected graphs, whose edge property is continuously changing. The algorithm can maintain high-quality clusters efficiently in presence of insertion and deletion (update) of edges. The algorithm, is motivated by the minimumcut tree based partitioning algorithm of [3] and [4]. It takes O(k3) time for each update processing, where k is the maximum size of any cluster. This is the worst case time complexity, and in general time taken is much less. To the best of our knowledge, this is the first clustering algorithm, for evolving graphs, providing strong theoretical quality guarantee on clusters.