For a large class of irregular grid applications, the structure of the mesh changes from one phase of the computation to the next. Eventually, as the graph evolves, the adapted mesh has to be repartitioned to ensure good load balance. If this new graph is partitioned from scratch, it will lead to an excessive migration of data among processors. In this paper, we present a new scheme for computing repartitionings of adaptively refined meshes. This scheme performs diffusion of vertices in a multilevel framework and minimizes vertex movement without significantly compromising the edge-cut.