Before revision:  We prove that for this requirement to hold , under certain conditions, it is necessary and sufficient for clusters to have low conductance, the ratio of edge boundary size to volume , which yields a measure of cluster quality.
After revision:  We prove under mild conditions that, in order for this requirement to hold , under certain conditions, it is necessary and sufficient for clusters to have low conductance, the ratio of edge boundary size to volume , which yields a measure of cluster quality.