Maximizing edge-ratio is NP-complete

Given a graph GG and a bipartition of its vertices, the edge-ratio is the minimum for both classes so defined of their number of internal edges divided by their number of cut edges. We prove that maximizing edge-ratio is NP-complete.

► We consider edge-ratio, a relatively new measure of clustering quality.
► We show that maximizing edge-ratio is NP-complete.
► Our reduction is from MAX CUT and establishes hardness of related problems.