Before revision:  Here, we give a cut sketch whose size scales with \sqrt{\beta We also show that this result is tight by exhibiting a matching lower bound of \sqrt{\beta .
After revision:  Here, we give a cut sketch whose size scales with \sqrt{\beta We also show an interesting application of digraph sparsification via cut balance by using it to give a very short proof of a celebrated maximum flow result of Karger and Levine (STOC 2002) .