  The $\mu$-conductance measure proposed by Lovasz and Simonovits is a
size-specific conductance score that identifies the set with smallest
conductance while disregarding those sets with volume smaller than a $\mu$
fraction of the whole graph. Using $\mu$-conductance enables us to study in new
ways. In this manuscript we propose a modified spectral cut that is a natural
relaxation of the integer program of $\mu$-conductance and show the optimum of
this program has a two-sided Cheeger inequality with $\mu$-conductance.
