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

翻译：Lovász和Simonovits提出的$μ$-电导度量是一种尺寸特定电导指标，它能识别具有最小电导的集合，同时忽略那些体积小于整个图$μ$比例的集合。使用$μ$-电导使我们能够以新的方式研究网络结构。在本文中，我们研究了一种针对$μ$-电导的改进谱割方法，该方法是$μ$-电导整数规划的自然松弛形式，并证明该规划的最优解与$μ$-电导之间存在双向Cheeger不等式。