The problem of variable selection is useful for identifying the principal drivers of differential gene-response under one or more treatments, phenotypes, or conditions. Once identified, such drivers can be targeted as potential knockouts or enhancers in drug discovery or diagnostic testing. In high throughput data such as gene or protein expression the large number of variables has made it impractical to implement all but the simplest univariate methods for variable selection, e.g., detecting significant shifts in t-test or Wilcoxon test statistics. We propose an alternative approach based on detecting significant shifts in patterns of connectivity of genes in a correlation graph or concentration graph. Remarkably, it is precisely when the sample size is small that the approach is scalable, e.g., to whole genome analysis. Furthermore a statistical performance analysis establishes phase transition behaviors and tight approximations to false discovery rate that can be used for error control. We will illustrate the approach on several gene expression datasets.