Gene expression analysis has become a ubiquitous tool for studying a wide range of human diseases. In a typical analysis we compare distinct phenotypic groups and attempt to identify genes that are, on average, significantly different between them. Here we describe an innovative approach to the analysis of gene expression data, one that identifies differences in expression variance between groups as an informative metric of the group phenotype. We find that genes with different expression variance profiles are not randomly distributed across cell signaling networks. Genes with low-expression variance, or higher constraint, are significantly more connected to other network members and tend to function as core members of signal transduction pathways. Genes with higher expression variance have fewer network connections and also tend to sit on the periphery of the cell. Using neural stem cells derived from patients suffering from Schizophrenia (SZ), Parkinson's disease (PD), and a healthy control group, we find marked differences in expression variance in cell signaling pathways that shed new light on potential mechanisms associated with these diverse neurological disorders. In particular, we find that expression variance of core networks in the SZ patient group was considerably constrained, while in contrast the PD patient group demonstrated much greater variance than expected. One hypothesis is that diminished variance in SZ patients corresponds to an increased degree of constraint in these pathways and a corresponding reduction in robustness of the stem cell networks. These results underscore the role that variation plays in biological systems and suggest that analysis of expression variance is far more important in disease than previously recognized. Furthermore, modeling patterns of variability in gene expression could fundamentally alter the way in which we think about how cellular networks are affected by disease processes.