Heterogeneity is a hallmark of stem cell populations, in part due to the molecular differences between cells undergoing self-renewal and those poised to differentiate. We examined phenotypic and molecular heterogeneity in pluripotent stem cell populations, using public gene expression data sets. A high degree of concordance was observed between global gene expression variability and the reported heterogeneity of different human pluripotent lines. Network analysis demonstrated that low-variability genes were the most highly connected, suggesting that these are the most stable elements of the gene regulatory network and are under the highest regulatory constraints. Known drivers of pluripotency were among these, with lowest expression variability of POU5F1 in cells with the highest capacity for self-renewal. Variability of gene expression provides a reliable measure of phenotypic and molecular heterogeneity and predicts those genes with the highest degree of regulatory constraint within the pluripotency network.