Significance Understanding gene regulatory networks is a topic of great interest because it can provide insights into cellular development, and identify factors that differ between normal and abnormal cells and phenotypes. Single-cell RNA sequencing provides a unique opportunity to gain understanding at the cellular level, but the technical features of the data create severe challenges when constructing gene networks. We develop a method that successfully skirts these challenges to estimate a cell-specific network for each single cell and cell type. Application of our algorithm to two brain cell samples furthers our understanding of autism spectrum disorder by examining the evolution of gene networks in fetal brain cells and comparing the networks of cells sampled from case and control subjects.