Constructing gene interaction networks (GINs) from high-throughput gene expression data is an important and challenging problem in systems biology. Existing algorithms produce networks that either have undirected and unweighted edges, or else are constrained to contain no cycles, both of which are biologically unrealistic. In the present paper we propose a new algorithm, based on a concept from probability theory known as the ϕ-mixing coefficient, that produces networks whose edges are weighted and directed, and are permitted to contain cycles. Specifically, we inferred networks for two subtypes of lung cancer small cell (SCLC) and non-small cell (NSCLC) as well as normal lung tissue. Then we compared with the outcomes of siRNA screening of 19,000+ genes on 11 NSCLC cell lines, and found that the higher the degree of a gene in the inferred network, the more essential it is to the survival of a cell. We also analyzed data from a ChIP-Seq experiment to determine putative downstream targets of ASCL1. The SCLC network was enriched for ChIP-seq neighbors of this oncogenic transcription factor, but not in the NSCLC network. We also reverse-engineered whole-genome interaction networks for two distinct subtypes of breast cancer, namely Luminal-A and Basal (also known as triple negative).