In this paper, we present a new application of the so-called phi-mixing coefficient between two random variables. Using the phi-mixing coefficient, as well as an analog of the well-known data processing inequality from information theory, we present a new algorithm for reverse-engineering gene interaction networks (GINs) from expression data, by viewing the expression levels of various genes as coupled random variables. Unlike existing methods, the GINs constructed using the algorithm presented here have edges that are both directed and weighted. Thus it is possible to infer both the direction as well as the strength of the interaction between genes. Several GINs have been constructed for various data sets in lung and ovarian cancer. One of the lung cancer networks is validated by comparing its predictions against the output of ChIP-seq data.