One of the most challenging problems in computational genomics is network discovery. All biological processes and outcomes, such as metabolism, development, and disease, are a function of interacting components that may quantified as a network (or pathway). There is information concerning these networks that can be extracted from genomic data and a broad spectrum of approaches have been suggested for inferring network connections. Computational approaches for network representation and analysis vary widely depending on the goals of the researcher. Our goal is to develop methodologies for discovering previously unknown network structure from population genomic data using a framework that provides clear predictions that can be experimentally validated. In line with this goal, we use probabilistic graphical models to represent networks, which reflect the conditional relationships among measured variables. A correctly inferred network graphical model makes specific predictions concerning the experimental consequences of altering a network component. An appeal of these models for network discovery is the linear form, which provides an optimal balance between interpretation and a representation that is not overly rich, such that conflicting network structures can be resolved. Our current work in this area includes development of scalable algorithms for directed graphs, theory and methodology for the extraction of cyclic networks, and simulation assessments of method performance when considering the effects of latent variables. We are applying our network discovery methods in collaboration with a number of groups whom have collected genetical genomic population data, studies that include both genotypes and measurements of gene expression. Figures coming soon.