Metabolic networks describe the interactions and reactions between different metabolites (e.g. sugars, fatty acids, amino acids) in a biological system, which together give rise to the chemical processes which make life possible. Efforts to further knowledge of the structure of metabolic networks have taken place for well over a century through the efforts of numerous biochemists and have revolutionized our understanding of biology and the capabilities of modern medicine. The introduction in the recent past of metabolomics technologies, which allow for the simultaneous measurement of the concentrations of a significant number of metabolites, has led to the development of mathematical and statistical algorithms that aim to use the information and data that these technologies have made available to make inferences about the structure of metabolic networks. In this thesis, I investigate the application of the graphical lasso algorithm to metabolomics data for the purposes of metabolic network inference. I use the graphical lasso on a metabolomics dataset collected by gas chromatography-mass spectrometry from Drosophila melanogaster to estimate graphical models of varying levels of sparsity that describe the conditional dependence structure of the observed metabolite concentrations. With these estimated models, I describe how they can be chosen from and interpreted in the context of both the data and the underlying biology to inform our knowledge of metabolic network structure.