Genome-scale stoichiometric models (GSMs) have been widely utilized to predict and understand cellular metabolism. GSMs and the flux predictions resulting from them have proven indispensable to fields ranging from metabolic engineering to human disease. Nonetheless, it is challenging to parse these flux predictions due to the inherent size and complexity of the GSMs. Several previous approaches have reduced this complexity by identifying key pathways contained within the genome-scale flux predictions. However, a reduction method that overlays carbon atom transitions on stoichiometry and flux predictions is lacking. To fill this gap, we developed NetFlow, an algorithm that leverages genome-scale carbon mapping to extract and quantitatively distinguish biologically relevant metabolic pathways from a given genome-scale flux prediction. NetFlow extends prior approaches by utilizing both full carbon mapping and context-specific flux predictions. Thus, NetFlow is uniquely able to quantitatively distinguish between biologically relevant pathways of carbon flow within the given flux map. NetFlow simulates 13C isotope labeling experiments to calculate the extent of carbon exchange, or carbon yield, between every metabolite in the given GSM. Based on the carbon yield, the carbon flow to or from any metabolite or between any pair of metabolites of interest can be isolated and readily visualized. The resulting pathways are much easier to interpret, which enables an in-depth mechanistic understanding of the metabolic phenotype of interest. Here, we first demonstrate NetFlow with a simple network. We then depict the utility of NetFlow on a model of central carbon metabolism in E. coli. Specifically, we isolated the production pathway for succinate synthesis in this model and the metabolic mechanism driving the predicted increase in succinate yield in a double knockout of E. coli. Finally, we describe the application of NetFlow to a GSM of lycopene-producing E. coli, which enabled the rapid identification of the mechanisms behind the measured increases in lycopene production following single, double, and triple knockouts.