Metabolic Graph Theory (MGT) addresses a fundamental limitation in systems biology: the gap between mass-flow stoichiometry and biophysical reality. While standard Flux Balance Analysis (FBA) identifies feasible mass-flow solutions, it often fails to account for the thermodynamic driving forces that make those flows physically possible. MGT bridges this gap by augmenting the stoichiometric matrix with Gibbs free energy annotations, effectively treating the metabolic network as a weighted graph of energy throughput rather than a simple connectivity map.