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Metabolic pathway analysis seeks to identify critical reactions in living organisms and plays an important role in synthetic biology. We present in this paper an algorithm, DOMINANT-EDGE PATHWAY, for identifying a thermodynamically favored dominant-edge pathway forming a particular metabolite product from a particular reactant in a metabolic reaction network. The metabolic network is represented as a graph based on the stoichiometry of the reactions. The problem is formulated to first identify the path between the reactant and product with a limiting reaction based on Gibbs free energy changes, and then to augment this path with supplementary pathways with the goal of balancing the overall stoichiometry. Results of three representative test cases show that our algorithm efficiently finds potentially preferred reaction routes, offering a substantial run-time advantage over commonly used enumeration-based approaches.