<p>Hybrid life cycle assessment (HLCA) methods combine bottom-up data from process-based inventories with top-down data from environmentally extended input–output tables. This is done to overcome limitations of data coverage and aggregation: While process inventory data is more detailed, it can never be complete. On the other hand, input–output tables offer full cost-coverage for economic inventories that are complete, but highly aggregated into broad economic sectors. Combining these complementary datasets gives a more complete picture of the environmental impact associated with products or services. To this end, different mathematical methods have been proposed. Of the four main methods currently recognized in literature, three combine this data into a hybrid matrix. The path-exchange method instead works at the graph-level by combining the supply-chain paths of both systems. Unlike matrix-based hybrid methods, the accuracy of results of the graph-based method is limited by the number of paths considered, unless remainders are again computed using a matrix-based approach. For the first time, we provide a concise mathematical description of the path-exchange algorithm and conduct a proof that it is not a distinct mathematical method. It is instead equivalent to the tiered-hybrid matrix method with binary correction for double-counting, where upstream flows are inferred from the sectoral system. Based on this finding, we conclude that the path-exchange method confers no distinct mathematical advantages over matrix-based alternatives. Our proof is an important step toward a unified methodological framework for HLCA.</p>