Efficiently deriving biosynthetic pathways from complex biochemical networks is crucial for advancing metabolic engineering. However, efficient analysis and navigation of big biochemical networks remain a challenge. Moreover, ranking the constructed pathways introduces further complexities. We propose a novel graph-based method for extracting biologically relevant metabolic pathways within large metabolic networks. The graph links metabolites as nodes via edges, representing reactant-product connections. Edges are assigned weights defining relations between two connected nodes. By incorporating further constraints based on compounds' molecular similarity, network connectivity and the availability of metabolites in the selected microorganism, we facilitate the rapid and reliable extraction of feasible metabolic pathways from large biochemical networks. Our method not only identifies pathways as a series of metabolites from source to target, but also delineates the specific enzymatic reactions for each step of the heterologous pathway. To illustrate the effectiveness of our approach, we provide a case study involving the bioproduction of butanol from E. coli.