A new graph-theory-based algorithm for SCWRL improves the speed and accuracy of protein side-chain prediction. The algorithm represents side chains as vertices in an undirected graph, with edges indicating interactions between residues. The graph is partitioned into connected subgraphs, which are further broken into biconnected components. These components are solved individually to find the minimum energy configuration, which is then combined to identify the global minimum energy conformation. This approach significantly reduces computational time, allowing predictions on 180 proteins with 34,342 side chains to be completed in under 7 minutes. The algorithm achieves 82.6% and 73.7% accuracy in predicting χ₁ and χ₁+₂ dihedral angles, respectively, using a backbone-dependent rotamer library and a linear repulsive steric energy function. The new algorithm enables SCWRL to be used in more demanding applications, such as sequence design and ab initio structure prediction, and allows for the inclusion of more complex energy functions and conformational flexibility, leading to increased accuracy. The algorithm is based on graph theory and uses a depth-first search to identify biconnected components and articulation points, which are then used to solve the side-chain combinatorial problem efficiently. The algorithm is implemented in object-oriented C++ and is freely available for nonprofit research groups. The results show that the new algorithm significantly reduces the size of the combinatorial problem and improves the efficiency of side-chain prediction.A new graph-theory-based algorithm for SCWRL improves the speed and accuracy of protein side-chain prediction. The algorithm represents side chains as vertices in an undirected graph, with edges indicating interactions between residues. The graph is partitioned into connected subgraphs, which are further broken into biconnected components. These components are solved individually to find the minimum energy configuration, which is then combined to identify the global minimum energy conformation. This approach significantly reduces computational time, allowing predictions on 180 proteins with 34,342 side chains to be completed in under 7 minutes. The algorithm achieves 82.6% and 73.7% accuracy in predicting χ₁ and χ₁+₂ dihedral angles, respectively, using a backbone-dependent rotamer library and a linear repulsive steric energy function. The new algorithm enables SCWRL to be used in more demanding applications, such as sequence design and ab initio structure prediction, and allows for the inclusion of more complex energy functions and conformational flexibility, leading to increased accuracy. The algorithm is based on graph theory and uses a depth-first search to identify biconnected components and articulation points, which are then used to solve the side-chain combinatorial problem efficiently. The algorithm is implemented in object-oriented C++ and is freely available for nonprofit research groups. The results show that the new algorithm significantly reduces the size of the combinatorial problem and improves the efficiency of side-chain prediction.