Protein folding plays an essential role in protein function and stability. Despite the explosion in our knowledge of structural and functional data, our understanding of protein folding is still very limited. In addition, methods such as folding core identification are gaining importance with the increased desire to engineer proteins with particular functions and efficiencies. However, defining the folding core can be challenging for both experiment and simulation. In this work, we use rigidity analysis to effectively sample and model the protein's energy landscape and identify the folding core. Our results show that rigidity analysis improves the accuracy of our approximate landscape models and produces landscape models that capture the subtle folding differences between protein G and its mutants, NuG1 and NuG2. We then validate our folding core identification against known experimental data and compare to other simulation tools. In addition to correlating well with experiment, our method can suggest other components of structure that have not been identified as part of the core because they were not previously measured experimentally.