Chain-of-thought prompting enables reasoning in large language models but produces explanations that are difficult to verify, expensive to generate, and not always faithful. We introduce a Structural Chain-of-Thought framework where models generate executable computational graphs instead of free-form reasoning. The final answer is obtained by deterministically executing the graph. The model is trained using graph-based reinforcement learning that rewards structural validity, answer correctness, and node overlap with reference graphs. Experiments across five benchmarks and four model families show that our method consistently improves accuracy over supervised graph training and can reduce generation length by up to 5-6x compared with standard GRPO and chain-of-thought supervised training. Our faithfulness experiments reveal that models trained with our approach tend to rely on deriving their answers from the generated graphs rather than producing post-hoc rationalizations as usually in chain-of-thought reasoning.

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