Existing robot policies based on learned visual embeddings lack explicit structure and are sensitive to visual distractions. Thus, the representations that drive their behaviour are often opaque, making their decision-making process difficult to interpret. To address this, we introduce Structured Image Representations (SIR), a method that leverages Scene Graphs (SGs) as an intermediate representation for robot policy learning. Our approach first constructs a fully connected graph, using 2D or 3D image-derived features as initial node representations. Then, a module learns to sparsify this graph end-to-end, creating a minimal, task-relevant sub-graph that is passed to the action generation model. This process makes our model intrinsically explainable. Evaluations on RoboCasa show that our sparse graph policies outperform image-based baselines on average with 19.5% vs 14.81% success rate. We also demonstrate that our graph-based representations are significantly more robust to distractor objects, showing almost no performance degradation, as opposed to image representations. Most importantly, we show that the learned sparse graphs are a powerful tool for model analysis. By analysing when the model’s sub-graph deviates from human expectation, such as by including distractor nodes or omitting key objects, we successfully uncover dataset biases, including spurious correlations and positional biases.