Physicians read electrocardiograms (ECGs) from waveform shape and timing, yet accurate deep-learning classifiers rarely show which waveform regions drive their predictions. We introduce LYNX-ECG, a graph neural network that represents each heartbeat as a sparse visibility graph of timestamped turning points. On CODE-Test, LYNX-ECG reaches a macro F1 score of 0.889, outperforming five baselines including the ECGFounder foundation model, while its graphs need about 14% of the storage of graphs built from every sample. Because each node maps to a specific ECG time, we can delete clinically defined waveform regions and alter beat timing to audit predictions. For conduction disorders, the clinically expected region was the strongest evidence in more than 90% of correct predictions. Bradycardia and tachycardia calls follow heart rate with conduction intervals held fixed, and atrial fibrillation calls vanish when beat-to-beat variation is removed. Sparse visibility graphs thus pair accurate ECG classification with clinically grounded, testable explanations.

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