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This paper addresses the challenge of accurately identifying the border of the pectoral muscle in mammograms, a critical step in the evaluation of image quality in breast cancer screening. The focus is on the medio-lateral oblique (MLO) view, where the pectoral muscle often appears in the top medial part of the image. The variability in muscle visibility across images introduces significant uncertainty, which this work seeks to address. Our main contribution is a novel modification of a deep graph convolutional network (GCN) that not only locates key points along the muscle boundary but also provides uncertainty estimates, which are useful for selecting images that must be evaluated by a human. We introduce a novel approach to estimate both aleatoric and epistemic uncertainties using a GCN framework. Aleatoric uncertainty captures variability in ground truth due to annotator differences, while epistemic uncertainty accounts for the model’s inherent limitations. Our method was tested on in-house annotated mammograms and the external InBreast dataset, demonstrating comparable accuracy to human annotators and robustness in the presence of domain shifts. The uncertainty estimates were found to be highly accurate, confirming their potential for identifying cases that require human review.