Myocardial perfusion imaging is a non-invasive imaging technique commonly used for the diagnosis of Coronary Artery Disease and is based on the injection of radiopharmaceutical tracers into the blood stream. The patient's heart is imaged while at rest and under stress in order to determine its capacity to react to the imposed challenge. Assessment of imaging data is commonly performed by visual inspection of polar maps showing the tracer uptake in a compact, two-dimensional representation of the left ventricle. This article presents a method for automatic classification of polar maps based on graph convolutional neural networks. Furthermore, it evaluates how well localization techniques developed for standard convolutional neural networks can be used for the localization of pathological segments with respect to clinically relevant areas. The method is evaluated using 946 labeled datasets and compared quantitatively to three other neural-network-based methods. The proposed model achieves an agreement with the human observer on 89.3% of rest test polar maps and on 91.1% of stress test polar maps. Localization performed on a fine 17-segment division of the polar maps achieves an agreement of 83.1% with the human observer, while localization on a coarse 3-segment division based on the vessel beds of the left ventricle has an agreement of 78.8% with the human observer. Our method could thus assist the decision-making process of physicians when analyzing polar map data obtained from myocardial perfusion images.