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Diabetic retinopathy (DR) is a serious ocular complication that can pose a serious risk to a patient's vision and overall health. Currently, the automatic grading of DR is mainly using deep learning techniques. However, the lesion information in DR images is complex, variable in shape and size, and randomly distributed in the images, which leads to some shortcomings of the current research methods, i.e., it is difficult to effectively extract the information of these various features, and it is difficult to establish the connection between the lesion information in different regions. To address these shortcomings, we design a multi-scale dynamic fusion (MSDF) module and combine it with graph convolution operations to propose a multi-scale dynamic graph convolutional network (MDGNet) in this paper. MDGNet firstly uses convolution kernels with different sizes to extract features with different shapes and sizes in the lesion regions, and then automatically learns the corresponding weights for feature fusion according to the contribution of different features to model grading. Finally, the graph convolution operation is used to link the lesion features in different regions. As a result, our proposed method can effectively combine local and global features, which is beneficial for the correct DR grading. We evaluate the effectiveness of method on two publicly available datasets, namely APTOS and DDR. Extensive experiments demonstrate that our proposed MDGNet achieves the best grading results on APTOS and DDR, and is more accurate and diverse for the extraction of lesion information. [ABSTRACT FROM AUTHOR]