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Cartoon face recognition is challenging as they typically have smooth color regions and emphasized edges, the key to recognizing cartoon faces is to precisely perceive their sparse and critical shape patterns. However, it is quite difficult to learn a shape-oriented representation for cartoon face recognition with convolutional neural networks (CNNs). To mitigate this issue, we propose the GraphJigsaw that constructs jigsaw puzzles at various stages in the classification network and solves the puzzles with the graph convolutional network (GCN) in a progressive manner. Solving the puzzles requires the model to spot the shape patterns of the cartoon faces as the texture information is quite limited. The key idea of GraphJigsaw is constructing a jigsaw puzzle by randomly shuffling the intermediate convolutional feature maps in the spatial dimension and exploiting the GCN to reason and recover the correct layout of the jigsaw fragments in a self-supervised manner. The proposed GraphJigsaw avoids training the classification model with the deconstructed images that would introduce noisy patterns and are harmful for the final classification. Specially, GraphJigsaw can be incorporated at various stages in a top-down manner within the classification model, which facilitates propagating the learned shape patterns gradually. GraphJigsaw does not rely on any extra manual annotation during the training process and incorporates no extra computation burden at inference time. Both quantitative and qualitative experimental results have verified the feasibility of our proposed GraphJigsaw, which consistently outperforms other face recognition or jigsaw-based methods on two popular cartoon face datasets with considerable improvements.