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However, the conventional softmax classifier, widely used in such tasks, fails to leverage the spatial information inherent in graph structures. To address this limitation, we propose a graph similarity regularized softmax for graph neural networks, which incorporates nonlocal total variation regularization into the softmax function to explicitly capture graph structural information. The weights in the nonlocal gradient and divergence operators are determined based on the graph\u2019s adjacency matrix. We implement this regularized softmax in two popular graph neural network architectures, GCN and GraphSAGE, and evaluate its performance on citation (assortative) and webpage linking (disassortative) datasets. Experimental results demonstrate that our method significantly improves node classification accuracy and generalization compared to baseline models. 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