Diffusion-convolutional neural networks (DCNNs) are a new model for graph-structured data that use a diffusion-convolution operation to learn representations from graph data for node classification. DCNNs offer a latent representation invariant to isomorphism, polynomial-time prediction and learning through tensor operations, and efficient GPU implementation. Experiments show DCNNs outperform probabilistic relational models and kernel-on-graph methods in node classification tasks. DCNNs provide flexible, accurate, and fast classification for node, edge, and graph data. The model is defined for node, graph, and edge classification tasks, with diffusion-convolutional representations derived from graph diffusion. DCNNs are trained using stochastic gradient descent and show strong performance on real datasets like Cora and Pubmed. They also perform well on graph classification tasks, though their effectiveness for whole graphs is less clear. DCNNs have limitations in scalability and capturing long-range dependencies. They are related to probabilistic relational models and kernel methods, but offer better performance with lower computational cost. Future work includes improving DCNNs for graph classification and making them more scalable. DCNNs are invariant under isomorphism, ensuring consistent representations for structurally similar graphs.Diffusion-convolutional neural networks (DCNNs) are a new model for graph-structured data that use a diffusion-convolution operation to learn representations from graph data for node classification. DCNNs offer a latent representation invariant to isomorphism, polynomial-time prediction and learning through tensor operations, and efficient GPU implementation. Experiments show DCNNs outperform probabilistic relational models and kernel-on-graph methods in node classification tasks. DCNNs provide flexible, accurate, and fast classification for node, edge, and graph data. The model is defined for node, graph, and edge classification tasks, with diffusion-convolutional representations derived from graph diffusion. DCNNs are trained using stochastic gradient descent and show strong performance on real datasets like Cora and Pubmed. They also perform well on graph classification tasks, though their effectiveness for whole graphs is less clear. DCNNs have limitations in scalability and capturing long-range dependencies. They are related to probabilistic relational models and kernel methods, but offer better performance with lower computational cost. Future work includes improving DCNNs for graph classification and making them more scalable. DCNNs are invariant under isomorphism, ensuring consistent representations for structurally similar graphs.