The paper introduces diffusion-convolutional neural networks (DCNNs), a novel model for graph-structured data. DCNNs incorporate a diffusion-convolution operation to learn representations from graph data, which are then used for node classification. Key features of DCNNs include: 1. **Invariance to Isomorphism**: The latent representation is invariant under graph isomorphism, ensuring that isomorphic graphs produce the same activations. 2. **Efficient Computation**: Prediction and learning can be represented as polynomial-time tensor operations, making them efficient for GPU implementation. 3. **Performance**: Experiments on real datasets show that DCNNs outperform probabilistic relational models and kernel-on-graph methods in node classification tasks. The model is designed to handle various classification tasks, including node, edge, and graph classification, with minimal preprocessing. The paper also discusses the limitations of DCNNs, such as scalability issues with large graphs and the inability to capture long-range spatial dependencies. Finally, the authors compare DCNNs with related methods, highlighting their advantages in terms of accuracy, flexibility, and speed.The paper introduces diffusion-convolutional neural networks (DCNNs), a novel model for graph-structured data. DCNNs incorporate a diffusion-convolution operation to learn representations from graph data, which are then used for node classification. Key features of DCNNs include: 1. **Invariance to Isomorphism**: The latent representation is invariant under graph isomorphism, ensuring that isomorphic graphs produce the same activations. 2. **Efficient Computation**: Prediction and learning can be represented as polynomial-time tensor operations, making them efficient for GPU implementation. 3. **Performance**: Experiments on real datasets show that DCNNs outperform probabilistic relational models and kernel-on-graph methods in node classification tasks. The model is designed to handle various classification tasks, including node, edge, and graph classification, with minimal preprocessing. The paper also discusses the limitations of DCNNs, such as scalability issues with large graphs and the inability to capture long-range spatial dependencies. Finally, the authors compare DCNNs with related methods, highlighting their advantages in terms of accuracy, flexibility, and speed.