Common graph pooling methods.

Graph Convolutional Networks (GCNs) are powerful deep learning methods for non-Euclidean structure data and achieve impressive performance in many fields. But most of the state-of-the-art GCN models are shallow structures with depths of no more than 3 to 4 layers, which greatly limits the ability of GCN models to extract high-level features of nodes. There are two main reasons for this: 1) Overlaying too many graph convolution layers will lead to the problem of over-smoothing. 2) Graph convolution is a kind of localized filter, which is easily affected by local properties. To solve the above problems, we first propose a novel general framework for graph neural networks called Non-local Message Passing (NLMP). Under this framework, very deep graph convolutional networks can be flexibly designed, and the over-smoothing phenomenon can be suppressed very effectively. Second, we propose a new spatial graph convolution layer to extract node multiscale high-level node features. Finally, we design an end-to-end Deep Graph Convolutional Neural Network II (DGCNNII) model for graph classification task, which is up to 32 layers deep. And the effectiveness of our proposed method is demonstrated by quantifying the graph smoothness of each layer and ablation studies. Experiments on benchmark graph classification datasets show that DGCNNII outperforms a large number of shallow graph neural network baseline methods.