Graph Neural Networks (GNNs) are powerful techniques in representation learning for graphs and have been increasingly deployed in a multitude of different applications that involve node- and graph-wise tasks. Most existing studies solve either the node-wise task or the graph-wise task independently while they are inherently correlated. This work proposes a unified model, AdamGNN, to interactively learn node and graph representations in a mutual-optimisation manner. Compared with existing GNN models and graph pooling methods, AdamGNN enhances the node representation with the learned multi-grained semantics and avoids losing node features and graph structure information during pooling. Specifically, a differentiable pooling operator is proposed to adaptively generate a multi-grained structure that involves meso- and macro-level semantic information in the graph. We also devise the unpooling operator and the flyback aggregator in AdamGNN to better leverage the multi-grained semantics to enhance node representations. The updated node representations can further adjust the graph representation in the next iteration. Experiments on 14 real-world graph datasets show that AdamGNN can significantly outperform 17 competing models on both node- and graph-wise tasks. The ablation studies confirm the effectiveness of AdamGNN's components, and the last empirical analysis further reveals the ingenious ability of AdamGNN in capturing long-range interactions.
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