Graph neural networks (GNN) have been proven to be mature enough for handling graph-structured data on node-level graph representation learning tasks. However, the graph pooling technique for learning expressive graph-level representation is critical yet still challenging. Existing pooling methods either struggle to capture the local substructure or fail to effectively utilize high-order dependency, thus diminishing the expression capability. In this paper we propose HAP, a hierarchical graph-level representation learning framework, which is adaptively sensitive to graph structures, i.e., HAP clusters local substructures incorporating with high-order dependencies. HAP utilizes a novel cross-level attention mechanism MOA to naturally focus more on close neighborhood while effectively capture higher-order dependency that may contain crucial information. It also learns a global graph content GCont that extracts the graph pattern properties to make the pre- and post-coarsening graph content maintain stable, thus providing global guidance in graph coarsening. This novel innovation also facilitates generalization across graphs with the same form of features. Extensive experiments on fourteen datasets show that HAP significantly outperforms twelve popular graph pooling methods on graph classification task with an maximum accuracy improvement of 22.79%, and exceeds the performance of state-of-the-art graph matching and graph similarity learning algorithms by over 3.5% and 16.7%.
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