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Graph Neural Networks (GNNs), which extend deep neural networks to graph-structured data, have attracted increasing attention. They have been proven to be powerful for numerous graph related tasks such as graph classification, link prediction, and node classification. To adapt GNNs to graph classification, recent works aim to learn graph-level representation through a hierarchical pooling procedure. One major direction is to select important nodes to hierarchically coarsen the input graph and gradually reduce the information into the graph representation. However, most of the existing methods only select important nodes, which can be redundant and cannot represent the original graph well. Meanwhile, the information of non-selected nodes is often overlooked when generating a new coarser graph, which may lead to the tremendous loss of important structural and node feature information. In this paper, we …