- Abstract: Pooling operations have shown to be effective on various tasks in computer vision and natural language processing. One challenge of performing pooling operations on graph data is the lack of locality that is not well-defined on graphs. Previous studies used global ranking methods to sample some of the important nodes, but most of them are not able to incorporate graph topology information in computing ranking scores. In this work, we propose the topology-aware pooling (TAP) layer that uses attention operators to generate ranking scores for each node by attending each node to its neighboring nodes. The ranking scores are generated locally while the selection is performed globally, which enables the pooling operation to consider topology information. To encourage better graph connectivity in the sampled graph, we propose to add a graph connectivity term to the computation of ranking scores in the TAP layer. Based on our TAP layer, we develop a network on graph data, known as the topology-aware pooling network. Experimental results on graph classification tasks demonstrate that our methods achieve consistently better performance than previous models.