  Graph pooling has been increasingly recognized as crucial for Graph Neural
Networks (GNNs) to facilitate hierarchical graph representation learning.
Existing graph pooling methods commonly consist of two stages: selecting
top-ranked nodes and discarding the remaining to construct coarsened graph
representations. However, this paper highlights two key issues with these
methods: 1) The process of selecting nodes to discard frequently employs
additional Graph Convolutional Networks or Multilayer Perceptrons, lacking a
thorough evaluation of each node's impact on the final graph representation and
subsequent prediction tasks. 2) Current graph pooling methods tend to directly
discard the noise segment (dropped) of the graph without accounting for the
latent information contained within these elements. To address the first issue,
we introduce a novel Graph Explicit Pooling (GrePool) method, which selects
nodes by explicitly leveraging the relationships between the nodes and final
representation vectors crucial for classification. The second issue is
addressed using an extended version of GrePool (i.e., GrePool+), which applies
a uniform loss on the discarded nodes. This addition is designed to augment the
training process and improve classification accuracy. Furthermore, we conduct
comprehensive experiments across 12 widely used datasets to validate our
proposed method's effectiveness, including the Open Graph Benchmark datasets.
Our experimental results uniformly demonstrate that GrePool outperforms 14
baseline methods for most datasets. Likewise, implementing GrePool+ enhances
GrePool's performance without incurring additional computational costs.
