Graph Neural Networks (GNNs) have emerged as powerful tools for graph learning, and one key challenge arising in GNNs is the development of effective pooling operations for learning meaningful graph representations. In this paper, we propose a novel Edge-Node Attention-based Hierarchical Pooling (ENAHPool) operation for GNNs. Unlike existing cluster-based pooling methods that suffer from ambiguous node assignments and uniform edge-node information aggregation, ENAHPool assigns each node exclusively to a cluster and employs attention mechanisms to perform weighted aggregation of both node features within clusters and edge connectivity strengths between clusters, resulting in more informative hierarchical representations. To further enhance the model performance, we introduce a Multi-Distance Message Passing Neural Network (MD-MPNN) that utilizes edge connectivity strength information to enable direct and selective message propagation across multiple distances, effectively mitigating the over-squashing problem in classical MPNNs. Experimental results demonstrate the effectiveness of the proposed method.

Graph Neural Networks (GNNs) are powerful tools for graph learning, but one of the important challenges is how to effectively extract representations for graph-level tasks. In this paper, we propose an end-to-end Simple Clustering Hierarchical Pooling (SCHPool) operation, which is based on Top-K node selection for learning expressive graph representations. Specifically, SCHPool considers each node and its local neighborhood as a cluster, and introduces a novel multi-view scoring function to evaluate node importance. Based on these scores, clusters centered around the Top-K nodes are retained. This design eliminates the need for complex clustering operations, significantly reducing computational overhead. Furthermore, during the coarsening process, SCHPool employs a lightweight yet comprehensive attention mechanism to adaptively aggregate both the node features within clusters and the edge connectivity strengths between clusters. This facilitates the construction of more informative coarsened graphs, enhancing model performance. Experimental results demonstrate the effectiveness of the proposed model.