ENAHPool: The Edge-Node Attention-based Hierarchical Pooling for Graph Neural Networks

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.