Towards Structure-captive Differentiable Graph Pooling via PageRank

Graph pooling has recently emerged as a critical component in graph neural networks (GNNs) for down-sampling and condensing graph representations. Effective graph representation learning requires the preservation of both informative node features and meaningful topological structures, yet existing pooling approaches often struggle to achieve this balance. In this work, we propose a structure-aware differentiable graph pooling method based on PageRank. While the conventional PageRank algorithm effectively encodes topological connectivity, it is not straightforward to incorporate it into a differentiable pooling framework. To address this, we develop a variant of PageRank that adaptively ranks nodes by jointly considering node attributes and structural information. Furthermore, we introduce a hybrid strategy that integrates standard PageRank with its adaptive variant, thereby achieving a principled trade-off between preserving structural connectivity and retaining feature expressiveness. The proposed pooling mechanism is fully differentiable and can be seamlessly integrated into various GNN architectures for both graph-level and node-level prediction tasks. Extensive experiments across multiple benchmark datasets demonstrate that our method consistently outperforms state-of-the-art pooling techniques in classification accuracy, while incurring only marginal computational overhead.